TSTP Solution File: SWW253+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW253+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 : n025.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 00:49:35 EDT 2023
% Result : Theorem 93.31s 13.18s
% Output : Proof 213.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW253+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 20:35:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 19.68/3.37 Prover 6: Preprocessing ...
% 19.68/3.40 Prover 3: Preprocessing ...
% 19.68/3.40 Prover 2: Preprocessing ...
% 20.44/3.46 Prover 1: Preprocessing ...
% 20.44/3.47 Prover 4: Preprocessing ...
% 20.44/3.49 Prover 5: Preprocessing ...
% 20.68/3.61 Prover 0: Preprocessing ...
% 53.68/7.87 Prover 1: Warning: ignoring some quantifiers
% 54.00/7.93 Prover 3: Warning: ignoring some quantifiers
% 55.38/8.13 Prover 3: Constructing countermodel ...
% 56.05/8.17 Prover 1: Constructing countermodel ...
% 59.16/8.63 Prover 6: Proving ...
% 62.17/8.99 Prover 4: Warning: ignoring some quantifiers
% 65.13/9.42 Prover 4: Constructing countermodel ...
% 69.34/9.98 Prover 5: Proving ...
% 69.79/10.03 Prover 0: Proving ...
% 72.62/10.44 Prover 2: Proving ...
% 79.33/11.24 Prover 2: stopped
% 79.33/11.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 87.58/12.36 Prover 7: Preprocessing ...
% 93.31/13.18 Prover 3: proved (12536ms)
% 93.31/13.18
% 93.31/13.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 93.31/13.18
% 93.31/13.18 Prover 0: stopped
% 93.31/13.18 Prover 5: stopped
% 93.78/13.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 93.78/13.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 93.78/13.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 93.78/13.21 Prover 6: stopped
% 93.78/13.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 102.44/14.31 Prover 7: Warning: ignoring some quantifiers
% 105.47/14.66 Prover 7: Constructing countermodel ...
% 106.62/14.81 Prover 10: Preprocessing ...
% 106.98/14.85 Prover 11: Preprocessing ...
% 106.98/14.94 Prover 13: Preprocessing ...
% 108.16/15.04 Prover 8: Preprocessing ...
% 114.61/15.99 Prover 1: stopped
% 114.61/16.00 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 118.63/16.42 Prover 10: Warning: ignoring some quantifiers
% 119.59/16.62 Prover 10: Constructing countermodel ...
% 122.32/16.92 Prover 8: Warning: ignoring some quantifiers
% 123.53/17.09 Prover 16: Preprocessing ...
% 123.53/17.09 Prover 8: Constructing countermodel ...
% 127.34/17.55 Prover 11: Warning: ignoring some quantifiers
% 127.34/17.56 Prover 13: Warning: ignoring some quantifiers
% 129.67/17.87 Prover 11: Constructing countermodel ...
% 129.67/17.94 Prover 13: Constructing countermodel ...
% 133.86/18.41 Prover 16: Warning: ignoring some quantifiers
% 134.79/18.53 Prover 16: Constructing countermodel ...
% 151.83/20.83 Prover 16: stopped
% 151.83/20.84 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 157.88/21.75 Prover 19: Preprocessing ...
% 172.63/23.76 Prover 13: stopped
% 175.47/24.13 Prover 19: Warning: ignoring some quantifiers
% 176.60/24.25 Prover 19: Constructing countermodel ...
% 202.03/27.67 Prover 19: stopped
% 204.66/27.98 Prover 4: stopped
% 209.67/28.81 Prover 10: Found proof (size 1329)
% 209.67/28.81 Prover 10: proved (15612ms)
% 209.67/28.82 Prover 11: stopped
% 209.67/28.82 Prover 7: stopped
% 209.67/28.83 Prover 8: stopped
% 209.67/28.83
% 209.67/28.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 209.67/28.83
% 211.40/30.09 % SZS output start Proof for theBenchmark
% 211.59/30.12 Assumptions after simplification:
% 211.59/30.12 ---------------------------------
% 211.59/30.12
% 211.59/30.12 (arity_Complex__Ocomplex__Fields_Ofield__inverse__zero)
% 211.59/30.12 $i(tc_Complex_Ocomplex) &
% 211.59/30.12 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex)
% 211.59/30.12
% 211.59/30.12 (arity_Complex__Ocomplex__Rings_Odivision__ring)
% 211.59/30.12 $i(tc_Complex_Ocomplex) & class_Rings_Odivision__ring(tc_Complex_Ocomplex)
% 211.59/30.12
% 211.59/30.12 (arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero)
% 211.59/30.12 $i(tc_Complex_Ocomplex) &
% 211.59/30.12 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex)
% 211.59/30.12
% 211.59/30.12 (arity_Complex__Ocomplex__Rings_Oidom)
% 211.59/30.12 $i(tc_Complex_Ocomplex) & class_Rings_Oidom(tc_Complex_Ocomplex)
% 211.59/30.12
% 211.59/30.12 (arity_Complex__Ocomplex__Rings_Ono__zero__divisors)
% 211.59/30.12 $i(tc_Complex_Ocomplex) & class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)
% 211.59/30.12
% 211.59/30.12 (arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors)
% 211.59/30.12 $i(tc_Complex_Ocomplex) &
% 211.59/30.12 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
% 211.59/30.12
% 211.59/30.12 (arity_Complex__Ocomplex__Rings_Ozero__neq__one)
% 211.59/30.12 $i(tc_Complex_Ocomplex) & class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
% 211.59/30.12
% 211.59/30.12 (arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero)
% 211.59/30.12 $i(tc_RealDef_Oreal) &
% 211.59/30.12 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
% 211.59/30.12
% 211.59/30.12 (arity_RealDef__Oreal__Rings_Olinordered__semidom)
% 211.59/30.12 $i(tc_RealDef_Oreal) & class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
% 211.59/30.12
% 211.59/30.12 (conj_0)
% 211.59/30.15 $i(tc_RealDef_Oreal) & $i(v_w____) & $i(v_q____) & $i(tc_Complex_Ocomplex) &
% 211.59/30.15 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 211.59/30.15 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 211.59/30.15 ? [v11: $i] : (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10) =
% 211.59/30.15 v11 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) = v7 &
% 211.59/30.15 c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, v9, v2) = v10 &
% 211.59/30.15 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v8 &
% 211.59/30.15 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2) = v3 &
% 211.59/30.15 c_Polynomial_Osmult(tc_Complex_Ocomplex, v3, v_q____) = v4 &
% 211.59/30.15 c_Polynomial_Opoly(tc_Complex_Ocomplex, v4) = v5 &
% 211.59/30.15 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 211.59/30.15 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v5, v_w____) =
% 211.59/30.15 v6 & hAPP(v0, v1) = v2 & hAPP(v0, v_w____) = v9 & $i(v11) & $i(v10) & $i(v9)
% 211.59/30.15 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 211.59/30.15 $i(v0) & ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v8) & ~
% 211.59/30.15 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v8)) |
% 211.59/30.15 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v8) & ~
% 211.59/30.15 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v8))))
% 211.59/30.15
% 211.59/30.15 (fact_BseqD)
% 211.59/30.15 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.59/30.15 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 211.59/30.15 ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~
% 211.59/30.15 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3) &
% 211.59/30.15 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: $i] :
% 211.59/30.15 ! [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5)
% 211.59/30.15 = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) |
% 211.59/30.15 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3)))))
% 211.59/30.15
% 211.59/30.15 (fact_BseqI)
% 211.59/30.16 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.59/30.16 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 211.59/30.16 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 211.59/30.16 class_RealVector_Oreal__normed__vector(v3) | ~
% 211.59/30.16 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | c_SEQ_OBseq(v3,
% 211.59/30.16 v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 211.59/30.16 (c_RealVector_Onorm__class_Onorm(v3, v5) = v6 & hAPP(v1, v4) = v5 & $i(v6)
% 211.59/30.16 & $i(v5) & $i(v4) & ~
% 211.59/30.16 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v2))))
% 211.59/30.16
% 211.59/30.16 (fact_Bseq__def)
% 211.59/30.16 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.59/30.16 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 211.59/30.16 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 211.59/30.16 class_RealVector_Oreal__normed__vector(v2) | ~
% 211.59/30.16 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | c_SEQ_OBseq(v2,
% 211.59/30.16 v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 211.59/30.16 (c_RealVector_Onorm__class_Onorm(v2, v5) = v6 & hAPP(v1, v4) = v5 & $i(v6)
% 211.59/30.16 & $i(v5) & $i(v4) & ~
% 211.59/30.16 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))) & ! [v1:
% 211.59/30.16 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~
% 211.59/30.16 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3) &
% 211.59/30.16 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: $i] :
% 211.59/30.16 ! [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5)
% 211.59/30.16 = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) |
% 211.59/30.16 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3)))))
% 211.59/30.16
% 211.59/30.16 (fact_Bseq__inverse__lemma)
% 211.59/30.16 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.59/30.16 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 211.59/30.16 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 211.59/30.16 (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~
% 211.59/30.16 (c_Rings_Oinverse__class_Oinverse(v3, v1) = v4) | ~
% 211.59/30.16 (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v2) = v6) | ~ $i(v3)
% 211.59/30.16 | ~ $i(v2) | ~ $i(v1) | ~
% 211.59/30.17 class_RealVector_Oreal__normed__div__algebra(v3) | ~
% 211.59/30.17 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 211.59/30.17 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v6) | ? [v7: $i]
% 211.59/30.17 : (c_RealVector_Onorm__class_Onorm(v3, v1) = v7 & $i(v7) & ~
% 211.59/30.17 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v7))))
% 211.59/30.17
% 211.59/30.17 (fact_INVERSE__ZERO)
% 211.59/30.17 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.59/30.17 (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v0) = v0 &
% 211.59/30.17 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0))
% 211.59/30.17
% 211.59/30.17 (fact_LIMSEQ__inverse__realpow__zero__lemma)
% 211.59/30.17 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 211.59/30.17 $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 211.59/30.17 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 211.59/30.17 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 211.59/30.17 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) & $i(v2) &
% 211.59/30.17 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 211.59/30.17 [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6)
% 211.59/30.17 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ $i(v4)
% 211.59/30.17 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) | ? [v9:
% 211.59/30.17 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 211.59/30.17 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 211.59/30.17 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & hAPP(v10,
% 211.59/30.17 v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & $i(v10) & $i(v9)
% 211.59/30.17 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 211.59/30.17
% 211.59/30.17 (fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096)
% 211.59/30.17 $i(v_c____) & $i(v_pa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 211.59/30.17 $i] : ? [v2: $i] : ? [v3: $i] :
% 211.59/30.17 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v2) =
% 211.59/30.17 v0 & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 211.59/30.17 v_pa____) = v0 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3 &
% 211.59/30.17 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v1 & $i(v3) & $i(v2) &
% 211.59/30.17 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~
% 211.59/30.17 (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, v4) = v5) | ~
% 211.59/30.17 $i(v4) | ? [v6: $i] : (hAPP(v3, v4) = v6 & hAPP(v1, v5) = v6 & $i(v6))))
% 211.59/30.17
% 211.59/30.17 (fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 211.59/30.18 $i(v_c____) & $i(v_pa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 211.59/30.18 $i] : ? [v2: $i] : ? [v3: $i] :
% 211.59/30.18 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v2) =
% 211.59/30.18 v0 & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 211.59/30.18 v_pa____) = v0 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3 &
% 211.59/30.18 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v1 & $i(v3) & $i(v2) &
% 211.59/30.18 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~
% 211.59/30.18 (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, v4) = v5) | ~
% 211.59/30.18 $i(v4) | ? [v6: $i] : (hAPP(v3, v4) = v6 & hAPP(v1, v5) = v6 & $i(v6))))
% 211.59/30.18
% 211.59/30.18 (fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096)
% 211.59/30.18 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 211.59/30.18 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 211.59/30.18 ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = v8) &
% 211.59/30.18 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2) = v3 &
% 211.59/30.18 c_Polynomial_Osmult(tc_Complex_Ocomplex, v3, v_q____) = v4 &
% 211.59/30.18 c_Polynomial_Opoly(tc_Complex_Ocomplex, v4) = v5 &
% 211.59/30.18 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 211.59/30.18 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v5, v7) = v9 &
% 211.59/30.18 hAPP(v5, v6) = v8 & hAPP(v0, v1) = v2 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 211.59/30.18 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 211.59/30.18
% 211.59/30.18 (fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096)
% 211.59/30.18 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] :
% 211.59/30.18 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 & $i(v0) & ~
% 211.59/30.18 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 211.59/30.18 tc_Complex_Ocomplex, v0))
% 211.59/30.18
% 211.59/30.18 (fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096)
% 211.59/30.18 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 211.59/30.18 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 211.59/30.18 ? [v8: $i] : (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 &
% 211.59/30.18 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2) = v4 &
% 211.59/30.18 c_Polynomial_Osmult(tc_Complex_Ocomplex, v4, v_q____) = v5 &
% 211.59/30.18 c_Polynomial_Opoly(tc_Complex_Ocomplex, v5) = v6 &
% 211.59/30.18 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 211.59/30.18 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v8, v2) = v2 &
% 211.59/30.18 hAPP(v6, v1) = v7 & hAPP(v3, v7) = v8 & hAPP(v0, v1) = v2 & $i(v8) & $i(v7)
% 211.59/30.18 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 211.59/30.18
% 211.59/30.18 (fact__096poly_Aq_Aw_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_A_K_Apoly_Aq_A0_096)
% 211.93/30.19 $i(v_w____) & $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 211.93/30.19 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 211.93/30.19 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 211.93/30.19 (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v2 &
% 211.93/30.19 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v4) = v5 &
% 211.93/30.19 c_Polynomial_Osmult(tc_Complex_Ocomplex, v5, v_q____) = v6 &
% 211.93/30.19 c_Polynomial_Opoly(tc_Complex_Ocomplex, v6) = v7 &
% 211.93/30.19 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 211.93/30.19 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v3 & hAPP(v9, v4) = v1 &
% 211.93/30.19 hAPP(v7, v_w____) = v8 & hAPP(v2, v8) = v9 & hAPP(v0, v3) = v4 & hAPP(v0,
% 211.93/30.19 v_w____) = v1 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 211.93/30.19 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 211.93/30.19
% 211.93/30.19 (fact_a00)
% 211.93/30.19 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 211.93/30.19 $i] : ( ~ (v2 = v1) & c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0
% 211.93/30.19 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v0, v1) = v2
% 211.93/30.19 & $i(v2) & $i(v1) & $i(v0))
% 211.93/30.19
% 211.93/30.19 (fact_c)
% 211.93/30.19 $i(v_c____) & $i(v_pa____) & $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) &
% 211.93/30.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 211.93/30.19 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 &
% 211.93/30.19 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 & hAPP(v0, v_c____) =
% 211.93/30.19 v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0,
% 211.93/30.19 v3) = v4) | ~ $i(v3) | ? [v5: $i] :
% 211.93/30.19 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = v5 & $i(v5) &
% 211.93/30.19 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v5))))
% 211.93/30.19
% 211.93/30.19 (fact_calculation)
% 211.93/30.19 $i(v_c____) & $i(v_pa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 211.93/30.19 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 211.93/30.19 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 &
% 211.93/30.19 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 & $i(v3) & $i(v2) &
% 211.93/30.19 $i(v0) & ((v4 = v2 & hAPP(v0, v3) = v2) | ( ~ (v2 = v1) & hAPP(v0, v_c____)
% 211.93/30.19 = v1 & $i(v1))))
% 211.93/30.19
% 211.93/30.19 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)
% 211.93/30.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 211.93/30.20 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 211.93/30.20 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 211.93/30.20 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | hAPP(v4, v0)
% 211.93/30.20 = v1))
% 211.93/30.20
% 211.93/30.20 (fact_complex__divide__def)
% 211.93/30.20 $i(tc_Complex_Ocomplex) & ? [v0: $i] :
% 211.93/30.20 (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v0 & $i(v0) & ! [v1:
% 211.93/30.20 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 211.93/30.20 (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v1) = v4) | ~
% 211.93/30.20 (hAPP(v3, v4) = v5) | ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 211.93/30.20 (c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, v2, v1) = v5 &
% 211.93/30.20 $i(v5))))
% 211.93/30.20
% 211.93/30.20 (fact_cq0)
% 211.93/30.20 $i(v_pa____) & $i(tc_RealDef_Oreal) & $i(v_q____) & $i(tc_Complex_Ocomplex) &
% 211.93/30.20 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 211.93/30.20 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v3 &
% 211.93/30.20 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v4 &
% 211.93/30.20 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 211.93/30.20 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v0, v1) = v2 &
% 211.93/30.20 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ( ~
% 211.93/30.20 (hAPP(v4, v5) = v6) | ~ $i(v5) | ? [v7: $i] :
% 211.93/30.20 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) = v7 & $i(v7) &
% 211.93/30.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v7))))
% 211.93/30.20
% 211.93/30.20 (fact_div__less__dividend)
% 211.93/30.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.20 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 211.93/30.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 211.93/30.20 $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 211.93/30.20 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v3) | ~
% 211.93/30.20 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~
% 211.93/30.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 211.93/30.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 211.93/30.20
% 211.93/30.20 (fact_divide_Ononneg__bounded)
% 211.93/30.21 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.21 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 211.93/30.21 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 211.93/30.21 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 211.93/30.21 class_RealVector_Oreal__normed__field(v3) | ? [v4: $i] : ($i(v4) &
% 211.93/30.21 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & ! [v5:
% 211.93/30.21 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 211.93/30.21 (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7, v4) =
% 211.93/30.21 v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9: $i] : ? [v10:
% 211.93/30.21 $i] : (c_RealVector_Onorm__class_Onorm(v3, v9) = v10 &
% 211.93/30.21 c_Rings_Oinverse__class_Odivide(v3, v5, v2) = v9 & $i(v10) & $i(v9)
% 211.93/30.21 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v8))))))
% 211.93/30.21
% 211.93/30.21 (fact_divide_Opos__bounded)
% 211.93/30.21 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.21 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 211.93/30.21 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 211.93/30.21 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 211.93/30.21 class_RealVector_Oreal__normed__field(v3) | ? [v4: $i] : ($i(v4) &
% 211.93/30.21 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! [v5: $i] :
% 211.93/30.21 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 211.93/30.21 (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7, v4) =
% 211.93/30.21 v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9: $i] : ? [v10:
% 211.93/30.21 $i] : (c_RealVector_Onorm__class_Onorm(v3, v9) = v10 &
% 211.93/30.21 c_Rings_Oinverse__class_Odivide(v3, v5, v2) = v9 & $i(v10) & $i(v9)
% 211.93/30.21 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v8))))))
% 211.93/30.21
% 211.93/30.21 (fact_divide__eq__eq)
% 211.93/30.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 211.93/30.21 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (c_Rings_Oinverse__class_Odivide(v3,
% 211.93/30.21 v2, v1) = v4) | ~ (c_Groups_Otimes__class_Otimes(v3) = v5) | ~
% 211.93/30.21 (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v0) = v6) | ~ $i(v3) | ~ $i(v2) | ~
% 211.93/30.21 $i(v1) | ~ $i(v0) | ~ class_Fields_Ofield__inverse__zero(v3) | ? [v8: $i]
% 211.93/30.21 : (( ~ (v4 = v0) | (c_Groups_Ozero__class_Ozero(v3) = v8 & $i(v8) & ( ~ (v8
% 211.93/30.21 = v1) | v1 = v0) & (v8 = v1 | v7 = v2))) & (v4 = v0 |
% 211.93/30.21 (c_Groups_Ozero__class_Ozero(v3) = v8 & $i(v8) & ((v8 = v1 & ~ (v1 =
% 211.93/30.21 v0)) | ( ~ (v8 = v1) & ~ (v7 = v2)))))))
% 211.93/30.21
% 211.93/30.21 (fact_divisors__zero)
% 211.93/30.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 211.93/30.22 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5)
% 211.93/30.22 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 211.93/30.22 class_Rings_Ono__zero__divisors(v2) | ? [v6: $i] :
% 211.93/30.22 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = v5) | v5 = v1 |
% 211.93/30.22 v5 = v0)))
% 211.93/30.22
% 211.93/30.22 (fact_dvd__mult__cancel1)
% 211.93/30.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 211.93/30.22 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 211.93/30.22 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 211.93/30.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 211.93/30.22 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~
% 211.93/30.22 (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 211.93/30.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) | ~
% 211.93/30.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3: $i] : !
% 211.93/30.22 [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) |
% 211.93/30.22 ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 211.93/30.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 211.93/30.22
% 211.93/30.22 (fact_dvd__mult__cancel2)
% 211.93/30.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 211.93/30.22 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 211.93/30.22 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 211.93/30.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 211.93/30.22 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~
% 211.93/30.22 (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 211.93/30.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) | ~
% 211.93/30.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3: $i] : !
% 211.93/30.22 [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) |
% 211.93/30.22 ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 211.93/30.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 211.93/30.22
% 211.93/30.22 (fact_ex__least__nat__less)
% 211.93/30.23 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.23 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 211.93/30.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 211.93/30.23 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) | ~ $i(v3) | ~
% 211.93/30.23 $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 211.93/30.23 $i] : ($i(v6) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7
% 211.93/30.23 & hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) &
% 211.93/30.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9: $i] :
% 211.93/30.23 ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9) | ~ hBOOL(v10) |
% 211.93/30.23 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) |
% 211.93/30.23 (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5))))))
% 211.93/30.23
% 211.93/30.23 (fact_expi__add)
% 211.93/30.23 $i(tc_Complex_Ocomplex) & ? [v0: $i] :
% 211.93/30.23 (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v0 & $i(v0) & ! [v1:
% 211.93/30.23 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 211.93/30.23 : ( ~ (c_Complex_Oexpi(v2) = v3) | ~ (c_Complex_Oexpi(v1) = v5) | ~
% 211.93/30.23 (hAPP(v4, v5) = v6) | ~ (hAPP(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ?
% 211.93/30.23 [v7: $i] : (c_Complex_Oexpi(v7) = v6 &
% 211.93/30.23 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v1) = v7 & $i(v7) &
% 211.93/30.23 $i(v6))))
% 211.93/30.23
% 211.93/30.23 (fact_expi__zero)
% 211.93/30.23 $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : (c_Complex_Oexpi(v0) =
% 211.93/30.23 v1 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v1 &
% 211.93/30.23 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v1) & $i(v0))
% 211.93/30.23
% 211.93/30.23 (fact_ge__natfloor__plus__one__imp__gt)
% 211.93/30.23 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.93/30.23 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 211.93/30.23 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) =
% 211.93/30.23 v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 211.93/30.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5: $i] :
% 211.93/30.23 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 & $i(v5) & ~
% 211.93/30.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v1))))
% 211.93/30.23
% 211.93/30.23 (fact_gr__implies__not0)
% 211.93/30.23 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 211.93/30.23 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 211.93/30.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 211.93/30.23
% 211.93/30.23 (fact_inverse__le__1__iff)
% 211.93/30.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 211.93/30.24 (c_Rings_Oinverse__class_Oinverse(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 211.93/30.24 class_Fields_Olinordered__field__inverse__zero(v1) | ? [v3: $i] : ? [v4:
% 211.93/30.24 $i] : (c_Groups_Oone__class_Oone(v1) = v3 & $i(v3) & ( ~
% 211.93/30.24 c_Orderings_Oord__class_Oless__eq(v1, v2, v3) |
% 211.93/30.24 c_Orderings_Oord__class_Oless__eq(v1, v3, v0) |
% 211.93/30.24 (c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v4) &
% 211.93/30.24 c_Orderings_Oord__class_Oless__eq(v1, v0, v4))) &
% 211.93/30.24 (c_Orderings_Oord__class_Oless__eq(v1, v2, v3) |
% 211.93/30.24 (c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v4) & ~
% 211.93/30.24 c_Orderings_Oord__class_Oless__eq(v1, v3, v0) & ~
% 211.93/30.24 c_Orderings_Oord__class_Oless__eq(v1, v0, v4)))))
% 211.93/30.24
% 211.93/30.24 (fact_inverse__less__1__iff)
% 211.93/30.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 211.93/30.24 (c_Rings_Oinverse__class_Oinverse(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 211.93/30.24 class_Fields_Olinordered__field__inverse__zero(v1) | ? [v3: $i] : ? [v4:
% 211.93/30.24 $i] : (c_Groups_Oone__class_Oone(v1) = v3 & $i(v3) & ( ~
% 211.93/30.24 c_Orderings_Oord__class_Oless(v1, v2, v3) |
% 211.93/30.24 c_Orderings_Oord__class_Oless(v1, v3, v0) |
% 211.93/30.24 (c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v4) &
% 211.93/30.24 c_Orderings_Oord__class_Oless__eq(v1, v0, v4))) &
% 211.93/30.24 (c_Orderings_Oord__class_Oless(v1, v2, v3) |
% 211.93/30.24 (c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v4) & ~
% 211.93/30.24 c_Orderings_Oord__class_Oless__eq(v1, v0, v4) & ~
% 211.93/30.24 c_Orderings_Oord__class_Oless(v1, v3, v0)))))
% 211.93/30.24
% 211.93/30.24 (fact_inverse__nonzero__iff__nonzero)
% 211.93/30.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 211.93/30.24 (c_Rings_Oinverse__class_Oinverse(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 211.93/30.24 class_Rings_Odivision__ring__inverse__zero(v1) | ? [v3: $i] :
% 211.93/30.24 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) &
% 211.93/30.24 ( ~ (v3 = v0) | v2 = v0)))
% 211.93/30.24
% 211.93/30.24 (fact_inverse__zero__imp__zero)
% 211.93/30.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 211.93/30.24 (c_Rings_Oinverse__class_Oinverse(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 211.93/30.24 class_Rings_Odivision__ring(v1) | ? [v3: $i] :
% 211.93/30.24 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0)))
% 211.93/30.24
% 211.93/30.24 (fact_le__mult__natfloor)
% 211.93/30.25 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 211.93/30.25 $i] : (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 211.93/30.25 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 211.93/30.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 211.93/30.25 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 211.93/30.25 : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~
% 211.93/30.25 (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v1,
% 211.93/30.25 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v9: $i]
% 211.93/30.25 : ? [v10: $i] : ? [v11: $i] : (c_RComplete_Onatfloor(v10) = v11 &
% 211.93/30.25 hAPP(v9, v3) = v10 & hAPP(v2, v4) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11))))
% 211.93/30.25
% 211.93/30.25 (fact_le__natfloor__eq)
% 211.93/30.25 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.93/30.25 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 211.93/30.25 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 211.93/30.25 v1) = v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 211.93/30.25 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)) & ! [v1: $i]
% 211.93/30.25 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 211.93/30.25 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ (c_RComplete_Onatfloor(v2) =
% 211.93/30.25 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)))
% 211.93/30.25
% 211.93/30.25 (fact_le__natfloor__eq__one)
% 211.93/30.25 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.25 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 211.93/30.25 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 211.93/30.25 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) |
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & ! [v2: $i]
% 211.93/30.25 : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) |
% 211.93/30.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3)))
% 211.93/30.25
% 211.93/30.25 (fact_less_Ohyps)
% 211.93/30.25 $i(tc_Nat_Onat) & $i(v_pa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ?
% 211.93/30.25 [v1: $i] :
% 211.93/30.25 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 211.93/30.25 v_pa____) = v0 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 &
% 211.93/30.25 $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 211.93/30.25 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 211.93/30.25 v2) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 211.93/30.25 v3, v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 211.93/30.25 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v4 & $i(v5) & $i(v4) &
% 211.93/30.25 (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 211.93/30.25 tc_Complex_Ocomplex, v4) | (v6 = v1 & hAPP(v4, v5) = v1)))))
% 211.93/30.25
% 211.93/30.25 (fact_less_Oprems)
% 211.93/30.25 $i(v_pa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] :
% 211.93/30.25 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 & $i(v0) & ~
% 211.93/30.25 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 211.93/30.25 tc_Complex_Ocomplex, v0))
% 211.93/30.25
% 211.93/30.25 (fact_less__nat__zero__code)
% 211.93/30.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 211.93/30.25 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 211.93/30.25
% 211.93/30.25 (fact_less__natfloor)
% 211.93/30.25 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.93/30.25 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 211.93/30.25 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 211.93/30.25 v1) = v3) | ~ (c_RComplete_Onatfloor(v2) = v4) | ~ $i(v2) | ~
% 211.93/30.25 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.25 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) |
% 211.93/30.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1)))
% 211.93/30.25
% 211.93/30.25 (fact_less__zeroE)
% 211.93/30.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 211.93/30.25 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 211.93/30.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 211.93/30.25
% 211.93/30.25 (fact_lgqr)
% 211.93/30.26 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 211.93/30.26 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 211.93/30.26 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v5) =
% 211.93/30.26 v0 & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 211.93/30.26 v_q____) = v0 & c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v3)
% 211.93/30.26 = v4 & c_Polynomial_Osmult(tc_Complex_Ocomplex, v4, v_q____) = v5 &
% 211.93/30.26 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v1 &
% 211.93/30.26 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 & hAPP(v1, v2) = v3 &
% 211.93/30.26 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 211.93/30.26
% 211.93/30.26 (fact_ln__add__one__self__le__self)
% 211.93/30.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 211.93/30.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 211.93/30.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 211.93/30.26 v1, v2) = v3) | ~ $i(v2) | ~
% 211.93/30.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v4: $i]
% 211.93/30.26 : (c_Transcendental_Oln(v3) = v4 & $i(v4) &
% 211.93/30.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2))))
% 211.93/30.26
% 211.93/30.26 (fact_ln__div)
% 211.93/30.26 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.93/30.26 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 211.93/30.26 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 211.93/30.26 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v3, v4) = v5) | ~
% 211.93/30.26 (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) = v4) | ~
% 211.93/30.26 $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 211.93/30.26 v0, v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 211.93/30.26 ? [v6: $i] : (c_Transcendental_Oln(v6) = v5 &
% 211.93/30.26 c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v6 & $i(v6)
% 211.93/30.26 & $i(v5))))
% 211.93/30.26
% 211.93/30.26 (fact_ln__eq__zero__iff)
% 211.93/30.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 211.93/30.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 211.93/30.26 [v2: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = v0) | ~ $i(v2) | ~
% 211.93/30.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)) & ! [v2: $i] :
% 211.93/30.26 (v2 = v0 | ~ (c_Transcendental_Oln(v1) = v2) | ~
% 211.93/30.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 211.93/30.26
% 211.93/30.26 (fact_ln__ge__zero)
% 211.93/30.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 211.93/30.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 211.93/30.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 211.93/30.26 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)))
% 211.93/30.26
% 211.93/30.26 (fact_ln__ge__zero__iff)
% 211.93/30.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 211.93/30.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 211.93/30.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 211.93/30.26 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) | ~
% 211.93/30.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i]
% 211.93/30.26 : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 211.93/30.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~
% 211.93/30.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 211.93/30.26
% 211.93/30.26 (fact_ln__ge__zero__imp__ge__one)
% 211.93/30.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 211.93/30.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 211.93/30.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 211.93/30.26 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~
% 211.93/30.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 211.93/30.26
% 211.93/30.26 (fact_ln__gt__zero)
% 211.93/30.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 211.93/30.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 211.93/30.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 211.93/30.26 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 211.93/30.26
% 211.93/30.26 (fact_ln__gt__zero__iff)
% 211.93/30.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.27 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 211.93/30.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 211.93/30.27 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 211.93/30.27 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] :
% 211.93/30.27 ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 211.93/30.27
% 211.93/30.27 (fact_ln__gt__zero__imp__gt__one)
% 211.93/30.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 211.93/30.27 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 211.93/30.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 211.93/30.27 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 211.93/30.27 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 211.93/30.27
% 211.93/30.27 (fact_ln__inj__iff)
% 211.93/30.27 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.93/30.27 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 211.93/30.27 ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = v3) |
% 211.93/30.27 ~ (c_Transcendental_Oln(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 211.93/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 211.93/30.27
% 211.93/30.27 (fact_ln__le__cancel__iff)
% 211.93/30.27 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 211.93/30.27 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 211.93/30.27 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 211.93/30.27 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.29/30.27 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v1: $i]
% 212.29/30.27 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) =
% 212.29/30.27 v3) | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.29/30.27 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4)))
% 212.29/30.27
% 212.29/30.27 (fact_ln__less__cancel__iff)
% 212.29/30.27 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.29/30.27 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.29/30.27 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 212.29/30.27 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! [v1: $i] :
% 212.29/30.27 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 212.29/30.27 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4)))
% 212.29/30.27
% 212.29/30.27 (fact_ln__less__self)
% 212.29/30.27 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.29/30.27 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.29/30.27 ! [v2: $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~ $i(v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)))
% 212.29/30.27
% 212.29/30.27 (fact_ln__less__zero)
% 212.29/30.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.29/30.27 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.29/30.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.29/30.27 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 212.29/30.27 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 212.29/30.27
% 212.29/30.27 (fact_ln__less__zero__iff)
% 212.29/30.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.29/30.27 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.29/30.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.29/30.27 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 212.29/30.27 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i] :
% 212.29/30.27 ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 212.29/30.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.29/30.28 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 212.29/30.28
% 212.29/30.28 (fact_ln__mult)
% 212.29/30.28 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.29/30.28 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.29/30.28 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.29/30.28 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 212.29/30.28 (c_Transcendental_Oln(v3) = v4) | ~ (c_Transcendental_Oln(v2) = v5) | ~
% 212.29/30.28 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~ $i(v3) |
% 212.29/30.28 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 212.29/30.28 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7: $i] :
% 212.29/30.28 ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7, v2) = v8 & hAPP(v1,
% 212.29/30.28 v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 212.29/30.28
% 212.29/30.28 (fact_ln__one)
% 212.29/30.28 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : (c_Transcendental_Oln(v0) =
% 212.29/30.28 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.29/30.28 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 212.29/30.28
% 212.29/30.28 (fact_ln__realpow)
% 212.29/30.28 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 212.29/30.28 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 212.29/30.28 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 212.29/30.28 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 212.29/30.28 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 212.29/30.28 : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) = v7) | ~
% 212.29/30.28 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6, v7) = v8) | ~
% 212.29/30.28 (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 212.29/30.28 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v9: $i] : ?
% 212.29/30.28 [v10: $i] : (c_Transcendental_Oln(v10) = v8 & hAPP(v9, v3) = v10 &
% 212.29/30.28 hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & $i(v8))))
% 212.34/30.28
% 212.34/30.28 (fact_mult_Ononneg__bounded)
% 212.34/30.28 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.28 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.28 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.28 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 212.34/30.28 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 212.34/30.28 ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & !
% 212.34/30.28 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 212.34/30.28 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 212.34/30.28 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 212.34/30.28 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) =
% 212.34/30.28 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~
% 212.34/30.28 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14:
% 212.34/30.28 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15
% 212.34/30.28 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 212.34/30.28 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 212.34/30.28 v12))))))
% 212.34/30.28
% 212.34/30.28 (fact_mult_Opos__bounded)
% 212.34/30.28 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.28 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.28 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.28 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 212.34/30.28 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 212.34/30.28 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 212.34/30.28 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 212.34/30.28 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 212.34/30.28 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 212.34/30.28 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) =
% 212.34/30.28 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~
% 212.34/30.28 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14:
% 212.34/30.28 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15
% 212.34/30.28 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 212.34/30.28 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 212.34/30.28 v12))))))
% 212.34/30.28
% 212.34/30.29 (fact_mult__eq__0__iff)
% 212.34/30.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 212.34/30.29 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5)
% 212.34/30.29 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.34/30.29 class_Rings_Oring__no__zero__divisors(v2) | ? [v6: $i] :
% 212.34/30.29 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = v5) | v5 = v1 |
% 212.34/30.29 v5 = v0) & (v6 = v5 | ( ~ (v6 = v1) & ~ (v6 = v0)))))
% 212.34/30.29
% 212.34/30.29 (fact_mult__eq__self__implies__10)
% 212.34/30.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.29 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.29 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 212.34/30.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 212.34/30.29 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5,
% 212.34/30.29 v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)))
% 212.34/30.29
% 212.34/30.29 (fact_mult__left_Ononneg__bounded)
% 212.34/30.29 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.29 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.29 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 212.34/30.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.29 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.29 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) &
% 212.34/30.29 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) & ! [v6:
% 212.34/30.29 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 212.34/30.29 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) =
% 212.34/30.29 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11:
% 212.34/30.29 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12
% 212.34/30.29 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 212.34/30.29 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 212.34/30.29 v9))))))
% 212.34/30.29
% 212.34/30.29 (fact_mult__left_Opos__bounded)
% 212.34/30.29 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.29 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.29 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 212.34/30.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.29 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.29 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) &
% 212.34/30.29 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v6: $i] :
% 212.34/30.29 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 212.34/30.29 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) =
% 212.34/30.29 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11:
% 212.34/30.29 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12
% 212.34/30.29 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 212.34/30.29 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 212.34/30.29 v9))))))
% 212.34/30.29
% 212.34/30.29 (fact_mult__less__cancel2)
% 212.34/30.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 212.34/30.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 212.34/30.30 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 212.34/30.30 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~
% 212.34/30.30 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 212.34/30.30 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 212.34/30.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : !
% 212.34/30.30 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 212.34/30.30 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 212.34/30.30 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 212.34/30.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] : !
% 212.34/30.30 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 212.34/30.30 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 212.34/30.30 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~
% 212.34/30.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 212.34/30.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 212.34/30.30
% 212.34/30.30 (fact_mult__right_Ononneg__bounded)
% 212.34/30.30 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.30 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.30 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.34/30.30 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~
% 212.34/30.30 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ?
% 212.34/30.30 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.30 v0, v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 212.34/30.30 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) =
% 212.34/30.30 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12:
% 212.34/30.30 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 212.34/30.30 = v11 & $i(v12) & $i(v11) &
% 212.34/30.30 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10))))))
% 212.34/30.30
% 212.34/30.30 (fact_mult__right_Opos__bounded)
% 212.34/30.30 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.30 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.30 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.34/30.30 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~
% 212.34/30.30 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ?
% 212.34/30.30 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.34/30.30 v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 212.34/30.30 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) =
% 212.34/30.30 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12:
% 212.34/30.30 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 212.34/30.30 = v11 & $i(v12) & $i(v11) &
% 212.34/30.30 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10))))))
% 212.34/30.30
% 212.34/30.30 (fact_nat__1__eq__mult__iff)
% 212.34/30.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.30 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 212.34/30.30 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 212.34/30.30 $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = v0) | ~
% 212.34/30.30 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 212.34/30.30 ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) |
% 212.34/30.30 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 212.34/30.30 (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2)))
% 212.34/30.30
% 212.34/30.30 (fact_nat__dvd__1__iff__1)
% 212.34/30.30 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 212.34/30.30 $i(v0) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 =
% 212.34/30.30 v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)))
% 212.34/30.30
% 212.34/30.30 (fact_nat__le__real__less)
% 212.34/30.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.31 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 212.34/30.31 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2)
% 212.34/30.31 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 212.34/30.31 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ?
% 212.34/30.31 [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 &
% 212.34/30.31 $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))) & !
% 212.34/30.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.31 v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.31 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 212.34/30.31 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 & $i(v5) & ~
% 212.34/30.31 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))))
% 212.34/30.31
% 212.34/30.31 (fact_nat__less__real__le)
% 212.34/30.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.31 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 212.34/30.31 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2)
% 212.34/30.31 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 212.34/30.31 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5:
% 212.34/30.31 $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 212.34/30.31 $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))) &
% 212.34/30.31 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.31 v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 212.34/30.31 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) & ~
% 212.34/30.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))))
% 212.34/30.31
% 212.34/30.31 (fact_nat__mult__1)
% 212.34/30.31 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.31 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 & $i(v2)
% 212.34/30.31 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3)
% 212.34/30.31 = v4) | ~ $i(v3)))
% 212.34/30.31
% 212.34/30.31 (fact_nat__mult__1__right)
% 212.34/30.31 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.31 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 212.34/30.31 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) =
% 212.34/30.31 v2))
% 212.34/30.31
% 212.34/30.31 (fact_nat__mult__eq__1__iff)
% 212.34/30.31 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.31 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 212.34/30.31 $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = v1) | ~
% 212.34/30.31 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 212.34/30.31 ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) |
% 212.34/30.31 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 212.34/30.31 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 212.34/30.31
% 212.34/30.31 (fact_natceiling__add)
% 212.34/30.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.31 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.31 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.31 v1) = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3)
% 212.34/30.31 = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v5: $i]
% 212.34/30.31 : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 212.34/30.31 c_RComplete_Onatceiling(v2) = v6 &
% 212.34/30.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 212.34/30.31 $i(v5))))
% 212.34/30.31
% 212.34/30.31 (fact_natceiling__add__one)
% 212.34/30.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 212.34/30.31 $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 212.34/30.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.31 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 212.34/30.31 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.31 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) |
% 212.34/30.31 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5:
% 212.34/30.31 $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 212.34/30.31 c_RComplete_Onatceiling(v3) = v6 &
% 212.34/30.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 212.34/30.31 $i(v5))))
% 212.34/30.31
% 212.34/30.31 (fact_natceiling__eq)
% 212.34/30.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.32 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2:
% 212.34/30.32 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 212.34/30.32 (c_RComplete_Onatceiling(v2) = v4) | ~
% 212.34/30.32 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~ $i(v3) | ~
% 212.34/30.32 $i(v2) | ? [v6: $i] : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v3) =
% 212.34/30.32 v6 & $i(v6) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 212.34/30.32 v2) | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 &
% 212.34/30.32 $i(v7) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 212.34/30.32 v7))))))
% 212.34/30.32
% 212.34/30.32 (fact_natceiling__le__eq)
% 212.34/30.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.32 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.32 v1) = v4) | ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 212.34/30.32 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1) | ~
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4)) & ! [v1: $i]
% 212.34/30.32 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.32 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ (c_RComplete_Onatceiling(v2)
% 212.34/30.32 = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) | ~
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1)))
% 212.34/30.32
% 212.34/30.32 (fact_natceiling__le__eq__one)
% 212.34/30.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.32 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 212.34/30.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 212.34/30.32 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) |
% 212.34/30.32 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) |
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i]
% 212.34/30.32 : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0)))
% 212.34/30.32
% 212.34/30.32 (fact_natceiling__neg)
% 212.34/30.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.32 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.32 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.32 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_RComplete_Onatceiling(v2) = v3) |
% 212.34/30.32 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 212.34/30.32 v0)))
% 212.34/30.32
% 212.34/30.32 (fact_natceiling__one)
% 212.34/30.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.32 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.32 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 212.34/30.32
% 212.34/30.32 (fact_natceiling__zero)
% 212.34/30.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.32 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) =
% 212.34/30.32 v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 212.34/30.32
% 212.34/30.32 (fact_natfloor__add)
% 212.34/30.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.32 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.32 v1) = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3)
% 212.34/30.32 = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v5: $i]
% 212.34/30.32 : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 212.34/30.32 c_RComplete_Onatfloor(v2) = v6 &
% 212.34/30.32 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 212.34/30.32 $i(v5))))
% 212.34/30.32
% 212.34/30.32 (fact_natfloor__add__one)
% 212.34/30.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 212.34/30.32 $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 212.34/30.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.32 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 212.34/30.32 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.32 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) |
% 212.34/30.32 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5:
% 212.34/30.32 $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 212.34/30.32 c_RComplete_Onatfloor(v3) = v6 &
% 212.34/30.32 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 212.34/30.32 $i(v5))))
% 212.34/30.32
% 212.34/30.32 (fact_natfloor__div__nat)
% 212.34/30.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.33 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 212.34/30.33 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.34/30.33 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v4) | ~
% 212.34/30.33 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) | ~
% 212.34/30.33 $i(v3) | ~ $i(v2) | ~
% 212.34/30.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~
% 212.34/30.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v6: $i] : ? [v7:
% 212.34/30.33 $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v2) = v6 &
% 212.34/30.33 c_RComplete_Onatfloor(v5) = v6 & c_RComplete_Onatfloor(v3) = v7 & $i(v7)
% 212.34/30.33 & $i(v6))))
% 212.34/30.33
% 212.34/30.33 (fact_natfloor__eq)
% 212.34/30.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.33 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 212.34/30.33 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 212.34/30.33 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RComplete_Onatfloor(v1) =
% 212.34/30.33 v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? [v5: $i]
% 212.34/30.33 : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) &
% 212.34/30.33 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 212.34/30.33
% 212.34/30.33 (fact_natfloor__neg)
% 212.34/30.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.33 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.33 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.33 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_RComplete_Onatfloor(v2) = v3) | ~
% 212.34/30.33 $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.33
% 212.34/30.33 (fact_natfloor__one)
% 212.34/30.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.33 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1
% 212.34/30.33 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 212.34/30.33
% 212.34/30.33 (fact_natfloor__zero)
% 212.34/30.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.33 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) =
% 212.34/30.33 v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 212.34/30.33
% 212.34/30.33 (fact_no__zero__divisors)
% 212.34/30.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 212.34/30.33 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5)
% 212.34/30.33 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.34/30.33 class_Rings_Ono__zero__divisors(v2) | ? [v6: $i] :
% 212.34/30.33 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = v5) | v5 = v1 |
% 212.34/30.33 v5 = v0)))
% 212.34/30.33
% 212.34/30.33 (fact_nonzero__imp__inverse__nonzero)
% 212.34/30.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.34/30.33 (c_Rings_Oinverse__class_Oinverse(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.34/30.33 class_Rings_Odivision__ring(v1) | ? [v3: $i] :
% 212.34/30.33 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0)))
% 212.34/30.33
% 212.34/30.33 (fact_norm__eq__zero)
% 212.34/30.33 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.33 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 212.34/30.33 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.33 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~ (v3 = v0)
% 212.34/30.33 | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = v1)) & (v3 = v0 | ( ~
% 212.34/30.33 (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 212.34/30.33
% 212.34/30.33 (fact_norm__ge__zero)
% 212.34/30.33 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.33 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 212.34/30.33 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.33 class_RealVector_Oreal__normed__vector(v2) |
% 212.34/30.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 212.34/30.33
% 212.34/30.33 (fact_norm__le__zero__iff)
% 212.34/30.33 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.33 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 212.34/30.33 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.33 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~
% 212.34/30.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | (v4 = v1
% 212.34/30.33 & c_Groups_Ozero__class_Ozero(v2) = v1)) &
% 212.34/30.33 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | ( ~ (v4 =
% 212.34/30.33 v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 212.34/30.33
% 212.34/30.33 (fact_norm__not__less__zero)
% 212.34/30.33 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.33 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 212.34/30.33 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.33 class_RealVector_Oreal__normed__vector(v2) | ~
% 212.34/30.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 212.34/30.33
% 212.34/30.33 (fact_norm__one)
% 212.34/30.33 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.33 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 212.34/30.33 [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_RealVector_Onorm__class_Onorm(v1,
% 212.34/30.33 v2) = v3) | ~ (c_Groups_Oone__class_Oone(v1) = v2) | ~ $i(v1) | ~
% 212.34/30.33 class_RealVector_Oreal__normed__algebra__1(v1)))
% 212.34/30.33
% 212.34/30.33 (fact_norm__ratiotest__lemma)
% 212.34/30.34 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.34 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.34 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.34 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.34 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v5,
% 212.34/30.34 v3) = v6) | ~ (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~
% 212.34/30.34 (hAPP(v7, v8) = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~
% 212.34/30.34 $i(v3) | ~ $i(v2) | ~
% 212.34/30.34 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) | ~
% 212.34/30.34 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) | ~
% 212.34/30.34 class_RealVector_Oreal__normed__vector(v5) |
% 212.34/30.34 c_Groups_Ozero__class_Ozero(v5) = v3))
% 212.34/30.34
% 212.34/30.34 (fact_norm__zero)
% 212.34/30.34 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.34 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 212.34/30.34 (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v1) | ~
% 212.34/30.34 class_RealVector_Oreal__normed__vector(v1)))
% 212.34/30.34
% 212.34/30.34 (fact_not__less0)
% 212.34/30.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 212.34/30.34 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 212.34/30.34 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 212.34/30.34
% 212.34/30.34 (fact_not__one__le__zero)
% 212.34/30.34 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 212.34/30.34 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~
% 212.34/30.34 c_Orderings_Oord__class_Oless__eq(v0, v1, v2)))
% 212.34/30.34
% 212.34/30.34 (fact_not__one__less__zero)
% 212.34/30.34 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 212.34/30.34 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~
% 212.34/30.34 c_Orderings_Oord__class_Oless(v0, v1, v2)))
% 212.34/30.34
% 212.34/30.34 (fact_not__real__of__nat__less__zero)
% 212.34/30.34 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.34 ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ~
% 212.34/30.34 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.34
% 212.34/30.34 (fact_not__real__square__gt__zero)
% 212.34/30.34 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.34 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.34 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.34 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3, v2) = v4) |
% 212.34/30.34 ~ (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 212.34/30.34 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2: $i] :
% 212.34/30.34 ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2) | ~
% 212.34/30.34 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 212.34/30.34
% 212.34/30.34 (fact_one__le__inverse__iff)
% 212.34/30.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.34/30.34 (c_Rings_Oinverse__class_Oinverse(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.34/30.34 class_Fields_Olinordered__field__inverse__zero(v1) | ? [v3: $i] : ? [v4:
% 212.34/30.34 $i] : (c_Groups_Oone__class_Oone(v1) = v3 & $i(v3) & ( ~
% 212.34/30.34 c_Orderings_Oord__class_Oless__eq(v1, v3, v2) |
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v4) &
% 212.34/30.34 c_Orderings_Oord__class_Oless__eq(v1, v0, v3) &
% 212.34/30.34 c_Orderings_Oord__class_Oless(v1, v4, v0))) & ( ~
% 212.34/30.34 c_Orderings_Oord__class_Oless__eq(v1, v0, v3) |
% 212.34/30.34 c_Orderings_Oord__class_Oless__eq(v1, v3, v2) |
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v4) & ~
% 212.34/30.34 c_Orderings_Oord__class_Oless(v1, v4, v0)))))
% 212.34/30.34
% 212.34/30.34 (fact_one__less__inverse__iff)
% 212.34/30.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.34/30.34 (c_Rings_Oinverse__class_Oinverse(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.34/30.34 class_Fields_Olinordered__field__inverse__zero(v1) | ? [v3: $i] : ? [v4:
% 212.34/30.34 $i] : (c_Groups_Oone__class_Oone(v1) = v3 & $i(v3) & ( ~
% 212.34/30.34 c_Orderings_Oord__class_Oless(v1, v3, v2) |
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v4) &
% 212.34/30.34 c_Orderings_Oord__class_Oless(v1, v4, v0) &
% 212.34/30.34 c_Orderings_Oord__class_Oless(v1, v0, v3))) & ( ~
% 212.34/30.34 c_Orderings_Oord__class_Oless(v1, v0, v3) |
% 212.34/30.34 c_Orderings_Oord__class_Oless(v1, v3, v2) |
% 212.34/30.34 (c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v4) & ~
% 212.34/30.34 c_Orderings_Oord__class_Oless(v1, v4, v0)))))
% 212.34/30.34
% 212.34/30.34 (fact_one__neq__zero)
% 212.34/30.34 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 212.34/30.34 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) &
% 212.34/30.34 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2)))
% 212.34/30.34
% 212.34/30.34 (fact_order__root)
% 212.34/30.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 212.34/30.34 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 212.34/30.34 $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~
% 212.34/30.34 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: $i] :
% 212.34/30.34 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) &
% 212.34/30.34 c_Polynomial_Oorder(v3, v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7
% 212.34/30.34 & c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | (v6 = v5
% 212.34/30.34 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & ((v8 = v2 &
% 212.34/30.34 tc_Polynomial_Opoly(v3) = v7 & c_Groups_Ozero__class_Ozero(v7) = v2
% 212.34/30.34 & $i(v7)) | ( ~ (v9 = v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 &
% 212.34/30.34 $i(v9)) | ( ~ (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 &
% 212.34/30.34 $i(v6))))))
% 212.34/30.34
% 212.34/30.34 (fact_pc0)
% 212.34/30.35 $i(v_c____) & $i(v_pa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 212.34/30.35 $i] : ? [v2: $i] : ( ~ (v2 = v1) & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.34/30.35 v_pa____) = v0 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 &
% 212.34/30.35 hAPP(v0, v_c____) = v1 & $i(v2) & $i(v1) & $i(v0))
% 212.34/30.35
% 212.34/30.35 (fact_poly__bound__exists)
% 212.34/30.35 $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i] :
% 212.34/30.35 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 212.34/30.35 ! [v2: $i] : ! [v3: $i] : ( ~ (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2)
% 212.34/30.35 = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : ($i(v4) &
% 212.34/30.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! [v5: $i] :
% 212.34/30.35 ! [v6: $i] : ( ~ (hAPP(v3, v5) = v6) | ~ $i(v5) | ? [v7: $i] : ? [v8:
% 212.34/30.35 $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) =
% 212.34/30.35 v8 & $i(v8) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.35 v8, v4)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 212.34/30.35 v5) = v7 & $i(v7) & ~
% 212.34/30.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v1)))))))
% 212.34/30.35
% 212.34/30.35 (fact_power__dvd__imp__le)
% 212.34/30.35 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.35 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 212.34/30.35 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 212.34/30.35 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 212.34/30.35 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 212.34/30.35 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 212.34/30.35 v6, v7) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 212.34/30.35 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)))
% 212.34/30.35
% 212.34/30.35 (fact_power__one__right)
% 212.34/30.35 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 212.34/30.35 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.35 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 212.34/30.35 $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | hAPP(v4, v0) =
% 212.34/30.35 v1))
% 212.34/30.35
% 212.34/30.35 (fact_pqc0)
% 212.34/30.35 $i(v_c____) & $i(v_pa____) & $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0:
% 212.34/30.35 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 212.34/30.35 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 &
% 212.34/30.35 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v2 &
% 212.34/30.35 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v3 & hAPP(v2, v3) = v1 &
% 212.34/30.35 hAPP(v0, v_c____) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 212.34/30.35
% 212.34/30.35 (fact_q_I2_J)
% 212.34/30.35 $i(v_c____) & $i(v_pa____) & $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0:
% 212.34/30.35 $i] : ? [v1: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v1
% 212.34/30.35 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 & $i(v1) & $i(v0) &
% 212.34/30.35 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ? [v4: $i]
% 212.34/30.35 : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, v2) = v4 &
% 212.34/30.35 hAPP(v1, v4) = v3 & $i(v4) & $i(v3))))
% 212.34/30.35
% 212.34/30.35 (fact_qnc)
% 212.34/30.35 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] :
% 212.34/30.35 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 & $i(v0) & ~
% 212.34/30.35 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.34/30.35 tc_Complex_Ocomplex, v0))
% 212.34/30.35
% 212.34/30.35 (fact_qr)
% 212.34/30.35 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 212.34/30.35 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 212.34/30.35 (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v1 &
% 212.34/30.35 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v3) = v4 &
% 212.34/30.35 c_Polynomial_Osmult(tc_Complex_Ocomplex, v4, v_q____) = v5 &
% 212.34/30.35 c_Polynomial_Opoly(tc_Complex_Ocomplex, v5) = v6 &
% 212.34/30.35 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.35 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 & hAPP(v0, v2) = v3 &
% 212.34/30.35 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] :
% 212.34/30.35 ! [v8: $i] : ( ~ (hAPP(v6, v7) = v8) | ~ $i(v7) | ? [v9: $i] : ? [v10:
% 212.34/30.35 $i] : (hAPP(v10, v3) = v9 & hAPP(v1, v8) = v10 & hAPP(v0, v7) = v9 &
% 212.34/30.35 $i(v10) & $i(v9))))
% 212.34/30.35
% 212.34/30.35 (fact_r01)
% 212.34/30.35 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 212.34/30.35 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 212.34/30.35 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v6 &
% 212.34/30.35 c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2) = v3 &
% 212.34/30.35 c_Polynomial_Osmult(tc_Complex_Ocomplex, v3, v_q____) = v4 &
% 212.34/30.35 c_Polynomial_Opoly(tc_Complex_Ocomplex, v4) = v5 &
% 212.34/30.35 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.35 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v5, v1) = v6 &
% 212.34/30.35 hAPP(v0, v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 212.34/30.35 $i(v0))
% 212.34/30.35
% 212.34/30.35 (fact_rcis__mult)
% 212.34/30.35 $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.35 c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v0 & $i(v1) & $i(v0) &
% 212.34/30.35 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.35 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (c_Complex_Orcis(v7, v8) = v9) | ~
% 212.34/30.35 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v2) = v8) | ~
% 212.34/30.35 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~
% 212.34/30.35 $i(v3) | ~ $i(v2) | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 212.34/30.35 (c_Complex_Orcis(v5, v4) = v10 & c_Complex_Orcis(v3, v2) = v12 & hAPP(v11,
% 212.34/30.35 v12) = v9 & hAPP(v0, v10) = v11 & $i(v12) & $i(v11) & $i(v10) &
% 212.34/30.35 $i(v9))))
% 212.34/30.35
% 212.34/30.35 (fact_rcis__zero__mod)
% 212.34/30.35 $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.35 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.35 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v1) & $i(v0) & !
% 212.34/30.35 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_Complex_Orcis(v0, v2) = v3) | ~
% 212.34/30.35 $i(v2)))
% 212.34/30.35
% 212.34/30.35 (fact_real__0__le__divide__iff)
% 212.34/30.36 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.36 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.36 ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.36 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 212.34/30.36 $i(v2) | ~ $i(v1) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & ! [v1: $i]
% 212.34/30.36 : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.36 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 212.34/30.36 $i(v2) | ~ $i(v1) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & ! [v1: $i]
% 212.34/30.36 : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.36 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 212.34/30.36 $i(v2) | ~ $i(v1) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & ! [v1: $i]
% 212.34/30.36 : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.36 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 212.34/30.36 $i(v2) | ~ $i(v1) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1)) & ! [v1: $i]
% 212.34/30.36 : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.36 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 212.34/30.36 $i(v2) | ~ $i(v1) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)) & ! [v1: $i]
% 212.34/30.36 : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.36 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 212.34/30.36 $i(v2) | ~ $i(v1) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 212.34/30.36
% 212.34/30.36 (fact_real__le__eq__diff)
% 212.34/30.36 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.36 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.36 ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.36 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2)
% 212.34/30.36 | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3,
% 212.34/30.36 v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 212.34/30.36 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.36 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2)
% 212.34/30.36 | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 212.34/30.36 v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 212.34/30.36
% 212.34/30.36 (fact_real__mult__1)
% 212.34/30.36 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.36 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.36 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v0, v1) = v2 &
% 212.34/30.36 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 212.34/30.36 (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 212.34/30.36
% 212.34/30.36 (fact_real__mult__inverse__cancel)
% 212.34/30.36 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.36 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.36 $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 212.34/30.36 (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v5) = v6) | ~
% 212.34/30.36 (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v4) = v9) | ~
% 212.34/30.36 (hAPP(v10, v2) = v11) | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v1, v9) = v10) |
% 212.34/30.36 ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 212.34/30.36 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v11) | ? [v12: $i] :
% 212.34/30.36 ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : (hAPP(v14, v2) = v15 &
% 212.34/30.36 hAPP(v12, v3) = v13 & hAPP(v1, v5) = v14 & hAPP(v1, v4) = v12 & $i(v15)
% 212.34/30.36 & $i(v14) & $i(v13) & $i(v12) & ~
% 212.34/30.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v15))))
% 212.34/30.36
% 212.34/30.36 (fact_real__mult__inverse__cancel2)
% 212.34/30.36 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.36 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.36 $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 212.34/30.36 (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v5) = v7) | ~
% 212.34/30.36 (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v4) = v10) | ~
% 212.34/30.36 (hAPP(v9, v10) = v11) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v1, v3) = v6) |
% 212.34/30.36 ~ (hAPP(v1, v2) = v9) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v11) | ? [v12: $i] :
% 212.34/30.36 ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : (hAPP(v14, v2) = v15 &
% 212.34/30.36 hAPP(v12, v3) = v13 & hAPP(v1, v5) = v14 & hAPP(v1, v4) = v12 & $i(v15)
% 212.34/30.36 & $i(v14) & $i(v13) & $i(v12) & ~
% 212.34/30.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v15))))
% 212.34/30.36
% 212.34/30.36 (fact_real__mult__inverse__left)
% 212.34/30.36 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.36 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 212.34/30.36 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 212.34/30.36 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 |
% 212.34/30.36 v3 = v0 | ~ (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v3) = v4)
% 212.34/30.36 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3)))
% 212.34/30.36
% 212.34/30.36 (fact_real__mult__le__cancel__iff1)
% 212.34/30.36 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.36 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.36 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~
% 212.34/30.36 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 212.34/30.36 $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) |
% 212.34/30.36 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i]
% 212.34/30.36 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 212.34/30.36 [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1,
% 212.34/30.36 v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 212.34/30.36 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | ~
% 212.34/30.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8)))
% 212.34/30.36
% 212.34/30.36 (fact_real__mult__le__cancel__iff2)
% 212.34/30.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.37 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 212.34/30.37 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i]
% 212.34/30.37 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 212.34/30.37 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 212.34/30.37 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7)))
% 212.34/30.37
% 212.34/30.37 (fact_real__mult__left__cancel)
% 212.34/30.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v0
% 212.34/30.37 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1,
% 212.34/30.37 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 212.34/30.37
% 212.34/30.37 (fact_real__mult__less__iff1)
% 212.34/30.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.37 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~
% 212.34/30.37 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 212.34/30.37 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i] :
% 212.34/30.37 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 212.34/30.37 $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3)
% 212.34/30.37 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8)))
% 212.34/30.37
% 212.34/30.37 (fact_real__mult__less__mono2)
% 212.34/30.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.37 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 212.34/30.37 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7)))
% 212.34/30.37
% 212.34/30.37 (fact_real__mult__order)
% 212.34/30.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 212.34/30.37 | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 212.34/30.37
% 212.34/30.37 (fact_real__mult__right__cancel)
% 212.34/30.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.37 $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) | ~ (hAPP(v5, v4) = v6)
% 212.34/30.37 | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3)
% 212.34/30.37 | ~ $i(v2)))
% 212.34/30.37
% 212.34/30.37 (fact_real__natfloor__add__one__gt)
% 212.34/30.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.37 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 212.34/30.37 [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 212.34/30.37 ? [v4: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 212.34/30.37 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 & $i(v4) &
% 212.34/30.37 $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 212.34/30.37
% 212.34/30.37 (fact_real__natfloor__gt__diff__one)
% 212.34/30.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.37 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 212.34/30.37 [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) =
% 212.34/30.37 v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 212.34/30.37 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1) = v3 &
% 212.34/30.37 $i(v4) & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 212.34/30.37 v4))))
% 212.34/30.37
% 212.34/30.37 (fact_real__natfloor__le)
% 212.34/30.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.37 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.37 ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~
% 212.34/30.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ? [v3: $i]
% 212.34/30.37 : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) &
% 212.34/30.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))))
% 212.34/30.37
% 212.34/30.37 (fact_real__of__nat__1)
% 212.34/30.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.37 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 212.34/30.37 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 212.34/30.37 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 212.34/30.37
% 212.34/30.37 (fact_real__of__nat__div2)
% 212.34/30.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.37 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.37 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.37 $i] : ! [v8: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,
% 212.34/30.37 v5, v7) = v8) | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) =
% 212.34/30.37 v6) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~
% 212.34/30.37 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.37 v1) = v4) | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3,
% 212.34/30.37 v4) = v5) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v8)))
% 212.34/30.37
% 212.34/30.37 (fact_real__of__nat__div3)
% 212.34/30.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.37 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 212.34/30.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.37 $i] : ! [v8: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,
% 212.34/30.37 v5, v7) = v8) | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) =
% 212.34/30.37 v6) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~
% 212.34/30.37 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.37 v1) = v4) | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3,
% 212.34/30.37 v4) = v5) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v0)))
% 212.34/30.37
% 212.34/30.37 (fact_real__of__nat__ge__zero)
% 212.34/30.38 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.38 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.38 ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) |
% 212.34/30.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)))
% 212.34/30.38
% 212.34/30.38 (fact_real__of__nat__gt__zero__cancel__iff)
% 212.34/30.38 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.38 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.38 [v2: $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 212.34/30.38 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] :
% 212.34/30.38 ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 212.34/30.38
% 212.34/30.38 (fact_real__of__nat__le__zero__cancel__iff)
% 212.34/30.38 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.38 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.38 [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) =
% 212.34/30.38 v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.38 v3, v0)) & ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) |
% 212.34/30.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.38
% 212.34/30.38 (fact_real__of__nat__zero)
% 212.34/30.38 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.38 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 212.34/30.38
% 212.34/30.38 (fact_real__of__nat__zero__iff)
% 212.34/30.38 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.38 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 212.34/30.38 [v2: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v0) | ~
% 212.34/30.38 $i(v2)) & ! [v2: $i] : (v2 = v0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) =
% 212.34/30.38 v2)))
% 212.34/30.38
% 212.34/30.38 (fact_real__two__squares__add__zero__iff)
% 212.34/30.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.38 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 212.34/30.38 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.38 $i] : (v3 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7)
% 212.34/30.38 = v1) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0,
% 212.34/30.38 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 212.34/30.38 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 212.34/30.38 : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1)
% 212.34/30.38 | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) = v4)
% 212.34/30.38 | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3:
% 212.34/30.38 $i] : ! [v4: $i] : (v4 = v1 | ~
% 212.34/30.38 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~
% 212.34/30.38 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 212.34/30.38
% 212.34/30.38 (fact_real__zero__not__eq__one)
% 212.34/30.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 212.34/30.38 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 212.34/30.38
% 212.34/30.38 (fact_realpow__pos__nth)
% 212.34/30.38 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 212.34/30.38 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) &
% 212.34/30.38 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v5: $i] : ?
% 212.34/30.38 [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) &
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 212.34/30.38
% 212.34/30.38 (fact_realpow__pos__nth__unique)
% 212.34/30.38 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 212.34/30.38 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) &
% 212.34/30.38 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v5: $i] : ?
% 212.34/30.38 [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) &
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & ! [v7: $i] :
% 212.34/30.38 ! [v8: $i] : (v7 = v5 | ~ (hAPP(v8, v4) = v3) | ~ (hAPP(v2, v7) = v8)
% 212.34/30.38 | ~ $i(v7) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 212.34/30.38 v7)))))
% 212.34/30.38
% 212.34/30.38 (fact_reduce__poly__simple)
% 212.34/30.38 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i]
% 212.34/30.38 : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 212.34/30.38 (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v4 &
% 212.34/30.38 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v5 &
% 212.34/30.38 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 &
% 212.34/30.38 c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.38 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v5) & $i(v4) &
% 212.34/30.38 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 212.34/30.38 : (v7 = v0 | v6 = v1 | ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | ~ $i(v6) | ?
% 212.34/30.38 [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 212.34/30.38 [v14: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v12) =
% 212.34/30.38 v13 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v13) = v14 &
% 212.34/30.38 hAPP(v10, v6) = v11 & hAPP(v8, v11) = v12 & hAPP(v4, v9) = v10 & $i(v14)
% 212.34/30.38 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 212.34/30.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v5))))
% 212.34/30.38
% 212.34/30.38 (fact_rnc)
% 212.34/30.38 $i(v_q____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 212.34/30.38 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 212.34/30.38 (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2) = v3 &
% 212.34/30.38 c_Polynomial_Osmult(tc_Complex_Ocomplex, v3, v_q____) = v4 &
% 212.34/30.39 c_Polynomial_Opoly(tc_Complex_Ocomplex, v4) = v5 &
% 212.34/30.39 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.39 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v0, v1) = v2 &
% 212.34/30.39 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 212.34/30.39 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.34/30.39 tc_Complex_Ocomplex, v5))
% 212.34/30.39
% 212.34/30.39 (fact_split__div)
% 212.34/30.39 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 212.34/30.39 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 212.34/30.39 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 212.34/30.39 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 212.34/30.39 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5)
% 212.34/30.39 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ? [v7: $i] :
% 212.34/30.39 ? [v8: $i] : (( ~ (v2 = v0) | (hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7))) &
% 212.34/30.39 (v2 = v0 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : !
% 212.34/30.39 [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10)
% 212.34/30.39 = v3) | ~ (hAPP(v8, v9) = v11) | ~ $i(v10) | ~ $i(v9) | ~
% 212.34/30.39 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) | ? [v12: $i]
% 212.34/30.39 : (hAPP(v4, v9) = v12 & $i(v12) & hBOOL(v12))))))) & ! [v2: $i] :
% 212.34/30.39 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 212.34/30.39 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5)
% 212.34/30.39 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | hBOOL(v6) | ? [v7: $i] : ?
% 212.34/30.39 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 212.34/30.39 [v13: $i] : ($i(v10) & $i(v9) & ((v12 = v3 & ~ (v2 = v0) &
% 212.34/30.39 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) = v3 & hAPP(v8,
% 212.34/30.39 v9) = v11 & hAPP(v4, v9) = v13 & hAPP(v1, v2) = v8 & $i(v13) &
% 212.34/30.39 $i(v11) & $i(v8) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10,
% 212.34/30.39 v2) & ~ hBOOL(v13)) | (v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & ~
% 212.34/30.39 hBOOL(v7))))))
% 212.34/30.39
% 212.34/30.39 (fact_zero__le__one)
% 212.34/30.39 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 212.34/30.39 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 212.34/30.39 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) &
% 212.34/30.39 c_Orderings_Oord__class_Oless__eq(v0, v2, v1)))
% 212.34/30.39
% 212.34/30.39 (fact_zero__less__norm__iff)
% 212.34/30.39 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 212.34/30.39 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 212.34/30.39 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 212.34/30.39 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.39 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~
% 212.34/30.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ( ~ (v4 =
% 212.34/30.39 v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) &
% 212.34/30.39 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | (v4 = v1 &
% 212.34/30.39 c_Groups_Ozero__class_Ozero(v2) = v1)))))
% 212.34/30.39
% 212.34/30.39 (fact_zero__less__one)
% 212.34/30.39 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 212.34/30.39 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 212.34/30.39 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) &
% 212.34/30.39 c_Orderings_Oord__class_Oless(v0, v2, v1)))
% 212.34/30.39
% 212.34/30.39 (fact_zero__neq__one)
% 212.34/30.39 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 212.34/30.39 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) &
% 212.34/30.39 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2)))
% 212.34/30.39
% 212.34/30.39 (function-axioms)
% 212.34/30.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 212.34/30.39 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 212.34/30.39 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 212.34/30.39 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v1) | ~
% 212.34/30.39 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 212.34/30.39 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Polynomial_Omonom(v4, v3, v2) = v1) | ~ (c_Polynomial_Omonom(v4, v3, v2)
% 212.34/30.39 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 212.34/30.39 $i] : (v1 = v0 | ~ (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~
% 212.34/30.39 (c_Power_Opower_Opower(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 212.34/30.39 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~
% 212.34/30.39 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 212.34/30.39 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~ (c_Polynomial_Oorder(v4, v3, v2)
% 212.34/30.39 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 212.34/30.39 $i] : (v1 = v0 | ~ (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 212.34/30.39 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 212.34/30.39 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v1) | ~
% 212.34/30.39 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 212.34/30.39 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Polynomial_Osmult(v4, v3, v2) = v1) | ~ (c_Polynomial_Osmult(v4, v3, v2)
% 212.34/30.39 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 212.34/30.39 | ~ (c_Complex_Orcis(v3, v2) = v1) | ~ (c_Complex_Orcis(v3, v2) = v0)) &
% 212.34/30.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_RealDef_Oreal(v3, v2) = v1) | ~ (c_RealDef_Oreal(v3, v2) = v0)) & !
% 212.34/30.39 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3,
% 212.34/30.39 v2) = v1) | ~ (tc_fun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 212.34/30.39 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_RealVector_Onorm__class_Onorm(v3,
% 212.34/30.39 v2) = v1) | ~ (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) & ! [v0:
% 212.34/30.39 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v1) | ~
% 212.34/30.39 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v0)) & ! [v0:
% 212.34/30.39 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Rings_Oinverse__class_Oinverse(v3, v2) = v1) | ~
% 212.34/30.39 (c_Rings_Oinverse__class_Oinverse(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 212.34/30.39 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Polynomial_Opoly(v3, v2) = v1)
% 212.34/30.39 | ~ (c_Polynomial_Opoly(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 212.34/30.39 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2)
% 212.34/30.39 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Transcendental_Oln(v2) = v1) | ~ (c_Transcendental_Oln(v2) = v0)) & !
% 212.34/30.39 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Power_Opower__class_Opower(v2) = v1) | ~
% 212.34/30.39 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 212.34/30.39 [v2: $i] : (v1 = v0 | ~ (c_RComplete_Onatfloor(v2) = v1) | ~
% 212.34/30.39 (c_RComplete_Onatfloor(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 212.34/30.39 : (v1 = v0 | ~ (c_Complex_Oexpi(v2) = v1) | ~ (c_Complex_Oexpi(v2) = v0)) &
% 212.34/30.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_RComplete_Onatceiling(v2) = v1) | ~ (c_RComplete_Onatceiling(v2) = v0))
% 212.34/30.39 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.39 (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0)) & !
% 212.34/30.39 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Groups_Oone__class_Oone(v2) = v1) | ~ (c_Groups_Oone__class_Oone(v2) =
% 212.34/30.39 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.39 (c_Groups_Otimes__class_Otimes(v2) = v1) | ~
% 212.34/30.39 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 212.34/30.39 [v2: $i] : (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 212.34/30.39 (c_Groups_Ozero__class_Ozero(v2) = v0))
% 212.34/30.39
% 212.34/30.39 Further assumptions not needed in the proof:
% 212.34/30.39 --------------------------------------------
% 212.34/30.40 arity_Complex__Ocomplex__Fields_Ofield,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Oab__group__add,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Oab__semigroup__add,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Ogroup__add,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Omonoid__add,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Omonoid__mult,
% 212.34/30.40 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ozero,
% 212.34/30.40 arity_Complex__Ocomplex__Int_Oring__char__0,
% 212.34/30.40 arity_Complex__Ocomplex__Power_Opower,
% 212.34/30.40 arity_Complex__Ocomplex__RealVector_Oreal__field,
% 212.34/30.40 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
% 212.34/30.40 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
% 212.34/30.40 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
% 212.34/30.40 arity_Complex__Ocomplex__RealVector_Oreal__normed__field,
% 212.34/30.40 arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Ocomm__ring,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Ocomm__ring__1,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Ocomm__semiring,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Odvd, arity_Complex__Ocomplex__Rings_Omult__zero,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Osemiring,
% 212.34/30.40 arity_Complex__Ocomplex__Rings_Osemiring__0,
% 212.34/30.40 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 212.34/30.40 arity_HOL__Obool__Orderings_Oord, arity_HOL__Obool__Orderings_Oorder,
% 212.34/30.40 arity_HOL__Obool__Orderings_Opreorder, arity_Int__Oint__Divides_Oring__div,
% 212.34/30.40 arity_Int__Oint__Divides_Osemiring__div,
% 212.34/30.40 arity_Int__Oint__Groups_Oab__group__add,
% 212.34/30.40 arity_Int__Oint__Groups_Oab__semigroup__add,
% 212.34/30.40 arity_Int__Oint__Groups_Oab__semigroup__mult,
% 212.34/30.40 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,
% 212.34/30.40 arity_Int__Oint__Groups_Ocancel__comm__monoid__add,
% 212.34/30.40 arity_Int__Oint__Groups_Ocancel__semigroup__add,
% 212.34/30.40 arity_Int__Oint__Groups_Ocomm__monoid__add,
% 212.34/30.40 arity_Int__Oint__Groups_Ocomm__monoid__mult,
% 212.34/30.40 arity_Int__Oint__Groups_Ogroup__add,
% 212.34/30.40 arity_Int__Oint__Groups_Olinordered__ab__group__add,
% 212.34/30.40 arity_Int__Oint__Groups_Omonoid__add, arity_Int__Oint__Groups_Omonoid__mult,
% 212.34/30.40 arity_Int__Oint__Groups_Oone, arity_Int__Oint__Groups_Oordered__ab__group__add,
% 212.34/30.40 arity_Int__Oint__Groups_Oordered__ab__semigroup__add,
% 212.34/30.40 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,
% 212.34/30.40 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,
% 212.34/30.40 arity_Int__Oint__Groups_Oordered__comm__monoid__add,
% 212.34/30.40 arity_Int__Oint__Groups_Ozero, arity_Int__Oint__Int_Oring__char__0,
% 212.34/30.40 arity_Int__Oint__Orderings_Olinorder, arity_Int__Oint__Orderings_Oord,
% 212.34/30.40 arity_Int__Oint__Orderings_Oorder, arity_Int__Oint__Orderings_Opreorder,
% 212.34/30.40 arity_Int__Oint__Power_Opower, arity_Int__Oint__Rings_Ocomm__ring,
% 212.34/30.40 arity_Int__Oint__Rings_Ocomm__ring__1, arity_Int__Oint__Rings_Ocomm__semiring,
% 212.34/30.40 arity_Int__Oint__Rings_Ocomm__semiring__0,
% 212.34/30.40 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Odvd,
% 212.34/30.40 arity_Int__Oint__Rings_Oidom,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__idom,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__ring,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__ring__strict,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__semidom,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__semiring,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__semiring__1,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__semiring__1__strict,
% 212.34/30.40 arity_Int__Oint__Rings_Olinordered__semiring__strict,
% 212.34/30.40 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors,
% 212.34/30.40 arity_Int__Oint__Rings_Oordered__cancel__semiring,
% 212.34/30.40 arity_Int__Oint__Rings_Oordered__comm__semiring,
% 212.34/30.40 arity_Int__Oint__Rings_Oordered__ring,
% 212.34/30.40 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring,
% 212.34/30.40 arity_Int__Oint__Rings_Oring__1,
% 212.34/30.40 arity_Int__Oint__Rings_Oring__1__no__zero__divisors,
% 212.34/30.40 arity_Int__Oint__Rings_Oring__no__zero__divisors,
% 212.34/30.40 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0,
% 212.34/30.40 arity_Int__Oint__Rings_Ozero__neq__one,
% 212.34/30.40 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 212.34/30.40 arity_Nat__Onat__Divides_Osemiring__div,
% 212.34/30.40 arity_Nat__Onat__Groups_Oab__semigroup__add,
% 212.34/30.40 arity_Nat__Onat__Groups_Oab__semigroup__mult,
% 212.34/30.40 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,
% 212.34/30.40 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,
% 212.34/30.40 arity_Nat__Onat__Groups_Ocancel__semigroup__add,
% 212.34/30.40 arity_Nat__Onat__Groups_Ocomm__monoid__add,
% 212.34/30.40 arity_Nat__Onat__Groups_Ocomm__monoid__mult,
% 212.34/30.40 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult,
% 212.34/30.40 arity_Nat__Onat__Groups_Oone,
% 212.34/30.40 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,
% 212.34/30.40 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,
% 212.34/30.40 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,
% 212.34/30.40 arity_Nat__Onat__Groups_Oordered__comm__monoid__add,
% 212.34/30.40 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Orderings_Olinorder,
% 212.34/30.40 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder,
% 212.34/30.40 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Power_Opower,
% 212.34/30.40 arity_Nat__Onat__Rings_Ocomm__semiring,
% 212.34/30.40 arity_Nat__Onat__Rings_Ocomm__semiring__0,
% 212.34/30.40 arity_Nat__Onat__Rings_Ocomm__semiring__1, arity_Nat__Onat__Rings_Odvd,
% 212.34/30.40 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,
% 212.34/30.40 arity_Nat__Onat__Rings_Olinordered__semidom,
% 212.34/30.40 arity_Nat__Onat__Rings_Olinordered__semiring,
% 212.34/30.40 arity_Nat__Onat__Rings_Olinordered__semiring__strict,
% 212.34/30.40 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors,
% 212.34/30.40 arity_Nat__Onat__Rings_Oordered__cancel__semiring,
% 212.34/30.40 arity_Nat__Onat__Rings_Oordered__comm__semiring,
% 212.34/30.40 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring,
% 212.34/30.40 arity_Nat__Onat__Rings_Osemiring__0, arity_Nat__Onat__Rings_Ozero__neq__one,
% 212.34/30.40 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 212.34/30.40 arity_Polynomial__Opoly__Divides_Oring__div,
% 212.34/30.40 arity_Polynomial__Opoly__Divides_Osemiring__div,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oab__group__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oab__semigroup__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Ogroup__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Omonoid__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Omonoid__mult,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oone,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,
% 212.34/30.40 arity_Polynomial__Opoly__Groups_Ozero,
% 212.34/30.40 arity_Polynomial__Opoly__Int_Oring__char__0,
% 212.34/30.40 arity_Polynomial__Opoly__Orderings_Olinorder,
% 212.34/30.40 arity_Polynomial__Opoly__Orderings_Oord,
% 212.34/30.40 arity_Polynomial__Opoly__Orderings_Oorder,
% 212.34/30.40 arity_Polynomial__Opoly__Orderings_Opreorder,
% 212.34/30.40 arity_Polynomial__Opoly__Power_Opower,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Ocomm__ring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Ocomm__ring__1,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Ocomm__semiring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Oidom,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__idom,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__ring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__semidom,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__semiring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Omult__zero,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Ono__zero__divisors,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Oordered__ring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Oordered__semiring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Osemiring,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Osemiring__0,
% 212.34/30.40 arity_Polynomial__Opoly__Rings_Ozero__neq__one,
% 212.34/30.40 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 212.34/30.40 arity_RealDef__Oreal__Fields_Ofield,
% 212.34/30.40 arity_RealDef__Oreal__Fields_Ofield__inverse__zero,
% 212.34/30.40 arity_RealDef__Oreal__Fields_Olinordered__field,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Oab__group__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Oab__semigroup__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Oab__semigroup__mult,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Ocomm__monoid__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Ogroup__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Omonoid__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Omonoid__mult, arity_RealDef__Oreal__Groups_Oone,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Oordered__ab__group__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,
% 212.34/30.40 arity_RealDef__Oreal__Groups_Ozero, arity_RealDef__Oreal__Int_Oring__char__0,
% 212.34/30.40 arity_RealDef__Oreal__Orderings_Olinorder, arity_RealDef__Oreal__Orderings_Oord,
% 212.34/30.40 arity_RealDef__Oreal__Orderings_Oorder,
% 212.34/30.40 arity_RealDef__Oreal__Orderings_Opreorder, arity_RealDef__Oreal__Power_Opower,
% 212.34/30.40 arity_RealDef__Oreal__RealVector_Oreal__field,
% 212.34/30.40 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
% 212.34/30.40 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
% 212.34/30.40 arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,
% 212.34/30.40 arity_RealDef__Oreal__RealVector_Oreal__normed__field,
% 212.34/30.40 arity_RealDef__Oreal__RealVector_Oreal__normed__vector,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Ocomm__ring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Ocomm__ring__1,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Ocomm__semiring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Ocomm__semiring__0,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Ocomm__semiring__1,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Odivision__ring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Odvd, arity_RealDef__Oreal__Rings_Oidom,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Olinordered__idom,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Olinordered__ring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Olinordered__ring__strict,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Olinordered__semiring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Olinordered__semiring__1,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Omult__zero,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Ono__zero__divisors,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Oordered__comm__semiring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Oordered__ring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Oordered__semiring,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Oring, arity_RealDef__Oreal__Rings_Oring__1,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Osemiring, arity_RealDef__Oreal__Rings_Osemiring__0,
% 212.34/30.40 arity_RealDef__Oreal__Rings_Ozero__neq__one,
% 212.34/30.40 arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 212.34/30.40 arity_fun__Orderings_Oord, arity_fun__Orderings_Oorder,
% 212.34/30.40 arity_fun__Orderings_Opreorder, fact_BseqI2_H, fact_DERIV__mult__lemma,
% 212.34/30.40 fact_DIVISION__BY__ZERO, fact_DeMoivre2,
% 212.34/30.40 fact_Divides_Otransfer__nat__int__function__closures_I1_J,
% 212.34/30.40 fact_Divides_Otransfer__nat__int__function__closures_I2_J,
% 212.34/30.40 fact_Nat_Oadd__0__right,
% 212.34/30.40 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,
% 212.34/30.40 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,
% 212.34/30.40 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,
% 212.34/30.40 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,
% 212.34/30.40 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,
% 212.34/30.40 fact_ab__semigroup__add__class_Oadd__ac_I1_J,
% 212.34/30.40 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_add1__zle__eq,
% 212.34/30.40 fact_add_Ocomm__neutral, fact_add__0, fact_add__0__iff, fact_add__0__left,
% 212.34/30.40 fact_add__0__right, fact_add__diff__cancel, fact_add__divide__distrib,
% 212.34/30.40 fact_add__divide__eq__iff, fact_add__eq__self__zero, fact_add__frac__eq,
% 212.34/30.40 fact_add__frac__num, fact_add__gr__0, fact_add__imp__eq, fact_add__increasing,
% 212.34/30.40 fact_add__increasing2, fact_add__is__0, fact_add__leD1, fact_add__leD2,
% 212.34/30.40 fact_add__leE, fact_add__le__cancel__left, fact_add__le__cancel__right,
% 212.34/30.40 fact_add__le__imp__le__left, fact_add__le__imp__le__right,
% 212.34/30.40 fact_add__le__less__mono, fact_add__le__mono, fact_add__le__mono1,
% 212.34/30.40 fact_add__left__cancel, fact_add__left__imp__eq, fact_add__left__mono,
% 212.34/30.40 fact_add__lessD1, fact_add__less__cancel__left, fact_add__less__cancel__right,
% 212.34/30.40 fact_add__less__imp__less__left, fact_add__less__imp__less__right,
% 212.34/30.40 fact_add__less__le__mono, fact_add__less__mono, fact_add__less__mono1,
% 212.34/30.40 fact_add__mono, fact_add__monom, fact_add__mult__distrib,
% 212.34/30.40 fact_add__mult__distrib2, fact_add__neg__neg, fact_add__neg__nonpos,
% 212.34/30.40 fact_add__nonneg__eq__0__iff, fact_add__nonneg__nonneg, fact_add__nonneg__pos,
% 212.34/30.40 fact_add__nonpos__neg, fact_add__nonpos__nonpos, fact_add__num__frac,
% 212.34/30.40 fact_add__poly__code_I1_J, fact_add__poly__code_I2_J, fact_add__pos__nonneg,
% 212.34/30.40 fact_add__pos__pos, fact_add__right__cancel, fact_add__right__imp__eq,
% 212.34/30.40 fact_add__right__mono, fact_add__scale__eq__noteq, fact_add__strict__increasing,
% 212.34/30.40 fact_add__strict__increasing2, fact_add__strict__left__mono,
% 212.34/30.40 fact_add__strict__mono, fact_add__strict__right__mono, fact_assms,
% 212.34/30.40 fact_combine__common__factor, fact_comm__mult__left__mono,
% 212.34/30.40 fact_comm__mult__strict__left__mono,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,
% 212.34/30.40 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,
% 212.34/30.40 fact_comm__semiring__class_Odistrib, fact_complex__mod__triangle__ineq2,
% 212.34/30.40 fact_complex__mod__triangle__sub, fact_constant__def, fact_convex__bound__le,
% 212.34/30.40 fact_convex__bound__lt, fact_crossproduct__eq, fact_crossproduct__noteq,
% 212.34/30.40 fact_decseq__def, fact_diff__0__right, fact_diff__add__assoc2,
% 212.34/30.40 fact_diff__add__cancel, fact_diff__divide__distrib, fact_diff__divide__eq__iff,
% 212.34/30.40 fact_diff__eq__diff__eq, fact_diff__eq__diff__less,
% 212.34/30.40 fact_diff__eq__diff__less__eq, fact_diff__frac__eq, fact_diff__monom,
% 212.34/30.40 fact_diff__mult__distrib, fact_diff__mult__distrib2, fact_diff__self,
% 212.34/30.40 fact_div__0, fact_div__add, fact_div__add1__eq, fact_div__add__self1,
% 212.34/30.40 fact_div__add__self2, fact_div__by__0, fact_div__by__1, fact_div__dvd__div,
% 212.34/30.40 fact_div__le__dividend, fact_div__le__mono, fact_div__le__mono2, fact_div__less,
% 212.34/30.40 fact_div__mod__equality, fact_div__mod__equality2, fact_div__mult1__eq,
% 212.34/30.40 fact_div__mult2__eq, fact_div__mult__div__if__dvd, fact_div__mult__mult1,
% 212.34/30.40 fact_div__mult__mult1__if, fact_div__mult__mult2, fact_div__mult__self1,
% 212.34/30.40 fact_div__mult__self1__is__id, fact_div__mult__self1__is__m,
% 212.34/30.40 fact_div__mult__self2, fact_div__mult__self2__is__id,
% 212.34/30.40 fact_div__mult__self__is__m, fact_div__mult__swap, fact_div__neg__neg__trivial,
% 212.34/30.40 fact_div__neg__pos__less0, fact_div__nonneg__neg__le0,
% 212.34/30.40 fact_div__nonpos__pos__le0, fact_div__pos__pos__trivial, fact_div__power,
% 212.34/30.40 fact_div__self, fact_div__smult__left, fact_div__smult__right, fact_divide_Oadd,
% 212.34/30.40 fact_divide_Odiff, fact_divide_Ozero, fact_divide__1, fact_divide__add__eq__iff,
% 212.34/30.40 fact_divide__diff__eq__iff, fact_divide__eq__imp, fact_divide__inverse,
% 212.34/30.40 fact_divide__le__0__iff, fact_divide__le__eq, fact_divide__left__mono,
% 212.34/30.40 fact_divide__left__mono__neg, fact_divide__less__0__iff, fact_divide__less__eq,
% 212.34/30.40 fact_divide__neg__neg, fact_divide__neg__pos, fact_divide__nonneg__neg,
% 212.34/30.40 fact_divide__nonneg__pos, fact_divide__nonpos__neg, fact_divide__nonpos__pos,
% 212.34/30.40 fact_divide__pos__neg, fact_divide__pos__pos, fact_divide__real__def,
% 212.34/30.40 fact_divide__right__mono, fact_divide__right__mono__neg, fact_divide__self,
% 212.34/30.40 fact_divide__self__if, fact_divide__strict__left__mono,
% 212.34/30.40 fact_divide__strict__left__mono__neg, fact_divide__strict__right__mono,
% 212.34/30.40 fact_divide__strict__right__mono__neg, fact_divide__zero,
% 212.34/30.40 fact_divide__zero__left, fact_division__ring__inverse__add,
% 212.34/30.40 fact_division__ring__inverse__diff, fact_divmod__int__rel__div__eq,
% 212.34/30.40 fact_divmod__int__rel__mod__eq,
% 212.34/30.40 fact_double__add__le__zero__iff__single__add__le__zero,
% 212.34/30.40 fact_double__add__less__zero__iff__single__add__less__zero,
% 212.34/30.40 fact_double__eq__0__iff, fact_double__zero__sym, fact_dvdI, fact_dvd_Oantisym,
% 212.34/30.40 fact_dvd_Oantisym__conv, fact_dvd_Oeq__iff, fact_dvd_Oeq__refl,
% 212.34/30.40 fact_dvd_Ole__imp__less__or__eq, fact_dvd_Ole__less, fact_dvd_Ole__less__trans,
% 212.34/30.40 fact_dvd_Ole__neq__trans, fact_dvd_Oless__asym, fact_dvd_Oless__asym_H,
% 212.34/30.40 fact_dvd_Oless__imp__le, fact_dvd_Oless__imp__neq, fact_dvd_Oless__imp__not__eq,
% 212.34/30.40 fact_dvd_Oless__imp__not__eq2, fact_dvd_Oless__imp__not__less,
% 212.34/30.40 fact_dvd_Oless__le, fact_dvd_Oless__le__trans, fact_dvd_Oless__not__sym,
% 212.34/30.40 fact_dvd_Oless__trans, fact_dvd_Oneq__le__trans, fact_dvd_Oord__eq__le__trans,
% 212.34/30.40 fact_dvd_Oord__eq__less__trans, fact_dvd_Oord__le__eq__trans,
% 212.34/30.40 fact_dvd_Oord__less__eq__trans, fact_dvd_Oorder__refl, fact_dvd_Oorder__trans,
% 212.34/30.40 fact_dvd__0__left, fact_dvd__0__right, fact_dvd__add, fact_dvd__antisym,
% 212.34/30.40 fact_dvd__diff, fact_dvd__diff__nat, fact_dvd__div__div__eq__mult,
% 212.34/30.40 fact_dvd__div__eq__mult, fact_dvd__div__mult, fact_dvd__div__mult__self,
% 212.34/30.40 fact_dvd__eq__mod__eq__0, fact_dvd__imp__le, fact_dvd__imp__mod__0,
% 212.34/30.40 fact_dvd__mod, fact_dvd__mod__iff, fact_dvd__mod__imp__dvd, fact_dvd__mult,
% 212.34/30.40 fact_dvd__mult2, fact_dvd__mult__cancel, fact_dvd__mult__cancel__left,
% 212.34/30.40 fact_dvd__mult__cancel__right, fact_dvd__mult__div__cancel,
% 212.34/30.40 fact_dvd__mult__left, fact_dvd__mult__right, fact_dvd__power,
% 212.34/30.40 fact_dvd__power__le, fact_dvd__power__same, fact_dvd__reduce, fact_dvd__refl,
% 212.34/30.40 fact_dvd__smult, fact_dvd__trans, fact_dvd__triv__left, fact_dvd__triv__right,
% 212.34/30.40 fact_eq__add__iff1, fact_eq__add__iff2, fact_eq__divide__eq,
% 212.34/30.40 fact_eq__divide__imp, fact_eq__iff__diff__eq__0, fact_eq__imp__le,
% 212.34/30.40 fact_even__less__0__iff, fact_ext,
% 212.34/30.40 fact_field__class_Onormalizing__field__rules_I2_J, fact_field__divide__inverse,
% 212.34/30.40 fact_field__inverse, fact_field__inverse__zero,
% 212.34/30.40 fact_field__le__mult__one__interval, fact_field__power__not__zero,
% 212.34/30.40 fact_frac__eq__eq, fact_frac__le, fact_frac__less, fact_frac__less2, fact_gr0I,
% 212.34/30.40 fact_gt__half__sum, fact_incseq__def, fact_inf__period_I4_J,
% 212.34/30.40 fact_int__0__less__1, fact_int__0__neq__1, fact_int__div__less__self,
% 212.34/30.40 fact_int__one__le__iff__zero__less, fact_inverse__1, fact_inverse__add,
% 212.34/30.40 fact_inverse__divide, fact_inverse__eq__1__iff, fact_inverse__eq__divide,
% 212.34/30.40 fact_inverse__eq__iff__eq, fact_inverse__eq__imp__eq, fact_inverse__inverse__eq,
% 212.34/30.40 fact_inverse__le__imp__le, fact_inverse__le__imp__le__neg,
% 212.34/30.40 fact_inverse__less__imp__less, fact_inverse__less__imp__less__neg,
% 212.34/30.40 fact_inverse__mult__distrib, fact_inverse__negative__iff__negative,
% 212.34/30.40 fact_inverse__negative__imp__negative,
% 212.34/30.40 fact_inverse__nonnegative__iff__nonnegative,
% 212.34/30.40 fact_inverse__nonpositive__iff__nonpositive,
% 212.34/30.40 fact_inverse__positive__iff__positive, fact_inverse__positive__imp__positive,
% 212.34/30.40 fact_inverse__unique, fact_inverse__zero, fact_le0, fact_leD, fact_leI,
% 212.34/30.40 fact_le__0__eq, fact_le__Suc__ex__iff, fact_le__add1, fact_le__add2,
% 212.34/30.40 fact_le__add__iff1, fact_le__add__iff2, fact_le__antisym, fact_le__cube,
% 212.34/30.40 fact_le__divide__eq, fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE,
% 212.34/30.40 fact_le__fun__def, fact_le__iff__add, fact_le__iff__diff__le__0,
% 212.34/30.40 fact_le__imp__0__less, fact_le__imp__inverse__le,
% 212.34/30.40 fact_le__imp__inverse__le__neg, fact_le__imp__power__dvd, fact_le__mod__geq,
% 212.34/30.40 fact_le__natfloor, fact_le__neq__implies__less, fact_le__refl, fact_le__square,
% 212.34/30.40 fact_le__trans, fact_left__add__mult__distrib, fact_left__inverse,
% 212.34/30.40 fact_less__1__mult, fact_less__add__eq__less, fact_less__add__iff1,
% 212.34/30.40 fact_less__add__iff2, fact_less__add__one, fact_less__divide__eq,
% 212.34/30.40 fact_less__eq__nat_Osimps_I1_J, fact_less__eq__real__def, fact_less__fun__def,
% 212.34/30.40 fact_less__half__sum, fact_less__iff__diff__less__0,
% 212.34/30.40 fact_less__imp__inverse__less, fact_less__imp__inverse__less__neg,
% 212.34/30.40 fact_less__imp__le__nat, fact_less__imp__neq, fact_less__irrefl__nat,
% 212.34/30.40 fact_less__le__not__le, fact_less__not__refl, fact_less__not__refl2,
% 212.34/30.40 fact_less__not__refl3, fact_less__or__eq__imp__le,
% 212.34/30.40 fact_linorder__antisym__conv1, fact_linorder__antisym__conv2,
% 212.34/30.40 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases,
% 212.34/30.40 fact_linorder__le__less__linear, fact_linorder__less__linear,
% 212.34/30.40 fact_linorder__linear, fact_linorder__neqE,
% 212.34/30.40 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat,
% 212.34/30.40 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less,
% 212.34/30.40 fact_mod__0, fact_mod__add__cong, fact_mod__add__eq, fact_mod__add__left__eq,
% 212.34/30.40 fact_mod__add__right__eq, fact_mod__add__self1, fact_mod__add__self2,
% 212.34/30.40 fact_mod__by__0, fact_mod__by__1, fact_mod__diff__cong, fact_mod__diff__eq,
% 212.34/30.40 fact_mod__diff__left__eq, fact_mod__diff__right__eq, fact_mod__div__equality,
% 212.34/30.40 fact_mod__div__equality2, fact_mod__div__trivial, fact_mod__eq__0__iff,
% 212.34/30.40 fact_mod__geq, fact_mod__if, fact_mod__le__divisor, fact_mod__lemma,
% 212.34/30.40 fact_mod__less, fact_mod__less__divisor, fact_mod__less__eq__dividend,
% 212.34/30.40 fact_mod__mod__cancel, fact_mod__mod__trivial, fact_mod__mult2__eq,
% 212.34/30.40 fact_mod__mult__cong, fact_mod__mult__distrib, fact_mod__mult__distrib2,
% 212.34/30.40 fact_mod__mult__eq, fact_mod__mult__left__eq, fact_mod__mult__mult1,
% 212.34/30.40 fact_mod__mult__mult2, fact_mod__mult__right__eq, fact_mod__mult__self1,
% 212.34/30.40 fact_mod__mult__self1__is__0, fact_mod__mult__self2,
% 212.34/30.40 fact_mod__mult__self2__is__0, fact_mod__mult__self3,
% 212.34/30.40 fact_mod__neg__neg__trivial, fact_mod__pos__neg__trivial,
% 212.34/30.40 fact_mod__pos__pos__trivial, fact_mod__self, fact_mod__smult__left,
% 212.34/30.40 fact_mod__smult__right, fact_monom__eq__0, fact_monom__eq__0__iff,
% 212.34/30.40 fact_monom__eq__iff, fact_mult_Oadd__left, fact_mult_Oadd__right,
% 212.34/30.40 fact_mult_Ocomm__neutral, fact_mult_Odiff__left, fact_mult_Odiff__right,
% 212.34/30.40 fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, fact_mult_Ozero__right,
% 212.34/30.40 fact_mult__0, fact_mult__0__right, fact_mult__1, fact_mult__1__left,
% 212.34/30.40 fact_mult__1__right, fact_mult__cancel1, fact_mult__cancel2,
% 212.34/30.40 fact_mult__diff__mult, fact_mult__divide__mult__cancel__left,
% 212.34/30.40 fact_mult__divide__mult__cancel__right, fact_mult__dvd__mono,
% 212.34/30.40 fact_mult__imp__div__pos__le, fact_mult__imp__div__pos__less,
% 212.34/30.40 fact_mult__imp__le__div__pos, fact_mult__imp__less__div__pos, fact_mult__is__0,
% 212.34/30.40 fact_mult__le__0__iff, fact_mult__le__cancel1, fact_mult__le__cancel2,
% 212.34/30.40 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos,
% 212.34/30.40 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1,
% 212.34/30.40 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Odiff,
% 212.34/30.40 fact_mult__left_Ozero, fact_mult__left__le__imp__le,
% 212.34/30.40 fact_mult__left__le__one__le, fact_mult__left__less__imp__less,
% 212.34/30.40 fact_mult__left__mono, fact_mult__left__mono__neg, fact_mult__less__cancel1,
% 212.34/30.40 fact_mult__less__cancel__left__disj, fact_mult__less__cancel__left__neg,
% 212.34/30.40 fact_mult__less__cancel__left__pos, fact_mult__less__cancel__right__disj,
% 212.34/30.40 fact_mult__less__imp__less__left, fact_mult__less__imp__less__right,
% 212.34/30.40 fact_mult__less__le__imp__less, fact_mult__less__mono1, fact_mult__less__mono2,
% 212.34/30.40 fact_mult__mono, fact_mult__mono_H, fact_mult__monom, fact_mult__neg__neg,
% 212.34/30.40 fact_mult__neg__pos, fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos,
% 212.34/30.40 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg,
% 212.34/30.40 fact_mult__nonpos__nonpos, fact_mult__poly__0__left, fact_mult__poly__0__right,
% 212.34/30.40 fact_mult__poly__add__left, fact_mult__pos__neg, fact_mult__pos__neg2,
% 212.34/30.40 fact_mult__pos__pos, fact_mult__right_Oadd, fact_mult__right_Odiff,
% 212.34/30.40 fact_mult__right_Ozero, fact_mult__right__le__imp__le,
% 212.34/30.40 fact_mult__right__le__one__le, fact_mult__right__less__imp__less,
% 212.34/30.40 fact_mult__right__mono, fact_mult__right__mono__neg, fact_mult__smult__left,
% 212.34/30.40 fact_mult__smult__right, fact_mult__strict__left__mono,
% 212.34/30.40 fact_mult__strict__left__mono__neg, fact_mult__strict__mono,
% 212.34/30.40 fact_mult__strict__mono_H, fact_mult__strict__right__mono,
% 212.34/30.40 fact_mult__strict__right__mono__neg, fact_mult__zero__left,
% 212.34/30.40 fact_mult__zero__right, fact_nat__0__less__mult__iff, fact_nat__add__assoc,
% 212.34/30.40 fact_nat__add__commute, fact_nat__add__left__cancel,
% 212.34/30.40 fact_nat__add__left__cancel__le, fact_nat__add__left__cancel__less,
% 212.34/30.40 fact_nat__add__left__commute, fact_nat__add__right__cancel,
% 212.34/30.40 fact_nat__dvd__not__less, fact_nat__le__linear, fact_nat__less__cases,
% 212.34/30.40 fact_nat__less__le, fact_nat__mult__assoc, fact_nat__mult__commute,
% 212.34/30.40 fact_nat__mult__div__cancel1, fact_nat__mult__div__cancel__disj,
% 212.34/30.40 fact_nat__mult__dvd__cancel1, fact_nat__mult__dvd__cancel__disj,
% 212.34/30.40 fact_nat__mult__eq__cancel1, fact_nat__mult__eq__cancel__disj,
% 212.34/30.40 fact_nat__mult__le__cancel1, fact_nat__mult__less__cancel1, fact_nat__neq__iff,
% 212.34/30.40 fact_nat__power__less__imp__less, fact_nat__zero__less__power__iff,
% 212.34/30.40 fact_natceiling__le, fact_natceiling__mono, fact_natceiling__real__of__nat,
% 212.34/30.40 fact_natfloor__mono, fact_natfloor__power, fact_natfloor__real__of__nat,
% 212.34/30.40 fact_neg__divide__le__eq, fact_neg__divide__less__eq,
% 212.34/30.40 fact_neg__imp__zdiv__neg__iff, fact_neg__imp__zdiv__nonneg__iff,
% 212.34/30.40 fact_neg__le__divide__eq, fact_neg__less__divide__eq, fact_neg__mod__bound,
% 212.34/30.40 fact_neg__mod__conj, fact_neg__mod__sign, fact_negative__imp__inverse__negative,
% 212.34/30.40 fact_neq0__conv, fact_nonneg1__imp__zdiv__pos__iff,
% 212.34/30.40 fact_nonzero__divide__eq__eq, fact_nonzero__eq__divide__eq,
% 212.34/30.40 fact_nonzero__inverse__eq__divide, fact_nonzero__inverse__eq__imp__eq,
% 212.34/30.40 fact_nonzero__inverse__inverse__eq, fact_nonzero__inverse__mult__distrib,
% 212.34/30.40 fact_nonzero__norm__divide, fact_nonzero__norm__inverse,
% 212.34/30.40 fact_nonzero__power__divide, fact_nonzero__power__inverse, fact_norm__add__less,
% 212.34/30.40 fact_norm__diff__ineq, fact_norm__diff__triangle__ineq, fact_norm__divide,
% 212.34/30.40 fact_norm__inverse, fact_norm__minus__commute, fact_norm__mult,
% 212.34/30.40 fact_norm__mult__ineq, fact_norm__mult__less, fact_norm__power,
% 212.34/30.40 fact_norm__power__ineq, fact_norm__triangle__ineq, fact_norm__triangle__ineq2,
% 212.34/30.40 fact_norm__triangle__ineq4, fact_not__add__less1, fact_not__add__less2,
% 212.34/30.40 fact_not__leE, fact_not__less__iff__gr__or__eq, fact_not__square__less__zero,
% 212.34/30.40 fact_not__sum__squares__lt__zero, fact_odd__less__0, fact_odd__nonzero,
% 212.34/30.40 fact_one__dvd, fact_one__le__inverse, fact_one__le__power,
% 212.34/30.40 fact_one__less__inverse, fact_one__less__power, fact_one__reorient,
% 212.34/30.40 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans,
% 212.34/30.40 fact_ord__less__eq__trans, fact_order__antisym, fact_order__antisym__conv,
% 212.34/30.40 fact_order__eq__iff, fact_order__eq__refl, fact_order__le__imp__less__or__eq,
% 212.34/30.40 fact_order__le__less, fact_order__le__less__trans, fact_order__le__neq__trans,
% 212.34/30.40 fact_order__less__asym, fact_order__less__asym_H, fact_order__less__imp__le,
% 212.34/30.40 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2,
% 212.34/30.40 fact_order__less__imp__not__less, fact_order__less__irrefl,
% 212.34/30.40 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym,
% 212.34/30.40 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl,
% 212.34/30.40 fact_order__trans, fact_plus__nat_Oadd__0, fact_poly__0, fact_poly__1,
% 212.34/30.40 fact_poly__add, fact_poly__diff, fact_poly__div__mult__right,
% 212.34/30.40 fact_poly__eq__iff, fact_poly__mod__mult__right, fact_poly__monom,
% 212.34/30.40 fact_poly__mult, fact_poly__power, fact_poly__replicate__append,
% 212.34/30.40 fact_poly__smult, fact_poly__zero, fact_pos__add__strict,
% 212.34/30.40 fact_pos__divide__le__eq, fact_pos__divide__less__eq,
% 212.34/30.40 fact_pos__imp__zdiv__neg__iff, fact_pos__imp__zdiv__nonneg__iff,
% 212.34/30.40 fact_pos__imp__zdiv__pos__iff, fact_pos__le__divide__eq,
% 212.34/30.40 fact_pos__less__divide__eq, fact_pos__mod__bound, fact_pos__mod__conj,
% 212.34/30.40 fact_pos__mod__sign, fact_pos__zmult__eq__1__iff,
% 212.34/30.40 fact_positive__imp__inverse__positive, fact_power_Opower_Opower__0,
% 212.34/30.40 fact_power__0, fact_power__0__left, fact_power__Suc__less, fact_power__add,
% 212.34/30.40 fact_power__commutes, fact_power__decreasing, fact_power__divide,
% 212.34/30.40 fact_power__eq__0__iff, fact_power__eq__imp__eq__base, fact_power__gt1__lemma,
% 212.34/30.40 fact_power__increasing, fact_power__increasing__iff, fact_power__inject__exp,
% 212.34/30.40 fact_power__inverse, fact_power__le__dvd, fact_power__le__imp__le__exp,
% 212.34/30.40 fact_power__less__imp__less__base, fact_power__less__imp__less__exp,
% 212.34/30.40 fact_power__less__power__Suc, fact_power__mono, fact_power__mult,
% 212.34/30.40 fact_power__mult__distrib, fact_power__one, fact_power__one__over,
% 212.34/30.40 fact_power__power__power, fact_power__real__of__nat,
% 212.34/30.40 fact_power__strict__decreasing, fact_power__strict__increasing,
% 212.34/30.40 fact_power__strict__increasing__iff, fact_power__strict__mono,
% 212.34/30.40 fact_psize__eq__0__iff, fact_q_I1_J, fact_q__neg__lemma, fact_q__pos__lemma,
% 212.34/30.40 fact_rcis__divide, fact_real__add__left__mono, fact_real__add__mult__distrib,
% 212.34/30.40 fact_real__divide__def, fact_real__divide__square__eq, fact_real__le__antisym,
% 212.34/30.40 fact_real__le__linear, fact_real__le__refl, fact_real__le__trans,
% 212.34/30.40 fact_real__less__def, fact_real__mult__assoc, fact_real__mult__commute,
% 212.34/30.40 fact_real__natceiling__ge, fact_real__of__nat__add, fact_real__of__nat__div,
% 212.34/30.40 fact_real__of__nat__div4, fact_real__of__nat__div__aux,
% 212.34/30.40 fact_real__of__nat__inject, fact_real__of__nat__le__iff,
% 212.34/30.40 fact_real__of__nat__less__iff, fact_real__of__nat__mult,
% 212.34/30.40 fact_real__of__nat__power, fact_real__squared__diff__one__factored,
% 212.34/30.40 fact_right__inverse, fact_right__inverse__eq, fact_right__minus__eq,
% 212.34/30.40 fact_self__quotient__aux1, fact_self__quotient__aux2,
% 212.34/30.40 fact_semiring__div__class_Omod__div__equality_H, fact_smult__0__left,
% 212.34/30.40 fact_smult__0__right, fact_smult__1__left, fact_smult__add__left,
% 212.34/30.40 fact_smult__add__right, fact_smult__diff__left, fact_smult__diff__right,
% 212.34/30.40 fact_smult__dvd__cancel, fact_smult__eq__0__iff, fact_smult__monom,
% 212.34/30.40 fact_smult__smult, fact_split__mod, fact_split__mult__neg__le,
% 212.34/30.40 fact_split__mult__pos__le, fact_split__neg__lemma, fact_split__pos__lemma,
% 212.34/30.40 fact_split__zdiv, fact_split__zmod, fact_sum__squares__eq__zero__iff,
% 212.34/30.40 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff,
% 212.34/30.40 fact_sum__squares__le__zero__iff, fact_termination__basic__simps_I1_J,
% 212.34/30.40 fact_termination__basic__simps_I2_J, fact_termination__basic__simps_I3_J,
% 212.34/30.40 fact_termination__basic__simps_I4_J, fact_termination__basic__simps_I5_J,
% 212.34/30.40 fact_times__divide__eq__right, fact_times__divide__times__eq,
% 212.34/30.40 fact_trans__le__add1, fact_trans__le__add2, fact_trans__less__add1,
% 212.34/30.40 fact_trans__less__add2, fact_unique__quotient__lemma,
% 212.34/30.40 fact_unique__quotient__lemma__neg, fact_xt1_I10_J, fact_xt1_I11_J,
% 212.34/30.40 fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J,
% 212.34/30.40 fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J,
% 212.34/30.40 fact_zadd__0, fact_zadd__0__right, fact_zadd__assoc, fact_zadd__commute,
% 212.34/30.40 fact_zadd__left__commute, fact_zadd__left__mono, fact_zadd__strict__right__mono,
% 212.34/30.40 fact_zadd__zless__mono, fact_zadd__zmult__distrib, fact_zadd__zmult__distrib2,
% 212.34/30.40 fact_zdiff__zmod__left, fact_zdiff__zmod__right, fact_zdiff__zmult__distrib,
% 212.34/30.40 fact_zdiff__zmult__distrib2, fact_zdiv__eq__0__iff, fact_zdiv__mono1,
% 212.34/30.40 fact_zdiv__mono1__neg, fact_zdiv__mono2, fact_zdiv__mono2__lemma,
% 212.34/30.40 fact_zdiv__mono2__neg, fact_zdiv__mono2__neg__lemma, fact_zdiv__self,
% 212.34/30.40 fact_zdiv__zadd1__eq, fact_zdiv__zero, fact_zdiv__zmod__equality,
% 212.34/30.40 fact_zdiv__zmod__equality2, fact_zdiv__zmult1__eq, fact_zdiv__zmult2__eq,
% 212.34/30.40 fact_zdvd__zmod, fact_zdvd__zmod__imp__zdvd, fact_zero__le__divide__iff,
% 212.34/30.40 fact_zero__le__double__add__iff__zero__le__single__add,
% 212.34/30.40 fact_zero__le__mult__iff, fact_zero__le__natceiling, fact_zero__le__natfloor,
% 212.34/30.40 fact_zero__le__power, fact_zero__le__square, fact_zero__less__divide__iff,
% 212.34/30.40 fact_zero__less__double__add__iff__zero__less__single__add,
% 212.34/30.40 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, fact_zero__less__power,
% 212.34/30.40 fact_zero__less__power__nat__eq, fact_zero__less__two, fact_zero__reorient,
% 212.34/30.40 fact_zle__add1__eq__le, fact_zle__antisym, fact_zle__linear, fact_zle__refl,
% 212.34/30.40 fact_zle__trans, fact_zless__add1__eq, fact_zless__imp__add1__zle,
% 212.34/30.40 fact_zless__le, fact_zless__linear, fact_zmod__eq__0__iff,
% 212.34/30.40 fact_zmod__eq__dvd__iff, fact_zmod__le__nonneg__dividend, fact_zmod__self,
% 212.34/30.40 fact_zmod__simps_I1_J, fact_zmod__simps_I2_J, fact_zmod__simps_I3_J,
% 212.34/30.40 fact_zmod__simps_I4_J, fact_zmod__zdiv__equality, fact_zmod__zdiv__trivial,
% 212.34/30.40 fact_zmod__zero, fact_zmod__zmult1__eq, fact_zmod__zmult2__eq,
% 212.34/30.40 fact_zmult2__lemma__aux1, fact_zmult2__lemma__aux2, fact_zmult2__lemma__aux3,
% 212.34/30.40 fact_zmult2__lemma__aux4, fact_zmult__1, fact_zmult__1__right,
% 212.34/30.40 fact_zmult__assoc, fact_zmult__commute, fact_zmult__zless__mono2,
% 212.34/30.40 fact_zpower__zadd__distrib, fact_zpower__zmod, fact_zpower__zpower
% 212.34/30.40
% 212.34/30.40 Those formulas are unsatisfiable:
% 212.34/30.40 ---------------------------------
% 212.34/30.40
% 212.34/30.40 Begin of proof
% 212.34/30.40 |
% 212.34/30.40 | ALPHA: (fact_a00) implies:
% 212.34/30.40 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 212.34/30.40 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.40 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v0, v1)
% 212.34/30.40 | = v2 & $i(v2) & $i(v1) & $i(v0))
% 212.34/30.40 |
% 212.34/30.40 | ALPHA: (fact__096poly_Aq_Aw_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_A_K_Apoly_Aq_A0_096)
% 212.34/30.40 | implies:
% 212.34/30.41 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.41 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 212.34/30.41 | (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v2 &
% 212.34/30.41 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v4) = v5 &
% 212.34/30.41 | c_Polynomial_Osmult(tc_Complex_Ocomplex, v5, v_q____) = v6 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v6) = v7 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v3 & hAPP(v9, v4)
% 212.34/30.41 | = v1 & hAPP(v7, v_w____) = v8 & hAPP(v2, v8) = v9 & hAPP(v0, v3) = v4
% 212.34/30.41 | & hAPP(v0, v_w____) = v1 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 212.34/30.41 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_qnc) implies:
% 212.34/30.41 | (3) ? [v0: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.41 | $i(v0) & ~
% 212.34/30.41 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.34/30.41 | tc_Complex_Ocomplex, v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_rnc) implies:
% 212.34/30.41 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.41 | ? [v5: $i] : (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2)
% 212.34/30.41 | = v3 & c_Polynomial_Osmult(tc_Complex_Ocomplex, v3, v_q____) = v4 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v4) = v5 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v0, v1)
% 212.34/30.41 | = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 212.34/30.41 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.34/30.41 | tc_Complex_Ocomplex, v5))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_lgqr) implies:
% 212.34/30.41 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.41 | ? [v5: $i] :
% 212.34/30.41 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.34/30.41 | v5) = v0 &
% 212.34/30.41 | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.34/30.41 | v_q____) = v0 &
% 212.34/30.41 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v3) = v4 &
% 212.34/30.41 | c_Polynomial_Osmult(tc_Complex_Ocomplex, v4, v_q____) = v5 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v1 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 & hAPP(v1, v2)
% 212.34/30.41 | = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096)
% 212.34/30.41 | implies:
% 212.34/30.41 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.41 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (
% 212.34/30.41 | ~ (v9 = v8) & c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,
% 212.34/30.41 | v2) = v3 & c_Polynomial_Osmult(tc_Complex_Ocomplex, v3, v_q____) =
% 212.34/30.41 | v4 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v4) = v5 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v5, v7)
% 212.34/30.41 | = v9 & hAPP(v5, v6) = v8 & hAPP(v0, v1) = v2 & $i(v9) & $i(v8) &
% 212.34/30.41 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 212.34/30.41 | $i(v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_r01) implies:
% 212.34/30.41 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.41 | ? [v5: $i] : ? [v6: $i] :
% 212.34/30.41 | (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v6 &
% 212.34/30.41 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2) = v3 &
% 212.34/30.41 | c_Polynomial_Osmult(tc_Complex_Ocomplex, v3, v_q____) = v4 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v4) = v5 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v5, v1)
% 212.34/30.41 | = v6 & hAPP(v0, v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 212.34/30.41 | & $i(v1) & $i(v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_qr) implies:
% 212.34/30.41 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.41 | ? [v5: $i] : ? [v6: $i] :
% 212.34/30.41 | (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v1 &
% 212.34/30.41 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v3) = v4 &
% 212.34/30.41 | c_Polynomial_Osmult(tc_Complex_Ocomplex, v4, v_q____) = v5 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v5) = v6 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 & hAPP(v0, v2)
% 212.34/30.41 | = v3 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 212.34/30.41 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v6, v7) = v8) | ~ $i(v7) | ?
% 212.34/30.41 | [v9: $i] : ? [v10: $i] : (hAPP(v10, v3) = v9 & hAPP(v1, v8) = v10
% 212.34/30.41 | & hAPP(v0, v7) = v9 & $i(v10) & $i(v9))))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096)
% 212.34/30.41 | implies:
% 212.34/30.41 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.41 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 212.34/30.41 | (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 &
% 212.34/30.41 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2) = v4 &
% 212.34/30.41 | c_Polynomial_Osmult(tc_Complex_Ocomplex, v4, v_q____) = v5 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v5) = v6 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v8, v2)
% 212.34/30.41 | = v2 & hAPP(v6, v1) = v7 & hAPP(v3, v7) = v8 & hAPP(v0, v1) = v2 &
% 212.34/30.41 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 212.34/30.41 | & $i(v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_norm__one) implies:
% 212.34/30.41 | (10) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 212.34/30.41 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~
% 212.34/30.41 | (c_Groups_Oone__class_Oone(v1) = v2) | ~ $i(v1) | ~
% 212.34/30.41 | class_RealVector_Oreal__normed__algebra__1(v1)))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_less_Oprems) implies:
% 212.34/30.41 | (11) ? [v0: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0
% 212.34/30.41 | & $i(v0) & ~
% 212.34/30.41 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.34/30.41 | tc_Complex_Ocomplex, v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_norm__not__less__zero) implies:
% 212.34/30.41 | (12) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.41 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 212.34/30.41 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ~
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_norm__eq__zero) implies:
% 212.34/30.41 | (13) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.41 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 212.34/30.41 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 212.34/30.41 | $i] : (( ~ (v3 = v0) | (v4 = v1 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(v2) = v1)) & (v3 = v0 | ( ~ (v4
% 212.34/30.41 | = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_norm__zero) implies:
% 212.34/30.41 | (14) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 212.34/30.41 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~
% 212.34/30.41 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v1) | ~
% 212.34/30.41 | class_RealVector_Oreal__normed__vector(v1)))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_zero__less__norm__iff) implies:
% 212.34/30.41 | (15) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.41 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 212.34/30.41 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 212.34/30.41 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.34/30.41 | v3) | ( ~ (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 &
% 212.34/30.41 | $i(v4))) & (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.34/30.41 | v0, v3) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) =
% 212.34/30.41 | v1)))))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_complex__divide__def) implies:
% 212.34/30.41 | (16) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v0
% 212.34/30.41 | & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 212.34/30.41 | ! [v5: $i] : ( ~
% 212.34/30.41 | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v1) = v4) |
% 212.34/30.41 | ~ (hAPP(v3, v4) = v5) | ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ~
% 212.34/30.41 | $i(v1) | (c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, v2,
% 212.34/30.41 | v1) = v5 & $i(v5))))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_pc0) implies:
% 212.34/30.41 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 & hAPP(v0,
% 212.34/30.41 | v_c____) = v1 & $i(v2) & $i(v1) & $i(v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_pqc0) implies:
% 212.34/30.41 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 212.34/30.41 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v2 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v3 & hAPP(v2, v3)
% 212.34/30.41 | = v1 & hAPP(v0, v_c____) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_less_Ohyps) implies:
% 212.34/30.41 | (19) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.41 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.34/30.41 | v_pa____) = v0 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 212.34/30.41 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.41 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.34/30.41 | v2) = v3) | ~ $i(v2) | ~
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0) | ? [v4: $i] :
% 212.34/30.41 | ? [v5: $i] : ? [v6: $i] :
% 212.34/30.41 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v4 & $i(v5) &
% 212.34/30.41 | $i(v4) &
% 212.34/30.41 | (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.34/30.41 | tc_Complex_Ocomplex, v4) | (v6 = v1 & hAPP(v4, v5) = v1)))))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_cq0) implies:
% 212.34/30.41 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.41 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v3 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v4 &
% 212.34/30.41 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v0, v1)
% 212.34/30.41 | = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : !
% 212.34/30.41 | [v6: $i] : ( ~ (hAPP(v4, v5) = v6) | ~ $i(v5) | ? [v7: $i] :
% 212.34/30.41 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) = v7 &
% 212.34/30.41 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3,
% 212.34/30.41 | v7))))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_real__mult__inverse__left) implies:
% 212.34/30.41 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.41 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 212.34/30.41 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 212.34/30.41 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 212.34/30.41 | (v6 = v2 | v3 = v0 | ~
% 212.34/30.41 | (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v3) = v4) | ~
% 212.34/30.41 | (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3)))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_real__mult__inverse__cancel) implies:
% 212.34/30.41 | (22) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.41 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.41 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.41 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 212.34/30.41 | [v11: $i] : ( ~ (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,
% 212.34/30.41 | v5) = v6) | ~
% 212.34/30.41 | (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v4) = v9) | ~
% 212.34/30.41 | (hAPP(v10, v2) = v11) | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v1, v9)
% 212.34/30.41 | = v10) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ~ $i(v4) | ~
% 212.34/30.41 | $i(v3) | ~ $i(v2) | ~
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) | ~
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v11) | ?
% 212.34/30.41 | [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 212.34/30.41 | (hAPP(v14, v2) = v15 & hAPP(v12, v3) = v13 & hAPP(v1, v5) = v14 &
% 212.34/30.41 | hAPP(v1, v4) = v12 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & ~
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v15))))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_real__mult__inverse__cancel2) implies:
% 212.34/30.41 | (23) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.41 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.41 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.41 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 212.34/30.41 | [v11: $i] : ( ~ (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,
% 212.34/30.41 | v5) = v7) | ~
% 212.34/30.41 | (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v4) = v10) |
% 212.34/30.41 | ~ (hAPP(v9, v10) = v11) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v1,
% 212.34/30.41 | v3) = v6) | ~ (hAPP(v1, v2) = v9) | ~ $i(v5) | ~ $i(v4) |
% 212.34/30.41 | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) | ~
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v11) | ?
% 212.34/30.41 | [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 212.34/30.41 | (hAPP(v14, v2) = v15 & hAPP(v12, v3) = v13 & hAPP(v1, v5) = v14 &
% 212.34/30.41 | hAPP(v1, v4) = v12 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & ~
% 212.34/30.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v15))))
% 212.34/30.41 |
% 212.34/30.41 | ALPHA: (fact_c) implies:
% 212.34/30.42 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.42 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 &
% 212.34/30.42 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 & hAPP(v0,
% 212.34/30.42 | v_c____) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4:
% 212.34/30.42 | $i] : ( ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ? [v5: $i] :
% 212.34/30.42 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = v5 &
% 212.34/30.42 | $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 212.34/30.42 | v5))))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_q_I2_J) implies:
% 212.34/30.42 | (25) ? [v0: $i] : ? [v1: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.34/30.42 | v_pa____) = v1 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____)
% 212.34/30.42 | = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0,
% 212.34/30.42 | v2) = v3) | ~ $i(v2) | ? [v4: $i] :
% 212.34/30.42 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, v2) =
% 212.34/30.42 | v4 & hAPP(v1, v4) = v3 & $i(v4) & $i(v3))))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__0__le__divide__iff) implies:
% 212.34/30.42 | (26) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.42 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.42 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) |
% 212.34/30.42 | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & !
% 212.34/30.42 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.42 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) |
% 212.34/30.42 | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & !
% 212.34/30.42 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.42 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) |
% 212.34/30.42 | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & !
% 212.34/30.42 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.42 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) |
% 212.34/30.42 | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1)) & !
% 212.34/30.42 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.42 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) |
% 212.34/30.42 | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)) & !
% 212.34/30.42 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.42 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v3) |
% 212.34/30.42 | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__mult__le__cancel__iff2) implies:
% 212.34/30.42 | (27) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.42 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 212.34/30.42 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 212.34/30.42 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) |
% 212.34/30.42 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & !
% 212.34/30.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 212.34/30.42 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 212.34/30.42 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__mult__le__cancel__iff1) implies:
% 212.34/30.42 | (28) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.42 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~
% 212.34/30.42 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) =
% 212.34/30.42 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & !
% 212.34/30.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 212.34/30.42 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5,
% 212.34/30.42 | v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) |
% 212.34/30.42 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_norm__ge__zero) implies:
% 212.34/30.42 | (29) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.42 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.42 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 212.34/30.42 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_norm__le__zero__iff) implies:
% 212.34/30.42 | (30) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.42 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.42 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 212.34/30.42 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 212.34/30.42 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.42 | v3, v0) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = v1))
% 212.34/30.42 | & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) |
% 212.34/30.42 | ( ~ (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 &
% 212.34/30.42 | $i(v4))))))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__mult__left__cancel) implies:
% 212.34/30.42 | (31) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.42 | $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 212.34/30.42 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 212.34/30.42 | ~ $i(v2)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__mult__right__cancel) implies:
% 212.34/30.42 | (32) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.42 | $i] : ! [v7: $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) |
% 212.34/30.42 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2)
% 212.34/30.42 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__zero__not__eq__one) implies:
% 212.34/30.42 | (33) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 212.34/30.42 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.42 | $i(v0))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__mult__1) implies:
% 212.34/30.42 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.42 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v0, v1)
% 212.34/30.42 | = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 212.34/30.42 | v3 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_INVERSE__ZERO) implies:
% 212.34/30.42 | (35) ? [v0: $i] : (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v0)
% 212.34/30.42 | = v0 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__mult__less__iff1) implies:
% 212.34/30.42 | (36) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.42 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~
% 212.34/30.42 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) =
% 212.34/30.42 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2:
% 212.34/30.42 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 212.34/30.42 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4)
% 212.34/30.42 | = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~
% 212.34/30.42 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__mult__order) implies:
% 212.34/30.42 | (37) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.34/30.42 | (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 212.34/30.42 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.34/30.42 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)
% 212.34/30.42 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_real__mult__less__mono2) implies:
% 212.34/30.42 | (38) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.42 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 212.34/30.42 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 212.34/30.42 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_calculation) implies:
% 212.34/30.42 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.42 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 & $i(v3) &
% 212.34/30.42 | $i(v2) & $i(v0) & ((v4 = v2 & hAPP(v0, v3) = v2) | ( ~ (v2 = v1) &
% 212.34/30.42 | hAPP(v0, v_c____) = v1 & $i(v1))))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_Bseq__inverse__lemma) implies:
% 212.34/30.42 | (40) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.42 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 212.34/30.42 | [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3,
% 212.34/30.42 | v4) = v5) | ~ (c_Rings_Oinverse__class_Oinverse(v3, v1) = v4)
% 212.34/30.42 | | ~ (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v2) = v6)
% 212.34/30.42 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.42 | class_RealVector_Oreal__normed__div__algebra(v3) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v6) | ?
% 212.34/30.42 | [v7: $i] : (c_RealVector_Onorm__class_Onorm(v3, v1) = v7 & $i(v7)
% 212.34/30.42 | & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 212.34/30.42 | v7))))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_norm__ratiotest__lemma) implies:
% 212.34/30.42 | (41) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.42 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 212.34/30.42 | (c_RealVector_Onorm__class_Onorm(v5, v3) = v6) | ~
% 212.34/30.42 | (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~ (hAPP(v7, v8)
% 212.34/30.42 | = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~
% 212.34/30.42 | $i(v3) | ~ $i(v2) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) | ~
% 212.34/30.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) | ~
% 212.34/30.42 | class_RealVector_Oreal__normed__vector(v5) |
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(v5) = v3))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_not__real__square__gt__zero) implies:
% 212.34/30.42 | (42) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.42 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.42 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3,
% 212.34/30.42 | v2) = v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 212.34/30.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2:
% 212.34/30.42 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) =
% 212.34/30.42 | v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.34/30.42 | v3)))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_order__root) implies:
% 212.34/30.42 | (43) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 212.34/30.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 212.34/30.42 | $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) =
% 212.34/30.42 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.42 | class_Rings_Oidom(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 212.34/30.42 | ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) & c_Polynomial_Oorder(v3,
% 212.34/30.42 | v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) |
% 212.34/30.42 | (v6 = v5 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) &
% 212.34/30.42 | ((v8 = v2 & tc_Polynomial_Opoly(v3) = v7 &
% 212.34/30.42 | c_Groups_Ozero__class_Ozero(v7) = v2 & $i(v7)) | ( ~ (v9 =
% 212.34/30.42 | v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & $i(v9)) | ( ~
% 212.34/30.42 | (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 &
% 212.34/30.42 | $i(v6))))))
% 212.34/30.42 |
% 212.34/30.42 | ALPHA: (fact_divide_Opos__bounded) implies:
% 212.34/30.43 | (44) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.43 | & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.43 | class_RealVector_Oreal__normed__field(v3) | ? [v4: $i] : ($i(v4)
% 212.34/30.43 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 212.34/30.43 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7,
% 212.34/30.43 | v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9:
% 212.34/30.43 | $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v3,
% 212.34/30.43 | v9) = v10 & c_Rings_Oinverse__class_Odivide(v3, v5, v2) =
% 212.34/30.43 | v9 & $i(v10) & $i(v9) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 212.34/30.43 | v8))))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_mult__eq__self__implies__10) implies:
% 212.34/30.43 | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.43 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.43 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) &
% 212.34/30.43 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 =
% 212.34/30.43 | v1 | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) |
% 212.34/30.43 | ~ $i(v3)))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_mult__less__cancel2) implies:
% 212.34/30.43 | (46) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 212.34/30.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 212.34/30.43 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5,
% 212.34/30.43 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) |
% 212.34/30.43 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i]
% 212.34/30.43 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.43 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) =
% 212.34/30.43 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 212.34/30.43 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i]
% 212.34/30.43 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 212.34/30.43 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) =
% 212.34/30.43 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 212.34/30.43 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_not__less0) implies:
% 212.34/30.43 | (47) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 212.34/30.43 | & ! [v1: $i] : ( ~ $i(v1) | ~
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_nat__mult__eq__1__iff) implies:
% 212.34/30.43 | (48) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.43 | v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) &
% 212.34/30.43 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~
% 212.34/30.43 | (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~
% 212.34/30.43 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~
% 212.34/30.43 | (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~
% 212.34/30.43 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (hAPP(v2, v1)
% 212.34/30.43 | = v3) | ~ (hAPP(v0, v1) = v2)))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_nat__mult__1__right) implies:
% 212.34/30.43 | (49) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.43 | v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) &
% 212.34/30.43 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~
% 212.34/30.43 | $i(v2) | hAPP(v3, v1) = v2))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_nat__1__eq__mult__iff) implies:
% 212.34/30.43 | (50) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.43 | v0 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) &
% 212.34/30.43 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~
% 212.34/30.43 | (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 212.34/30.43 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~
% 212.34/30.43 | (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 212.34/30.43 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (hAPP(v2, v0)
% 212.34/30.43 | = v3) | ~ (hAPP(v1, v0) = v2)))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_nat__mult__1) implies:
% 212.34/30.43 | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.43 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.43 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2
% 212.34/30.43 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 |
% 212.34/30.43 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_real__two__squares__add__zero__iff) implies:
% 212.34/30.43 | (52) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)
% 212.34/30.43 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.43 | $i] : ! [v7: $i] : (v3 = v1 | ~
% 212.34/30.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~
% 212.34/30.43 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) =
% 212.34/30.43 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 212.34/30.43 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 212.34/30.43 | [v7: $i] : (v2 = v1 | ~
% 212.34/30.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~
% 212.34/30.43 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) =
% 212.34/30.43 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 212.34/30.43 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 212.34/30.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~
% 212.34/30.43 | (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 212.34/30.43 | implies:
% 212.34/30.43 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 212.34/30.43 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.34/30.43 | v2) = v0 &
% 212.34/30.43 | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.34/30.43 | v_pa____) = v0 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3
% 212.34/30.43 | & c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v1 & $i(v3) &
% 212.34/30.43 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~
% 212.34/30.43 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, v4) =
% 212.34/30.43 | v5) | ~ $i(v4) | ? [v6: $i] : (hAPP(v3, v4) = v6 & hAPP(v1,
% 212.34/30.43 | v5) = v6 & $i(v6))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_mult__left_Opos__bounded) implies:
% 212.34/30.43 | (54) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.43 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 212.34/30.43 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] :
% 212.34/30.43 | ($i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)
% 212.34/30.43 | & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8,
% 212.34/30.43 | v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10:
% 212.34/30.43 | $i] : ? [v11: $i] : ? [v12: $i] :
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10,
% 212.34/30.43 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 212.34/30.43 | $i(v10) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 212.34/30.43 | v9))))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_mult__right_Opos__bounded) implies:
% 212.34/30.43 | (55) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.43 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5)
% 212.34/30.43 | | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.43 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] :
% 212.34/30.43 | ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6)
% 212.34/30.43 | & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9,
% 212.34/30.43 | v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11:
% 212.34/30.43 | $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3,
% 212.34/30.43 | v11) = v12 & hAPP(v5, v7) = v11 & $i(v12) & $i(v11) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 212.34/30.43 | v10))))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_mult_Opos__bounded) implies:
% 212.34/30.43 | (56) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.43 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2)
% 212.34/30.43 | = v3) | ~ $i(v2) | ~
% 212.34/30.43 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 212.34/30.43 | ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)
% 212.34/30.43 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : !
% 212.34/30.43 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11,
% 212.34/30.43 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) =
% 212.34/30.43 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ?
% 212.34/30.43 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13,
% 212.34/30.43 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 212.34/30.43 | $i(v13) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 212.34/30.43 | v12))))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_poly__bound__exists) implies:
% 212.34/30.43 | (57) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.43 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.43 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3) | ~ $i(v2) |
% 212.34/30.43 | ~ $i(v1) | ? [v4: $i] : ($i(v4) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 212.34/30.43 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v3, v5) = v6) | ~ $i(v5) |
% 212.34/30.43 | ? [v7: $i] : ? [v8: $i] :
% 212.34/30.43 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) =
% 212.34/30.43 | v8 & $i(v8) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 212.34/30.43 | v4)) |
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) =
% 212.34/30.43 | v7 & $i(v7) & ~
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 212.34/30.43 | v1)))))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_ex__least__nat__less) implies:
% 212.34/30.43 | (58) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.43 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0)
% 212.34/30.43 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4)
% 212.34/30.43 | | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i]
% 212.34/30.43 | : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 212.34/30.43 | ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 &
% 212.34/30.43 | hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9:
% 212.34/30.43 | $i] : ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9)
% 212.34/30.43 | | ~ hBOOL(v10) | ~
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) |
% 212.34/30.43 | (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5))))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_divide_Ononneg__bounded) implies:
% 212.34/30.43 | (59) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.43 | & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.43 | class_RealVector_Oreal__normed__field(v3) | ? [v4: $i] : ($i(v4)
% 212.34/30.43 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) &
% 212.34/30.43 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7,
% 212.34/30.43 | v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9:
% 212.34/30.43 | $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v3,
% 212.34/30.43 | v9) = v10 & c_Rings_Oinverse__class_Odivide(v3, v5, v2) =
% 212.34/30.43 | v9 & $i(v10) & $i(v9) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 212.34/30.43 | v8))))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_mult_Ononneg__bounded) implies:
% 212.34/30.43 | (60) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.43 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2)
% 212.34/30.43 | = v3) | ~ $i(v2) | ~
% 212.34/30.43 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 212.34/30.43 | ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 212.34/30.43 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] :
% 212.34/30.43 | ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11,
% 212.34/30.43 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) =
% 212.34/30.43 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ?
% 212.34/30.43 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 212.34/30.43 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13,
% 212.34/30.43 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 212.34/30.43 | $i(v13) &
% 212.34/30.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 212.34/30.43 | v12))))))
% 212.34/30.43 |
% 212.34/30.43 | ALPHA: (fact_mult__right_Ononneg__bounded) implies:
% 212.34/30.43 | (61) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.43 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.34/30.44 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5)
% 212.34/30.44 | | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.44 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] :
% 212.34/30.44 | ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 212.34/30.44 | v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 212.34/30.44 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~
% 212.34/30.44 | (hAPP(v9, v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ?
% 212.34/30.44 | [v11: $i] : ? [v12: $i] :
% 212.34/30.44 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 212.34/30.44 | = v11 & $i(v12) & $i(v11) &
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 212.34/30.44 | v10))))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_mult__left_Ononneg__bounded) implies:
% 212.34/30.44 | (62) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 212.34/30.44 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.44 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 212.34/30.44 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] :
% 212.34/30.44 | ($i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 212.34/30.44 | v5) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 212.34/30.44 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~
% 212.34/30.44 | (hAPP(v8, v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ?
% 212.34/30.44 | [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 212.34/30.44 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10,
% 212.34/30.44 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 212.34/30.44 | $i(v10) &
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 212.34/30.44 | v9))))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_Bseq__def) implies:
% 212.34/30.44 | (63) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 212.34/30.44 | $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2)
% 212.34/30.44 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 212.34/30.44 | c_SEQ_OBseq(v2, v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 212.34/30.44 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6 & hAPP(v1, v4) = v5
% 212.34/30.44 | & $i(v6) & $i(v5) & $i(v4) & ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))) &
% 212.34/30.44 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_SEQ_OBseq(v2, v1) | ~
% 212.34/30.44 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3)
% 212.34/30.44 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & !
% 212.34/30.44 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 212.34/30.44 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v1,
% 212.34/30.44 | v4) = v5) | ~ $i(v4) |
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 212.34/30.44 | v3)))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natceiling__add__one) implies:
% 212.34/30.44 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.44 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 212.34/30.44 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~
% 212.34/30.44 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.44 | v0, v3) | ? [v5: $i] : ? [v6: $i] :
% 212.34/30.44 | (c_RComplete_Onatceiling(v4) = v5 & c_RComplete_Onatceiling(v3) =
% 212.34/30.44 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 &
% 212.34/30.44 | $i(v6) & $i(v5))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_expi__zero) implies:
% 212.34/30.44 | (65) ? [v0: $i] : ? [v1: $i] : (c_Complex_Oexpi(v0) = v1 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v1) &
% 212.34/30.44 | $i(v0))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natceiling__zero) implies:
% 212.34/30.44 | (66) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.44 | $i(v0))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natceiling__one) implies:
% 212.34/30.44 | (67) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natceiling__neg) implies:
% 212.34/30.44 | (68) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 212.34/30.44 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.44 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 212.34/30.44 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natceiling__le__eq__one) implies:
% 212.34/30.44 | (69) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.44 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) &
% 212.34/30.44 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.44 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) |
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 212.34/30.44 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~
% 212.34/30.44 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.44 | v2, v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3,
% 212.34/30.44 | v0)))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_expi__add) implies:
% 212.34/30.44 | (70) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v0
% 212.34/30.44 | & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 212.34/30.44 | ! [v5: $i] : ! [v6: $i] : ( ~ (c_Complex_Oexpi(v2) = v3) | ~
% 212.34/30.44 | (c_Complex_Oexpi(v1) = v5) | ~ (hAPP(v4, v5) = v6) | ~ (hAPP(v0,
% 212.34/30.44 | v3) = v4) | ~ $i(v2) | ~ $i(v1) | ? [v7: $i] :
% 212.34/30.44 | (c_Complex_Oexpi(v7) = v6 &
% 212.34/30.44 | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v1) = v7 &
% 212.34/30.44 | $i(v7) & $i(v6))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natfloor__add__one) implies:
% 212.34/30.44 | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.44 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 212.34/30.44 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~
% 212.34/30.44 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.44 | v0, v3) | ? [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4)
% 212.34/30.44 | = v5 & c_RComplete_Onatfloor(v3) = v6 &
% 212.34/30.44 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 212.34/30.44 | $i(v5))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natceiling__eq) implies:
% 212.34/30.44 | (72) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.44 | v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.44 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5
% 212.34/30.44 | = v4 | ~ (c_RComplete_Onatceiling(v2) = v4) | ~
% 212.34/30.44 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~
% 212.34/30.44 | $i(v3) | ~ $i(v2) | ? [v6: $i] : ? [v7: $i] :
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & $i(v6) & ( ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v2) |
% 212.34/30.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 &
% 212.34/30.44 | $i(v7) & ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 212.34/30.44 | v7))))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_BseqD) implies:
% 212.34/30.44 | (73) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_SEQ_OBseq(v2, v1) | ~
% 212.34/30.44 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3)
% 212.34/30.44 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & !
% 212.34/30.44 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 212.34/30.44 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v1,
% 212.34/30.44 | v4) = v5) | ~ $i(v4) |
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 212.34/30.44 | v3)))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_BseqI) implies:
% 212.34/30.44 | (74) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 212.34/30.44 | $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__normed__vector(v3)
% 212.34/30.44 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.44 | c_SEQ_OBseq(v3, v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 212.34/30.44 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6 & hAPP(v1, v4) = v5
% 212.34/30.44 | & $i(v6) & $i(v5) & $i(v4) & ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v2))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_real__of__nat__ge__zero) implies:
% 212.34/30.44 | (75) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) |
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_real__natfloor__add__one__gt) implies:
% 212.34/30.44 | (76) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1)
% 212.34/30.44 | = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 212.34/30.44 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 &
% 212.34/30.44 | $i(v4) & $i(v3) &
% 212.34/30.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_real__natfloor__le) implies:
% 212.34/30.44 | (77) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1)
% 212.34/30.44 | = v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ?
% 212.34/30.44 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) &
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_le__natfloor__eq) implies:
% 212.34/30.44 | (78) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 212.34/30.44 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)) & !
% 212.34/30.44 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 212.34/30.44 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_real__of__nat__zero) implies:
% 212.34/30.44 | (79) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 212.34/30.44 | $i(v0))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_real__of__nat__zero__iff) implies:
% 212.34/30.44 | (80) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 212.34/30.44 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.44 | $i(v0) & ! [v2: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.44 | v2) = v0) | ~ $i(v2)) & ! [v2: $i] : (v2 = v0 | ~
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2)))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_not__real__of__nat__less__zero) implies:
% 212.34/30.44 | (81) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_less__natfloor) implies:
% 212.34/30.44 | (82) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 212.34/30.44 | (c_RComplete_Onatfloor(v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) |
% 212.34/30.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1)))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natfloor__add) implies:
% 212.34/30.44 | (83) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 212.34/30.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 212.34/30.44 | $i(v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 212.34/30.44 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 212.34/30.44 | c_RComplete_Onatfloor(v2) = v6 &
% 212.34/30.44 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 212.34/30.44 | $i(v5))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_ge__natfloor__plus__one__imp__gt) implies:
% 212.34/30.44 | (84) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 212.34/30.44 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 212.34/30.44 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5:
% 212.34/30.44 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 &
% 212.34/30.44 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5,
% 212.34/30.44 | v1))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_real__of__nat__1) implies:
% 212.34/30.44 | (85) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natfloor__eq) implies:
% 212.34/30.44 | (86) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4
% 212.34/30.44 | = v2 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 212.34/30.44 | (c_RComplete_Onatfloor(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ?
% 212.34/30.44 | [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0)
% 212.34/30.44 | = v5 & $i(v5) & ~
% 212.34/30.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natfloor__zero) implies:
% 212.34/30.44 | (87) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.44 | $i(v0))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_natfloor__one) implies:
% 212.34/30.44 | (88) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 212.34/30.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 212.34/30.44 |
% 212.34/30.44 | ALPHA: (fact_real__of__nat__le__zero__cancel__iff) implies:
% 212.34/30.45 | (89) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 212.34/30.45 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)) & !
% 212.34/30.45 | [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) |
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_natfloor__neg) implies:
% 212.34/30.45 | (90) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 212.34/30.45 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 212.34/30.45 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_real__of__nat__gt__zero__cancel__iff) implies:
% 212.34/30.45 | (91) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 212.34/30.45 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2:
% 212.34/30.45 | $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) |
% 212.34/30.45 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.34/30.45 | v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_nat__less__real__le) implies:
% 212.34/30.45 | (92) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.45 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i]
% 212.34/30.45 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 212.34/30.45 | $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5,
% 212.34/30.45 | v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 212.34/30.45 | : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 212.34/30.45 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 212.34/30.45 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.45 | v5, v4))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_nat__le__real__less) implies:
% 212.34/30.45 | (93) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.45 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5:
% 212.34/30.45 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) =
% 212.34/30.45 | v5 & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.34/30.45 | v3, v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 212.34/30.45 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5:
% 212.34/30.45 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) =
% 212.34/30.45 | v5 & $i(v5) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.34/30.45 | v3, v5))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_natceiling__le__eq) implies:
% 212.34/30.45 | (94) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 212.34/30.45 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4)) & !
% 212.34/30.45 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 212.34/30.45 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1)))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_le__natfloor__eq__one) implies:
% 212.34/30.45 | (95) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.45 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) &
% 212.34/30.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2)
% 212.34/30.45 | = v3) | ~ $i(v2) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) |
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & !
% 212.34/30.45 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~
% 212.34/30.45 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.45 | v1, v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 212.34/30.45 | v3)))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_natceiling__add) implies:
% 212.34/30.45 | (96) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 212.34/30.45 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 212.34/30.45 | $i(v2) | ~ $i(v1) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 212.34/30.45 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 212.34/30.45 | c_RComplete_Onatceiling(v2) = v6 &
% 212.34/30.45 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 212.34/30.45 | $i(v5))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_le__mult__natfloor) implies:
% 212.34/30.45 | (97) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.45 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 212.34/30.45 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 212.34/30.45 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 212.34/30.45 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~
% 212.34/30.45 | (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~
% 212.34/30.45 | (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ?
% 212.34/30.45 | [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 212.34/30.45 | (c_RComplete_Onatfloor(v10) = v11 & hAPP(v9, v3) = v10 & hAPP(v2,
% 212.34/30.45 | v4) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_natfloor__div__nat) implies:
% 212.34/30.45 | (98) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.45 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 212.34/30.45 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.34/30.45 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v4) | ~
% 212.34/30.45 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) |
% 212.34/30.45 | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v6: $i] :
% 212.34/30.45 | ? [v7: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v2) =
% 212.34/30.45 | v6 & c_RComplete_Onatfloor(v5) = v6 & c_RComplete_Onatfloor(v3)
% 212.34/30.45 | = v7 & $i(v7) & $i(v6))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_LIMSEQ__inverse__realpow__zero__lemma) implies:
% 212.34/30.45 | (99) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 212.34/30.45 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 212.34/30.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 212.34/30.45 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) & $i(v2)
% 212.34/30.45 | & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 212.34/30.45 | [v7: $i] : ! [v8: $i] : ( ~
% 212.34/30.45 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) | ~
% 212.34/30.45 | (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~
% 212.34/30.45 | $i(v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.45 | v0, v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 212.34/30.45 | $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 212.34/30.45 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 &
% 212.34/30.45 | hAPP(v10, v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) &
% 212.34/30.45 | $i(v10) & $i(v9) &
% 212.34/30.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)
% 212.34/30.45 | implies:
% 212.34/30.45 | (100) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 212.34/30.45 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.45 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 212.34/30.45 | | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) |
% 212.34/30.45 | hAPP(v4, v0) = v1))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_split__div) implies:
% 212.34/30.45 | (101) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.45 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 212.34/30.45 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 212.34/30.45 | : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~
% 212.34/30.45 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.45 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : (( ~ (v2 = v0) |
% 212.34/30.45 | (hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7))) & (v2 = v0 |
% 212.34/30.45 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : !
% 212.34/30.45 | [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 212.34/30.45 | v11, v10) = v3) | ~ (hAPP(v8, v9) = v11) | ~
% 212.34/30.45 | $i(v10) | ~ $i(v9) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) | ?
% 212.34/30.45 | [v12: $i] : (hAPP(v4, v9) = v12 & $i(v12) &
% 212.34/30.45 | hBOOL(v12))))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 212.34/30.45 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 212.34/30.45 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~
% 212.34/30.45 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 212.34/30.45 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 212.34/30.45 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v10) &
% 212.34/30.45 | $i(v9) & ((v12 = v3 & ~ (v2 = v0) &
% 212.34/30.45 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) = v3 &
% 212.34/30.45 | hAPP(v8, v9) = v11 & hAPP(v4, v9) = v13 & hAPP(v1, v2) = v8
% 212.34/30.45 | & $i(v13) & $i(v11) & $i(v8) &
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) & ~
% 212.34/30.45 | hBOOL(v13)) | (v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & ~
% 212.34/30.45 | hBOOL(v7))))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_power__one__right) implies:
% 212.34/30.45 | (102) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 212.34/30.45 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.45 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 212.34/30.45 | | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) |
% 212.34/30.45 | hAPP(v4, v0) = v1))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_div__less__dividend) implies:
% 212.34/30.45 | (103) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 212.34/30.45 | v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) &
% 212.34/30.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.45 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~
% 212.34/30.45 | $i(v3) | ~ $i(v2) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_reduce__poly__simple) implies:
% 212.34/30.45 | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.45 | ? [v5: $i] : (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v4
% 212.34/30.45 | & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v5 &
% 212.34/30.45 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 &
% 212.34/30.45 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v5) &
% 212.34/30.45 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ! [v7:
% 212.34/30.45 | $i] : ! [v8: $i] : (v7 = v0 | v6 = v1 | ~ (hAPP(v3, v7) = v8) |
% 212.34/30.45 | ~ $i(v7) | ~ $i(v6) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i]
% 212.34/30.45 | : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 212.34/30.45 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v12) = v13
% 212.34/30.45 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v13) =
% 212.34/30.45 | v14 & hAPP(v10, v6) = v11 & hAPP(v8, v11) = v12 & hAPP(v4, v9)
% 212.34/30.45 | = v10 & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) &
% 212.34/30.45 | $i(v9) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14,
% 212.34/30.45 | v5))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_realpow__pos__nth__unique) implies:
% 212.34/30.45 | (105) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.45 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) &
% 212.34/30.45 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~
% 212.34/30.45 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 212.34/30.45 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ?
% 212.34/30.45 | [v5: $i] : ? [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 &
% 212.34/30.45 | $i(v6) & $i(v5) &
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & !
% 212.34/30.45 | [v7: $i] : ! [v8: $i] : (v7 = v5 | ~ (hAPP(v8, v4) = v3) | ~
% 212.34/30.45 | (hAPP(v2, v7) = v8) | ~ $i(v7) | ~
% 212.34/30.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v7)))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_rcis__zero__mod) implies:
% 212.34/30.45 | (106) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.45 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.45 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v1) &
% 212.34/30.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 212.34/30.45 | (c_Complex_Orcis(v0, v2) = v3) | ~ $i(v2)))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_rcis__mult) implies:
% 212.34/30.45 | (107) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.45 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v0 & $i(v1) &
% 212.34/30.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 212.34/30.45 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 212.34/30.45 | (c_Complex_Orcis(v7, v8) = v9) | ~
% 212.34/30.45 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v2) = v8) | ~
% 212.34/30.45 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v5) | ~
% 212.34/30.45 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v10: $i] : ? [v11: $i] : ?
% 212.34/30.45 | [v12: $i] : (c_Complex_Orcis(v5, v4) = v10 & c_Complex_Orcis(v3,
% 212.34/30.45 | v2) = v12 & hAPP(v11, v12) = v9 & hAPP(v0, v10) = v11 &
% 212.34/30.45 | $i(v12) & $i(v11) & $i(v10) & $i(v9))))
% 212.34/30.45 |
% 212.34/30.45 | ALPHA: (fact_realpow__pos__nth) implies:
% 212.34/30.46 | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.46 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) &
% 212.34/30.46 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~
% 212.34/30.46 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 212.34/30.46 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ?
% 212.34/30.46 | [v5: $i] : ? [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 &
% 212.34/30.46 | $i(v6) & $i(v5) &
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__realpow) implies:
% 212.34/30.46 | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.46 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) &
% 212.34/30.46 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 212.34/30.46 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) =
% 212.34/30.46 | v7) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6,
% 212.34/30.46 | v7) = v8) | ~ (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 212.34/30.46 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ?
% 212.34/30.46 | [v9: $i] : ? [v10: $i] : (c_Transcendental_Oln(v10) = v8 &
% 212.34/30.46 | hAPP(v9, v3) = v10 & hAPP(v1, v4) = v9 & $i(v10) & $i(v9) &
% 212.34/30.46 | $i(v8))))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__less__cancel__iff) implies:
% 212.34/30.46 | (110) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 212.34/30.46 | ~ (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1)
% 212.34/30.46 | = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & !
% 212.34/30.46 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.46 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 212.34/30.46 | v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__inj__iff) implies:
% 212.34/30.46 | (111) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 212.34/30.46 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 212.34/30.46 | v3) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__less__self) implies:
% 212.34/30.46 | (112) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Transcendental_Oln(v1)
% 212.34/30.46 | = v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__one) implies:
% 212.34/30.46 | (113) ? [v0: $i] : ? [v1: $i] : (c_Transcendental_Oln(v0) = v1 &
% 212.34/30.46 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 212.34/30.46 | $i(v0))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__le__cancel__iff) implies:
% 212.34/30.46 | (114) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 212.34/30.46 | ~ (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1)
% 212.34/30.46 | = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 212.34/30.46 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 212.34/30.46 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 212.34/30.46 | v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__ge__zero) implies:
% 212.34/30.46 | (115) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 212.34/30.46 | = v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__gt__zero) implies:
% 212.34/30.46 | (116) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 212.34/30.46 | = v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__gt__zero__iff) implies:
% 212.34/30.46 | (117) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 212.34/30.46 | = v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & !
% 212.34/30.46 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 212.34/30.46 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.34/30.46 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.34/30.46 | v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__eq__zero__iff) implies:
% 212.34/30.46 | (118) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) =
% 212.34/30.46 | v0) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)) & !
% 212.34/30.46 | [v2: $i] : (v2 = v0 | ~ (c_Transcendental_Oln(v1) = v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__less__zero__iff) implies:
% 212.34/30.46 | (119) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 212.34/30.46 | = v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & !
% 212.34/30.46 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 212.34/30.46 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 212.34/30.46 | v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.34/30.46 | v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__less__zero) implies:
% 212.34/30.46 | (120) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 212.34/30.46 | = v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__gt__zero__imp__gt__one) implies:
% 212.34/30.46 | (121) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 212.34/30.46 | = v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__ge__zero__iff) implies:
% 212.34/30.46 | (122) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 212.34/30.46 | = v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & !
% 212.34/30.46 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 212.34/30.46 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.46 | v0, v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.34/30.46 | v0, v2) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.46 | v1, v2)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__ge__zero__imp__ge__one) implies:
% 212.34/30.46 | (123) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 212.34/30.46 | = v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__mult) implies:
% 212.34/30.46 | (124) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 212.34/30.46 | [v6: $i] : ( ~ (c_Transcendental_Oln(v3) = v4) | ~
% 212.34/30.46 | (c_Transcendental_Oln(v2) = v5) | ~
% 212.34/30.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~
% 212.34/30.46 | $i(v3) | ~ $i(v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7:
% 212.34/30.46 | $i] : ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7,
% 212.34/30.46 | v2) = v8 & hAPP(v1, v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__add__one__self__le__self) implies:
% 212.34/30.46 | (125) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 212.34/30.46 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.46 | v0, v2) | ? [v4: $i] : (c_Transcendental_Oln(v3) = v4 & $i(v4)
% 212.34/30.46 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4,
% 212.34/30.46 | v2))))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_real__of__nat__div3) implies:
% 212.34/30.46 | (126) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 212.34/30.46 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 212.34/30.46 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5, v7) = v8) |
% 212.34/30.46 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v6) | ~
% 212.34/30.46 | (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~
% 212.34/30.46 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 212.34/30.46 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 212.34/30.46 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5)
% 212.34/30.46 | | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v0)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_real__le__eq__diff) implies:
% 212.34/30.46 | (127) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.46 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) |
% 212.34/30.46 | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 212.34/30.46 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.46 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) |
% 212.34/30.46 | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 212.34/30.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_nat__dvd__1__iff__1) implies:
% 212.34/30.46 | (128) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 212.34/30.46 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 =
% 212.34/30.46 | v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1,
% 212.34/30.46 | v0)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_dvd__mult__cancel2) implies:
% 212.34/30.46 | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 212.34/30.46 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 212.34/30.46 | (v3 = v2 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~
% 212.34/30.46 | $i(v4) | ~ $i(v3) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6,
% 212.34/30.46 | v4) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) &
% 212.34/30.46 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) |
% 212.34/30.46 | ~ (hAPP(v1, v2) = v4) | ~ $i(v3) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 212.34/30.46 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_dvd__mult__cancel1) implies:
% 212.34/30.46 | (130) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 212.34/30.46 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 212.34/30.46 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 212.34/30.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 212.34/30.46 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 212.34/30.46 | (v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~
% 212.34/30.46 | $i(v4) | ~ $i(v3) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6,
% 212.34/30.46 | v4) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) &
% 212.34/30.46 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) |
% 212.34/30.46 | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 212.34/30.46 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_ln__div) implies:
% 212.34/30.46 | (131) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 212.34/30.46 | [v5: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v3,
% 212.34/30.46 | v4) = v5) | ~ (c_Transcendental_Oln(v2) = v3) | ~
% 212.34/30.46 | (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 212.34/30.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ? [v6:
% 212.34/30.46 | $i] : (c_Transcendental_Oln(v6) = v5 &
% 212.34/30.46 | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v1) = v6
% 212.34/30.46 | & $i(v6) & $i(v5))))
% 212.34/30.46 |
% 212.34/30.46 | ALPHA: (fact_power__dvd__imp__le) implies:
% 212.34/30.47 | (132) ? [v0: $i] : ? [v1: $i] :
% 212.34/30.47 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 212.34/30.47 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 212.34/30.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 212.34/30.47 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 212.34/30.47 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 212.34/30.47 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | ~
% 212.34/30.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 212.34/30.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)))
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (fact_real__natfloor__gt__diff__one) implies:
% 212.34/30.47 | (133) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 212.34/30.47 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 212.34/30.47 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) |
% 212.34/30.47 | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 212.34/30.47 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 &
% 212.34/30.47 | c_RComplete_Onatfloor(v1) = v3 & $i(v4) & $i(v3) &
% 212.34/30.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))))
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (fact_real__of__nat__div2) implies:
% 212.34/30.47 | (134) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 212.34/30.47 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 212.34/30.47 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 212.34/30.47 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5, v7) = v8) |
% 212.34/30.47 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v6) | ~
% 212.34/30.47 | (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~
% 212.34/30.47 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 212.34/30.47 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 212.34/30.47 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5)
% 212.34/30.47 | | ~ $i(v2) | ~ $i(v1) |
% 212.34/30.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v8)))
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero)
% 212.34/30.47 | implies:
% 212.34/30.47 | (135) class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_RealDef__Oreal__Rings_Olinordered__semidom) implies:
% 212.34/30.47 | (136) class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero)
% 212.34/30.47 | implies:
% 212.34/30.47 | (137) class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) implies:
% 212.34/30.47 | (138) class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) implies:
% 212.34/30.47 | (139) class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_Complex__Ocomplex__Rings_Ono__zero__divisors) implies:
% 212.34/30.47 | (140) class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_Complex__Ocomplex__Rings_Odivision__ring) implies:
% 212.34/30.47 | (141) class_Rings_Odivision__ring(tc_Complex_Ocomplex)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_Complex__Ocomplex__Rings_Ozero__neq__one) implies:
% 212.34/30.47 | (142) class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (arity_Complex__Ocomplex__Rings_Oidom) implies:
% 212.34/30.47 | (143) class_Rings_Oidom(tc_Complex_Ocomplex)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (conj_0) implies:
% 212.34/30.47 | (144) $i(tc_Complex_Ocomplex)
% 212.34/30.47 | (145) $i(tc_RealDef_Oreal)
% 212.34/30.47 | (146) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 212.34/30.47 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 212.34/30.47 | ? [v10: $i] : ? [v11: $i] :
% 212.34/30.47 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10) = v11 &
% 212.34/30.47 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) = v7 &
% 212.34/30.47 | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, v9, v2) = v10
% 212.34/30.47 | & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v8 &
% 212.34/30.47 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v2) = v3 &
% 212.34/30.47 | c_Polynomial_Osmult(tc_Complex_Ocomplex, v3, v_q____) = v4 &
% 212.34/30.47 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v4) = v5 &
% 212.34/30.47 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = v0 &
% 212.34/30.47 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v5,
% 212.34/30.47 | v_w____) = v6 & hAPP(v0, v1) = v2 & hAPP(v0, v_w____) = v9 &
% 212.34/30.47 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 212.34/30.47 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 212.34/30.47 | ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v8) & ~
% 212.34/30.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v8)) |
% 212.34/30.47 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v8) & ~
% 212.34/30.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v8))))
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (function-axioms) implies:
% 212.34/30.47 | (147) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.47 | (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 212.34/30.47 | (c_Groups_Ozero__class_Ozero(v2) = v0))
% 212.34/30.47 | (148) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.47 | (c_Groups_Otimes__class_Otimes(v2) = v1) | ~
% 212.34/30.47 | (c_Groups_Otimes__class_Otimes(v2) = v0))
% 212.34/30.47 | (149) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 212.34/30.47 | (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 212.34/30.47 | (c_Groups_Oone__class_Oone(v2) = v0))
% 212.34/30.47 | (150) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 212.34/30.47 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0))
% 212.34/30.47 | (151) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 212.34/30.47 | (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2)
% 212.34/30.47 | = v0))
% 212.34/30.47 | (152) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 212.34/30.47 | (c_Rings_Oinverse__class_Oinverse(v3, v2) = v1) | ~
% 212.34/30.47 | (c_Rings_Oinverse__class_Oinverse(v3, v2) = v0))
% 212.34/30.47 | (153) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 212.34/30.47 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 212.34/30.47 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v0))
% 212.34/30.47 | (154) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 212.34/30.47 | (v1 = v0 | ~ (c_Polynomial_Osmult(v4, v3, v2) = v1) | ~
% 212.34/30.47 | (c_Polynomial_Osmult(v4, v3, v2) = v0))
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (11) with fresh symbol all_691_0 gives:
% 212.34/30.47 | (155) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_691_0 &
% 212.34/30.47 | $i(all_691_0) & ~
% 212.34/30.47 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.34/30.47 | tc_Complex_Ocomplex, all_691_0)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (155) implies:
% 212.34/30.47 | (156) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_691_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (35) with fresh symbol all_693_0 gives:
% 212.34/30.47 | (157) c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, all_693_0) =
% 212.34/30.47 | all_693_0 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_693_0
% 212.34/30.47 | & $i(all_693_0)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (157) implies:
% 212.34/30.47 | (158) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_693_0
% 212.34/30.47 | (159) c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, all_693_0) =
% 212.34/30.47 | all_693_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (3) with fresh symbol all_699_0 gives:
% 212.34/30.47 | (160) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_699_0 &
% 212.34/30.47 | $i(all_699_0) & ~
% 212.34/30.47 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.34/30.47 | tc_Complex_Ocomplex, all_699_0)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (160) implies:
% 212.34/30.47 | (161) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_699_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (47) with fresh symbol all_707_0 gives:
% 212.34/30.47 | (162) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_707_0 & $i(all_707_0)
% 212.34/30.47 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 212.34/30.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_707_0))
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (162) implies:
% 212.34/30.47 | (163) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_707_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (81) with fresh symbol all_734_0 gives:
% 212.34/30.47 | (164) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_734_0 &
% 212.34/30.47 | $i(all_734_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.47 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ~
% 212.34/30.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_734_0))
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (164) implies:
% 212.34/30.47 | (165) $i(all_734_0)
% 212.34/30.47 | (166) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_734_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (33) with fresh symbols all_737_0, all_737_1 gives:
% 212.34/30.47 | (167) ~ (all_737_0 = all_737_1) &
% 212.34/30.47 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_737_0 &
% 212.34/30.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_737_1 &
% 212.34/30.47 | $i(all_737_0) & $i(all_737_1)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (167) implies:
% 212.34/30.47 | (168) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_737_1
% 212.34/30.47 | (169) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_737_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (65) with fresh symbols all_746_0, all_746_1 gives:
% 212.34/30.47 | (170) c_Complex_Oexpi(all_746_1) = all_746_0 &
% 212.34/30.47 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_746_0 &
% 212.34/30.47 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_746_1 &
% 212.34/30.47 | $i(all_746_0) & $i(all_746_1)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (170) implies:
% 212.34/30.47 | (171) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_746_1
% 212.34/30.47 | (172) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_746_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (66) with fresh symbols all_749_0, all_749_1 gives:
% 212.34/30.47 | (173) c_RComplete_Onatceiling(all_749_1) = all_749_0 &
% 212.34/30.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_749_0 &
% 212.34/30.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_749_1 &
% 212.34/30.47 | $i(all_749_0) & $i(all_749_1)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (173) implies:
% 212.34/30.47 | (174) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_749_1
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (67) with fresh symbols all_752_0, all_752_1 gives:
% 212.34/30.47 | (175) c_RComplete_Onatceiling(all_752_1) = all_752_0 &
% 212.34/30.47 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_752_0 &
% 212.34/30.47 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_752_1 &
% 212.34/30.47 | $i(all_752_0) & $i(all_752_1)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (175) implies:
% 212.34/30.47 | (176) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_752_1
% 212.34/30.47 | (177) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_752_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (85) with fresh symbols all_754_0, all_754_1 gives:
% 212.34/30.47 | (178) c_RealDef_Oreal(tc_Nat_Onat, all_754_1) = all_754_0 &
% 212.34/30.47 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_754_1 &
% 212.34/30.47 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_754_0 &
% 212.34/30.47 | $i(all_754_0) & $i(all_754_1)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (178) implies:
% 212.34/30.47 | (179) $i(all_754_1)
% 212.34/30.47 | (180) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_754_0
% 212.34/30.47 | (181) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_754_1
% 212.34/30.47 | (182) c_RealDef_Oreal(tc_Nat_Onat, all_754_1) = all_754_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (113) with fresh symbols all_759_0, all_759_1 gives:
% 212.34/30.47 | (183) c_Transcendental_Oln(all_759_1) = all_759_0 &
% 212.34/30.47 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_759_1 &
% 212.34/30.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_759_0 &
% 212.34/30.47 | $i(all_759_0) & $i(all_759_1)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (183) implies:
% 212.34/30.47 | (184) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_759_0
% 212.34/30.47 | (185) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_759_1
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (79) with fresh symbols all_769_0, all_769_1 gives:
% 212.34/30.47 | (186) c_RealDef_Oreal(tc_Nat_Onat, all_769_1) = all_769_0 &
% 212.34/30.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_769_1 &
% 212.34/30.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_769_0 &
% 212.34/30.47 | $i(all_769_0) & $i(all_769_1)
% 212.34/30.47 |
% 212.34/30.47 | ALPHA: (186) implies:
% 212.34/30.47 | (187) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_769_0
% 212.34/30.47 |
% 212.34/30.47 | DELTA: instantiating (75) with fresh symbol all_771_0 gives:
% 212.34/30.48 | (188) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_771_0 &
% 212.34/30.48 | $i(all_771_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.48 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) |
% 212.34/30.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_771_0, v1))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (188) implies:
% 212.34/30.48 | (189) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_771_0
% 212.34/30.48 | (190) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) =
% 212.34/30.48 | v1) | ~ $i(v0) |
% 212.34/30.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_771_0, v1))
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (87) with fresh symbols all_774_0, all_774_1 gives:
% 212.34/30.48 | (191) c_RComplete_Onatfloor(all_774_1) = all_774_0 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_774_0 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_774_1 &
% 212.34/30.48 | $i(all_774_0) & $i(all_774_1)
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (191) implies:
% 212.34/30.48 | (192) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_774_1
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (88) with fresh symbols all_785_0, all_785_1 gives:
% 212.34/30.48 | (193) c_RComplete_Onatfloor(all_785_1) = all_785_0 &
% 212.34/30.48 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_785_0 &
% 212.34/30.48 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_785_1 &
% 212.34/30.48 | $i(all_785_0) & $i(all_785_1)
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (193) implies:
% 212.34/30.48 | (194) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_785_1
% 212.34/30.48 | (195) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_785_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (112) with fresh symbol all_806_0 gives:
% 212.34/30.48 | (196) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_806_0 &
% 212.34/30.48 | $i(all_806_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.48 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_806_0, v0) |
% 212.34/30.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (196) implies:
% 212.34/30.48 | (197) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_806_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (128) with fresh symbol all_813_0 gives:
% 212.34/30.48 | (198) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_813_0 & $i(all_813_0) &
% 212.34/30.48 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_813_0, all_813_0) & ! [v0:
% 212.34/30.48 | any] : (v0 = all_813_0 | ~ $i(v0) | ~
% 212.34/30.48 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_813_0))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (198) implies:
% 212.34/30.48 | (199) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_813_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (1) with fresh symbols all_833_0, all_833_1, all_833_2
% 212.34/30.48 | gives:
% 212.34/30.48 | (200) ~ (all_833_0 = all_833_1) & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.34/30.48 | v_q____) = all_833_2 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_833_1 &
% 212.34/30.48 | hAPP(all_833_2, all_833_1) = all_833_0 & $i(all_833_0) &
% 212.34/30.48 | $i(all_833_1) & $i(all_833_2)
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (200) implies:
% 212.34/30.48 | (201) $i(all_833_1)
% 212.34/30.48 | (202) hAPP(all_833_2, all_833_1) = all_833_0
% 212.34/30.48 | (203) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_833_1
% 212.34/30.48 | (204) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_833_2
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (29) with fresh symbol all_849_0 gives:
% 212.34/30.48 | (205) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_849_0 &
% 212.34/30.48 | $i(all_849_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.34/30.48 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 212.34/30.48 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) |
% 212.34/30.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_849_0, v2))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (205) implies:
% 212.34/30.48 | (206) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_849_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (14) with fresh symbol all_860_0 gives:
% 212.34/30.48 | (207) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_860_0 &
% 212.34/30.48 | $i(all_860_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 212.34/30.48 | all_860_0 | ~ (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~
% 212.34/30.48 | (c_Groups_Ozero__class_Ozero(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.48 | class_RealVector_Oreal__normed__vector(v0))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (207) implies:
% 212.34/30.48 | (208) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_860_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (17) with fresh symbols all_880_0, all_880_1, all_880_2
% 212.34/30.48 | gives:
% 212.34/30.48 | (209) ~ (all_880_0 = all_880_1) & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.34/30.48 | v_pa____) = all_880_2 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_880_0 &
% 212.34/30.48 | hAPP(all_880_2, v_c____) = all_880_1 & $i(all_880_0) & $i(all_880_1)
% 212.34/30.48 | & $i(all_880_2)
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (209) implies:
% 212.34/30.48 | (210) ~ (all_880_0 = all_880_1)
% 212.34/30.48 | (211) $i(all_880_1)
% 212.34/30.48 | (212) hAPP(all_880_2, v_c____) = all_880_1
% 212.34/30.48 | (213) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_880_0
% 212.34/30.48 | (214) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_880_2
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (106) with fresh symbols all_888_0, all_888_1 gives:
% 212.34/30.48 | (215) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_888_1 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_888_0 &
% 212.34/30.48 | $i(all_888_0) & $i(all_888_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 212.34/30.48 | all_888_0 | ~ (c_Complex_Orcis(all_888_1, v0) = v1) | ~ $i(v0))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (215) implies:
% 212.34/30.48 | (216) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_888_0
% 212.34/30.48 | (217) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_888_1
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (49) with fresh symbols all_891_0, all_891_1 gives:
% 212.34/30.48 | (218) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_891_0 &
% 212.34/30.48 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_891_1 &
% 212.34/30.48 | $i(all_891_0) & $i(all_891_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.48 | (hAPP(all_891_1, v0) = v1) | ~ $i(v0) | hAPP(v1, all_891_0) = v0)
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (218) implies:
% 212.34/30.48 | (219) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_891_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (12) with fresh symbol all_904_0 gives:
% 212.34/30.48 | (220) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_904_0 &
% 212.34/30.48 | $i(all_904_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.34/30.48 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 212.34/30.48 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ~
% 212.34/30.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, all_904_0))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (220) implies:
% 212.34/30.48 | (221) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_904_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (10) with fresh symbol all_910_0 gives:
% 212.34/30.48 | (222) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_910_0 &
% 212.34/30.48 | $i(all_910_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 212.34/30.48 | all_910_0 | ~ (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~
% 212.34/30.48 | (c_Groups_Oone__class_Oone(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.48 | class_RealVector_Oreal__normed__algebra__1(v0))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (222) implies:
% 212.34/30.48 | (223) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_910_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (116) with fresh symbols all_944_0, all_944_1 gives:
% 212.34/30.48 | (224) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_944_1 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_944_0 &
% 212.34/30.48 | $i(all_944_0) & $i(all_944_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.48 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_944_1, v0) |
% 212.34/30.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_944_0, v1))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (224) implies:
% 212.34/30.48 | (225) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_944_0
% 212.34/30.48 | (226) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_944_1
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (115) with fresh symbols all_950_0, all_950_1 gives:
% 212.34/30.48 | (227) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_950_1 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_950_0 &
% 212.34/30.48 | $i(all_950_0) & $i(all_950_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.48 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_950_1, v0)
% 212.34/30.48 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_950_0,
% 212.34/30.48 | v1))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (227) implies:
% 212.34/30.48 | (228) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_950_0
% 212.34/30.48 | (229) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_950_1
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (90) with fresh symbols all_956_0, all_956_1 gives:
% 212.34/30.48 | (230) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_956_0 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_956_1 &
% 212.34/30.48 | $i(all_956_0) & $i(all_956_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 212.34/30.48 | all_956_0 | ~ (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_956_1))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (230) implies:
% 212.34/30.48 | (231) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_956_1
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (68) with fresh symbols all_959_0, all_959_1 gives:
% 212.34/30.48 | (232) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_959_0 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_959_1 &
% 212.34/30.48 | $i(all_959_0) & $i(all_959_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 212.34/30.48 | all_959_0 | ~ (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_959_1))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (232) implies:
% 212.34/30.48 | (233) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_959_1
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (77) with fresh symbol all_962_0 gives:
% 212.34/30.48 | (234) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_962_0 &
% 212.34/30.48 | $i(all_962_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.48 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_962_0, v0)
% 212.34/30.48 | | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v2) &
% 212.34/30.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (234) implies:
% 212.34/30.48 | (235) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_962_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (100) with fresh symbol all_971_0 gives:
% 212.34/30.48 | (236) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_971_0 & $i(all_971_0) &
% 212.34/30.48 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.48 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 212.34/30.48 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) |
% 212.34/30.48 | hAPP(v3, all_971_0) = v0)
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (236) implies:
% 212.34/30.48 | (237) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_971_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (102) with fresh symbol all_974_0 gives:
% 212.34/30.48 | (238) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_974_0 & $i(all_974_0) &
% 212.34/30.48 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.48 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 212.34/30.48 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Omonoid__mult(v1) | hAPP(v3,
% 212.34/30.48 | all_974_0) = v0)
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (238) implies:
% 212.34/30.48 | (239) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_974_0
% 212.34/30.48 |
% 212.34/30.48 | DELTA: instantiating (18) with fresh symbols all_980_0, all_980_1, all_980_2,
% 212.34/30.48 | all_980_3 gives:
% 212.34/30.48 | (240) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_980_3 &
% 212.34/30.48 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_980_1 &
% 212.34/30.48 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_980_0 &
% 212.34/30.48 | hAPP(all_980_1, all_980_0) = all_980_2 & hAPP(all_980_3, v_c____) =
% 212.34/30.48 | all_980_2 & $i(all_980_0) & $i(all_980_1) & $i(all_980_2) &
% 212.34/30.48 | $i(all_980_3)
% 212.34/30.48 |
% 212.34/30.48 | ALPHA: (240) implies:
% 212.34/30.48 | (241) hAPP(all_980_3, v_c____) = all_980_2
% 212.34/30.48 | (242) hAPP(all_980_1, all_980_0) = all_980_2
% 212.34/30.48 | (243) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_980_0
% 212.34/30.48 | (244) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_980_1
% 212.34/30.48 | (245) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_980_3
% 212.34/30.48 |
% 212.34/30.49 | DELTA: instantiating (111) with fresh symbol all_982_0 gives:
% 212.34/30.49 | (246) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_982_0 &
% 212.34/30.49 | $i(all_982_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 212.34/30.49 | ~ (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 212.34/30.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_982_0, v1) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_982_0, v0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (246) implies:
% 212.34/30.49 | (247) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_982_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (80) with fresh symbols all_985_0, all_985_1 gives:
% 212.34/30.49 | (248) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_985_0 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_985_1 &
% 212.34/30.49 | $i(all_985_0) & $i(all_985_1) & ! [v0: any] : (v0 = all_985_0 | ~
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = all_985_1) | ~ $i(v0)) & !
% 212.34/30.49 | [v0: int] : (v0 = all_985_1 | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.49 | all_985_0) = v0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (248) implies:
% 212.34/30.49 | (249) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_985_1
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (123) with fresh symbols all_988_0, all_988_1 gives:
% 212.34/30.49 | (250) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_988_0 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_988_1 &
% 212.34/30.49 | $i(all_988_0) & $i(all_988_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.49 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_988_1, v1)
% 212.34/30.49 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_988_1, v0)
% 212.34/30.49 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_988_0,
% 212.34/30.49 | v0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (250) implies:
% 212.34/30.49 | (251) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_988_1
% 212.34/30.49 | (252) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_988_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (34) with fresh symbols all_992_0, all_992_1, all_992_2
% 212.34/30.49 | gives:
% 212.34/30.49 | (253) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_992_1 &
% 212.34/30.49 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_992_2 &
% 212.34/30.49 | hAPP(all_992_2, all_992_1) = all_992_0 & $i(all_992_0) &
% 212.34/30.49 | $i(all_992_1) & $i(all_992_2) & ! [v0: $i] : ! [v1: $i] : (v1 = v0
% 212.34/30.49 | | ~ (hAPP(all_992_0, v0) = v1) | ~ $i(v0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (253) implies:
% 212.34/30.49 | (254) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_992_1
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (76) with fresh symbol all_995_0 gives:
% 212.34/30.49 | (255) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_995_0 &
% 212.34/30.49 | $i(all_995_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.49 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 212.34/30.49 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 &
% 212.34/30.49 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_995_0) = v3
% 212.34/30.49 | & $i(v3) & $i(v2) &
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (255) implies:
% 212.34/30.49 | (256) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_995_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (51) with fresh symbols all_998_0, all_998_1, all_998_2
% 212.34/30.49 | gives:
% 212.34/30.49 | (257) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_998_1 &
% 212.34/30.49 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_998_2 &
% 212.34/30.49 | hAPP(all_998_2, all_998_1) = all_998_0 & $i(all_998_0) &
% 212.34/30.49 | $i(all_998_1) & $i(all_998_2) & ! [v0: $i] : ! [v1: $i] : (v1 = v0
% 212.34/30.49 | | ~ (hAPP(all_998_0, v0) = v1) | ~ $i(v0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (257) implies:
% 212.34/30.49 | (258) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_998_1
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (121) with fresh symbols all_1004_0, all_1004_1 gives:
% 212.34/30.49 | (259) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1004_0 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1004_1 &
% 212.34/30.49 | $i(all_1004_0) & $i(all_1004_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.49 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1004_1, v1) |
% 212.34/30.49 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1004_1, v0) |
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1004_0, v0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (259) implies:
% 212.34/30.49 | (260) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1004_1
% 212.34/30.49 | (261) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1004_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (120) with fresh symbols all_1007_0, all_1007_1 gives:
% 212.34/30.49 | (262) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1007_0 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1007_1 &
% 212.34/30.49 | $i(all_1007_0) & $i(all_1007_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.49 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1007_0) |
% 212.34/30.49 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1007_1, v0) |
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_1007_1))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (262) implies:
% 212.34/30.49 | (263) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1007_1
% 212.34/30.49 | (264) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1007_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (82) with fresh symbol all_1013_0 gives:
% 212.34/30.49 | (265) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1013_0 &
% 212.34/30.49 | $i(all_1013_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.34/30.49 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 212.34/30.49 | (c_RComplete_Onatfloor(v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1013_0, v1)
% 212.34/30.49 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) |
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (265) implies:
% 212.34/30.49 | (266) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1013_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (16) with fresh symbol all_1022_0 gives:
% 212.34/30.49 | (267) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1022_0 &
% 212.34/30.49 | $i(all_1022_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.34/30.49 | $i] : ! [v4: $i] : ( ~
% 212.34/30.49 | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v0) = v3) |
% 212.34/30.49 | ~ (hAPP(v2, v3) = v4) | ~ (hAPP(all_1022_0, v1) = v2) | ~ $i(v1)
% 212.34/30.49 | | ~ $i(v0) | (c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,
% 212.34/30.49 | v1, v0) = v4 & $i(v4)))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (267) implies:
% 212.34/30.49 | (268) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1022_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (133) with fresh symbol all_1025_0 gives:
% 212.34/30.49 | (269) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1025_0 &
% 212.34/30.49 | $i(all_1025_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.49 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, all_1025_0) =
% 212.34/30.49 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] :
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & c_RComplete_Onatfloor(v0)
% 212.34/30.49 | = v2 & $i(v3) & $i(v2) &
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (269) implies:
% 212.34/30.49 | (270) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1025_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (103) with fresh symbols all_1031_0, all_1031_1 gives:
% 212.34/30.49 | (271) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1031_1 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1031_0 &
% 212.34/30.49 | $i(all_1031_0) & $i(all_1031_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 212.34/30.49 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v2) |
% 212.34/30.49 | ~ $i(v1) | ~ $i(v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1031_0, v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1031_1, v1) |
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (271) implies:
% 212.34/30.49 | (272) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1031_1
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (125) with fresh symbols all_1046_0, all_1046_1 gives:
% 212.34/30.49 | (273) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1046_0 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1046_1 &
% 212.34/30.49 | $i(all_1046_0) & $i(all_1046_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.49 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1046_0, v0) =
% 212.34/30.49 | v1) | ~ $i(v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1046_1, v0)
% 212.34/30.49 | | ? [v2: $i] : (c_Transcendental_Oln(v1) = v2 & $i(v2) &
% 212.34/30.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (273) implies:
% 212.34/30.49 | (274) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1046_1
% 212.34/30.49 | (275) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1046_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (84) with fresh symbol all_1055_0 gives:
% 212.34/30.49 | (276) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1055_0 & $i(all_1055_0)
% 212.34/30.49 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 212.34/30.49 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v4:
% 212.34/30.49 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, all_1055_0) =
% 212.34/30.49 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 212.34/30.49 | v4, v0)))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (276) implies:
% 212.34/30.49 | (277) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1055_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (89) with fresh symbols all_1073_0, all_1073_1 gives:
% 212.34/30.49 | (278) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1073_0 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1073_1 &
% 212.34/30.49 | $i(all_1073_0) & $i(all_1073_1) & ! [v0: any] : ! [v1: $i] : (v0 =
% 212.34/30.49 | all_1073_0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0)
% 212.34/30.49 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 212.34/30.49 | all_1073_1)) & ! [v0: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 212.34/30.49 | all_1073_0) = v0) |
% 212.34/30.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 212.34/30.49 | all_1073_1))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (278) implies:
% 212.34/30.49 | (279) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1073_1
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (25) with fresh symbols all_1083_0, all_1083_1 gives:
% 212.34/30.49 | (280) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1083_0 &
% 212.34/30.49 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1083_1 &
% 212.34/30.49 | $i(all_1083_0) & $i(all_1083_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.49 | (hAPP(all_1083_1, v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 212.34/30.49 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, v0) = v2
% 212.34/30.49 | & hAPP(all_1083_0, v2) = v1 & $i(v2) & $i(v1)))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (280) implies:
% 212.34/30.49 | (281) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1083_1
% 212.34/30.49 | (282) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1083_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (39) with fresh symbols all_1092_0, all_1092_1,
% 212.34/30.49 | all_1092_2, all_1092_3, all_1092_4 gives:
% 212.34/30.49 | (283) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1092_4 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1092_2 &
% 212.34/30.49 | $i(all_1092_1) & $i(all_1092_2) & $i(all_1092_4) & ((all_1092_0 =
% 212.34/30.49 | all_1092_2 & hAPP(all_1092_4, all_1092_1) = all_1092_2) | ( ~
% 212.34/30.49 | (all_1092_2 = all_1092_3) & hAPP(all_1092_4, v_c____) =
% 212.34/30.49 | all_1092_3 & $i(all_1092_3)))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (283) implies:
% 212.34/30.49 | (284) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1092_2
% 212.34/30.49 | (285) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1092_4
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (118) with fresh symbols all_1094_0, all_1094_1 gives:
% 212.34/30.49 | (286) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1094_0 &
% 212.34/30.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1094_1 &
% 212.34/30.49 | $i(all_1094_0) & $i(all_1094_1) & ! [v0: any] : (v0 = all_1094_0 |
% 212.34/30.49 | ~ (c_Transcendental_Oln(v0) = all_1094_1) | ~ $i(v0) | ~
% 212.34/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1094_1, v0)) &
% 212.34/30.49 | ! [v0: int] : (v0 = all_1094_1 | ~ (c_Transcendental_Oln(all_1094_0)
% 212.34/30.49 | = v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.34/30.49 | all_1094_1, all_1094_0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (286) implies:
% 212.34/30.49 | (287) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1094_1
% 212.34/30.49 | (288) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1094_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (134) with fresh symbol all_1106_0 gives:
% 212.34/30.49 | (289) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1106_0 &
% 212.34/30.49 | $i(all_1106_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.34/30.49 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 212.34/30.49 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v4, v6) = v7) | ~
% 212.34/30.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v5) | ~
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v5) = v6) | ~
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 212.34/30.49 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v3) = v4) |
% 212.34/30.49 | ~ $i(v1) | ~ $i(v0) |
% 212.34/30.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1106_0,
% 212.34/30.49 | v7))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (289) implies:
% 212.34/30.49 | (290) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1106_0
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (24) with fresh symbols all_1109_0, all_1109_1,
% 212.34/30.49 | all_1109_2 gives:
% 212.34/30.49 | (291) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1109_1) =
% 212.34/30.49 | all_1109_0 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) =
% 212.34/30.49 | all_1109_2 & hAPP(all_1109_2, v_c____) = all_1109_1 & $i(all_1109_0)
% 212.34/30.49 | & $i(all_1109_1) & $i(all_1109_2) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.34/30.49 | (hAPP(all_1109_2, v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 212.34/30.49 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 &
% 212.34/30.49 | $i(v2) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.34/30.49 | all_1109_0, v2)))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (291) implies:
% 212.34/30.49 | (292) hAPP(all_1109_2, v_c____) = all_1109_1
% 212.34/30.49 | (293) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1109_2
% 212.34/30.49 |
% 212.34/30.49 | DELTA: instantiating (126) with fresh symbol all_1112_0 gives:
% 212.34/30.49 | (294) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1112_0 &
% 212.34/30.49 | $i(all_1112_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.34/30.49 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 212.34/30.49 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v4, v6) = v7) | ~
% 212.34/30.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v5) | ~
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v5) = v6) | ~
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 212.34/30.49 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 212.34/30.49 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v3) = v4) |
% 212.34/30.49 | ~ $i(v1) | ~ $i(v0) |
% 212.34/30.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 212.34/30.49 | all_1112_0))
% 212.34/30.49 |
% 212.34/30.49 | ALPHA: (294) implies:
% 212.88/30.49 | (295) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1112_0
% 212.88/30.49 |
% 212.88/30.49 | DELTA: instantiating (37) with fresh symbols all_1115_0, all_1115_1 gives:
% 212.88/30.49 | (296) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1115_0 &
% 212.88/30.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1115_1 &
% 212.88/30.49 | $i(all_1115_0) & $i(all_1115_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 212.88/30.49 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1115_0,
% 212.88/30.49 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.88/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1115_1, v1) |
% 212.88/30.49 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1115_1, v0) |
% 212.88/30.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1115_1, v3))
% 212.88/30.49 |
% 212.88/30.50 | ALPHA: (296) implies:
% 212.88/30.50 | (297) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1115_1
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (86) with fresh symbol all_1131_0 gives:
% 212.88/30.50 | (298) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1131_0 &
% 212.88/30.50 | $i(all_1131_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.88/30.50 | $i] : (v3 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 212.88/30.50 | (c_RComplete_Onatfloor(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ?
% 212.88/30.50 | [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 212.88/30.50 | all_1131_0) = v4 & $i(v4) & ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (298) implies:
% 212.88/30.50 | (299) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1131_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (42) with fresh symbols all_1137_0, all_1137_1 gives:
% 212.88/30.50 | (300) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1137_0 &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1137_1 &
% 212.88/30.50 | $i(all_1137_0) & $i(all_1137_1) & ! [v0: any] : ! [v1: $i] : !
% 212.88/30.50 | [v2: $i] : (v0 = all_1137_1 | ~ (hAPP(v1, v0) = v2) | ~
% 212.88/30.50 | (hAPP(all_1137_0, v0) = v1) | ~ $i(v0) |
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1137_1, v2)) &
% 212.88/30.50 | ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(v0, all_1137_1) = v1) | ~
% 212.88/30.50 | (hAPP(all_1137_0, all_1137_1) = v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1137_1, v1))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (300) implies:
% 212.88/30.50 | (301) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1137_1
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (69) with fresh symbols all_1143_0, all_1143_1 gives:
% 212.88/30.50 | (302) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1143_1 &
% 212.88/30.50 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1143_0 &
% 212.88/30.50 | $i(all_1143_0) & $i(all_1143_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.50 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1143_1) |
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 212.88/30.50 | all_1143_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.50 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_1143_0)
% 212.88/30.50 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1143_1))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (302) implies:
% 212.88/30.50 | (303) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1143_0
% 212.88/30.50 | (304) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1143_1
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (21) with fresh symbols all_1149_0, all_1149_1,
% 212.88/30.50 | all_1149_2 gives:
% 212.88/30.50 | (305) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1149_0 &
% 212.88/30.50 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1149_1 &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1149_2 &
% 212.88/30.50 | $i(all_1149_0) & $i(all_1149_1) & $i(all_1149_2) & ! [v0: any] : !
% 212.88/30.50 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = all_1149_0 | v0 =
% 212.88/30.50 | all_1149_2 | ~ (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,
% 212.88/30.50 | v0) = v1) | ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1149_1, v1) =
% 212.88/30.50 | v2) | ~ $i(v0))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (305) implies:
% 212.88/30.50 | (306) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1149_2
% 212.88/30.50 | (307) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1149_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (31) with fresh symbols all_1155_0, all_1155_1 gives:
% 212.88/30.50 | (308) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1155_0 &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1155_1 &
% 212.88/30.50 | $i(all_1155_0) & $i(all_1155_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 212.88/30.50 | any] : ! [v3: $i] : ! [v4: $i] : (v2 = all_1155_1 | v1 = v0 | ~
% 212.88/30.50 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1155_0,
% 212.88/30.50 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (308) implies:
% 212.88/30.50 | (309) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1155_1
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (45) with fresh symbols all_1158_0, all_1158_1,
% 212.88/30.50 | all_1158_2 gives:
% 212.88/30.50 | (310) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1158_1 &
% 212.88/30.50 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1158_2 &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1158_0 &
% 212.88/30.50 | $i(all_1158_0) & $i(all_1158_1) & $i(all_1158_2) & ! [v0: any] : !
% 212.88/30.50 | [v1: any] : ! [v2: $i] : (v1 = all_1158_0 | v0 = all_1158_1 | ~
% 212.88/30.50 | (hAPP(v2, v0) = v1) | ~ (hAPP(all_1158_2, v1) = v2) | ~ $i(v1) |
% 212.88/30.50 | ~ $i(v0))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (310) implies:
% 212.88/30.50 | (311) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1158_1
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (91) with fresh symbols all_1163_0, all_1163_1 gives:
% 212.88/30.50 | (312) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1163_0 &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1163_1 &
% 212.88/30.50 | $i(all_1163_0) & $i(all_1163_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.50 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1163_0, v0) |
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1163_1, v1)) &
% 212.88/30.50 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) =
% 212.88/30.50 | v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1163_1, v1) |
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1163_0, v0))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (312) implies:
% 212.88/30.50 | (313) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1163_1
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (95) with fresh symbols all_1166_0, all_1166_1 gives:
% 212.88/30.50 | (314) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1166_1 &
% 212.88/30.50 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1166_0 &
% 212.88/30.50 | $i(all_1166_0) & $i(all_1166_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.50 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1166_1, v1) |
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1166_0,
% 212.88/30.50 | v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0)
% 212.88/30.50 | = v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1166_0, v0)
% 212.88/30.50 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1166_1, v1))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (314) implies:
% 212.88/30.50 | (315) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1166_0
% 212.88/30.50 | (316) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1166_1
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (96) with fresh symbol all_1171_0 gives:
% 212.88/30.50 | (317) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1171_0 &
% 212.88/30.50 | $i(all_1171_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.88/30.50 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 212.88/30.50 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 212.88/30.50 | $i(v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1171_0, v1)
% 212.88/30.50 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatceiling(v3) = v4 &
% 212.88/30.50 | c_RComplete_Onatceiling(v1) = v5 &
% 212.88/30.50 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) &
% 212.88/30.50 | $i(v4)))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (317) implies:
% 212.88/30.50 | (318) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1171_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (73) with fresh symbol all_1174_0 gives:
% 212.88/30.50 | (319) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1174_0 &
% 212.88/30.50 | $i(all_1174_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 212.88/30.50 | ~ c_SEQ_OBseq(v1, v0) | ~
% 212.88/30.50 | class_RealVector_Oreal__normed__vector(v1) | ? [v2: $i] : ($i(v2)
% 212.88/30.50 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1174_0, v2)
% 212.88/30.50 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.88/30.50 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v0,
% 212.88/30.50 | v3) = v4) | ~ $i(v3) |
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (319) implies:
% 212.88/30.50 | (320) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1174_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (70) with fresh symbol all_1180_0 gives:
% 212.88/30.50 | (321) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1180_0 &
% 212.88/30.50 | $i(all_1180_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.88/30.50 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Complex_Oexpi(v1) = v2) |
% 212.88/30.50 | ~ (c_Complex_Oexpi(v0) = v4) | ~ (hAPP(v3, v4) = v5) | ~
% 212.88/30.50 | (hAPP(all_1180_0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] :
% 212.88/30.50 | (c_Complex_Oexpi(v6) = v5 &
% 212.88/30.50 | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v1, v0) = v6 &
% 212.88/30.50 | $i(v6) & $i(v5)))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (321) implies:
% 212.88/30.50 | (322) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1180_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (127) with fresh symbol all_1189_0 gives:
% 212.88/30.50 | (323) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1189_0 &
% 212.88/30.50 | $i(all_1189_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.88/30.50 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 212.88/30.50 | $i(v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1189_0)
% 212.88/30.50 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 212.88/30.50 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.88/30.50 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 212.88/30.50 | $i(v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 212.88/30.50 | all_1189_0))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (323) implies:
% 212.88/30.50 | (324) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1189_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (83) with fresh symbol all_1192_0 gives:
% 212.88/30.50 | (325) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1192_0 &
% 212.88/30.50 | $i(all_1192_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.88/30.50 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 212.88/30.50 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 212.88/30.50 | $i(v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1192_0, v1)
% 212.88/30.50 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatfloor(v3) = v4 &
% 212.88/30.50 | c_RComplete_Onatfloor(v1) = v5 &
% 212.88/30.50 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) &
% 212.88/30.50 | $i(v4)))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (325) implies:
% 212.88/30.50 | (326) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1192_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (5) with fresh symbols all_1201_0, all_1201_1,
% 212.88/30.50 | all_1201_2, all_1201_3, all_1201_4, all_1201_5 gives:
% 212.88/30.50 | (327) c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.88/30.50 | all_1201_0) = all_1201_5 &
% 212.88/30.50 | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.88/30.50 | v_q____) = all_1201_5 &
% 212.88/30.50 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1201_2) =
% 212.88/30.50 | all_1201_1 & c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1,
% 212.88/30.50 | v_q____) = all_1201_0 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.88/30.50 | v_q____) = all_1201_4 &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1201_3 &
% 212.88/30.50 | hAPP(all_1201_4, all_1201_3) = all_1201_2 & $i(all_1201_0) &
% 212.88/30.50 | $i(all_1201_1) & $i(all_1201_2) & $i(all_1201_3) & $i(all_1201_4) &
% 212.88/30.50 | $i(all_1201_5)
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (327) implies:
% 212.88/30.50 | (328) hAPP(all_1201_4, all_1201_3) = all_1201_2
% 212.88/30.50 | (329) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1201_3
% 212.88/30.50 | (330) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1201_4
% 212.88/30.50 | (331) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1, v_q____) =
% 212.88/30.50 | all_1201_0
% 212.88/30.50 | (332) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1201_2) =
% 212.88/30.50 | all_1201_1
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (131) with fresh symbol all_1211_0 gives:
% 212.88/30.50 | (333) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1211_0 &
% 212.88/30.50 | $i(all_1211_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.88/30.50 | $i] : ! [v4: $i] : ( ~
% 212.88/30.50 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 212.88/30.50 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 212.88/30.50 | v3) | ~ $i(v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1211_0, v1) |
% 212.88/30.50 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1211_0, v0) |
% 212.88/30.50 | ? [v5: $i] : (c_Transcendental_Oln(v5) = v4 &
% 212.88/30.50 | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v0) = v5 &
% 212.88/30.50 | $i(v5) & $i(v4)))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (333) implies:
% 212.88/30.50 | (334) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1211_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (53) with fresh symbols all_1214_0, all_1214_1,
% 212.88/30.50 | all_1214_2, all_1214_3 gives:
% 212.88/30.50 | (335) c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.88/30.50 | all_1214_1) = all_1214_3 &
% 212.88/30.50 | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.88/30.50 | v_pa____) = all_1214_3 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.88/30.50 | all_1214_1) = all_1214_0 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.88/30.50 | v_pa____) = all_1214_2 & $i(all_1214_0) & $i(all_1214_1) &
% 212.88/30.50 | $i(all_1214_2) & $i(all_1214_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.50 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, v0) =
% 212.88/30.50 | v1) | ~ $i(v0) | ? [v2: $i] : (hAPP(all_1214_0, v0) = v2 &
% 212.88/30.50 | hAPP(all_1214_2, v1) = v2 & $i(v2)))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (335) implies:
% 212.88/30.50 | (336) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1214_2
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (13) with fresh symbol all_1217_0 gives:
% 212.88/30.50 | (337) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1217_0 &
% 212.88/30.50 | $i(all_1217_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.88/30.50 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 212.88/30.50 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 212.88/30.50 | $i] : (( ~ (v2 = all_1217_0) | (v3 = v0 &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(v1) = v0)) & (v2 = all_1217_0 | (
% 212.88/30.50 | ~ (v3 = v0) & c_Groups_Ozero__class_Ozero(v1) = v3 &
% 212.88/30.50 | $i(v3)))))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (337) implies:
% 212.88/30.50 | (338) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1217_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (30) with fresh symbol all_1220_0 gives:
% 212.88/30.50 | (339) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1220_0 &
% 212.88/30.50 | $i(all_1220_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.88/30.50 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 212.88/30.50 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 212.88/30.50 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.88/30.50 | v2, all_1220_0) | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1)
% 212.88/30.50 | = v0)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 212.88/30.50 | v2, all_1220_0) | ( ~ (v3 = v0) &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3)))))
% 212.88/30.50 |
% 212.88/30.50 | ALPHA: (339) implies:
% 212.88/30.50 | (340) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1220_0
% 212.88/30.50 |
% 212.88/30.50 | DELTA: instantiating (19) with fresh symbols all_1226_0, all_1226_1 gives:
% 212.88/30.50 | (341) c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.88/30.50 | v_pa____) = all_1226_1 &
% 212.88/30.50 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1226_0 &
% 212.88/30.50 | $i(all_1226_0) & $i(all_1226_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.50 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.88/30.50 | v0) = v1) | ~ $i(v0) | ~
% 212.88/30.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, all_1226_1) | ?
% 212.88/30.50 | [v2: $i] : ? [v3: $i] : ? [v4: int] :
% 212.88/30.50 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v0) = v2 & $i(v3) & $i(v2)
% 212.88/30.50 | &
% 212.88/30.50 | (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.88/30.50 | tc_Complex_Ocomplex, v2) | (v4 = all_1226_0 & hAPP(v2, v3) =
% 212.88/30.50 | all_1226_0))))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (341) implies:
% 212.88/30.51 | (342) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1226_0
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (53) with fresh symbols all_1235_0, all_1235_1,
% 212.88/30.51 | all_1235_2, all_1235_3 gives:
% 212.88/30.51 | (343) c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.88/30.51 | all_1235_1) = all_1235_3 &
% 212.88/30.51 | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,
% 212.88/30.51 | v_pa____) = all_1235_3 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.88/30.51 | all_1235_1) = all_1235_0 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.88/30.51 | v_pa____) = all_1235_2 & $i(all_1235_0) & $i(all_1235_1) &
% 212.88/30.51 | $i(all_1235_2) & $i(all_1235_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.51 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, v0) =
% 212.88/30.51 | v1) | ~ $i(v0) | ? [v2: $i] : (hAPP(all_1235_0, v0) = v2 &
% 212.88/30.51 | hAPP(all_1235_2, v1) = v2 & $i(v2)))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (343) implies:
% 212.88/30.51 | (344) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1235_2
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (32) with fresh symbols all_1238_0, all_1238_1 gives:
% 212.88/30.51 | (345) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1238_0 &
% 212.88/30.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1238_1 &
% 212.88/30.51 | $i(all_1238_0) & $i(all_1238_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 212.88/30.51 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1238_1 |
% 212.88/30.51 | v1 = v0 | ~ (hAPP(v5, v2) = v4) | ~ (hAPP(v3, v2) = v4) | ~
% 212.88/30.51 | (hAPP(all_1238_0, v1) = v3) | ~ (hAPP(all_1238_0, v0) = v5) | ~
% 212.88/30.51 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (345) implies:
% 212.88/30.51 | (346) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1238_1
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (4) with fresh symbols all_1241_0, all_1241_1,
% 212.88/30.51 | all_1241_2, all_1241_3, all_1241_4, all_1241_5 gives:
% 212.88/30.51 | (347) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1241_3) =
% 212.88/30.51 | all_1241_2 & c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1241_2,
% 212.88/30.51 | v_q____) = all_1241_1 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.88/30.51 | all_1241_1) = all_1241_0 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 212.88/30.51 | v_q____) = all_1241_5 &
% 212.88/30.51 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1241_4 &
% 212.88/30.51 | hAPP(all_1241_5, all_1241_4) = all_1241_3 & $i(all_1241_0) &
% 212.88/30.51 | $i(all_1241_1) & $i(all_1241_2) & $i(all_1241_3) & $i(all_1241_4) &
% 212.88/30.51 | $i(all_1241_5) & ~
% 212.88/30.51 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,
% 212.88/30.51 | tc_Complex_Ocomplex, all_1241_0)
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (347) implies:
% 212.88/30.51 | (348) $i(all_1241_1)
% 212.88/30.51 | (349) hAPP(all_1241_5, all_1241_4) = all_1241_3
% 212.88/30.51 | (350) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1241_4
% 212.88/30.51 | (351) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1241_5
% 212.88/30.51 | (352) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1241_1) = all_1241_0
% 212.88/30.51 | (353) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1241_2, v_q____) =
% 212.88/30.51 | all_1241_1
% 212.88/30.51 | (354) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1241_3) =
% 212.88/30.51 | all_1241_2
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (15) with fresh symbol all_1263_0 gives:
% 212.88/30.51 | (355) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1263_0 &
% 212.88/30.51 | $i(all_1263_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 212.88/30.51 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 212.88/30.51 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 212.88/30.51 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.88/30.51 | all_1263_0, v2) | ( ~ (v3 = v0) &
% 212.88/30.51 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3))) &
% 212.88/30.51 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1263_0, v2)
% 212.88/30.51 | | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1) = v0))))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (355) implies:
% 212.88/30.51 | (356) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1263_0
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (38) with fresh symbols all_1269_0, all_1269_1 gives:
% 212.88/30.51 | (357) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1269_0 &
% 212.88/30.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1269_1 &
% 212.88/30.51 | $i(all_1269_0) & $i(all_1269_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 212.88/30.51 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 212.88/30.51 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1269_0, v2) = v3) |
% 212.88/30.51 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1269_1, v2) |
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v5))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (357) implies:
% 212.88/30.51 | (358) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1269_1
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (132) with fresh symbols all_1275_0, all_1275_1 gives:
% 212.88/30.51 | (359) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1275_1 &
% 212.88/30.51 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1275_0 & $i(all_1275_0)
% 212.88/30.51 | & $i(all_1275_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.88/30.51 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~
% 212.88/30.51 | (hAPP(v3, v0) = v5) | ~ (hAPP(all_1275_1, v2) = v3) | ~ $i(v2) |
% 212.88/30.51 | ~ $i(v1) | ~ $i(v0) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4,
% 212.88/30.51 | v5) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1275_0,
% 212.88/30.51 | v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (359) implies:
% 212.88/30.51 | (360) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1275_0
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (40) with fresh symbol all_1278_0 gives:
% 212.88/30.51 | (361) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1278_0 &
% 212.88/30.51 | $i(all_1278_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 212.88/30.51 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 212.88/30.51 | (c_RealVector_Onorm__class_Onorm(v2, v3) = v4) | ~
% 212.88/30.51 | (c_Rings_Oinverse__class_Oinverse(v2, v0) = v3) | ~
% 212.88/30.51 | (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v1) = v5) | ~
% 212.88/30.51 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 212.88/30.51 | class_RealVector_Oreal__normed__div__algebra(v2) | ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1278_0, v1) |
% 212.88/30.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5) | ?
% 212.88/30.51 | [v6: $i] : (c_RealVector_Onorm__class_Onorm(v2, v0) = v6 & $i(v6) &
% 212.88/30.51 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v6)))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (361) implies:
% 212.88/30.51 | (362) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1278_0
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (119) with fresh symbols all_1281_0, all_1281_1 gives:
% 212.88/30.51 | (363) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1281_0 &
% 212.88/30.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1281_1 &
% 212.88/30.51 | $i(all_1281_0) & $i(all_1281_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.51 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_1281_1) |
% 212.88/30.51 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1281_1, v0) |
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1281_0)) &
% 212.88/30.51 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Transcendental_Oln(v0) = v1) | ~
% 212.88/30.51 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 212.88/30.51 | all_1281_0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.88/30.51 | all_1281_1, v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.88/30.51 | v1, all_1281_1))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (363) implies:
% 212.88/30.51 | (364) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1281_1
% 212.88/30.51 | (365) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1281_0
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (117) with fresh symbols all_1284_0, all_1284_1 gives:
% 212.88/30.51 | (366) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1284_0 &
% 212.88/30.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1284_1 &
% 212.88/30.51 | $i(all_1284_0) & $i(all_1284_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 212.88/30.51 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1284_0, v0) |
% 212.88/30.51 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1284_1, v0) |
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1284_1, v1)) &
% 212.88/30.51 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Transcendental_Oln(v0) = v1) | ~
% 212.88/30.51 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 212.88/30.51 | all_1284_1, v1) | ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1284_1, v0) |
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1284_0, v0))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (366) implies:
% 212.88/30.51 | (367) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1284_1
% 212.88/30.51 | (368) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1284_0
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (71) with fresh symbols all_1293_0, all_1293_1,
% 212.88/30.51 | all_1293_2 gives:
% 212.88/30.51 | (369) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1293_0 &
% 212.88/30.51 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1293_1 &
% 212.88/30.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1293_2 &
% 212.88/30.51 | $i(all_1293_0) & $i(all_1293_1) & $i(all_1293_2) & ! [v0: $i] : !
% 212.88/30.51 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 212.88/30.51 | all_1293_1) = v1) | ~ $i(v0) | ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1293_2, v0)
% 212.88/30.51 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatfloor(v1) = v2 &
% 212.88/30.51 | c_RComplete_Onatfloor(v0) = v3 &
% 212.88/30.51 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1293_0) = v2 &
% 212.88/30.51 | $i(v3) & $i(v2)))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (369) implies:
% 212.88/30.51 | (370) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1293_2
% 212.88/30.51 | (371) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1293_1
% 212.88/30.51 | (372) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1293_0
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (74) with fresh symbol all_1302_0 gives:
% 212.88/30.51 | (373) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1302_0 &
% 212.88/30.51 | $i(all_1302_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 212.88/30.51 | | ~ $i(v1) | ~ $i(v0) | ~
% 212.88/30.51 | class_RealVector_Oreal__normed__vector(v2) | ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1302_0, v1) |
% 212.88/30.51 | c_SEQ_OBseq(v2, v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 212.88/30.51 | (c_RealVector_Onorm__class_Onorm(v2, v4) = v5 & hAPP(v0, v3) = v4 &
% 212.88/30.51 | $i(v5) & $i(v4) & $i(v3) & ~
% 212.88/30.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1)))
% 212.88/30.51 |
% 212.88/30.51 | ALPHA: (373) implies:
% 212.88/30.51 | (374) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1302_0
% 212.88/30.51 |
% 212.88/30.51 | DELTA: instantiating (122) with fresh symbols all_1304_0, all_1304_1 gives:
% 213.38/30.51 | (375) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1304_0 &
% 213.38/30.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1304_1 &
% 213.38/30.51 | $i(all_1304_0) & $i(all_1304_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 213.38/30.51 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 213.38/30.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1304_0, v0)
% 213.38/30.51 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1304_1,
% 213.38/30.51 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.51 | all_1304_1, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 213.38/30.51 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 213.38/30.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1304_1, v1)
% 213.38/30.51 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1304_1,
% 213.38/30.51 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.51 | all_1304_0, v0))
% 213.38/30.51 |
% 213.38/30.51 | ALPHA: (375) implies:
% 213.38/30.51 | (376) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1304_1
% 213.38/30.51 | (377) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1304_0
% 213.38/30.51 |
% 213.38/30.51 | DELTA: instantiating (64) with fresh symbols all_1325_0, all_1325_1,
% 213.38/30.51 | all_1325_2 gives:
% 213.38/30.51 | (378) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1325_0 &
% 213.38/30.51 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1325_1 &
% 213.38/30.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1325_2 &
% 213.38/30.51 | $i(all_1325_0) & $i(all_1325_1) & $i(all_1325_2) & ! [v0: $i] : !
% 213.38/30.51 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 213.38/30.51 | all_1325_1) = v1) | ~ $i(v0) | ~
% 213.38/30.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1325_2, v0)
% 213.38/30.51 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatceiling(v1) = v2 &
% 213.38/30.51 | c_RComplete_Onatceiling(v0) = v3 &
% 213.38/30.51 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1325_0) = v2 &
% 213.38/30.51 | $i(v3) & $i(v2)))
% 213.38/30.51 |
% 213.38/30.51 | ALPHA: (378) implies:
% 213.38/30.51 | (379) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1325_2
% 213.38/30.51 | (380) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1325_1
% 213.38/30.51 | (381) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1325_0
% 213.38/30.51 |
% 213.38/30.51 | DELTA: instantiating (20) with fresh symbols all_1346_0, all_1346_1,
% 213.38/30.51 | all_1346_2, all_1346_3, all_1346_4 gives:
% 213.38/30.51 | (382) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1346_2) =
% 213.38/30.51 | all_1346_1 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) =
% 213.38/30.51 | all_1346_0 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) =
% 213.38/30.51 | all_1346_4 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 213.38/30.51 | all_1346_3 & hAPP(all_1346_4, all_1346_3) = all_1346_2 &
% 213.38/30.51 | $i(all_1346_0) & $i(all_1346_1) & $i(all_1346_2) & $i(all_1346_3) &
% 213.38/30.51 | $i(all_1346_4) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1346_0,
% 213.38/30.51 | v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 213.38/30.51 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 &
% 213.38/30.51 | $i(v2) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.51 | all_1346_1, v2)))
% 213.38/30.51 |
% 213.38/30.51 | ALPHA: (382) implies:
% 213.38/30.51 | (383) hAPP(all_1346_4, all_1346_3) = all_1346_2
% 213.38/30.51 | (384) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1346_3
% 213.38/30.51 | (385) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1346_4
% 213.38/30.51 | (386) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1346_0
% 213.38/30.51 |
% 213.38/30.51 | DELTA: instantiating (98) with fresh symbols all_1355_0, all_1355_1 gives:
% 213.38/30.51 | (387) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1355_1 &
% 213.38/30.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1355_0 &
% 213.38/30.51 | $i(all_1355_0) & $i(all_1355_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.51 | $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) |
% 213.38/30.51 | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v2) = v3)
% 213.38/30.51 | | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1355_1, v1)
% 213.38/30.51 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1355_0, v0) |
% 213.38/30.51 | ? [v4: $i] : ? [v5: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,
% 213.38/30.51 | v5, v0) = v4 & c_RComplete_Onatfloor(v3) = v4 &
% 213.38/30.51 | c_RComplete_Onatfloor(v1) = v5 & $i(v5) & $i(v4)))
% 213.38/30.51 |
% 213.38/30.51 | ALPHA: (387) implies:
% 213.38/30.51 | (388) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1355_1
% 213.38/30.51 |
% 213.38/30.51 | DELTA: instantiating (7) with fresh symbols all_1358_0, all_1358_1,
% 213.38/30.51 | all_1358_2, all_1358_3, all_1358_4, all_1358_5, all_1358_6 gives:
% 213.38/30.51 | (389) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1358_0 &
% 213.38/30.51 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1358_4) =
% 213.38/30.51 | all_1358_3 & c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1358_3,
% 213.38/30.51 | v_q____) = all_1358_2 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.51 | all_1358_2) = all_1358_1 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.51 | v_q____) = all_1358_6 &
% 213.38/30.51 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1358_5 &
% 213.38/30.51 | hAPP(all_1358_1, all_1358_5) = all_1358_0 & hAPP(all_1358_6,
% 213.38/30.51 | all_1358_5) = all_1358_4 & $i(all_1358_0) & $i(all_1358_1) &
% 213.38/30.51 | $i(all_1358_2) & $i(all_1358_3) & $i(all_1358_4) & $i(all_1358_5) &
% 213.38/30.51 | $i(all_1358_6)
% 213.38/30.51 |
% 213.38/30.51 | ALPHA: (389) implies:
% 213.38/30.51 | (390) hAPP(all_1358_6, all_1358_5) = all_1358_4
% 213.38/30.51 | (391) hAPP(all_1358_1, all_1358_5) = all_1358_0
% 213.38/30.51 | (392) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1358_5
% 213.38/30.51 | (393) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1358_6
% 213.38/30.51 | (394) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1358_2) = all_1358_1
% 213.38/30.51 | (395) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1358_3, v_q____) =
% 213.38/30.51 | all_1358_2
% 213.38/30.51 | (396) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1358_4) =
% 213.38/30.51 | all_1358_3
% 213.38/30.51 | (397) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1358_0
% 213.38/30.51 |
% 213.38/30.51 | DELTA: instantiating (57) with fresh symbol all_1363_0 gives:
% 213.38/30.52 | (398) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1363_0 &
% 213.38/30.52 | $i(all_1363_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 213.38/30.52 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v2) | ~ $i(v1) | ~
% 213.38/30.52 | $i(v0) | ? [v3: $i] : ($i(v3) &
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1363_0, v3) &
% 213.38/30.52 | ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ $i(v4) |
% 213.38/30.52 | ? [v6: $i] : ? [v7: $i] :
% 213.38/30.52 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7
% 213.38/30.52 | & $i(v7) &
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 213.38/30.52 | v3)) |
% 213.38/30.52 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) =
% 213.38/30.52 | v6 & $i(v6) & ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 213.38/30.52 | v0))))))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (398) implies:
% 213.38/30.52 | (399) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1363_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (108) with fresh symbols all_1365_0, all_1365_1,
% 213.38/30.52 | all_1365_2 gives:
% 213.38/30.52 | (400) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1365_0 &
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1365_2 &
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1365_1 &
% 213.38/30.52 | $i(all_1365_0) & $i(all_1365_1) & $i(all_1365_2) & ! [v0: $i] : !
% 213.38/30.52 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1365_2, v1) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1365_1, v0) |
% 213.38/30.52 | ? [v2: $i] : ? [v3: $i] : (hAPP(v3, v1) = v0 & hAPP(all_1365_0,
% 213.38/30.52 | v2) = v3 & $i(v3) & $i(v2) &
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1365_1, v2)))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (400) implies:
% 213.38/30.52 | (401) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1365_1
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (72) with fresh symbols all_1368_0, all_1368_1 gives:
% 213.38/30.52 | (402) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1368_0 &
% 213.38/30.52 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1368_1 &
% 213.38/30.52 | $i(all_1368_0) & $i(all_1368_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.52 | $i] : ! [v3: $i] : (v3 = v2 | ~ (c_RComplete_Onatceiling(v0) =
% 213.38/30.52 | v2) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1,
% 213.38/30.52 | all_1368_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ?
% 213.38/30.52 | [v5: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 & $i(v4) & ( ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0) |
% 213.38/30.52 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, all_1368_1)
% 213.38/30.52 | = v5 & $i(v5) & ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 213.38/30.52 | v5)))))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (402) implies:
% 213.38/30.52 | (403) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1368_1
% 213.38/30.52 | (404) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1368_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (78) with fresh symbol all_1380_0 gives:
% 213.38/30.52 | (405) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1380_0 &
% 213.38/30.52 | $i(all_1380_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.38/30.52 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 213.38/30.52 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1380_0, v1)
% 213.38/30.52 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)) & !
% 213.38/30.52 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 213.38/30.52 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 213.38/30.52 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1380_0, v1)
% 213.38/30.52 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (405) implies:
% 213.38/30.52 | (406) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1380_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (94) with fresh symbol all_1398_0 gives:
% 213.38/30.52 | (407) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1398_0 &
% 213.38/30.52 | $i(all_1398_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.38/30.52 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 213.38/30.52 | (c_RComplete_Onatceiling(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1398_0, v1)
% 213.38/30.52 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)) & !
% 213.38/30.52 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 213.38/30.52 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 213.38/30.52 | (c_RComplete_Onatceiling(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1398_0, v1)
% 213.38/30.52 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (407) implies:
% 213.38/30.52 | (408) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1398_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (41) with fresh symbols all_1401_0, all_1401_1 gives:
% 213.38/30.52 | (409) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1401_0 &
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1401_1 &
% 213.38/30.52 | $i(all_1401_0) & $i(all_1401_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.52 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 213.38/30.52 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v1) = v4) | ~
% 213.38/30.52 | (c_RealVector_Onorm__class_Onorm(v3, v0) = v6) | ~ (hAPP(v5, v6) =
% 213.38/30.52 | v7) | ~ (hAPP(all_1401_0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 213.38/30.52 | $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v7) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1401_1)
% 213.38/30.52 | | ~ class_RealVector_Oreal__normed__vector(v3) |
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(v3) = v1)
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (409) implies:
% 213.38/30.52 | (410) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1401_1
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (124) with fresh symbols all_1431_0, all_1431_1 gives:
% 213.38/30.52 | (411) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1431_0 &
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1431_1 &
% 213.38/30.52 | $i(all_1431_0) & $i(all_1431_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.52 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v1) =
% 213.38/30.52 | v2) | ~ (c_Transcendental_Oln(v0) = v3) | ~
% 213.38/30.52 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 213.38/30.52 | $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1431_1, v1) |
% 213.38/30.52 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1431_1, v0) |
% 213.38/30.52 | ? [v5: $i] : ? [v6: $i] : (c_Transcendental_Oln(v6) = v4 &
% 213.38/30.52 | hAPP(v5, v0) = v6 & hAPP(all_1431_0, v1) = v5 & $i(v6) & $i(v5) &
% 213.38/30.52 | $i(v4)))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (411) implies:
% 213.38/30.52 | (412) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1431_1
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (48) with fresh symbols all_1437_0, all_1437_1 gives:
% 213.38/30.52 | (413) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1437_0 &
% 213.38/30.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1437_1 &
% 213.38/30.52 | $i(all_1437_0) & $i(all_1437_1) & ! [v0: $i] : ! [v1: any] : !
% 213.38/30.52 | [v2: $i] : (v1 = all_1437_0 | ~ (hAPP(v2, v0) = all_1437_0) | ~
% 213.38/30.52 | (hAPP(all_1437_1, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any]
% 213.38/30.52 | : ! [v1: $i] : ! [v2: $i] : (v0 = all_1437_0 | ~ (hAPP(v2, v0) =
% 213.38/30.52 | all_1437_0) | ~ (hAPP(all_1437_1, v1) = v2) | ~ $i(v1) | ~
% 213.38/30.52 | $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1437_0 | ~
% 213.38/30.52 | (hAPP(v0, all_1437_0) = v1) | ~ (hAPP(all_1437_1, all_1437_0) =
% 213.38/30.52 | v0))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (413) implies:
% 213.38/30.52 | (414) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1437_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (50) with fresh symbols all_1443_0, all_1443_1 gives:
% 213.38/30.52 | (415) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1443_1 &
% 213.38/30.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1443_0 &
% 213.38/30.52 | $i(all_1443_0) & $i(all_1443_1) & ! [v0: $i] : ! [v1: any] : !
% 213.38/30.52 | [v2: $i] : (v1 = all_1443_1 | ~ (hAPP(v2, v0) = all_1443_1) | ~
% 213.38/30.52 | (hAPP(all_1443_0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any]
% 213.38/30.52 | : ! [v1: $i] : ! [v2: $i] : (v0 = all_1443_1 | ~ (hAPP(v2, v0) =
% 213.38/30.52 | all_1443_1) | ~ (hAPP(all_1443_0, v1) = v2) | ~ $i(v1) | ~
% 213.38/30.52 | $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1443_1 | ~
% 213.38/30.52 | (hAPP(v0, all_1443_1) = v1) | ~ (hAPP(all_1443_0, all_1443_1) =
% 213.38/30.52 | v0))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (415) implies:
% 213.38/30.52 | (416) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1443_1
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (129) with fresh symbols all_1463_0, all_1463_1,
% 213.38/30.52 | all_1463_2 gives:
% 213.38/30.52 | (417) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1463_0 &
% 213.38/30.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1463_1 &
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1463_2 &
% 213.38/30.52 | $i(all_1463_0) & $i(all_1463_1) & $i(all_1463_2) & ! [v0: any] : !
% 213.38/30.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = all_1463_0 | ~
% 213.38/30.52 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1463_1, v0) = v2) | ~ $i(v1) |
% 213.38/30.52 | ~ $i(v0) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v1) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1463_2, v1)) & !
% 213.38/30.52 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, v0) = v2) | ~
% 213.38/30.52 | (hAPP(all_1463_1, all_1463_0) = v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1463_2, v0) |
% 213.38/30.52 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (417) implies:
% 213.38/30.52 | (418) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1463_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (114) with fresh symbol all_1469_0 gives:
% 213.38/30.52 | (419) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1469_0 &
% 213.38/30.52 | $i(all_1469_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.38/30.52 | $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~
% 213.38/30.52 | (c_Transcendental_Oln(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1469_0, v1) |
% 213.38/30.52 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1469_0, v0) |
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 213.38/30.52 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 213.38/30.52 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 213.38/30.52 | v3) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1469_0, v1) |
% 213.38/30.52 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1469_0, v0) |
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (419) implies:
% 213.38/30.52 | (420) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1469_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (130) with fresh symbols all_1472_0, all_1472_1,
% 213.38/30.52 | all_1472_2 gives:
% 213.38/30.52 | (421) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1472_0 &
% 213.38/30.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1472_1 &
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1472_2 &
% 213.38/30.52 | $i(all_1472_0) & $i(all_1472_1) & $i(all_1472_2) & ! [v0: any] : !
% 213.38/30.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = all_1472_0 | ~
% 213.38/30.52 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1472_1, v1) = v2) | ~ $i(v1) |
% 213.38/30.52 | ~ $i(v0) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v1) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1472_2, v1)) & !
% 213.38/30.52 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1472_0) =
% 213.38/30.52 | v2) | ~ (hAPP(all_1472_1, v0) = v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1472_2, v0) |
% 213.38/30.52 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (421) implies:
% 213.38/30.52 | (422) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1472_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (110) with fresh symbol all_1475_0 gives:
% 213.38/30.52 | (423) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1475_0 &
% 213.38/30.52 | $i(all_1475_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.38/30.52 | $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~
% 213.38/30.52 | (c_Transcendental_Oln(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1475_0, v1) |
% 213.38/30.52 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1475_0, v0) |
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0:
% 213.38/30.52 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 213.38/30.52 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 213.38/30.52 | v3) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1475_0, v1) |
% 213.38/30.52 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1475_0, v0) |
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (423) implies:
% 213.38/30.52 | (424) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1475_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (44) with fresh symbols all_1478_0, all_1478_1 gives:
% 213.38/30.52 | (425) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1478_0 &
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1478_1 &
% 213.38/30.52 | $i(all_1478_0) & $i(all_1478_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 213.38/30.52 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__field(v1) |
% 213.38/30.52 | ? [v2: $i] : ($i(v2) &
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1478_1, v2) &
% 213.38/30.52 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 213.38/30.52 | (c_RealVector_Onorm__class_Onorm(v1, v3) = v4) | ~ (hAPP(v5,
% 213.38/30.52 | v2) = v6) | ~ (hAPP(all_1478_0, v4) = v5) | ~ $i(v3) | ?
% 213.38/30.52 | [v7: $i] : ? [v8: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 213.38/30.52 | v7) = v8 & c_Rings_Oinverse__class_Odivide(v1, v3, v0) = v7
% 213.38/30.52 | & $i(v8) & $i(v7) &
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 213.38/30.52 | v6)))))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (425) implies:
% 213.38/30.52 | (426) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1478_1
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (59) with fresh symbols all_1492_0, all_1492_1 gives:
% 213.38/30.52 | (427) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1492_0 &
% 213.38/30.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1492_1 &
% 213.38/30.52 | $i(all_1492_0) & $i(all_1492_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 213.38/30.52 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__field(v1) |
% 213.38/30.52 | ? [v2: $i] : ($i(v2) &
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1492_1,
% 213.38/30.52 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 213.38/30.52 | ~ (c_RealVector_Onorm__class_Onorm(v1, v3) = v4) | ~ (hAPP(v5,
% 213.38/30.52 | v2) = v6) | ~ (hAPP(all_1492_0, v4) = v5) | ~ $i(v3) | ?
% 213.38/30.52 | [v7: $i] : ? [v8: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 213.38/30.52 | v7) = v8 & c_Rings_Oinverse__class_Odivide(v1, v3, v0) = v7
% 213.38/30.52 | & $i(v8) & $i(v7) &
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 213.38/30.52 | v6)))))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (427) implies:
% 213.38/30.52 | (428) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1492_1
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (93) with fresh symbol all_1494_0 gives:
% 213.38/30.52 | (429) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1494_0 &
% 213.38/30.52 | $i(all_1494_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.38/30.52 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 213.38/30.52 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 213.38/30.52 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 213.38/30.52 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 213.38/30.52 | all_1494_0) = v4 & $i(v4) &
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) & !
% 213.38/30.52 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 213.38/30.52 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 213.38/30.52 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 213.38/30.52 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 213.38/30.52 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 213.38/30.52 | all_1494_0) = v4 & $i(v4) & ~
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4)))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (429) implies:
% 213.38/30.52 | (430) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1494_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (92) with fresh symbol all_1509_0 gives:
% 213.38/30.52 | (431) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1509_0 &
% 213.38/30.52 | $i(all_1509_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.38/30.52 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 213.38/30.52 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 213.38/30.52 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i]
% 213.38/30.52 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1509_0) =
% 213.38/30.52 | v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.52 | v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.38/30.52 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 213.38/30.52 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 213.38/30.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] :
% 213.38/30.52 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1509_0) = v4
% 213.38/30.52 | & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.52 | v4, v3)))
% 213.38/30.52 |
% 213.38/30.52 | ALPHA: (431) implies:
% 213.38/30.52 | (432) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1509_0
% 213.38/30.52 |
% 213.38/30.52 | DELTA: instantiating (109) with fresh symbols all_1521_0, all_1521_1,
% 213.38/30.52 | all_1521_2 gives:
% 213.38/30.53 | (433) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1521_1 &
% 213.38/30.53 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1521_0 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1521_2 &
% 213.38/30.53 | $i(all_1521_0) & $i(all_1521_1) & $i(all_1521_2) & ! [v0: $i] : !
% 213.38/30.53 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 213.38/30.53 | ~ (c_Transcendental_Oln(v1) = v4) | ~
% 213.38/30.53 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ (hAPP(v3, v4) = v5) |
% 213.38/30.53 | ~ (hAPP(all_1521_0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1521_2, v1) |
% 213.38/30.53 | ? [v6: $i] : ? [v7: $i] : (c_Transcendental_Oln(v7) = v5 &
% 213.38/30.53 | hAPP(v6, v0) = v7 & hAPP(all_1521_1, v1) = v6 & $i(v7) & $i(v6) &
% 213.38/30.53 | $i(v5)))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (433) implies:
% 213.38/30.53 | (434) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1521_2
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (6) with fresh symbols all_1524_0, all_1524_1,
% 213.38/30.53 | all_1524_2, all_1524_3, all_1524_4, all_1524_5, all_1524_6, all_1524_7,
% 213.38/30.53 | all_1524_8, all_1524_9 gives:
% 213.38/30.53 | (435) ~ (all_1524_0 = all_1524_1) &
% 213.38/30.53 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1524_7) =
% 213.38/30.53 | all_1524_6 & c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1524_6,
% 213.38/30.53 | v_q____) = all_1524_5 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.53 | all_1524_5) = all_1524_4 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.53 | v_q____) = all_1524_9 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1524_8 &
% 213.38/30.53 | hAPP(all_1524_4, all_1524_2) = all_1524_0 & hAPP(all_1524_4,
% 213.38/30.53 | all_1524_3) = all_1524_1 & hAPP(all_1524_9, all_1524_8) =
% 213.38/30.53 | all_1524_7 & $i(all_1524_0) & $i(all_1524_1) & $i(all_1524_2) &
% 213.38/30.53 | $i(all_1524_3) & $i(all_1524_4) & $i(all_1524_5) & $i(all_1524_6) &
% 213.38/30.53 | $i(all_1524_7) & $i(all_1524_8) & $i(all_1524_9)
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (435) implies:
% 213.38/30.53 | (436) hAPP(all_1524_9, all_1524_8) = all_1524_7
% 213.38/30.53 | (437) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1524_8
% 213.38/30.53 | (438) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1524_9
% 213.38/30.53 | (439) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1524_5) = all_1524_4
% 213.38/30.53 | (440) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1524_6, v_q____) =
% 213.38/30.53 | all_1524_5
% 213.38/30.53 | (441) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1524_7) =
% 213.38/30.53 | all_1524_6
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (9) with fresh symbols all_1526_0, all_1526_1,
% 213.38/30.53 | all_1526_2, all_1526_3, all_1526_4, all_1526_5, all_1526_6, all_1526_7,
% 213.38/30.53 | all_1526_8 gives:
% 213.38/30.53 | (442) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1526_5 &
% 213.38/30.53 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1526_6) =
% 213.38/30.53 | all_1526_4 & c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1526_4,
% 213.38/30.53 | v_q____) = all_1526_3 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.53 | all_1526_3) = all_1526_2 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.53 | v_q____) = all_1526_8 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1526_7 &
% 213.38/30.53 | hAPP(all_1526_0, all_1526_6) = all_1526_6 & hAPP(all_1526_2,
% 213.38/30.53 | all_1526_7) = all_1526_1 & hAPP(all_1526_5, all_1526_1) =
% 213.38/30.53 | all_1526_0 & hAPP(all_1526_8, all_1526_7) = all_1526_6 &
% 213.38/30.53 | $i(all_1526_0) & $i(all_1526_1) & $i(all_1526_2) & $i(all_1526_3) &
% 213.38/30.53 | $i(all_1526_4) & $i(all_1526_5) & $i(all_1526_6) & $i(all_1526_7) &
% 213.38/30.53 | $i(all_1526_8)
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (442) implies:
% 213.38/30.53 | (443) $i(all_1526_1)
% 213.38/30.53 | (444) hAPP(all_1526_8, all_1526_7) = all_1526_6
% 213.38/30.53 | (445) hAPP(all_1526_5, all_1526_1) = all_1526_0
% 213.38/30.53 | (446) hAPP(all_1526_2, all_1526_7) = all_1526_1
% 213.38/30.53 | (447) hAPP(all_1526_0, all_1526_6) = all_1526_6
% 213.38/30.53 | (448) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1526_7
% 213.38/30.53 | (449) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1526_8
% 213.38/30.53 | (450) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1526_3) = all_1526_2
% 213.38/30.53 | (451) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1526_4, v_q____) =
% 213.38/30.53 | all_1526_3
% 213.38/30.53 | (452) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1526_6) =
% 213.38/30.53 | all_1526_4
% 213.38/30.53 | (453) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1526_5
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (61) with fresh symbols all_1537_0, all_1537_1 gives:
% 213.38/30.53 | (454) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1537_0 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1537_1 &
% 213.38/30.53 | $i(all_1537_0) & $i(all_1537_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.53 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) |
% 213.38/30.53 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.53 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4)
% 213.38/30.53 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1537_1,
% 213.38/30.53 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (
% 213.38/30.53 | ~ (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7,
% 213.38/30.53 | v4) = v8) | ~ (hAPP(all_1537_0, v6) = v7) | ~ $i(v5) | ?
% 213.38/30.53 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 213.38/30.53 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) &
% 213.38/30.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 213.38/30.53 | v8)))))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (454) implies:
% 213.38/30.53 | (455) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1537_1
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (107) with fresh symbols all_1543_0, all_1543_1 gives:
% 213.38/30.53 | (456) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1543_0 &
% 213.38/30.53 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1543_1 &
% 213.38/30.53 | $i(all_1543_0) & $i(all_1543_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.53 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 213.38/30.53 | [v7: $i] : ( ~ (c_Complex_Orcis(v5, v6) = v7) | ~
% 213.38/30.53 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v0) = v6) | ~
% 213.38/30.53 | (hAPP(v4, v1) = v5) | ~ (hAPP(all_1543_0, v3) = v4) | ~ $i(v3) |
% 213.38/30.53 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ?
% 213.38/30.53 | [v10: $i] : (c_Complex_Orcis(v3, v2) = v8 & c_Complex_Orcis(v1, v0)
% 213.38/30.53 | = v10 & hAPP(v9, v10) = v7 & hAPP(all_1543_1, v8) = v9 & $i(v10)
% 213.38/30.53 | & $i(v9) & $i(v8) & $i(v7)))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (456) implies:
% 213.38/30.53 | (457) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1543_1
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (105) with fresh symbols all_1549_0, all_1549_1,
% 213.38/30.53 | all_1549_2 gives:
% 213.38/30.53 | (458) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1549_0 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1549_2 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1549_1 &
% 213.38/30.53 | $i(all_1549_0) & $i(all_1549_1) & $i(all_1549_2) & ! [v0: $i] : !
% 213.38/30.53 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1549_2, v1) | ~
% 213.38/30.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1549_1, v0) |
% 213.38/30.53 | ? [v2: $i] : ? [v3: $i] : (hAPP(v3, v1) = v0 & hAPP(all_1549_0,
% 213.38/30.53 | v2) = v3 & $i(v3) & $i(v2) &
% 213.38/30.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1549_1, v2) &
% 213.38/30.53 | ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v1) = v0) |
% 213.38/30.53 | ~ (hAPP(all_1549_0, v4) = v5) | ~ $i(v4) | ~
% 213.38/30.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1549_1,
% 213.38/30.53 | v4))))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (458) implies:
% 213.38/30.53 | (459) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1549_1
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (55) with fresh symbols all_1555_0, all_1555_1 gives:
% 213.38/30.53 | (460) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1555_0 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1555_1 &
% 213.38/30.53 | $i(all_1555_0) & $i(all_1555_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.53 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) |
% 213.38/30.53 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.53 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4)
% 213.38/30.53 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1555_1, v4)
% 213.38/30.53 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 213.38/30.53 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7,
% 213.38/30.53 | v4) = v8) | ~ (hAPP(all_1555_0, v6) = v7) | ~ $i(v5) | ?
% 213.38/30.53 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 213.38/30.53 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) &
% 213.38/30.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 213.38/30.53 | v8)))))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (460) implies:
% 213.38/30.53 | (461) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1555_1
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (97) with fresh symbols all_1558_0, all_1558_1,
% 213.38/30.53 | all_1558_2 gives:
% 213.38/30.53 | (462) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1558_1 &
% 213.38/30.53 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1558_0 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1558_2 &
% 213.38/30.53 | $i(all_1558_0) & $i(all_1558_1) & $i(all_1558_2) & ! [v0: $i] : !
% 213.38/30.53 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 213.38/30.53 | ~ (c_RComplete_Onatfloor(v1) = v2) | ~ (c_RComplete_Onatfloor(v0)
% 213.38/30.53 | = v4) | ~ (hAPP(v3, v4) = v5) | ~ (hAPP(all_1558_1, v2) = v3) |
% 213.38/30.53 | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1558_2, v1)
% 213.38/30.53 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.53 | all_1558_2, v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 213.38/30.53 | (c_RComplete_Onatfloor(v7) = v8 & hAPP(v6, v0) = v7 &
% 213.38/30.53 | hAPP(all_1558_0, v1) = v6 & $i(v8) & $i(v7) & $i(v6) &
% 213.38/30.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v8)))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (462) implies:
% 213.38/30.53 | (463) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1558_2
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (8) with fresh symbols all_1561_0, all_1561_1,
% 213.38/30.53 | all_1561_2, all_1561_3, all_1561_4, all_1561_5, all_1561_6 gives:
% 213.38/30.53 | (464) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1561_5 &
% 213.38/30.53 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1561_3) =
% 213.38/30.53 | all_1561_2 & c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1561_2,
% 213.38/30.53 | v_q____) = all_1561_1 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.53 | all_1561_1) = all_1561_0 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.53 | v_q____) = all_1561_6 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1561_4 &
% 213.38/30.53 | hAPP(all_1561_6, all_1561_4) = all_1561_3 & $i(all_1561_0) &
% 213.38/30.53 | $i(all_1561_1) & $i(all_1561_2) & $i(all_1561_3) & $i(all_1561_4) &
% 213.38/30.53 | $i(all_1561_5) & $i(all_1561_6) & ! [v0: $i] : ! [v1: $i] : ( ~
% 213.38/30.53 | (hAPP(all_1561_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i]
% 213.38/30.53 | : (hAPP(v3, all_1561_3) = v2 & hAPP(all_1561_5, v1) = v3 &
% 213.38/30.53 | hAPP(all_1561_6, v0) = v2 & $i(v3) & $i(v2)))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (464) implies:
% 213.38/30.53 | (465) hAPP(all_1561_6, all_1561_4) = all_1561_3
% 213.38/30.53 | (466) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1561_4
% 213.38/30.53 | (467) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1561_6
% 213.38/30.53 | (468) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1561_1) = all_1561_0
% 213.38/30.53 | (469) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1561_2, v_q____) =
% 213.38/30.53 | all_1561_1
% 213.38/30.53 | (470) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1561_3) =
% 213.38/30.53 | all_1561_2
% 213.38/30.53 | (471) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1561_5
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (54) with fresh symbols all_1585_0, all_1585_1 gives:
% 213.38/30.53 | (472) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1585_0 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1585_1 &
% 213.38/30.53 | $i(all_1585_0) & $i(all_1585_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.53 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~
% 213.38/30.53 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3:
% 213.38/30.53 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.38/30.53 | all_1585_1, v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 213.38/30.53 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) |
% 213.38/30.53 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(all_1585_0, v5) = v6) | ~
% 213.38/30.53 | $i(v4) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 213.38/30.53 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) =
% 213.38/30.53 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 213.38/30.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 213.38/30.53 | v7)))))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (472) implies:
% 213.38/30.53 | (473) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1585_1
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (62) with fresh symbols all_1587_0, all_1587_1 gives:
% 213.38/30.53 | (474) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1587_0 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1587_1 &
% 213.38/30.53 | $i(all_1587_0) & $i(all_1587_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.53 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~
% 213.38/30.53 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3:
% 213.38/30.53 | $i] : ($i(v3) &
% 213.38/30.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1587_1,
% 213.38/30.53 | v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (
% 213.38/30.53 | ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v6,
% 213.38/30.53 | v3) = v7) | ~ (hAPP(all_1587_0, v5) = v6) | ~ $i(v4) | ?
% 213.38/30.53 | [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 213.38/30.53 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) =
% 213.38/30.53 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 213.38/30.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 213.38/30.53 | v7)))))
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (474) implies:
% 213.38/30.53 | (475) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1587_1
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (2) with fresh symbols all_1589_0, all_1589_1,
% 213.38/30.53 | all_1589_2, all_1589_3, all_1589_4, all_1589_5, all_1589_6, all_1589_7,
% 213.38/30.53 | all_1589_8, all_1589_9 gives:
% 213.38/30.53 | (476) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1589_7 &
% 213.38/30.53 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1589_5) =
% 213.38/30.53 | all_1589_4 & c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1589_4,
% 213.38/30.53 | v_q____) = all_1589_3 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.53 | all_1589_3) = all_1589_2 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.53 | v_q____) = all_1589_9 &
% 213.38/30.53 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1589_6 &
% 213.38/30.53 | hAPP(all_1589_0, all_1589_5) = all_1589_8 & hAPP(all_1589_2, v_w____)
% 213.38/30.53 | = all_1589_1 & hAPP(all_1589_7, all_1589_1) = all_1589_0 &
% 213.38/30.53 | hAPP(all_1589_9, all_1589_6) = all_1589_5 & hAPP(all_1589_9, v_w____)
% 213.38/30.53 | = all_1589_8 & $i(all_1589_0) & $i(all_1589_1) & $i(all_1589_2) &
% 213.38/30.53 | $i(all_1589_3) & $i(all_1589_4) & $i(all_1589_5) & $i(all_1589_6) &
% 213.38/30.53 | $i(all_1589_7) & $i(all_1589_8) & $i(all_1589_9)
% 213.38/30.53 |
% 213.38/30.53 | ALPHA: (476) implies:
% 213.38/30.53 | (477) hAPP(all_1589_9, v_w____) = all_1589_8
% 213.38/30.53 | (478) hAPP(all_1589_9, all_1589_6) = all_1589_5
% 213.38/30.53 | (479) hAPP(all_1589_7, all_1589_1) = all_1589_0
% 213.38/30.53 | (480) hAPP(all_1589_2, v_w____) = all_1589_1
% 213.38/30.53 | (481) hAPP(all_1589_0, all_1589_5) = all_1589_8
% 213.38/30.53 | (482) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1589_6
% 213.38/30.53 | (483) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1589_9
% 213.38/30.53 | (484) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1589_3) = all_1589_2
% 213.38/30.53 | (485) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1589_4, v_q____) =
% 213.38/30.53 | all_1589_3
% 213.38/30.53 | (486) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1589_5) =
% 213.38/30.53 | all_1589_4
% 213.38/30.53 | (487) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1589_7
% 213.38/30.53 |
% 213.38/30.53 | DELTA: instantiating (27) with fresh symbols all_1609_0, all_1609_1 gives:
% 213.38/30.54 | (488) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1609_0 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1609_1 &
% 213.38/30.54 | $i(all_1609_0) & $i(all_1609_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.54 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 213.38/30.54 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1609_0, v2) = v3) |
% 213.38/30.54 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1609_1, v2) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 213.38/30.54 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 213.38/30.54 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 213.38/30.54 | (hAPP(all_1609_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 213.38/30.54 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1609_1, v2) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (488) implies:
% 213.38/30.54 | (489) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1609_1
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (58) with fresh symbols all_1615_0, all_1615_1 gives:
% 213.38/30.54 | (490) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1615_0 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1615_1 &
% 213.38/30.54 | $i(all_1615_0) & $i(all_1615_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.54 | $i] : ( ~ (hAPP(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | hBOOL(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 213.38/30.54 | ($i(v4) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4,
% 213.38/30.54 | all_1615_0) = v5 & hAPP(v1, v5) = v6 & $i(v6) & $i(v5) &
% 213.38/30.54 | hBOOL(v6) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4,
% 213.38/30.54 | v0) & ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v1, v7) = v8) |
% 213.38/30.54 | ~ $i(v7) | ~ hBOOL(v8) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v7, v4))) |
% 213.38/30.54 | (hAPP(v1, all_1615_1) = v3 & $i(v3) & hBOOL(v3)))))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (490) implies:
% 213.38/30.54 | (491) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1615_0
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (99) with fresh symbols all_1621_0, all_1621_1,
% 213.38/30.54 | all_1621_2, all_1621_3 gives:
% 213.38/30.54 | (492) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1621_0 &
% 213.38/30.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1621_1 &
% 213.38/30.54 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1621_2 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1621_3 &
% 213.38/30.54 | $i(all_1621_0) & $i(all_1621_1) & $i(all_1621_2) & $i(all_1621_3) &
% 213.38/30.54 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 213.38/30.54 | ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1621_1) =
% 213.38/30.54 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1621_0, v2) = v3) |
% 213.38/30.54 | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1621_3, v1)
% 213.38/30.54 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 213.38/30.54 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v5 &
% 213.38/30.54 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, all_1621_1) =
% 213.38/30.54 | v8 & hAPP(v6, v1) = v7 & hAPP(all_1621_2, v5) = v6 & $i(v8) &
% 213.38/30.54 | $i(v7) & $i(v6) & $i(v5) &
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v4)))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (492) implies:
% 213.38/30.54 | (493) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1621_3
% 213.38/30.54 | (494) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1621_1
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (52) with fresh symbols all_1624_0, all_1624_1 gives:
% 213.38/30.54 | (495) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1624_1 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1624_0 &
% 213.38/30.54 | $i(all_1624_0) & $i(all_1624_1) & ! [v0: $i] : ! [v1: any] : !
% 213.38/30.54 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = all_1624_0
% 213.38/30.54 | | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) =
% 213.38/30.54 | all_1624_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) |
% 213.38/30.54 | ~ (hAPP(all_1624_1, v1) = v2) | ~ (hAPP(all_1624_1, v0) = v4) | ~
% 213.38/30.54 | $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : !
% 213.38/30.54 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v0 = all_1624_0 | ~
% 213.38/30.54 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) =
% 213.38/30.54 | all_1624_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) |
% 213.38/30.54 | ~ (hAPP(all_1624_1, v1) = v2) | ~ (hAPP(all_1624_1, v0) = v4) | ~
% 213.38/30.54 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 213.38/30.54 | (v2 = all_1624_0 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 213.38/30.54 | v1, v1) = v2) | ~ (hAPP(v0, all_1624_0) = v1) | ~
% 213.38/30.54 | (hAPP(all_1624_1, all_1624_0) = v0))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (495) implies:
% 213.38/30.54 | (496) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1624_0
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (28) with fresh symbols all_1627_0, all_1627_1 gives:
% 213.38/30.54 | (497) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1627_0 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1627_1 &
% 213.38/30.54 | $i(all_1627_0) & $i(all_1627_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.54 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 213.38/30.54 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1627_0,
% 213.38/30.54 | v1) = v3) | ~ (hAPP(all_1627_0, v0) = v5) | ~ $i(v2) | ~
% 213.38/30.54 | $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1627_1, v2) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 213.38/30.54 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 213.38/30.54 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) =
% 213.38/30.54 | v4) | ~ (hAPP(all_1627_0, v1) = v3) | ~ (hAPP(all_1627_0, v0) =
% 213.38/30.54 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1627_1, v2) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (497) implies:
% 213.38/30.54 | (498) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1627_1
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (60) with fresh symbols all_1630_0, all_1630_1 gives:
% 213.38/30.54 | (499) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1630_0 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1630_1 &
% 213.38/30.54 | $i(all_1630_0) & $i(all_1630_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 213.38/30.54 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~
% 213.38/30.54 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2)
% 213.38/30.54 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1630_1,
% 213.38/30.54 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 213.38/30.54 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 213.38/30.54 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~
% 213.38/30.54 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9,
% 213.38/30.54 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1630_0,
% 213.38/30.54 | v8) = v9) | ~ (hAPP(all_1630_0, v5) = v6) | ~ $i(v4) | ~
% 213.38/30.54 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 213.38/30.54 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4)
% 213.38/30.54 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) &
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 213.38/30.54 | v10)))))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (499) implies:
% 213.38/30.54 | (500) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1630_1
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (56) with fresh symbols all_1633_0, all_1633_1 gives:
% 213.38/30.54 | (501) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1633_0 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1633_1 &
% 213.38/30.54 | $i(all_1633_0) & $i(all_1633_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 213.38/30.54 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~
% 213.38/30.54 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2)
% 213.38/30.54 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1633_1, v2)
% 213.38/30.54 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 213.38/30.54 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 213.38/30.54 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~
% 213.38/30.54 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9,
% 213.38/30.54 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1633_0,
% 213.38/30.54 | v8) = v9) | ~ (hAPP(all_1633_0, v5) = v6) | ~ $i(v4) | ~
% 213.38/30.54 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 213.38/30.54 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4)
% 213.38/30.54 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) &
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 213.38/30.54 | v10)))))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (501) implies:
% 213.38/30.54 | (502) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1633_1
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (63) with fresh symbol all_1636_0 gives:
% 213.38/30.54 | (503) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1636_0 &
% 213.38/30.54 | $i(all_1636_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 213.38/30.54 | | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | class_RealVector_Oreal__normed__vector(v1) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1636_0, v2) |
% 213.38/30.54 | c_SEQ_OBseq(v1, v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 213.38/30.54 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5 & hAPP(v0, v3) = v4 &
% 213.38/30.54 | $i(v5) & $i(v4) & $i(v3) & ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))) &
% 213.38/30.54 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 213.38/30.54 | | ? [v2: $i] : ($i(v2) &
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1636_0, v2) &
% 213.38/30.54 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 213.38/30.54 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v0,
% 213.38/30.54 | v3) = v4) | ~ $i(v3) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (503) implies:
% 213.38/30.54 | (504) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1636_0
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (36) with fresh symbols all_1639_0, all_1639_1 gives:
% 213.38/30.54 | (505) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1639_0 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1639_1 &
% 213.38/30.54 | $i(all_1639_0) & $i(all_1639_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.54 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 213.38/30.54 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1639_0,
% 213.38/30.54 | v1) = v3) | ~ (hAPP(all_1639_0, v0) = v5) | ~ $i(v2) | ~
% 213.38/30.54 | $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1639_1, v2) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0:
% 213.38/30.54 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 213.38/30.54 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) =
% 213.38/30.54 | v4) | ~ (hAPP(all_1639_0, v1) = v3) | ~ (hAPP(all_1639_0, v0) =
% 213.38/30.54 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1639_1, v2) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (505) implies:
% 213.38/30.54 | (506) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1639_1
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (23) with fresh symbols all_1642_0, all_1642_1 gives:
% 213.38/30.54 | (507) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1642_0 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1642_1 &
% 213.38/30.54 | $i(all_1642_0) & $i(all_1642_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.54 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 213.38/30.54 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 213.38/30.54 | (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v3) = v5) | ~
% 213.38/30.54 | (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v2) = v8) | ~
% 213.38/30.54 | (hAPP(v7, v8) = v9) | ~ (hAPP(v4, v5) = v6) | ~ (hAPP(all_1642_0,
% 213.38/30.54 | v1) = v4) | ~ (hAPP(all_1642_0, v0) = v7) | ~ $i(v3) | ~
% 213.38/30.54 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1642_1, v3) |
% 213.38/30.54 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1642_1, v2) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v9) | ? [v10:
% 213.38/30.54 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : (hAPP(v12, v0)
% 213.38/30.54 | = v13 & hAPP(v10, v1) = v11 & hAPP(all_1642_0, v3) = v12 &
% 213.38/30.54 | hAPP(all_1642_0, v2) = v10 & $i(v13) & $i(v12) & $i(v11) &
% 213.38/30.54 | $i(v10) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 213.38/30.54 | v13)))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (507) implies:
% 213.38/30.54 | (508) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1642_1
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (22) with fresh symbols all_1645_0, all_1645_1 gives:
% 213.38/30.54 | (509) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1645_0 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1645_1 &
% 213.38/30.54 | $i(all_1645_0) & $i(all_1645_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.54 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 213.38/30.54 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 213.38/30.54 | (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v3) = v4) | ~
% 213.38/30.54 | (c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, v2) = v7) | ~
% 213.38/30.54 | (hAPP(v8, v0) = v9) | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(all_1645_0,
% 213.38/30.54 | v7) = v8) | ~ (hAPP(all_1645_0, v4) = v5) | ~ $i(v3) | ~
% 213.38/30.54 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1645_1, v3) |
% 213.38/30.54 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1645_1, v2) |
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v9) | ? [v10:
% 213.38/30.54 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : (hAPP(v12, v0)
% 213.38/30.54 | = v13 & hAPP(v10, v1) = v11 & hAPP(all_1645_0, v3) = v12 &
% 213.38/30.54 | hAPP(all_1645_0, v2) = v10 & $i(v13) & $i(v12) & $i(v11) &
% 213.38/30.54 | $i(v10) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 213.38/30.54 | v13)))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (509) implies:
% 213.38/30.54 | (510) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1645_1
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (146) with fresh symbols all_1651_0, all_1651_1,
% 213.38/30.54 | all_1651_2, all_1651_3, all_1651_4, all_1651_5, all_1651_6, all_1651_7,
% 213.38/30.54 | all_1651_8, all_1651_9, all_1651_10, all_1651_11 gives:
% 213.38/30.54 | (511) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1651_1) =
% 213.38/30.54 | all_1651_0 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 213.38/30.54 | all_1651_5) = all_1651_4 &
% 213.38/30.54 | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, all_1651_2,
% 213.38/30.54 | all_1651_9) = all_1651_1 &
% 213.38/30.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1651_3 &
% 213.38/30.54 | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1651_9) =
% 213.38/30.54 | all_1651_8 & c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1651_8,
% 213.38/30.54 | v_q____) = all_1651_7 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.54 | all_1651_7) = all_1651_6 & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 213.38/30.54 | v_q____) = all_1651_11 &
% 213.38/30.54 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1651_10 &
% 213.38/30.54 | hAPP(all_1651_6, v_w____) = all_1651_5 & hAPP(all_1651_11,
% 213.38/30.54 | all_1651_10) = all_1651_9 & hAPP(all_1651_11, v_w____) = all_1651_2
% 213.38/30.54 | & $i(all_1651_0) & $i(all_1651_1) & $i(all_1651_2) & $i(all_1651_3) &
% 213.38/30.54 | $i(all_1651_4) & $i(all_1651_5) & $i(all_1651_6) & $i(all_1651_7) &
% 213.38/30.54 | $i(all_1651_8) & $i(all_1651_9) & $i(all_1651_10) & $i(all_1651_11) &
% 213.38/30.54 | ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0,
% 213.38/30.54 | all_1651_3) & ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.38/30.54 | all_1651_3)) | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.38/30.54 | all_1651_4, all_1651_3) & ~
% 213.38/30.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0,
% 213.38/30.54 | all_1651_3)))
% 213.38/30.54 |
% 213.38/30.54 | ALPHA: (511) implies:
% 213.38/30.54 | (512) $i(all_1651_5)
% 213.38/30.54 | (513) $i(all_1651_2)
% 213.38/30.54 | (514) hAPP(all_1651_11, v_w____) = all_1651_2
% 213.38/30.54 | (515) hAPP(all_1651_11, all_1651_10) = all_1651_9
% 213.38/30.54 | (516) hAPP(all_1651_6, v_w____) = all_1651_5
% 213.38/30.54 | (517) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1651_10
% 213.38/30.54 | (518) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____) = all_1651_11
% 213.38/30.54 | (519) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1651_7) = all_1651_6
% 213.38/30.54 | (520) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1651_8, v_q____) =
% 213.38/30.54 | all_1651_7
% 213.38/30.54 | (521) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_1651_9) =
% 213.38/30.54 | all_1651_8
% 213.38/30.54 | (522) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1651_3
% 213.38/30.54 | (523) c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, all_1651_2,
% 213.38/30.54 | all_1651_9) = all_1651_1
% 213.38/30.54 | (524) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1651_5) =
% 213.38/30.54 | all_1651_4
% 213.38/30.54 | (525) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1651_1) =
% 213.38/30.54 | all_1651_0
% 213.38/30.54 | (526) (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0,
% 213.38/30.54 | all_1651_3) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.38/30.54 | all_1651_4, all_1651_3)) |
% 213.38/30.54 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.38/30.54 | all_1651_3) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.38/30.54 | all_1651_0, all_1651_3))
% 213.38/30.54 |
% 213.38/30.54 | DELTA: instantiating (43) with fresh symbol all_1653_0 gives:
% 213.38/30.55 | (527) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1653_0 &
% 213.38/30.55 | $i(all_1653_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 213.38/30.55 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(v2, v1) = v3) | ~
% 213.38/30.55 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 213.38/30.55 | ? [v8: any] : (((v8 = all_1653_0 & ~ (v7 = v1) &
% 213.38/30.55 | c_Polynomial_Oorder(v2, v0, v1) = all_1653_0 &
% 213.38/30.55 | tc_Polynomial_Opoly(v2) = v6 &
% 213.38/30.55 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6)) | (v5
% 213.38/30.55 | = v4 & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) & ((v7
% 213.38/30.55 | = v1 & tc_Polynomial_Opoly(v2) = v6 &
% 213.38/30.55 | c_Groups_Ozero__class_Ozero(v6) = v1 & $i(v6)) | ( ~ (v8 =
% 213.38/30.55 | all_1653_0) & c_Polynomial_Oorder(v2, v0, v1) = v8 &
% 213.38/30.55 | $i(v8)) | ( ~ (v5 = v4) & c_Groups_Ozero__class_Ozero(v2) =
% 213.38/30.55 | v5 & $i(v5)))))
% 213.38/30.55 |
% 213.38/30.55 | ALPHA: (527) implies:
% 213.38/30.55 | (528) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1653_0
% 213.38/30.55 | (529) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 213.38/30.55 | ( ~ (c_Polynomial_Opoly(v2, v1) = v3) | ~ (hAPP(v3, v0) = v4) | ~
% 213.38/30.55 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Oidom(v2) | ? [v5:
% 213.38/30.55 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (((v8 =
% 213.38/30.55 | all_1653_0 & ~ (v7 = v1) & c_Polynomial_Oorder(v2, v0, v1) =
% 213.38/30.55 | all_1653_0 & tc_Polynomial_Opoly(v2) = v6 &
% 213.38/30.55 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6)) | (v5
% 213.38/30.55 | = v4 & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) & ((v7
% 213.38/30.55 | = v1 & tc_Polynomial_Opoly(v2) = v6 &
% 213.38/30.55 | c_Groups_Ozero__class_Ozero(v6) = v1 & $i(v6)) | ( ~ (v8 =
% 213.38/30.55 | all_1653_0) & c_Polynomial_Oorder(v2, v0, v1) = v8 &
% 213.38/30.55 | $i(v8)) | ( ~ (v5 = v4) & c_Groups_Ozero__class_Ozero(v2) =
% 213.38/30.55 | v5 & $i(v5)))))
% 213.38/30.55 |
% 213.38/30.55 | DELTA: instantiating (104) with fresh symbols all_1656_0, all_1656_1,
% 213.38/30.55 | all_1656_2, all_1656_3, all_1656_4, all_1656_5 gives:
% 213.38/30.55 | (530) c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = all_1656_1 &
% 213.38/30.55 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1656_0 &
% 213.38/30.55 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1656_3 &
% 213.38/30.55 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1656_2 &
% 213.38/30.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1656_4 &
% 213.38/30.55 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1656_5 &
% 213.38/30.55 | $i(all_1656_0) & $i(all_1656_1) & $i(all_1656_2) & $i(all_1656_3) &
% 213.38/30.55 | $i(all_1656_4) & $i(all_1656_5) & ? [v0: any] : ! [v1: any] : !
% 213.38/30.55 | [v2: $i] : (v1 = all_1656_5 | v0 = all_1656_4 | ~ (hAPP(all_1656_2,
% 213.38/30.55 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 213.38/30.55 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 213.38/30.55 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, all_1656_3, v6) =
% 213.38/30.55 | v7 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v7) =
% 213.38/30.55 | v8 & hAPP(v4, v0) = v5 & hAPP(v2, v5) = v6 & hAPP(all_1656_1, v3)
% 213.38/30.55 | = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 213.38/30.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, all_1656_0)))
% 213.38/30.55 |
% 213.38/30.55 | ALPHA: (530) implies:
% 213.38/30.55 | (531) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1656_5
% 213.38/30.55 | (532) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1656_4
% 213.38/30.55 | (533) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1656_2
% 213.38/30.55 | (534) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1656_3
% 213.38/30.55 | (535) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1656_0
% 213.38/30.55 |
% 213.38/30.55 | DELTA: instantiating (46) with fresh symbols all_1667_0, all_1667_1 gives:
% 213.38/30.55 | (536) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1667_1 &
% 213.38/30.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1667_0 &
% 213.38/30.55 | $i(all_1667_0) & $i(all_1667_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.55 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 213.38/30.55 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1667_1,
% 213.38/30.55 | v2) = v3) | ~ (hAPP(all_1667_1, v0) = v5) | ~ $i(v2) | ~
% 213.38/30.55 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 213.38/30.55 | v4, v6) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0)) &
% 213.38/30.55 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 213.38/30.55 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1)
% 213.38/30.55 | = v4) | ~ (hAPP(all_1667_1, v2) = v3) | ~ (hAPP(all_1667_1, v0)
% 213.38/30.55 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) |
% 213.38/30.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1667_0, v1)) & !
% 213.38/30.55 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 213.38/30.55 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) =
% 213.38/30.55 | v4) | ~ (hAPP(all_1667_1, v2) = v3) | ~ (hAPP(all_1667_1, v0) =
% 213.38/30.55 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1667_0, v1) |
% 213.38/30.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))
% 213.38/30.55 |
% 213.38/30.55 | ALPHA: (536) implies:
% 213.38/30.55 | (537) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1667_0
% 213.38/30.55 |
% 213.38/30.55 | DELTA: instantiating (26) with fresh symbol all_1670_0 gives:
% 213.38/30.55 | (538) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1670_0 &
% 213.38/30.55 | $i(all_1670_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 213.38/30.55 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v0) = v2) |
% 213.38/30.55 | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, all_1670_0)
% 213.38/30.55 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 213.38/30.55 | all_1670_0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.55 | all_1670_0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 213.38/30.55 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v0) = v2) |
% 213.38/30.55 | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, all_1670_0)
% 213.38/30.55 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.55 | all_1670_0, v1) |
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1670_0,
% 213.38/30.55 | v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 213.38/30.55 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v0) = v2) |
% 213.38/30.55 | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_1670_0)
% 213.38/30.55 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.55 | all_1670_0, v0) |
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1670_0,
% 213.38/30.55 | v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 213.38/30.55 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v0) = v2) |
% 213.38/30.55 | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1670_0, v2)
% 213.38/30.55 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 213.38/30.55 | all_1670_0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.55 | all_1670_0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 213.38/30.55 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v0) = v2) |
% 213.38/30.55 | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1670_0, v2)
% 213.38/30.55 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 213.38/30.55 | all_1670_0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.55 | all_1670_0, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 213.38/30.55 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v0) = v2) |
% 213.38/30.55 | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1670_0, v1)
% 213.38/30.55 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.38/30.55 | all_1670_0, v0) |
% 213.38/30.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1670_0,
% 213.38/30.55 | v2))
% 213.38/30.55 |
% 213.38/30.55 | ALPHA: (538) implies:
% 213.38/30.55 | (539) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1670_0
% 213.38/30.55 |
% 213.38/30.55 | DELTA: instantiating (101) with fresh symbols all_1688_0, all_1688_1 gives:
% 213.38/30.55 | (540) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1688_0 &
% 213.38/30.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1688_1 &
% 213.38/30.55 | $i(all_1688_0) & $i(all_1688_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.55 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 213.38/30.55 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v3) | ~
% 213.38/30.55 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 213.38/30.55 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : (( ~ (v0 = all_1688_1) |
% 213.38/30.55 | (hAPP(v2, all_1688_1) = v5 & $i(v5) & hBOOL(v5))) & (v0 =
% 213.38/30.55 | all_1688_1 | (hAPP(all_1688_0, v0) = v6 & $i(v6) & ! [v7: $i]
% 213.38/30.55 | : ! [v8: $i] : ! [v9: $i] : ( ~
% 213.38/30.55 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v9, v8) = v1) |
% 213.38/30.55 | ~ (hAPP(v6, v7) = v9) | ~ $i(v8) | ~ $i(v7) | ~
% 213.38/30.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v8, v0) | ?
% 213.38/30.55 | [v10: $i] : (hAPP(v2, v7) = v10 & $i(v10) &
% 213.38/30.55 | hBOOL(v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 213.38/30.55 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 213.38/30.55 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v3) | ~
% 213.38/30.55 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 213.38/30.55 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 213.38/30.55 | $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & $i(v7) & ((v10 = v1
% 213.38/30.55 | & ~ (v0 = all_1688_1) &
% 213.38/30.55 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v9, v8) = v1 &
% 213.38/30.55 | hAPP(v6, v7) = v9 & hAPP(v2, v7) = v11 & hAPP(all_1688_0, v0)
% 213.38/30.55 | = v6 & $i(v11) & $i(v9) & $i(v6) &
% 213.38/30.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v8, v0) & ~
% 213.38/30.55 | hBOOL(v11)) | (v0 = all_1688_1 & hAPP(v2, all_1688_1) = v5 &
% 213.38/30.55 | $i(v5) & ~ hBOOL(v5)))))
% 213.38/30.55 |
% 213.38/30.55 | ALPHA: (540) implies:
% 213.38/30.55 | (541) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1688_1
% 213.38/30.55 |
% 213.38/30.55 | GROUND_INST: instantiating (147) with all_833_1, all_888_0,
% 213.38/30.55 | tc_Complex_Ocomplex, simplifying with (203), (216) gives:
% 213.38/30.55 | (542) all_888_0 = all_833_1
% 213.38/30.55 |
% 213.38/30.55 | GROUND_INST: instantiating (147) with all_746_1, all_888_0,
% 213.38/30.55 | tc_Complex_Ocomplex, simplifying with (171), (216) gives:
% 213.38/30.55 | (543) all_888_0 = all_746_1
% 213.38/30.55 |
% 213.38/30.55 | GROUND_INST: instantiating (147) with all_888_0, all_980_0,
% 213.38/30.55 | tc_Complex_Ocomplex, simplifying with (216), (243) gives:
% 213.38/30.55 | (544) all_980_0 = all_888_0
% 213.38/30.55 |
% 213.38/30.55 | GROUND_INST: instantiating (147) with all_980_0, all_1092_2,
% 213.38/30.55 | tc_Complex_Ocomplex, simplifying with (243), (284) gives:
% 213.38/30.55 | (545) all_1092_2 = all_980_0
% 213.38/30.55 |
% 213.38/30.55 | GROUND_INST: instantiating (147) with all_1092_2, all_1201_3,
% 213.38/30.55 | tc_Complex_Ocomplex, simplifying with (284), (329) gives:
% 213.38/30.55 | (546) all_1201_3 = all_1092_2
% 213.38/30.55 |
% 213.38/30.55 | GROUND_INST: instantiating (147) with all_1201_3, all_1226_0,
% 213.38/30.55 | tc_Complex_Ocomplex, simplifying with (329), (342) gives:
% 213.38/30.55 | (547) all_1226_0 = all_1201_3
% 213.38/30.55 |
% 213.38/30.55 | GROUND_INST: instantiating (147) with all_1226_0, all_1241_4,
% 213.38/30.55 | tc_Complex_Ocomplex, simplifying with (342), (350) gives:
% 213.38/30.55 | (548) all_1241_4 = all_1226_0
% 213.38/30.55 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1358_5, all_1524_8,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (392), (437) gives:
% 213.38/30.56 | (549) all_1524_8 = all_1358_5
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1524_8, all_1526_7,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (437), (448) gives:
% 213.38/30.56 | (550) all_1526_7 = all_1524_8
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1526_7, all_1561_4,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (448), (466) gives:
% 213.38/30.56 | (551) all_1561_4 = all_1526_7
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1561_4, all_1589_6,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (466), (482) gives:
% 213.38/30.56 | (552) all_1589_6 = all_1561_4
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1589_6, all_1651_10,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (482), (517) gives:
% 213.38/30.56 | (553) all_1651_10 = all_1589_6
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_880_0, all_1651_10,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (213), (517) gives:
% 213.38/30.56 | (554) all_1651_10 = all_880_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1358_5, all_1656_5,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (392), (531) gives:
% 213.38/30.56 | (555) all_1656_5 = all_1358_5
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1346_3, all_1656_5,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (384), (531) gives:
% 213.38/30.56 | (556) all_1656_5 = all_1346_3
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1241_4, all_1656_5,
% 213.38/30.56 | tc_Complex_Ocomplex, simplifying with (350), (531) gives:
% 213.38/30.56 | (557) all_1656_5 = all_1241_4
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_759_0, all_888_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (184), (217) gives:
% 213.38/30.56 | (558) all_888_1 = all_759_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_888_1, all_956_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (217), (231) gives:
% 213.38/30.56 | (559) all_956_1 = all_888_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_956_1, all_985_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (231), (249) gives:
% 213.38/30.56 | (560) all_985_1 = all_956_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_860_0, all_988_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (208), (251) gives:
% 213.38/30.56 | (561) all_988_1 = all_860_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_737_1, all_988_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (168), (251) gives:
% 213.38/30.56 | (562) all_988_1 = all_737_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_904_0, all_1094_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (221), (287) gives:
% 213.38/30.56 | (563) all_1094_1 = all_904_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_759_0, all_1094_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (184), (287) gives:
% 213.38/30.56 | (564) all_1094_1 = all_759_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_959_1, all_1106_0, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (233), (290) gives:
% 213.38/30.56 | (565) all_1106_0 = all_959_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_904_0, all_1106_0, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (221), (290) gives:
% 213.38/30.56 | (566) all_1106_0 = all_904_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1046_1, all_1115_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (274), (297) gives:
% 213.38/30.56 | (567) all_1115_1 = all_1046_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1004_1, all_1149_2,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (260), (306) gives:
% 213.38/30.56 | (568) all_1149_2 = all_1004_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_988_1, all_1149_2, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (251), (306) gives:
% 213.38/30.56 | (569) all_1149_2 = all_988_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1046_1, all_1171_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (274), (318) gives:
% 213.38/30.56 | (570) all_1171_0 = all_1046_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_944_0, all_1171_0, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (225), (318) gives:
% 213.38/30.56 | (571) all_1171_0 = all_944_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1155_1, all_1174_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (309), (320) gives:
% 213.38/30.56 | (572) all_1174_0 = all_1155_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1189_0, all_1192_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (324), (326) gives:
% 213.38/30.56 | (573) all_1192_0 = all_1189_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_985_1, all_1192_0, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (249), (326) gives:
% 213.38/30.56 | (574) all_1192_0 = all_985_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1189_0, all_1217_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (324), (338) gives:
% 213.38/30.56 | (575) all_1217_0 = all_1189_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1174_0, all_1238_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (320), (346) gives:
% 213.38/30.56 | (576) all_1238_1 = all_1174_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1149_2, all_1263_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (306), (356) gives:
% 213.38/30.56 | (577) all_1263_0 = all_1149_2
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1192_0, all_1269_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (326), (358) gives:
% 213.38/30.56 | (578) all_1269_1 = all_1192_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1171_0, all_1278_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (318), (362) gives:
% 213.38/30.56 | (579) all_1278_0 = all_1171_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1163_1, all_1278_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (313), (362) gives:
% 213.38/30.56 | (580) all_1278_0 = all_1163_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_888_1, all_1278_0, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (217), (362) gives:
% 213.38/30.56 | (581) all_1278_0 = all_888_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_774_1, all_1278_0, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (192), (362) gives:
% 213.38/30.56 | (582) all_1278_0 = all_774_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1269_1, all_1284_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (358), (367) gives:
% 213.38/30.56 | (583) all_1284_1 = all_1269_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1238_1, all_1293_2,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (346), (370) gives:
% 213.38/30.56 | (584) all_1293_2 = all_1238_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1302_0, all_1304_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (374), (376) gives:
% 213.38/30.56 | (585) all_1304_1 = all_1302_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1293_2, all_1363_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (370), (399) gives:
% 213.38/30.56 | (586) all_1363_0 = all_1293_2
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1094_1, all_1365_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (287), (401) gives:
% 213.38/30.56 | (587) all_1365_1 = all_1094_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_769_0, all_1365_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (187), (401) gives:
% 213.38/30.56 | (588) all_1365_1 = all_769_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1217_0, all_1398_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (338), (408) gives:
% 213.38/30.56 | (589) all_1398_0 = all_1217_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1007_1, all_1398_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (263), (408) gives:
% 213.38/30.56 | (590) all_1398_0 = all_1007_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1284_1, all_1431_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (367), (412) gives:
% 213.38/30.56 | (591) all_1431_1 = all_1284_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1304_1, all_1469_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (376), (420) gives:
% 213.38/30.56 | (592) all_1469_0 = all_1304_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1115_1, all_1475_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (297), (424) gives:
% 213.38/30.56 | (593) all_1475_0 = all_1115_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_849_0, all_1475_0, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (206), (424) gives:
% 213.38/30.56 | (594) all_1475_0 = all_849_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1475_0, all_1478_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (424), (426) gives:
% 213.38/30.56 | (595) all_1478_1 = all_1475_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1401_1, all_1492_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (410), (428) gives:
% 213.38/30.56 | (596) all_1492_1 = all_1401_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1263_0, all_1492_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (356), (428) gives:
% 213.38/30.56 | (597) all_1492_1 = all_1263_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_982_0, all_1492_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (247), (428) gives:
% 213.38/30.56 | (598) all_1492_1 = all_982_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1192_0, all_1521_2,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (326), (434) gives:
% 213.38/30.56 | (599) all_1521_2 = all_1192_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1073_1, all_1521_2,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (279), (434) gives:
% 213.38/30.56 | (600) all_1521_2 = all_1073_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1363_0, all_1537_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (399), (455) gives:
% 213.38/30.56 | (601) all_1537_1 = all_1363_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1537_1, all_1549_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (455), (459) gives:
% 213.38/30.56 | (602) all_1549_1 = all_1537_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1211_0, all_1555_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (334), (461) gives:
% 213.38/30.56 | (603) all_1555_1 = all_1211_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1469_0, all_1558_2,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (420), (463) gives:
% 213.38/30.56 | (604) all_1558_2 = all_1469_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1549_1, all_1585_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (459), (473) gives:
% 213.38/30.56 | (605) all_1585_1 = all_1549_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_734_0, all_1585_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (166), (473) gives:
% 213.38/30.56 | (606) all_1585_1 = all_734_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1106_0, all_1609_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (290), (489) gives:
% 213.38/30.56 | (607) all_1609_1 = all_1106_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_950_0, all_1609_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (228), (489) gives:
% 213.38/30.56 | (608) all_1609_1 = all_950_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1431_1, all_1621_3,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (412), (493) gives:
% 213.38/30.56 | (609) all_1621_3 = all_1431_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1558_2, all_1624_0,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (463), (496) gives:
% 213.38/30.56 | (610) all_1624_0 = all_1558_2
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1478_1, all_1627_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (426), (498) gives:
% 213.38/30.56 | (611) all_1627_1 = all_1478_1
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1325_2, all_1627_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (379), (498) gives:
% 213.38/30.56 | (612) all_1627_1 = all_1325_2
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1621_3, all_1630_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (493), (500) gives:
% 213.38/30.56 | (613) all_1630_1 = all_1621_3
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_771_0, all_1630_1, tc_RealDef_Oreal,
% 213.38/30.56 | simplifying with (189), (500) gives:
% 213.38/30.56 | (614) all_1630_1 = all_771_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1380_0, all_1633_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (406), (502) gives:
% 213.38/30.56 | (615) all_1633_1 = all_1380_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1302_0, all_1633_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (374), (502) gives:
% 213.38/30.56 | (616) all_1633_1 = all_1302_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1174_0, all_1633_1,
% 213.38/30.56 | tc_RealDef_Oreal, simplifying with (320), (502) gives:
% 213.38/30.56 | (617) all_1633_1 = all_1174_0
% 213.38/30.56 |
% 213.38/30.56 | GROUND_INST: instantiating (147) with all_1137_1, all_1633_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (301), (502) gives:
% 213.38/30.57 | (618) all_1633_1 = all_1137_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1633_1, all_1636_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (502), (504) gives:
% 213.38/30.57 | (619) all_1636_0 = all_1633_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1587_1, all_1636_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (475), (504) gives:
% 213.38/30.57 | (620) all_1636_0 = all_1587_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1555_1, all_1636_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (461), (504) gives:
% 213.38/30.57 | (621) all_1636_0 = all_1555_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1281_1, all_1636_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (364), (504) gives:
% 213.38/30.57 | (622) all_1636_0 = all_1281_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_962_0, all_1636_0, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (235), (504) gives:
% 213.38/30.57 | (623) all_1636_0 = all_962_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_959_1, all_1636_0, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (233), (504) gives:
% 213.38/30.57 | (624) all_1636_0 = all_959_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1624_0, all_1639_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (496), (506) gives:
% 213.38/30.57 | (625) all_1639_1 = all_1624_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1013_0, all_1639_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (266), (506) gives:
% 213.38/30.57 | (626) all_1639_1 = all_1013_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_888_1, all_1642_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (217), (508) gives:
% 213.38/30.57 | (627) all_1642_1 = all_888_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_860_0, all_1642_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (208), (508) gives:
% 213.38/30.57 | (628) all_1642_1 = all_860_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_806_0, all_1642_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (197), (508) gives:
% 213.38/30.57 | (629) all_1642_1 = all_806_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_693_0, all_1642_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (158), (508) gives:
% 213.38/30.57 | (630) all_1642_1 = all_693_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1521_2, all_1645_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (434), (510) gives:
% 213.38/30.57 | (631) all_1645_1 = all_1521_2
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1220_0, all_1645_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (340), (510) gives:
% 213.38/30.57 | (632) all_1645_1 = all_1220_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1171_0, all_1670_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (318), (539) gives:
% 213.38/30.57 | (633) all_1670_0 = all_1171_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_749_1, all_1670_0, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (174), (539) gives:
% 213.38/30.57 | (634) all_1670_0 = all_749_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1653_0, all_1656_4, tc_Nat_Onat,
% 213.38/30.57 | simplifying with (528), (532) gives:
% 213.38/30.57 | (635) all_1656_4 = all_1653_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1656_4, all_1667_0, tc_Nat_Onat,
% 213.38/30.57 | simplifying with (532), (537) gives:
% 213.38/30.57 | (636) all_1667_0 = all_1656_4
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_1667_0, all_1688_1, tc_Nat_Onat,
% 213.38/30.57 | simplifying with (537), (541) gives:
% 213.38/30.57 | (637) all_1688_1 = all_1667_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (147) with all_707_0, all_1688_1, tc_Nat_Onat,
% 213.38/30.57 | simplifying with (163), (541) gives:
% 213.38/30.57 | (638) all_1688_1 = all_707_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_833_2, all_980_1, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (204), (244) gives:
% 213.38/30.57 | (639) all_980_1 = all_833_2
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_980_1, all_1083_1, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (244), (281) gives:
% 213.38/30.57 | (640) all_1083_1 = all_980_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1083_1, all_1201_4, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (281), (330) gives:
% 213.38/30.57 | (641) all_1201_4 = all_1083_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1201_4, all_1346_4, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (330), (385) gives:
% 213.38/30.57 | (642) all_1346_4 = all_1201_4
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_699_0, all_1346_4, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (161), (385) gives:
% 213.38/30.57 | (643) all_1346_4 = all_699_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1346_4, all_1358_6, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (385), (393) gives:
% 213.38/30.57 | (644) all_1358_6 = all_1346_4
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1358_6, all_1524_9, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (393), (438) gives:
% 213.38/30.57 | (645) all_1524_9 = all_1358_6
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1524_9, all_1526_8, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (438), (449) gives:
% 213.38/30.57 | (646) all_1526_8 = all_1524_9
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1526_8, all_1561_6, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (449), (467) gives:
% 213.38/30.57 | (647) all_1561_6 = all_1526_8
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1589_9, all_1651_11, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (483), (518) gives:
% 213.38/30.57 | (648) all_1651_11 = all_1589_9
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1561_6, all_1651_11, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (467), (518) gives:
% 213.38/30.57 | (649) all_1651_11 = all_1561_6
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1241_5, all_1651_11, v_q____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (351), (518) gives:
% 213.38/30.57 | (650) all_1651_11 = all_1241_5
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_880_2, all_980_3, v_pa____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (214), (245) gives:
% 213.38/30.57 | (651) all_980_3 = all_880_2
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_980_3, all_1083_0, v_pa____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (245), (282) gives:
% 213.38/30.57 | (652) all_1083_0 = all_980_3
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1083_0, all_1092_4, v_pa____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (282), (285) gives:
% 213.38/30.57 | (653) all_1092_4 = all_1083_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1092_4, all_1109_2, v_pa____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (285), (293) gives:
% 213.38/30.57 | (654) all_1109_2 = all_1092_4
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1109_2, all_1214_2, v_pa____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (293), (336) gives:
% 213.38/30.57 | (655) all_1214_2 = all_1109_2
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1214_2, all_1235_2, v_pa____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (336), (344) gives:
% 213.38/30.57 | (656) all_1235_2 = all_1214_2
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_1235_2, all_1346_0, v_pa____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (344), (386) gives:
% 213.38/30.57 | (657) all_1346_0 = all_1235_2
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (151) with all_691_0, all_1346_0, v_pa____,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (156), (386) gives:
% 213.38/30.57 | (658) all_1346_0 = all_691_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (148) with all_1180_0, all_1526_5,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (322), (453) gives:
% 213.38/30.57 | (659) all_1526_5 = all_1180_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (148) with all_1526_5, all_1543_1,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (453), (457) gives:
% 213.38/30.57 | (660) all_1543_1 = all_1526_5
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (148) with all_1543_1, all_1561_5,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (457), (471) gives:
% 213.38/30.57 | (661) all_1561_5 = all_1543_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (148) with all_1561_5, all_1589_7,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (471), (487) gives:
% 213.38/30.57 | (662) all_1589_7 = all_1561_5
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (148) with all_1589_7, all_1656_2,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (487), (533) gives:
% 213.38/30.57 | (663) all_1656_2 = all_1589_7
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (148) with all_1022_0, all_1656_2,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (268), (533) gives:
% 213.38/30.57 | (664) all_1656_2 = all_1022_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1358_0, all_1656_3,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (397), (534) gives:
% 213.38/30.57 | (665) all_1656_3 = all_1358_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_746_0, all_1656_3,
% 213.38/30.57 | tc_Complex_Ocomplex, simplifying with (172), (534) gives:
% 213.38/30.57 | (666) all_1656_3 = all_746_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_737_0, all_759_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (169), (185) gives:
% 213.38/30.57 | (667) all_759_1 = all_737_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_759_1, all_785_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (185), (194) gives:
% 213.38/30.57 | (668) all_785_1 = all_759_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_785_1, all_944_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (194), (226) gives:
% 213.38/30.57 | (669) all_944_1 = all_785_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_944_1, all_950_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (226), (229) gives:
% 213.38/30.57 | (670) all_950_1 = all_944_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_950_1, all_988_0, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (229), (252) gives:
% 213.38/30.57 | (671) all_988_0 = all_950_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_988_0, all_992_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (252), (254) gives:
% 213.38/30.57 | (672) all_992_1 = all_988_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_992_1, all_995_0, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (254), (256) gives:
% 213.38/30.57 | (673) all_995_0 = all_992_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_944_1, all_1007_0, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (226), (264) gives:
% 213.38/30.57 | (674) all_1007_0 = all_944_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1007_0, all_1094_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (264), (288) gives:
% 213.38/30.57 | (675) all_1094_0 = all_1007_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_995_0, all_1131_0, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (256), (299) gives:
% 213.38/30.57 | (676) all_1131_0 = all_995_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1046_0, all_1143_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (275), (303) gives:
% 213.38/30.57 | (677) all_1143_0 = all_1046_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1094_0, all_1149_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (288), (307) gives:
% 213.38/30.57 | (678) all_1149_0 = all_1094_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1143_0, all_1166_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (303), (315) gives:
% 213.38/30.57 | (679) all_1166_0 = all_1143_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1149_0, all_1281_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (307), (365) gives:
% 213.38/30.57 | (680) all_1281_0 = all_1149_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1281_0, all_1284_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (365), (368) gives:
% 213.38/30.57 | (681) all_1284_0 = all_1281_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1131_0, all_1293_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (299), (371) gives:
% 213.38/30.57 | (682) all_1293_1 = all_1131_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1293_1, all_1304_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (371), (377) gives:
% 213.38/30.57 | (683) all_1304_0 = all_1293_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1304_0, all_1325_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (377), (380) gives:
% 213.38/30.57 | (684) all_1325_1 = all_1304_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1166_0, all_1355_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (315), (388) gives:
% 213.38/30.57 | (685) all_1355_1 = all_1166_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_752_1, all_1355_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (176), (388) gives:
% 213.38/30.57 | (686) all_1355_1 = all_752_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1046_0, all_1368_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (275), (403) gives:
% 213.38/30.57 | (687) all_1368_1 = all_1046_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1025_0, all_1368_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (270), (403) gives:
% 213.38/30.57 | (688) all_1368_1 = all_1025_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_759_1, all_1368_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (185), (403) gives:
% 213.38/30.57 | (689) all_1368_1 = all_759_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1325_1, all_1494_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (380), (430) gives:
% 213.38/30.57 | (690) all_1494_0 = all_1325_1
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1112_0, all_1509_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (295), (432) gives:
% 213.38/30.57 | (691) all_1509_0 = all_1112_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1007_0, all_1509_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (264), (432) gives:
% 213.38/30.57 | (692) all_1509_0 = all_1007_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_910_0, all_1509_0, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (223), (432) gives:
% 213.38/30.57 | (693) all_1509_0 = all_910_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1494_0, all_1621_1,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (430), (494) gives:
% 213.38/30.57 | (694) all_1621_1 = all_1494_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_754_0, all_1621_1, tc_RealDef_Oreal,
% 213.38/30.57 | simplifying with (180), (494) gives:
% 213.38/30.57 | (695) all_1621_1 = all_754_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1284_0, all_1651_3,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (368), (522) gives:
% 213.38/30.57 | (696) all_1651_3 = all_1284_0
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1651_3, all_1656_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (522), (535) gives:
% 213.38/30.57 | (697) all_1656_0 = all_1651_3
% 213.38/30.57 |
% 213.38/30.57 | GROUND_INST: instantiating (149) with all_1004_0, all_1656_0,
% 213.38/30.57 | tc_RealDef_Oreal, simplifying with (261), (535) gives:
% 213.38/30.57 | (698) all_1656_0 = all_1004_0
% 213.38/30.57 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_754_1, all_785_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (181), (195) gives:
% 213.38/30.58 | (699) all_785_0 = all_754_1
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_785_0, all_891_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (195), (219) gives:
% 213.38/30.58 | (700) all_891_0 = all_785_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_891_0, all_974_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (219), (239) gives:
% 213.38/30.58 | (701) all_974_0 = all_891_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_891_0, all_1055_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (219), (277) gives:
% 213.38/30.58 | (702) all_1055_0 = all_891_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1158_1, all_1275_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (311), (360) gives:
% 213.38/30.58 | (703) all_1275_0 = all_1158_1
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_813_0, all_1275_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (199), (360) gives:
% 213.38/30.58 | (704) all_1275_0 = all_813_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1031_1, all_1293_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (272), (372) gives:
% 213.38/30.58 | (705) all_1293_0 = all_1031_1
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_974_0, all_1325_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (239), (381) gives:
% 213.38/30.58 | (706) all_1325_0 = all_974_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1325_0, all_1368_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (381), (404) gives:
% 213.38/30.58 | (707) all_1368_0 = all_1325_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1293_0, all_1368_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (372), (404) gives:
% 213.38/30.58 | (708) all_1368_0 = all_1293_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1158_1, all_1368_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (311), (404) gives:
% 213.38/30.58 | (709) all_1368_0 = all_1158_1
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1055_0, all_1437_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (277), (414) gives:
% 213.38/30.58 | (710) all_1437_0 = all_1055_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_752_0, all_1437_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (177), (414) gives:
% 213.38/30.58 | (711) all_1437_0 = all_752_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1325_0, all_1463_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (381), (418) gives:
% 213.38/30.58 | (712) all_1463_0 = all_1325_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_998_1, all_1463_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (258), (418) gives:
% 213.38/30.58 | (713) all_1463_0 = all_998_1
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1443_1, all_1472_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (416), (422) gives:
% 213.38/30.58 | (714) all_1472_0 = all_1443_1
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1368_0, all_1472_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (404), (422) gives:
% 213.38/30.58 | (715) all_1472_0 = all_1368_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1166_1, all_1472_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (316), (422) gives:
% 213.38/30.58 | (716) all_1472_0 = all_1166_1
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1143_1, all_1615_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (304), (491) gives:
% 213.38/30.58 | (717) all_1615_0 = all_1143_1
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_1055_0, all_1615_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (277), (491) gives:
% 213.38/30.58 | (718) all_1615_0 = all_1055_0
% 213.38/30.58 |
% 213.38/30.58 | GROUND_INST: instantiating (149) with all_971_0, all_1615_0, tc_Nat_Onat,
% 213.38/30.58 | simplifying with (237), (491) gives:
% 213.38/30.58 | (719) all_1615_0 = all_971_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (637), (638) imply:
% 213.38/30.58 | (720) all_1667_0 = all_707_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (720) implies:
% 213.38/30.58 | (721) all_1667_0 = all_707_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (633), (634) imply:
% 213.38/30.58 | (722) all_1171_0 = all_749_1
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (722) implies:
% 213.38/30.58 | (723) all_1171_0 = all_749_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (636), (721) imply:
% 213.38/30.58 | (724) all_1656_4 = all_707_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (724) implies:
% 213.38/30.58 | (725) all_1656_4 = all_707_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (697), (698) imply:
% 213.38/30.58 | (726) all_1651_3 = all_1004_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (726) implies:
% 213.38/30.58 | (727) all_1651_3 = all_1004_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (663), (664) imply:
% 213.38/30.58 | (728) all_1589_7 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (728) implies:
% 213.38/30.58 | (729) all_1589_7 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (665), (666) imply:
% 213.38/30.58 | (730) all_1358_0 = all_746_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (730) implies:
% 213.38/30.58 | (731) all_1358_0 = all_746_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (635), (725) imply:
% 213.38/30.58 | (732) all_1653_0 = all_707_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (732) implies:
% 213.38/30.58 | (733) all_1653_0 = all_707_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (556), (557) imply:
% 213.38/30.58 | (734) all_1346_3 = all_1241_4
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (555), (556) imply:
% 213.38/30.58 | (735) all_1358_5 = all_1346_3
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (735) implies:
% 213.38/30.58 | (736) all_1358_5 = all_1346_3
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (696), (727) imply:
% 213.38/30.58 | (737) all_1284_0 = all_1004_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (737) implies:
% 213.38/30.58 | (738) all_1284_0 = all_1004_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (553), (554) imply:
% 213.38/30.58 | (739) all_1589_6 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (739) implies:
% 213.38/30.58 | (740) all_1589_6 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (648), (649) imply:
% 213.38/30.58 | (741) all_1589_9 = all_1561_6
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (648), (650) imply:
% 213.38/30.58 | (742) all_1589_9 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (631), (632) imply:
% 213.38/30.58 | (743) all_1521_2 = all_1220_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (743) implies:
% 213.38/30.58 | (744) all_1521_2 = all_1220_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (628), (629) imply:
% 213.38/30.58 | (745) all_860_0 = all_806_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (745) implies:
% 213.38/30.58 | (746) all_860_0 = all_806_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (627), (629) imply:
% 213.38/30.58 | (747) all_888_1 = all_806_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (747) implies:
% 213.38/30.58 | (748) all_888_1 = all_806_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (629), (630) imply:
% 213.38/30.58 | (749) all_806_0 = all_693_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (625), (626) imply:
% 213.38/30.58 | (750) all_1624_0 = all_1013_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (750) implies:
% 213.38/30.58 | (751) all_1624_0 = all_1013_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (620), (624) imply:
% 213.38/30.58 | (752) all_1587_1 = all_959_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (620), (623) imply:
% 213.38/30.58 | (753) all_1587_1 = all_962_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (620), (622) imply:
% 213.38/30.58 | (754) all_1587_1 = all_1281_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (619), (620) imply:
% 213.38/30.58 | (755) all_1633_1 = all_1587_1
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (755) implies:
% 213.38/30.58 | (756) all_1633_1 = all_1587_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (620), (621) imply:
% 213.38/30.58 | (757) all_1587_1 = all_1555_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (615), (756) imply:
% 213.38/30.58 | (758) all_1587_1 = all_1380_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (758) implies:
% 213.38/30.58 | (759) all_1587_1 = all_1380_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (615), (618) imply:
% 213.38/30.58 | (760) all_1380_0 = all_1137_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (615), (617) imply:
% 213.38/30.58 | (761) all_1380_0 = all_1174_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (615), (616) imply:
% 213.38/30.58 | (762) all_1380_0 = all_1302_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (613), (614) imply:
% 213.38/30.58 | (763) all_1621_3 = all_771_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (763) implies:
% 213.38/30.58 | (764) all_1621_3 = all_771_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (611), (612) imply:
% 213.38/30.58 | (765) all_1478_1 = all_1325_2
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (765) implies:
% 213.38/30.58 | (766) all_1478_1 = all_1325_2
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (610), (751) imply:
% 213.38/30.58 | (767) all_1558_2 = all_1013_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (767) implies:
% 213.38/30.58 | (768) all_1558_2 = all_1013_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (694), (695) imply:
% 213.38/30.58 | (769) all_1494_0 = all_754_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (769) implies:
% 213.38/30.58 | (770) all_1494_0 = all_754_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (609), (764) imply:
% 213.38/30.58 | (771) all_1431_1 = all_771_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (771) implies:
% 213.38/30.58 | (772) all_1431_1 = all_771_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (717), (719) imply:
% 213.38/30.58 | (773) all_1143_1 = all_971_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (717), (718) imply:
% 213.38/30.58 | (774) all_1143_1 = all_1055_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (607), (608) imply:
% 213.38/30.58 | (775) all_1106_0 = all_950_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (775) implies:
% 213.38/30.58 | (776) all_1106_0 = all_950_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (552), (740) imply:
% 213.38/30.58 | (777) all_1561_4 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (777) implies:
% 213.38/30.58 | (778) all_1561_4 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (662), (729) imply:
% 213.38/30.58 | (779) all_1561_5 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (779) implies:
% 213.38/30.58 | (780) all_1561_5 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (741), (742) imply:
% 213.38/30.58 | (781) all_1561_6 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (781) implies:
% 213.38/30.58 | (782) all_1561_6 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (753), (754) imply:
% 213.38/30.58 | (783) all_1281_1 = all_962_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (752), (754) imply:
% 213.38/30.58 | (784) all_1281_1 = all_959_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (754), (757) imply:
% 213.38/30.58 | (785) all_1555_1 = all_1281_1
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (785) implies:
% 213.38/30.58 | (786) all_1555_1 = all_1281_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (754), (759) imply:
% 213.38/30.58 | (787) all_1380_0 = all_1281_1
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (787) implies:
% 213.38/30.58 | (788) all_1380_0 = all_1281_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (605), (606) imply:
% 213.38/30.58 | (789) all_1549_1 = all_734_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (789) implies:
% 213.38/30.58 | (790) all_1549_1 = all_734_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (551), (778) imply:
% 213.38/30.58 | (791) all_1526_7 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (791) implies:
% 213.38/30.58 | (792) all_1526_7 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (661), (780) imply:
% 213.38/30.58 | (793) all_1543_1 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (793) implies:
% 213.38/30.58 | (794) all_1543_1 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (647), (782) imply:
% 213.38/30.58 | (795) all_1526_8 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (795) implies:
% 213.38/30.58 | (796) all_1526_8 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (604), (768) imply:
% 213.38/30.58 | (797) all_1469_0 = all_1013_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (797) implies:
% 213.38/30.58 | (798) all_1469_0 = all_1013_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (603), (786) imply:
% 213.38/30.58 | (799) all_1281_1 = all_1211_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (799) implies:
% 213.38/30.58 | (800) all_1281_1 = all_1211_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (602), (790) imply:
% 213.38/30.58 | (801) all_1537_1 = all_734_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (801) implies:
% 213.38/30.58 | (802) all_1537_1 = all_734_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (660), (794) imply:
% 213.38/30.58 | (803) all_1526_5 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (803) implies:
% 213.38/30.58 | (804) all_1526_5 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (601), (802) imply:
% 213.38/30.58 | (805) all_1363_0 = all_734_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (805) implies:
% 213.38/30.58 | (806) all_1363_0 = all_734_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (659), (804) imply:
% 213.38/30.58 | (807) all_1180_0 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (807) implies:
% 213.38/30.58 | (808) all_1180_0 = all_1022_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (550), (792) imply:
% 213.38/30.58 | (809) all_1524_8 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (809) implies:
% 213.38/30.58 | (810) all_1524_8 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (646), (796) imply:
% 213.38/30.58 | (811) all_1524_9 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (811) implies:
% 213.38/30.58 | (812) all_1524_9 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (549), (810) imply:
% 213.38/30.58 | (813) all_1358_5 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (813) implies:
% 213.38/30.58 | (814) all_1358_5 = all_880_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (645), (812) imply:
% 213.38/30.58 | (815) all_1358_6 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (815) implies:
% 213.38/30.58 | (816) all_1358_6 = all_1241_5
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (600), (744) imply:
% 213.38/30.58 | (817) all_1220_0 = all_1073_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (599), (744) imply:
% 213.38/30.58 | (818) all_1220_0 = all_1192_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (691), (692) imply:
% 213.38/30.58 | (819) all_1112_0 = all_1007_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (691), (693) imply:
% 213.38/30.58 | (820) all_1112_0 = all_910_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (690), (770) imply:
% 213.38/30.58 | (821) all_1325_1 = all_754_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (821) implies:
% 213.38/30.58 | (822) all_1325_1 = all_754_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (596), (598) imply:
% 213.38/30.58 | (823) all_1401_1 = all_982_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (596), (597) imply:
% 213.38/30.58 | (824) all_1401_1 = all_1263_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (595), (766) imply:
% 213.38/30.58 | (825) all_1475_0 = all_1325_2
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (825) implies:
% 213.38/30.58 | (826) all_1475_0 = all_1325_2
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (593), (826) imply:
% 213.38/30.58 | (827) all_1325_2 = all_1115_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (594), (826) imply:
% 213.38/30.58 | (828) all_1325_2 = all_849_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (714), (715) imply:
% 213.38/30.58 | (829) all_1443_1 = all_1368_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (714), (716) imply:
% 213.38/30.58 | (830) all_1443_1 = all_1166_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (592), (798) imply:
% 213.38/30.58 | (831) all_1304_1 = all_1013_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (831) implies:
% 213.38/30.58 | (832) all_1304_1 = all_1013_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (712), (713) imply:
% 213.38/30.58 | (833) all_1325_0 = all_998_1
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (833) implies:
% 213.38/30.58 | (834) all_1325_0 = all_998_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (829), (830) imply:
% 213.38/30.58 | (835) all_1368_0 = all_1166_1
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (835) implies:
% 213.38/30.58 | (836) all_1368_0 = all_1166_1
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (710), (711) imply:
% 213.38/30.58 | (837) all_1055_0 = all_752_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (837) implies:
% 213.38/30.58 | (838) all_1055_0 = all_752_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (591), (772) imply:
% 213.38/30.58 | (839) all_1284_1 = all_771_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (839) implies:
% 213.38/30.58 | (840) all_1284_1 = all_771_0
% 213.38/30.58 |
% 213.38/30.58 | COMBINE_EQS: (823), (824) imply:
% 213.38/30.58 | (841) all_1263_0 = all_982_0
% 213.38/30.58 |
% 213.38/30.58 | SIMP: (841) implies:
% 213.38/30.59 | (842) all_1263_0 = all_982_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (589), (590) imply:
% 213.38/30.59 | (843) all_1217_0 = all_1007_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (843) implies:
% 213.38/30.59 | (844) all_1217_0 = all_1007_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (760), (762) imply:
% 213.38/30.59 | (845) all_1302_0 = all_1137_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (845) implies:
% 213.38/30.59 | (846) all_1302_0 = all_1137_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (760), (761) imply:
% 213.38/30.59 | (847) all_1174_0 = all_1137_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (847) implies:
% 213.38/30.59 | (848) all_1174_0 = all_1137_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (760), (788) imply:
% 213.38/30.59 | (849) all_1281_1 = all_1137_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (849) implies:
% 213.38/30.59 | (850) all_1281_1 = all_1137_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (709), (836) imply:
% 213.38/30.59 | (851) all_1166_1 = all_1158_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (708), (836) imply:
% 213.38/30.59 | (852) all_1293_0 = all_1166_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (852) implies:
% 213.38/30.59 | (853) all_1293_0 = all_1166_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (707), (836) imply:
% 213.38/30.59 | (854) all_1325_0 = all_1166_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (854) implies:
% 213.38/30.59 | (855) all_1325_0 = all_1166_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (687), (688) imply:
% 213.38/30.59 | (856) all_1046_0 = all_1025_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (856) implies:
% 213.38/30.59 | (857) all_1046_0 = all_1025_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (688), (689) imply:
% 213.38/30.59 | (858) all_1025_0 = all_759_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (587), (588) imply:
% 213.38/30.59 | (859) all_1094_1 = all_769_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (859) implies:
% 213.38/30.59 | (860) all_1094_1 = all_769_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (586), (806) imply:
% 213.38/30.59 | (861) all_1293_2 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (861) implies:
% 213.38/30.59 | (862) all_1293_2 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (736), (814) imply:
% 213.38/30.59 | (863) all_1346_3 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (863) implies:
% 213.38/30.59 | (864) all_1346_3 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (644), (816) imply:
% 213.38/30.59 | (865) all_1346_4 = all_1241_5
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (865) implies:
% 213.38/30.59 | (866) all_1346_4 = all_1241_5
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (685), (686) imply:
% 213.38/30.59 | (867) all_1166_0 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (867) implies:
% 213.38/30.59 | (868) all_1166_0 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (657), (658) imply:
% 213.38/30.59 | (869) all_1235_2 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (869) implies:
% 213.38/30.59 | (870) all_1235_2 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (734), (864) imply:
% 213.38/30.59 | (871) all_1241_4 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (871) implies:
% 213.38/30.59 | (872) all_1241_4 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (642), (866) imply:
% 213.38/30.59 | (873) all_1241_5 = all_1201_4
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (643), (866) imply:
% 213.38/30.59 | (874) all_1241_5 = all_699_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (706), (834) imply:
% 213.38/30.59 | (875) all_998_1 = all_974_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (834), (855) imply:
% 213.38/30.59 | (876) all_1166_1 = all_998_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (876) implies:
% 213.38/30.59 | (877) all_1166_1 = all_998_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (684), (822) imply:
% 213.38/30.59 | (878) all_1304_0 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (878) implies:
% 213.38/30.59 | (879) all_1304_0 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (827), (828) imply:
% 213.38/30.59 | (880) all_1115_1 = all_849_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (880) implies:
% 213.38/30.59 | (881) all_1115_1 = all_849_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (683), (879) imply:
% 213.38/30.59 | (882) all_1293_1 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (882) implies:
% 213.38/30.59 | (883) all_1293_1 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (585), (832) imply:
% 213.38/30.59 | (884) all_1302_0 = all_1013_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (884) implies:
% 213.38/30.59 | (885) all_1302_0 = all_1013_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (846), (885) imply:
% 213.38/30.59 | (886) all_1137_1 = all_1013_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (886) implies:
% 213.38/30.59 | (887) all_1137_1 = all_1013_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (705), (853) imply:
% 213.38/30.59 | (888) all_1166_1 = all_1031_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (888) implies:
% 213.38/30.59 | (889) all_1166_1 = all_1031_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (682), (883) imply:
% 213.38/30.59 | (890) all_1131_0 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (890) implies:
% 213.38/30.59 | (891) all_1131_0 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (584), (862) imply:
% 213.38/30.59 | (892) all_1238_1 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (892) implies:
% 213.38/30.59 | (893) all_1238_1 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (681), (738) imply:
% 213.38/30.59 | (894) all_1281_0 = all_1004_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (894) implies:
% 213.38/30.59 | (895) all_1281_0 = all_1004_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (583), (840) imply:
% 213.38/30.59 | (896) all_1269_1 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (896) implies:
% 213.38/30.59 | (897) all_1269_1 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (680), (895) imply:
% 213.38/30.59 | (898) all_1149_0 = all_1004_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (898) implies:
% 213.38/30.59 | (899) all_1149_0 = all_1004_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (784), (800) imply:
% 213.38/30.59 | (900) all_1211_0 = all_959_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (783), (800) imply:
% 213.38/30.59 | (901) all_1211_0 = all_962_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (800), (850) imply:
% 213.38/30.59 | (902) all_1211_0 = all_1137_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (579), (580) imply:
% 213.38/30.59 | (903) all_1171_0 = all_1163_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (903) implies:
% 213.38/30.59 | (904) all_1171_0 = all_1163_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (580), (581) imply:
% 213.38/30.59 | (905) all_1163_1 = all_888_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (580), (582) imply:
% 213.38/30.59 | (906) all_1163_1 = all_774_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (703), (704) imply:
% 213.38/30.59 | (907) all_1158_1 = all_813_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (907) implies:
% 213.38/30.59 | (908) all_1158_1 = all_813_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (578), (897) imply:
% 213.38/30.59 | (909) all_1192_0 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (909) implies:
% 213.38/30.59 | (910) all_1192_0 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (577), (842) imply:
% 213.38/30.59 | (911) all_1149_2 = all_982_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (911) implies:
% 213.38/30.59 | (912) all_1149_2 = all_982_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (548), (872) imply:
% 213.38/30.59 | (913) all_1226_0 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (913) implies:
% 213.38/30.59 | (914) all_1226_0 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (873), (874) imply:
% 213.38/30.59 | (915) all_1201_4 = all_699_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (915) implies:
% 213.38/30.59 | (916) all_1201_4 = all_699_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (576), (893) imply:
% 213.38/30.59 | (917) all_1174_0 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (917) implies:
% 213.38/30.59 | (918) all_1174_0 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (656), (870) imply:
% 213.38/30.59 | (919) all_1214_2 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (919) implies:
% 213.38/30.59 | (920) all_1214_2 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (547), (914) imply:
% 213.38/30.59 | (921) all_1201_3 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (921) implies:
% 213.38/30.59 | (922) all_1201_3 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (817), (818) imply:
% 213.38/30.59 | (923) all_1192_0 = all_1073_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (923) implies:
% 213.38/30.59 | (924) all_1192_0 = all_1073_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (575), (844) imply:
% 213.38/30.59 | (925) all_1189_0 = all_1007_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (925) implies:
% 213.38/30.59 | (926) all_1189_0 = all_1007_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (655), (920) imply:
% 213.38/30.59 | (927) all_1109_2 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (927) implies:
% 213.38/30.59 | (928) all_1109_2 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (900), (901) imply:
% 213.38/30.59 | (929) all_962_0 = all_959_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (901), (902) imply:
% 213.38/30.59 | (930) all_1137_1 = all_962_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (930) implies:
% 213.38/30.59 | (931) all_1137_1 = all_962_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (546), (922) imply:
% 213.38/30.59 | (932) all_1092_2 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (932) implies:
% 213.38/30.59 | (933) all_1092_2 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (641), (916) imply:
% 213.38/30.59 | (934) all_1083_1 = all_699_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (934) implies:
% 213.38/30.59 | (935) all_1083_1 = all_699_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (574), (924) imply:
% 213.38/30.59 | (936) all_1073_1 = all_985_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (573), (924) imply:
% 213.38/30.59 | (937) all_1189_0 = all_1073_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (937) implies:
% 213.38/30.59 | (938) all_1189_0 = all_1073_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (910), (924) imply:
% 213.38/30.59 | (939) all_1073_1 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (926), (938) imply:
% 213.38/30.59 | (940) all_1073_1 = all_1007_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (940) implies:
% 213.38/30.59 | (941) all_1073_1 = all_1007_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (572), (848) imply:
% 213.38/30.59 | (942) all_1155_1 = all_1137_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (572), (918) imply:
% 213.38/30.59 | (943) all_1155_1 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (570), (571) imply:
% 213.38/30.59 | (944) all_1046_1 = all_944_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (944) implies:
% 213.38/30.59 | (945) all_1046_1 = all_944_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (571), (904) imply:
% 213.38/30.59 | (946) all_1163_1 = all_944_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (946) implies:
% 213.38/30.59 | (947) all_1163_1 = all_944_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (571), (723) imply:
% 213.38/30.59 | (948) all_944_0 = all_749_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (679), (868) imply:
% 213.38/30.59 | (949) all_1143_0 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (949) implies:
% 213.38/30.59 | (950) all_1143_0 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (877), (889) imply:
% 213.38/30.59 | (951) all_1031_1 = all_998_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (851), (889) imply:
% 213.38/30.59 | (952) all_1158_1 = all_1031_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (952) implies:
% 213.38/30.59 | (953) all_1158_1 = all_1031_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (905), (906) imply:
% 213.38/30.59 | (954) all_888_1 = all_774_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (954) implies:
% 213.38/30.59 | (955) all_888_1 = all_774_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (906), (947) imply:
% 213.38/30.59 | (956) all_944_0 = all_774_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (956) implies:
% 213.38/30.59 | (957) all_944_0 = all_774_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (908), (953) imply:
% 213.38/30.59 | (958) all_1031_1 = all_813_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (958) implies:
% 213.38/30.59 | (959) all_1031_1 = all_813_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (942), (943) imply:
% 213.38/30.59 | (960) all_1137_1 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (960) implies:
% 213.38/30.59 | (961) all_1137_1 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (678), (899) imply:
% 213.38/30.59 | (962) all_1094_0 = all_1004_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (962) implies:
% 213.38/30.59 | (963) all_1094_0 = all_1004_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (568), (569) imply:
% 213.38/30.59 | (964) all_1004_1 = all_988_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (568), (912) imply:
% 213.38/30.59 | (965) all_1004_1 = all_982_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (677), (950) imply:
% 213.38/30.59 | (966) all_1046_0 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (966) implies:
% 213.38/30.59 | (967) all_1046_0 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (773), (774) imply:
% 213.38/30.59 | (968) all_1055_0 = all_971_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (968) implies:
% 213.38/30.59 | (969) all_1055_0 = all_971_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (887), (931) imply:
% 213.38/30.59 | (970) all_1013_0 = all_962_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (887), (961) imply:
% 213.38/30.59 | (971) all_1013_0 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (676), (891) imply:
% 213.38/30.59 | (972) all_995_0 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (972) implies:
% 213.38/30.59 | (973) all_995_0 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (567), (881) imply:
% 213.38/30.59 | (974) all_1046_1 = all_849_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (974) implies:
% 213.38/30.59 | (975) all_1046_1 = all_849_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (819), (820) imply:
% 213.38/30.59 | (976) all_1007_0 = all_910_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (976) implies:
% 213.38/30.59 | (977) all_1007_0 = all_910_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (654), (928) imply:
% 213.38/30.59 | (978) all_1092_4 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (978) implies:
% 213.38/30.59 | (979) all_1092_4 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (565), (776) imply:
% 213.38/30.59 | (980) all_959_1 = all_950_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (980) implies:
% 213.38/30.59 | (981) all_959_1 = all_950_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (566), (776) imply:
% 213.38/30.59 | (982) all_950_0 = all_904_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (675), (963) imply:
% 213.38/30.59 | (983) all_1007_0 = all_1004_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (983) implies:
% 213.38/30.59 | (984) all_1007_0 = all_1004_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (564), (860) imply:
% 213.38/30.59 | (985) all_769_0 = all_759_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (563), (860) imply:
% 213.38/30.59 | (986) all_904_0 = all_769_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (986) implies:
% 213.38/30.59 | (987) all_904_0 = all_769_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (545), (933) imply:
% 213.38/30.59 | (988) all_980_0 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (988) implies:
% 213.38/30.59 | (989) all_980_0 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (653), (979) imply:
% 213.38/30.59 | (990) all_1083_0 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (990) implies:
% 213.38/30.59 | (991) all_1083_0 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (652), (991) imply:
% 213.38/30.59 | (992) all_980_3 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (992) implies:
% 213.38/30.59 | (993) all_980_3 = all_691_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (640), (935) imply:
% 213.38/30.59 | (994) all_980_1 = all_699_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (994) implies:
% 213.38/30.59 | (995) all_980_1 = all_699_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (936), (941) imply:
% 213.38/30.59 | (996) all_1007_1 = all_985_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (939), (941) imply:
% 213.38/30.59 | (997) all_1007_1 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (838), (969) imply:
% 213.38/30.59 | (998) all_971_0 = all_752_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (702), (969) imply:
% 213.38/30.59 | (999) all_971_0 = all_891_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (857), (967) imply:
% 213.38/30.59 | (1000) all_1025_0 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1000) implies:
% 213.38/30.59 | (1001) all_1025_0 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (945), (975) imply:
% 213.38/30.59 | (1002) all_944_0 = all_849_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1002) implies:
% 213.38/30.59 | (1003) all_944_0 = all_849_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (951), (959) imply:
% 213.38/30.59 | (1004) all_998_1 = all_813_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1004) implies:
% 213.38/30.59 | (1005) all_998_1 = all_813_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (858), (1001) imply:
% 213.38/30.59 | (1006) all_759_1 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1006) implies:
% 213.38/30.59 | (1007) all_759_1 = all_752_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (970), (971) imply:
% 213.38/30.59 | (1008) all_962_0 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1008) implies:
% 213.38/30.59 | (1009) all_962_0 = all_734_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (674), (984) imply:
% 213.38/30.59 | (1010) all_1004_0 = all_944_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (977), (984) imply:
% 213.38/30.59 | (1011) all_1004_0 = all_910_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (996), (997) imply:
% 213.38/30.59 | (1012) all_985_1 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1012) implies:
% 213.38/30.59 | (1013) all_985_1 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (1010), (1011) imply:
% 213.38/30.59 | (1014) all_944_1 = all_910_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1014) implies:
% 213.38/30.59 | (1015) all_944_1 = all_910_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (964), (965) imply:
% 213.38/30.59 | (1016) all_988_1 = all_982_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1016) implies:
% 213.38/30.59 | (1017) all_988_1 = all_982_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (875), (1005) imply:
% 213.38/30.59 | (1018) all_974_0 = all_813_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1018) implies:
% 213.38/30.59 | (1019) all_974_0 = all_813_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (673), (973) imply:
% 213.38/30.59 | (1020) all_992_1 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1020) implies:
% 213.38/30.59 | (1021) all_992_1 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (672), (1021) imply:
% 213.38/30.59 | (1022) all_988_0 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1022) implies:
% 213.38/30.59 | (1023) all_988_0 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (671), (1023) imply:
% 213.38/30.59 | (1024) all_950_1 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1024) implies:
% 213.38/30.59 | (1025) all_950_1 = all_754_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (561), (1017) imply:
% 213.38/30.59 | (1026) all_982_0 = all_860_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (562), (1017) imply:
% 213.38/30.59 | (1027) all_982_0 = all_737_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (560), (1013) imply:
% 213.38/30.59 | (1028) all_956_1 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1028) implies:
% 213.38/30.59 | (1029) all_956_1 = all_771_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (1026), (1027) imply:
% 213.38/30.59 | (1030) all_860_0 = all_737_1
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1030) implies:
% 213.38/30.59 | (1031) all_860_0 = all_737_1
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (544), (989) imply:
% 213.38/30.59 | (1032) all_888_0 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | SIMP: (1032) implies:
% 213.38/30.59 | (1033) all_888_0 = all_880_0
% 213.38/30.59 |
% 213.38/30.59 | COMBINE_EQS: (639), (995) imply:
% 213.38/30.59 | (1034) all_833_2 = all_699_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1034) implies:
% 213.38/30.60 | (1035) all_833_2 = all_699_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (651), (993) imply:
% 213.38/30.60 | (1036) all_880_2 = all_691_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1036) implies:
% 213.38/30.60 | (1037) all_880_2 = all_691_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (701), (1019) imply:
% 213.38/30.60 | (1038) all_891_0 = all_813_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1038) implies:
% 213.38/30.60 | (1039) all_891_0 = all_813_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (998), (999) imply:
% 213.38/30.60 | (1040) all_891_0 = all_752_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1040) implies:
% 213.38/30.60 | (1041) all_891_0 = all_752_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (929), (1009) imply:
% 213.38/30.60 | (1042) all_959_1 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1042) implies:
% 213.38/30.60 | (1043) all_959_1 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (981), (1043) imply:
% 213.38/30.60 | (1044) all_950_0 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1044) implies:
% 213.38/30.60 | (1045) all_950_0 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (559), (1029) imply:
% 213.38/30.60 | (1046) all_888_1 = all_771_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1046) implies:
% 213.38/30.60 | (1047) all_888_1 = all_771_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (982), (1045) imply:
% 213.38/30.60 | (1048) all_904_0 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1048) implies:
% 213.38/30.60 | (1049) all_904_0 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (670), (1025) imply:
% 213.38/30.60 | (1050) all_944_1 = all_754_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1050) implies:
% 213.38/30.60 | (1051) all_944_1 = all_754_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (957), (1003) imply:
% 213.38/30.60 | (1052) all_849_0 = all_774_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (948), (1003) imply:
% 213.38/30.60 | (1053) all_849_0 = all_749_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (669), (1015) imply:
% 213.38/30.60 | (1054) all_910_0 = all_785_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1015), (1051) imply:
% 213.38/30.60 | (1055) all_910_0 = all_754_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1054), (1055) imply:
% 213.38/30.60 | (1056) all_785_1 = all_754_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1056) implies:
% 213.38/30.60 | (1057) all_785_1 = all_754_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (987), (1049) imply:
% 213.38/30.60 | (1058) all_769_0 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1058) implies:
% 213.38/30.60 | (1059) all_769_0 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (700), (1039) imply:
% 213.38/30.60 | (1060) all_813_0 = all_785_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1039), (1041) imply:
% 213.38/30.60 | (1061) all_813_0 = all_752_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (543), (1033) imply:
% 213.38/30.60 | (1062) all_880_0 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (542), (1033) imply:
% 213.38/30.60 | (1063) all_880_0 = all_833_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (748), (1047) imply:
% 213.38/30.60 | (1064) all_806_0 = all_771_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1064) implies:
% 213.38/30.60 | (1065) all_806_0 = all_771_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (955), (1047) imply:
% 213.38/30.60 | (1066) all_774_1 = all_771_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1066) implies:
% 213.38/30.60 | (1067) all_774_1 = all_771_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (558), (1047) imply:
% 213.38/30.60 | (1068) all_771_0 = all_759_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1062), (1063) imply:
% 213.38/30.60 | (1069) all_833_1 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (746), (1031) imply:
% 213.38/30.60 | (1070) all_806_0 = all_737_1
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1070) implies:
% 213.38/30.60 | (1071) all_806_0 = all_737_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1052), (1053) imply:
% 213.38/30.60 | (1072) all_774_1 = all_749_1
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1072) implies:
% 213.38/30.60 | (1073) all_774_1 = all_749_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1060), (1061) imply:
% 213.38/30.60 | (1074) all_785_0 = all_752_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1074) implies:
% 213.38/30.60 | (1075) all_785_0 = all_752_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (749), (1071) imply:
% 213.38/30.60 | (1076) all_737_1 = all_693_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1065), (1071) imply:
% 213.38/30.60 | (1077) all_771_0 = all_737_1
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1077) implies:
% 213.38/30.60 | (1078) all_771_0 = all_737_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (699), (1075) imply:
% 213.38/30.60 | (1079) all_754_1 = all_752_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1079) implies:
% 213.38/30.60 | (1080) all_754_1 = all_752_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (668), (1057) imply:
% 213.38/30.60 | (1081) all_759_1 = all_754_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1081) implies:
% 213.38/30.60 | (1082) all_759_1 = all_754_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1067), (1073) imply:
% 213.38/30.60 | (1083) all_771_0 = all_749_1
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1083) implies:
% 213.38/30.60 | (1084) all_771_0 = all_749_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1068), (1084) imply:
% 213.38/30.60 | (1085) all_759_0 = all_749_1
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1085) implies:
% 213.38/30.60 | (1086) all_759_0 = all_749_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1078), (1084) imply:
% 213.38/30.60 | (1087) all_749_1 = all_737_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (985), (1059) imply:
% 213.38/30.60 | (1088) all_759_0 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1088) implies:
% 213.38/30.60 | (1089) all_759_0 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1086), (1089) imply:
% 213.38/30.60 | (1090) all_749_1 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1090) implies:
% 213.38/30.60 | (1091) all_749_1 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (667), (1082) imply:
% 213.38/30.60 | (1092) all_754_0 = all_737_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1007), (1082) imply:
% 213.38/30.60 | (1093) all_754_0 = all_752_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1092), (1093) imply:
% 213.38/30.60 | (1094) all_752_1 = all_737_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1087), (1091) imply:
% 213.38/30.60 | (1095) all_737_1 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1095) implies:
% 213.38/30.60 | (1096) all_737_1 = all_734_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1076), (1096) imply:
% 213.38/30.60 | (1097) all_734_0 = all_693_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1091), (1097) imply:
% 213.38/30.60 | (1098) all_749_1 = all_693_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1084), (1098) imply:
% 213.38/30.60 | (1099) all_771_0 = all_693_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1055), (1092) imply:
% 213.38/30.60 | (1100) all_910_0 = all_737_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (989), (1062) imply:
% 213.38/30.60 | (1101) all_980_0 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (1011), (1100) imply:
% 213.38/30.60 | (1102) all_1004_0 = all_737_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (922), (1062) imply:
% 213.38/30.60 | (1103) all_1201_3 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (872), (1062) imply:
% 213.38/30.60 | (1104) all_1241_4 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (864), (1062) imply:
% 213.38/30.60 | (1105) all_1346_3 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (816), (874) imply:
% 213.38/30.60 | (1106) all_1358_6 = all_699_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (814), (1062) imply:
% 213.38/30.60 | (1107) all_1358_5 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (812), (874) imply:
% 213.38/30.60 | (1108) all_1524_9 = all_699_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (810), (1062) imply:
% 213.38/30.60 | (1109) all_1524_8 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (796), (874) imply:
% 213.38/30.60 | (1110) all_1526_8 = all_699_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (792), (1062) imply:
% 213.38/30.60 | (1111) all_1526_7 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (782), (874) imply:
% 213.38/30.60 | (1112) all_1561_6 = all_699_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (778), (1062) imply:
% 213.38/30.60 | (1113) all_1561_4 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (742), (874) imply:
% 213.38/30.60 | (1114) all_1589_9 = all_699_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (740), (1062) imply:
% 213.38/30.60 | (1115) all_1589_6 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (648), (1114) imply:
% 213.38/30.60 | (1116) all_1651_11 = all_699_0
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (554), (1062) imply:
% 213.38/30.60 | (1117) all_1651_10 = all_746_1
% 213.38/30.60 |
% 213.38/30.60 | COMBINE_EQS: (727), (1102) imply:
% 213.38/30.60 | (1118) all_1651_3 = all_737_0
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (210), (1062) imply:
% 213.38/30.60 | (1119) ~ (all_880_1 = all_746_1)
% 213.38/30.60 |
% 213.38/30.60 | SIMP: (1119) implies:
% 213.38/30.60 | (1120) ~ (all_880_1 = all_746_1)
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (182), (1080), (1092) imply:
% 213.38/30.60 | (1121) c_RealDef_Oreal(tc_Nat_Onat, all_752_0) = all_737_0
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (515), (1116), (1117) imply:
% 213.38/30.60 | (1122) hAPP(all_699_0, all_746_1) = all_1651_9
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (514), (1116) imply:
% 213.38/30.60 | (1123) hAPP(all_699_0, v_w____) = all_1651_2
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (479), (729) imply:
% 213.38/30.60 | (1124) hAPP(all_1022_0, all_1589_1) = all_1589_0
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (478), (1114), (1115) imply:
% 213.38/30.60 | (1125) hAPP(all_699_0, all_746_1) = all_1589_5
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (477), (1114) imply:
% 213.38/30.60 | (1126) hAPP(all_699_0, v_w____) = all_1589_8
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (465), (1112), (1113) imply:
% 213.38/30.60 | (1127) hAPP(all_699_0, all_746_1) = all_1561_3
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (446), (1111) imply:
% 213.38/30.60 | (1128) hAPP(all_1526_2, all_746_1) = all_1526_1
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (445), (804) imply:
% 213.38/30.60 | (1129) hAPP(all_1022_0, all_1526_1) = all_1526_0
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (444), (1110), (1111) imply:
% 213.38/30.60 | (1130) hAPP(all_699_0, all_746_1) = all_1526_6
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (436), (1108), (1109) imply:
% 213.38/30.60 | (1131) hAPP(all_699_0, all_746_1) = all_1524_7
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (391), (731), (1107) imply:
% 213.38/30.60 | (1132) hAPP(all_1358_1, all_746_1) = all_746_0
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (390), (1106), (1107) imply:
% 213.38/30.60 | (1133) hAPP(all_699_0, all_746_1) = all_1358_4
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (383), (643), (1105) imply:
% 213.38/30.60 | (1134) hAPP(all_699_0, all_746_1) = all_1346_2
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (349), (874), (1104) imply:
% 213.38/30.60 | (1135) hAPP(all_699_0, all_746_1) = all_1241_3
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (328), (916), (1103) imply:
% 213.38/30.60 | (1136) hAPP(all_699_0, all_746_1) = all_1201_2
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (292), (928) imply:
% 213.38/30.60 | (1137) hAPP(all_691_0, v_c____) = all_1109_1
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (242), (995), (1101) imply:
% 213.38/30.60 | (1138) hAPP(all_699_0, all_746_1) = all_980_2
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (241), (993) imply:
% 213.38/30.60 | (1139) hAPP(all_691_0, v_c____) = all_980_2
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (212), (1037) imply:
% 213.38/30.60 | (1140) hAPP(all_691_0, v_c____) = all_880_1
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (202), (1035), (1069) imply:
% 213.38/30.60 | (1141) hAPP(all_699_0, all_746_1) = all_833_0
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (201), (1069) imply:
% 213.38/30.60 | (1142) $i(all_746_1)
% 213.38/30.60 |
% 213.38/30.60 | REDUCE: (179), (1080) imply:
% 213.38/30.60 | (1143) $i(all_752_0)
% 213.38/30.60 |
% 213.79/30.60 | REDUCE: (165), (1097) imply:
% 213.79/30.60 | (1144) $i(all_693_0)
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_980_2, all_1109_1, v_c____,
% 213.79/30.60 | all_691_0, simplifying with (1137), (1139) gives:
% 213.79/30.60 | (1145) all_1109_1 = all_980_2
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_880_1, all_1109_1, v_c____,
% 213.79/30.60 | all_691_0, simplifying with (1137), (1140) gives:
% 213.79/30.60 | (1146) all_1109_1 = all_880_1
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1589_8, all_1651_2, v_w____,
% 213.79/30.60 | all_699_0, simplifying with (1123), (1126) gives:
% 213.79/30.60 | (1147) all_1651_2 = all_1589_8
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_980_2, all_1201_2, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1136), (1138) gives:
% 213.79/30.60 | (1148) all_1201_2 = all_980_2
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1201_2, all_1241_3, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1135), (1136) gives:
% 213.79/30.60 | (1149) all_1241_3 = all_1201_2
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1346_2, all_1358_4, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1133), (1134) gives:
% 213.79/30.60 | (1150) all_1358_4 = all_1346_2
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1241_3, all_1358_4, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1133), (1135) gives:
% 213.79/30.60 | (1151) all_1358_4 = all_1241_3
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1358_4, all_1524_7, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1131), (1133) gives:
% 213.79/30.60 | (1152) all_1524_7 = all_1358_4
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1561_3, all_1589_5, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1125), (1127) gives:
% 213.79/30.60 | (1153) all_1589_5 = all_1561_3
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1526_6, all_1589_5, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1125), (1130) gives:
% 213.79/30.60 | (1154) all_1589_5 = all_1526_6
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1524_7, all_1589_5, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1125), (1131) gives:
% 213.79/30.60 | (1155) all_1589_5 = all_1524_7
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_1561_3, all_1651_9, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1122), (1127) gives:
% 213.79/30.60 | (1156) all_1651_9 = all_1561_3
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (150) with all_833_0, all_1651_9, all_746_1,
% 213.79/30.60 | all_699_0, simplifying with (1122), (1141) gives:
% 213.79/30.60 | (1157) all_1651_9 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1156), (1157) imply:
% 213.79/30.60 | (1158) all_1561_3 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1158) implies:
% 213.79/30.60 | (1159) all_1561_3 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1153), (1154) imply:
% 213.79/30.60 | (1160) all_1561_3 = all_1526_6
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1160) implies:
% 213.79/30.60 | (1161) all_1561_3 = all_1526_6
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1154), (1155) imply:
% 213.79/30.60 | (1162) all_1526_6 = all_1524_7
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1159), (1161) imply:
% 213.79/30.60 | (1163) all_1526_6 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1163) implies:
% 213.79/30.60 | (1164) all_1526_6 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1162), (1164) imply:
% 213.79/30.60 | (1165) all_1524_7 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1165) implies:
% 213.79/30.60 | (1166) all_1524_7 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1152), (1166) imply:
% 213.79/30.60 | (1167) all_1358_4 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1167) implies:
% 213.79/30.60 | (1168) all_1358_4 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1150), (1151) imply:
% 213.79/30.60 | (1169) all_1346_2 = all_1241_3
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1150), (1168) imply:
% 213.79/30.60 | (1170) all_1346_2 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1169), (1170) imply:
% 213.79/30.60 | (1171) all_1241_3 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1171) implies:
% 213.79/30.60 | (1172) all_1241_3 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1149), (1172) imply:
% 213.79/30.60 | (1173) all_1201_2 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1173) implies:
% 213.79/30.60 | (1174) all_1201_2 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1148), (1174) imply:
% 213.79/30.60 | (1175) all_980_2 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1175) implies:
% 213.79/30.60 | (1176) all_980_2 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1145), (1146) imply:
% 213.79/30.60 | (1177) all_980_2 = all_880_1
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1176), (1177) imply:
% 213.79/30.60 | (1178) all_880_1 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | SIMP: (1178) implies:
% 213.79/30.60 | (1179) all_880_1 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | COMBINE_EQS: (1154), (1164) imply:
% 213.79/30.60 | (1180) all_1589_5 = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (1120), (1179) imply:
% 213.79/30.60 | (1181) ~ (all_833_0 = all_746_1)
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (523), (1147), (1157) imply:
% 213.79/30.60 | (1182) c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, all_1589_8,
% 213.79/30.60 | all_833_0) = all_1651_1
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (521), (1157) imply:
% 213.79/30.60 | (1183) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_833_0) =
% 213.79/30.60 | all_1651_8
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (486), (1180) imply:
% 213.79/30.60 | (1184) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_833_0) =
% 213.79/30.60 | all_1589_4
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (470), (1159) imply:
% 213.79/30.60 | (1185) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_833_0) =
% 213.79/30.60 | all_1561_2
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (452), (1164) imply:
% 213.79/30.60 | (1186) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_833_0) =
% 213.79/30.60 | all_1526_4
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (441), (1166) imply:
% 213.79/30.60 | (1187) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_833_0) =
% 213.79/30.60 | all_1524_6
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (396), (1168) imply:
% 213.79/30.60 | (1188) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_833_0) =
% 213.79/30.60 | all_1358_3
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (354), (1172) imply:
% 213.79/30.60 | (1189) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_833_0) =
% 213.79/30.60 | all_1241_2
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (332), (1174) imply:
% 213.79/30.60 | (1190) c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, all_833_0) =
% 213.79/30.60 | all_1201_1
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (481), (1180) imply:
% 213.79/30.60 | (1191) hAPP(all_1589_0, all_833_0) = all_1589_8
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (447), (1164) imply:
% 213.79/30.60 | (1192) hAPP(all_1526_0, all_833_0) = all_833_0
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (513), (1147) imply:
% 213.79/30.60 | (1193) $i(all_1589_8)
% 213.79/30.60 |
% 213.79/30.60 | REDUCE: (211), (1179) imply:
% 213.79/30.60 | (1194) $i(all_833_0)
% 213.79/30.60 |
% 213.79/30.60 | GROUND_INST: instantiating (152) with all_1358_3, all_1561_2, all_833_0,
% 213.79/30.60 | tc_Complex_Ocomplex, simplifying with (1185), (1188) gives:
% 213.79/30.60 | (1195) all_1561_2 = all_1358_3
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (152) with all_1201_1, all_1561_2, all_833_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1185), (1190) gives:
% 213.79/30.61 | (1196) all_1561_2 = all_1201_1
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (152) with all_1241_2, all_1589_4, all_833_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1184), (1189) gives:
% 213.79/30.61 | (1197) all_1589_4 = all_1241_2
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (152) with all_1589_4, all_1651_8, all_833_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1183), (1184) gives:
% 213.79/30.61 | (1198) all_1651_8 = all_1589_4
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (152) with all_1526_4, all_1651_8, all_833_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1183), (1186) gives:
% 213.79/30.61 | (1199) all_1651_8 = all_1526_4
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (152) with all_1524_6, all_1651_8, all_833_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1183), (1187) gives:
% 213.79/30.61 | (1200) all_1651_8 = all_1524_6
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (152) with all_1358_3, all_1651_8, all_833_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1183), (1188) gives:
% 213.79/30.61 | (1201) all_1651_8 = all_1358_3
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1199), (1201) imply:
% 213.79/30.61 | (1202) all_1526_4 = all_1358_3
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1199), (1200) imply:
% 213.79/30.61 | (1203) all_1526_4 = all_1524_6
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1198), (1199) imply:
% 213.79/30.61 | (1204) all_1589_4 = all_1526_4
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1204) implies:
% 213.79/30.61 | (1205) all_1589_4 = all_1526_4
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1197), (1205) imply:
% 213.79/30.61 | (1206) all_1526_4 = all_1241_2
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1206) implies:
% 213.79/30.61 | (1207) all_1526_4 = all_1241_2
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1195), (1196) imply:
% 213.79/30.61 | (1208) all_1358_3 = all_1201_1
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1208) implies:
% 213.79/30.61 | (1209) all_1358_3 = all_1201_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1203), (1207) imply:
% 213.79/30.61 | (1210) all_1524_6 = all_1241_2
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1202), (1203) imply:
% 213.79/30.61 | (1211) all_1524_6 = all_1358_3
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1210), (1211) imply:
% 213.79/30.61 | (1212) all_1358_3 = all_1241_2
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1212) implies:
% 213.79/30.61 | (1213) all_1358_3 = all_1241_2
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1209), (1213) imply:
% 213.79/30.61 | (1214) all_1241_2 = all_1201_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1210), (1214) imply:
% 213.79/30.61 | (1215) all_1524_6 = all_1201_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1203), (1215) imply:
% 213.79/30.61 | (1216) all_1526_4 = all_1201_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1197), (1214) imply:
% 213.79/30.61 | (1217) all_1589_4 = all_1201_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1199), (1216) imply:
% 213.79/30.61 | (1218) all_1651_8 = all_1201_1
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (520), (1218) imply:
% 213.79/30.61 | (1219) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1, v_q____) =
% 213.79/30.61 | all_1651_7
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (485), (1217) imply:
% 213.79/30.61 | (1220) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1, v_q____) =
% 213.79/30.61 | all_1589_3
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (469), (1196) imply:
% 213.79/30.61 | (1221) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1, v_q____) =
% 213.79/30.61 | all_1561_1
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (451), (1216) imply:
% 213.79/30.61 | (1222) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1, v_q____) =
% 213.79/30.61 | all_1526_3
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (440), (1215) imply:
% 213.79/30.61 | (1223) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1, v_q____) =
% 213.79/30.61 | all_1524_5
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (395), (1209) imply:
% 213.79/30.61 | (1224) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1, v_q____) =
% 213.79/30.61 | all_1358_2
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (353), (1214) imply:
% 213.79/30.61 | (1225) c_Polynomial_Osmult(tc_Complex_Ocomplex, all_1201_1, v_q____) =
% 213.79/30.61 | all_1241_1
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (154) with all_1526_3, all_1561_1, v_q____,
% 213.79/30.61 | all_1201_1, tc_Complex_Ocomplex, simplifying with (1221), (1222)
% 213.79/30.61 | gives:
% 213.79/30.61 | (1226) all_1561_1 = all_1526_3
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (154) with all_1524_5, all_1561_1, v_q____,
% 213.79/30.61 | all_1201_1, tc_Complex_Ocomplex, simplifying with (1221), (1223)
% 213.79/30.61 | gives:
% 213.79/30.61 | (1227) all_1561_1 = all_1524_5
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (154) with all_1358_2, all_1561_1, v_q____,
% 213.79/30.61 | all_1201_1, tc_Complex_Ocomplex, simplifying with (1221), (1224)
% 213.79/30.61 | gives:
% 213.79/30.61 | (1228) all_1561_1 = all_1358_2
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (154) with all_1201_0, all_1589_3, v_q____,
% 213.79/30.61 | all_1201_1, tc_Complex_Ocomplex, simplifying with (331), (1220)
% 213.79/30.61 | gives:
% 213.79/30.61 | (1229) all_1589_3 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (154) with all_1526_3, all_1589_3, v_q____,
% 213.79/30.61 | all_1201_1, tc_Complex_Ocomplex, simplifying with (1220), (1222)
% 213.79/30.61 | gives:
% 213.79/30.61 | (1230) all_1589_3 = all_1526_3
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (154) with all_1358_2, all_1651_7, v_q____,
% 213.79/30.61 | all_1201_1, tc_Complex_Ocomplex, simplifying with (1219), (1224)
% 213.79/30.61 | gives:
% 213.79/30.61 | (1231) all_1651_7 = all_1358_2
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (154) with all_1241_1, all_1651_7, v_q____,
% 213.79/30.61 | all_1201_1, tc_Complex_Ocomplex, simplifying with (1219), (1225)
% 213.79/30.61 | gives:
% 213.79/30.61 | (1232) all_1651_7 = all_1241_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1231), (1232) imply:
% 213.79/30.61 | (1233) all_1358_2 = all_1241_1
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1233) implies:
% 213.79/30.61 | (1234) all_1358_2 = all_1241_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1229), (1230) imply:
% 213.79/30.61 | (1235) all_1526_3 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1235) implies:
% 213.79/30.61 | (1236) all_1526_3 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1226), (1227) imply:
% 213.79/30.61 | (1237) all_1526_3 = all_1524_5
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1237) implies:
% 213.79/30.61 | (1238) all_1526_3 = all_1524_5
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1227), (1228) imply:
% 213.79/30.61 | (1239) all_1524_5 = all_1358_2
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1236), (1238) imply:
% 213.79/30.61 | (1240) all_1524_5 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1240) implies:
% 213.79/30.61 | (1241) all_1524_5 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1239), (1241) imply:
% 213.79/30.61 | (1242) all_1358_2 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1242) implies:
% 213.79/30.61 | (1243) all_1358_2 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1234), (1243) imply:
% 213.79/30.61 | (1244) all_1241_1 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1244) implies:
% 213.79/30.61 | (1245) all_1241_1 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1227), (1241) imply:
% 213.79/30.61 | (1246) all_1561_1 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1232), (1245) imply:
% 213.79/30.61 | (1247) all_1651_7 = all_1201_0
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (519), (1247) imply:
% 213.79/30.61 | (1248) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1201_0) = all_1651_6
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (484), (1229) imply:
% 213.79/30.61 | (1249) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1201_0) = all_1589_2
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (468), (1246) imply:
% 213.79/30.61 | (1250) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1201_0) = all_1561_0
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (450), (1236) imply:
% 213.79/30.61 | (1251) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1201_0) = all_1526_2
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (439), (1241) imply:
% 213.79/30.61 | (1252) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1201_0) = all_1524_4
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (394), (1243) imply:
% 213.79/30.61 | (1253) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1201_0) = all_1358_1
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (352), (1245) imply:
% 213.79/30.61 | (1254) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1201_0) = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (348), (1245) imply:
% 213.79/30.61 | (1255) $i(all_1201_0)
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (151) with all_1526_2, all_1561_0, all_1201_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1250), (1251) gives:
% 213.79/30.61 | (1256) all_1561_0 = all_1526_2
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (151) with all_1524_4, all_1561_0, all_1201_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1250), (1252) gives:
% 213.79/30.61 | (1257) all_1561_0 = all_1524_4
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (151) with all_1358_1, all_1561_0, all_1201_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1250), (1253) gives:
% 213.79/30.61 | (1258) all_1561_0 = all_1358_1
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (151) with all_1561_0, all_1589_2, all_1201_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1249), (1250) gives:
% 213.79/30.61 | (1259) all_1589_2 = all_1561_0
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (151) with all_1589_2, all_1651_6, all_1201_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1248), (1249) gives:
% 213.79/30.61 | (1260) all_1651_6 = all_1589_2
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (151) with all_1241_0, all_1651_6, all_1201_0,
% 213.79/30.61 | tc_Complex_Ocomplex, simplifying with (1248), (1254) gives:
% 213.79/30.61 | (1261) all_1651_6 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1260), (1261) imply:
% 213.79/30.61 | (1262) all_1589_2 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1262) implies:
% 213.79/30.61 | (1263) all_1589_2 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1259), (1263) imply:
% 213.79/30.61 | (1264) all_1561_0 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1264) implies:
% 213.79/30.61 | (1265) all_1561_0 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1256), (1258) imply:
% 213.79/30.61 | (1266) all_1526_2 = all_1358_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1256), (1257) imply:
% 213.79/30.61 | (1267) all_1526_2 = all_1524_4
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1256), (1265) imply:
% 213.79/30.61 | (1268) all_1526_2 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1266), (1267) imply:
% 213.79/30.61 | (1269) all_1524_4 = all_1358_1
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1267), (1268) imply:
% 213.79/30.61 | (1270) all_1524_4 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | COMBINE_EQS: (1269), (1270) imply:
% 213.79/30.61 | (1271) all_1358_1 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | SIMP: (1271) implies:
% 213.79/30.61 | (1272) all_1358_1 = all_1241_0
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (516), (1261) imply:
% 213.79/30.61 | (1273) hAPP(all_1241_0, v_w____) = all_1651_5
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (480), (1263) imply:
% 213.79/30.61 | (1274) hAPP(all_1241_0, v_w____) = all_1589_1
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (1128), (1268) imply:
% 213.79/30.61 | (1275) hAPP(all_1241_0, all_746_1) = all_1526_1
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (1132), (1272) imply:
% 213.79/30.61 | (1276) hAPP(all_1241_0, all_746_1) = all_746_0
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (150) with all_1589_1, all_1651_5, v_w____,
% 213.79/30.61 | all_1241_0, simplifying with (1273), (1274) gives:
% 213.79/30.61 | (1277) all_1651_5 = all_1589_1
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (150) with all_746_0, all_1526_1, all_746_1,
% 213.79/30.61 | all_1241_0, simplifying with (1275), (1276) gives:
% 213.79/30.61 | (1278) all_1526_1 = all_746_0
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (524), (1277) imply:
% 213.79/30.61 | (1279) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1589_1) =
% 213.79/30.61 | all_1651_4
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (1129), (1278) imply:
% 213.79/30.61 | (1280) hAPP(all_1022_0, all_746_0) = all_1526_0
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (512), (1277) imply:
% 213.79/30.61 | (1281) $i(all_1589_1)
% 213.79/30.61 |
% 213.79/30.61 | REDUCE: (443), (1278) imply:
% 213.79/30.61 | (1282) $i(all_746_0)
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (529) with all_746_1, all_1201_0,
% 213.79/30.61 | tc_Complex_Ocomplex, all_1241_0, all_746_0, simplifying with
% 213.79/30.61 | (143), (144), (1142), (1254), (1255), (1276) gives:
% 213.79/30.61 | (1283) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (((v3 =
% 213.79/30.61 | all_1653_0 & ~ (v2 = all_1201_0) &
% 213.79/30.61 | c_Polynomial_Oorder(tc_Complex_Ocomplex, all_746_1,
% 213.79/30.61 | all_1201_0) = all_1653_0 &
% 213.79/30.61 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v1 &
% 213.79/30.61 | c_Groups_Ozero__class_Ozero(v1) = v2 & $i(v2) & $i(v1)) | (v0
% 213.79/30.61 | = all_746_0 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 213.79/30.61 | = all_746_0 & $i(all_746_0))) & ((v2 = all_1201_0 &
% 213.79/30.61 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v1 &
% 213.79/30.61 | c_Groups_Ozero__class_Ozero(v1) = all_1201_0 & $i(v1)) | ( ~
% 213.79/30.61 | (v3 = all_1653_0) & c_Polynomial_Oorder(tc_Complex_Ocomplex,
% 213.79/30.61 | all_746_1, all_1201_0) = v3 & $i(v3)) | ( ~ (v0 = all_746_0)
% 213.79/30.61 | & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 213.79/30.61 | $i(v0))))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_inverse__nonzero__iff__nonzero) with
% 213.79/30.61 | all_833_0, tc_Complex_Ocomplex, all_1201_1, simplifying with
% 213.79/30.61 | (137), (144), (1190), (1194) gives:
% 213.79/30.61 | (1284) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0
% 213.79/30.61 | & $i(v0) & ( ~ (v0 = all_1201_1) | all_1201_1 = all_833_0) & ( ~
% 213.79/30.61 | (v0 = all_833_0) | all_1201_1 = all_833_0))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_nonzero__imp__inverse__nonzero) with
% 213.79/30.61 | all_833_0, tc_Complex_Ocomplex, all_1201_1, simplifying with
% 213.79/30.61 | (141), (144), (1190), (1194) gives:
% 213.79/30.61 | (1285) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0
% 213.79/30.61 | & $i(v0) & ( ~ (v0 = all_1201_1) | all_1201_1 = all_833_0))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_one__le__inverse__iff) with all_693_0,
% 213.79/30.61 | tc_RealDef_Oreal, all_693_0, simplifying with (135), (145),
% 213.79/30.61 | (159), (1144) gives:
% 213.79/30.61 | (1286) ? [v0: $i] : ? [v1: $i] :
% 213.79/30.61 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ( ~
% 213.79/30.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 213.79/30.61 | all_693_0) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.61 | v1 & $i(v1) &
% 213.79/30.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.61 | v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 213.79/30.61 | all_693_0))) & ( ~
% 213.79/30.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.61 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 213.79/30.61 | all_693_0) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.61 | v1 & $i(v1) & ~
% 213.79/30.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 213.79/30.61 | all_693_0))))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_inverse__le__1__iff) with all_693_0,
% 213.79/30.61 | tc_RealDef_Oreal, all_693_0, simplifying with (135), (145),
% 213.79/30.61 | (159), (1144) gives:
% 213.79/30.61 | (1287) ? [v0: $i] : ? [v1: $i] :
% 213.79/30.61 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ( ~
% 213.79/30.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.61 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 213.79/30.61 | all_693_0) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.61 | v1 & $i(v1) &
% 213.79/30.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.61 | v1))) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.79/30.61 | all_693_0, v0) |
% 213.79/30.61 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 213.79/30.61 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 213.79/30.61 | all_693_0) & ~
% 213.79/30.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.61 | v1))))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_one__less__inverse__iff) with all_693_0,
% 213.79/30.61 | tc_RealDef_Oreal, all_693_0, simplifying with (135), (145),
% 213.79/30.61 | (159), (1144) gives:
% 213.79/30.61 | (1288) ? [v0: $i] : ? [v1: $i] :
% 213.79/30.61 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ( ~
% 213.79/30.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_693_0) |
% 213.79/30.61 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 213.79/30.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_693_0)
% 213.79/30.61 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_693_0,
% 213.79/30.61 | v0))) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.61 | all_693_0, v0) |
% 213.79/30.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_693_0) |
% 213.79/30.61 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 213.79/30.61 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 213.79/30.61 | all_693_0))))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_inverse__less__1__iff) with all_693_0,
% 213.79/30.61 | tc_RealDef_Oreal, all_693_0, simplifying with (135), (145),
% 213.79/30.61 | (159), (1144) gives:
% 213.79/30.61 | (1289) ? [v0: $i] : ? [v1: $i] :
% 213.79/30.61 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ( ~
% 213.79/30.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_693_0, v0) |
% 213.79/30.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_693_0) |
% 213.79/30.61 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 213.79/30.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.61 | v1))) & (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.61 | all_693_0, v0) |
% 213.79/30.61 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 213.79/30.61 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.79/30.61 | all_693_0, v1) & ~
% 213.79/30.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 213.79/30.61 | all_693_0))))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_mult__eq__0__iff) with all_833_0, all_1589_1,
% 213.79/30.61 | tc_Complex_Ocomplex, all_1022_0, all_1589_0, all_1589_8,
% 213.79/30.61 | simplifying with (138), (144), (268), (1124), (1191), (1194),
% 213.79/30.61 | (1281) gives:
% 213.79/30.61 | (1290) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0
% 213.79/30.61 | & $i(v0) & ( ~ (v0 = all_1589_8) | all_1589_1 = all_1589_8 |
% 213.79/30.61 | all_1589_8 = all_833_0) & (v0 = all_1589_8 | ( ~ (v0 =
% 213.79/30.61 | all_1589_1) & ~ (v0 = all_833_0))))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_no__zero__divisors) with all_833_0,
% 213.79/30.61 | all_1589_1, tc_Complex_Ocomplex, all_1022_0, all_1589_0,
% 213.79/30.61 | all_1589_8, simplifying with (140), (144), (268), (1124), (1191),
% 213.79/30.61 | (1194), (1281) gives:
% 213.79/30.61 | (1291) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0
% 213.79/30.61 | & $i(v0) & ( ~ (v0 = all_1589_8) | all_1589_1 = all_1589_8 |
% 213.79/30.61 | all_1589_8 = all_833_0))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_mult__eq__0__iff) with all_833_0, all_746_0,
% 213.79/30.61 | tc_Complex_Ocomplex, all_1022_0, all_1526_0, all_833_0,
% 213.79/30.61 | simplifying with (138), (144), (268), (1192), (1194), (1280),
% 213.79/30.61 | (1282) gives:
% 213.79/30.61 | (1292) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0
% 213.79/30.61 | & $i(v0) & ( ~ (v0 = all_746_0) | all_833_0 = all_746_0))
% 213.79/30.61 |
% 213.79/30.61 | GROUND_INST: instantiating (fact_zero__neq__one) with tc_Complex_Ocomplex,
% 213.79/30.61 | all_746_0, simplifying with (142), (144), (172) gives:
% 213.79/30.61 | (1293) ? [v0: any] : ( ~ (v0 = all_746_0) &
% 213.79/30.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v0))
% 213.79/30.61 |
% 213.79/30.62 | GROUND_INST: instantiating (fact_zero__le__one) with tc_RealDef_Oreal,
% 213.79/30.62 | all_737_0, simplifying with (136), (145), (169) gives:
% 213.79/30.62 | (1294) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 213.79/30.62 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 213.79/30.62 | all_737_0))
% 213.79/30.62 |
% 213.79/30.62 | GROUND_INST: instantiating (fact_zero__less__one) with tc_RealDef_Oreal,
% 213.79/30.62 | all_737_0, simplifying with (136), (145), (169) gives:
% 213.79/30.62 | (1295) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 213.79/30.62 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 213.79/30.62 | all_737_0))
% 213.79/30.62 |
% 213.79/30.62 | GROUND_INST: instantiating (fact_not__one__le__zero) with tc_RealDef_Oreal,
% 213.79/30.62 | all_737_0, simplifying with (136), (145), (169) gives:
% 213.79/30.62 | (1296) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 213.79/30.62 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.79/30.62 | all_737_0, v0))
% 213.79/30.62 |
% 213.79/30.62 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_RealDef_Oreal,
% 213.79/30.62 | all_737_0, simplifying with (136), (145), (169) gives:
% 213.79/30.62 | (1297) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 213.79/30.62 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.62 | all_737_0, v0))
% 213.79/30.62 |
% 213.79/30.62 | GROUND_INST: instantiating (fact_divide__eq__eq) with all_1589_1, all_833_0,
% 213.79/30.62 | all_1589_8, tc_Complex_Ocomplex, all_1651_1, all_1022_0,
% 213.79/30.62 | all_1589_0, all_1589_8, simplifying with (139), (144), (268),
% 213.79/30.62 | (1124), (1182), (1191), (1193), (1194), (1281) gives:
% 213.79/30.62 | (1298) ? [v0: $i] : (( ~ (all_1651_1 = all_1589_1) |
% 213.79/30.62 | (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v0)
% 213.79/30.62 | & ( ~ (v0 = all_833_0) | all_1589_1 = all_833_0))) &
% 213.79/30.62 | (all_1651_1 = all_1589_1 | (v0 = all_833_0 & ~ (all_1589_1 =
% 213.79/30.62 | all_833_0) &
% 213.79/30.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 213.79/30.62 | all_833_0)))
% 213.79/30.62 |
% 213.79/30.62 | GROUND_INST: instantiating (190) with all_752_0, all_737_0, simplifying with
% 213.79/30.62 | (1121), (1143) gives:
% 213.79/30.62 | (1299) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_771_0,
% 213.79/30.62 | all_737_0)
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1294) with fresh symbol all_1762_0 gives:
% 213.79/30.62 | (1300) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1762_0 &
% 213.79/30.62 | $i(all_1762_0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.79/30.62 | all_1762_0, all_737_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1300) implies:
% 213.79/30.62 | (1301) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1762_0,
% 213.79/30.62 | all_737_0)
% 213.79/30.62 | (1302) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1762_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1293) with fresh symbol all_1764_0 gives:
% 213.79/30.62 | (1303) ~ (all_1764_0 = all_746_0) &
% 213.79/30.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1764_0 &
% 213.79/30.62 | $i(all_1764_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1303) implies:
% 213.79/30.62 | (1304) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1764_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1297) with fresh symbol all_1780_0 gives:
% 213.79/30.62 | (1305) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1780_0 &
% 213.79/30.62 | $i(all_1780_0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.62 | all_737_0, all_1780_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1305) implies:
% 213.79/30.62 | (1306) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1780_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1296) with fresh symbol all_1782_0 gives:
% 213.79/30.62 | (1307) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1782_0 &
% 213.79/30.62 | $i(all_1782_0) & ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_737_0,
% 213.79/30.62 | all_1782_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1307) implies:
% 213.79/30.62 | (1308) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1782_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1295) with fresh symbol all_1784_0 gives:
% 213.79/30.62 | (1309) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1784_0 &
% 213.79/30.62 | $i(all_1784_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.62 | all_1784_0, all_737_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1309) implies:
% 213.79/30.62 | (1310) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1784_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1285) with fresh symbol all_1791_0 gives:
% 213.79/30.62 | (1311) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1791_0 &
% 213.79/30.62 | $i(all_1791_0) & ( ~ (all_1791_0 = all_1201_1) | all_1201_1 =
% 213.79/30.62 | all_833_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1311) implies:
% 213.79/30.62 | (1312) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1791_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1292) with fresh symbol all_1795_0 gives:
% 213.79/30.62 | (1313) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1795_0 &
% 213.79/30.62 | $i(all_1795_0) & ( ~ (all_1795_0 = all_746_0) | all_833_0 =
% 213.79/30.62 | all_746_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1313) implies:
% 213.79/30.62 | (1314) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1795_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1291) with fresh symbol all_1797_0 gives:
% 213.79/30.62 | (1315) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1797_0 &
% 213.79/30.62 | $i(all_1797_0) & ( ~ (all_1797_0 = all_1589_8) | all_1589_1 =
% 213.79/30.62 | all_1589_8 | all_1589_8 = all_833_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1315) implies:
% 213.79/30.62 | (1316) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1797_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1284) with fresh symbol all_1818_0 gives:
% 213.79/30.62 | (1317) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1818_0 &
% 213.79/30.62 | $i(all_1818_0) & ( ~ (all_1818_0 = all_1201_1) | all_1201_1 =
% 213.79/30.62 | all_833_0) & ( ~ (all_1818_0 = all_833_0) | all_1201_1 =
% 213.79/30.62 | all_833_0)
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1317) implies:
% 213.79/30.62 | (1318) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1818_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1290) with fresh symbol all_1829_0 gives:
% 213.79/30.62 | (1319) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1829_0 &
% 213.79/30.62 | $i(all_1829_0) & ( ~ (all_1829_0 = all_1589_8) | all_1589_1 =
% 213.79/30.62 | all_1589_8 | all_1589_8 = all_833_0) & (all_1829_0 = all_1589_8 |
% 213.79/30.62 | ( ~ (all_1829_0 = all_1589_1) & ~ (all_1829_0 = all_833_0)))
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1319) implies:
% 213.79/30.62 | (1320) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1829_0
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1298) with fresh symbol all_1833_0 gives:
% 213.79/30.62 | (1321) ( ~ (all_1651_1 = all_1589_1) |
% 213.79/30.62 | (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1833_0 &
% 213.79/30.62 | $i(all_1833_0) & ( ~ (all_1833_0 = all_833_0) | all_1589_1 =
% 213.79/30.62 | all_833_0))) & (all_1651_1 = all_1589_1 | (all_1833_0 =
% 213.79/30.62 | all_833_0 & ~ (all_1589_1 = all_833_0) &
% 213.79/30.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_833_0))
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1321) implies:
% 213.79/30.62 | (1322) all_1651_1 = all_1589_1 | (all_1833_0 = all_833_0 & ~ (all_1589_1 =
% 213.79/30.62 | all_833_0) & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 213.79/30.62 | all_833_0)
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1288) with fresh symbols all_1879_0, all_1879_1 gives:
% 213.79/30.62 | (1323) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1879_1 &
% 213.79/30.62 | $i(all_1879_1) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.62 | all_1879_1, all_693_0) |
% 213.79/30.62 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1879_0 &
% 213.79/30.62 | $i(all_1879_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.62 | all_1879_0, all_693_0) &
% 213.79/30.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1879_1))) & ( ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1879_1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.62 | all_1879_1, all_693_0) |
% 213.79/30.62 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1879_0 &
% 213.79/30.62 | $i(all_1879_0) & ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1879_0,
% 213.79/30.62 | all_693_0)))
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1323) implies:
% 213.79/30.62 | (1324) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1879_1
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1287) with fresh symbols all_1881_0, all_1881_1 gives:
% 213.79/30.62 | (1325) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1881_1 &
% 213.79/30.62 | $i(all_1881_1) & ( ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1881_1) |
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1881_1,
% 213.79/30.62 | all_693_0) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.62 | all_1881_0 & $i(all_1881_0) &
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1881_0))) &
% 213.79/30.62 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1881_1) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.62 | all_1881_0 & $i(all_1881_0) & ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1881_1,
% 213.79/30.62 | all_693_0) & ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1881_0)))
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1325) implies:
% 213.79/30.62 | (1326) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1881_1
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1289) with fresh symbols all_1883_0, all_1883_1 gives:
% 213.79/30.62 | (1327) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1883_1 &
% 213.79/30.62 | $i(all_1883_1) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.62 | all_693_0, all_1883_1) |
% 213.79/30.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1883_1,
% 213.79/30.62 | all_693_0) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.62 | all_1883_0 & $i(all_1883_0) &
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1883_0))) &
% 213.79/30.62 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1883_1) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.62 | all_1883_0 & $i(all_1883_0) & ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1883_0) & ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1883_1,
% 213.79/30.62 | all_693_0)))
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1327) implies:
% 213.79/30.62 | (1328) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1883_1
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1286) with fresh symbols all_1885_0, all_1885_1 gives:
% 213.79/30.62 | (1329) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1885_1 &
% 213.79/30.62 | $i(all_1885_1) & ( ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1885_1,
% 213.79/30.62 | all_693_0) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.62 | all_1885_0 & $i(all_1885_0) &
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1885_1) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.62 | all_1885_0, all_693_0))) & ( ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1885_1) |
% 213.79/30.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1885_1,
% 213.79/30.62 | all_693_0) | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 213.79/30.62 | all_1885_0 & $i(all_1885_0) & ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1885_0,
% 213.79/30.62 | all_693_0)))
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1329) implies:
% 213.79/30.62 | (1330) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1885_1
% 213.79/30.62 | (1331) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_1885_1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.79/30.62 | all_1885_1, all_693_0) |
% 213.79/30.62 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1885_0 &
% 213.79/30.62 | $i(all_1885_0) & ~
% 213.79/30.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1885_0,
% 213.79/30.62 | all_693_0))
% 213.79/30.62 |
% 213.79/30.62 | DELTA: instantiating (1283) with fresh symbols all_1905_0, all_1905_1,
% 213.79/30.62 | all_1905_2, all_1905_3 gives:
% 213.79/30.62 | (1332) ((all_1905_0 = all_1653_0 & ~ (all_1905_1 = all_1201_0) &
% 213.79/30.62 | c_Polynomial_Oorder(tc_Complex_Ocomplex, all_746_1, all_1201_0)
% 213.79/30.62 | = all_1653_0 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) =
% 213.79/30.62 | all_1905_2 & c_Groups_Ozero__class_Ozero(all_1905_2) =
% 213.79/30.62 | all_1905_1 & $i(all_1905_1) & $i(all_1905_2)) | (all_1905_3 =
% 213.79/30.62 | all_746_0 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 213.79/30.62 | all_746_0 & $i(all_746_0))) & ((all_1905_1 = all_1201_0 &
% 213.79/30.62 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1905_2 &
% 213.79/30.62 | c_Groups_Ozero__class_Ozero(all_1905_2) = all_1201_0 &
% 213.79/30.62 | $i(all_1905_2)) | ( ~ (all_1905_0 = all_1653_0) &
% 213.79/30.62 | c_Polynomial_Oorder(tc_Complex_Ocomplex, all_746_1, all_1201_0)
% 213.79/30.62 | = all_1905_0 & $i(all_1905_0)) | ( ~ (all_1905_3 = all_746_0) &
% 213.79/30.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1905_3 &
% 213.79/30.62 | $i(all_1905_3)))
% 213.79/30.62 |
% 213.79/30.62 | ALPHA: (1332) implies:
% 213.79/30.62 | (1333) (all_1905_1 = all_1201_0 & tc_Polynomial_Opoly(tc_Complex_Ocomplex)
% 213.79/30.62 | = all_1905_2 & c_Groups_Ozero__class_Ozero(all_1905_2) =
% 213.79/30.62 | all_1201_0 & $i(all_1905_2)) | ( ~ (all_1905_0 = all_1653_0) &
% 213.79/30.62 | c_Polynomial_Oorder(tc_Complex_Ocomplex, all_746_1, all_1201_0) =
% 213.79/30.62 | all_1905_0 & $i(all_1905_0)) | ( ~ (all_1905_3 = all_746_0) &
% 213.79/30.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1905_3 &
% 213.79/30.62 | $i(all_1905_3))
% 213.79/30.62 | (1334) (all_1905_0 = all_1653_0 & ~ (all_1905_1 = all_1201_0) &
% 213.79/30.62 | c_Polynomial_Oorder(tc_Complex_Ocomplex, all_746_1, all_1201_0) =
% 213.79/30.62 | all_1653_0 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1905_2
% 213.79/30.62 | & c_Groups_Ozero__class_Ozero(all_1905_2) = all_1905_1 &
% 213.79/30.62 | $i(all_1905_1) & $i(all_1905_2)) | (all_1905_3 = all_746_0 &
% 213.79/30.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_746_0 &
% 213.79/30.62 | $i(all_746_0))
% 213.79/30.62 |
% 213.79/30.62 | REDUCE: (1099), (1299) imply:
% 213.79/30.62 | (1335) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.62 | all_737_0)
% 213.79/30.62 |
% 213.79/30.62 | BETA: splitting (1334) gives:
% 213.79/30.62 |
% 213.79/30.62 | Case 1:
% 213.79/30.62 | |
% 213.79/30.62 | | (1336) all_1905_0 = all_1653_0 & ~ (all_1905_1 = all_1201_0) &
% 213.79/30.62 | | c_Polynomial_Oorder(tc_Complex_Ocomplex, all_746_1, all_1201_0) =
% 213.79/30.62 | | all_1653_0 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1905_2
% 213.79/30.62 | | & c_Groups_Ozero__class_Ozero(all_1905_2) = all_1905_1 &
% 213.79/30.62 | | $i(all_1905_1) & $i(all_1905_2)
% 213.79/30.62 | |
% 213.79/30.62 | | ALPHA: (1336) implies:
% 213.79/30.62 | | (1337) all_1905_0 = all_1653_0
% 213.79/30.62 | | (1338) ~ (all_1905_1 = all_1201_0)
% 213.79/30.62 | |
% 213.79/30.62 | | COMBINE_EQS: (733), (1337) imply:
% 213.79/30.62 | | (1339) all_1905_0 = all_707_0
% 213.79/30.62 | |
% 213.79/30.62 | | BETA: splitting (1333) gives:
% 213.79/30.62 | |
% 213.79/30.62 | | Case 1:
% 213.79/30.62 | | |
% 213.79/30.62 | | | (1340) all_1905_1 = all_1201_0 &
% 213.79/30.62 | | | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1905_2 &
% 213.79/30.62 | | | c_Groups_Ozero__class_Ozero(all_1905_2) = all_1201_0 &
% 213.79/30.62 | | | $i(all_1905_2)
% 213.79/30.62 | | |
% 213.79/30.62 | | | ALPHA: (1340) implies:
% 213.79/30.62 | | | (1341) all_1905_1 = all_1201_0
% 213.79/30.62 | | |
% 213.79/30.62 | | | REDUCE: (1338), (1341) imply:
% 213.79/30.62 | | | (1342) $false
% 213.79/30.62 | | |
% 213.79/30.62 | | | CLOSE: (1342) is inconsistent.
% 213.79/30.62 | | |
% 213.79/30.62 | | Case 2:
% 213.79/30.62 | | |
% 213.79/30.62 | | | (1343) ( ~ (all_1905_0 = all_1653_0) &
% 213.79/30.62 | | | c_Polynomial_Oorder(tc_Complex_Ocomplex, all_746_1,
% 213.79/30.62 | | | all_1201_0) = all_1905_0 & $i(all_1905_0)) | ( ~ (all_1905_3
% 213.79/30.62 | | | = all_746_0) &
% 213.79/30.62 | | | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1905_3
% 213.79/30.62 | | | & $i(all_1905_3))
% 213.79/30.62 | | |
% 213.79/30.62 | | | BETA: splitting (1343) gives:
% 213.79/30.62 | | |
% 213.79/30.62 | | | Case 1:
% 213.79/30.62 | | | |
% 213.79/30.62 | | | | (1344) ~ (all_1905_0 = all_1653_0) &
% 213.79/30.62 | | | | c_Polynomial_Oorder(tc_Complex_Ocomplex, all_746_1,
% 213.79/30.62 | | | | all_1201_0) = all_1905_0 & $i(all_1905_0)
% 213.79/30.62 | | | |
% 213.79/30.62 | | | | ALPHA: (1344) implies:
% 213.79/30.62 | | | | (1345) ~ (all_1905_0 = all_1653_0)
% 213.79/30.62 | | | |
% 213.79/30.62 | | | | REDUCE: (733), (1339), (1345) imply:
% 213.79/30.62 | | | | (1346) $false
% 213.79/30.62 | | | |
% 213.79/30.62 | | | | CLOSE: (1346) is inconsistent.
% 213.79/30.62 | | | |
% 213.79/30.62 | | | Case 2:
% 213.79/30.62 | | | |
% 213.79/30.62 | | | | (1347) ~ (all_1905_3 = all_746_0) &
% 213.79/30.62 | | | | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1905_3
% 213.79/30.62 | | | | & $i(all_1905_3)
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | ALPHA: (1347) implies:
% 213.79/30.63 | | | | (1348) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1905_3
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1795_0, all_1797_0,
% 213.79/30.63 | | | | tc_Complex_Ocomplex, simplifying with (1314), (1316) gives:
% 213.79/30.63 | | | | (1349) all_1797_0 = all_1795_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1791_0, all_1797_0,
% 213.79/30.63 | | | | tc_Complex_Ocomplex, simplifying with (1312), (1316) gives:
% 213.79/30.63 | | | | (1350) all_1797_0 = all_1791_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1795_0, all_1818_0,
% 213.79/30.63 | | | | tc_Complex_Ocomplex, simplifying with (1314), (1318) gives:
% 213.79/30.63 | | | | (1351) all_1818_0 = all_1795_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1764_0, all_1818_0,
% 213.79/30.63 | | | | tc_Complex_Ocomplex, simplifying with (1304), (1318) gives:
% 213.79/30.63 | | | | (1352) all_1818_0 = all_1764_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1795_0, all_1829_0,
% 213.79/30.63 | | | | tc_Complex_Ocomplex, simplifying with (1314), (1320) gives:
% 213.79/30.63 | | | | (1353) all_1829_0 = all_1795_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_746_1, all_1905_3,
% 213.79/30.63 | | | | tc_Complex_Ocomplex, simplifying with (171), (1348) gives:
% 213.79/30.63 | | | | (1354) all_1905_3 = all_746_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1829_0, all_1905_3,
% 213.79/30.63 | | | | tc_Complex_Ocomplex, simplifying with (1320), (1348) gives:
% 213.79/30.63 | | | | (1355) all_1905_3 = all_1829_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_693_0, all_1784_0,
% 213.79/30.63 | | | | tc_RealDef_Oreal, simplifying with (158), (1310) gives:
% 213.79/30.63 | | | | (1356) all_1784_0 = all_693_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1782_0, all_1784_0,
% 213.79/30.63 | | | | tc_RealDef_Oreal, simplifying with (1308), (1310) gives:
% 213.79/30.63 | | | | (1357) all_1784_0 = all_1782_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1780_0, all_1784_0,
% 213.79/30.63 | | | | tc_RealDef_Oreal, simplifying with (1306), (1310) gives:
% 213.79/30.63 | | | | (1358) all_1784_0 = all_1780_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (147) with all_1762_0, all_1784_0,
% 213.79/30.63 | | | | tc_RealDef_Oreal, simplifying with (1302), (1310) gives:
% 213.79/30.63 | | | | (1359) all_1784_0 = all_1762_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (149) with all_737_0, all_1883_1,
% 213.79/30.63 | | | | tc_RealDef_Oreal, simplifying with (169), (1328) gives:
% 213.79/30.63 | | | | (1360) all_1883_1 = all_737_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (149) with all_1881_1, all_1883_1,
% 213.79/30.63 | | | | tc_RealDef_Oreal, simplifying with (1326), (1328) gives:
% 213.79/30.63 | | | | (1361) all_1883_1 = all_1881_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (149) with all_1881_1, all_1885_1,
% 213.79/30.63 | | | | tc_RealDef_Oreal, simplifying with (1326), (1330) gives:
% 213.79/30.63 | | | | (1362) all_1885_1 = all_1881_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | GROUND_INST: instantiating (149) with all_1879_1, all_1885_1,
% 213.79/30.63 | | | | tc_RealDef_Oreal, simplifying with (1324), (1330) gives:
% 213.79/30.63 | | | | (1363) all_1885_1 = all_1879_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1354), (1355) imply:
% 213.79/30.63 | | | | (1364) all_1829_0 = all_746_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | SIMP: (1364) implies:
% 213.79/30.63 | | | | (1365) all_1829_0 = all_746_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1362), (1363) imply:
% 213.79/30.63 | | | | (1366) all_1881_1 = all_1879_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | SIMP: (1366) implies:
% 213.79/30.63 | | | | (1367) all_1881_1 = all_1879_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1360), (1361) imply:
% 213.79/30.63 | | | | (1368) all_1881_1 = all_737_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | SIMP: (1368) implies:
% 213.79/30.63 | | | | (1369) all_1881_1 = all_737_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1367), (1369) imply:
% 213.79/30.63 | | | | (1370) all_1879_1 = all_737_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1353), (1365) imply:
% 213.79/30.63 | | | | (1371) all_1795_0 = all_746_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | SIMP: (1371) implies:
% 213.79/30.63 | | | | (1372) all_1795_0 = all_746_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1351), (1352) imply:
% 213.79/30.63 | | | | (1373) all_1795_0 = all_1764_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | SIMP: (1373) implies:
% 213.79/30.63 | | | | (1374) all_1795_0 = all_1764_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1349), (1350) imply:
% 213.79/30.63 | | | | (1375) all_1795_0 = all_1791_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | SIMP: (1375) implies:
% 213.79/30.63 | | | | (1376) all_1795_0 = all_1791_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1374), (1376) imply:
% 213.79/30.63 | | | | (1377) all_1791_0 = all_1764_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1372), (1376) imply:
% 213.79/30.63 | | | | (1378) all_1791_0 = all_746_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1377), (1378) imply:
% 213.79/30.63 | | | | (1379) all_1764_0 = all_746_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | SIMP: (1379) implies:
% 213.79/30.63 | | | | (1380) all_1764_0 = all_746_1
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1356), (1357) imply:
% 213.79/30.63 | | | | (1381) all_1782_0 = all_693_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1357), (1359) imply:
% 213.79/30.63 | | | | (1382) all_1782_0 = all_1762_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1357), (1358) imply:
% 213.79/30.63 | | | | (1383) all_1782_0 = all_1780_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1381), (1383) imply:
% 213.79/30.63 | | | | (1384) all_1780_0 = all_693_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1382), (1383) imply:
% 213.79/30.63 | | | | (1385) all_1780_0 = all_1762_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1384), (1385) imply:
% 213.79/30.63 | | | | (1386) all_1762_0 = all_693_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | COMBINE_EQS: (1363), (1370) imply:
% 213.79/30.63 | | | | (1387) all_1885_1 = all_737_0
% 213.79/30.63 | | | |
% 213.79/30.63 | | | | REF_CLOSE: (147), (153), (171), (525), (526), (1118), (1181), (1279),
% 213.79/30.63 | | | | (1322), (1331), (1335), (1387) are inconsistent by sub-proof
% 213.79/30.63 | | | | #1.
% 213.79/30.63 | | | |
% 213.79/30.63 | | | End of split
% 213.79/30.63 | | |
% 213.79/30.63 | | End of split
% 213.79/30.63 | |
% 213.79/30.63 | Case 2:
% 213.79/30.63 | |
% 213.79/30.63 | |
% 213.79/30.63 | | GROUND_INST: instantiating (149) with all_737_0, all_1885_1,
% 213.79/30.63 | | tc_RealDef_Oreal, simplifying with (169), (1330) gives:
% 213.79/30.63 | | (1388) all_1885_1 = all_737_0
% 213.79/30.63 | |
% 213.79/30.63 | | REF_CLOSE: (147), (153), (171), (525), (526), (1118), (1181), (1279),
% 213.79/30.63 | | (1322), (1331), (1335), (1388) are inconsistent by sub-proof #1.
% 213.79/30.63 | |
% 213.79/30.63 | End of split
% 213.79/30.63 |
% 213.79/30.63 End of proof
% 213.79/30.63
% 213.79/30.63 Sub-proof #1 shows that the following formulas are inconsistent:
% 213.79/30.63 ----------------------------------------------------------------
% 213.79/30.63 (1) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1589_1) =
% 213.79/30.63 all_1651_4
% 213.79/30.63 (2) ~ (all_833_0 = all_746_1)
% 213.79/30.63 (3) all_1651_3 = all_737_0
% 213.79/30.64 (4) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_746_1
% 213.79/30.64 (5) all_1885_1 = all_737_0
% 213.79/30.64 (6) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1651_1) =
% 213.79/30.64 all_1651_0
% 213.79/30.64 (7) all_1651_1 = all_1589_1 | (all_1833_0 = all_833_0 & ~ (all_1589_1 =
% 213.79/30.64 all_833_0) & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 213.79/30.64 all_833_0)
% 213.79/30.64 (8) (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0, all_1651_3)
% 213.79/30.64 & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 all_1651_3)) | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.64 all_1651_4, all_1651_3) & ~
% 213.79/30.64 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0,
% 213.79/30.64 all_1651_3))
% 213.79/30.64 (9) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0, all_737_0)
% 213.79/30.64 (10) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.64 all_1885_1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 213.79/30.64 all_1885_1, all_693_0) |
% 213.79/30.64 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1885_0 &
% 213.79/30.64 $i(all_1885_0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 213.79/30.64 all_1885_0, all_693_0))
% 213.79/30.64 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 213.79/30.64 (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 213.79/30.64 (c_RealVector_Onorm__class_Onorm(v3, v2) = v0))
% 213.79/30.64 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 213.79/30.64 (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 213.79/30.64 (c_Groups_Ozero__class_Ozero(v2) = v0))
% 213.79/30.64
% 213.79/30.64 Begin of proof
% 213.79/30.64 |
% 213.79/30.64 | BETA: splitting (7) gives:
% 213.79/30.64 |
% 213.79/30.64 | Case 1:
% 213.79/30.64 | |
% 213.79/30.64 | | (13) all_1651_1 = all_1589_1
% 213.79/30.64 | |
% 213.79/30.64 | | REDUCE: (6), (13) imply:
% 213.79/30.64 | | (14) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1589_1) =
% 213.79/30.64 | | all_1651_0
% 213.79/30.64 | |
% 213.79/30.64 | | BETA: splitting (10) gives:
% 213.79/30.64 | |
% 213.79/30.64 | | Case 1:
% 213.79/30.64 | | |
% 213.79/30.64 | | | (15) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.64 | | | all_1885_1)
% 213.79/30.64 | | |
% 213.79/30.64 | | | REDUCE: (5), (15) imply:
% 213.79/30.64 | | | (16) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_693_0,
% 213.79/30.64 | | | all_737_0)
% 213.79/30.64 | | |
% 213.79/30.64 | | | PRED_UNIFY: (9), (16) imply:
% 213.79/30.64 | | | (17) $false
% 213.79/30.64 | | |
% 213.79/30.64 | | | CLOSE: (17) is inconsistent.
% 213.79/30.64 | | |
% 213.79/30.64 | | Case 2:
% 213.79/30.64 | | |
% 213.79/30.64 | | |
% 213.79/30.64 | | | GROUND_INST: instantiating (11) with all_1651_4, all_1651_0, all_1589_1,
% 213.79/30.64 | | | tc_Complex_Ocomplex, simplifying with (1), (14) gives:
% 213.79/30.64 | | | (18) all_1651_0 = all_1651_4
% 213.79/30.64 | | |
% 213.79/30.64 | | | BETA: splitting (8) gives:
% 213.79/30.64 | | |
% 213.79/30.64 | | | Case 1:
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | (19) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0,
% 213.79/30.64 | | | | all_1651_3) & ~
% 213.79/30.64 | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 | | | | all_1651_3)
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | ALPHA: (19) implies:
% 213.79/30.64 | | | | (20) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 | | | | all_1651_3)
% 213.79/30.64 | | | | (21) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0,
% 213.79/30.64 | | | | all_1651_3)
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | REDUCE: (3), (18), (21) imply:
% 213.79/30.64 | | | | (22) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 | | | | all_737_0)
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | REDUCE: (3), (20) imply:
% 213.79/30.64 | | | | (23) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 | | | | all_737_0)
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | PRED_UNIFY: (22), (23) imply:
% 213.79/30.64 | | | | (24) $false
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | CLOSE: (24) is inconsistent.
% 213.79/30.64 | | | |
% 213.79/30.64 | | | Case 2:
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | (25) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 | | | | all_1651_3) & ~
% 213.79/30.64 | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0,
% 213.79/30.64 | | | | all_1651_3)
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | ALPHA: (25) implies:
% 213.79/30.64 | | | | (26) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_0,
% 213.79/30.64 | | | | all_1651_3)
% 213.79/30.64 | | | | (27) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 | | | | all_1651_3)
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | REDUCE: (3), (27) imply:
% 213.79/30.64 | | | | (28) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 | | | | all_737_0)
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | REDUCE: (3), (18), (26) imply:
% 213.79/30.64 | | | | (29) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1651_4,
% 213.79/30.64 | | | | all_737_0)
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | PRED_UNIFY: (28), (29) imply:
% 213.79/30.64 | | | | (30) $false
% 213.79/30.64 | | | |
% 213.79/30.64 | | | | CLOSE: (30) is inconsistent.
% 213.79/30.64 | | | |
% 213.79/30.64 | | | End of split
% 213.79/30.64 | | |
% 213.79/30.64 | | End of split
% 213.79/30.64 | |
% 213.79/30.64 | Case 2:
% 213.79/30.64 | |
% 213.79/30.64 | | (31) all_1833_0 = all_833_0 & ~ (all_1589_1 = all_833_0) &
% 213.79/30.64 | | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_833_0
% 213.79/30.64 | |
% 213.79/30.64 | | ALPHA: (31) implies:
% 213.79/30.64 | | (32) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_833_0
% 213.79/30.64 | |
% 213.79/30.64 | | GROUND_INST: instantiating (12) with all_746_1, all_833_0,
% 213.79/30.64 | | tc_Complex_Ocomplex, simplifying with (4), (32) gives:
% 213.79/30.64 | | (33) all_833_0 = all_746_1
% 213.79/30.64 | |
% 213.79/30.64 | | REDUCE: (2), (33) imply:
% 213.79/30.64 | | (34) $false
% 213.79/30.64 | |
% 213.79/30.64 | | CLOSE: (34) is inconsistent.
% 213.79/30.64 | |
% 213.79/30.64 | End of split
% 213.79/30.64 |
% 213.79/30.64 End of proof
% 213.79/30.64 % SZS output end Proof for theBenchmark
% 213.79/30.64
% 213.79/30.64 30019ms
%------------------------------------------------------------------------------