TSTP Solution File: SWW233+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW233+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 : n024.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 00:49:32 EDT 2023
% Result : Theorem 122.82s 16.90s
% Output : Proof 261.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW233+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 : n024.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 21:15:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 21.37/3.57 Prover 4: Preprocessing ...
% 21.37/3.57 Prover 1: Preprocessing ...
% 21.37/3.57 Prover 5: Preprocessing ...
% 21.37/3.57 Prover 6: Preprocessing ...
% 21.37/3.57 Prover 0: Preprocessing ...
% 21.37/3.57 Prover 2: Preprocessing ...
% 21.37/3.57 Prover 3: Preprocessing ...
% 54.10/7.85 Prover 1: Warning: ignoring some quantifiers
% 55.54/7.99 Prover 3: Warning: ignoring some quantifiers
% 55.54/8.09 Prover 3: Constructing countermodel ...
% 57.25/8.26 Prover 1: Constructing countermodel ...
% 58.92/8.43 Prover 6: Proving ...
% 68.39/9.69 Prover 4: Warning: ignoring some quantifiers
% 70.36/9.97 Prover 4: Constructing countermodel ...
% 70.78/10.08 Prover 5: Proving ...
% 75.42/10.62 Prover 0: Proving ...
% 84.38/11.83 Prover 2: Proving ...
% 84.38/11.83 Prover 2: stopped
% 84.38/11.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 90.81/12.69 Prover 7: Preprocessing ...
% 101.14/13.97 Prover 5: stopped
% 101.14/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 107.66/14.83 Prover 8: Preprocessing ...
% 110.52/15.20 Prover 7: Warning: ignoring some quantifiers
% 111.93/15.40 Prover 7: Constructing countermodel ...
% 116.67/15.99 Prover 1: stopped
% 116.67/16.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 119.80/16.40 Prover 8: Warning: ignoring some quantifiers
% 122.08/16.73 Prover 8: Constructing countermodel ...
% 122.08/16.77 Prover 9: Preprocessing ...
% 122.82/16.89 Prover 3: proved (16246ms)
% 122.82/16.89
% 122.82/16.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 122.82/16.90
% 122.82/16.90 Prover 6: stopped
% 122.82/16.91 Prover 0: stopped
% 122.82/16.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 122.82/16.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 122.82/16.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 136.50/18.70 Prover 13: Preprocessing ...
% 137.14/18.74 Prover 10: Preprocessing ...
% 137.14/18.76 Prover 11: Preprocessing ...
% 146.91/20.07 Prover 10: Warning: ignoring some quantifiers
% 148.44/20.20 Prover 10: Constructing countermodel ...
% 153.75/20.89 Prover 9: Warning: ignoring some quantifiers
% 154.05/20.93 Prover 13: Warning: ignoring some quantifiers
% 154.69/21.01 Prover 9: Constructing countermodel ...
% 154.69/21.01 Prover 9: stopped
% 154.69/21.01 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 156.13/21.19 Prover 11: Warning: ignoring some quantifiers
% 156.13/21.20 Prover 13: Constructing countermodel ...
% 157.48/21.39 Prover 11: Constructing countermodel ...
% 162.26/21.99 Prover 16: Preprocessing ...
% 172.99/23.45 Prover 16: Warning: ignoring some quantifiers
% 173.71/23.59 Prover 16: Constructing countermodel ...
% 185.48/25.18 Prover 16: stopped
% 185.48/25.18 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 192.06/26.10 Prover 13: stopped
% 195.13/26.58 Prover 19: Preprocessing ...
% 204.85/27.95 Prover 19: Warning: ignoring some quantifiers
% 204.85/27.96 Prover 4: stopped
% 205.83/28.06 Prover 19: Constructing countermodel ...
% 224.18/30.95 Prover 7: stopped
% 224.18/30.95 Prover 19: stopped
% 254.37/37.76 Prover 10: Found proof (size 2446)
% 254.37/37.76 Prover 10: proved (20850ms)
% 254.37/37.76 Prover 8: stopped
% 254.37/37.78 Prover 11: stopped
% 254.37/37.78
% 254.37/37.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 254.37/37.78
% 257.98/41.01 % SZS output start Proof for theBenchmark
% 258.07/41.04 Assumptions after simplification:
% 258.07/41.04 ---------------------------------
% 258.07/41.04
% 258.07/41.04 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector)
% 258.07/41.05 $i(tc_Complex_Ocomplex) &
% 258.07/41.05 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 258.07/41.05
% 258.07/41.05 (arity_Nat__Onat__Groups_Oone)
% 258.07/41.05 $i(tc_Nat_Onat) & class_Groups_Oone(tc_Nat_Onat)
% 258.07/41.05
% 258.07/41.05 (arity_Nat__Onat__Power_Opower)
% 258.07/41.05 $i(tc_Nat_Onat) & class_Power_Opower(tc_Nat_Onat)
% 258.07/41.05
% 258.07/41.05 (arity_Nat__Onat__Rings_Ocomm__semiring__1)
% 258.07/41.05 $i(tc_Nat_Onat) & class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
% 258.07/41.05
% 258.07/41.05 (arity_Nat__Onat__Rings_Olinordered__semidom)
% 258.07/41.05 $i(tc_Nat_Onat) & class_Rings_Olinordered__semidom(tc_Nat_Onat)
% 258.07/41.05
% 258.07/41.05 (arity_Nat__Onat__Rings_Ozero__neq__one)
% 258.07/41.05 $i(tc_Nat_Onat) & class_Rings_Ozero__neq__one(tc_Nat_Onat)
% 258.07/41.05
% 258.07/41.05 (arity_RealDef__Oreal__Groups_Oab__semigroup__add)
% 258.07/41.05 $i(tc_RealDef_Oreal) & class_Groups_Oab__semigroup__add(tc_RealDef_Oreal)
% 258.07/41.05
% 258.07/41.05 (arity_RealDef__Oreal__Groups_Olinordered__ab__group__add)
% 258.07/41.05 $i(tc_RealDef_Oreal) &
% 258.07/41.05 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)
% 258.07/41.05
% 258.07/41.05 (arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs)
% 258.07/41.05 $i(tc_RealDef_Oreal) &
% 258.07/41.05 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
% 258.07/41.05
% 258.07/41.05 (arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add)
% 258.07/41.05 $i(tc_RealDef_Oreal) &
% 258.07/41.05 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
% 258.07/41.05
% 258.07/41.05 (arity_RealDef__Oreal__RealVector_Oreal__normed__vector)
% 258.07/41.05 $i(tc_RealDef_Oreal) &
% 258.07/41.05 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
% 258.07/41.05
% 258.07/41.05 (arity_RealDef__Oreal__Rings_Ocomm__semiring__1)
% 258.07/41.05 $i(tc_RealDef_Oreal) & class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
% 258.07/41.05
% 258.07/41.05 (arity_RealDef__Oreal__Rings_Olinordered__semidom)
% 258.07/41.05 $i(tc_RealDef_Oreal) & class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
% 258.07/41.05
% 258.07/41.05 (arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)
% 258.07/41.05 $i(tc_RealDef_Oreal) &
% 258.07/41.05 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
% 258.07/41.05
% 258.07/41.05 (conj_0)
% 258.26/41.07 $i(v_z____) & $i(v_r____) & $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) &
% 258.26/41.07 ? [v0: $i] : (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____) =
% 258.26/41.07 v0 & $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 258.26/41.07 v_r____, v0))
% 258.26/41.07
% 258.26/41.07 (fact_BseqD)
% 258.26/41.07 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.26/41.07 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 258.26/41.07 ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~
% 258.26/41.07 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3) &
% 258.26/41.07 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: $i] :
% 258.26/41.07 ! [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5)
% 258.26/41.07 = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) |
% 258.26/41.07 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3)))))
% 258.26/41.07
% 258.26/41.07 (fact_BseqI)
% 258.26/41.08 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.26/41.08 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 258.26/41.08 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.26/41.08 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 258.26/41.08 class_RealVector_Oreal__normed__vector(v3) | c_SEQ_OBseq(v3, v1) | ? [v4:
% 258.26/41.08 $i] : ? [v5: $i] : ? [v6: $i] : (c_RealVector_Onorm__class_Onorm(v3,
% 258.26/41.08 v5) = v6 & hAPP(v1, v4) = v5 & $i(v6) & $i(v5) & $i(v4) & ~
% 258.26/41.08 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v2))))
% 258.26/41.08
% 258.26/41.08 (fact_Bseq__def)
% 258.26/41.08 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.26/41.08 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 258.26/41.08 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.26/41.08 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 258.26/41.08 class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1) | ? [v4:
% 258.26/41.08 $i] : ? [v5: $i] : ? [v6: $i] : (c_RealVector_Onorm__class_Onorm(v2,
% 258.26/41.08 v5) = v6 & hAPP(v1, v4) = v5 & $i(v6) & $i(v5) & $i(v4) & ~
% 258.26/41.08 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))) & ! [v1:
% 258.26/41.08 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~
% 258.26/41.08 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3) &
% 258.26/41.08 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: $i] :
% 258.26/41.08 ! [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5)
% 258.26/41.08 = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) |
% 258.26/41.08 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3)))))
% 258.26/41.08
% 258.26/41.08 (fact_LIMSEQ__inverse__realpow__zero__lemma)
% 258.26/41.08 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 258.26/41.08 $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 258.26/41.08 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 258.26/41.08 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 258.26/41.08 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) & $i(v2) &
% 258.26/41.08 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 258.26/41.08 [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6)
% 258.26/41.08 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ $i(v4)
% 258.26/41.08 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) | ? [v9:
% 258.26/41.09 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 258.26/41.09 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 258.26/41.09 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & hAPP(v10,
% 258.26/41.09 v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & $i(v10) & $i(v9)
% 258.26/41.09 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 258.26/41.09
% 258.26/41.09 (fact_Nat_Oadd__0__right)
% 258.26/41.09 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.26/41.09 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 258.26/41.09 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)))
% 258.26/41.09
% 258.26/41.09 (fact_One__nat__def)
% 258.26/41.09 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 &
% 258.26/41.09 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.26/41.09 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0))
% 258.26/41.09
% 258.26/41.09 (fact_Suc__diff__1)
% 258.26/41.09 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 258.26/41.09 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 258.26/41.09 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.26/41.09 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 258.26/41.09 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 258.26/41.09 v0, v2) | c_Nat_OSuc(v3) = v2))
% 258.26/41.09
% 258.26/41.09 (fact_Suc__eq__plus1)
% 258.26/41.09 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.26/41.09 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 258.26/41.09 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) |
% 258.26/41.09 (c_Nat_OSuc(v1) = v2 & $i(v2))))
% 258.26/41.09
% 258.26/41.09 (fact_Suc__eq__plus1__left)
% 258.26/41.09 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.26/41.09 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 258.26/41.09 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) |
% 258.26/41.09 (c_Nat_OSuc(v1) = v2 & $i(v2))))
% 258.26/41.09
% 258.26/41.09 (fact_Suc__neq__Zero)
% 258.26/41.09 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.26/41.09 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 258.26/41.09
% 258.26/41.09 (fact_Suc__not__Zero)
% 258.26/41.10 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.26/41.10 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 258.26/41.10
% 258.26/41.10 (fact_Suc__pred)
% 258.26/41.10 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 258.26/41.10 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.26/41.10 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 258.26/41.10 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 258.26/41.10 v0, v2) | c_Nat_OSuc(v3) = v2))
% 258.26/41.10
% 258.26/41.10 (fact_Suc__pred_H)
% 258.26/41.10 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 258.26/41.10 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 258.26/41.10 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.26/41.10 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 258.26/41.10 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 258.26/41.10 v0, v2) | c_Nat_OSuc(v3) = v2))
% 258.26/41.10
% 258.26/41.10 (fact_Zero__neq__Suc)
% 258.26/41.10 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.26/41.10 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 258.26/41.10
% 258.26/41.10 (fact_Zero__not__Suc)
% 258.26/41.10 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.26/41.10 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 258.26/41.10
% 258.26/41.10 (fact__096_B_Bthesis_O_A_I_B_Br_O_AALL_Az_O_Ar_A_060_061_Acmod_Az_A_N_N_062_Ad_A_L_Acmod_Aa_A_060_061_Acmod_A_Ipoly_A_IpCons_Ac_Acs_J_Az_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 258.26/41.11 $i(v_aa____) & $i(v_da____) & $i(v_c____) & $i(v_cs____) &
% 258.26/41.11 $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] :
% 258.26/41.11 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 258.26/41.11 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3 &
% 258.26/41.11 c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) = v2 &
% 258.26/41.11 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, v0) = v1 &
% 258.26/41.11 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____) = v0 & $i(v4)
% 258.26/41.11 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ( ~
% 258.26/41.11 (hAPP(v3, v5) = v6) | ~ $i(v5) | ? [v7: $i] : ? [v8: $i] :
% 258.26/41.11 ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) = v8 & $i(v8) &
% 258.26/41.11 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v8)) |
% 258.26/41.11 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7 & $i(v7)
% 258.26/41.11 & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v7)))))
% 258.26/41.11
% 258.26/41.11 (fact_ab__semigroup__add__class_Oadd__ac_I1_J)
% 258.26/41.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 258.26/41.11 $i] : ( ~ (c_Groups_Oplus__class_Oplus(v3, v4, v0) = v5) | ~
% 258.26/41.11 (c_Groups_Oplus__class_Oplus(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 258.26/41.11 $i(v1) | ~ $i(v0) | ~ class_Groups_Oab__semigroup__add(v3) | ? [v6: $i] :
% 258.26/41.11 (c_Groups_Oplus__class_Oplus(v3, v2, v6) = v5 &
% 258.26/41.11 c_Groups_Oplus__class_Oplus(v3, v1, v0) = v6 & $i(v6) & $i(v5)))
% 258.26/41.11
% 258.26/41.11 (fact_abs__add__one__gt__zero)
% 258.26/41.11 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.26/41.11 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 258.26/41.11 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 258.26/41.11 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,
% 258.26/41.11 v2) = v3) | ~ $i(v2) | ? [v4: $i] :
% 258.26/41.11 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v3) = v4 & $i(v4) &
% 258.26/41.11 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))))
% 258.26/41.11
% 258.26/41.11 (fact_abs__add__one__not__less__self)
% 258.26/41.11 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.26/41.11 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 258.26/41.11 [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~
% 258.26/41.11 $i(v1) | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 258.26/41.11 v0) = v3 & $i(v3) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 258.26/41.11 v3, v1))))
% 258.26/41.11
% 258.26/41.11 (fact_abs__eq__0)
% 258.26/41.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1,
% 258.26/41.11 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.26/41.11 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] :
% 258.26/41.11 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) &
% 258.26/41.11 ( ~ (v3 = v0) | v2 = v0)))
% 258.26/41.11
% 258.26/41.11 (fact_abs__ge__self)
% 258.26/41.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1,
% 258.26/41.12 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.26/41.12 class_Groups_Oordered__ab__group__add__abs(v1) |
% 258.26/41.12 c_Orderings_Oord__class_Oless__eq(v1, v0, v2))
% 258.26/41.12
% 258.26/41.12 (fact_abs__ge__zero)
% 258.26/41.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1,
% 258.26/41.12 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.26/41.12 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] :
% 258.26/41.12 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) &
% 258.26/41.12 c_Orderings_Oord__class_Oless__eq(v1, v3, v2)))
% 258.26/41.12
% 258.26/41.12 (fact_abs__le__zero__iff)
% 258.26/41.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1,
% 258.26/41.12 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.26/41.12 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] :
% 258.26/41.12 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v0) |
% 258.26/41.12 c_Orderings_Oord__class_Oless__eq(v1, v2, v0)) & (v3 = v0 | ~
% 258.26/41.12 c_Orderings_Oord__class_Oless__eq(v1, v2, v3))))
% 258.26/41.12
% 258.26/41.12 (fact_abs__norm__cancel)
% 258.26/41.12 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 258.26/41.12 (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.26/41.12 class_RealVector_Oreal__normed__vector(v1) |
% 258.26/41.12 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v2 & $i(v2)))
% 258.26/41.12
% 258.26/41.12 (fact_abs__not__less__zero)
% 258.26/41.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1,
% 258.26/41.12 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.26/41.12 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] :
% 258.26/41.12 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ~
% 258.26/41.12 c_Orderings_Oord__class_Oless(v1, v2, v3)))
% 258.26/41.12
% 258.26/41.12 (fact_abs__real__of__nat__cancel)
% 258.26/41.12 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ( ~
% 258.26/41.12 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) |
% 258.26/41.12 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v1 & $i(v1)))
% 258.26/41.12
% 258.26/41.12 (fact_add__0__iff)
% 258.26/41.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.26/41.13 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.26/41.13 $i(v0) | ~
% 258.26/41.13 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(v2) |
% 258.26/41.13 ? [v4: $i] : (( ~ (v3 = v1) | (v4 = v0 & c_Groups_Ozero__class_Ozero(v2) =
% 258.26/41.13 v0)) & (v3 = v1 | ( ~ (v4 = v0) & c_Groups_Ozero__class_Ozero(v2) = v4
% 258.26/41.13 & $i(v4)))))
% 258.26/41.13
% 258.26/41.13 (fact_add__eq__if)
% 258.26/41.13 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 258.26/41.13 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 258.26/41.13 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.26/41.13 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | ~
% 258.26/41.13 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~
% 258.26/41.13 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = v5) | ~ $i(v3) | ~
% 258.26/41.13 $i(v2) | ? [v6: $i] : (c_Nat_OSuc(v5) = v6 &
% 258.26/41.13 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v6 & $i(v6))) & !
% 258.26/41.13 [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 258.26/41.13 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = v3) | ~ $i(v2)))
% 258.26/41.13
% 258.26/41.13 (fact_add__eq__self__zero)
% 258.26/41.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.26/41.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 258.26/41.13 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ $i(v2) | ~
% 258.26/41.13 $i(v1)))
% 258.26/41.13
% 258.26/41.13 (fact_add__gr__0)
% 258.26/41.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.26/41.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.26/41.13 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 258.26/41.13 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 258.26/41.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 258.26/41.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i] : !
% 258.26/41.13 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2,
% 258.26/41.13 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.26/41.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 258.26/41.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : !
% 258.26/41.13 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2,
% 258.26/41.13 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.26/41.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) |
% 258.26/41.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 258.26/41.13
% 258.26/41.13 (fact_add__increasing2)
% 258.26/41.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.26/41.13 (c_Groups_Oplus__class_Oplus(v3, v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 258.26/41.13 $i(v1) | ~ $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v3) | ~
% 258.26/41.13 c_Orderings_Oord__class_Oless__eq(v3, v1, v0) |
% 258.26/41.13 c_Orderings_Oord__class_Oless__eq(v3, v1, v4) | ? [v5: $i] :
% 258.26/41.13 (c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5) & ~
% 258.26/41.13 c_Orderings_Oord__class_Oless__eq(v3, v5, v2)))
% 258.26/41.13
% 258.26/41.13 (fact_add__is__0)
% 258.26/41.14 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.26/41.14 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~
% 258.26/41.14 $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~
% 258.26/41.14 $i(v1)) & ! [v1: $i] : (v1 = v0 | ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1)))
% 258.26/41.14
% 258.26/41.14 (fact_add__is__1)
% 258.26/41.14 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 258.26/41.14 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.26/41.14 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 258.26/41.14 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 258.26/41.14 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 258.26/41.14 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 258.26/41.14 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] :
% 258.26/41.14 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2)))
% 258.26/41.14
% 258.26/41.14 (fact_add__neg__neg)
% 258.26/41.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.26/41.14 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.26/41.14 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.26/41.14 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.26/41.14 c_Orderings_Oord__class_Oless(v2, v1, v4) | ~
% 258.26/41.14 c_Orderings_Oord__class_Oless(v2, v0, v4) |
% 258.26/41.14 c_Orderings_Oord__class_Oless(v2, v3, v4))))
% 258.26/41.14
% 258.26/41.14 (fact_add__neg__nonpos)
% 258.63/41.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.14 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.14 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.63/41.14 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.63/41.14 c_Orderings_Oord__class_Oless(v2, v1, v4) | ~
% 258.63/41.14 c_Orderings_Oord__class_Oless__eq(v2, v0, v4) |
% 258.63/41.14 c_Orderings_Oord__class_Oless(v2, v3, v4))))
% 258.63/41.14
% 258.63/41.14 (fact_add__nonneg__eq__0__iff)
% 258.63/41.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.14 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.14 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.63/41.14 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.63/41.14 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) | ~
% 258.63/41.14 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) | (( ~ (v4 = v3) | (v3 =
% 258.63/41.14 v0 & v1 = v0)) & ( ~ (v4 = v0) | ~ (v1 = v0) | v3 = v0)))))
% 258.63/41.14
% 258.63/41.14 (fact_add__nonneg__nonneg)
% 258.63/41.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.14 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.14 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.63/41.14 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.63/41.14 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) | ~
% 258.63/41.14 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) |
% 258.63/41.14 c_Orderings_Oord__class_Oless__eq(v2, v4, v3))))
% 258.63/41.15
% 258.63/41.15 (fact_add__nonneg__pos)
% 258.63/41.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.15 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.63/41.15 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v4, v0) | ~
% 258.63/41.15 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) |
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v4, v3))))
% 258.63/41.15
% 258.63/41.15 (fact_add__nonpos__neg)
% 258.63/41.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.15 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.63/41.15 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v0, v4) | ~
% 258.63/41.15 c_Orderings_Oord__class_Oless__eq(v2, v1, v4) |
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v3, v4))))
% 258.63/41.15
% 258.63/41.15 (fact_add__nonpos__nonpos)
% 258.63/41.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.15 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.63/41.15 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.63/41.15 c_Orderings_Oord__class_Oless__eq(v2, v1, v4) | ~
% 258.63/41.15 c_Orderings_Oord__class_Oless__eq(v2, v0, v4) |
% 258.63/41.15 c_Orderings_Oord__class_Oless__eq(v2, v3, v4))))
% 258.63/41.15
% 258.63/41.15 (fact_add__pos__nonneg)
% 258.63/41.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.15 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.63/41.15 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v4, v1) | ~
% 258.63/41.15 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) |
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v4, v3))))
% 258.63/41.15
% 258.63/41.15 (fact_add__pos__pos)
% 258.63/41.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.15 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 258.63/41.15 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v4, v1) | ~
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v4, v0) |
% 258.63/41.15 c_Orderings_Oord__class_Oless(v2, v4, v3))))
% 258.63/41.15
% 258.63/41.15 (fact_add__strict__increasing)
% 258.63/41.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v3, v2, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 258.63/41.15 $i(v1) | ~ $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v3) | ~
% 258.63/41.15 c_Orderings_Oord__class_Oless__eq(v3, v1, v0) |
% 258.63/41.15 c_Orderings_Oord__class_Oless(v3, v1, v4) | ? [v5: $i] :
% 258.63/41.15 (c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5) & ~
% 258.63/41.15 c_Orderings_Oord__class_Oless(v3, v5, v2)))
% 258.63/41.15
% 258.63/41.15 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)
% 258.63/41.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 258.63/41.15 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (c_Groups_Oplus__class_Oplus(v4, v5,
% 258.63/41.15 v6) = v7) | ~ (c_Groups_Oplus__class_Oplus(v4, v3, v1) = v5) | ~
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v4, v2, v0) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 258.63/41.15 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v4) | ?
% 258.63/41.15 [v8: $i] : ? [v9: $i] : (c_Groups_Oplus__class_Oplus(v4, v8, v9) = v7 &
% 258.63/41.15 c_Groups_Oplus__class_Oplus(v4, v3, v2) = v8 &
% 258.63/41.15 c_Groups_Oplus__class_Oplus(v4, v1, v0) = v9 & $i(v9) & $i(v8) & $i(v7)))
% 258.63/41.15
% 258.63/41.15 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)
% 258.63/41.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.15 $i(v0) | ~ class_Rings_Ocomm__semiring__1(v2) |
% 258.63/41.15 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3 & $i(v3)))
% 258.63/41.15
% 258.63/41.15 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.63/41.16 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 258.63/41.16 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | ? [v5: $i] :
% 258.63/41.16 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5))))
% 258.63/41.16
% 258.63/41.16 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.63/41.16 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.63/41.16 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 258.63/41.16 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | hAPP(v4, v0)
% 258.63/41.16 = v1))
% 258.63/41.16
% 258.63/41.16 (fact_diff__0__eq__0)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 258.63/41.16 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1)))
% 258.63/41.16
% 258.63/41.16 (fact_diff__Suc__1)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.63/41.16 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) |
% 258.63/41.16 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v1))
% 258.63/41.16
% 258.63/41.16 (fact_diff__Suc__eq__diff__pred)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.63/41.16 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.63/41.16 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~
% 258.63/41.16 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ $i(v2) | ~
% 258.63/41.16 $i(v1) | ? [v5: $i] : (c_Nat_OSuc(v1) = v5 &
% 258.63/41.16 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) = v4 & $i(v5) &
% 258.63/41.16 $i(v4))))
% 258.63/41.16
% 258.63/41.16 (fact_diff__Suc__less)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.63/41.16 (c_Nat_OSuc(v1) = v3) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 258.63/41.16 v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 258.63/41.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 258.63/41.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 258.63/41.16
% 258.63/41.16 (fact_diff__add__0)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0
% 258.63/41.16 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~
% 258.63/41.16 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 258.63/41.16 $i(v1)))
% 258.63/41.16
% 258.63/41.16 (fact_diff__is__0__eq)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 258.63/41.16 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 258.63/41.16 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & !
% 258.63/41.16 [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 258.63/41.16 v1) = v0) | ~ $i(v2) | ~ $i(v1) |
% 258.63/41.16 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 258.63/41.16
% 258.63/41.16 (fact_diff__is__0__eq_H)
% 258.63/41.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 258.63/41.16 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 258.63/41.16 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 258.63/41.16
% 258.63/41.16 (fact_diff__less)
% 258.63/41.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.63/41.17 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~
% 258.63/41.17 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 258.63/41.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) |
% 258.63/41.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1)))
% 258.63/41.17
% 258.63/41.17 (fact_diff__self__eq__0)
% 258.63/41.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 258.63/41.17 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ $i(v1)))
% 258.63/41.17
% 258.63/41.17 (fact_diffs0__imp__equal)
% 258.63/41.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 258.63/41.17 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ $i(v2) | ~
% 258.63/41.17 $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) &
% 258.63/41.17 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & $i(v3))))
% 258.63/41.17
% 258.63/41.17 (fact_div__1)
% 258.63/41.17 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 258.63/41.17 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.63/41.17 $i] : ! [v3: $i] : (v3 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,
% 258.63/41.17 v2, v1) = v3) | ~ $i(v2)))
% 258.63/41.17
% 258.63/41.17 (fact_div__Suc)
% 258.63/41.17 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 258.63/41.17 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.63/41.17 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 258.63/41.17 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 258.63/41.17 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v7) | ~
% 258.63/41.17 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v8) | ~
% 258.63/41.17 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v9, v2) = v10) | ~
% 258.63/41.17 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~
% 258.63/41.17 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5) | ~
% 258.63/41.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, v8) = v9) | ~
% 258.63/41.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v10) = v11) | ~
% 258.63/41.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v5) = v6) | ~ $i(v3) | ~
% 258.63/41.17 $i(v2) | ? [v12: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v12, v2)
% 258.63/41.17 = v11 & c_Nat_OSuc(v3) = v12 & $i(v12) & $i(v11))))
% 258.63/41.17
% 258.63/41.17 (fact_div__geq)
% 258.63/41.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.63/41.17 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~
% 258.63/41.17 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~
% 258.63/41.17 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 258.63/41.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v5: $i] :
% 258.63/41.17 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 & c_Nat_OSuc(v4) =
% 258.63/41.17 v5 & $i(v5))))
% 258.63/41.17
% 258.63/41.17 (fact_div__if)
% 258.63/41.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.63/41.17 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~
% 258.63/41.17 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~
% 258.63/41.17 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v5:
% 258.63/41.17 $i] : ? [v6: $i] : (( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1,
% 258.63/41.17 v2) | (v5 = v0 & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) =
% 258.63/41.17 v0)) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | (v6 =
% 258.63/41.17 v5 & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 &
% 258.63/41.17 c_Nat_OSuc(v4) = v5 & $i(v5))))))
% 258.63/41.17
% 258.63/41.17 (fact_div__le__mono2)
% 258.63/41.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 258.63/41.17 $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v3) = v5) | ~
% 258.63/41.17 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v4) | ~ $i(v3) | ~
% 258.63/41.17 $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)
% 258.63/41.17 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 258.63/41.17 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)))
% 258.63/41.17
% 258.63/41.17 (fact_div__less)
% 258.63/41.18 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.63/41.18 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 258.63/41.18 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 258.63/41.18 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)))
% 258.63/41.18
% 258.63/41.18 (fact_div__less__dividend)
% 258.81/41.18 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.18 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.81/41.18 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 258.81/41.18 $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.81/41.18 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v3) | ~
% 258.81/41.18 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~
% 258.81/41.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 258.81/41.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 258.81/41.18
% 258.81/41.18 (fact_div__mult__self1__is__m)
% 258.81/41.18 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.18 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 258.81/41.18 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.81/41.18 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 |
% 258.81/41.18 ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = v6) | ~ (hAPP(v4,
% 258.81/41.18 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 258.81/41.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 258.81/41.18
% 258.81/41.18 (fact_div__mult__self__is__m)
% 258.81/41.18 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.18 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 258.81/41.18 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.81/41.18 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 |
% 258.81/41.18 ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = v6) | ~ (hAPP(v4,
% 258.81/41.18 v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 258.81/41.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 258.81/41.18
% 258.81/41.18 (fact_double__add__less__zero__iff__single__add__less__zero)
% 258.81/41.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oplus__class_Oplus(v1,
% 258.81/41.18 v0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.81/41.18 class_Groups_Olinordered__ab__group__add(v1) | ? [v3: $i] :
% 258.81/41.18 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~
% 258.81/41.18 c_Orderings_Oord__class_Oless(v1, v2, v3) |
% 258.81/41.18 c_Orderings_Oord__class_Oless(v1, v0, v3)) & ( ~
% 258.81/41.18 c_Orderings_Oord__class_Oless(v1, v0, v3) |
% 258.81/41.18 c_Orderings_Oord__class_Oless(v1, v2, v3))))
% 258.81/41.18
% 258.81/41.18 (fact_double__eq__0__iff)
% 258.81/41.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oplus__class_Oplus(v1,
% 258.81/41.18 v0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.81/41.18 class_Groups_Olinordered__ab__group__add(v1) | ? [v3: $i] :
% 258.81/41.18 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) &
% 258.81/41.18 ( ~ (v3 = v0) | v2 = v0)))
% 258.81/41.18
% 258.81/41.18 (fact_double__zero__sym)
% 258.81/41.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oplus__class_Oplus(v1,
% 258.81/41.18 v0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.81/41.18 class_Groups_Olinordered__ab__group__add(v1) | ? [v3: $i] :
% 258.81/41.18 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) &
% 258.81/41.18 ( ~ (v3 = v0) | v2 = v0)))
% 258.81/41.18
% 258.81/41.18 (fact_ex__least__nat__less)
% 258.81/41.18 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.18 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 258.81/41.18 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 258.81/41.18 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) | ~ $i(v3) | ~
% 258.81/41.18 $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 258.81/41.18 $i] : ($i(v6) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7
% 258.81/41.18 & hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) &
% 258.81/41.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9: $i] :
% 258.81/41.18 ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9) | ~ hBOOL(v10) |
% 258.81/41.18 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) |
% 258.81/41.18 (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5))))))
% 258.81/41.18
% 258.81/41.18 (fact_ge__natfloor__plus__one__imp__gt)
% 258.81/41.19 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.81/41.19 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 258.81/41.19 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) =
% 258.81/41.19 v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 258.81/41.19 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5: $i] :
% 258.81/41.19 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 & $i(v5) & ~
% 258.81/41.19 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v1))))
% 258.81/41.19
% 258.81/41.19 (fact_gr0I)
% 258.81/41.19 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.19 & $i(v0) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) |
% 258.81/41.19 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)))
% 258.81/41.19
% 258.81/41.19 (fact_gr0__conv__Suc)
% 258.81/41.19 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.19 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2)
% 258.81/41.19 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & !
% 258.81/41.19 [v1: $i] : ( ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 258.81/41.19 v1) | ? [v2: $i] : (c_Nat_OSuc(v2) = v1 & $i(v2))))
% 258.81/41.19
% 258.81/41.19 (fact_gr__implies__not0)
% 258.81/41.19 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.19 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 258.81/41.19 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 258.81/41.19
% 258.81/41.19 (fact_h)
% 258.81/41.19 $i(v_z____) & $i(v_r____) & $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) &
% 258.81/41.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 258.81/41.19 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 258.81/41.19 c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_r____) = v1 &
% 258.81/41.19 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v1) = v2 &
% 258.81/41.19 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____) = v3 & $i(v3)
% 258.81/41.19 & $i(v2) & $i(v1) & $i(v0) &
% 258.81/41.19 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3))
% 258.81/41.19
% 258.81/41.19 (fact_int__power__div__base)
% 258.81/41.19 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 258.81/41.19 ? [v3: $i] : (c_Nat_OSuc(v0) = v3 & c_Power_Opower__class_Opower(tc_Int_Oint)
% 258.81/41.19 = v2 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 &
% 258.81/41.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 258.81/41.19 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 258.81/41.19 : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v3) = v7) | ~
% 258.81/41.19 (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~
% 258.81/41.19 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 258.81/41.19 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v9: $i] :
% 258.81/41.19 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v9, v4) = v8 & hAPP(v6, v5) = v9
% 258.81/41.19 & $i(v9) & $i(v8))))
% 258.81/41.19
% 258.81/41.19 (fact_int__val__lemma)
% 258.81/41.19 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 258.81/41.19 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 258.81/41.19 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.81/41.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 258.81/41.19 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, v5) =
% 258.81/41.19 v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 258.81/41.19 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v6) | ? [v7: $i] : ?
% 258.81/41.19 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 258.81/41.19 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ($i(v10) & $i(v8) & ((v9 = v3 &
% 258.81/41.19 hAPP(v4, v8) = v3 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 258.81/41.19 v8, v5)) | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v12, v13) =
% 258.81/41.19 v14 & c_Groups_Oabs__class_Oabs(tc_Int_Oint, v14) = v15 &
% 258.81/41.19 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v10, v0) = v11 & hAPP(v4,
% 258.81/41.19 v11) = v12 & hAPP(v4, v10) = v13 & $i(v15) & $i(v14) & $i(v13) &
% 258.81/41.19 $i(v12) & $i(v11) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10,
% 258.81/41.19 v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v15, v1))
% 258.81/41.19 | (hAPP(v4, v2) = v7 & $i(v7) & ~
% 258.81/41.19 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v7, v3))))))
% 258.81/41.19
% 258.81/41.19 (fact_le0)
% 258.81/41.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.20 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) |
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1)))
% 258.81/41.20
% 258.81/41.20 (fact_le__0__eq)
% 258.81/41.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.20 & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) & ! [v1:
% 258.81/41.20 $i] : (v1 = v0 | ~ $i(v1) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)))
% 258.81/41.20
% 258.81/41.20 (fact_le__div__geq)
% 258.81/41.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.20 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.81/41.20 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~
% 258.81/41.20 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~
% 258.81/41.20 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 258.81/41.20 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 & c_Nat_OSuc(v4) =
% 258.81/41.20 v5 & $i(v5))))
% 258.81/41.20
% 258.81/41.20 (fact_le__mult__natfloor)
% 258.81/41.20 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 258.81/41.20 $i] : (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 258.81/41.20 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 258.81/41.20 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 258.81/41.20 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 258.81/41.20 : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~
% 258.81/41.20 (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v1,
% 258.81/41.20 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v9: $i]
% 258.81/41.20 : ? [v10: $i] : ? [v11: $i] : (c_RComplete_Onatfloor(v10) = v11 &
% 258.81/41.20 hAPP(v9, v3) = v10 & hAPP(v2, v4) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11))))
% 258.81/41.20
% 258.81/41.20 (fact_le__natfloor__eq)
% 258.81/41.20 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.81/41.20 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 258.81/41.20 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 258.81/41.20 v1) = v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 258.81/41.20 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)) & ! [v1: $i]
% 258.81/41.20 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.81/41.20 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ (c_RComplete_Onatfloor(v2) =
% 258.81/41.20 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)))
% 258.81/41.20
% 258.81/41.20 (fact_le__natfloor__eq__one)
% 258.81/41.20 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.20 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 258.81/41.20 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 258.81/41.20 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) |
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & ! [v2: $i]
% 258.81/41.20 : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) |
% 258.81/41.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3)))
% 258.81/41.20
% 258.81/41.20 (fact_lemmaCauchy)
% 258.81/41.21 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.81/41.21 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 258.81/41.21 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 258.81/41.21 (c_RealVector_Onorm__class_Onorm(v4, v5) = v6) | ~ (hAPP(v1, v2) = v5) |
% 258.81/41.21 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.81/41.21 class_RealVector_Oreal__normed__vector(v4) | ~ class_Orderings_Oord(v3) |
% 258.81/41.21 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 258.81/41.21 ($i(v8) & ((c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 &
% 258.81/41.21 c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1, v8) = v9 &
% 258.81/41.21 $i(v11) & $i(v10) & $i(v9) & c_Orderings_Oord__class_Oless__eq(v3,
% 258.81/41.21 v2, v8) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 258.81/41.21 v0)) | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7
% 258.81/41.21 & $i(v7) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 258.81/41.21 (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~ (hAPP(v1,
% 258.81/41.21 v12) = v13) | ~ $i(v12) | ~
% 258.81/41.21 c_Orderings_Oord__class_Oless__eq(v3, v2, v12) |
% 258.81/41.21 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v7)))))))
% 258.81/41.21
% 258.81/41.21 (fact_lemma__NBseq__def)
% 258.81/41.21 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.81/41.21 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 258.81/41.21 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Nat_OSuc(v3) = v4) | ~
% 258.81/41.21 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.81/41.21 class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ? [v6: $i] :
% 258.81/41.21 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v5) &
% 258.81/41.21 ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 &
% 258.81/41.21 c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 &
% 258.81/41.21 $i(v9) & $i(v8) & $i(v6) & ~
% 258.81/41.21 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v6)) |
% 258.81/41.21 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v10:
% 258.81/41.21 $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 258.81/41.21 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1,
% 258.81/41.21 v10) = v11) | ~ $i(v10) |
% 258.81/41.21 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v5))))))
% 258.81/41.21 & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 258.81/41.21 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 258.81/41.21 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : ? [v5: $i] :
% 258.81/41.21 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v4) &
% 258.81/41.21 ((c_Nat_OSuc(v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 & $i(v6) &
% 258.81/41.21 $i(v5) & ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 258.81/41.21 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1,
% 258.81/41.21 v10) = v11) | ~ $i(v10) |
% 258.81/41.21 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v6))) |
% 258.81/41.21 (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 &
% 258.81/41.21 $i(v9) & $i(v8) & ~
% 258.81/41.21 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3))))))
% 258.81/41.21
% 258.81/41.21 (fact_lemma__NBseq__def2)
% 258.81/41.21 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.81/41.21 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 258.81/41.21 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Nat_OSuc(v3) = v4) | ~
% 258.81/41.21 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.81/41.21 class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ? [v6: $i] :
% 258.81/41.21 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v5) &
% 258.81/41.21 ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 &
% 258.81/41.21 c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 &
% 258.81/41.21 $i(v9) & $i(v8) & $i(v6) & ~
% 258.81/41.21 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v6)) |
% 258.81/41.21 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v10:
% 258.81/41.21 $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 258.81/41.21 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1,
% 258.81/41.21 v10) = v11) | ~ $i(v10) |
% 258.81/41.21 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v5))))))
% 258.81/41.21 & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 258.81/41.21 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 258.81/41.21 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : ? [v5: $i] :
% 258.81/41.21 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v4) &
% 258.81/41.21 ((c_Nat_OSuc(v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 & $i(v6) &
% 258.81/41.21 $i(v5) & ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 258.81/41.21 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1,
% 258.81/41.21 v10) = v11) | ~ $i(v10) |
% 258.81/41.21 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v6))) |
% 258.81/41.21 (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 &
% 258.81/41.21 $i(v9) & $i(v8) & ~
% 258.81/41.21 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3))))))
% 258.81/41.21
% 258.81/41.21 (fact_lemma__interval)
% 258.81/41.22 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.81/41.22 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 258.81/41.22 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4: $i] :
% 258.81/41.22 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 258.81/41.22 [v5: $i] : ! [v6: $i] : ( ~
% 258.81/41.22 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~
% 258.81/41.22 $i(v5) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1) |
% 258.81/41.22 ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 &
% 258.81/41.22 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 258.81/41.22 v4))) & ! [v5: $i] : ! [v6: $i] : ( ~
% 258.81/41.22 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~
% 258.81/41.22 $i(v5) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5) |
% 258.81/41.22 ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 &
% 258.81/41.22 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 258.81/41.22 v4))))))
% 258.81/41.22
% 258.81/41.22 (fact_lemma__interval__lt)
% 258.81/41.22 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.81/41.22 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 258.81/41.22 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4: $i] :
% 258.81/41.22 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 258.81/41.22 [v5: $i] : ! [v6: $i] : ( ~
% 258.81/41.22 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~
% 258.81/41.22 $i(v5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v5, v1) | ?
% 258.81/41.22 [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 &
% 258.81/41.22 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 258.81/41.22 v4))) & ! [v5: $i] : ! [v6: $i] : ( ~
% 258.81/41.22 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~
% 258.81/41.22 $i(v5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5) | ?
% 258.81/41.22 [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 &
% 258.81/41.22 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 258.81/41.22 v4))))))
% 258.81/41.22
% 258.81/41.22 (fact_less__Suc0)
% 258.81/41.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 258.81/41.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] : (v2 = v0
% 258.81/41.22 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)))
% 258.81/41.22
% 258.81/41.22 (fact_less__Suc__eq)
% 258.81/41.22 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 258.81/41.22 (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! [v1:
% 258.81/41.22 $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) |
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)) & ! [v0: $i] : ! [v1:
% 258.81/41.22 $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))
% 258.81/41.22
% 258.81/41.22 (fact_less__Suc__eq__0__disj)
% 258.81/41.22 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.22 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 258.81/41.22 (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~ $i(v2) |
% 258.81/41.22 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) |
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v1: $i] : !
% 258.81/41.22 [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v2) |
% 258.81/41.22 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4:
% 258.81/41.22 $i] : (c_Nat_OSuc(v4) = v2 & $i(v4) &
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1: $i] : !
% 258.81/41.22 [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) |
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)))
% 258.81/41.22
% 258.81/41.22 (fact_less__add__one)
% 258.81/41.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 258.81/41.22 (c_Groups_Oone__class_Oone(v1) = v2) | ~ (c_Groups_Oplus__class_Oplus(v1,
% 258.81/41.22 v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 258.81/41.22 class_Rings_Olinordered__semidom(v1) | c_Orderings_Oord__class_Oless(v1, v0,
% 258.81/41.22 v3))
% 258.81/41.22
% 258.81/41.22 (fact_less__eq__nat_Osimps_I1_J)
% 258.81/41.22 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.22 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) |
% 258.81/41.22 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1)))
% 258.81/41.22
% 258.81/41.22 (fact_less__nat__zero__code)
% 258.81/41.22 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.22 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 258.81/41.22
% 258.81/41.22 (fact_less__natfloor)
% 258.81/41.22 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 258.81/41.22 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 258.81/41.22 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 258.81/41.22 v1) = v3) | ~ (c_RComplete_Onatfloor(v2) = v4) | ~ $i(v2) | ~
% 258.81/41.22 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~
% 258.81/41.22 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 258.81/41.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1)))
% 258.81/41.22
% 258.81/41.22 (fact_less__zeroE)
% 258.81/41.23 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 258.81/41.23 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 258.81/41.23
% 258.81/41.23 (fact_ln__add__one__self__le__self)
% 258.81/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 258.81/41.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 258.81/41.23 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 258.81/41.23 v1, v2) = v3) | ~ $i(v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v4: $i]
% 258.81/41.23 : (c_Transcendental_Oln(v3) = v4 & $i(v4) &
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2))))
% 258.81/41.23
% 258.81/41.23 (fact_ln__eq__zero__iff)
% 258.81/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 258.81/41.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 258.81/41.23 [v2: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = v0) | ~ $i(v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)) & ! [v2: $i] :
% 258.81/41.23 (v2 = v0 | ~ (c_Transcendental_Oln(v1) = v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 258.81/41.23
% 258.81/41.23 (fact_ln__ge__zero)
% 258.81/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 258.81/41.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 258.81/41.23 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 258.81/41.23 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)))
% 258.81/41.23
% 258.81/41.23 (fact_ln__ge__zero__iff)
% 258.81/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 258.81/41.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 258.81/41.23 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 258.81/41.23 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) |
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i]
% 258.81/41.23 : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 258.81/41.23
% 258.81/41.23 (fact_ln__ge__zero__imp__ge__one)
% 258.81/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 258.81/41.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 258.81/41.23 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 258.81/41.23 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 258.81/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 258.81/41.23
% 258.81/41.23 (fact_ln__gt__zero)
% 258.81/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 258.81/41.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 258.81/41.23 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 258.81/41.23 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 258.81/41.23
% 258.81/41.23 (fact_ln__gt__zero__iff)
% 258.81/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 258.81/41.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 258.81/41.23 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 258.81/41.23 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] :
% 258.81/41.23 ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 258.81/41.23
% 258.81/41.23 (fact_ln__gt__zero__imp__gt__one)
% 258.81/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 258.81/41.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 258.81/41.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 258.81/41.23 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 258.81/41.23 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 258.81/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 258.81/41.23
% 258.81/41.23 (fact_ln__inj__iff)
% 259.09/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.23 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.23 ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = v3) |
% 259.09/41.23 ~ (c_Transcendental_Oln(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 259.09/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 259.09/41.23
% 259.09/41.23 (fact_ln__le__cancel__iff)
% 259.09/41.23 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.23 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.23 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 259.09/41.23 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 259.09/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~
% 259.09/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) |
% 259.09/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v1: $i]
% 259.09/41.23 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) =
% 259.09/41.23 v3) | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 259.09/41.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~
% 259.09/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 259.09/41.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4)))
% 259.09/41.23
% 259.09/41.23 (fact_ln__less__cancel__iff)
% 259.09/41.24 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.24 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.24 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 259.09/41.24 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! [v1: $i] :
% 259.09/41.24 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 259.09/41.24 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4)))
% 259.09/41.24
% 259.09/41.24 (fact_ln__less__self)
% 259.09/41.24 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.24 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.24 ! [v2: $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~ $i(v1) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)))
% 259.09/41.24
% 259.09/41.24 (fact_ln__less__zero)
% 259.09/41.24 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.24 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.09/41.24 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.24 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 259.09/41.24 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 259.09/41.24
% 259.09/41.24 (fact_ln__less__zero__iff)
% 259.09/41.24 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.24 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.09/41.24 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.24 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 259.09/41.24 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i] :
% 259.09/41.24 ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 259.09/41.24
% 259.09/41.24 (fact_ln__mult)
% 259.09/41.24 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.24 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.24 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.24 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.09/41.24 (c_Transcendental_Oln(v3) = v4) | ~ (c_Transcendental_Oln(v2) = v5) | ~
% 259.09/41.24 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~ $i(v3) |
% 259.09/41.24 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 259.09/41.24 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7: $i] :
% 259.09/41.24 ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7, v2) = v8 & hAPP(v1,
% 259.09/41.24 v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 259.09/41.24
% 259.09/41.24 (fact_ln__one)
% 259.09/41.24 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : (c_Transcendental_Oln(v0) =
% 259.09/41.24 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.09/41.24 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 259.09/41.24
% 259.09/41.24 (fact_ln__realpow)
% 259.09/41.24 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 259.09/41.24 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 259.09/41.24 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 259.09/41.24 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 259.09/41.24 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.24 : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) = v7) | ~
% 259.09/41.24 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6, v7) = v8) | ~
% 259.09/41.24 (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v9: $i] : ?
% 259.09/41.24 [v10: $i] : (c_Transcendental_Oln(v10) = v8 & hAPP(v9, v3) = v10 &
% 259.09/41.24 hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & $i(v8))))
% 259.09/41.24
% 259.09/41.24 (fact_minus__nat_Odiff__0)
% 259.09/41.24 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.24 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 259.09/41.24 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)))
% 259.09/41.24
% 259.09/41.24 (fact_mod__1)
% 259.09/41.24 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 259.09/41.24 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.24 $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat,
% 259.09/41.24 v2, v1) = v3) | ~ $i(v2)))
% 259.09/41.24
% 259.09/41.24 (fact_mod__Suc)
% 259.09/41.24 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.24 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0
% 259.09/41.24 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~
% 259.09/41.24 (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? [v6: $i]
% 259.09/41.24 : ( ~ (v6 = v1) & c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v5 &
% 259.09/41.24 c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5))) & ! [v1: $i] : ! [v2: $i] : !
% 259.09/41.24 [v3: $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3,
% 259.09/41.24 v1) = v4) | ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5:
% 259.09/41.24 $i] : ? [v6: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) =
% 259.09/41.24 v5 & c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5) & (v6 = v4 | v6 = v1))))
% 259.09/41.24
% 259.09/41.24 (fact_mod__eq__0__iff)
% 259.09/41.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.25 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.25 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~
% 259.09/41.25 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v4) | ~ $i(v3) | ~
% 259.09/41.25 $i(v2) | ? [v5: $i] : (hAPP(v1, v2) = v5 & $i(v5) & ! [v6: $i] : ( ~
% 259.09/41.25 (hAPP(v5, v6) = v3) | ~ $i(v6)))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 259.09/41.25 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v0) | ~ $i(v3) | ~
% 259.09/41.25 $i(v2) | ? [v4: $i] : ? [v5: $i] : (hAPP(v4, v5) = v3 & hAPP(v1, v2) =
% 259.09/41.25 v4 & $i(v5) & $i(v4))))
% 259.09/41.25
% 259.09/41.25 (fact_mod__le__divisor)
% 259.09/41.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.25 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.09/41.25 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~
% 259.09/41.25 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.09/41.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)))
% 259.09/41.25
% 259.09/41.25 (fact_mod__less__divisor)
% 259.09/41.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.25 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.09/41.25 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~
% 259.09/41.25 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.09/41.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 259.09/41.25
% 259.09/41.25 (fact_mult_Ononneg__bounded)
% 259.09/41.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.25 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.25 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 259.09/41.25 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 259.09/41.25 ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & !
% 259.09/41.25 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 259.09/41.25 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 259.09/41.25 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 259.09/41.25 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) =
% 259.09/41.25 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~
% 259.09/41.25 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14:
% 259.09/41.25 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15
% 259.09/41.25 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 259.09/41.25 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 259.09/41.25 v12))))))
% 259.09/41.25
% 259.09/41.25 (fact_mult_Opos__bounded)
% 259.09/41.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.25 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.25 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 259.09/41.25 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 259.09/41.25 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 259.09/41.25 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 259.09/41.25 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 259.09/41.25 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 259.09/41.25 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) =
% 259.09/41.25 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~
% 259.09/41.25 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14:
% 259.09/41.25 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15
% 259.09/41.25 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 259.09/41.25 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 259.09/41.25 v12))))))
% 259.09/41.25
% 259.09/41.25 (fact_mult__0)
% 259.09/41.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.09/41.25 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) &
% 259.09/41.25 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v2, v3) =
% 259.09/41.25 v4) | ~ $i(v3)))
% 259.09/41.25
% 259.09/41.25 (fact_mult__0__right)
% 259.09/41.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.25 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.25 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) =
% 259.09/41.25 v1))
% 259.09/41.25
% 259.09/41.25 (fact_mult__cancel1)
% 259.09/41.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.25 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.25 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 |
% 259.09/41.25 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) |
% 259.09/41.25 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.25 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~
% 259.09/41.25 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.25 $i(v2)))
% 259.09/41.25
% 259.09/41.25 (fact_mult__cancel2)
% 259.09/41.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.25 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.25 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.25 : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0,
% 259.09/41.25 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 259.09/41.25 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.25 : (v4 = v2 | v3 = v1 | ~ (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~
% 259.09/41.25 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.25 $i(v2)))
% 259.09/41.25
% 259.09/41.25 (fact_mult__eq__1__iff)
% 259.09/41.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 259.09/41.25 v2 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.25 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v3) = v2) |
% 259.09/41.25 ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4:
% 259.09/41.25 $i] : ! [v5: $i] : (v3 = v2 | ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) =
% 259.09/41.25 v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 259.09/41.25 (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v2) = v3)))
% 259.09/41.25
% 259.09/41.25 (fact_mult__eq__if)
% 259.09/41.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.09/41.26 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.26 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 259.09/41.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.26 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 259.09/41.26 $i] : (v4 = v0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) =
% 259.09/41.26 v5) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~
% 259.09/41.26 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ?
% 259.09/41.26 [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & $i(v9) & $i(v8))) & !
% 259.09/41.26 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v0 | ~ (hAPP(v4, v3) = v5) |
% 259.09/41.26 ~ (hAPP(v1, v0) = v4) | ~ $i(v3)))
% 259.09/41.26
% 259.09/41.26 (fact_mult__eq__self__implies__10)
% 259.09/41.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.09/41.26 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.26 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 259.09/41.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.26 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5,
% 259.09/41.26 v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)))
% 259.09/41.26
% 259.09/41.26 (fact_mult__is__0)
% 259.09/41.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.26 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.26 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) = v4) | ~
% 259.09/41.26 (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 259.09/41.26 : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v0, v2) = v3) | ~ $i(v2)) &
% 259.09/41.26 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4,
% 259.09/41.26 v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)))
% 259.09/41.26
% 259.09/41.26 (fact_mult__le__cancel1)
% 259.09/41.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.26 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.26 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.26 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5)
% 259.09/41.26 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) |
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 259.09/41.26 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 259.09/41.26 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 259.09/41.26 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : !
% 259.09/41.26 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 259.09/41.26 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 259.09/41.26 $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 259.09/41.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)))
% 259.09/41.26
% 259.09/41.26 (fact_mult__le__cancel2)
% 259.09/41.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.26 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.26 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.26 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~
% 259.09/41.26 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.26 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) |
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : !
% 259.09/41.26 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 259.09/41.26 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 259.09/41.26 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) |
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)) & ! [v2: $i] : !
% 259.09/41.26 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 259.09/41.26 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 259.09/41.26 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 259.09/41.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)))
% 259.09/41.26
% 259.09/41.26 (fact_mult__left_Ononneg__bounded)
% 259.09/41.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.26 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 259.09/41.26 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.26 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.26 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) &
% 259.09/41.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) & ! [v6:
% 259.09/41.26 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.09/41.26 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) =
% 259.09/41.26 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11:
% 259.09/41.26 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12
% 259.09/41.26 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 259.09/41.26 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 259.09/41.26 v9))))))
% 259.09/41.26
% 259.09/41.26 (fact_mult__left_Opos__bounded)
% 259.09/41.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 259.09/41.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.27 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) &
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v6: $i] :
% 259.09/41.27 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.09/41.27 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) =
% 259.09/41.27 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11:
% 259.09/41.27 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12
% 259.09/41.27 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 259.09/41.27 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 259.09/41.27 v9))))))
% 259.09/41.27
% 259.09/41.27 (fact_mult__less__cancel1)
% 259.09/41.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.27 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.27 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5)
% 259.09/41.27 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 259.09/41.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 259.09/41.27 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 259.09/41.27 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i] : !
% 259.09/41.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 259.09/41.27 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 259.09/41.27 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 259.09/41.27
% 259.09/41.27 (fact_mult__less__cancel2)
% 259.09/41.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.27 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.27 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~
% 259.09/41.27 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.27 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : !
% 259.09/41.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 259.09/41.27 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 259.09/41.27 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] : !
% 259.09/41.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 259.09/41.27 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 259.09/41.27 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 259.09/41.27
% 259.09/41.27 (fact_mult__less__mono1)
% 259.09/41.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.27 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.27 : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5, v2) = v6) | ~
% 259.09/41.27 (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.27 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 259.09/41.27
% 259.09/41.27 (fact_mult__less__mono2)
% 259.09/41.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.27 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.27 : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ (hAPP(v1, v2) = v5)
% 259.09/41.27 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 259.09/41.27
% 259.09/41.27 (fact_mult__right_Ononneg__bounded)
% 259.09/41.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~
% 259.09/41.27 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ?
% 259.09/41.27 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.09/41.27 v0, v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 259.09/41.27 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) =
% 259.09/41.27 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12:
% 259.09/41.27 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 259.09/41.27 = v11 & $i(v12) & $i(v11) &
% 259.09/41.27 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10))))))
% 259.09/41.27
% 259.09/41.27 (fact_mult__right_Opos__bounded)
% 259.09/41.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.27 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~
% 259.09/41.27 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ?
% 259.09/41.27 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 259.09/41.27 v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 259.09/41.27 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) =
% 259.09/41.27 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12:
% 259.09/41.27 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 259.09/41.27 = v11 & $i(v12) & $i(v11) &
% 259.09/41.27 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10))))))
% 259.09/41.27
% 259.09/41.27 (fact_n__less__m__mult__n)
% 259.09/41.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 259.09/41.27 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 259.09/41.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.27 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) =
% 259.09/41.27 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 259.09/41.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)))
% 259.09/41.27
% 259.09/41.27 (fact_n__less__n__mult__m)
% 259.09/41.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 259.09/41.28 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 259.09/41.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.28 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) =
% 259.09/41.28 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)))
% 259.09/41.28
% 259.09/41.28 (fact_nat0__intermed__int__val)
% 259.09/41.28 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.09/41.28 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 259.09/41.28 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 259.09/41.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.28 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, v5) =
% 259.09/41.28 v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.28 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v6) | ? [v7: $i] : ?
% 259.09/41.28 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 259.09/41.28 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ($i(v10) & $i(v8) & ((v9 = v3 &
% 259.09/41.28 hAPP(v4, v8) = v3 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 259.09/41.28 v8, v5)) | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v12, v13) =
% 259.09/41.28 v14 & c_Groups_Oabs__class_Oabs(tc_Int_Oint, v14) = v15 &
% 259.09/41.28 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v10, v0) = v11 & hAPP(v4,
% 259.09/41.28 v11) = v12 & hAPP(v4, v10) = v13 & $i(v15) & $i(v14) & $i(v13) &
% 259.09/41.28 $i(v12) & $i(v11) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10,
% 259.09/41.28 v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v15, v1))
% 259.09/41.28 | (hAPP(v4, v2) = v7 & $i(v7) & ~
% 259.09/41.28 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v7, v3))))))
% 259.09/41.28
% 259.09/41.28 (fact_nat_Osimps_I2_J)
% 259.09/41.28 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.28 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 259.09/41.28
% 259.09/41.28 (fact_nat_Osimps_I3_J)
% 259.09/41.28 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.28 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 259.09/41.28
% 259.09/41.28 (fact_nat__0__less__mult__iff)
% 259.09/41.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.28 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.28 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) |
% 259.09/41.28 ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : !
% 259.09/41.28 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 259.09/41.28 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i] : !
% 259.09/41.28 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 259.09/41.28 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)))
% 259.09/41.28
% 259.09/41.28 (fact_nat__1__eq__mult__iff)
% 259.09/41.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.28 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.28 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i]
% 259.09/41.28 : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = v0) | ~
% 259.09/41.28 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 259.09/41.28 ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) |
% 259.09/41.28 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 259.09/41.28 (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2)))
% 259.09/41.28
% 259.09/41.28 (fact_nat__diff__split)
% 259.09/41.28 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.28 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.28 $i] : ! [v6: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 259.09/41.28 v1) = v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2)
% 259.09/41.28 | ~ (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 259.09/41.28 ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) & hBOOL(v7))) &
% 259.09/41.28 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.28 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 259.09/41.28 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v5) | ~
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] :
% 259.09/41.28 (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! [v1: $i] : ! [v2: $i] : !
% 259.09/41.28 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.28 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 259.09/41.28 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) |
% 259.09/41.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] : ? [v7:
% 259.09/41.28 $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3,
% 259.09/41.28 v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : ! [v2:
% 259.09/41.28 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.28 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 259.09/41.28 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | ? [v6:
% 259.09/41.28 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ((v8 = v2 &
% 259.09/41.28 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v7) = v2 & hAPP(v3, v7)
% 259.09/41.28 = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, v0) = v6 & $i(v6) & ~
% 259.09/41.28 hBOOL(v6))))))
% 259.09/41.28
% 259.09/41.28 (fact_nat__diff__split__asm)
% 259.09/41.29 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.29 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.29 $i] : ! [v6: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 259.09/41.29 v1) = v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2)
% 259.09/41.29 | ~ (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 259.09/41.29 ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) & hBOOL(v7))) &
% 259.09/41.29 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.29 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 259.09/41.29 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v5) | ~
% 259.09/41.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] :
% 259.09/41.29 (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! [v1: $i] : ! [v2: $i] : !
% 259.09/41.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.29 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 259.09/41.29 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) |
% 259.09/41.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] : ? [v7:
% 259.09/41.29 $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3,
% 259.09/41.29 v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : ! [v2:
% 259.09/41.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.29 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 259.09/41.29 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | ? [v6:
% 259.09/41.29 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ((v8 = v2 &
% 259.09/41.29 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v7) = v2 & hAPP(v3, v7)
% 259.09/41.29 = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, v0) = v6 & $i(v6) & ~
% 259.09/41.29 hBOOL(v6))))))
% 259.09/41.29
% 259.09/41.29 (fact_nat__le__real__less)
% 259.09/41.29 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.29 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 259.09/41.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2)
% 259.09/41.29 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 259.09/41.29 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ?
% 259.09/41.29 [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 &
% 259.09/41.29 $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))) & !
% 259.09/41.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.29 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 259.09/41.29 v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 259.09/41.29 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 259.09/41.29 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 & $i(v5) & ~
% 259.09/41.29 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))))
% 259.09/41.29
% 259.09/41.29 (fact_nat__less__real__le)
% 259.09/41.29 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.29 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 259.09/41.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2)
% 259.09/41.29 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 259.09/41.29 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5:
% 259.09/41.29 $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 259.09/41.29 $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))) &
% 259.09/41.29 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.29 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 259.09/41.29 v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 259.09/41.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 259.09/41.29 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) & ~
% 259.09/41.29 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))))
% 259.09/41.29
% 259.09/41.29 (fact_nat__lt__two__imp__zero__or__one)
% 259.09/41.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 259.09/41.29 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 259.09/41.29 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ $i(v3) | ~
% 259.09/41.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 259.09/41.29
% 259.09/41.29 (fact_nat__mult__1)
% 259.09/41.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.09/41.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) &
% 259.09/41.29 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3) =
% 259.09/41.29 v4) | ~ $i(v3)))
% 259.09/41.29
% 259.09/41.29 (fact_nat__mult__1__right)
% 259.09/41.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 259.09/41.29 : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = v2))
% 259.09/41.29
% 259.09/41.29 (fact_nat__mult__div__cancel1)
% 259.09/41.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.29 : ! [v8: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) |
% 259.09/41.29 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) |
% 259.09/41.29 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 259.09/41.29 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8))))
% 259.09/41.29
% 259.09/41.29 (fact_nat__mult__div__cancel__disj)
% 259.09/41.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.29 : ! [v8: $i] : (v4 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6,
% 259.09/41.29 v7) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.09/41.29 (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 259.09/41.29 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8))) & ! [v2:
% 259.09/41.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.29 : (v7 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v6) = v7) | ~
% 259.09/41.29 (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v1, v0) = v4) | ~
% 259.09/41.29 $i(v3) | ~ $i(v2)))
% 259.09/41.29
% 259.09/41.29 (fact_nat__mult__eq__1__iff)
% 259.09/41.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 259.09/41.29 : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = v1) | ~
% 259.09/41.29 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 259.09/41.29 ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) |
% 259.09/41.29 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 259.09/41.29 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 259.09/41.29
% 259.09/41.29 (fact_nat__mult__eq__cancel1)
% 259.09/41.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 |
% 259.09/41.29 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) |
% 259.09/41.29 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 259.09/41.30
% 259.09/41.30 (fact_nat__mult__eq__cancel__disj)
% 259.09/41.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.09/41.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.30 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 |
% 259.09/41.30 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) |
% 259.09/41.30 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.30 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~
% 259.09/41.30 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.30 $i(v2)))
% 259.09/41.30
% 259.09/41.30 (fact_nat__mult__le__cancel1)
% 259.09/41.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.30 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.30 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5)
% 259.09/41.30 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) |
% 259.09/41.30 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 259.09/41.30 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 259.09/41.30 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 259.09/41.30 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 259.09/41.30 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)))
% 259.09/41.30
% 259.09/41.30 (fact_nat__mult__less__cancel1)
% 259.09/41.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.09/41.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.30 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.30 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5)
% 259.09/41.30 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 259.09/41.30 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 259.09/41.30 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 259.09/41.30 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 259.09/41.30
% 259.09/41.30 (fact_nat__one__le__power)
% 259.09/41.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 259.09/41.30 v1 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 &
% 259.09/41.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.30 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) =
% 259.09/41.30 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) |
% 259.09/41.30 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)))
% 259.09/41.30
% 259.09/41.30 (fact_nat__power__eq__Suc__0__iff)
% 259.09/41.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 259.09/41.30 v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 259.09/41.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.30 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v3) = v5) |
% 259.09/41.30 ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.30 $i] : (v5 = v2 | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, v3) = v4) | ~
% 259.09/41.30 $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 |
% 259.09/41.30 ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)))
% 259.09/41.30
% 259.09/41.30 (fact_nat__power__less__imp__less)
% 259.09/41.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.30 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.09/41.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.30 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.09/41.30 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5)
% 259.09/41.30 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 259.09/41.30
% 259.09/41.30 (fact_nat__zero__less__power__iff)
% 259.09/41.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.30 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.09/41.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.30 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4,
% 259.09/41.30 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : !
% 259.09/41.30 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 259.09/41.30 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 259.09/41.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : !
% 259.09/41.30 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) |
% 259.09/41.30 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 259.09/41.30
% 259.09/41.30 (fact_natceiling__add)
% 259.09/41.30 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.30 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.30 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 259.09/41.30 v1) = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3)
% 259.09/41.30 = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.30 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v5: $i]
% 259.09/41.30 : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 259.09/41.30 c_RComplete_Onatceiling(v2) = v6 &
% 259.09/41.30 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 259.09/41.30 $i(v5))))
% 259.09/41.30
% 259.09/41.30 (fact_natceiling__add__one)
% 259.09/41.30 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 259.09/41.30 $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 259.09/41.30 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.09/41.30 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 259.09/41.30 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.30 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) |
% 259.09/41.30 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5:
% 259.09/41.30 $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 259.09/41.30 c_RComplete_Onatceiling(v3) = v6 &
% 259.09/41.30 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 259.09/41.30 $i(v5))))
% 259.09/41.30
% 259.09/41.30 (fact_natceiling__eq)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 259.09/41.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 259.09/41.31 (c_RComplete_Onatceiling(v2) = v4) | ~
% 259.09/41.31 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~ $i(v3) | ~
% 259.09/41.31 $i(v2) | ? [v6: $i] : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v3) =
% 259.09/41.31 v6 & $i(v6) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 259.09/41.31 v2) | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 &
% 259.09/41.31 $i(v7) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 259.09/41.31 v7))))))
% 259.09/41.31
% 259.09/41.31 (fact_natceiling__le__eq)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.31 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.31 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 259.09/41.31 v1) = v4) | ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 259.09/41.31 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1) | ~
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4)) & ! [v1: $i]
% 259.09/41.31 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.31 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ (c_RComplete_Onatceiling(v2)
% 259.09/41.31 = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) | ~
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1)))
% 259.09/41.31
% 259.09/41.31 (fact_natceiling__le__eq__one)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 259.09/41.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.31 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) |
% 259.09/41.31 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) |
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i]
% 259.09/41.31 : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0)))
% 259.09/41.31
% 259.09/41.31 (fact_natceiling__neg)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.09/41.31 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.31 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_RComplete_Onatceiling(v2) = v3) |
% 259.09/41.31 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 259.09/41.31 v0)))
% 259.09/41.31
% 259.09/41.31 (fact_natceiling__one)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 259.09/41.31 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 259.09/41.31
% 259.09/41.31 (fact_natceiling__zero)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) =
% 259.09/41.31 v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 259.09/41.31
% 259.09/41.31 (fact_natfloor__add)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.31 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.31 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 259.09/41.31 v1) = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3)
% 259.09/41.31 = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v5: $i]
% 259.09/41.31 : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 259.09/41.31 c_RComplete_Onatfloor(v2) = v6 &
% 259.09/41.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 259.09/41.31 $i(v5))))
% 259.09/41.31
% 259.09/41.31 (fact_natfloor__add__one)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 259.09/41.31 $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 259.09/41.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.09/41.31 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 259.09/41.31 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.31 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) |
% 259.09/41.31 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5:
% 259.09/41.31 $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 259.09/41.31 c_RComplete_Onatfloor(v3) = v6 &
% 259.09/41.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 259.09/41.31 $i(v5))))
% 259.09/41.31
% 259.09/41.31 (fact_natfloor__div__nat)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.09/41.31 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.31 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) | ~
% 259.09/41.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v6: $i]
% 259.09/41.31 : ? [v7: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v2) = v6 &
% 259.09/41.31 c_RComplete_Onatfloor(v5) = v6 & c_RComplete_Onatfloor(v3) = v7 & $i(v7)
% 259.09/41.31 & $i(v6))))
% 259.09/41.31
% 259.09/41.31 (fact_natfloor__eq)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.31 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 259.09/41.31 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 259.09/41.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RComplete_Onatfloor(v1) =
% 259.09/41.31 v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? [v5: $i]
% 259.09/41.31 : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) &
% 259.09/41.31 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 259.09/41.31
% 259.09/41.31 (fact_natfloor__neg)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.09/41.31 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.31 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_RComplete_Onatfloor(v2) = v3) | ~
% 259.09/41.31 $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 259.09/41.31
% 259.09/41.31 (fact_natfloor__one)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1
% 259.09/41.31 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 259.09/41.31
% 259.09/41.31 (fact_natfloor__power)
% 259.09/41.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.31 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.09/41.31 c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.31 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.09/41.31 (c_RComplete_Onatfloor(v3) = v4) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1,
% 259.09/41.31 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ? [v7: $i] : ? [v8: $i] : ?
% 259.09/41.31 [v9: $i] : ? [v10: $i] : ((v10 = v6 & c_RComplete_Onatfloor(v9) = v6 &
% 259.09/41.31 hAPP(v8, v2) = v9 & hAPP(v0, v3) = v8 & $i(v9) & $i(v8) & $i(v6)) | (
% 259.09/41.31 ~ (v7 = v3) & c_RealDef_Oreal(tc_Nat_Onat, v4) = v7 & $i(v7)))))
% 259.09/41.31
% 259.09/41.31 (fact_natfloor__zero)
% 259.09/41.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.32 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) =
% 259.09/41.32 v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 259.09/41.32
% 259.09/41.32 (fact_neq0__conv)
% 259.09/41.32 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.32 & $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1:
% 259.09/41.32 $i] : (v1 = v0 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 259.09/41.32 v0, v1)))
% 259.09/41.32
% 259.09/41.32 (fact_norm__eq__zero)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.32 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 259.09/41.32 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.32 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~ (v3 = v0)
% 259.09/41.32 | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = v1)) & (v3 = v0 | ( ~
% 259.09/41.32 (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 259.09/41.32
% 259.09/41.32 (fact_norm__ge__zero)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.32 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 259.09/41.32 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.32 class_RealVector_Oreal__normed__vector(v2) |
% 259.09/41.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 259.09/41.32
% 259.09/41.32 (fact_norm__le__zero__iff)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.32 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 259.09/41.32 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.32 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~
% 259.09/41.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | (v4 = v1
% 259.09/41.32 & c_Groups_Ozero__class_Ozero(v2) = v1)) &
% 259.09/41.32 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | ( ~ (v4 =
% 259.09/41.32 v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 259.09/41.32
% 259.09/41.32 (fact_norm__not__less__zero)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.32 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 259.09/41.32 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.32 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~
% 259.09/41.32 class_RealVector_Oreal__normed__vector(v2)))
% 259.09/41.32
% 259.09/41.32 (fact_norm__one)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 259.09/41.32 [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Groups_Oone__class_Oone(v1) = v2)
% 259.09/41.32 | ~ (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~
% 259.09/41.32 class_RealVector_Oreal__normed__algebra__1(v1)))
% 259.09/41.32
% 259.09/41.32 (fact_norm__ratiotest__lemma)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.32 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.32 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.32 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.09/41.32 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v5,
% 259.09/41.32 v3) = v6) | ~ (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~
% 259.09/41.32 (hAPP(v7, v8) = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~
% 259.09/41.32 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v5) | ~
% 259.09/41.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) | ~
% 259.09/41.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) |
% 259.09/41.32 c_Groups_Ozero__class_Ozero(v5) = v3))
% 259.09/41.32
% 259.09/41.32 (fact_norm__sgn)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.09/41.32 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.32 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.32 (c_Groups_Osgn__class_Osgn(v3, v2) = v4) | ~
% 259.09/41.32 (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) |
% 259.09/41.32 ~ class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ((v5 = v1 |
% 259.09/41.32 (v6 = v2 & c_Groups_Ozero__class_Ozero(v3) = v2)) & (v5 = v0 | ( ~ (v6
% 259.09/41.32 = v2) & c_Groups_Ozero__class_Ozero(v3) = v6 & $i(v6))))))
% 259.09/41.32
% 259.09/41.32 (fact_norm__zero)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.32 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 259.09/41.32 (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v1) | ~
% 259.09/41.32 class_RealVector_Oreal__normed__vector(v1)))
% 259.09/41.32
% 259.09/41.32 (fact_not__less0)
% 259.09/41.32 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.32 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 259.09/41.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 259.09/41.32
% 259.09/41.32 (fact_not__one__le__zero)
% 259.09/41.32 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 259.09/41.32 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~
% 259.09/41.32 c_Orderings_Oord__class_Oless__eq(v0, v1, v2)))
% 259.09/41.32
% 259.09/41.32 (fact_not__one__less__zero)
% 259.09/41.32 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 259.09/41.32 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~
% 259.09/41.32 c_Orderings_Oord__class_Oless(v0, v1, v2)))
% 259.09/41.32
% 259.09/41.32 (fact_not__real__of__nat__less__zero)
% 259.09/41.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.32 ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ~
% 259.09/41.32 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 259.09/41.32
% 259.09/41.32 (fact_not__real__square__gt__zero)
% 259.09/41.32 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.32 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.32 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.32 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3, v2) = v4) |
% 259.09/41.32 ~ (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 259.09/41.32 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2: $i] :
% 259.09/41.32 ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2) | ~
% 259.09/41.32 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 259.09/41.32
% 259.09/41.32 (fact_one__is__add)
% 259.09/41.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 259.09/41.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.09/41.33 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 259.09/41.33 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 259.09/41.33 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~
% 259.09/41.33 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 259.09/41.33 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~
% 259.09/41.33 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 259.09/41.33 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~
% 259.09/41.33 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 259.09/41.33 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~
% 259.09/41.33 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] :
% 259.09/41.33 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2)))
% 259.09/41.33
% 259.09/41.33 (fact_one__le__mult__iff)
% 259.09/41.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 259.09/41.33 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 259.09/41.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.33 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) =
% 259.09/41.33 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) |
% 259.09/41.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)) & ! [v3: $i] : !
% 259.09/41.33 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = v6) | ~
% 259.09/41.33 (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) |
% 259.09/41.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) & ! [v3: $i] : !
% 259.09/41.33 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = v6) | ~
% 259.09/41.33 (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) | ~
% 259.09/41.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) |
% 259.09/41.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)))
% 259.09/41.33
% 259.09/41.33 (fact_one__less__mult)
% 259.09/41.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 259.09/41.33 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 259.09/41.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 259.09/41.33 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) =
% 259.09/41.33 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 259.09/41.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 259.09/41.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6)))
% 259.09/41.33
% 259.09/41.33 (fact_one__less__power)
% 259.09/41.33 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.33 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.33 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~
% 259.09/41.33 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.33 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 259.09/41.33 class_Rings_Olinordered__semidom(v3) | ? [v7: $i] :
% 259.09/41.33 (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~
% 259.09/41.33 c_Orderings_Oord__class_Oless(v3, v7, v2) |
% 259.09/41.33 c_Orderings_Oord__class_Oless(v3, v7, v6)))))
% 259.09/41.33
% 259.09/41.33 (fact_one__neq__zero)
% 259.09/41.33 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 259.09/41.33 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) &
% 259.09/41.33 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2)))
% 259.09/41.33
% 259.09/41.33 (fact_order__root)
% 259.09/41.33 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.33 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.33 $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~
% 259.09/41.33 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: $i] :
% 259.09/41.33 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) &
% 259.09/41.33 c_Polynomial_Oorder(v3, v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7
% 259.09/41.33 & c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | (v6 = v5
% 259.09/41.33 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & ((v8 = v2 &
% 259.09/41.33 tc_Polynomial_Opoly(v3) = v7 & c_Groups_Ozero__class_Ozero(v7) = v2
% 259.09/41.33 & $i(v7)) | ( ~ (v9 = v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 &
% 259.09/41.33 $i(v9)) | ( ~ (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 &
% 259.09/41.33 $i(v6))))))
% 259.09/41.33
% 259.09/41.33 (fact_plus__nat_Oadd__0)
% 259.09/41.33 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.33 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 259.09/41.33 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1)))
% 259.09/41.33
% 259.09/41.33 (fact_poly__bound__exists)
% 259.09/41.33 $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i] :
% 259.09/41.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 259.09/41.33 ! [v2: $i] : ! [v3: $i] : ( ~ (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2)
% 259.09/41.33 = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : ($i(v4) &
% 259.09/41.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! [v5: $i] :
% 259.09/41.33 ! [v6: $i] : ( ~ (hAPP(v3, v5) = v6) | ~ $i(v5) | ? [v7: $i] : ? [v8:
% 259.09/41.33 $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) =
% 259.09/41.33 v8 & $i(v8) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.09/41.33 v8, v4)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 259.09/41.33 v5) = v7 & $i(v7) & ~
% 259.09/41.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v1)))))))
% 259.09/41.33
% 259.09/41.33 (fact_poly__cont)
% 259.09/41.33 $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i] :
% 259.09/41.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.33 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.33 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v4) | ~ (hAPP(v4, v2) =
% 259.09/41.33 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v6: $i] :
% 259.09/41.33 ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6) & !
% 259.09/41.33 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.09/41.33 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v8, v5) = v9) | ~
% 259.09/41.33 (hAPP(v4, v7) = v8) | ~ $i(v7) | ? [v10: $i] : ? [v11: $i] : ?
% 259.09/41.33 [v12: $i] : ((c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v7,
% 259.09/41.33 v2) = v10 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 259.09/41.33 v10) = v11 & $i(v11) & $i(v10) & ( ~
% 259.09/41.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v6) | ~
% 259.09/41.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v11))) |
% 259.09/41.33 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v9) = v12 &
% 259.09/41.33 $i(v12) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12,
% 259.09/41.33 v3)))))))
% 259.09/41.33
% 259.09/41.33 (fact_power_Opower_Opower__0)
% 259.09/41.33 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.33 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.33 $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | ~
% 259.09/41.33 (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 259.09/41.33 hAPP(v6, v0) = v3))
% 259.09/41.33
% 259.09/41.33 (fact_power__0)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.34 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.34 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 259.09/41.34 $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] :
% 259.09/41.34 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5))))
% 259.09/41.34
% 259.09/41.34 (fact_power__0__left)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.34 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.34 $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~
% 259.09/41.34 (c_Power_Opower__class_Opower(v2) = v3) | ~
% 259.09/41.34 (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | ~
% 259.09/41.34 (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.34 class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2)) & ! [v1: $i] :
% 259.09/41.34 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.09/41.34 (c_Power_Opower__class_Opower(v1) = v2) | ~
% 259.09/41.34 (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | ~
% 259.09/41.34 (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ class_Rings_Osemiring__0(v1) | ~
% 259.09/41.34 class_Power_Opower(v1) | (c_Groups_Oone__class_Oone(v1) = v5 & $i(v5))))
% 259.09/41.34
% 259.09/41.34 (fact_power__Suc__0)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 259.09/41.34 (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 259.09/41.34 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 & $i(v3) &
% 259.09/41.34 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~
% 259.09/41.34 (hAPP(v3, v4) = v5) | ~ $i(v4)))
% 259.09/41.34
% 259.09/41.34 (fact_power__eq__0__iff)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.34 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.34 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~
% 259.09/41.34 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.34 $i(v1) | ~ class_Power_Opower(v3) | ~
% 259.09/41.34 class_Rings_Ono__zero__divisors(v3) | ~ class_Rings_Omult__zero(v3) | ~
% 259.09/41.34 class_Rings_Ozero__neq__one(v3) | ? [v7: $i] :
% 259.09/41.34 (c_Groups_Ozero__class_Ozero(v3) = v7 & $i(v7) & ( ~ (v7 = v6) | (v6 = v2
% 259.09/41.34 & ~ (v1 = v0))) & ( ~ (v7 = v2) | v6 = v2 | v1 = v0))))
% 259.09/41.34
% 259.09/41.34 (fact_power__eq__if)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 259.09/41.34 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.09/41.34 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 &
% 259.09/41.34 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 259.09/41.34 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 259.09/41.34 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 259.09/41.34 : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~
% 259.09/41.34 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ (hAPP(v7,
% 259.09/41.34 v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = v7) | ~
% 259.09/41.34 (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, v5) = v10 &
% 259.09/41.34 $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | ~
% 259.09/41.34 (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4)))
% 259.09/41.34
% 259.09/41.34 (fact_power__eq__imp__eq__base)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.34 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.34 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~
% 259.09/41.34 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v2) = v7) | ~
% 259.09/41.34 (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v1) = v8) | ~
% 259.09/41.34 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.34 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 259.09/41.34 class_Rings_Olinordered__semidom(v4) | ? [v9: $i] :
% 259.09/41.34 (c_Groups_Ozero__class_Ozero(v4) = v9 & $i(v9) & ( ~
% 259.09/41.34 c_Orderings_Oord__class_Oless__eq(v4, v9, v3) | ~
% 259.09/41.34 c_Orderings_Oord__class_Oless__eq(v4, v9, v1)))))
% 259.09/41.34
% 259.09/41.34 (fact_power__one__right)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 259.09/41.34 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.09/41.34 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 259.09/41.34 $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | hAPP(v4, v0) =
% 259.09/41.34 v1))
% 259.09/41.34
% 259.09/41.34 (fact_power__real__of__nat)
% 259.09/41.34 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.34 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.09/41.34 c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.34 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.09/41.34 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4) | ~ (hAPP(v5, v2) = v6) | ~
% 259.09/41.34 (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ? [v7: $i] : ? [v8: $i] :
% 259.09/41.34 (c_RealDef_Oreal(tc_Nat_Onat, v8) = v6 & hAPP(v7, v2) = v8 & hAPP(v1, v3)
% 259.09/41.34 = v7 & $i(v8) & $i(v7) & $i(v6))))
% 259.09/41.34
% 259.09/41.34 (fact_power__strict__mono)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.34 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.09/41.34 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.09/41.34 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9) | ~
% 259.09/41.34 (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v8) | ~
% 259.09/41.34 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.09/41.34 c_Orderings_Oord__class_Oless(v4, v3, v2) | ~
% 259.09/41.34 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 259.09/41.34 class_Rings_Olinordered__semidom(v4) | c_Orderings_Oord__class_Oless(v4,
% 259.09/41.34 v7, v9) | ? [v10: $i] : (c_Groups_Ozero__class_Ozero(v4) = v10 &
% 259.09/41.34 $i(v10) & ~ c_Orderings_Oord__class_Oless__eq(v4, v10, v3))))
% 259.09/41.34
% 259.09/41.34 (fact_psize__eq__0__iff)
% 259.09/41.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.09/41.34 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.09/41.34 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | ~
% 259.09/41.34 $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i] : ? [v5: $i]
% 259.09/41.34 : (( ~ (v3 = v0) | (v5 = v1 & tc_Polynomial_Opoly(v2) = v4 &
% 259.09/41.34 c_Groups_Ozero__class_Ozero(v4) = v1 & $i(v4))) & (v3 = v0 | ( ~ (v5
% 259.09/41.34 = v1) & tc_Polynomial_Opoly(v2) = v4 &
% 259.09/41.34 c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))))))
% 259.09/41.34
% 259.09/41.34 (fact_r)
% 259.09/41.35 $i(v_aa____) & $i(v_da____) & $i(v_c____) & $i(v_cs____) & $i(v_r____) &
% 259.09/41.35 $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.35 ? [v2: $i] : ? [v3: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3 &
% 259.09/41.35 c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) = v2 &
% 259.09/41.35 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, v0) = v1 &
% 259.09/41.35 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____) = v0 & $i(v3)
% 259.09/41.35 & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v4) =
% 259.09/41.35 v5) | ~ $i(v4) | ? [v6: $i] : ? [v7: $i] :
% 259.09/41.35 ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7 & $i(v7) &
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v7)) |
% 259.09/41.35 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = v6 & $i(v6)
% 259.09/41.35 & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r____,
% 259.09/41.35 v6)))))
% 259.09/41.35
% 259.09/41.35 (fact_rabs__ratiotest__lemma)
% 259.09/41.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.35 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.09/41.35 $i] : ! [v8: $i] : (v3 = v0 | ~
% 259.09/41.35 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v5) | ~
% 259.09/41.35 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v7) | ~ (hAPP(v6, v7)
% 259.09/41.35 = v8) | ~ (hAPP(v1, v4) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v8) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0)))
% 259.09/41.35
% 259.09/41.35 (fact_rcis__zero__mod)
% 259.09/41.35 $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.35 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.09/41.35 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v1) & $i(v0) & !
% 259.09/41.35 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_Complex_Orcis(v0, v2) = v3) | ~
% 259.09/41.35 $i(v2)))
% 259.09/41.35
% 259.09/41.35 (fact_real__le__eq__diff)
% 259.09/41.35 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.09/41.35 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.09/41.35 ! [v2: $i] : ! [v3: $i] : ( ~
% 259.09/41.35 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2)
% 259.09/41.35 | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3,
% 259.09/41.35 v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 259.09/41.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.09/41.35 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2)
% 259.09/41.35 | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 259.09/41.35 v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 259.09/41.35
% 259.09/41.35 (fact_real__le__trans)
% 259.09/41.35 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 259.09/41.35 ~ $i(v1) | ~ $i(v0) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))
% 259.09/41.35
% 259.09/41.35 (fact_real__less__def)
% 259.09/41.35 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~
% 259.09/41.35 $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 259.09/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0: $i] : !
% 259.09/41.35 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) |
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & ! [v0: $i] :
% 259.09/41.35 ( ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v0))
% 259.09/41.35
% 259.09/41.35 (fact_real__mult__1)
% 259.09/41.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.09/41.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 259.09/41.35 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & hAPP(v0, v1) = v2 &
% 259.09/41.35 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 259.09/41.35 (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 259.09/41.35
% 259.09/41.35 (fact_real__mult__le__cancel__iff1)
% 259.09/41.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.35 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.09/41.35 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~
% 259.09/41.35 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 259.09/41.35 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) |
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i]
% 259.09/41.35 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 259.09/41.35 [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1,
% 259.09/41.35 v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 259.09/41.35 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) |
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8)))
% 259.09/41.35
% 259.09/41.35 (fact_real__mult__le__cancel__iff2)
% 259.09/41.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.09/41.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.09/41.35 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.09/41.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.09/41.35 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 259.09/41.35 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) |
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i]
% 259.09/41.35 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 259.09/41.35 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 259.09/41.35 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) |
% 259.09/41.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7)))
% 259.09/41.35
% 259.09/41.35 (fact_real__mult__left__cancel)
% 259.33/41.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.35 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v0
% 259.33/41.35 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1,
% 259.33/41.35 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 259.33/41.35
% 259.33/41.35 (fact_real__mult__less__iff1)
% 259.33/41.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.35 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.33/41.35 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~
% 259.33/41.35 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 259.33/41.35 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~
% 259.33/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 259.33/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i] :
% 259.33/41.35 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 259.33/41.35 $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3)
% 259.33/41.35 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 259.33/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 259.33/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8)))
% 259.33/41.35
% 259.33/41.35 (fact_real__mult__less__mono2)
% 259.33/41.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.35 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.33/41.35 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 259.33/41.35 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 259.33/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 259.33/41.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7)))
% 259.33/41.35
% 259.33/41.35 (fact_real__mult__order)
% 259.33/41.36 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.36 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 259.33/41.36 | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 259.33/41.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 259.33/41.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 259.33/41.36
% 259.33/41.36 (fact_real__mult__right__cancel)
% 259.33/41.36 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.36 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.33/41.36 $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) | ~ (hAPP(v5, v4) = v6)
% 259.33/41.36 | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3)
% 259.33/41.36 | ~ $i(v2)))
% 259.33/41.36
% 259.33/41.36 (fact_real__natceiling__ge)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ( ~
% 259.33/41.36 (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 259.33/41.36 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v2) &
% 259.33/41.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)))
% 259.33/41.36
% 259.33/41.36 (fact_real__natfloor__add__one__gt)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.36 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 259.33/41.36 [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 259.33/41.36 ? [v4: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 259.33/41.36 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 & $i(v4) &
% 259.33/41.36 $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 259.33/41.36
% 259.33/41.36 (fact_real__natfloor__gt__diff__one)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.36 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 259.33/41.36 [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) =
% 259.33/41.36 v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 259.33/41.36 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1) = v3 &
% 259.33/41.36 $i(v4) & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 259.33/41.36 v4))))
% 259.33/41.36
% 259.33/41.36 (fact_real__natfloor__le)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.36 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.33/41.36 ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~
% 259.33/41.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ? [v3: $i]
% 259.33/41.36 : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) &
% 259.33/41.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))))
% 259.33/41.36
% 259.33/41.36 (fact_real__norm__def)
% 259.33/41.36 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ( ~
% 259.33/41.36 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) |
% 259.33/41.36 (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v0) = v1 & $i(v1)))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__1)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.36 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 259.33/41.36 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 259.33/41.36 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__Suc)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.36 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 259.33/41.36 [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ? [v3:
% 259.33/41.36 $i] : ? [v4: $i] : (c_Nat_OSuc(v1) = v3 & c_RealDef_Oreal(tc_Nat_Onat,
% 259.33/41.36 v3) = v4 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v0) = v4
% 259.33/41.36 & $i(v4) & $i(v3))))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__Suc__gt__zero)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.36 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.33/41.36 ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 259.33/41.36 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) &
% 259.33/41.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__div__aux)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.36 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : !
% 259.33/41.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.33/41.36 $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.33/41.36 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v7, v3) = v8) | ~
% 259.33/41.36 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v6) | ~
% 259.33/41.36 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v4) | ~
% 259.33/41.36 (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 259.33/41.36 v4) = v5) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 259.33/41.36 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v8) = v9) | ~ $i(v2) |
% 259.33/41.36 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ?
% 259.33/41.36 [v10: $i] : (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v10, v3) =
% 259.33/41.36 v9 & c_RealDef_Oreal(tc_Nat_Onat, v1) = v10 & $i(v10) & $i(v9))))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__ge__zero)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.36 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.33/41.36 ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) |
% 259.33/41.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__gt__zero__cancel__iff)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.36 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.33/41.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.36 [v2: $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 259.33/41.36 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 259.33/41.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] :
% 259.33/41.36 ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 259.33/41.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 259.33/41.36 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__le__zero__cancel__iff)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.36 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.33/41.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.36 [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) =
% 259.33/41.36 v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.33/41.36 v3, v0)) & ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) |
% 259.33/41.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__one)
% 259.33/41.36 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 259.33/41.36 $i] : (c_Nat_OSuc(v0) = v1 & c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 &
% 259.33/41.36 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 259.33/41.36 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0))
% 259.33/41.36
% 259.33/41.36 (fact_real__of__nat__power)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 259.33/41.37 c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 259.33/41.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.33/41.37 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4) | ~ (hAPP(v5, v2) = v6) | ~
% 259.33/41.37 (hAPP(v1, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ? [v7: $i] : ? [v8: $i] :
% 259.33/41.37 (c_RealDef_Oreal(tc_Nat_Onat, v8) = v6 & hAPP(v7, v2) = v8 & hAPP(v0, v3)
% 259.33/41.37 = v7 & $i(v8) & $i(v7) & $i(v6))))
% 259.33/41.37
% 259.33/41.37 (fact_real__of__nat__zero)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 259.33/41.37
% 259.33/41.37 (fact_real__of__nat__zero__iff)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.37 [v2: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v0) | ~
% 259.33/41.37 $i(v2)) & ! [v2: $i] : (v2 = v0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) =
% 259.33/41.37 v2)))
% 259.33/41.37
% 259.33/41.37 (fact_real__sgn__pos)
% 259.33/41.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.37 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 259.33/41.37 (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)))
% 259.33/41.37
% 259.33/41.37 (fact_real__two__squares__add__zero__iff)
% 259.33/41.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 259.33/41.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.33/41.37 $i] : (v3 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7)
% 259.33/41.37 = v1) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0,
% 259.33/41.37 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 259.33/41.37 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.33/41.37 : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1)
% 259.33/41.37 | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) = v4)
% 259.33/41.37 | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3:
% 259.33/41.37 $i] : ! [v4: $i] : (v4 = v1 | ~
% 259.33/41.37 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~
% 259.33/41.37 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 259.33/41.37
% 259.33/41.37 (fact_real__zero__not__eq__one)
% 259.33/41.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 259.33/41.37 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 259.33/41.37
% 259.33/41.37 (fact_realpow__minus__mult)
% 259.33/41.37 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.33/41.37 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.33/41.37 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 259.33/41.37 (c_Power_Opower__class_Opower(v4) = v6) | ~
% 259.33/41.37 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~
% 259.33/41.37 (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = v11) | ~
% 259.33/41.37 (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v9) = v10) |
% 259.33/41.37 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ class_Groups_Omonoid__mult(v4) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3) = v11 &
% 259.33/41.37 $i(v11))))
% 259.33/41.37
% 259.33/41.37 (fact_realpow__num__eq__if)
% 259.33/41.37 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.33/41.37 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.33/41.37 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 259.33/41.37 (c_Power_Opower__class_Opower(v4) = v5) | ~
% 259.33/41.37 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~
% 259.33/41.37 (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ (hAPP(v8, v10) = v11) | ~
% 259.33/41.37 (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ (hAPP(v5, v2) = v6) |
% 259.33/41.37 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ class_Power_Opower(v4) | ? [v12:
% 259.33/41.37 $i] : ? [v13: $i] : (( ~ (v3 = v0) | (v13 = v12 &
% 259.33/41.37 c_Groups_Oone__class_Oone(v4) = v12 & hAPP(v6, v0) = v12 & $i(v12)))
% 259.33/41.37 & (v3 = v0 | (v12 = v11 & hAPP(v6, v3) = v11 & $i(v11))))))
% 259.33/41.37
% 259.33/41.37 (fact_realpow__pos__nth)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 259.33/41.37 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) &
% 259.33/41.37 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v5: $i] : ?
% 259.33/41.37 [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) &
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 259.33/41.37
% 259.33/41.37 (fact_realpow__pos__nth__unique)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 259.33/41.37 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) &
% 259.33/41.37 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v5: $i] : ?
% 259.33/41.37 [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) &
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & ! [v7: $i] :
% 259.33/41.37 ! [v8: $i] : (v7 = v5 | ~ (hAPP(v8, v4) = v3) | ~ (hAPP(v2, v7) = v8)
% 259.33/41.37 | ~ $i(v7) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 259.33/41.37 v7)))))
% 259.33/41.37
% 259.33/41.37 (fact_realpow__two__diff)
% 259.33/41.37 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 259.33/41.37 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 259.33/41.37 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.37 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 259.33/41.37 $i] : ( ~ (c_Power_Opower__class_Opower(v5) = v6) | ~
% 259.33/41.37 (c_Groups_Ominus__class_Ominus(v5, v8, v10) = v11) | ~ (hAPP(v9, v2) =
% 259.33/41.37 v10) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6,
% 259.33/41.37 v3) = v9) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 259.33/41.37 class_Rings_Ocomm__ring__1(v5) | ? [v12: $i] : ? [v13: $i] : ? [v14:
% 259.33/41.37 $i] : ? [v15: $i] : (c_Groups_Ominus__class_Ominus(v5, v4, v3) = v13 &
% 259.33/41.37 c_Groups_Otimes__class_Otimes(v5) = v12 &
% 259.33/41.37 c_Groups_Oplus__class_Oplus(v5, v4, v3) = v15 & hAPP(v14, v15) = v11 &
% 259.33/41.37 hAPP(v12, v13) = v14 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 259.33/41.37 $i(v11))))
% 259.33/41.37
% 259.33/41.37 (fact_reals__Archimedean3)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 259.33/41.37 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: $i] : ?
% 259.33/41.37 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) =
% 259.33/41.37 v5 & hAPP(v6, v3) = v7 & hAPP(v1, v5) = v6 & $i(v7) & $i(v6) & $i(v5) &
% 259.33/41.37 $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v7))))
% 259.33/41.37
% 259.33/41.37 (fact_reals__Archimedean4)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.37 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v4: $i]
% 259.33/41.37 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 259.33/41.37 [v10: $i] : ? [v11: $i] : (c_Nat_OSuc(v4) = v8 &
% 259.33/41.37 c_RealDef_Oreal(tc_Nat_Onat, v8) = v9 & c_RealDef_Oreal(tc_Nat_Onat, v4)
% 259.33/41.37 = v5 & hAPP(v10, v3) = v11 & hAPP(v6, v3) = v7 & hAPP(v1, v9) = v10 &
% 259.33/41.37 hAPP(v1, v5) = v6 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 259.33/41.37 $i(v6) & $i(v5) & $i(v4) &
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v11) &
% 259.33/41.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v2))))
% 259.33/41.37
% 259.33/41.37 (fact_reals__Archimedean6)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.37 [v2: $i] : ( ~ $i(v2) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v3: $i]
% 259.33/41.37 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (c_RealDef_Oreal(tc_Nat_Onat,
% 259.33/41.37 v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 &
% 259.33/41.37 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & $i(v6) &
% 259.33/41.37 $i(v5) & $i(v4) & $i(v3) &
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6) &
% 259.33/41.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 259.33/41.37
% 259.33/41.37 (fact_reals__Archimedean6a)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.37 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : (
% 259.33/41.37 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1)
% 259.33/41.37 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (c_Nat_OSuc(v2)
% 259.33/41.37 = v4 & c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 &
% 259.33/41.37 c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v5) & $i(v4) & $i(v3) &
% 259.33/41.37 $i(v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) &
% 259.33/41.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))))
% 259.33/41.37
% 259.33/41.37 (fact_reduce__poly__simple)
% 259.33/41.37 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0: $i]
% 259.33/41.37 : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 259.33/41.37 (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v4 &
% 259.33/41.37 c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 &
% 259.33/41.37 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v5 &
% 259.33/41.37 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v5) & $i(v4) &
% 259.33/41.37 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 259.33/41.37 : (v7 = v0 | v6 = v1 | ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | ~ $i(v6) | ?
% 259.33/41.37 [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 259.33/41.37 [v14: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v12) =
% 259.33/41.37 v13 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v13) = v14 &
% 259.33/41.37 hAPP(v10, v6) = v11 & hAPP(v8, v11) = v12 & hAPP(v4, v9) = v10 & $i(v14)
% 259.33/41.37 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v5))))
% 259.33/41.37
% 259.33/41.37 (fact_split__div)
% 259.33/41.37 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.37 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.33/41.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.33/41.37 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.33/41.37 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5)
% 259.33/41.37 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ? [v7: $i] :
% 259.33/41.37 ? [v8: $i] : (( ~ (v2 = v0) | (hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7))) &
% 259.33/41.37 (v2 = v0 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : !
% 259.33/41.37 [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10)
% 259.33/41.37 = v3) | ~ (hAPP(v8, v9) = v11) | ~ $i(v10) | ~ $i(v9) | ~
% 259.33/41.37 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) | ? [v12: $i]
% 259.33/41.37 : (hAPP(v4, v9) = v12 & $i(v12) & hBOOL(v12))))))) & ! [v2: $i] :
% 259.33/41.37 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.33/41.37 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5)
% 259.33/41.37 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | hBOOL(v6) | ? [v7: $i] : ?
% 259.33/41.37 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 259.33/41.37 [v13: $i] : ($i(v10) & $i(v9) & ((v12 = v3 & ~ (v2 = v0) &
% 259.33/41.37 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) = v3 & hAPP(v8,
% 259.33/41.37 v9) = v11 & hAPP(v4, v9) = v13 & hAPP(v1, v2) = v8 & $i(v13) &
% 259.33/41.37 $i(v11) & $i(v8) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10,
% 259.33/41.37 v2) & ~ hBOOL(v13)) | (v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & ~
% 259.33/41.37 hBOOL(v7))))))
% 259.33/41.37
% 259.33/41.37 (fact_split__div_H)
% 259.33/41.38 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.38 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.33/41.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.33/41.38 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.33/41.38 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5)
% 259.33/41.38 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ? [v7: $i] :
% 259.33/41.38 ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 259.33/41.38 ? [v13: $i] : ($i(v9) & ((v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) &
% 259.33/41.38 hBOOL(v7)) | (c_Nat_OSuc(v9) = v11 & hAPP(v8, v11) = v12 & hAPP(v8,
% 259.33/41.38 v9) = v10 & hAPP(v4, v9) = v13 & hAPP(v1, v2) = v8 & $i(v13) &
% 259.33/41.38 $i(v12) & $i(v11) & $i(v10) & $i(v8) & hBOOL(v13) &
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v12) &
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v10, v3))))) & !
% 259.33/41.38 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.33/41.38 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5)
% 259.33/41.38 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | hBOOL(v6) | ? [v7: $i] : ?
% 259.33/41.38 [v8: $i] : (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : !
% 259.33/41.38 [v11: $i] : ( ~ (c_Nat_OSuc(v9) = v10) | ~ (hAPP(v8, v10) = v11) | ~
% 259.33/41.38 $i(v9) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v11) | ?
% 259.33/41.38 [v12: $i] : ? [v13: $i] : ((hAPP(v8, v9) = v12 & $i(v12) & ~
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v12, v3)) |
% 259.33/41.38 (hAPP(v4, v9) = v13 & $i(v13) & ~ hBOOL(v13)))) & ( ~ (v2 = v0) |
% 259.33/41.38 (hAPP(v4, v0) = v7 & $i(v7) & ~ hBOOL(v7))))))
% 259.33/41.38
% 259.33/41.38 (fact_split__div__lemma)
% 259.33/41.38 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.38 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.33/41.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.33/41.38 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 259.33/41.38 : ! [v8: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v4) = v8) |
% 259.33/41.38 ~ (c_Nat_OSuc(v3) = v6) | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v1, v4) = v5)
% 259.33/41.38 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ? [v9: $i] : (( ~
% 259.33/41.38 (v8 = v3) | (hAPP(v5, v3) = v9 & $i(v9) &
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v7) &
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v2))) & (v8 = v3
% 259.33/41.38 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v7) | (hAPP(v5,
% 259.33/41.38 v3) = v9 & $i(v9) & ~
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v2))))))
% 259.33/41.38
% 259.33/41.38 (fact_unimodular__reduce__norm)
% 259.33/41.38 $i(c_Complex_Oii) & $i(tc_RealDef_Oreal) & $i(tc_Complex_Ocomplex) & ? [v0:
% 259.33/41.38 $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.33/41.38 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v1 & $i(v1) & $i(v0) & !
% 259.33/41.38 [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.38 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, v1) = v3) | ~
% 259.33/41.38 $i(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 259.33/41.38 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v4 = v0) &
% 259.33/41.38 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 &
% 259.33/41.38 $i(v4)) | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2,
% 259.33/41.38 c_Complex_Oii) = v10 &
% 259.33/41.38 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10) = v11 &
% 259.33/41.38 $i(v11) & $i(v10) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 259.33/41.38 v11, v0)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2,
% 259.33/41.38 v1) = v5 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5)
% 259.33/41.38 = v6 & $i(v6) & $i(v5) &
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v0)) |
% 259.33/41.38 (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, c_Complex_Oii) =
% 259.33/41.38 v8 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9 &
% 259.33/41.38 $i(v9) & $i(v8) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9,
% 259.33/41.38 v0)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) =
% 259.33/41.38 v7 & $i(v7) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 259.33/41.38 v0)))))
% 259.33/41.38
% 259.33/41.38 (fact_zero__le__double__add__iff__zero__le__single__add)
% 259.33/41.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oplus__class_Oplus(v1,
% 259.33/41.38 v0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 259.33/41.38 class_Groups_Olinordered__ab__group__add(v1) | ? [v3: $i] :
% 259.33/41.38 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(v1, v3, v2) |
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(v1, v3, v0)) & ( ~
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(v1, v3, v0) |
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(v1, v3, v2))))
% 259.33/41.38
% 259.33/41.38 (fact_zero__le__natceiling)
% 259.33/41.38 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.33/41.38 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatceiling(v1) =
% 259.33/41.38 v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 259.33/41.38 v2)))
% 259.33/41.38
% 259.33/41.38 (fact_zero__le__natfloor)
% 259.33/41.38 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.33/41.38 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2)
% 259.33/41.38 | ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2)))
% 259.33/41.38
% 259.33/41.38 (fact_zero__le__one)
% 259.33/41.38 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 259.33/41.38 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 259.33/41.38 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) &
% 259.33/41.38 c_Orderings_Oord__class_Oless__eq(v0, v2, v1)))
% 259.33/41.38
% 259.33/41.38 (fact_zero__less__Suc)
% 259.33/41.38 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.33/41.38 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1)
% 259.33/41.38 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)))
% 259.33/41.38
% 259.33/41.38 (fact_zero__less__abs__iff)
% 259.33/41.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1,
% 259.33/41.38 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 259.33/41.38 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] :
% 259.33/41.38 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v0) | ~
% 259.33/41.38 c_Orderings_Oord__class_Oless(v1, v0, v2)) & (v3 = v0 |
% 259.33/41.38 c_Orderings_Oord__class_Oless(v1, v3, v2))))
% 259.33/41.38
% 259.33/41.38 (fact_zero__less__diff)
% 259.33/41.38 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 259.33/41.38 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.38 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 259.33/41.38 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : !
% 259.33/41.38 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 259.33/41.38 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 259.33/41.38
% 259.33/41.38 (fact_zero__less__norm__iff)
% 259.33/41.38 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 259.33/41.38 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 259.33/41.38 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 259.33/41.38 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.33/41.38 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ( ~ (v4 =
% 259.33/41.38 v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) &
% 259.33/41.38 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | (v4 = v1 &
% 259.33/41.38 c_Groups_Ozero__class_Ozero(v2) = v1)))))
% 259.33/41.38
% 259.33/41.38 (fact_zero__less__one)
% 259.33/41.38 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 259.33/41.38 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 259.33/41.38 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) &
% 259.33/41.38 c_Orderings_Oord__class_Oless(v0, v2, v1)))
% 259.33/41.38
% 259.33/41.38 (fact_zero__less__power__nat__eq)
% 259.33/41.38 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 259.33/41.38 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.33/41.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 259.33/41.38 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4,
% 259.33/41.38 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : !
% 259.33/41.38 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 259.33/41.38 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : !
% 259.33/41.38 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) |
% 259.33/41.38 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 259.33/41.38
% 259.33/41.38 (fact_zero__less__zpower__abs__iff)
% 259.33/41.38 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.33/41.38 (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 &
% 259.33/41.38 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 259.33/41.38 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 259.33/41.38 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 =
% 259.33/41.38 v0 | ~ (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v4) = v5) | ~ (hAPP(v6,
% 259.33/41.38 v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v7)) & ! [v3: $i] : !
% 259.33/41.38 [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~
% 259.33/41.38 (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v0) = v4) | ~ (hAPP(v5, v3) = v6)
% 259.33/41.38 | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ~
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v6)) & ! [v3: $i] : !
% 259.33/41.38 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.33/41.38 (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v3) = v4) | ~ (hAPP(v5, v2) = v6)
% 259.33/41.38 | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) |
% 259.33/41.38 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v6)))
% 259.33/41.38
% 259.33/41.38 (fact_zero__neq__one)
% 259.33/41.38 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 259.33/41.38 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) &
% 259.33/41.38 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2)))
% 259.33/41.38
% 259.33/41.38 (function-axioms)
% 259.33/41.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.33/41.38 $i] : ! [v6: $i] : (v1 = v0 | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3,
% 259.33/41.38 v2) = v1) | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, v2) = v0)) & !
% 259.33/41.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 259.33/41.38 : (v1 = v0 | ~ (c_If(v5, v4, v3, v2) = v1) | ~ (c_If(v5, v4, v3, v2) = v0))
% 259.33/41.38 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 =
% 259.33/41.38 v0 | ~ (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v1) | ~
% 259.33/41.38 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 259.33/41.38 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 259.33/41.38 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v1) | ~
% 259.33/41.38 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 259.33/41.38 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 259.33/41.38 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~
% 259.33/41.38 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 259.33/41.38 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 259.33/41.38 (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ (c_Power_Opower_Opower(v4, v3,
% 259.33/41.38 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 259.33/41.38 [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Opcompose(v4, v3, v2) = v1) | ~
% 259.33/41.38 (c_Polynomial_Opcompose(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 259.33/41.38 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Oorder(v4,
% 259.33/41.38 v3, v2) = v1) | ~ (c_Polynomial_Oorder(v4, v3, v2) = v0)) & ! [v0: $i]
% 259.33/41.38 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 259.33/41.38 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 259.33/41.38 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 259.33/41.38 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 259.33/41.38 (c_Polynomial_OpCons(v4, v3, v2) = v1) | ~ (c_Polynomial_OpCons(v4, v3, v2)
% 259.33/41.38 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 259.33/41.38 $i] : (v1 = v0 | ~ (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 259.33/41.38 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 259.33/41.38 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Complex_Orcis(v3, v2) = v1) |
% 259.33/41.38 ~ (c_Complex_Orcis(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 259.33/41.38 : ! [v3: $i] : (v1 = v0 | ~ (c_Nat__Transfer_Otsub(v3, v2) = v1) | ~
% 259.33/41.38 (c_Nat__Transfer_Otsub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 259.33/41.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (c_fequal(v3, v2) = v1) | ~ (c_fequal(v3,
% 259.33/41.38 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 259.33/41.38 = v0 | ~ (c_RealDef_Oreal(v3, v2) = v1) | ~ (c_RealDef_Oreal(v3, v2) =
% 259.33/41.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 259.33/41.38 ~ (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) = v0))
% 259.33/41.38 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 259.33/41.38 (c_Groups_Osgn__class_Osgn(v3, v2) = v1) | ~ (c_Groups_Osgn__class_Osgn(v3,
% 259.33/41.38 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 259.33/41.38 = v0 | ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v1) |
% 259.33/41.38 ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v0)) & !
% 259.33/41.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3,
% 259.33/41.38 v2) = v1) | ~ (tc_fun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 259.33/41.38 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Groups_Oabs__class_Oabs(v3, v2) =
% 259.33/41.38 v1) | ~ (c_Groups_Oabs__class_Oabs(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 259.33/41.38 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 259.33/41.38 (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 259.33/41.38 (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 259.33/41.38 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3,
% 259.33/41.38 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 259.33/41.38 (c_Complex_Ocis(v2) = v1) | ~ (c_Complex_Ocis(v2) = v0)) & ! [v0: $i] : !
% 259.33/41.38 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Nat_OSuc(v2) = v1) | ~
% 259.33/41.38 (c_Nat_OSuc(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 259.33/41.38 | ~ (c_Complex_Oexpi(v2) = v1) | ~ (c_Complex_Oexpi(v2) = v0)) & ! [v0:
% 259.33/41.38 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Transcendental_Oln(v2) =
% 259.33/41.38 v1) | ~ (c_Transcendental_Oln(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 259.33/41.38 [v2: $i] : (v1 = v0 | ~ (c_Power_Opower__class_Opower(v2) = v1) | ~
% 259.33/41.38 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 259.33/41.38 [v2: $i] : (v1 = v0 | ~ (c_RComplete_Onatfloor(v2) = v1) | ~
% 259.33/41.38 (c_RComplete_Onatfloor(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 259.33/41.38 : (v1 = v0 | ~ (c_RComplete_Onatceiling(v2) = v1) | ~
% 259.33/41.38 (c_RComplete_Onatceiling(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 259.33/41.38 $i] : (v1 = v0 | ~ (c_Groups_Otimes__class_Otimes(v2) = v1) | ~
% 259.33/41.38 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 259.33/41.38 [v2: $i] : (v1 = v0 | ~ (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 259.33/41.38 (c_Groups_Oone__class_Oone(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 259.33/41.38 $i] : (v1 = v0 | ~ (tc_Polynomial_Opoly(v2) = v1) | ~
% 259.33/41.38 (tc_Polynomial_Opoly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 259.33/41.38 (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 259.33/41.38 (c_Groups_Ozero__class_Ozero(v2) = v0))
% 259.33/41.38
% 259.33/41.38 Further assumptions not needed in the proof:
% 259.33/41.38 --------------------------------------------
% 259.33/41.39 arity_Complex__Ocomplex__Fields_Ofield,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Oab__group__add,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Oab__semigroup__add,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Ogroup__add,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Omonoid__add,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Omonoid__mult,
% 259.33/41.39 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ozero,
% 259.33/41.39 arity_Complex__Ocomplex__Int_Oring__char__0,
% 259.33/41.39 arity_Complex__Ocomplex__Power_Opower,
% 259.33/41.39 arity_Complex__Ocomplex__RealVector_Oreal__field,
% 259.33/41.39 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
% 259.33/41.39 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
% 259.33/41.39 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Ocomm__ring,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Ocomm__ring__1,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Ocomm__semiring,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Oidom,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Omult__zero,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Ono__zero__divisors,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Osemiring,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Osemiring__0,
% 259.33/41.39 arity_Complex__Ocomplex__Rings_Ozero__neq__one,
% 259.33/41.39 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 259.33/41.39 arity_HOL__Obool__Orderings_Oord, arity_HOL__Obool__Orderings_Oorder,
% 259.33/41.39 arity_HOL__Obool__Orderings_Opreorder, arity_Int__Oint__Divides_Oring__div,
% 259.33/41.39 arity_Int__Oint__Divides_Osemiring__div,
% 259.33/41.39 arity_Int__Oint__Groups_Oab__group__add,
% 259.33/41.39 arity_Int__Oint__Groups_Oab__semigroup__add,
% 259.33/41.39 arity_Int__Oint__Groups_Oab__semigroup__mult,
% 259.33/41.39 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,
% 259.33/41.39 arity_Int__Oint__Groups_Ocancel__comm__monoid__add,
% 259.33/41.39 arity_Int__Oint__Groups_Ocancel__semigroup__add,
% 259.33/41.39 arity_Int__Oint__Groups_Ocomm__monoid__add,
% 259.33/41.39 arity_Int__Oint__Groups_Ocomm__monoid__mult,
% 259.33/41.39 arity_Int__Oint__Groups_Ogroup__add,
% 259.33/41.39 arity_Int__Oint__Groups_Olinordered__ab__group__add,
% 259.33/41.39 arity_Int__Oint__Groups_Omonoid__add, arity_Int__Oint__Groups_Omonoid__mult,
% 259.33/41.39 arity_Int__Oint__Groups_Oone, arity_Int__Oint__Groups_Oordered__ab__group__add,
% 259.33/41.39 arity_Int__Oint__Groups_Oordered__ab__group__add__abs,
% 259.33/41.39 arity_Int__Oint__Groups_Oordered__ab__semigroup__add,
% 259.33/41.39 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,
% 259.33/41.39 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,
% 259.33/41.39 arity_Int__Oint__Groups_Oordered__comm__monoid__add,
% 259.33/41.39 arity_Int__Oint__Groups_Osgn__if, arity_Int__Oint__Groups_Ozero,
% 259.33/41.39 arity_Int__Oint__Int_Oring__char__0, arity_Int__Oint__Orderings_Olinorder,
% 259.33/41.39 arity_Int__Oint__Orderings_Oord, arity_Int__Oint__Orderings_Oorder,
% 259.33/41.39 arity_Int__Oint__Orderings_Opreorder, arity_Int__Oint__Power_Opower,
% 259.33/41.39 arity_Int__Oint__Rings_Ocomm__ring, arity_Int__Oint__Rings_Ocomm__ring__1,
% 259.33/41.39 arity_Int__Oint__Rings_Ocomm__semiring,
% 259.33/41.39 arity_Int__Oint__Rings_Ocomm__semiring__0,
% 259.33/41.39 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Oidom,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__idom,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__ring,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__ring__strict,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__semidom,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__semiring,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__semiring__1,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__semiring__1__strict,
% 259.33/41.39 arity_Int__Oint__Rings_Olinordered__semiring__strict,
% 259.33/41.39 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors,
% 259.33/41.39 arity_Int__Oint__Rings_Oordered__cancel__semiring,
% 259.33/41.39 arity_Int__Oint__Rings_Oordered__comm__semiring,
% 259.33/41.39 arity_Int__Oint__Rings_Oordered__ring,
% 259.33/41.39 arity_Int__Oint__Rings_Oordered__ring__abs,
% 259.33/41.39 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring,
% 259.33/41.39 arity_Int__Oint__Rings_Oring__1,
% 259.33/41.39 arity_Int__Oint__Rings_Oring__1__no__zero__divisors,
% 259.33/41.39 arity_Int__Oint__Rings_Oring__no__zero__divisors,
% 259.33/41.39 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0,
% 259.33/41.39 arity_Int__Oint__Rings_Ozero__neq__one,
% 259.33/41.39 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 259.33/41.39 arity_Nat__Onat__Divides_Osemiring__div,
% 259.33/41.39 arity_Nat__Onat__Groups_Oab__semigroup__add,
% 259.33/41.39 arity_Nat__Onat__Groups_Oab__semigroup__mult,
% 259.33/41.39 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,
% 259.33/41.39 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,
% 259.33/41.39 arity_Nat__Onat__Groups_Ocancel__semigroup__add,
% 259.33/41.39 arity_Nat__Onat__Groups_Ocomm__monoid__add,
% 259.33/41.39 arity_Nat__Onat__Groups_Ocomm__monoid__mult,
% 259.33/41.39 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult,
% 259.33/41.39 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,
% 259.33/41.39 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,
% 259.33/41.39 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,
% 259.33/41.39 arity_Nat__Onat__Groups_Oordered__comm__monoid__add,
% 259.33/41.39 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Orderings_Olinorder,
% 259.33/41.39 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder,
% 259.33/41.39 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Rings_Ocomm__semiring,
% 259.33/41.39 arity_Nat__Onat__Rings_Ocomm__semiring__0,
% 259.33/41.39 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,
% 259.33/41.39 arity_Nat__Onat__Rings_Olinordered__semiring,
% 259.33/41.39 arity_Nat__Onat__Rings_Olinordered__semiring__strict,
% 259.33/41.39 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors,
% 259.33/41.39 arity_Nat__Onat__Rings_Oordered__cancel__semiring,
% 259.33/41.39 arity_Nat__Onat__Rings_Oordered__comm__semiring,
% 259.33/41.39 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring,
% 259.33/41.39 arity_Nat__Onat__Rings_Osemiring__0,
% 259.33/41.39 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 259.33/41.39 arity_Polynomial__Opoly__Divides_Oring__div,
% 259.33/41.39 arity_Polynomial__Opoly__Divides_Osemiring__div,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oab__group__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oab__semigroup__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Ogroup__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Omonoid__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Omonoid__mult,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oone,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,
% 259.33/41.39 arity_Polynomial__Opoly__Groups_Osgn__if, arity_Polynomial__Opoly__Groups_Ozero,
% 259.33/41.39 arity_Polynomial__Opoly__Int_Oring__char__0,
% 259.33/41.39 arity_Polynomial__Opoly__Orderings_Olinorder,
% 259.33/41.39 arity_Polynomial__Opoly__Orderings_Oord,
% 259.33/41.39 arity_Polynomial__Opoly__Orderings_Oorder,
% 259.33/41.39 arity_Polynomial__Opoly__Orderings_Opreorder,
% 259.33/41.39 arity_Polynomial__Opoly__Power_Opower,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Ocomm__ring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Ocomm__ring__1,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Ocomm__semiring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oidom,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__idom,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__ring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__semidom,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__semiring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Omult__zero,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Ono__zero__divisors,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oordered__ring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oordered__ring__abs,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oordered__semiring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Osemiring,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Osemiring__0,
% 259.33/41.39 arity_Polynomial__Opoly__Rings_Ozero__neq__one,
% 259.33/41.39 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 259.33/41.39 arity_RealDef__Oreal__Fields_Ofield,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Oab__group__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Oab__semigroup__mult,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Ocomm__monoid__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Ogroup__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Omonoid__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Omonoid__mult, arity_RealDef__Oreal__Groups_Oone,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Oordered__ab__group__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,
% 259.33/41.39 arity_RealDef__Oreal__Groups_Osgn__if, arity_RealDef__Oreal__Groups_Ozero,
% 259.33/41.39 arity_RealDef__Oreal__Int_Oring__char__0,
% 259.33/41.39 arity_RealDef__Oreal__Orderings_Olinorder, arity_RealDef__Oreal__Orderings_Oord,
% 259.33/41.39 arity_RealDef__Oreal__Orderings_Oorder,
% 259.33/41.39 arity_RealDef__Oreal__Orderings_Opreorder, arity_RealDef__Oreal__Power_Opower,
% 259.33/41.39 arity_RealDef__Oreal__RealVector_Oreal__field,
% 259.33/41.39 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
% 259.33/41.39 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
% 259.33/41.39 arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Ocomm__ring,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Ocomm__ring__1,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Ocomm__semiring,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Ocomm__semiring__0,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oidom,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Olinordered__idom,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Olinordered__ring,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Olinordered__ring__strict,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Olinordered__semiring,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Olinordered__semiring__1,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Omult__zero,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Ono__zero__divisors,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oordered__comm__semiring,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oordered__ring,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oordered__ring__abs,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oordered__semiring,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oring, arity_RealDef__Oreal__Rings_Oring__1,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Osemiring, arity_RealDef__Oreal__Rings_Osemiring__0,
% 259.33/41.39 arity_RealDef__Oreal__Rings_Ozero__neq__one, arity_fun__Orderings_Oord,
% 259.33/41.39 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, fact_BseqI2_H,
% 259.33/41.39 fact_Bseq__iff, fact_Bseq__iff1a, fact_DERIV__mult__lemma,
% 259.33/41.39 fact_DIVISION__BY__ZERO, fact_DeMoivre2, fact_Deriv_Oadd__diff__add,
% 259.33/41.39 fact_Divides_Omod__div__equality_H,
% 259.33/41.39 fact_Divides_Otransfer__nat__int__function__closures_I1_J,
% 259.33/41.39 fact_Divides_Otransfer__nat__int__function__closures_I2_J, fact_H,
% 259.33/41.39 fact_Nat_Odiff__diff__eq,
% 259.33/41.39 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,
% 259.33/41.39 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,
% 259.33/41.39 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,
% 259.33/41.39 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,
% 259.33/41.39 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,
% 259.33/41.39 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,
% 259.33/41.39 fact_Suc__diff__diff, fact_Suc__diff__le, fact_Suc__inject, fact_Suc__leD,
% 259.33/41.39 fact_Suc__leI, fact_Suc__le__eq, fact_Suc__le__lessD, fact_Suc__le__mono,
% 259.33/41.39 fact_Suc__lessD, fact_Suc__lessI, fact_Suc__less__SucD, fact_Suc__less__eq,
% 259.33/41.39 fact_Suc__mono, fact_Suc__mult__cancel1, fact_Suc__mult__le__cancel1,
% 259.33/41.39 fact_Suc__mult__less__cancel1, fact_Suc__n__not__le__n, fact_Suc__n__not__n,
% 259.33/41.39 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_abs__add__abs,
% 259.33/41.39 fact_abs__diff__less__iff, fact_abs__diff__triangle__ineq, fact_abs__eq__mult,
% 259.33/41.39 fact_abs__idempotent, fact_abs__le__D1, fact_abs__minus__commute,
% 259.33/41.39 fact_abs__mult, fact_abs__mult__less, fact_abs__mult__pos, fact_abs__mult__self,
% 259.33/41.39 fact_abs__of__nonneg, fact_abs__of__pos, fact_abs__one, fact_abs__sgn,
% 259.33/41.39 fact_abs__triangle__ineq, fact_abs__triangle__ineq2,
% 259.33/41.39 fact_abs__triangle__ineq2__sym, fact_abs__triangle__ineq3,
% 259.33/41.39 fact_abs__triangle__ineq4, fact_abs__zero, fact_abs__zmult__eq__1,
% 259.33/41.39 fact_add1__zle__eq, fact_add_Ocomm__neutral, fact_add__0, fact_add__0__left,
% 259.33/41.39 fact_add__0__right, fact_add__Suc, fact_add__Suc__right, fact_add__Suc__shift,
% 259.33/41.39 fact_add__diff__assoc, fact_add__diff__assoc2, fact_add__diff__cancel,
% 259.33/41.39 fact_add__diff__inverse, fact_add__imp__eq, fact_add__increasing,
% 259.33/41.39 fact_add__leD1, fact_add__leD2, fact_add__leE, fact_add__le__cancel__left,
% 259.33/41.39 fact_add__le__cancel__right, fact_add__le__imp__le__left,
% 259.33/41.39 fact_add__le__imp__le__right, fact_add__le__less__mono, fact_add__le__mono,
% 259.33/41.39 fact_add__le__mono1, fact_add__left__cancel, fact_add__left__imp__eq,
% 259.33/41.39 fact_add__left__mono, fact_add__lessD1, fact_add__less__cancel__left,
% 259.33/41.39 fact_add__less__cancel__right, fact_add__less__imp__less__left,
% 259.33/41.39 fact_add__less__imp__less__right, fact_add__less__le__mono,
% 259.33/41.39 fact_add__less__mono, fact_add__less__mono1, fact_add__mono,
% 259.33/41.39 fact_add__mult__distrib, fact_add__mult__distrib2, fact_add__pCons,
% 259.33/41.39 fact_add__poly__code_I1_J, fact_add__poly__code_I2_J, fact_add__right__cancel,
% 259.33/41.39 fact_add__right__imp__eq, fact_add__right__mono, fact_add__scale__eq__noteq,
% 259.33/41.39 fact_add__strict__increasing2, fact_add__strict__left__mono,
% 259.33/41.39 fact_add__strict__mono, fact_add__strict__right__mono, fact_assms,
% 259.33/41.39 fact_cis__real__of__nat__Suc__mult, fact_combine__common__factor,
% 259.33/41.39 fact_comm__mult__left__mono, fact_comm__mult__strict__left__mono,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,
% 259.33/41.39 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,
% 259.33/41.39 fact_comm__semiring__class_Odistrib, fact_complex__i__not__one,
% 259.33/41.39 fact_complex__i__not__zero, fact_complex__mod__rcis,
% 259.33/41.39 fact_complex__mod__triangle__ineq2, fact_complex__mod__triangle__sub,
% 259.33/41.39 fact_convex__bound__le, fact_convex__bound__lt, fact_crossproduct__eq,
% 259.33/41.39 fact_crossproduct__noteq, fact_decr__lemma, fact_decr__mult__lemma,
% 259.33/41.39 fact_decseq__def, fact_diff__0__right, fact_diff__Suc__Suc,
% 259.33/41.39 fact_diff__Suc__diff__eq1, fact_diff__Suc__diff__eq2, fact_diff__add__assoc,
% 259.33/41.39 fact_diff__add__assoc2, fact_diff__add__cancel, fact_diff__add__inverse,
% 259.33/41.39 fact_diff__add__inverse2, fact_diff__cancel, fact_diff__cancel2,
% 259.33/41.39 fact_diff__commute, fact_diff__diff__cancel, fact_diff__diff__left,
% 259.33/41.39 fact_diff__diff__right, fact_diff__eq__diff__eq, fact_diff__eq__diff__less,
% 259.33/41.39 fact_diff__eq__diff__less__eq, fact_diff__le__mono, fact_diff__le__mono2,
% 259.33/41.39 fact_diff__le__self, fact_diff__less__Suc, fact_diff__less__mono,
% 259.33/41.39 fact_diff__less__mono2, fact_diff__mult__distrib, fact_diff__mult__distrib2,
% 259.33/41.39 fact_diff__pCons, fact_diff__poly__code_I2_J, fact_diff__self, fact_div__0,
% 259.33/41.39 fact_div__add1__eq, fact_div__add__self1, fact_div__add__self2, fact_div__by__0,
% 259.33/41.39 fact_div__by__1, fact_div__le__dividend, fact_div__le__mono,
% 259.33/41.39 fact_div__mod__equality, fact_div__mod__equality2, fact_div__mod__equality_H,
% 259.33/41.39 fact_div__mult1__eq, fact_div__mult2__eq, fact_div__mult__mult1,
% 259.33/41.39 fact_div__mult__mult1__if, fact_div__mult__mult2, fact_div__mult__self1,
% 259.33/41.39 fact_div__mult__self1__is__id, fact_div__mult__self2,
% 259.33/41.39 fact_div__mult__self2__is__id, fact_div__neg__neg__trivial,
% 259.33/41.39 fact_div__neg__pos__less0, fact_div__nonneg__neg__le0,
% 259.33/41.39 fact_div__nonpos__pos__le0, fact_div__pos__pos__trivial, fact_div__self,
% 259.33/41.39 fact_divisors__zero, fact_divmod__int__rel__div__eq,
% 259.33/41.39 fact_divmod__int__rel__mod__eq,
% 259.33/41.39 fact_double__add__le__zero__iff__single__add__le__zero, fact_eq__add__iff1,
% 259.33/41.39 fact_eq__add__iff2, fact_eq__diff__iff, fact_eq__iff__diff__eq__0,
% 259.33/41.39 fact_eq__imp__le, fact_even__less__0__iff, fact_expi__add, fact_expi__zero,
% 259.33/41.39 fact_ext, fact_field__power__not__zero, fact_incr__lemma,
% 259.33/41.39 fact_incr__mult__lemma, fact_incseq__def, fact_int__0__less__1,
% 259.33/41.39 fact_int__0__neq__1, fact_int__div__less__self,
% 259.33/41.39 fact_int__one__le__iff__zero__less, fact_leD, fact_leI, fact_le__SucE,
% 259.33/41.39 fact_le__SucI, fact_le__Suc__eq, fact_le__Suc__ex__iff, fact_le__add1,
% 259.33/41.39 fact_le__add2, fact_le__add__diff, fact_le__add__diff__inverse,
% 259.33/41.39 fact_le__add__diff__inverse2, fact_le__add__iff1, fact_le__add__iff2,
% 259.33/41.39 fact_le__antisym, fact_le__cube, fact_le__diff__conv, fact_le__diff__conv2,
% 259.33/41.39 fact_le__diff__iff, fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE,
% 259.33/41.39 fact_le__fun__def, fact_le__iff__add, fact_le__iff__diff__le__0,
% 259.33/41.39 fact_le__imp__0__less, fact_le__imp__diff__is__add, fact_le__imp__less__Suc,
% 259.33/41.39 fact_le__less__Suc__eq, fact_le__mod__geq, fact_le__natfloor,
% 259.33/41.39 fact_le__neq__implies__less, fact_le__refl, fact_le__square, fact_le__trans,
% 259.33/41.39 fact_left__add__mult__distrib, fact_lemma__realpow__diff, fact_lessI,
% 259.33/41.39 fact_less__1__mult, fact_less__SucE, fact_less__SucI, fact_less__Suc__eq__le,
% 259.33/41.39 fact_less__add__Suc1, fact_less__add__Suc2, fact_less__add__eq__less,
% 259.33/41.39 fact_less__add__iff1, fact_less__add__iff2, fact_less__antisym,
% 259.33/41.39 fact_less__bin__lemma, fact_less__diff__conv, fact_less__diff__iff,
% 259.33/41.39 fact_less__eq__Suc__le, fact_less__eq__poly__def, fact_less__eq__real__def,
% 259.33/41.39 fact_less__fun__def, fact_less__iff__Suc__add, fact_less__iff__diff__less__0,
% 259.33/41.39 fact_less__imp__diff__less, fact_less__imp__le__nat, fact_less__imp__neq,
% 259.33/41.39 fact_less__irrefl__nat, fact_less__le__not__le, fact_less__not__refl,
% 259.33/41.39 fact_less__not__refl2, fact_less__not__refl3, fact_less__or__eq__imp__le,
% 259.33/41.39 fact_less__poly__def, fact_less__trans__Suc, fact_linorder__antisym__conv1,
% 259.33/41.39 fact_linorder__antisym__conv2, fact_linorder__antisym__conv3,
% 259.33/41.39 fact_linorder__cases, fact_linorder__le__cases, fact_linorder__le__less__linear,
% 259.33/41.39 fact_linorder__less__linear, fact_linorder__linear, fact_linorder__neqE,
% 259.33/41.39 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat,
% 259.33/41.39 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less,
% 259.33/41.39 fact_mod__0, fact_mod__Suc__eq__Suc__mod, fact_mod__add__cong,
% 259.33/41.39 fact_mod__add__eq, fact_mod__add__left__eq, fact_mod__add__right__eq,
% 259.33/41.39 fact_mod__add__self1, fact_mod__add__self2, fact_mod__by__0, fact_mod__by__1,
% 259.33/41.39 fact_mod__diff__cong, fact_mod__diff__eq, fact_mod__diff__left__eq,
% 259.33/41.39 fact_mod__diff__right__eq, fact_mod__div__equality, fact_mod__div__equality2,
% 259.33/41.39 fact_mod__div__trivial, fact_mod__geq, fact_mod__if, fact_mod__less,
% 259.33/41.39 fact_mod__less__eq__dividend, fact_mod__mod__trivial, fact_mod__mult2__eq,
% 259.33/41.39 fact_mod__mult__cong, fact_mod__mult__distrib, fact_mod__mult__distrib2,
% 259.33/41.39 fact_mod__mult__eq, fact_mod__mult__left__eq, fact_mod__mult__mult1,
% 259.33/41.39 fact_mod__mult__mult2, fact_mod__mult__right__eq, fact_mod__mult__self1,
% 259.33/41.39 fact_mod__mult__self1__is__0, fact_mod__mult__self2,
% 259.33/41.39 fact_mod__mult__self2__is__0, fact_mod__mult__self3, fact_mod__mult__self4,
% 259.33/41.39 fact_mod__neg__neg__trivial, fact_mod__pos__neg__trivial,
% 259.33/41.39 fact_mod__pos__pos__trivial, fact_mod__self, fact_mult_Oadd__left,
% 259.33/41.39 fact_mult_Oadd__right, fact_mult_Obounded, fact_mult_Ocomm__neutral,
% 259.33/41.39 fact_mult_Odiff__left, fact_mult_Odiff__right, fact_mult_Oprod__diff__prod,
% 259.33/41.39 fact_mult_Ozero__left, fact_mult_Ozero__right, fact_mult__1, fact_mult__1__left,
% 259.33/41.39 fact_mult__1__right, fact_mult__Suc, fact_mult__Suc__right,
% 259.33/41.39 fact_mult__diff__mult, fact_mult__div__cancel, fact_mult__eq__0__iff,
% 259.33/41.39 fact_mult__le__0__iff, fact_mult__le__cancel__left__neg,
% 259.33/41.39 fact_mult__le__cancel__left__pos, fact_mult__le__less__imp__less,
% 259.33/41.39 fact_mult__le__mono, fact_mult__le__mono1, fact_mult__le__mono2,
% 259.33/41.39 fact_mult__left_Oadd, fact_mult__left_Odiff, fact_mult__left_Ozero,
% 259.33/41.39 fact_mult__left__le__imp__le, fact_mult__left__le__one__le,
% 259.33/41.39 fact_mult__left__less__imp__less, fact_mult__left__mono,
% 259.33/41.39 fact_mult__left__mono__neg, fact_mult__less__cancel__left__disj,
% 259.33/41.39 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos,
% 259.33/41.39 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left,
% 259.33/41.39 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less,
% 259.33/41.39 fact_mult__mono, fact_mult__mono_H, fact_mult__neg__neg, fact_mult__neg__pos,
% 259.33/41.39 fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos,
% 259.33/41.39 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg,
% 259.33/41.39 fact_mult__nonpos__nonpos, fact_mult__poly__0__left, fact_mult__poly__0__right,
% 259.33/41.39 fact_mult__poly__add__left, fact_mult__pos__neg, fact_mult__pos__neg2,
% 259.33/41.39 fact_mult__pos__pos, fact_mult__right_Oadd, fact_mult__right_Odiff,
% 259.33/41.39 fact_mult__right_Ozero, fact_mult__right__le__imp__le,
% 259.33/41.39 fact_mult__right__le__one__le, fact_mult__right__less__imp__less,
% 259.33/41.39 fact_mult__right__mono, fact_mult__right__mono__neg, fact_mult__sgn__abs,
% 259.33/41.39 fact_mult__strict__left__mono, fact_mult__strict__left__mono__neg,
% 259.33/41.39 fact_mult__strict__mono, fact_mult__strict__mono_H,
% 259.33/41.39 fact_mult__strict__right__mono, fact_mult__strict__right__mono__neg,
% 259.33/41.39 fact_mult__zero__left, fact_mult__zero__right, fact_n__not__Suc__n,
% 259.33/41.39 fact_nat_Oinject, fact_nat__add__assoc, fact_nat__add__commute,
% 259.33/41.39 fact_nat__add__left__cancel, fact_nat__add__left__cancel__le,
% 259.33/41.39 fact_nat__add__left__cancel__less, fact_nat__add__left__commute,
% 259.33/41.39 fact_nat__add__right__cancel, fact_nat__diff__add__eq1,
% 259.33/41.39 fact_nat__diff__add__eq2, fact_nat__eq__add__iff1, fact_nat__eq__add__iff2,
% 259.33/41.39 fact_nat__le__add__iff1, fact_nat__le__add__iff2, fact_nat__le__linear,
% 259.33/41.39 fact_nat__less__add__iff1, fact_nat__less__add__iff2, fact_nat__less__cases,
% 259.33/41.39 fact_nat__less__le, fact_nat__mult__assoc, fact_nat__mult__commute,
% 259.33/41.39 fact_nat__neq__iff, fact_natceiling__le, fact_natceiling__mono,
% 259.33/41.39 fact_natceiling__real__of__nat, fact_natceiling__subtract, fact_natfloor__mono,
% 259.33/41.39 fact_natfloor__real__of__nat, fact_natfloor__subtract,
% 259.33/41.39 fact_neg__imp__zdiv__neg__iff, fact_neg__imp__zdiv__nonneg__iff,
% 259.33/41.39 fact_neg__mod__bound, fact_neg__mod__conj, fact_neg__mod__sign,
% 259.33/41.39 fact_no__zero__divisors, fact_nonneg1__imp__zdiv__pos__iff,
% 259.33/41.39 fact_norm__add__less, fact_norm__diff__ineq, fact_norm__diff__triangle__ineq,
% 259.33/41.39 fact_norm__minus__commute, fact_norm__mult, fact_norm__mult__ineq,
% 259.33/41.39 fact_norm__mult__less, fact_norm__power, fact_norm__power__ineq,
% 259.33/41.39 fact_norm__triangle__ineq, fact_norm__triangle__ineq2,
% 259.33/41.39 fact_norm__triangle__ineq3, fact_norm__triangle__ineq4, fact_not__add__less1,
% 259.33/41.39 fact_not__add__less2, fact_not__leE, fact_not__less__eq, fact_not__less__eq__eq,
% 259.33/41.39 fact_not__less__iff__gr__or__eq, fact_not__less__less__Suc__eq,
% 259.33/41.39 fact_not__pos__poly__0, fact_not__square__less__zero,
% 259.33/41.39 fact_not__sum__squares__lt__zero, fact_odd__less__0, fact_odd__nonzero,
% 259.33/41.39 fact_one__le__power, fact_one__poly__def, fact_one__reorient,
% 259.33/41.39 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans,
% 259.33/41.39 fact_ord__less__eq__trans, fact_order__antisym, fact_order__antisym__conv,
% 259.33/41.39 fact_order__eq__iff, fact_order__eq__refl, fact_order__le__imp__less__or__eq,
% 259.33/41.39 fact_order__le__less, fact_order__le__less__trans, fact_order__le__neq__trans,
% 259.33/41.39 fact_order__less__asym, fact_order__less__asym_H, fact_order__less__imp__le,
% 259.33/41.39 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2,
% 259.33/41.39 fact_order__less__imp__not__less, fact_order__less__irrefl,
% 259.33/41.39 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym,
% 259.33/41.39 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl,
% 259.33/41.39 fact_order__trans, fact_pCons_Ohyps, fact_pCons_Oprems, fact_pCons__0__0,
% 259.33/41.39 fact_pCons__eq__0__iff, fact_pCons__eq__iff, fact_pcompose__0,
% 259.33/41.39 fact_pcompose__pCons, fact_poly__0, fact_poly__1, fact_poly__add,
% 259.33/41.39 fact_poly__diff, fact_poly__div__mult__right, fact_poly__eq__iff,
% 259.33/41.39 fact_poly__mod__mult__right, fact_poly__mult, fact_poly__pCons,
% 259.33/41.39 fact_poly__pcompose, fact_poly__power, fact_poly__rec_Osimps, fact_poly__rec__0,
% 259.33/41.39 fact_poly__rec__pCons, fact_poly__zero, fact_pos__add__strict,
% 259.33/41.39 fact_pos__imp__zdiv__neg__iff, fact_pos__imp__zdiv__nonneg__iff,
% 259.33/41.39 fact_pos__imp__zdiv__pos__iff, fact_pos__mod__bound, fact_pos__mod__conj,
% 259.33/41.39 fact_pos__mod__sign, fact_pos__poly__add, fact_pos__poly__mult,
% 259.33/41.39 fact_pos__poly__pCons, fact_pos__zmult__eq__1__iff,
% 259.33/41.39 fact_power_Opower_Opower__Suc, fact_power__0__Suc, fact_power__Suc,
% 259.33/41.39 fact_power__Suc2, fact_power__Suc__less, fact_power__Suc__less__one,
% 259.33/41.39 fact_power__abs, fact_power__add, fact_power__commutes, fact_power__decreasing,
% 259.33/41.39 fact_power__gt1, fact_power__gt1__lemma, fact_power__increasing,
% 259.33/41.39 fact_power__increasing__iff, fact_power__inject__base, fact_power__inject__exp,
% 259.33/41.39 fact_power__le__imp__le__base, fact_power__le__imp__le__exp,
% 259.33/41.39 fact_power__less__imp__less__base, fact_power__less__imp__less__exp,
% 259.33/41.39 fact_power__less__power__Suc, fact_power__mono, fact_power__mult,
% 259.33/41.39 fact_power__mult__distrib, fact_power__one, fact_power__power__power,
% 259.33/41.39 fact_power__strict__decreasing, fact_power__strict__increasing,
% 259.33/41.39 fact_power__strict__increasing__iff, fact_q__neg__lemma, fact_q__pos__lemma,
% 259.33/41.39 fact_rcis__mult, fact_real__add__left__mono, fact_real__add__mult__distrib,
% 259.33/41.39 fact_real__le__antisym, fact_real__le__linear, fact_real__le__refl,
% 259.33/41.39 fact_real__mult__assoc, fact_real__mult__commute, fact_real__of__nat__add,
% 259.33/41.39 fact_real__of__nat__diff, fact_real__of__nat__div4, fact_real__of__nat__inject,
% 259.33/41.39 fact_real__of__nat__le__iff, fact_real__of__nat__less__iff,
% 259.33/41.39 fact_real__of__nat__mult, fact_real__squared__diff__one__factored,
% 259.33/41.39 fact_realpow__Suc__le__self, fact_right__minus__eq, fact_self__quotient__aux1,
% 259.33/41.39 fact_self__quotient__aux2, fact_semiring__div__class_Omod__div__equality_H,
% 259.33/41.39 fact_sgn0, fact_sgn__0__0, fact_sgn__1__pos, fact_sgn__greater, fact_sgn__less,
% 259.33/41.39 fact_sgn__mult, fact_sgn__one, fact_sgn__pos, fact_sgn__sgn, fact_sgn__times,
% 259.33/41.39 fact_sgn__zero, fact_sgn__zero__iff, fact_split__mult__neg__le,
% 259.33/41.39 fact_split__mult__pos__le, fact_split__neg__lemma, fact_split__pos__lemma,
% 259.33/41.39 fact_split__zdiv, fact_split__zmod, fact_sum__squares__eq__zero__iff,
% 259.33/41.39 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff,
% 259.33/41.39 fact_sum__squares__le__zero__iff, fact_termination__basic__simps_I1_J,
% 259.33/41.39 fact_termination__basic__simps_I2_J, fact_termination__basic__simps_I3_J,
% 259.33/41.39 fact_termination__basic__simps_I4_J, fact_termination__basic__simps_I5_J,
% 259.33/41.39 fact_trans__le__add1, fact_trans__le__add2, fact_trans__less__add1,
% 259.33/41.39 fact_trans__less__add2, fact_tsub__def, fact_tsub__eq,
% 259.33/41.39 fact_unique__quotient__lemma, fact_unique__quotient__lemma__neg, fact_xt1_I10_J,
% 259.33/41.39 fact_xt1_I11_J, fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J,
% 259.33/41.39 fact_xt1_I4_J, fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J,
% 259.33/41.39 fact_xt1_I9_J, fact_zabs__less__one__iff, fact_zadd__0, fact_zadd__0__right,
% 259.33/41.39 fact_zadd__assoc, fact_zadd__commute, fact_zadd__left__commute,
% 259.33/41.39 fact_zadd__left__mono, fact_zadd__strict__right__mono, fact_zadd__zless__mono,
% 259.33/41.39 fact_zadd__zmult__distrib, fact_zadd__zmult__distrib2, fact_zdiff__zmod__left,
% 259.33/41.39 fact_zdiff__zmod__right, fact_zdiff__zmult__distrib,
% 259.33/41.39 fact_zdiff__zmult__distrib2, fact_zdiv__eq__0__iff, fact_zdiv__mono1,
% 259.33/41.39 fact_zdiv__mono1__neg, fact_zdiv__mono2, fact_zdiv__mono2__lemma,
% 259.33/41.39 fact_zdiv__mono2__neg, fact_zdiv__mono2__neg__lemma, fact_zdiv__self,
% 259.33/41.39 fact_zdiv__zadd1__eq, fact_zdiv__zero, fact_zdiv__zmod__equality,
% 259.33/41.39 fact_zdiv__zmod__equality2, fact_zdiv__zmult1__eq, fact_zdiv__zmult2__eq,
% 259.33/41.39 fact_zero__le__mult__iff, fact_zero__le__power, fact_zero__le__power__abs,
% 259.33/41.39 fact_zero__le__square, fact_zero__le__zpower__abs,
% 259.33/41.39 fact_zero__less__double__add__iff__zero__less__single__add,
% 259.33/41.39 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, fact_zero__less__power,
% 259.33/41.39 fact_zero__less__two, fact_zero__reorient, fact_zle__add1__eq__le,
% 259.33/41.39 fact_zle__antisym, fact_zle__diff1__eq, fact_zle__linear, fact_zle__refl,
% 259.33/41.39 fact_zle__trans, fact_zless__add1__eq, fact_zless__imp__add1__zle,
% 259.33/41.39 fact_zless__le, fact_zless__linear, fact_zmod__eq__0__iff,
% 259.33/41.39 fact_zmod__le__nonneg__dividend, fact_zmod__self, fact_zmod__simps_I1_J,
% 259.33/41.39 fact_zmod__simps_I2_J, fact_zmod__simps_I3_J, fact_zmod__simps_I4_J,
% 259.33/41.39 fact_zmod__zdiv__equality, fact_zmod__zdiv__equality_H,
% 259.33/41.39 fact_zmod__zdiv__trivial, fact_zmod__zero, fact_zmod__zmult1__eq,
% 259.33/41.39 fact_zmod__zmult2__eq, fact_zmult2__lemma__aux1, fact_zmult2__lemma__aux2,
% 259.33/41.39 fact_zmult2__lemma__aux3, fact_zmult2__lemma__aux4, fact_zmult__1,
% 259.33/41.39 fact_zmult__1__right, fact_zmult__assoc, fact_zmult__commute,
% 259.33/41.39 fact_zmult__div__cancel, fact_zmult__zless__mono2, fact_zpower__zadd__distrib,
% 259.33/41.39 fact_zpower__zmod, fact_zpower__zpower, help_c__fequal__1, help_c__fequal__2
% 259.33/41.39
% 259.33/41.39 Those formulas are unsatisfiable:
% 259.33/41.39 ---------------------------------
% 259.33/41.39
% 259.33/41.39 Begin of proof
% 259.33/41.39 |
% 259.33/41.39 | ALPHA: (fact_h) implies:
% 259.33/41.40 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 259.33/41.40 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.33/41.40 | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_r____) = v1 &
% 259.33/41.40 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v1) = v2 &
% 259.33/41.40 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____) = v3 &
% 259.33/41.40 | $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__le__trans) implies:
% 259.33/41.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 259.33/41.40 | $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 259.33/41.40 | v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 259.33/41.40 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_norm__one) implies:
% 259.33/41.40 | (3) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.33/41.40 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 259.33/41.40 | (c_Groups_Oone__class_Oone(v1) = v2) | ~
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~
% 259.33/41.40 | class_RealVector_Oreal__normed__algebra__1(v1)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_norm__le__zero__iff) implies:
% 259.33/41.40 | (4) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.33/41.40 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 259.33/41.40 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 259.33/41.40 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.33/41.40 | v3, v0) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = v1)) &
% 259.33/41.40 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | (
% 259.33/41.40 | ~ (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 &
% 259.33/41.40 | $i(v4))))))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__norm__def) implies:
% 259.33/41.40 | (5) ! [v0: $i] : ! [v1: $i] : ( ~
% 259.33/41.40 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) |
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v0) = v1 &
% 259.33/41.40 | $i(v1)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__zero__not__eq__one) implies:
% 259.33/41.40 | (6) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 259.33/41.40 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_norm__ge__zero) implies:
% 259.33/41.40 | (7) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.33/41.40 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 259.33/41.40 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_norm__eq__zero) implies:
% 259.33/41.40 | (8) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.33/41.40 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 259.33/41.40 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 259.33/41.40 | $i] : (( ~ (v3 = v0) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2)
% 259.33/41.40 | = v1)) & (v3 = v0 | ( ~ (v4 = v1) &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_norm__zero) implies:
% 259.33/41.40 | (9) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.33/41.40 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~
% 259.33/41.40 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v1) | ~
% 259.33/41.40 | class_RealVector_Oreal__normed__vector(v1)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_abs__norm__cancel) implies:
% 259.33/41.40 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 259.33/41.40 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) |
% 259.33/41.40 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v2 & $i(v2)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_psize__eq__0__iff) implies:
% 259.33/41.40 | (11) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.40 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.40 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) |
% 259.33/41.40 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i] :
% 259.33/41.40 | ? [v5: $i] : (( ~ (v3 = v0) | (v5 = v1 & tc_Polynomial_Opoly(v2) =
% 259.33/41.40 | v4 & c_Groups_Ozero__class_Ozero(v4) = v1 & $i(v4))) & (v3 =
% 259.33/41.40 | v0 | ( ~ (v5 = v1) & tc_Polynomial_Opoly(v2) = v4 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))))))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_norm__sgn) implies:
% 259.33/41.40 | (12) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.33/41.40 | (c_Groups_Osgn__class_Osgn(v3, v2) = v4) | ~
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ $i(v3) | ~
% 259.33/41.40 | $i(v2) | ~ class_RealVector_Oreal__normed__vector(v3) | ? [v6:
% 259.33/41.40 | $i] : ((v5 = v1 | (v6 = v2 & c_Groups_Ozero__class_Ozero(v3) =
% 259.33/41.40 | v2)) & (v5 = v0 | ( ~ (v6 = v2) &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(v3) = v6 & $i(v6))))))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_abs__add__one__gt__zero) implies:
% 259.33/41.40 | (13) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.40 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2)
% 259.33/41.40 | | ? [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 259.33/41.40 | v3) = v4 & $i(v4) &
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_r) implies:
% 259.33/41.40 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 259.33/41.40 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3 &
% 259.33/41.40 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) = v2 &
% 259.33/41.40 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, v0) = v1 &
% 259.33/41.40 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____) = v0
% 259.33/41.40 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (
% 259.33/41.40 | ~ (hAPP(v3, v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? [v7: $i] :
% 259.33/41.40 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7 &
% 259.33/41.40 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.33/41.40 | v1, v7)) |
% 259.33/41.40 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = v6 &
% 259.33/41.40 | $i(v6) & ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r____,
% 259.33/41.40 | v6)))))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__mult__less__mono2) implies:
% 259.33/41.40 | (15) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.40 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 259.33/41.40 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 259.33/41.40 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__mult__order) implies:
% 259.33/41.40 | (16) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.33/41.40 | (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 259.33/41.40 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 259.33/41.40 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)
% 259.33/41.40 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__mult__less__iff1) implies:
% 259.33/41.40 | (17) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.40 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~
% 259.33/41.40 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) =
% 259.33/41.40 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2:
% 259.33/41.40 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.33/41.40 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4)
% 259.33/41.40 | = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~
% 259.33/41.40 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__mult__le__cancel__iff2) implies:
% 259.33/41.40 | (18) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.40 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 259.33/41.40 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 259.33/41.40 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & !
% 259.33/41.40 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.33/41.40 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.33/41.40 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__mult__le__cancel__iff1) implies:
% 259.33/41.40 | (19) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.40 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~
% 259.33/41.40 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) =
% 259.33/41.40 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & !
% 259.33/41.40 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.33/41.40 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5,
% 259.33/41.40 | v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) |
% 259.33/41.40 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__sgn__pos) implies:
% 259.33/41.40 | (20) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 259.33/41.40 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2)
% 259.33/41.40 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__mult__left__cancel) implies:
% 259.33/41.40 | (21) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.40 | $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 259.33/41.40 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 259.33/41.40 | ~ $i(v2)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__mult__right__cancel) implies:
% 259.33/41.40 | (22) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.40 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.40 | $i] : ! [v7: $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) |
% 259.33/41.40 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2)
% 259.33/41.40 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__less__def) implies:
% 259.33/41.40 | (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 259.33/41.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 259.33/41.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0))
% 259.33/41.40 |
% 259.33/41.40 | ALPHA: (fact_real__mult__1) implies:
% 259.33/41.41 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 259.33/41.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & hAPP(v0, v1) = v2
% 259.33/41.41 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 |
% 259.33/41.41 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_real__le__eq__diff) implies:
% 259.33/41.41 | (25) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.33/41.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.41 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) |
% 259.33/41.41 | ~ $i(v2) | ~ $i(v1) | ~
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) |
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 259.33/41.41 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.41 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) |
% 259.33/41.41 | ~ $i(v2) | ~ $i(v1) | ~
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_norm__not__less__zero) implies:
% 259.33/41.41 | (26) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.33/41.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.41 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 259.33/41.41 | $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3,
% 259.33/41.41 | v0) | ~ class_RealVector_Oreal__normed__vector(v2)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_real__two__squares__add__zero__iff) implies:
% 259.33/41.41 | (27) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)
% 259.33/41.41 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.41 | $i] : ! [v7: $i] : (v3 = v1 | ~
% 259.33/41.41 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~
% 259.33/41.41 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) =
% 259.33/41.41 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 259.33/41.41 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.33/41.41 | [v7: $i] : (v2 = v1 | ~
% 259.33/41.41 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~
% 259.33/41.41 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) =
% 259.33/41.41 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 259.33/41.41 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 259.33/41.41 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~
% 259.33/41.41 | (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_zero__less__norm__iff) implies:
% 259.33/41.41 | (28) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.33/41.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.33/41.41 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 259.33/41.41 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 259.33/41.41 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 259.33/41.41 | v3) | ( ~ (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 &
% 259.33/41.41 | $i(v4))) & (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 259.33/41.41 | v0, v3) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) =
% 259.33/41.41 | v1)))))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_abs__add__one__not__less__self) implies:
% 259.33/41.41 | (29) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.33/41.41 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 259.33/41.41 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1)
% 259.33/41.41 | | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 259.33/41.41 | v0) = v3 & $i(v3) & ~
% 259.33/41.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1))))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact__096_B_Bthesis_O_A_I_B_Br_O_AALL_Az_O_Ar_A_060_061_Acmod_Az_A_N_N_062_Ad_A_L_Acmod_Aa_A_060_061_Acmod_A_Ipoly_A_IpCons_Ac_Acs_J_Az_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 259.33/41.41 | implies:
% 259.33/41.41 | (30) $i(v_da____)
% 259.33/41.41 | (31) $i(v_aa____)
% 259.33/41.41 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 259.33/41.41 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3 &
% 259.33/41.41 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) = v2 &
% 259.33/41.41 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, v0) = v1 &
% 259.33/41.41 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____) = v0
% 259.33/41.41 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6:
% 259.33/41.41 | $i] : ( ~ (hAPP(v3, v5) = v6) | ~ $i(v5) | ? [v7: $i] : ? [v8:
% 259.33/41.41 | $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6)
% 259.33/41.41 | = v8 & $i(v8) &
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v8)) |
% 259.33/41.41 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7 &
% 259.33/41.41 | $i(v7) & ~
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4,
% 259.33/41.41 | v7)))))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_norm__ratiotest__lemma) implies:
% 259.33/41.41 | (33) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.41 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.41 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.33/41.41 | (c_RealVector_Onorm__class_Onorm(v5, v3) = v6) | ~
% 259.33/41.41 | (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~ (hAPP(v7, v8)
% 259.33/41.41 | = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~
% 259.33/41.41 | $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v5)
% 259.33/41.41 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) |
% 259.33/41.41 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) |
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(v5) = v3))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_mult__eq__if) implies:
% 259.33/41.41 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.33/41.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 259.33/41.41 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.33/41.41 | [v7: $i] : ! [v8: $i] : (v4 = v0 | ~
% 259.33/41.41 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~
% 259.33/41.41 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~
% 259.33/41.41 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~
% 259.33/41.41 | $i(v3) | ? [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 &
% 259.33/41.41 | $i(v9) & $i(v8))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 259.33/41.41 | (v5 = v0 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v0) = v4) | ~
% 259.33/41.41 | $i(v3)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_rabs__ratiotest__lemma) implies:
% 259.33/41.41 | (35) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.41 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 259.33/41.41 | $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v0 | ~
% 259.33/41.41 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v5) | ~
% 259.33/41.41 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v7) | ~
% 259.33/41.41 | (hAPP(v6, v7) = v8) | ~ (hAPP(v1, v4) = v6) | ~ $i(v4) | ~
% 259.33/41.41 | $i(v3) | ~ $i(v2) | ~
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v8) | ~
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_not__real__square__gt__zero) implies:
% 259.33/41.41 | (36) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.41 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3,
% 259.33/41.41 | v2) = v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 259.33/41.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2:
% 259.33/41.41 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) =
% 259.33/41.41 | v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 259.33/41.41 | v3)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_order__root) implies:
% 259.33/41.41 | (37) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.33/41.41 | $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) =
% 259.33/41.41 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.33/41.41 | class_Rings_Oidom(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 259.33/41.41 | ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) & c_Polynomial_Oorder(v3,
% 259.33/41.41 | v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) |
% 259.33/41.41 | (v6 = v5 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) &
% 259.33/41.41 | ((v8 = v2 & tc_Polynomial_Opoly(v3) = v7 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(v7) = v2 & $i(v7)) | ( ~ (v9 =
% 259.33/41.41 | v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & $i(v9)) | ( ~
% 259.33/41.41 | (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 &
% 259.33/41.41 | $i(v6))))))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_mult_Opos__bounded) implies:
% 259.33/41.41 | (38) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.33/41.41 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2)
% 259.33/41.41 | = v3) | ~ $i(v2) | ~
% 259.33/41.41 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 259.33/41.41 | ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)
% 259.33/41.41 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : !
% 259.33/41.41 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 259.33/41.41 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 259.33/41.41 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11,
% 259.33/41.41 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) =
% 259.33/41.41 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ?
% 259.33/41.41 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 259.33/41.41 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13,
% 259.33/41.41 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 259.33/41.41 | $i(v13) &
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 259.33/41.41 | v12))))))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_nat__mult__1) implies:
% 259.33/41.41 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.33/41.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 &
% 259.33/41.41 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 259.33/41.41 | (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_nat__1__eq__mult__iff) implies:
% 259.33/41.41 | (40) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.33/41.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 259.33/41.41 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) =
% 259.33/41.41 | v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 259.33/41.41 | $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) =
% 259.33/41.41 | v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 259.33/41.41 | $i] : ! [v3: $i] : (v3 = v0 | ~ (hAPP(v2, v0) = v3) | ~
% 259.33/41.41 | (hAPP(v1, v0) = v2)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_nat__mult__1__right) implies:
% 259.33/41.41 | (41) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.33/41.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.33/41.41 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) |
% 259.33/41.41 | hAPP(v3, v1) = v2))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_nat__mult__eq__1__iff) implies:
% 259.33/41.41 | (42) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.33/41.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.33/41.41 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) =
% 259.33/41.41 | v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 259.33/41.41 | $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) =
% 259.33/41.41 | v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 259.33/41.41 | $i] : ! [v3: $i] : (v3 = v1 | ~ (hAPP(v2, v1) = v3) | ~
% 259.33/41.41 | (hAPP(v0, v1) = v2)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_diff__0__eq__0) implies:
% 259.33/41.41 | (43) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.41 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 259.33/41.41 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~
% 259.33/41.41 | $i(v1)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_mult__0) implies:
% 259.33/41.41 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 &
% 259.33/41.41 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 259.33/41.41 | (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_less__eq__nat_Osimps_I1_J) implies:
% 259.33/41.41 | (45) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.41 | & ? [v1: $i] : ( ~ $i(v1) |
% 259.33/41.41 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_plus__nat_Oadd__0) implies:
% 259.33/41.41 | (46) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.41 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 259.33/41.41 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~
% 259.33/41.41 | $i(v1)))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_mult__0__right) implies:
% 259.33/41.41 | (47) ? [v0: $i] : ? [v1: $i] :
% 259.33/41.41 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.33/41.41 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.33/41.41 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) |
% 259.33/41.41 | hAPP(v3, v1) = v1))
% 259.33/41.41 |
% 259.33/41.41 | ALPHA: (fact_Nat_Oadd__0__right) implies:
% 259.33/41.42 | (48) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.42 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 259.33/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~
% 259.33/41.42 | $i(v1)))
% 259.33/41.42 |
% 259.33/41.42 | ALPHA: (fact_minus__nat_Odiff__0) implies:
% 259.33/41.42 | (49) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.42 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 259.33/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~
% 259.33/41.42 | $i(v1)))
% 259.33/41.42 |
% 259.33/41.42 | ALPHA: (fact_le__0__eq) implies:
% 259.33/41.42 | (50) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.42 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) & ! [v1:
% 259.33/41.42 | $i] : (v1 = v0 | ~ $i(v1) | ~
% 259.33/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)))
% 259.33/41.42 |
% 259.33/41.42 | ALPHA: (fact_diff__self__eq__0) implies:
% 259.33/41.42 | (51) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.42 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 259.33/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~
% 259.33/41.42 | $i(v1)))
% 259.33/41.42 |
% 259.33/41.42 | ALPHA: (fact_diff__add__0) implies:
% 259.33/41.42 | (52) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 |
% 259.33/41.42 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~
% 259.33/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 259.33/41.42 | $i(v2) | ~ $i(v1)))
% 259.33/41.42 |
% 259.33/41.42 | ALPHA: (fact_diff__is__0__eq) implies:
% 259.33/41.42 | (53) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 259.33/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 259.33/41.42 | $i(v2) | ~ $i(v1) | ~
% 259.33/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & ! [v1:
% 259.33/41.42 | $i] : ! [v2: $i] : ( ~
% 259.33/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v0) | ~
% 259.33/41.42 | $i(v2) | ~ $i(v1) |
% 259.33/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 259.33/41.42 |
% 259.33/41.42 | ALPHA: (fact_add__is__0) implies:
% 259.33/41.42 | (54) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.33/41.42 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 259.33/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~
% 259.33/41.42 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 259.33/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~
% 259.33/41.42 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : (v1 = v0 | ~
% 259.33/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1)))
% 259.33/41.42 |
% 259.33/41.42 | ALPHA: (fact_mult__is__0) implies:
% 259.87/41.42 | (55) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.87/41.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.87/41.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) =
% 259.87/41.42 | v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : !
% 259.87/41.42 | [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~
% 259.87/41.42 | (hAPP(v0, v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : !
% 259.87/41.42 | [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~
% 259.87/41.42 | (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_mult__cancel2) implies:
% 259.87/41.42 | (56) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.87/41.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.87/41.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.42 | ! [v7: $i] : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) =
% 259.87/41.42 | v5) | ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~
% 259.87/41.42 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 259.87/41.42 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v2 | v3 = v1 | ~
% 259.87/41.42 | (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) =
% 259.87/41.42 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 259.87/41.42 | $i(v2)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_diff__is__0__eq_H) implies:
% 259.87/41.42 | (57) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 259.87/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 259.87/41.42 | $i(v2) | ~ $i(v1) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_mult__eq__self__implies__10) implies:
% 259.87/41.42 | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.87/41.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.87/41.42 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 259.87/41.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) &
% 259.87/41.42 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 =
% 259.87/41.42 | v1 | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) |
% 259.87/41.42 | ~ $i(v3)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_diffs0__imp__equal) implies:
% 259.87/41.42 | (59) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.42 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 259.87/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~
% 259.87/41.42 | $i(v2) | ~ $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) &
% 259.87/41.42 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 &
% 259.87/41.42 | $i(v3))))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_add__eq__self__zero) implies:
% 259.87/41.42 | (60) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.42 | & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 259.87/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~
% 259.87/41.42 | $i(v2) | ~ $i(v1)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_neq0__conv) implies:
% 259.87/41.42 | (61) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.42 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1:
% 259.87/41.42 | $i] : (v1 = v0 | ~ $i(v1) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_nat__diff__split__asm) implies:
% 259.87/41.42 | (62) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.87/41.42 | $i] : ! [v6: $i] : ( ~
% 259.87/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~
% 259.87/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2) | ~
% 259.87/41.42 | (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | $i(v1) | ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7)
% 259.87/41.42 | & hBOOL(v7))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 259.87/41.42 | [v4: $i] : ! [v5: $i] : ( ~
% 259.87/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~
% 259.87/41.42 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.42 | hBOOL(v5) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)
% 259.87/41.42 | | ? [v6: $i] : (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & !
% 259.87/41.42 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 259.87/41.42 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~
% 259.87/41.42 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.42 | hBOOL(v5) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) |
% 259.87/41.42 | ? [v6: $i] : ? [v7: $i] :
% 259.87/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3,
% 259.87/41.42 | v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : !
% 259.87/41.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.87/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~
% 259.87/41.42 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.42 | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 259.87/41.42 | : ($i(v7) & ((v8 = v2 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 259.87/41.42 | v1, v7) = v2 & hAPP(v3, v7) = v9 & $i(v9) & ~ hBOOL(v9))
% 259.87/41.42 | | (hAPP(v3, v0) = v6 & $i(v6) & ~ hBOOL(v6))))))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_zero__less__diff) implies:
% 259.87/41.42 | (63) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 259.87/41.42 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 259.87/41.42 | v1, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) &
% 259.87/41.42 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.42 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 259.87/41.42 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 259.87/41.42 | v0, v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_add__gr__0) implies:
% 259.87/41.42 | (64) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 259.87/41.42 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 259.87/41.42 | v0, v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i]
% 259.87/41.42 | : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 259.87/41.42 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 259.87/41.42 | v0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) &
% 259.87/41.42 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.42 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 259.87/41.42 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 259.87/41.42 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_nat__0__less__mult__iff) implies:
% 259.87/41.42 | (65) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.87/41.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 259.87/41.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4,
% 259.87/41.42 | v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 259.87/41.42 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i]
% 259.87/41.42 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 259.87/41.42 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i]
% 259.87/41.42 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 259.87/41.42 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_mult__less__cancel1) implies:
% 259.87/41.42 | (66) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.87/41.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.87/41.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.42 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.42 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i]
% 259.87/41.42 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.87/41.42 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.42 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i]
% 259.87/41.42 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.87/41.42 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.42 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_mult__less__cancel2) implies:
% 259.87/41.42 | (67) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.87/41.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.87/41.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.42 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5,
% 259.87/41.42 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) |
% 259.87/41.42 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i]
% 259.87/41.42 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.87/41.42 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) =
% 259.87/41.42 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 259.87/41.42 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i]
% 259.87/41.42 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.87/41.42 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) =
% 259.87/41.42 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 259.87/41.42 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_mult__le__cancel1) implies:
% 259.87/41.42 | (68) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.87/41.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.87/41.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.42 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.42 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2:
% 259.87/41.42 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.87/41.42 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.42 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)) & ! [v2:
% 259.87/41.42 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.87/41.42 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.42 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 259.87/41.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)))
% 259.87/41.42 |
% 259.87/41.42 | ALPHA: (fact_mult__le__cancel2) implies:
% 259.87/41.43 | (69) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.43 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5,
% 259.87/41.43 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) |
% 259.87/41.43 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2:
% 259.87/41.43 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.87/41.43 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3)
% 259.87/41.43 | = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 259.87/41.43 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)) & ! [v2:
% 259.87/41.43 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.87/41.43 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3)
% 259.87/41.43 | = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 259.87/41.43 | $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_diff__less) implies:
% 259.87/41.43 | (70) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.43 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.43 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~
% 259.87/41.43 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 259.87/41.43 | v0, v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)
% 259.87/41.43 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_not__less0) implies:
% 259.87/41.43 | (71) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.43 | & ! [v1: $i] : ( ~ $i(v1) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_mult__less__mono1) implies:
% 259.87/41.43 | (72) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.43 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5,
% 259.87/41.43 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) |
% 259.87/41.43 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_mult__less__mono2) implies:
% 259.87/41.43 | (73) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.43 | ! [v7: $i] : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~
% 259.87/41.43 | (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_gr0I) implies:
% 259.87/41.43 | (74) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.43 | & ? [v1: $i] : (v1 = v0 | ~ $i(v1) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_nat__mult__eq__cancel__disj) implies:
% 259.87/41.43 | (75) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.43 | (v6 = v5 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~
% 259.87/41.43 | (hAPP(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : !
% 259.87/41.43 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | v3 =
% 259.87/41.43 | v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~
% 259.87/41.43 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_nat__mult__less__cancel1) implies:
% 259.87/41.43 | (76) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.43 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.43 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i]
% 259.87/41.43 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.87/41.43 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.43 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_nat__mult__eq__cancel1) implies:
% 259.87/41.43 | (77) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.43 | (v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~
% 259.87/41.43 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_nat__mult__le__cancel1) implies:
% 259.87/41.43 | (78) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.43 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.43 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2:
% 259.87/41.43 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.87/41.43 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 259.87/41.43 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natceiling__add__one) implies:
% 259.87/41.43 | (79) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.87/41.43 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 259.87/41.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 259.87/41.43 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~
% 259.87/41.43 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.87/41.43 | v0, v3) | ? [v5: $i] : ? [v6: $i] :
% 259.87/41.43 | (c_RComplete_Onatceiling(v4) = v5 & c_RComplete_Onatceiling(v3) =
% 259.87/41.43 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 &
% 259.87/41.43 | $i(v6) & $i(v5))))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_mult__right_Opos__bounded) implies:
% 259.87/41.43 | (80) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.87/41.43 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5)
% 259.87/41.43 | | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.43 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] :
% 259.87/41.43 | ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6)
% 259.87/41.43 | & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 259.87/41.43 | (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9,
% 259.87/41.43 | v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11:
% 259.87/41.43 | $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3,
% 259.87/41.43 | v11) = v12 & hAPP(v5, v7) = v11 & $i(v12) & $i(v11) &
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 259.87/41.43 | v10))))))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_mult__left_Opos__bounded) implies:
% 259.87/41.43 | (81) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 259.87/41.43 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 259.87/41.43 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] :
% 259.87/41.43 | ($i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)
% 259.87/41.43 | & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.87/41.43 | (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8,
% 259.87/41.43 | v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10:
% 259.87/41.43 | $i] : ? [v11: $i] : ? [v12: $i] :
% 259.87/41.43 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10,
% 259.87/41.43 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 259.87/41.43 | $i(v10) &
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 259.87/41.43 | v9))))))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natceiling__zero) implies:
% 259.87/41.43 | (82) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.43 | $i(v0))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_zero__le__natceiling) implies:
% 259.87/41.43 | (83) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.43 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatceiling(v1) = v2)
% 259.87/41.43 | | ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 259.87/41.43 | v2)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natceiling__one) implies:
% 259.87/41.43 | (84) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 &
% 259.87/41.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natceiling__neg) implies:
% 259.87/41.43 | (85) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 259.87/41.43 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.43 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 259.87/41.43 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natceiling__le__eq__one) implies:
% 259.87/41.43 | (86) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 259.87/41.43 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) &
% 259.87/41.43 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.43 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~
% 259.87/41.43 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.87/41.43 | v2, v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3,
% 259.87/41.43 | v0)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natfloor__add__one) implies:
% 259.87/41.43 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.87/41.43 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 259.87/41.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 259.87/41.43 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~
% 259.87/41.43 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.87/41.43 | v0, v3) | ? [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4)
% 259.87/41.43 | = v5 & c_RComplete_Onatfloor(v3) = v6 &
% 259.87/41.43 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 259.87/41.43 | $i(v5))))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natfloor__zero) implies:
% 259.87/41.43 | (88) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.43 | $i(v0))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_zero__le__natfloor) implies:
% 259.87/41.43 | (89) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.43 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) |
% 259.87/41.43 | ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 259.87/41.43 | v2)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natfloor__one) implies:
% 259.87/41.43 | (90) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 &
% 259.87/41.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natfloor__neg) implies:
% 259.87/41.43 | (91) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 259.87/41.43 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.43 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 259.87/41.43 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_le__natfloor__eq__one) implies:
% 259.87/41.43 | (92) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 259.87/41.43 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) &
% 259.87/41.43 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2)
% 259.87/41.43 | = v3) | ~ $i(v2) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) |
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & !
% 259.87/41.43 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~
% 259.87/41.43 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.87/41.43 | v1, v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 259.87/41.43 | v3)))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_le__mult__natfloor) implies:
% 259.87/41.43 | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.87/41.43 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 259.87/41.43 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 259.87/41.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 259.87/41.43 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 259.87/41.43 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~
% 259.87/41.43 | (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~
% 259.87/41.43 | (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ?
% 259.87/41.43 | [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 259.87/41.43 | (c_RComplete_Onatfloor(v10) = v11 & hAPP(v9, v3) = v10 & hAPP(v2,
% 259.87/41.43 | v4) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11))))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_natceiling__eq) implies:
% 259.87/41.43 | (94) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 259.87/41.43 | v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.43 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5
% 259.87/41.43 | = v4 | ~ (c_RComplete_Onatceiling(v2) = v4) | ~
% 259.87/41.43 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~
% 259.87/41.43 | $i(v3) | ~ $i(v2) | ? [v6: $i] : ? [v7: $i] :
% 259.87/41.43 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & $i(v6) & ( ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v2) |
% 259.87/41.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 &
% 259.87/41.43 | $i(v7) & ~
% 259.87/41.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 259.87/41.43 | v7))))))
% 259.87/41.43 |
% 259.87/41.43 | ALPHA: (fact_poly__bound__exists) implies:
% 259.87/41.44 | (95) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.44 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3) | ~ $i(v2) |
% 259.87/41.44 | ~ $i(v1) | ? [v4: $i] : ($i(v4) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 259.87/41.44 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v3, v5) = v6) | ~ $i(v5) |
% 259.87/41.44 | ? [v7: $i] : ? [v8: $i] :
% 259.87/41.44 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) =
% 259.87/41.44 | v8 & $i(v8) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 259.87/41.44 | v4)) |
% 259.87/41.44 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) =
% 259.87/41.44 | v7 & $i(v7) & ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 259.87/41.44 | v1)))))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__of__nat__ge__zero) implies:
% 259.87/41.44 | (96) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_abs__real__of__nat__cancel) implies:
% 259.87/41.44 | (97) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) =
% 259.87/41.44 | v1) | ~ $i(v0) | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1)
% 259.87/41.44 | = v1 & $i(v1)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__of__nat__zero__iff) implies:
% 259.87/41.44 | (98) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 259.87/41.44 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.44 | $i(v0) & ! [v2: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 259.87/41.44 | v2) = v0) | ~ $i(v2)) & ! [v2: $i] : (v2 = v0 | ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__of__nat__zero) implies:
% 259.87/41.44 | (99) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 259.87/41.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 259.87/41.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 259.87/41.44 | $i(v0))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_not__real__of__nat__less__zero) implies:
% 259.87/41.44 | (100) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__of__nat__1) implies:
% 259.87/41.44 | (101) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 259.87/41.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 259.87/41.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__natceiling__ge) implies:
% 259.87/41.44 | (102) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatceiling(v0) = v1) |
% 259.87/41.44 | ~ $i(v0) | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 &
% 259.87/41.44 | $i(v2) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 259.87/41.44 | v2)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__of__nat__le__zero__cancel__iff) implies:
% 259.87/41.44 | (103) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 259.87/41.44 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1)
% 259.87/41.44 | & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)) & !
% 259.87/41.44 | [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__natfloor__le) implies:
% 259.87/41.44 | (104) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1)
% 259.87/41.44 | = v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ?
% 259.87/41.44 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__of__nat__gt__zero__cancel__iff) implies:
% 259.87/41.44 | (105) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 259.87/41.44 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1)
% 259.87/41.44 | & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & !
% 259.87/41.44 | [v2: $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) =
% 259.87/41.44 | v3) | ~ $i(v2) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_nat__less__real__le) implies:
% 259.87/41.44 | (106) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 259.87/41.44 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.44 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5:
% 259.87/41.44 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) =
% 259.87/41.44 | v5 & $i(v5) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))) &
% 259.87/41.44 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i]
% 259.87/41.44 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 259.87/41.44 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.87/41.44 | v5, v4))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_nat__le__real__less) implies:
% 259.87/41.44 | (107) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 259.87/41.44 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.44 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ?
% 259.87/41.44 | [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0)
% 259.87/41.44 | = v5 & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 259.87/41.44 | v3, v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 259.87/41.44 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5:
% 259.87/41.44 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) =
% 259.87/41.44 | v5 & $i(v5) & ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_le__natfloor__eq) implies:
% 259.87/41.44 | (108) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 259.87/41.44 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 259.87/41.44 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)) & !
% 259.87/41.44 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 259.87/41.44 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_natceiling__le__eq) implies:
% 259.87/41.44 | (109) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 259.87/41.44 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 259.87/41.44 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4)) & !
% 259.87/41.44 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 259.87/41.44 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__natfloor__add__one__gt) implies:
% 259.87/41.44 | (110) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1)
% 259.87/41.44 | = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 259.87/41.44 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 &
% 259.87/41.44 | $i(v4) & $i(v3) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_real__natfloor__gt__diff__one) implies:
% 259.87/41.44 | (111) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 259.87/41.44 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) |
% 259.87/41.44 | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 &
% 259.87/41.44 | c_RComplete_Onatfloor(v1) = v3 & $i(v4) & $i(v3) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_less__natfloor) implies:
% 259.87/41.44 | (112) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 259.87/41.44 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 259.87/41.44 | (c_RComplete_Onatfloor(v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1)))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_natfloor__add) implies:
% 259.87/41.44 | (113) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 259.87/41.44 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 259.87/41.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 259.87/41.44 | $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 259.87/41.44 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 259.87/41.44 | c_RComplete_Onatfloor(v2) = v6 &
% 259.87/41.44 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6)
% 259.87/41.44 | & $i(v5))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_ge__natfloor__plus__one__imp__gt) implies:
% 259.87/41.44 | (114) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 259.87/41.44 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 259.87/41.44 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5:
% 259.87/41.44 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 &
% 259.87/41.44 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5,
% 259.87/41.44 | v1))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_natfloor__eq) implies:
% 259.87/41.44 | (115) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 259.87/41.44 | (v4 = v2 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 259.87/41.44 | (c_RComplete_Onatfloor(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ?
% 259.87/41.44 | [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0)
% 259.87/41.44 | = v5 & $i(v5) & ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_natceiling__add) implies:
% 259.87/41.44 | (116) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 259.87/41.44 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 259.87/41.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 259.87/41.44 | $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 259.87/41.44 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 259.87/41.44 | c_RComplete_Onatceiling(v2) = v6 &
% 259.87/41.44 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6)
% 259.87/41.44 | & $i(v5))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_reals__Archimedean6) implies:
% 259.87/41.44 | (117) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 259.87/41.44 | v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.44 | $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 259.87/41.44 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 259.87/41.44 | (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 &
% 259.87/41.44 | c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 &
% 259.87/41.44 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 &
% 259.87/41.44 | $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_lemma__interval) implies:
% 259.87/41.44 | (118) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 259.87/41.44 | $i(v2) | ~ $i(v1) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4:
% 259.87/41.44 | $i] : ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 259.87/41.44 | v0, v4) & ! [v5: $i] : ! [v6: $i] : ( ~
% 259.87/41.44 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) =
% 259.87/41.44 | v6) | ~ $i(v5) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1) |
% 259.87/41.44 | ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,
% 259.87/41.44 | v6) = v7 & $i(v7) & ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v4))) &
% 259.87/41.44 | ! [v5: $i] : ! [v6: $i] : ( ~
% 259.87/41.44 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) =
% 259.87/41.44 | v6) | ~ $i(v5) |
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5) |
% 259.87/41.44 | ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,
% 259.87/41.44 | v6) = v7 & $i(v7) & ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 259.87/41.44 | v4))))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_ex__least__nat__less) implies:
% 259.87/41.44 | (119) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 259.87/41.44 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 259.87/41.44 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3,
% 259.87/41.44 | v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v4) | ? [v5:
% 259.87/41.44 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 259.87/41.44 | ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 &
% 259.87/41.44 | hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & !
% 259.87/41.44 | [v9: $i] : ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~
% 259.87/41.44 | $i(v9) | ~ hBOOL(v10) | ~
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6)))
% 259.87/41.44 | | (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5))))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_mult_Ononneg__bounded) implies:
% 259.87/41.44 | (120) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.87/41.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.44 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.44 | (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ $i(v2) | ~
% 259.87/41.44 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 259.87/41.44 | ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 259.87/41.44 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] :
% 259.87/41.44 | ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 259.87/41.44 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 259.87/41.44 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~
% 259.87/41.44 | (hAPP(v11, v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~
% 259.87/41.44 | (hAPP(v1, v10) = v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) |
% 259.87/41.44 | ~ $i(v5) | ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 259.87/41.44 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13,
% 259.87/41.44 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 259.87/41.44 | $i(v13) &
% 259.87/41.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 259.87/41.44 | v12))))))
% 259.87/41.44 |
% 259.87/41.44 | ALPHA: (fact_mult__right_Ononneg__bounded) implies:
% 259.87/41.45 | (121) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.87/41.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 259.87/41.45 | ~ (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) =
% 259.87/41.45 | v5) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.45 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] :
% 259.87/41.45 | ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 259.87/41.45 | v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i]
% 259.87/41.45 | : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~
% 259.87/41.45 | (hAPP(v9, v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) |
% 259.87/41.45 | ? [v11: $i] : ? [v12: $i] :
% 259.87/41.45 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5,
% 259.87/41.45 | v7) = v11 & $i(v12) & $i(v11) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 259.87/41.45 | v10))))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_mult__left_Ononneg__bounded) implies:
% 259.87/41.45 | (122) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.87/41.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.45 | $i(v0) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.45 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2)
% 259.87/41.45 | | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] :
% 259.87/41.45 | ($i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 259.87/41.45 | v5) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 259.87/41.45 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~
% 259.87/41.45 | (hAPP(v8, v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ?
% 259.87/41.45 | [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 259.87/41.45 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10,
% 259.87/41.45 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 259.87/41.45 | $i(v10) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 259.87/41.45 | v9))))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_unimodular__reduce__norm) implies:
% 259.87/41.45 | (123) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.45 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.87/41.45 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v1 & $i(v1) &
% 259.87/41.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 259.87/41.45 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, v1) = v3)
% 259.87/41.45 | | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 259.87/41.45 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 259.87/41.45 | (( ~ (v4 = v0) &
% 259.87/41.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4
% 259.87/41.45 | & $i(v4)) |
% 259.87/41.45 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2,
% 259.87/41.45 | c_Complex_Oii) = v10 &
% 259.87/41.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10) =
% 259.87/41.45 | v11 & $i(v11) & $i(v10) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v0)) |
% 259.87/41.45 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v1) = v5
% 259.87/41.45 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) =
% 259.87/41.45 | v6 & $i(v6) & $i(v5) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v0)) |
% 259.87/41.45 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2,
% 259.87/41.45 | c_Complex_Oii) = v8 &
% 259.87/41.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9
% 259.87/41.45 | & $i(v9) & $i(v8) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v0)) |
% 259.87/41.45 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v7
% 259.87/41.45 | & $i(v7) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 259.87/41.45 | v7, v0)))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_poly__cont) implies:
% 259.87/41.45 | (124) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 259.87/41.45 | [v5: $i] : ( ~ (c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v4) |
% 259.87/41.45 | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v6:
% 259.87/41.45 | $i] : ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 259.87/41.45 | v0, v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.87/41.45 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v8, v5) =
% 259.87/41.45 | v9) | ~ (hAPP(v4, v7) = v8) | ~ $i(v7) | ? [v10: $i] :
% 259.87/41.45 | ? [v11: $i] : ? [v12: $i] :
% 259.87/41.45 | ((c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v7, v2)
% 259.87/41.45 | = v10 &
% 259.87/41.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10)
% 259.87/41.45 | = v11 & $i(v11) & $i(v10) & ( ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 259.87/41.45 | v6) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 259.87/41.45 | v11))) |
% 259.87/41.45 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v9) =
% 259.87/41.45 | v12 & $i(v12) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12,
% 259.87/41.45 | v3)))))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_lemma__interval__lt) implies:
% 259.87/41.45 | (125) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 259.87/41.45 | $i(v2) | ~ $i(v1) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4:
% 259.87/41.45 | $i] : ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 259.87/41.45 | v0, v4) & ! [v5: $i] : ! [v6: $i] : ( ~
% 259.87/41.45 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) =
% 259.87/41.45 | v6) | ~ $i(v5) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v5, v1) | ?
% 259.87/41.45 | [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) =
% 259.87/41.45 | v7 & $i(v7) & ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v4))) &
% 259.87/41.45 | ! [v5: $i] : ! [v6: $i] : ( ~
% 259.87/41.45 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) =
% 259.87/41.45 | v6) | ~ $i(v5) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5) | ?
% 259.87/41.45 | [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) =
% 259.87/41.45 | v7 & $i(v7) & ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 259.87/41.45 | v4))))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_lemmaCauchy) implies:
% 259.87/41.45 | (126) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 259.87/41.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 259.87/41.45 | [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v4,
% 259.87/41.45 | v5) = v6) | ~ (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) |
% 259.87/41.45 | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.45 | class_RealVector_Oreal__normed__vector(v4) | ~
% 259.87/41.45 | class_Orderings_Oord(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9:
% 259.87/41.45 | $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) &
% 259.87/41.45 | ((c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 &
% 259.87/41.45 | c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1,
% 259.87/41.45 | v8) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless__eq(v3, v2, v8) & ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v0)) |
% 259.87/41.45 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 &
% 259.87/41.45 | $i(v7) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 259.87/41.45 | (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~
% 259.87/41.45 | (hAPP(v1, v12) = v13) | ~ $i(v12) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless__eq(v3, v2, v12) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14,
% 259.87/41.45 | v7)))))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_reals__Archimedean3) implies:
% 259.87/41.45 | (127) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.87/41.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.45 | $i(v0) & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4:
% 259.87/41.45 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 259.87/41.45 | (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & hAPP(v6, v3) = v7 &
% 259.87/41.45 | hAPP(v1, v5) = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v7))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_LIMSEQ__inverse__realpow__zero__lemma) implies:
% 259.87/41.45 | (128) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 259.87/41.45 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 259.87/41.45 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 259.87/41.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 259.87/41.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) &
% 259.87/41.45 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 259.87/41.45 | : ! [v7: $i] : ! [v8: $i] : ( ~
% 259.87/41.45 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) | ~
% 259.87/41.45 | (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~
% 259.87/41.45 | $i(v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 259.87/41.45 | v0, v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 259.87/41.45 | $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 259.87/41.45 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 &
% 259.87/41.45 | hAPP(v10, v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) &
% 259.87/41.45 | $i(v10) & $i(v9) &
% 259.87/41.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_Bseq__def) implies:
% 259.87/41.45 | (129) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.45 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 259.87/41.45 | $i(v2) | ~ $i(v1) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 259.87/41.45 | class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1)
% 259.87/41.45 | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 259.87/41.45 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6 & hAPP(v1, v4) = v5
% 259.87/41.45 | & $i(v6) & $i(v5) & $i(v4) & ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))) &
% 259.87/41.45 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.45 | c_SEQ_OBseq(v2, v1) | ~
% 259.87/41.45 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] :
% 259.87/41.45 | ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)
% 259.87/41.45 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.87/41.45 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v1,
% 259.87/41.45 | v4) = v5) | ~ $i(v4) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 259.87/41.45 | v3)))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)
% 259.87/41.45 | implies:
% 259.87/41.45 | (130) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 259.87/41.45 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.45 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 259.87/41.45 | | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) |
% 259.87/41.45 | hAPP(v4, v0) = v1))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)
% 259.87/41.45 | implies:
% 259.87/41.45 | (131) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.45 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.45 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 259.87/41.45 | | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) |
% 259.87/41.45 | ? [v5: $i] : (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0)
% 259.87/41.45 | = v5 & $i(v5))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_realpow__minus__mult) implies:
% 259.87/41.45 | (132) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 259.87/41.45 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 259.87/41.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 259.87/41.45 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 259.87/41.45 | ! [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v4) = v6) | ~
% 259.87/41.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~
% 259.87/41.45 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) =
% 259.87/41.45 | v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~
% 259.87/41.45 | (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.45 | class_Groups_Omonoid__mult(v4) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7,
% 259.87/41.45 | v3) = v11 & $i(v11))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_realpow__num__eq__if) implies:
% 259.87/41.45 | (133) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 259.87/41.45 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 259.87/41.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 259.87/41.45 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 259.87/41.45 | ! [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v4) = v5) | ~
% 259.87/41.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~
% 259.87/41.45 | (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ (hAPP(v8, v10) =
% 259.87/41.45 | v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~
% 259.87/41.45 | (hAPP(v5, v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.45 | class_Power_Opower(v4) | ? [v12: $i] : ? [v13: $i] : (( ~ (v3 =
% 259.87/41.45 | v0) | (v13 = v12 & c_Groups_Oone__class_Oone(v4) = v12 &
% 259.87/41.45 | hAPP(v6, v0) = v12 & $i(v12))) & (v3 = v0 | (v12 = v11 &
% 259.87/41.45 | hAPP(v6, v3) = v11 & $i(v11))))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_power__strict__mono) implies:
% 259.87/41.45 | (134) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.45 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.87/41.45 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 259.87/41.45 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9)
% 259.87/41.45 | | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 259.87/41.45 | v2) = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.45 | ~ c_Orderings_Oord__class_Oless(v4, v3, v2) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 259.87/41.45 | class_Rings_Olinordered__semidom(v4) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless(v4, v7, v9) | ? [v10: $i] :
% 259.87/41.45 | (c_Groups_Ozero__class_Ozero(v4) = v10 & $i(v10) & ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless__eq(v4, v10, v3))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_one__less__power) implies:
% 259.87/41.45 | (135) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.45 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.87/41.45 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) |
% 259.87/41.45 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~
% 259.87/41.45 | $i(v2) | ~ $i(v1) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 259.87/41.45 | class_Rings_Olinordered__semidom(v3) | ? [v7: $i] :
% 259.87/41.45 | (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(v3, v7, v2) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless(v3, v7, v6)))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_zero__less__zpower__abs__iff) implies:
% 259.87/41.45 | (136) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 259.87/41.45 | (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 &
% 259.87/41.45 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 259.87/41.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) &
% 259.87/41.45 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 259.87/41.45 | [v7: $i] : (v4 = v0 | ~ (c_Groups_Oabs__class_Oabs(tc_Int_Oint,
% 259.87/41.45 | v4) = v5) | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) |
% 259.87/41.45 | ~ $i(v4) | ~ $i(v3) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v7)) & ! [v3: $i]
% 259.87/41.45 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~
% 259.87/41.45 | (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v0) = v4) | ~ (hAPP(v5,
% 259.87/41.45 | v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v6)) & ! [v3: $i]
% 259.87/41.45 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.87/41.45 | (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v3) = v4) | ~ (hAPP(v5,
% 259.87/41.45 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v6)))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_nat__power__less__imp__less) implies:
% 259.87/41.45 | (137) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.45 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.87/41.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 259.87/41.45 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 259.87/41.45 | : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) |
% 259.87/41.45 | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 259.87/41.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_real__of__nat__power) implies:
% 259.87/41.45 | (138) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.45 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 259.87/41.45 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 & $i(v1) &
% 259.87/41.45 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 259.87/41.45 | [v6: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4) | ~
% 259.87/41.45 | (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ~
% 259.87/41.45 | $i(v2) | ? [v7: $i] : ? [v8: $i] :
% 259.87/41.45 | (c_RealDef_Oreal(tc_Nat_Onat, v8) = v6 & hAPP(v7, v2) = v8 &
% 259.87/41.45 | hAPP(v0, v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 259.87/41.45 |
% 259.87/41.45 | ALPHA: (fact_power__real__of__nat) implies:
% 259.87/41.46 | (139) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.46 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.87/41.46 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 259.87/41.46 | [v6: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4) | ~
% 259.87/41.46 | (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~
% 259.87/41.46 | $i(v2) | ? [v7: $i] : ? [v8: $i] :
% 259.87/41.46 | (c_RealDef_Oreal(tc_Nat_Onat, v8) = v6 & hAPP(v7, v2) = v8 &
% 259.87/41.46 | hAPP(v1, v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_natfloor__power) implies:
% 259.87/41.46 | (140) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.46 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.87/41.46 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v0 & $i(v1) &
% 259.87/41.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 259.87/41.46 | [v6: $i] : ( ~ (c_RComplete_Onatfloor(v3) = v4) | ~ (hAPP(v5, v2)
% 259.87/41.46 | = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ?
% 259.87/41.46 | [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ((v10 = v6
% 259.87/41.46 | & c_RComplete_Onatfloor(v9) = v6 & hAPP(v8, v2) = v9 &
% 259.87/41.46 | hAPP(v0, v3) = v8 & $i(v9) & $i(v8) & $i(v6)) | ( ~ (v7 = v3)
% 259.87/41.46 | & c_RealDef_Oreal(tc_Nat_Onat, v4) = v7 & $i(v7)))))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_power__eq__if) implies:
% 259.87/41.46 | (141) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 259.87/41.46 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.87/41.46 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 &
% 259.87/41.46 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 259.87/41.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) &
% 259.87/41.46 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 259.87/41.46 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~
% 259.87/41.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~
% 259.87/41.46 | (hAPP(v7, v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4)
% 259.87/41.46 | = v7) | ~ (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) |
% 259.87/41.46 | (hAPP(v6, v5) = v10 & $i(v10))) & ! [v4: $i] : ! [v5: $i] : !
% 259.87/41.46 | [v6: $i] : (v6 = v2 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) =
% 259.87/41.46 | v5) | ~ $i(v4)))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_power__one__right) implies:
% 259.87/41.46 | (142) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 259.87/41.46 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.46 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 259.87/41.46 | | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) |
% 259.87/41.46 | hAPP(v4, v0) = v1))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_power__eq__0__iff) implies:
% 259.87/41.46 | (143) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.46 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.87/41.46 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) |
% 259.87/41.46 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~
% 259.87/41.46 | $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v3) | ~
% 259.87/41.46 | class_Rings_Ono__zero__divisors(v3) | ~
% 259.87/41.46 | class_Rings_Omult__zero(v3) | ~ class_Rings_Ozero__neq__one(v3)
% 259.87/41.46 | | ? [v7: $i] : (c_Groups_Ozero__class_Ozero(v3) = v7 & $i(v7) &
% 259.87/41.46 | ( ~ (v7 = v6) | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2) | v6
% 259.87/41.46 | = v2 | v1 = v0))))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_power__0) implies:
% 259.87/41.46 | (144) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.46 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 259.87/41.46 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 259.87/41.46 | | ~ $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i]
% 259.87/41.46 | : (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 &
% 259.87/41.46 | $i(v5))))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_power__0__left) implies:
% 259.87/41.46 | (145) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.46 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.87/41.46 | $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~
% 259.87/41.46 | (c_Power_Opower__class_Opower(v2) = v3) | ~
% 259.87/41.46 | (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) |
% 259.87/41.46 | ~ (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.46 | class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2)) & !
% 259.87/41.46 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 259.87/41.46 | ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~
% 259.87/41.46 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) |
% 259.87/41.46 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~
% 259.87/41.46 | class_Rings_Osemiring__0(v1) | ~ class_Power_Opower(v1) |
% 259.87/41.46 | (c_Groups_Oone__class_Oone(v1) = v5 & $i(v5))))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_power__eq__imp__eq__base) implies:
% 259.87/41.46 | (146) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.46 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.87/41.46 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~
% 259.87/41.46 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v2) = v7)
% 259.87/41.46 | | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 259.87/41.46 | v1) = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 259.87/41.46 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 259.87/41.46 | class_Rings_Olinordered__semidom(v4) | ? [v9: $i] :
% 259.87/41.46 | (c_Groups_Ozero__class_Ozero(v4) = v9 & $i(v9) & ( ~
% 259.87/41.46 | c_Orderings_Oord__class_Oless__eq(v4, v9, v3) | ~
% 259.87/41.46 | c_Orderings_Oord__class_Oless__eq(v4, v9, v1)))))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_reduce__poly__simple) implies:
% 259.87/41.46 | (147) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 259.87/41.46 | ? [v5: $i] : (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v4
% 259.87/41.46 | & c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 &
% 259.87/41.46 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v5 &
% 259.87/41.46 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 &
% 259.87/41.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 259.87/41.46 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v5) &
% 259.87/41.46 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ! [v7:
% 259.87/41.46 | $i] : ! [v8: $i] : (v7 = v0 | v6 = v1 | ~ (hAPP(v3, v7) = v8) |
% 259.87/41.46 | ~ $i(v7) | ~ $i(v6) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i]
% 259.87/41.46 | : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 259.87/41.46 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v12) = v13
% 259.87/41.46 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v13) =
% 259.87/41.46 | v14 & hAPP(v10, v6) = v11 & hAPP(v8, v11) = v12 & hAPP(v4, v9)
% 259.87/41.46 | = v10 & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) &
% 259.87/41.46 | $i(v9) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14,
% 259.87/41.46 | v5))))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_zero__less__power__nat__eq) implies:
% 259.87/41.46 | (148) ? [v0: $i] : ? [v1: $i] :
% 259.87/41.46 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 259.87/41.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 259.87/41.46 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 |
% 259.87/41.46 | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 259.87/41.46 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 259.87/41.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i]
% 259.87/41.46 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 259.87/41.46 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 259.87/41.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i]
% 259.87/41.46 | : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~
% 259.87/41.46 | (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 259.87/41.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_power_Opower_Opower__0) implies:
% 259.87/41.46 | (149) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 259.87/41.46 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 259.87/41.46 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5)
% 259.87/41.46 | | ~ (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 259.87/41.46 | $i(v1) | hAPP(v6, v0) = v3))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_BseqD) implies:
% 259.87/41.46 | (150) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 259.87/41.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 259.87/41.46 | c_SEQ_OBseq(v2, v1) | ~
% 259.87/41.46 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] :
% 259.87/41.46 | ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)
% 259.87/41.46 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 259.87/41.46 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v1,
% 259.87/41.46 | v4) = v5) | ~ $i(v4) |
% 259.87/41.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 259.87/41.46 | v3)))))
% 259.87/41.46 |
% 259.87/41.46 | ALPHA: (fact_rcis__zero__mod) implies:
% 260.06/41.46 | (151) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.46 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v1) &
% 260.06/41.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 260.06/41.46 | (c_Complex_Orcis(v0, v2) = v3) | ~ $i(v2)))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_BseqI) implies:
% 260.06/41.46 | (152) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 260.06/41.46 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 260.06/41.46 | class_RealVector_Oreal__normed__vector(v3) | c_SEQ_OBseq(v3, v1)
% 260.06/41.46 | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 260.06/41.46 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6 & hAPP(v1, v4) = v5
% 260.06/41.46 | & $i(v6) & $i(v5) & $i(v4) & ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v2))))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_realpow__pos__nth__unique) implies:
% 260.06/41.46 | (153) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 260.06/41.46 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) &
% 260.06/41.46 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~
% 260.06/41.46 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 260.06/41.46 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ?
% 260.06/41.46 | [v5: $i] : ? [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 &
% 260.06/41.46 | $i(v6) & $i(v5) &
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & !
% 260.06/41.46 | [v7: $i] : ! [v8: $i] : (v7 = v5 | ~ (hAPP(v8, v4) = v3) | ~
% 260.06/41.46 | (hAPP(v2, v7) = v8) | ~ $i(v7) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v7)))))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_realpow__pos__nth) implies:
% 260.06/41.46 | (154) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 260.06/41.46 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) &
% 260.06/41.46 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~
% 260.06/41.46 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 260.06/41.46 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ?
% 260.06/41.46 | [v5: $i] : ? [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 &
% 260.06/41.46 | $i(v6) & $i(v5) &
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__realpow) implies:
% 260.06/41.46 | (155) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 260.06/41.46 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 260.06/41.46 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) &
% 260.06/41.46 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 260.06/41.46 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) =
% 260.06/41.46 | v7) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6,
% 260.06/41.46 | v7) = v8) | ~ (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 260.06/41.46 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ?
% 260.06/41.46 | [v9: $i] : ? [v10: $i] : (c_Transcendental_Oln(v10) = v8 &
% 260.06/41.46 | hAPP(v9, v3) = v10 & hAPP(v1, v4) = v9 & $i(v10) & $i(v9) &
% 260.06/41.46 | $i(v8))))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__less__self) implies:
% 260.06/41.46 | (156) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Transcendental_Oln(v1)
% 260.06/41.46 | = v2) | ~ $i(v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__inj__iff) implies:
% 260.06/41.46 | (157) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 260.06/41.46 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 260.06/41.46 | v3) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__less__cancel__iff) implies:
% 260.06/41.46 | (158) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 260.06/41.46 | ~ (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1)
% 260.06/41.46 | = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & !
% 260.06/41.46 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.46 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 260.06/41.46 | v4) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4)))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__one) implies:
% 260.06/41.46 | (159) ? [v0: $i] : ? [v1: $i] : (c_Transcendental_Oln(v0) = v1 &
% 260.06/41.46 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 260.06/41.46 | $i(v0))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__le__cancel__iff) implies:
% 260.06/41.46 | (160) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 260.06/41.46 | ~ (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1)
% 260.06/41.46 | = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) |
% 260.06/41.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 260.06/41.46 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.46 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 260.06/41.46 | v4) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 260.06/41.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4)))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__ge__zero) implies:
% 260.06/41.46 | (161) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 260.06/41.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 260.06/41.46 | = v3) | ~ $i(v2) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 260.06/41.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__gt__zero) implies:
% 260.06/41.46 | (162) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.46 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 260.06/41.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 260.06/41.46 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 260.06/41.46 | = v3) | ~ $i(v2) | ~
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 260.06/41.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 260.06/41.46 |
% 260.06/41.46 | ALPHA: (fact_ln__gt__zero__iff) implies:
% 260.06/41.47 | (163) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 260.06/41.47 | = v3) | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & !
% 260.06/41.47 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 260.06/41.47 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.06/41.47 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.06/41.47 | v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_ln__eq__zero__iff) implies:
% 260.06/41.47 | (164) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) =
% 260.06/41.47 | v0) | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)) & !
% 260.06/41.47 | [v2: $i] : (v2 = v0 | ~ (c_Transcendental_Oln(v1) = v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_ln__less__zero__iff) implies:
% 260.06/41.47 | (165) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 260.06/41.47 | = v3) | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & !
% 260.06/41.47 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 260.06/41.47 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 260.06/41.47 | v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.06/41.47 | v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_ln__less__zero) implies:
% 260.06/41.47 | (166) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 260.06/41.47 | = v3) | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_ln__gt__zero__imp__gt__one) implies:
% 260.06/41.47 | (167) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 260.06/41.47 | = v3) | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_ln__ge__zero__imp__ge__one) implies:
% 260.06/41.47 | (168) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 260.06/41.47 | = v3) | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_ln__ge__zero__iff) implies:
% 260.06/41.47 | (169) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 260.06/41.47 | = v3) | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & !
% 260.06/41.47 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 260.06/41.47 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.06/41.47 | v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.06/41.47 | v0, v3) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.06/41.47 | v1, v2)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_ln__mult) implies:
% 260.06/41.47 | (170) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 260.06/41.47 | [v6: $i] : ( ~ (c_Transcendental_Oln(v3) = v4) | ~
% 260.06/41.47 | (c_Transcendental_Oln(v2) = v5) | ~
% 260.06/41.47 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~
% 260.06/41.47 | $i(v3) | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7:
% 260.06/41.47 | $i] : ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7,
% 260.06/41.47 | v2) = v8 & hAPP(v1, v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_ln__add__one__self__le__self) implies:
% 260.06/41.47 | (171) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.47 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 260.06/41.47 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.06/41.47 | v0, v2) | ? [v4: $i] : (c_Transcendental_Oln(v3) = v4 & $i(v4)
% 260.06/41.47 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4,
% 260.06/41.47 | v2))))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_nat0__intermed__int__val) implies:
% 260.06/41.47 | (172) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 260.06/41.47 | (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 260.06/41.47 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 260.06/41.47 | ~ (hAPP(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v6) | ? [v7:
% 260.06/41.47 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 260.06/41.47 | ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 260.06/41.47 | ($i(v10) & $i(v8) & ((v9 = v3 & hAPP(v4, v8) = v3 &
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v5)) |
% 260.06/41.47 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v12, v13) = v14 &
% 260.06/41.47 | c_Groups_Oabs__class_Oabs(tc_Int_Oint, v14) = v15 &
% 260.06/41.47 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v10, v0) = v11 &
% 260.06/41.47 | hAPP(v4, v11) = v12 & hAPP(v4, v10) = v13 & $i(v15) &
% 260.06/41.47 | $i(v14) & $i(v13) & $i(v12) & $i(v11) &
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v5) & ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v15, v1)) |
% 260.06/41.47 | (hAPP(v4, v2) = v7 & $i(v7) & ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v7, v3))))))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_lemma__NBseq__def) implies:
% 260.06/41.47 | (173) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.47 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 260.06/41.47 | ~ (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.47 | class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ?
% 260.06/41.47 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) &
% 260.06/41.47 | $i(v5) & ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 &
% 260.06/41.47 | c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7)
% 260.06/41.47 | = v8 & $i(v9) & $i(v8) & $i(v6) & ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9,
% 260.06/41.47 | v6)) | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.06/41.47 | v0, v5) & ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : (
% 260.06/41.47 | ~ (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~
% 260.06/41.47 | (hAPP(v1, v10) = v11) | ~ $i(v10) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 260.06/41.47 | v5)))))) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 260.06/41.47 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 260.06/41.47 | class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : ?
% 260.06/41.47 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 260.06/41.47 | : ($i(v7) & $i(v4) & ((c_Nat_OSuc(v4) = v5 &
% 260.06/41.47 | c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 & $i(v6) & $i(v5) &
% 260.06/41.47 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 260.06/41.47 | (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~
% 260.06/41.47 | (hAPP(v1, v10) = v11) | ~ $i(v10) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 260.06/41.47 | v6))) | (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 &
% 260.06/41.47 | hAPP(v1, v7) = v8 & $i(v9) & $i(v8) & ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9,
% 260.06/41.47 | v3))))))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_lemma__NBseq__def2) implies:
% 260.06/41.47 | (174) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.47 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 260.06/41.47 | ~ (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.47 | class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ?
% 260.06/41.47 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) &
% 260.06/41.47 | $i(v5) & ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 &
% 260.06/41.47 | c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7)
% 260.06/41.47 | = v8 & $i(v9) & $i(v8) & $i(v6) & ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v6)) |
% 260.06/41.47 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & !
% 260.06/41.47 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 260.06/41.47 | (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~
% 260.06/41.47 | (hAPP(v1, v10) = v11) | ~ $i(v10) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 260.06/41.47 | v5)))))) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 260.06/41.47 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 260.06/41.47 | class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : ?
% 260.06/41.47 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 260.06/41.47 | : ($i(v7) & $i(v4) & ((c_Nat_OSuc(v4) = v5 &
% 260.06/41.47 | c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 & $i(v6) & $i(v5) &
% 260.06/41.47 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 260.06/41.47 | (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~
% 260.06/41.47 | (hAPP(v1, v10) = v11) | ~ $i(v10) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12,
% 260.06/41.47 | v6))) | (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 &
% 260.06/41.47 | hAPP(v1, v7) = v8 & $i(v9) & $i(v8) & ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9,
% 260.06/41.47 | v3))))))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_zero__less__Suc) implies:
% 260.06/41.47 | (175) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.47 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1)
% 260.06/41.47 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_mult__eq__1__iff) implies:
% 260.06/41.47 | (176) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 260.06/41.47 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) &
% 260.06/41.47 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~
% 260.06/41.47 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~
% 260.06/41.47 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v2 | ~
% 260.06/41.47 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~
% 260.06/41.47 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (hAPP(v3, v2)
% 260.06/41.47 | = v4) | ~ (hAPP(v0, v2) = v3)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_One__nat__def) implies:
% 260.06/41.47 | (177) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 &
% 260.06/41.47 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_Suc__eq__plus1) implies:
% 260.06/41.47 | (178) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 260.06/41.47 | ! [v1: $i] : ! [v2: $i] : ( ~
% 260.06/41.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~
% 260.06/41.47 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2))))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_Suc__eq__plus1__left) implies:
% 260.06/41.47 | (179) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 260.06/41.47 | ! [v1: $i] : ! [v2: $i] : ( ~
% 260.06/41.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~
% 260.06/41.47 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2))))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_diff__Suc__1) implies:
% 260.06/41.47 | (180) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 260.06/41.47 | ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) |
% 260.06/41.47 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v1))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_diff__Suc__eq__diff__pred) implies:
% 260.06/41.47 | (181) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 260.06/41.47 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.47 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~
% 260.06/41.47 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~
% 260.06/41.47 | $i(v2) | ~ $i(v1) | ? [v5: $i] : (c_Nat_OSuc(v1) = v5 &
% 260.06/41.47 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) = v4 &
% 260.06/41.47 | $i(v5) & $i(v4))))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_nat_Osimps_I3_J) implies:
% 260.06/41.47 | (182) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.47 | & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_less__Suc__eq) implies:
% 260.06/41.47 | (183) ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_one__is__add) implies:
% 260.06/41.47 | (184) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.47 | ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 260.06/41.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~
% 260.06/41.47 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 =
% 260.06/41.47 | v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) |
% 260.06/41.47 | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 |
% 260.06/41.47 | v2 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) =
% 260.06/41.47 | v1) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2
% 260.06/41.47 | = v1 | v2 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3,
% 260.06/41.47 | v2) = v1) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : (v2 = v1 |
% 260.06/41.47 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & !
% 260.06/41.47 | [v2: $i] : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 260.06/41.47 | v0, v1) = v2)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_nat__lt__two__imp__zero__or__one) implies:
% 260.06/41.47 | (185) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 260.06/41.47 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 260.06/41.47 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 260.06/41.47 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_less__Suc__eq__0__disj) implies:
% 260.06/41.47 | (186) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.47 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.47 | (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~
% 260.06/41.47 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v1: $i]
% 260.06/41.47 | : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (c_Nat_OSuc(v1) = v3) |
% 260.06/41.47 | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4: $i]
% 260.06/41.47 | : (c_Nat_OSuc(v4) = v2 & $i(v4) &
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1:
% 260.06/41.47 | $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) |
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_less__Suc0) implies:
% 260.06/41.47 | (187) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] :
% 260.06/41.47 | (v2 = v0 | ~ $i(v2) | ~
% 260.06/41.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)))
% 260.06/41.47 |
% 260.06/41.47 | ALPHA: (fact_gr0__conv__Suc) implies:
% 260.06/41.47 | (188) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.47 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2)
% 260.06/41.47 | | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))
% 260.06/41.47 | & ! [v1: $i] : ( ~ $i(v1) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v2: $i]
% 260.06/41.48 | : (c_Nat_OSuc(v2) = v1 & $i(v2))))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_nat__power__eq__Suc__0__iff) implies:
% 260.06/41.48 | (189) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 260.06/41.48 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~
% 260.06/41.48 | (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & !
% 260.06/41.48 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v1)
% 260.06/41.48 | = v5) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3)) & ! [v3: $i] : !
% 260.06/41.48 | [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3) =
% 260.06/41.48 | v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_power__Suc__0) implies:
% 260.06/41.48 | (190) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 260.06/41.48 | (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0
% 260.06/41.48 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3
% 260.06/41.48 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] :
% 260.06/41.48 | (v5 = v2 | ~ (hAPP(v3, v4) = v5) | ~ $i(v4)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_n__less__m__mult__n) implies:
% 260.06/41.48 | (191) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.48 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 260.06/41.48 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~
% 260.06/41.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 260.06/41.48 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_n__less__n__mult__m) implies:
% 260.06/41.48 | (192) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.48 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 260.06/41.48 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~
% 260.06/41.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 260.06/41.48 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_one__less__mult) implies:
% 260.06/41.48 | (193) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.48 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 260.06/41.48 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~
% 260.06/41.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 260.06/41.48 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_Suc__pred) implies:
% 260.06/41.48 | (194) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.48 | ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.48 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 260.06/41.48 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 260.06/41.48 | c_Nat_OSuc(v3) = v2))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_diff__Suc__less) implies:
% 260.06/41.48 | (195) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.48 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.48 | (c_Nat_OSuc(v1) = v3) | ~
% 260.06/41.48 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~
% 260.06/41.48 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_one__le__mult__iff) implies:
% 260.06/41.48 | (196) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.48 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 260.06/41.48 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~
% 260.06/41.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1,
% 260.06/41.48 | v6) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)) &
% 260.06/41.48 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.06/41.48 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~
% 260.06/41.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1,
% 260.06/41.48 | v6) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) &
% 260.06/41.48 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.06/41.48 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~
% 260.06/41.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1,
% 260.06/41.48 | v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)
% 260.06/41.48 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_real__of__nat__Suc__gt__zero) implies:
% 260.06/41.48 | (197) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.48 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~
% 260.06/41.48 | $i(v1) | ? [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 260.06/41.48 | $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.06/41.48 | v3))))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_real__of__nat__one) implies:
% 260.06/41.48 | (198) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.48 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 &
% 260.06/41.48 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 260.06/41.48 | $i(v0))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_real__of__nat__Suc) implies:
% 260.06/41.48 | (199) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 260.06/41.48 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 260.06/41.48 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ? [v3: $i]
% 260.06/41.48 | : ? [v4: $i] : (c_Nat_OSuc(v1) = v3 &
% 260.06/41.48 | c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 &
% 260.06/41.48 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v0) = v4 &
% 260.06/41.48 | $i(v4) & $i(v3))))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_nat__one__le__power) implies:
% 260.06/41.48 | (200) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.48 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 260.06/41.48 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~
% 260.06/41.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1,
% 260.06/41.48 | v4) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_Suc__pred_H) implies:
% 260.06/41.48 | (201) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 260.06/41.48 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.48 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 260.06/41.48 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 260.06/41.48 | c_Nat_OSuc(v3) = v2))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_add__eq__if) implies:
% 260.06/41.48 | (202) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 260.06/41.48 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 260.06/41.48 | (v3 = v0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) =
% 260.06/41.48 | v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) =
% 260.06/41.48 | v5) | ~ $i(v3) | ~ $i(v2) | ? [v6: $i] : (c_Nat_OSuc(v5) =
% 260.06/41.48 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v6 &
% 260.06/41.48 | $i(v6))) & ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 260.06/41.48 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = v3) | ~
% 260.06/41.48 | $i(v2)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_realpow__two__diff) implies:
% 260.06/41.48 | (203) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 260.06/41.48 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 260.06/41.48 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 260.06/41.48 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 260.06/41.48 | [v10: $i] : ! [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v5) =
% 260.06/41.48 | v6) | ~ (c_Groups_Ominus__class_Ominus(v5, v8, v10) = v11) |
% 260.06/41.48 | ~ (hAPP(v9, v2) = v10) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6,
% 260.06/41.48 | v4) = v7) | ~ (hAPP(v6, v3) = v9) | ~ $i(v5) | ~ $i(v4) |
% 260.06/41.48 | ~ $i(v3) | ~ class_Rings_Ocomm__ring__1(v5) | ? [v12: $i] : ?
% 260.06/41.48 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 260.06/41.48 | (c_Groups_Ominus__class_Ominus(v5, v4, v3) = v13 &
% 260.06/41.48 | c_Groups_Otimes__class_Otimes(v5) = v12 &
% 260.06/41.48 | c_Groups_Oplus__class_Oplus(v5, v4, v3) = v15 & hAPP(v14, v15)
% 260.06/41.48 | = v11 & hAPP(v12, v13) = v14 & $i(v15) & $i(v14) & $i(v13) &
% 260.06/41.48 | $i(v12) & $i(v11))))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_reals__Archimedean4) implies:
% 260.06/41.48 | (204) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.48 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 260.06/41.48 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 260.06/41.48 | : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (c_Nat_OSuc(v4) =
% 260.06/41.48 | v8 & c_RealDef_Oreal(tc_Nat_Onat, v8) = v9 &
% 260.06/41.48 | c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & hAPP(v10, v3) = v11 &
% 260.06/41.48 | hAPP(v6, v3) = v7 & hAPP(v1, v9) = v10 & hAPP(v1, v5) = v6 &
% 260.06/41.48 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 260.06/41.48 | & $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 260.06/41.48 | v11) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.06/41.48 | v7, v2))))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_int__power__div__base) implies:
% 260.06/41.48 | (205) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 260.06/41.48 | (c_Nat_OSuc(v0) = v3 & c_Power_Opower__class_Opower(tc_Int_Oint) = v2
% 260.06/41.48 | & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) &
% 260.06/41.48 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 260.06/41.48 | $i] : ! [v8: $i] : ( ~
% 260.06/41.48 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v3) = v7) | ~
% 260.06/41.48 | (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v4) = v6) | ~ $i(v5) | ~
% 260.06/41.48 | $i(v4) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) |
% 260.06/41.48 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v9:
% 260.06/41.48 | $i] : (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v9, v4) = v8 &
% 260.06/41.48 | hAPP(v6, v5) = v9 & $i(v9) & $i(v8))))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_reals__Archimedean6a) implies:
% 260.06/41.48 | (206) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.06/41.48 | $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ?
% 260.06/41.48 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 260.06/41.48 | (c_Nat_OSuc(v2) = v4 & c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 &
% 260.06/41.48 | c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v5) & $i(v4) &
% 260.06/41.48 | $i(v3) & $i(v2) &
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) &
% 260.06/41.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_div__1) implies:
% 260.06/41.48 | (207) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.48 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 260.06/41.48 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~
% 260.06/41.48 | $i(v2)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_div__less) implies:
% 260.06/41.48 | (208) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.48 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 260.06/41.48 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~
% 260.06/41.48 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_nat__mult__div__cancel__disj) implies:
% 260.06/41.48 | (209) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.48 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 260.06/41.48 | : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~
% 260.06/41.48 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) | ~
% 260.06/41.48 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) =
% 260.06/41.48 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 260.06/41.48 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8)))
% 260.06/41.48 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 260.06/41.48 | $i] : ! [v7: $i] : (v7 = v0 | ~
% 260.06/41.48 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v6) = v7) | ~
% 260.06/41.48 | (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v1, v0) =
% 260.06/41.48 | v4) | ~ $i(v3) | ~ $i(v2)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_div__le__mono2) implies:
% 260.06/41.48 | (210) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.48 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 260.06/41.48 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v3) = v5)
% 260.06/41.48 | | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v4) | ~
% 260.06/41.48 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 260.06/41.48 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_div__mult__self1__is__m) implies:
% 260.06/41.48 | (211) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.48 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 260.06/41.48 | : (v6 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) =
% 260.06/41.48 | v6) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~
% 260.06/41.48 | $i(v3) | ~ $i(v2) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_div__mult__self__is__m) implies:
% 260.06/41.48 | (212) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.48 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 260.06/41.48 | : (v6 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) =
% 260.06/41.48 | v6) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~
% 260.06/41.48 | $i(v3) | ~ $i(v2) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_nat__mult__div__cancel1) implies:
% 260.06/41.48 | (213) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 260.06/41.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.48 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 260.06/41.48 | : ! [v7: $i] : ! [v8: $i] : ( ~
% 260.06/41.48 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) | ~
% 260.06/41.48 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) =
% 260.06/41.48 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 260.06/41.48 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8))))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_div__less__dividend) implies:
% 260.06/41.48 | (214) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 260.06/41.48 | v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) &
% 260.06/41.48 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.48 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~
% 260.06/41.48 | $i(v3) | ~ $i(v2) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 260.06/41.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 260.06/41.48 |
% 260.06/41.48 | ALPHA: (fact_div__if) implies:
% 260.06/41.49 | (215) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.49 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~
% 260.06/41.49 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~
% 260.06/41.49 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v5: $i]
% 260.06/41.49 | : ? [v6: $i] : (( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.49 | v1, v2) | (v5 = v0 &
% 260.06/41.49 | c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v0)) &
% 260.06/41.49 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | (v6 = v5
% 260.06/41.49 | & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 &
% 260.06/41.49 | c_Nat_OSuc(v4) = v5 & $i(v5))))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_div__geq) implies:
% 260.06/41.49 | (216) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.49 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~
% 260.06/41.49 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~
% 260.06/41.49 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v5: $i]
% 260.06/41.49 | : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 &
% 260.06/41.49 | c_Nat_OSuc(v4) = v5 & $i(v5))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_split__div) implies:
% 260.06/41.49 | (217) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.49 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 260.06/41.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.49 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 260.06/41.49 | : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~
% 260.06/41.49 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 260.06/41.49 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : (( ~ (v2 = v0) |
% 260.06/41.49 | (hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7))) & (v2 = v0 |
% 260.06/41.49 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : !
% 260.06/41.49 | [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 260.06/41.49 | v11, v10) = v3) | ~ (hAPP(v8, v9) = v11) | ~
% 260.06/41.49 | $i(v10) | ~ $i(v9) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) | ?
% 260.06/41.49 | [v12: $i] : (hAPP(v4, v9) = v12 & $i(v12) &
% 260.06/41.49 | hBOOL(v12))))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 260.06/41.49 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~
% 260.06/41.49 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 260.06/41.49 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 260.06/41.49 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v10) &
% 260.06/41.49 | $i(v9) & ((v12 = v3 & ~ (v2 = v0) &
% 260.06/41.49 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) = v3 &
% 260.06/41.49 | hAPP(v8, v9) = v11 & hAPP(v4, v9) = v13 & hAPP(v1, v2) = v8
% 260.06/41.49 | & $i(v13) & $i(v11) & $i(v8) &
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) & ~
% 260.06/41.49 | hBOOL(v13)) | (v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & ~
% 260.06/41.49 | hBOOL(v7))))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_split__div__lemma) implies:
% 260.06/41.49 | (218) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.49 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 260.06/41.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.49 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 260.06/41.49 | : ! [v7: $i] : ! [v8: $i] : ( ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v4) = v8) | ~
% 260.06/41.49 | (c_Nat_OSuc(v3) = v6) | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v1, v4)
% 260.06/41.49 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ? [v9: $i]
% 260.06/41.49 | : (( ~ (v8 = v3) | (hAPP(v5, v3) = v9 & $i(v9) &
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v7) &
% 260.06/41.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v2))) &
% 260.06/41.49 | (v8 = v3 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2,
% 260.06/41.49 | v7) | (hAPP(v5, v3) = v9 & $i(v9) & ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v2))))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_split__div_H) implies:
% 260.06/41.49 | (219) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.49 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 260.06/41.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.49 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 260.06/41.49 | : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~
% 260.06/41.49 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 260.06/41.49 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 260.06/41.49 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v9) &
% 260.06/41.49 | ((v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7)) |
% 260.06/41.49 | (c_Nat_OSuc(v9) = v11 & hAPP(v8, v11) = v12 & hAPP(v8, v9) =
% 260.06/41.49 | v10 & hAPP(v4, v9) = v13 & hAPP(v1, v2) = v8 & $i(v13) &
% 260.06/41.49 | $i(v12) & $i(v11) & $i(v10) & $i(v8) & hBOOL(v13) &
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v12) &
% 260.06/41.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v10, v3)))))
% 260.06/41.49 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 260.06/41.49 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5)
% 260.06/41.49 | | ~ (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 260.06/41.49 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : (hAPP(v1, v2) = v8 &
% 260.06/41.49 | $i(v8) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 260.06/41.49 | (c_Nat_OSuc(v9) = v10) | ~ (hAPP(v8, v10) = v11) | ~ $i(v9)
% 260.06/41.49 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v11) | ?
% 260.06/41.49 | [v12: $i] : ? [v13: $i] : ((hAPP(v8, v9) = v12 & $i(v12) &
% 260.06/41.49 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v12,
% 260.06/41.49 | v3)) | (hAPP(v4, v9) = v13 & $i(v13) & ~ hBOOL(v13))))
% 260.06/41.49 | & ( ~ (v2 = v0) | (hAPP(v4, v0) = v7 & $i(v7) & ~
% 260.06/41.49 | hBOOL(v7))))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_le__div__geq) implies:
% 260.06/41.49 | (220) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.49 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~
% 260.06/41.49 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~
% 260.06/41.49 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5:
% 260.06/41.49 | $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 &
% 260.06/41.49 | c_Nat_OSuc(v4) = v5 & $i(v5))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_natfloor__div__nat) implies:
% 260.06/41.49 | (221) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.49 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 260.06/41.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) &
% 260.06/41.49 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 260.06/41.49 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5)
% 260.06/41.49 | | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v4) | ~ $i(v3) | ~
% 260.06/41.49 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 260.06/41.49 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 260.06/41.49 | ? [v6: $i] : ? [v7: $i] :
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v2) = v6 &
% 260.06/41.49 | c_RComplete_Onatfloor(v5) = v6 & c_RComplete_Onatfloor(v3) = v7
% 260.06/41.49 | & $i(v7) & $i(v6))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_div__Suc) implies:
% 260.06/41.49 | (222) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.49 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 260.06/41.49 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 260.06/41.49 | $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v7)
% 260.06/41.49 | | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v8) | ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v9, v2) = v10) | ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5) | ~
% 260.06/41.49 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, v8) = v9) | ~
% 260.06/41.49 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v10) = v11) | ~
% 260.06/41.49 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v5) = v6) | ~
% 260.06/41.49 | $i(v3) | ~ $i(v2) | ? [v12: $i] :
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v12, v2) = v11 &
% 260.06/41.49 | c_Nat_OSuc(v3) = v12 & $i(v12) & $i(v11))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_real__of__nat__div__aux) implies:
% 260.06/41.49 | (223) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.49 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 260.06/41.49 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 260.06/41.49 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v7, v3) = v8)
% 260.06/41.49 | | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v6) | ~
% 260.06/41.49 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v4) | ~
% 260.06/41.49 | (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~
% 260.06/41.49 | (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5) | ~
% 260.06/41.49 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 260.06/41.49 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v8) = v9) | ~
% 260.06/41.49 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v10: $i]
% 260.06/41.49 | : (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v10, v3) =
% 260.06/41.49 | v9 & c_RealDef_Oreal(tc_Nat_Onat, v1) = v10 & $i(v10) &
% 260.06/41.49 | $i(v9))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_mod__eq__0__iff) implies:
% 260.06/41.49 | (224) ? [v0: $i] : ? [v1: $i] :
% 260.06/41.49 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 260.06/41.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.49 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~
% 260.06/41.49 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v4) | ~
% 260.06/41.49 | $i(v3) | ~ $i(v2) | ? [v5: $i] : (hAPP(v1, v2) = v5 & $i(v5) &
% 260.06/41.49 | ! [v6: $i] : ( ~ (hAPP(v5, v6) = v3) | ~ $i(v6)))) & ! [v2:
% 260.06/41.49 | $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat,
% 260.06/41.49 | v3, v2) = v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ? [v5:
% 260.06/41.49 | $i] : (hAPP(v4, v5) = v3 & hAPP(v1, v2) = v4 & $i(v5) &
% 260.06/41.49 | $i(v4))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_mod__less__divisor) implies:
% 260.06/41.49 | (225) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.49 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.49 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~
% 260.06/41.49 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_mod__Suc) implies:
% 260.06/41.49 | (226) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.49 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0
% 260.06/41.49 | | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~
% 260.06/41.49 | (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ?
% 260.06/41.49 | [v6: $i] : ( ~ (v6 = v1) &
% 260.06/41.49 | c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v5 &
% 260.06/41.49 | c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5))) & ! [v1: $i] : ! [v2:
% 260.06/41.49 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.06/41.49 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~
% 260.06/41.49 | (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ?
% 260.06/41.49 | [v6: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v5
% 260.06/41.49 | & c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5) & (v6 = v4 | v6 =
% 260.06/41.49 | v1))))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_mod__1) implies:
% 260.06/41.49 | (227) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 260.06/41.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 260.06/41.49 | ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 260.06/41.49 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v3) | ~
% 260.06/41.49 | $i(v2)))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (fact_mod__le__divisor) implies:
% 260.06/41.49 | (228) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 260.06/41.49 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.49 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~
% 260.06/41.49 | $i(v2) | ~ $i(v1) | ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 260.06/41.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_Nat__Onat__Rings_Olinordered__semidom) implies:
% 260.06/41.49 | (229) class_Rings_Olinordered__semidom(tc_Nat_Onat)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_Nat__Onat__Rings_Ocomm__semiring__1) implies:
% 260.06/41.49 | (230) class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_Nat__Onat__Rings_Ozero__neq__one) implies:
% 260.06/41.49 | (231) class_Rings_Ozero__neq__one(tc_Nat_Onat)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_Nat__Onat__Power_Opower) implies:
% 260.06/41.49 | (232) class_Power_Opower(tc_Nat_Onat)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_Nat__Onat__Groups_Oone) implies:
% 260.06/41.49 | (233) $i(tc_Nat_Onat)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)
% 260.06/41.49 | implies:
% 260.06/41.49 | (234) class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) implies:
% 260.06/41.49 | (235) class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) implies:
% 260.06/41.49 | (236) class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) implies:
% 260.06/41.49 | (237) class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_RealDef__Oreal__RealVector_Oreal__normed__vector) implies:
% 260.06/41.49 | (238) class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_RealDef__Oreal__Rings_Olinordered__semidom) implies:
% 260.06/41.49 | (239) class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_RealDef__Oreal__Groups_Oab__semigroup__add) implies:
% 260.06/41.49 | (240) class_Groups_Oab__semigroup__add(tc_RealDef_Oreal)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_RealDef__Oreal__Rings_Ocomm__semiring__1) implies:
% 260.06/41.49 | (241) class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) implies:
% 260.06/41.49 | (242) class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (conj_0) implies:
% 260.06/41.49 | (243) $i(tc_Complex_Ocomplex)
% 260.06/41.49 | (244) $i(tc_RealDef_Oreal)
% 260.06/41.49 | (245) $i(v_r____)
% 260.06/41.49 | (246) $i(v_z____)
% 260.06/41.49 | (247) ? [v0: $i] : (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 260.06/41.49 | v_z____) = v0 & $i(v0) & ~
% 260.06/41.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r____, v0))
% 260.06/41.49 |
% 260.06/41.49 | ALPHA: (function-axioms) implies:
% 260.06/41.49 | (248) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 260.06/41.49 | (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 260.06/41.49 | (c_Groups_Ozero__class_Ozero(v2) = v0))
% 260.06/41.49 | (249) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 260.06/41.49 | (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 260.06/41.49 | (c_Groups_Oone__class_Oone(v2) = v0))
% 260.06/41.49 | (250) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 260.06/41.49 | (c_Power_Opower__class_Opower(v2) = v1) | ~
% 260.06/41.49 | (c_Power_Opower__class_Opower(v2) = v0))
% 260.06/41.49 | (251) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 260.06/41.49 | (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0))
% 260.06/41.50 | (252) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 260.06/41.50 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 260.06/41.50 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v0))
% 260.06/41.50 | (253) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 260.06/41.50 | (c_RealDef_Oreal(v3, v2) = v1) | ~ (c_RealDef_Oreal(v3, v2) = v0))
% 260.06/41.50 | (254) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 260.06/41.50 | (v1 = v0 | ~ (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 260.06/41.50 | (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0))
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (247) with fresh symbol all_648_0 gives:
% 260.06/41.50 | (255) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____) =
% 260.06/41.50 | all_648_0 & $i(all_648_0) & ~
% 260.06/41.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r____,
% 260.06/41.50 | all_648_0)
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (255) implies:
% 260.06/41.50 | (256) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r____,
% 260.06/41.50 | all_648_0)
% 260.06/41.50 | (257) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____) =
% 260.06/41.50 | all_648_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (182) with fresh symbol all_650_0 gives:
% 260.06/41.50 | (258) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_650_0 & $i(all_650_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_650_0) | ~ $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (258) implies:
% 260.06/41.50 | (259) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_650_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (45) with fresh symbol all_659_0 gives:
% 260.06/41.50 | (260) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_659_0 & $i(all_659_0)
% 260.06/41.50 | & ? [v0: $i] : ( ~ $i(v0) |
% 260.06/41.50 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_659_0, v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (260) implies:
% 260.06/41.50 | (261) $i(all_659_0)
% 260.06/41.50 | (262) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_659_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (182) with fresh symbol all_661_0 gives:
% 260.06/41.50 | (263) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_661_0 & $i(all_661_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_661_0) | ~ $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (263) implies:
% 260.06/41.50 | (264) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_661_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (182) with fresh symbol all_664_0 gives:
% 260.06/41.50 | (265) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_664_0 & $i(all_664_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_664_0) | ~ $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (265) implies:
% 260.06/41.50 | (266) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_664_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (182) with fresh symbol all_667_0 gives:
% 260.06/41.50 | (267) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_667_0 & $i(all_667_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_667_0) | ~ $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (267) implies:
% 260.06/41.50 | (268) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_667_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (182) with fresh symbol all_670_0 gives:
% 260.06/41.50 | (269) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_670_0 & $i(all_670_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_670_0) | ~ $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (269) implies:
% 260.06/41.50 | (270) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_670_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (71) with fresh symbol all_673_0 gives:
% 260.06/41.50 | (271) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_673_0 & $i(all_673_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 260.06/41.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_673_0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (271) implies:
% 260.06/41.50 | (272) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_673_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (71) with fresh symbol all_676_0 gives:
% 260.06/41.50 | (273) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_676_0 & $i(all_676_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 260.06/41.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_676_0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (273) implies:
% 260.06/41.50 | (274) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_676_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (182) with fresh symbol all_679_0 gives:
% 260.06/41.50 | (275) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_679_0 & $i(all_679_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_679_0) | ~ $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (275) implies:
% 260.06/41.50 | (276) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_679_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (45) with fresh symbol all_682_0 gives:
% 260.06/41.50 | (277) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_682_0 & $i(all_682_0)
% 260.06/41.50 | & ? [v0: $i] : ( ~ $i(v0) |
% 260.06/41.50 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_682_0, v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (277) implies:
% 260.06/41.50 | (278) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_682_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (71) with fresh symbol all_686_0 gives:
% 260.06/41.50 | (279) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_686_0 & $i(all_686_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 260.06/41.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_686_0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (279) implies:
% 260.06/41.50 | (280) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_686_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (71) with fresh symbol all_692_0 gives:
% 260.06/41.50 | (281) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_692_0 & $i(all_692_0)
% 260.06/41.50 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 260.06/41.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_692_0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (281) implies:
% 260.06/41.50 | (282) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_692_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (43) with fresh symbol all_695_0 gives:
% 260.06/41.50 | (283) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_695_0 & $i(all_695_0)
% 260.06/41.50 | & ! [v0: $i] : ! [v1: int] : (v1 = all_695_0 | ~
% 260.06/41.50 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, all_695_0, v0) = v1) |
% 260.06/41.50 | ~ $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (283) implies:
% 260.06/41.50 | (284) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_695_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (74) with fresh symbol all_698_0 gives:
% 260.06/41.50 | (285) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_698_0 & $i(all_698_0)
% 260.06/41.50 | & ? [v0: any] : (v0 = all_698_0 | ~ $i(v0) |
% 260.06/41.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_698_0, v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (285) implies:
% 260.06/41.50 | (286) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_698_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (48) with fresh symbol all_700_0 gives:
% 260.06/41.50 | (287) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_700_0 & $i(all_700_0)
% 260.06/41.50 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 260.06/41.50 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_700_0) = v1) | ~
% 260.06/41.50 | $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (287) implies:
% 260.06/41.50 | (288) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_700_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (180) with fresh symbol all_705_0 gives:
% 260.06/41.50 | (289) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_705_0 & $i(all_705_0) &
% 260.06/41.50 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 260.06/41.50 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_705_0) = v0)
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (289) implies:
% 260.06/41.50 | (290) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_705_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (46) with fresh symbol all_710_0 gives:
% 260.06/41.50 | (291) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_710_0 & $i(all_710_0)
% 260.06/41.50 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 260.06/41.50 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_710_0, v0) = v1) | ~
% 260.06/41.50 | $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (291) implies:
% 260.06/41.50 | (292) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_710_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (6) with fresh symbols all_713_0, all_713_1 gives:
% 260.06/41.50 | (293) ~ (all_713_0 = all_713_1) &
% 260.06/41.50 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_713_0 &
% 260.06/41.50 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_713_1 &
% 260.06/41.50 | $i(all_713_0) & $i(all_713_1)
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (293) implies:
% 260.06/41.50 | (294) ~ (all_713_0 = all_713_1)
% 260.06/41.50 | (295) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_713_1
% 260.06/41.50 | (296) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_713_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (84) with fresh symbols all_720_0, all_720_1 gives:
% 260.06/41.50 | (297) c_RComplete_Onatceiling(all_720_1) = all_720_0 &
% 260.06/41.50 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_720_0 &
% 260.06/41.50 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_720_1 &
% 260.06/41.50 | $i(all_720_0) & $i(all_720_1)
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (297) implies:
% 260.06/41.50 | (298) $i(all_720_1)
% 260.06/41.50 | (299) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_720_1
% 260.06/41.50 | (300) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_720_0
% 260.06/41.50 | (301) c_RComplete_Onatceiling(all_720_1) = all_720_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (90) with fresh symbols all_722_0, all_722_1 gives:
% 260.06/41.50 | (302) c_RComplete_Onatfloor(all_722_1) = all_722_0 &
% 260.06/41.50 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_722_0 &
% 260.06/41.50 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_722_1 &
% 260.06/41.50 | $i(all_722_0) & $i(all_722_1)
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (302) implies:
% 260.06/41.50 | (303) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_722_1
% 260.06/41.50 | (304) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_722_0
% 260.06/41.50 | (305) c_RComplete_Onatfloor(all_722_1) = all_722_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (89) with fresh symbol all_724_0 gives:
% 260.06/41.50 | (306) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_724_0 & $i(all_724_0)
% 260.06/41.50 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0) = v1) |
% 260.06/41.50 | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.06/41.50 | all_724_0, v1))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (306) implies:
% 260.06/41.50 | (307) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_724_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (49) with fresh symbol all_727_0 gives:
% 260.06/41.50 | (308) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_727_0 & $i(all_727_0)
% 260.06/41.50 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 260.06/41.50 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_727_0) = v1) |
% 260.06/41.50 | ~ $i(v0))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (308) implies:
% 260.06/41.50 | (309) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_727_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (83) with fresh symbol all_730_0 gives:
% 260.06/41.50 | (310) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_730_0 & $i(all_730_0)
% 260.06/41.50 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatceiling(v0) = v1)
% 260.06/41.50 | | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.06/41.50 | all_730_0, v1))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (310) implies:
% 260.06/41.50 | (311) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_730_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (88) with fresh symbols all_733_0, all_733_1 gives:
% 260.06/41.50 | (312) c_RComplete_Onatfloor(all_733_1) = all_733_0 &
% 260.06/41.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_733_0 &
% 260.06/41.50 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_733_1 &
% 260.06/41.50 | $i(all_733_0) & $i(all_733_1)
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (312) implies:
% 260.06/41.50 | (313) $i(all_733_1)
% 260.06/41.50 | (314) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_733_1
% 260.06/41.50 | (315) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_733_0
% 260.06/41.50 | (316) c_RComplete_Onatfloor(all_733_1) = all_733_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (96) with fresh symbol all_735_0 gives:
% 260.06/41.50 | (317) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_735_0 &
% 260.06/41.50 | $i(all_735_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.50 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) |
% 260.06/41.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_735_0, v1))
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (317) implies:
% 260.06/41.50 | (318) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_735_0
% 260.06/41.50 |
% 260.06/41.50 | DELTA: instantiating (159) with fresh symbols all_742_0, all_742_1 gives:
% 260.06/41.50 | (319) c_Transcendental_Oln(all_742_1) = all_742_0 &
% 260.06/41.50 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_742_1 &
% 260.06/41.50 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_742_0 &
% 260.06/41.50 | $i(all_742_0) & $i(all_742_1)
% 260.06/41.50 |
% 260.06/41.50 | ALPHA: (319) implies:
% 260.06/41.50 | (320) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_742_0
% 260.06/41.51 | (321) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_742_1
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (82) with fresh symbols all_755_0, all_755_1 gives:
% 260.06/41.51 | (322) c_RComplete_Onatceiling(all_755_1) = all_755_0 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_755_0 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_755_1 &
% 260.06/41.51 | $i(all_755_0) & $i(all_755_1)
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (322) implies:
% 260.06/41.51 | (323) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_755_1
% 260.06/41.51 | (324) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_755_0
% 260.06/41.51 | (325) c_RComplete_Onatceiling(all_755_1) = all_755_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (100) with fresh symbol all_759_0 gives:
% 260.06/41.51 | (326) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_759_0 &
% 260.06/41.51 | $i(all_759_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.51 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ~
% 260.06/41.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_759_0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (326) implies:
% 260.06/41.51 | (327) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_759_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (177) with fresh symbols all_770_0, all_770_1 gives:
% 260.06/41.51 | (328) c_Nat_OSuc(all_770_0) = all_770_1 &
% 260.06/41.51 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_770_1 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_770_0 & $i(all_770_0)
% 260.06/41.51 | & $i(all_770_1)
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (328) implies:
% 260.06/41.51 | (329) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_770_0
% 260.06/41.51 | (330) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_770_1
% 260.06/41.51 | (331) c_Nat_OSuc(all_770_0) = all_770_1
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (51) with fresh symbol all_772_0 gives:
% 260.06/41.51 | (332) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_772_0 & $i(all_772_0)
% 260.06/41.51 | & ! [v0: $i] : ! [v1: int] : (v1 = all_772_0 | ~
% 260.06/41.51 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v0) = v1) | ~
% 260.06/41.51 | $i(v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (332) implies:
% 260.06/41.51 | (333) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_772_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (175) with fresh symbol all_775_0 gives:
% 260.06/41.51 | (334) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_775_0 & $i(all_775_0)
% 260.06/41.51 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 260.06/41.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_775_0, v1))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (334) implies:
% 260.06/41.51 | (335) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_775_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (101) with fresh symbols all_778_0, all_778_1 gives:
% 260.06/41.51 | (336) c_RealDef_Oreal(tc_Nat_Onat, all_778_1) = all_778_0 &
% 260.06/41.51 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_778_1 &
% 260.06/41.51 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_778_0 &
% 260.06/41.51 | $i(all_778_0) & $i(all_778_1)
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (336) implies:
% 260.06/41.51 | (337) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_778_0
% 260.06/41.51 | (338) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_778_1
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (99) with fresh symbols all_780_0, all_780_1 gives:
% 260.06/41.51 | (339) c_RealDef_Oreal(tc_Nat_Onat, all_780_1) = all_780_0 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_780_1 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_780_0 &
% 260.06/41.51 | $i(all_780_0) & $i(all_780_1)
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (339) implies:
% 260.06/41.51 | (340) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_780_0
% 260.06/41.51 | (341) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_780_1
% 260.06/41.51 | (342) c_RealDef_Oreal(tc_Nat_Onat, all_780_1) = all_780_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (61) with fresh symbol all_786_0 gives:
% 260.06/41.51 | (343) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_786_0 & $i(all_786_0)
% 260.06/41.51 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_786_0, all_786_0)
% 260.06/41.51 | & ? [v0: any] : (v0 = all_786_0 | ~ $i(v0) |
% 260.06/41.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_786_0, v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (343) implies:
% 260.06/41.51 | (344) ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_786_0, all_786_0)
% 260.06/41.51 | (345) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_786_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (50) with fresh symbol all_788_0 gives:
% 260.06/41.51 | (346) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_788_0 & $i(all_788_0)
% 260.06/41.51 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_788_0,
% 260.06/41.51 | all_788_0) & ! [v0: any] : (v0 = all_788_0 | ~ $i(v0) | ~
% 260.06/41.51 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, all_788_0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (346) implies:
% 260.06/41.51 | (347) c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_788_0, all_788_0)
% 260.06/41.51 | (348) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_788_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (178) with fresh symbol all_797_0 gives:
% 260.06/41.51 | (349) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_797_0 & $i(all_797_0) &
% 260.06/41.51 | ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.51 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_797_0) = v1) | ~
% 260.06/41.51 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1)))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (349) implies:
% 260.06/41.51 | (350) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_797_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (60) with fresh symbol all_809_0 gives:
% 260.06/41.51 | (351) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_809_0 & $i(all_809_0)
% 260.06/41.51 | & ! [v0: any] : ! [v1: $i] : (v0 = all_809_0 | ~
% 260.06/41.51 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v1) | ~ $i(v1)
% 260.06/41.51 | | ~ $i(v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (351) implies:
% 260.06/41.51 | (352) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_809_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (179) with fresh symbol all_812_0 gives:
% 260.06/41.51 | (353) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_812_0 & $i(all_812_0) &
% 260.06/41.51 | ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.51 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_812_0, v0) = v1) | ~
% 260.06/41.51 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1)))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (353) implies:
% 260.06/41.51 | (354) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_812_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (156) with fresh symbol all_815_0 gives:
% 260.06/41.51 | (355) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_815_0 &
% 260.06/41.51 | $i(all_815_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.51 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_815_0, v0) |
% 260.06/41.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (355) implies:
% 260.06/41.51 | (356) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_815_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (228) with fresh symbol all_824_0 gives:
% 260.06/41.51 | (357) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_824_0 & $i(all_824_0)
% 260.06/41.51 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.06/41.51 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1)
% 260.06/41.51 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.51 | all_824_0, v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.06/41.51 | v2, v1))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (357) implies:
% 260.06/41.51 | (358) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_824_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (208) with fresh symbol all_827_0 gives:
% 260.06/41.51 | (359) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_827_0 & $i(all_827_0)
% 260.06/41.51 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_827_0 | ~
% 260.06/41.51 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)
% 260.06/41.51 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1,
% 260.06/41.51 | v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (359) implies:
% 260.06/41.51 | (360) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_827_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (197) with fresh symbol all_832_0 gives:
% 260.06/41.51 | (361) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_832_0 &
% 260.06/41.51 | $i(all_832_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1)
% 260.06/41.51 | | ~ $i(v0) | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2
% 260.06/41.51 | & $i(v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.06/41.51 | all_832_0, v2)))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (361) implies:
% 260.06/41.51 | (362) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_832_0
% 260.06/41.51 | (363) ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 260.06/41.51 | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v2) &
% 260.06/41.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_832_0, v2)))
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (57) with fresh symbol all_842_0 gives:
% 260.06/41.51 | (364) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_842_0 & $i(all_842_0)
% 260.06/41.51 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_842_0 | ~
% 260.06/41.51 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~
% 260.06/41.51 | $i(v1) | ~ $i(v0) | ~
% 260.06/41.51 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (364) implies:
% 260.06/41.51 | (365) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_842_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (7) with fresh symbol all_845_0 gives:
% 260.06/41.51 | (366) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_845_0 &
% 260.06/41.51 | $i(all_845_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.06/41.51 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 260.06/41.51 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) |
% 260.06/41.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_845_0, v2))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (366) implies:
% 260.06/41.51 | (367) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_845_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (29) with fresh symbol all_853_0 gives:
% 260.06/41.51 | (368) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_853_0 &
% 260.06/41.51 | $i(all_853_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.51 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 260.06/41.51 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 260.06/41.51 | all_853_0) = v2 & $i(v2) & ~
% 260.06/41.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (368) implies:
% 260.06/41.51 | (369) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_853_0
% 260.06/41.51 | (370) ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.51 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 260.06/41.51 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 260.06/41.51 | all_853_0) = v2 & $i(v2) & ~
% 260.06/41.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (151) with fresh symbols all_856_0, all_856_1 gives:
% 260.06/41.51 | (371) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_856_1 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_856_0 &
% 260.06/41.51 | $i(all_856_0) & $i(all_856_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 260.06/41.51 | all_856_0 | ~ (c_Complex_Orcis(all_856_1, v0) = v1) | ~ $i(v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (371) implies:
% 260.06/41.51 | (372) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_856_1
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (198) with fresh symbols all_861_0, all_861_1, all_861_2
% 260.06/41.51 | gives:
% 260.06/41.51 | (373) c_Nat_OSuc(all_861_2) = all_861_1 & c_RealDef_Oreal(tc_Nat_Onat,
% 260.06/41.51 | all_861_1) = all_861_0 &
% 260.06/41.51 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_861_0 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_861_2 & $i(all_861_0)
% 260.06/41.51 | & $i(all_861_1) & $i(all_861_2)
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (373) implies:
% 260.06/41.51 | (374) $i(all_861_1)
% 260.06/41.51 | (375) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_861_2
% 260.06/41.51 | (376) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_861_0
% 260.06/41.51 | (377) c_RealDef_Oreal(tc_Nat_Onat, all_861_1) = all_861_0
% 260.06/41.51 | (378) c_Nat_OSuc(all_861_2) = all_861_1
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (225) with fresh symbol all_875_0 gives:
% 260.06/41.51 | (379) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_875_0 & $i(all_875_0)
% 260.06/41.51 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.06/41.51 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1)
% 260.06/41.51 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.51 | all_875_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2,
% 260.06/41.51 | v1))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (379) implies:
% 260.06/41.51 | (380) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_875_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (227) with fresh symbols all_878_0, all_878_1 gives:
% 260.06/41.51 | (381) c_Nat_OSuc(all_878_1) = all_878_0 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_878_1 & $i(all_878_0)
% 260.06/41.51 | & $i(all_878_1) & ! [v0: $i] : ! [v1: int] : (v1 = all_878_1 | ~
% 260.06/41.51 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, all_878_0) = v1) | ~
% 260.06/41.51 | $i(v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (381) implies:
% 260.06/41.51 | (382) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_878_1
% 260.06/41.51 | (383) c_Nat_OSuc(all_878_1) = all_878_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (41) with fresh symbols all_881_0, all_881_1 gives:
% 260.06/41.51 | (384) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_881_1 &
% 260.06/41.51 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_881_0 & $i(all_881_0) &
% 260.06/41.51 | $i(all_881_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_881_1, v0)
% 260.06/41.51 | = v1) | ~ $i(v0) | hAPP(v1, all_881_0) = v0)
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (384) implies:
% 260.06/41.51 | (385) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_881_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (47) with fresh symbols all_884_0, all_884_1 gives:
% 260.06/41.51 | (386) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_884_1 &
% 260.06/41.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_884_0 & $i(all_884_0)
% 260.06/41.51 | & $i(all_884_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_884_1,
% 260.06/41.51 | v0) = v1) | ~ $i(v0) | hAPP(v1, all_884_0) = all_884_0)
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (386) implies:
% 260.06/41.51 | (387) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_884_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (52) with fresh symbol all_887_0 gives:
% 260.06/41.51 | (388) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_887_0 & $i(all_887_0)
% 260.06/41.51 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 260.06/41.51 | all_887_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2)
% 260.06/41.51 | = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) =
% 260.06/41.51 | v2) | ~ $i(v1) | ~ $i(v0))
% 260.06/41.51 |
% 260.06/41.51 | ALPHA: (388) implies:
% 260.06/41.51 | (389) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_887_0
% 260.06/41.51 |
% 260.06/41.51 | DELTA: instantiating (3) with fresh symbol all_890_0 gives:
% 260.06/41.52 | (390) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_890_0 &
% 260.06/41.52 | $i(all_890_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 260.06/41.52 | all_890_0 | ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 260.06/41.52 | (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~ $i(v0) | ~
% 260.06/41.52 | class_RealVector_Oreal__normed__algebra__1(v0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (390) implies:
% 260.06/41.52 | (391) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_890_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (26) with fresh symbol all_893_0 gives:
% 260.06/41.52 | (392) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_893_0 &
% 260.06/41.52 | $i(all_893_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.06/41.52 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 260.06/41.52 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 260.06/41.52 | all_893_0) | ~ class_RealVector_Oreal__normed__vector(v1))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (392) implies:
% 260.06/41.52 | (393) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_893_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (207) with fresh symbols all_902_0, all_902_1 gives:
% 260.06/41.52 | (394) c_Nat_OSuc(all_902_1) = all_902_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_902_1 & $i(all_902_0)
% 260.06/41.52 | & $i(all_902_1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 260.06/41.52 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, all_902_0) = v1) | ~
% 260.06/41.52 | $i(v0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (394) implies:
% 260.06/41.52 | (395) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_902_1
% 260.06/41.52 | (396) c_Nat_OSuc(all_902_1) = all_902_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (9) with fresh symbol all_911_0 gives:
% 260.06/41.52 | (397) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_911_0 &
% 260.06/41.52 | $i(all_911_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 260.06/41.52 | all_911_0 | ~ (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~
% 260.06/41.52 | (c_Groups_Ozero__class_Ozero(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.52 | class_RealVector_Oreal__normed__vector(v0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (397) implies:
% 260.06/41.52 | (398) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_911_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (194) with fresh symbols all_920_0, all_920_1 gives:
% 260.06/41.52 | (399) c_Nat_OSuc(all_920_1) = all_920_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_920_1 & $i(all_920_0)
% 260.06/41.52 | & $i(all_920_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_920_0) = v1) |
% 260.06/41.52 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_920_1,
% 260.06/41.52 | v0) | c_Nat_OSuc(v1) = v0)
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (399) implies:
% 260.06/41.52 | (400) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_920_1
% 260.06/41.52 | (401) c_Nat_OSuc(all_920_1) = all_920_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (201) with fresh symbols all_923_0, all_923_1 gives:
% 260.06/41.52 | (402) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_923_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_923_1 & $i(all_923_0)
% 260.06/41.52 | & $i(all_923_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_923_0) = v1) |
% 260.06/41.52 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_923_1,
% 260.06/41.52 | v0) | c_Nat_OSuc(v1) = v0)
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (402) implies:
% 260.06/41.52 | (403) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_923_1
% 260.06/41.52 | (404) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_923_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (91) with fresh symbols all_926_0, all_926_1 gives:
% 260.06/41.52 | (405) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_926_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_926_1 &
% 260.06/41.52 | $i(all_926_0) & $i(all_926_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 260.06/41.52 | all_926_0 | ~ (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_926_1))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (405) implies:
% 260.06/41.52 | (406) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_926_1
% 260.06/41.52 | (407) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_926_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (187) with fresh symbols all_929_0, all_929_1 gives:
% 260.06/41.52 | (408) c_Nat_OSuc(all_929_1) = all_929_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_929_1 & $i(all_929_0)
% 260.06/41.52 | & $i(all_929_1) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.52 | all_929_1, all_929_0) & ! [v0: any] : (v0 = all_929_1 | ~ $i(v0)
% 260.06/41.52 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_929_0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (408) implies:
% 260.06/41.52 | (409) c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_929_1, all_929_0)
% 260.06/41.52 | (410) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_929_1
% 260.06/41.52 | (411) c_Nat_OSuc(all_929_1) = all_929_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (104) with fresh symbol all_935_0 gives:
% 260.06/41.52 | (412) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_935_0 &
% 260.06/41.52 | $i(all_935_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_935_0, v0)
% 260.06/41.52 | | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v2) &
% 260.06/41.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (412) implies:
% 260.06/41.52 | (413) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_935_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (142) with fresh symbol all_941_0 gives:
% 260.06/41.52 | (414) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_941_0 & $i(all_941_0) &
% 260.06/41.52 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.52 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 260.06/41.52 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Omonoid__mult(v1) | hAPP(v3,
% 260.06/41.52 | all_941_0) = v0)
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (414) implies:
% 260.06/41.52 | (415) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_941_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (195) with fresh symbol all_947_0 gives:
% 260.06/41.52 | (416) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_947_0 & $i(all_947_0)
% 260.06/41.52 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.52 | (c_Nat_OSuc(v0) = v2) | ~
% 260.06/41.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~
% 260.06/41.52 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.52 | all_947_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3,
% 260.06/41.52 | v1))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (416) implies:
% 260.06/41.52 | (417) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_947_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (201) with fresh symbols all_950_0, all_950_1 gives:
% 260.06/41.52 | (418) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_950_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_950_1 & $i(all_950_0)
% 260.06/41.52 | & $i(all_950_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_950_0) = v1) |
% 260.06/41.52 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_950_1,
% 260.06/41.52 | v0) | c_Nat_OSuc(v1) = v0)
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (418) implies:
% 260.06/41.52 | (419) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_950_1
% 260.06/41.52 | (420) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_950_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (85) with fresh symbols all_959_0, all_959_1 gives:
% 260.06/41.52 | (421) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_959_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_959_1 &
% 260.06/41.52 | $i(all_959_0) & $i(all_959_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 260.06/41.52 | all_959_0 | ~ (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_959_1))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (421) implies:
% 260.06/41.52 | (422) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_959_1
% 260.06/41.52 | (423) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_959_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (161) with fresh symbols all_962_0, all_962_1 gives:
% 260.06/41.52 | (424) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_962_1 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_962_0 &
% 260.06/41.52 | $i(all_962_0) & $i(all_962_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_962_1, v0)
% 260.06/41.52 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_962_0,
% 260.06/41.52 | v1))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (424) implies:
% 260.06/41.52 | (425) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_962_0
% 260.06/41.52 | (426) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_962_1
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (20) with fresh symbols all_965_0, all_965_1 gives:
% 260.06/41.52 | (427) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_965_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_965_1 &
% 260.06/41.52 | $i(all_965_0) & $i(all_965_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 260.06/41.52 | all_965_0 | ~ (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) =
% 260.06/41.52 | v1) | ~ $i(v0) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_965_1, v0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (427) implies:
% 260.06/41.52 | (428) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_965_1
% 260.06/41.52 | (429) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_965_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (162) with fresh symbols all_974_0, all_974_1 gives:
% 260.06/41.52 | (430) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_974_1 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_974_0 &
% 260.06/41.52 | $i(all_974_0) & $i(all_974_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_974_1, v0) |
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_974_0, v1))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (430) implies:
% 260.06/41.52 | (431) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_974_0
% 260.06/41.52 | (432) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_974_1
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (70) with fresh symbol all_994_0 gives:
% 260.06/41.52 | (433) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_994_0 & $i(all_994_0)
% 260.06/41.52 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.06/41.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~
% 260.06/41.52 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.52 | all_994_0, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.52 | all_994_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2,
% 260.06/41.52 | v0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (433) implies:
% 260.06/41.52 | (434) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_994_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (130) with fresh symbol all_997_0 gives:
% 260.06/41.52 | (435) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_997_0 & $i(all_997_0) &
% 260.06/41.52 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.52 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 260.06/41.52 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) |
% 260.06/41.52 | hAPP(v3, all_997_0) = v0)
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (435) implies:
% 260.06/41.52 | (436) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_997_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (39) with fresh symbols all_1000_0, all_1000_1,
% 260.06/41.52 | all_1000_2 gives:
% 260.06/41.52 | (437) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1000_2 &
% 260.06/41.52 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1000_1 &
% 260.06/41.52 | hAPP(all_1000_2, all_1000_1) = all_1000_0 & $i(all_1000_0) &
% 260.06/41.52 | $i(all_1000_1) & $i(all_1000_2) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 260.06/41.52 | v0 | ~ (hAPP(all_1000_0, v0) = v1) | ~ $i(v0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (437) implies:
% 260.06/41.52 | (438) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1000_1
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (13) with fresh symbols all_1003_0, all_1003_1 gives:
% 260.06/41.52 | (439) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1003_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1003_1 &
% 260.06/41.52 | $i(all_1003_0) & $i(all_1003_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 260.06/41.52 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.06/41.52 | all_1003_0, v1) = v2 & $i(v2) &
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1003_1, v2)))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (439) implies:
% 260.06/41.52 | (440) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1003_1
% 260.06/41.52 | (441) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1003_0
% 260.06/41.52 | (442) ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 260.06/41.52 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.06/41.52 | all_1003_0, v1) = v2 & $i(v2) &
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1003_1, v2)))
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (112) with fresh symbol all_1006_0 gives:
% 260.06/41.52 | (443) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1006_0 &
% 260.06/41.52 | $i(all_1006_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.06/41.52 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 260.06/41.52 | (c_RComplete_Onatfloor(v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1006_0, v1)
% 260.06/41.52 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (443) implies:
% 260.06/41.52 | (444) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1006_0
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (110) with fresh symbol all_1009_0 gives:
% 260.06/41.52 | (445) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1009_0 &
% 260.06/41.52 | $i(all_1009_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 260.06/41.52 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 &
% 260.06/41.52 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1009_0) =
% 260.06/41.52 | v3 & $i(v3) & $i(v2) &
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (445) implies:
% 260.06/41.52 | (446) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1009_0
% 260.06/41.52 | (447) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0) = v1) | ~
% 260.06/41.52 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat,
% 260.06/41.52 | v1) = v2 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 260.06/41.52 | all_1009_0) = v3 & $i(v3) & $i(v2) &
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (44) with fresh symbols all_1013_0, all_1013_1,
% 260.06/41.52 | all_1013_2 gives:
% 260.06/41.52 | (448) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1013_2 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1013_1 &
% 260.06/41.52 | hAPP(all_1013_2, all_1013_1) = all_1013_0 & $i(all_1013_0) &
% 260.06/41.52 | $i(all_1013_1) & $i(all_1013_2) & ! [v0: $i] : ! [v1: int] : (v1 =
% 260.06/41.52 | all_1013_1 | ~ (hAPP(all_1013_0, v0) = v1) | ~ $i(v0))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (448) implies:
% 260.06/41.52 | (449) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1013_1
% 260.06/41.52 |
% 260.06/41.52 | DELTA: instantiating (166) with fresh symbols all_1016_0, all_1016_1 gives:
% 260.06/41.52 | (450) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1016_0 &
% 260.06/41.52 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1016_1 &
% 260.06/41.52 | $i(all_1016_0) & $i(all_1016_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.52 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1016_0) |
% 260.06/41.52 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1016_1, v0) |
% 260.06/41.52 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_1016_1))
% 260.06/41.52 |
% 260.06/41.52 | ALPHA: (450) implies:
% 260.06/41.53 | (451) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1016_1
% 260.06/41.53 | (452) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1016_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (111) with fresh symbol all_1019_0 gives:
% 260.06/41.53 | (453) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1019_0 &
% 260.06/41.53 | $i(all_1019_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.53 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, all_1019_0) =
% 260.06/41.53 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] :
% 260.06/41.53 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & c_RComplete_Onatfloor(v0)
% 260.06/41.53 | = v2 & $i(v3) & $i(v2) &
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (453) implies:
% 260.06/41.53 | (454) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1019_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (1) with fresh symbols all_1022_0, all_1022_1,
% 260.06/41.53 | all_1022_2, all_1022_3 gives:
% 260.06/41.53 | (455) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1022_3 &
% 260.06/41.53 | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_r____) = all_1022_2 &
% 260.06/41.53 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1022_3, all_1022_2)
% 260.06/41.53 | = all_1022_1 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 260.06/41.53 | v_z____) = all_1022_0 & $i(all_1022_0) & $i(all_1022_1) &
% 260.06/41.53 | $i(all_1022_2) & $i(all_1022_3) &
% 260.06/41.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_1,
% 260.06/41.53 | all_1022_0)
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (455) implies:
% 260.06/41.53 | (456) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_1,
% 260.06/41.53 | all_1022_0)
% 260.06/41.53 | (457) $i(all_1022_2)
% 260.06/41.53 | (458) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____) =
% 260.06/41.53 | all_1022_0
% 260.06/41.53 | (459) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1022_3, all_1022_2)
% 260.06/41.53 | = all_1022_1
% 260.06/41.53 | (460) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_r____) = all_1022_2
% 260.06/41.53 | (461) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1022_3
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (168) with fresh symbols all_1024_0, all_1024_1 gives:
% 260.06/41.53 | (462) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1024_0 &
% 260.06/41.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1024_1 &
% 260.06/41.53 | $i(all_1024_0) & $i(all_1024_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.53 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1024_1, v0) |
% 260.06/41.53 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1024_1,
% 260.06/41.53 | v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.06/41.53 | all_1024_0, v0))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (462) implies:
% 260.06/41.53 | (463) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1024_1
% 260.06/41.53 | (464) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1024_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (98) with fresh symbols all_1027_0, all_1027_1 gives:
% 260.06/41.53 | (465) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1027_0 &
% 260.06/41.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1027_1 &
% 260.06/41.53 | $i(all_1027_0) & $i(all_1027_1) & ! [v0: any] : (v0 = all_1027_0 |
% 260.06/41.53 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = all_1027_1) | ~ $i(v0)) & !
% 260.06/41.53 | [v0: int] : (v0 = all_1027_1 | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 260.06/41.53 | all_1027_0) = v0))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (465) implies:
% 260.06/41.53 | (466) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1027_1
% 260.06/41.53 | (467) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1027_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (167) with fresh symbols all_1030_0, all_1030_1 gives:
% 260.06/41.53 | (468) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1030_0 &
% 260.06/41.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1030_1 &
% 260.06/41.53 | $i(all_1030_0) & $i(all_1030_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.53 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1030_1, v1) |
% 260.06/41.53 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1030_1, v0) |
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1030_0, v0))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (468) implies:
% 260.06/41.53 | (469) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1030_1
% 260.06/41.53 | (470) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1030_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (59) with fresh symbol all_1033_0 gives:
% 260.06/41.53 | (471) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1033_0 &
% 260.06/41.53 | $i(all_1033_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 260.06/41.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = all_1033_0) |
% 260.06/41.53 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = all_1033_0) &
% 260.06/41.53 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2 &
% 260.06/41.53 | $i(v2)))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (471) implies:
% 260.06/41.53 | (472) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1033_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (24) with fresh symbols all_1036_0, all_1036_1,
% 260.06/41.53 | all_1036_2 gives:
% 260.06/41.53 | (473) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1036_2 &
% 260.06/41.53 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1036_1 &
% 260.06/41.53 | hAPP(all_1036_2, all_1036_1) = all_1036_0 & $i(all_1036_0) &
% 260.06/41.53 | $i(all_1036_1) & $i(all_1036_2) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 260.06/41.53 | v0 | ~ (hAPP(all_1036_0, v0) = v1) | ~ $i(v0))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (473) implies:
% 260.06/41.53 | (474) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1036_1
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (149) with fresh symbol all_1042_0 gives:
% 260.06/41.53 | (475) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1042_0 &
% 260.06/41.53 | $i(all_1042_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.06/41.53 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower_Opower(v3,
% 260.06/41.53 | v2, v1) = v4) | ~ (hAPP(v4, v0) = v5) | ~ $i(v3) | ~ $i(v2)
% 260.06/41.53 | | ~ $i(v1) | ~ $i(v0) | hAPP(v5, all_1042_0) = v2)
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (475) implies:
% 260.06/41.53 | (476) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1042_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (157) with fresh symbol all_1045_0 gives:
% 260.06/41.53 | (477) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1045_0 &
% 260.06/41.53 | $i(all_1045_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 260.06/41.53 | ~ (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 260.06/41.53 | v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1045_0, v1) |
% 260.06/41.53 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1045_0, v0))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (477) implies:
% 260.06/41.53 | (478) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1045_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (199) with fresh symbol all_1048_0 gives:
% 260.06/41.53 | (479) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1048_0 &
% 260.06/41.53 | $i(all_1048_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.53 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 260.06/41.53 | ? [v3: $i] : (c_Nat_OSuc(v0) = v2 & c_RealDef_Oreal(tc_Nat_Onat,
% 260.06/41.53 | v2) = v3 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 260.06/41.53 | all_1048_0) = v3 & $i(v3) & $i(v2)))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (479) implies:
% 260.06/41.53 | (480) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1048_0
% 260.06/41.53 | (481) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) =
% 260.06/41.53 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : (c_Nat_OSuc(v0) =
% 260.06/41.53 | v2 & c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 260.06/41.53 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1048_0) =
% 260.06/41.53 | v3 & $i(v3) & $i(v2)))
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (131) with fresh symbol all_1051_0 gives:
% 260.06/41.53 | (482) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1051_0 &
% 260.06/41.53 | $i(all_1051_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.06/41.53 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2,
% 260.06/41.53 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.06/41.53 | class_Rings_Ocomm__semiring__1(v1) | ? [v4: $i] :
% 260.06/41.53 | (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, all_1051_0) = v4 &
% 260.06/41.53 | $i(v4)))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (482) implies:
% 260.06/41.53 | (483) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1051_0
% 260.06/41.53 | (484) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.53 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 260.06/41.53 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | ?
% 260.06/41.53 | [v4: $i] : (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3,
% 260.06/41.53 | all_1051_0) = v4 & $i(v4)))
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (144) with fresh symbol all_1063_0 gives:
% 260.06/41.53 | (485) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1063_0 &
% 260.06/41.53 | $i(all_1063_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.06/41.53 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2,
% 260.06/41.53 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ class_Power_Opower(v1) |
% 260.06/41.53 | ? [v4: $i] : (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3,
% 260.06/41.53 | all_1063_0) = v4 & $i(v4)))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (485) implies:
% 260.06/41.53 | (486) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1063_0
% 260.06/41.53 | (487) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.53 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 260.06/41.53 | ~ $i(v1) | ~ $i(v0) | ~ class_Power_Opower(v1) | ? [v4: $i] :
% 260.06/41.53 | (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, all_1063_0) = v4 &
% 260.06/41.53 | $i(v4)))
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (185) with fresh symbols all_1066_0, all_1066_1,
% 260.06/41.53 | all_1066_2 gives:
% 260.06/41.53 | (488) c_Nat_OSuc(all_1066_1) = all_1066_0 & c_Nat_OSuc(all_1066_2) =
% 260.06/41.53 | all_1066_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1066_2 &
% 260.06/41.53 | $i(all_1066_0) & $i(all_1066_1) & $i(all_1066_2) & ! [v0: any] : (v0
% 260.06/41.53 | = all_1066_1 | v0 = all_1066_2 | ~ $i(v0) | ~
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1066_0))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (488) implies:
% 260.06/41.53 | (489) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1066_2
% 260.06/41.53 | (490) c_Nat_OSuc(all_1066_2) = all_1066_1
% 260.06/41.53 | (491) c_Nat_OSuc(all_1066_1) = all_1066_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (103) with fresh symbols all_1075_0, all_1075_1 gives:
% 260.06/41.53 | (492) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1075_0 &
% 260.06/41.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1075_1 &
% 260.06/41.53 | $i(all_1075_0) & $i(all_1075_1) & ! [v0: any] : ! [v1: $i] : (v0 =
% 260.06/41.53 | all_1075_0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0)
% 260.06/41.53 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 260.06/41.53 | all_1075_1)) & ! [v0: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 260.06/41.53 | all_1075_0) = v0) |
% 260.06/41.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.06/41.53 | all_1075_1))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (492) implies:
% 260.06/41.53 | (493) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1075_1
% 260.06/41.53 | (494) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1075_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (188) with fresh symbol all_1090_0 gives:
% 260.06/41.53 | (495) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1090_0 &
% 260.06/41.53 | $i(all_1090_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) =
% 260.06/41.53 | v0) | ~ $i(v1) | ~ $i(v0) |
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1090_0, v0)) & !
% 260.06/41.53 | [v0: $i] : ( ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.53 | all_1090_0, v0) | ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & $i(v1)))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (495) implies:
% 260.06/41.53 | (496) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1090_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (214) with fresh symbols all_1093_0, all_1093_1 gives:
% 260.06/41.53 | (497) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1093_1 &
% 260.06/41.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1093_0 &
% 260.06/41.53 | $i(all_1093_0) & $i(all_1093_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.06/41.53 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v2) |
% 260.06/41.53 | ~ $i(v1) | ~ $i(v0) | ~
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1093_0, v0) | ~
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1093_1, v1) |
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (497) implies:
% 260.06/41.53 | (498) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1093_0
% 260.06/41.53 | (499) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1093_1
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (181) with fresh symbol all_1111_0 gives:
% 260.06/41.53 | (500) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1111_0 & $i(all_1111_0)
% 260.06/41.53 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~
% 260.06/41.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1111_0) = v2) |
% 260.06/41.53 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (c_Nat_OSuc(v0) = v4 &
% 260.06/41.53 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v4) = v3 & $i(v4)
% 260.06/41.53 | & $i(v3)))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (500) implies:
% 260.06/41.53 | (501) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1111_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (114) with fresh symbol all_1114_0 gives:
% 260.06/41.53 | (502) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1114_0 & $i(all_1114_0)
% 260.06/41.53 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.06/41.53 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 260.06/41.53 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v4:
% 260.06/41.53 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, all_1114_0) =
% 260.06/41.53 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.06/41.53 | v4, v0)))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (502) implies:
% 260.06/41.53 | (503) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1114_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (210) with fresh symbol all_1120_0 gives:
% 260.06/41.53 | (504) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1120_0 &
% 260.06/41.53 | $i(all_1120_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.06/41.53 | $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,
% 260.06/41.53 | v0, v2) = v4) | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0,
% 260.06/41.53 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.06/41.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1120_0, v2) | ~
% 260.06/41.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) |
% 260.06/41.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v4))
% 260.06/41.53 |
% 260.06/41.53 | ALPHA: (504) implies:
% 260.06/41.53 | (505) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1120_0
% 260.06/41.53 |
% 260.06/41.53 | DELTA: instantiating (171) with fresh symbols all_1123_0, all_1123_1 gives:
% 260.06/41.54 | (506) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1123_0 &
% 260.06/41.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1123_1 &
% 260.06/41.54 | $i(all_1123_0) & $i(all_1123_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.54 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1123_0, v0) =
% 260.06/41.54 | v1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1123_1, v0)
% 260.06/41.54 | | ? [v2: $i] : (c_Transcendental_Oln(v1) = v2 & $i(v2) &
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (506) implies:
% 260.06/41.54 | (507) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1123_1
% 260.06/41.54 | (508) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1123_0
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (211) with fresh symbols all_1138_0, all_1138_1 gives:
% 260.06/41.54 | (509) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1138_0 &
% 260.06/41.54 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1138_1 &
% 260.06/41.54 | $i(all_1138_0) & $i(all_1138_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.06/41.54 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~
% 260.06/41.54 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v1) = v4) | ~
% 260.06/41.54 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1138_0, v1) = v2) | ~ $i(v1) |
% 260.06/41.54 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.54 | all_1138_1, v1))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (509) implies:
% 260.06/41.54 | (510) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1138_1
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (220) with fresh symbol all_1144_0 gives:
% 260.06/41.54 | (511) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1144_0 &
% 260.06/41.54 | $i(all_1144_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.06/41.54 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) |
% 260.06/41.54 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~
% 260.06/41.54 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.54 | all_1144_0, v1) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 260.06/41.54 | $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v4 &
% 260.06/41.54 | c_Nat_OSuc(v3) = v4 & $i(v4)))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (511) implies:
% 260.06/41.54 | (512) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1144_0
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (190) with fresh symbols all_1153_0, all_1153_1,
% 260.06/41.54 | all_1153_2, all_1153_3 gives:
% 260.06/41.54 | (513) c_Nat_OSuc(all_1153_2) = all_1153_1 &
% 260.06/41.54 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1153_3 &
% 260.06/41.54 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1153_2 &
% 260.06/41.54 | hAPP(all_1153_3, all_1153_1) = all_1153_0 & $i(all_1153_0) &
% 260.06/41.54 | $i(all_1153_1) & $i(all_1153_2) & $i(all_1153_3) & ! [v0: $i] : !
% 260.06/41.54 | [v1: int] : (v1 = all_1153_1 | ~ (hAPP(all_1153_0, v0) = v1) | ~
% 260.06/41.54 | $i(v0))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (513) implies:
% 260.06/41.54 | (514) hAPP(all_1153_3, all_1153_1) = all_1153_0
% 260.06/41.54 | (515) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1153_2
% 260.06/41.54 | (516) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1153_3
% 260.06/41.54 | (517) c_Nat_OSuc(all_1153_2) = all_1153_1
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (164) with fresh symbols all_1159_0, all_1159_1 gives:
% 260.06/41.54 | (518) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1159_0 &
% 260.06/41.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1159_1 &
% 260.06/41.54 | $i(all_1159_0) & $i(all_1159_1) & ! [v0: any] : (v0 = all_1159_0 |
% 260.06/41.54 | ~ (c_Transcendental_Oln(v0) = all_1159_1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1159_1, v0)) &
% 260.06/41.54 | ! [v0: int] : (v0 = all_1159_1 | ~ (c_Transcendental_Oln(all_1159_0)
% 260.06/41.54 | = v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.06/41.54 | all_1159_1, all_1159_0))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (518) implies:
% 260.06/41.54 | (519) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1159_1
% 260.06/41.54 | (520) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1159_0
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (115) with fresh symbol all_1162_0 gives:
% 260.06/41.54 | (521) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1162_0 &
% 260.06/41.54 | $i(all_1162_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.06/41.54 | $i] : (v3 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.06/41.54 | (c_RComplete_Onatfloor(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ?
% 260.06/41.54 | [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 260.06/41.54 | all_1162_0) = v4 & $i(v4) & ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (521) implies:
% 260.06/41.54 | (522) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1162_0
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (16) with fresh symbols all_1165_0, all_1165_1 gives:
% 260.06/41.54 | (523) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1165_0 &
% 260.06/41.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1165_1 &
% 260.06/41.54 | $i(all_1165_0) & $i(all_1165_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.06/41.54 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1165_0,
% 260.06/41.54 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1165_1, v1) |
% 260.06/41.54 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1165_1, v0) |
% 260.06/41.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1165_1, v3))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (523) implies:
% 260.06/41.54 | (524) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1165_1
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (216) with fresh symbol all_1174_0 gives:
% 260.06/41.54 | (525) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1174_0 &
% 260.06/41.54 | $i(all_1174_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.06/41.54 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) |
% 260.06/41.54 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~
% 260.06/41.54 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.54 | all_1174_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 260.06/41.54 | v1) | ? [v4: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0,
% 260.06/41.54 | v1) = v4 & c_Nat_OSuc(v3) = v4 & $i(v4)))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (525) implies:
% 260.06/41.54 | (526) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1174_0
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (53) with fresh symbol all_1177_0 gives:
% 260.06/41.54 | (527) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1177_0 &
% 260.06/41.54 | $i(all_1177_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 260.06/41.54 | all_1177_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0)
% 260.06/41.54 | = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0:
% 260.06/41.54 | $i] : ! [v1: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,
% 260.06/41.54 | v1, v0) = all_1177_0) | ~ $i(v1) | ~ $i(v0) |
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (527) implies:
% 260.06/41.54 | (528) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1177_0
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (212) with fresh symbols all_1180_0, all_1180_1 gives:
% 260.06/41.54 | (529) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1180_0 &
% 260.06/41.54 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1180_1 &
% 260.06/41.54 | $i(all_1180_0) & $i(all_1180_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.06/41.54 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~
% 260.06/41.54 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v1) = v4) | ~
% 260.06/41.54 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1180_0, v0) = v2) | ~ $i(v1) |
% 260.06/41.54 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.06/41.54 | all_1180_1, v1))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (529) implies:
% 260.06/41.54 | (530) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1180_1
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (86) with fresh symbols all_1186_0, all_1186_1 gives:
% 260.06/41.54 | (531) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1186_1 &
% 260.06/41.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1186_0 &
% 260.06/41.54 | $i(all_1186_0) & $i(all_1186_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.54 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1186_1) |
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.06/41.54 | all_1186_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.54 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_1186_0)
% 260.06/41.54 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1186_1))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (531) implies:
% 260.06/41.54 | (532) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1186_0
% 260.06/41.54 | (533) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1186_1
% 260.06/41.54 |
% 260.06/41.54 | DELTA: instantiating (92) with fresh symbols all_1189_0, all_1189_1 gives:
% 260.06/41.54 | (534) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1189_1 &
% 260.06/41.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1189_0 &
% 260.06/41.54 | $i(all_1189_0) & $i(all_1189_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.06/41.54 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1189_1, v1) |
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1189_0,
% 260.06/41.54 | v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0)
% 260.06/41.54 | = v1) | ~ $i(v0) | ~
% 260.06/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1189_0, v0)
% 260.06/41.54 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1189_1, v1))
% 260.06/41.54 |
% 260.06/41.54 | ALPHA: (534) implies:
% 260.06/41.54 | (535) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1189_0
% 260.41/41.54 | (536) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1189_1
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (36) with fresh symbols all_1192_0, all_1192_1 gives:
% 260.41/41.54 | (537) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1192_0 &
% 260.41/41.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1192_1 &
% 260.41/41.54 | $i(all_1192_0) & $i(all_1192_1) & ! [v0: any] : ! [v1: $i] : !
% 260.41/41.54 | [v2: $i] : (v0 = all_1192_1 | ~ (hAPP(v1, v0) = v2) | ~
% 260.41/41.54 | (hAPP(all_1192_0, v0) = v1) | ~ $i(v0) |
% 260.41/41.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1192_1, v2)) &
% 260.41/41.54 | ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(v0, all_1192_1) = v1) | ~
% 260.41/41.54 | (hAPP(all_1192_0, all_1192_1) = v0) | ~
% 260.41/41.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1192_1, v1))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (537) implies:
% 260.41/41.54 | (538) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1192_1
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (77) with fresh symbols all_1198_0, all_1198_1 gives:
% 260.41/41.54 | (539) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1198_0 &
% 260.41/41.54 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1198_1 &
% 260.41/41.54 | $i(all_1198_0) & $i(all_1198_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.54 | $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (hAPP(v3, v1) = v4)
% 260.41/41.54 | | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1198_0, v2) = v3) | ~
% 260.41/41.54 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1198_1, v2))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (539) implies:
% 260.41/41.54 | (540) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1198_1
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (54) with fresh symbol all_1201_0 gives:
% 260.41/41.54 | (541) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1201_0 &
% 260.41/41.54 | $i(all_1201_0) & ! [v0: $i] : ! [v1: any] : (v1 = all_1201_0 | ~
% 260.41/41.54 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1201_0) |
% 260.41/41.54 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 =
% 260.41/41.54 | all_1201_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) =
% 260.41/41.54 | all_1201_0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 =
% 260.41/41.54 | all_1201_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 260.41/41.54 | all_1201_0, all_1201_0) = v0))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (541) implies:
% 260.41/41.54 | (542) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1201_0
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (25) with fresh symbol all_1204_0 gives:
% 260.41/41.54 | (543) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1204_0 &
% 260.41/41.54 | $i(all_1204_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.54 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 260.41/41.54 | $i(v1) | ~ $i(v0) | ~
% 260.41/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1204_0)
% 260.41/41.54 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 260.41/41.54 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.54 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 260.41/41.54 | $i(v1) | ~ $i(v0) | ~
% 260.41/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 260.41/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 260.41/41.54 | all_1204_0))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (543) implies:
% 260.41/41.54 | (544) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1204_0
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (105) with fresh symbols all_1209_0, all_1209_1 gives:
% 260.41/41.54 | (545) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1209_0 &
% 260.41/41.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1209_1 &
% 260.41/41.54 | $i(all_1209_0) & $i(all_1209_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.41/41.54 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ~
% 260.41/41.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1209_0, v0) |
% 260.41/41.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1209_1, v1)) &
% 260.41/41.54 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) =
% 260.41/41.54 | v1) | ~ $i(v0) | ~
% 260.41/41.54 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1209_1, v1) |
% 260.41/41.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1209_0, v0))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (545) implies:
% 260.41/41.54 | (546) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1209_1
% 260.41/41.54 | (547) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1209_0
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (21) with fresh symbols all_1214_0, all_1214_1 gives:
% 260.41/41.54 | (548) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1214_0 &
% 260.41/41.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1214_1 &
% 260.41/41.54 | $i(all_1214_0) & $i(all_1214_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.54 | any] : ! [v3: $i] : ! [v4: $i] : (v2 = all_1214_1 | v1 = v0 | ~
% 260.41/41.54 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1214_0,
% 260.41/41.54 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (548) implies:
% 260.41/41.54 | (549) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1214_1
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (63) with fresh symbol all_1220_0 gives:
% 260.41/41.54 | (550) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1220_0 &
% 260.41/41.54 | $i(all_1220_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.54 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~
% 260.41/41.54 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.54 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1220_0,
% 260.41/41.54 | v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.54 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~
% 260.41/41.54 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.54 | all_1220_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 260.41/41.54 | v1))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (550) implies:
% 260.41/41.54 | (551) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1220_0
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (116) with fresh symbol all_1229_0 gives:
% 260.41/41.54 | (552) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1229_0 &
% 260.41/41.54 | $i(all_1229_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.54 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 260.41/41.54 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 260.41/41.54 | $i(v1) | ~ $i(v0) | ~
% 260.41/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1229_0, v1)
% 260.41/41.54 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatceiling(v3) = v4 &
% 260.41/41.54 | c_RComplete_Onatceiling(v1) = v5 &
% 260.41/41.54 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) &
% 260.41/41.54 | $i(v4)))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (552) implies:
% 260.41/41.54 | (553) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1229_0
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (113) with fresh symbol all_1232_0 gives:
% 260.41/41.54 | (554) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1232_0 &
% 260.41/41.54 | $i(all_1232_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.54 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 260.41/41.54 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 260.41/41.54 | $i(v1) | ~ $i(v0) | ~
% 260.41/41.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1232_0, v1)
% 260.41/41.54 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatfloor(v3) = v4 &
% 260.41/41.54 | c_RComplete_Onatfloor(v1) = v5 &
% 260.41/41.54 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) &
% 260.41/41.54 | $i(v4)))
% 260.41/41.54 |
% 260.41/41.54 | ALPHA: (554) implies:
% 260.41/41.54 | (555) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1232_0
% 260.41/41.54 |
% 260.41/41.54 | DELTA: instantiating (58) with fresh symbols all_1235_0, all_1235_1,
% 260.41/41.54 | all_1235_2 gives:
% 260.41/41.55 | (556) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1235_2 &
% 260.41/41.55 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1235_1 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1235_0 &
% 260.41/41.55 | $i(all_1235_0) & $i(all_1235_1) & $i(all_1235_2) & ! [v0: any] : !
% 260.41/41.55 | [v1: any] : ! [v2: $i] : (v1 = all_1235_0 | v0 = all_1235_1 | ~
% 260.41/41.55 | (hAPP(v2, v0) = v1) | ~ (hAPP(all_1235_2, v1) = v2) | ~ $i(v1) |
% 260.41/41.55 | ~ $i(v0))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (556) implies:
% 260.41/41.55 | (557) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1235_0
% 260.41/41.55 | (558) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1235_1
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (200) with fresh symbols all_1247_0, all_1247_1,
% 260.41/41.55 | all_1247_2 gives:
% 260.41/41.55 | (559) c_Nat_OSuc(all_1247_2) = all_1247_1 &
% 260.41/41.55 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1247_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1247_2 &
% 260.41/41.55 | $i(all_1247_0) & $i(all_1247_1) & $i(all_1247_2) & ! [v0: $i] : !
% 260.41/41.55 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~
% 260.41/41.55 | (hAPP(all_1247_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1247_1, v1) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1247_1, v3))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (559) implies:
% 260.41/41.55 | (560) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1247_2
% 260.41/41.55 | (561) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1247_0
% 260.41/41.55 | (562) c_Nat_OSuc(all_1247_2) = all_1247_1
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (150) with fresh symbol all_1250_0 gives:
% 260.41/41.55 | (563) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1250_0 &
% 260.41/41.55 | $i(all_1250_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 260.41/41.55 | ~ c_SEQ_OBseq(v1, v0) | ~
% 260.41/41.55 | class_RealVector_Oreal__normed__vector(v1) | ? [v2: $i] : ($i(v2)
% 260.41/41.55 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1250_0, v2)
% 260.41/41.55 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 260.41/41.55 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v0,
% 260.41/41.55 | v3) = v4) | ~ $i(v3) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (563) implies:
% 260.41/41.55 | (564) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1250_0
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (28) with fresh symbol all_1253_0 gives:
% 260.41/41.55 | (565) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1253_0 &
% 260.41/41.55 | $i(all_1253_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.55 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 260.41/41.55 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 260.41/41.55 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.41/41.55 | all_1253_0, v2) | ( ~ (v3 = v0) &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3))) &
% 260.41/41.55 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1253_0, v2)
% 260.41/41.55 | | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1) = v0))))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (565) implies:
% 260.41/41.55 | (566) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1253_0
% 260.41/41.55 | (567) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.55 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 260.41/41.55 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 260.41/41.55 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.41/41.55 | all_1253_0, v2) | ( ~ (v3 = v0) &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3))) &
% 260.41/41.55 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1253_0, v2)
% 260.41/41.55 | | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1) = v0))))
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (192) with fresh symbols all_1256_0, all_1256_1,
% 260.41/41.55 | all_1256_2 gives:
% 260.41/41.55 | (568) c_Nat_OSuc(all_1256_2) = all_1256_1 &
% 260.41/41.55 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1256_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1256_2 &
% 260.41/41.55 | $i(all_1256_0) & $i(all_1256_1) & $i(all_1256_2) & ! [v0: $i] : !
% 260.41/41.55 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~
% 260.41/41.55 | (hAPP(all_1256_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1256_1, v1) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1256_1, v0) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (568) implies:
% 260.41/41.55 | (569) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1256_2
% 260.41/41.55 | (570) c_Nat_OSuc(all_1256_2) = all_1256_1
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (22) with fresh symbols all_1259_0, all_1259_1 gives:
% 260.41/41.55 | (571) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1259_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1259_1 &
% 260.41/41.55 | $i(all_1259_0) & $i(all_1259_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.55 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1259_1 |
% 260.41/41.55 | v1 = v0 | ~ (hAPP(v5, v2) = v4) | ~ (hAPP(v3, v2) = v4) | ~
% 260.41/41.55 | (hAPP(all_1259_0, v1) = v3) | ~ (hAPP(all_1259_0, v0) = v5) | ~
% 260.41/41.55 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (571) implies:
% 260.41/41.55 | (572) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1259_1
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (193) with fresh symbols all_1270_0, all_1270_1,
% 260.41/41.55 | all_1270_2 gives:
% 260.41/41.55 | (573) c_Nat_OSuc(all_1270_2) = all_1270_1 &
% 260.41/41.55 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1270_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1270_2 &
% 260.41/41.55 | $i(all_1270_0) & $i(all_1270_1) & $i(all_1270_2) & ! [v0: $i] : !
% 260.41/41.55 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~
% 260.41/41.55 | (hAPP(all_1270_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1270_1, v1) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1270_1, v0) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1270_1, v3))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (573) implies:
% 260.41/41.55 | (574) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1270_2
% 260.41/41.55 | (575) c_Nat_OSuc(all_1270_2) = all_1270_1
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (191) with fresh symbols all_1279_0, all_1279_1,
% 260.41/41.55 | all_1279_2 gives:
% 260.41/41.55 | (576) c_Nat_OSuc(all_1279_2) = all_1279_1 &
% 260.41/41.55 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1279_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1279_2 &
% 260.41/41.55 | $i(all_1279_0) & $i(all_1279_1) & $i(all_1279_2) & ! [v0: $i] : !
% 260.41/41.55 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~
% 260.41/41.55 | (hAPP(all_1279_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1279_1, v1) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1279_1, v0) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (576) implies:
% 260.41/41.55 | (577) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1279_2
% 260.41/41.55 | (578) c_Nat_OSuc(all_1279_2) = all_1279_1
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (206) with fresh symbol all_1282_0 gives:
% 260.41/41.55 | (579) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1282_0 &
% 260.41/41.55 | $i(all_1282_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1282_0, v0)
% 260.41/41.55 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 260.41/41.55 | (c_Nat_OSuc(v1) = v3 & c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 &
% 260.41/41.55 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v4) & $i(v3) & $i(v2)
% 260.41/41.55 | & $i(v1) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.41/41.55 | v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 260.41/41.55 | v0)))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (579) implies:
% 260.41/41.55 | (580) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1282_0
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (15) with fresh symbols all_1288_0, all_1288_1 gives:
% 260.41/41.55 | (581) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1288_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1288_1 &
% 260.41/41.55 | $i(all_1288_0) & $i(all_1288_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.55 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 260.41/41.55 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1288_0, v2) = v3) |
% 260.41/41.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1288_1, v2) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v5))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (581) implies:
% 260.41/41.55 | (582) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1288_1
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (8) with fresh symbol all_1303_0 gives:
% 260.41/41.55 | (583) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1303_0 &
% 260.41/41.55 | $i(all_1303_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.55 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 260.41/41.55 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 260.41/41.55 | $i] : (( ~ (v2 = all_1303_0) | (v3 = v0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(v1) = v0)) & (v2 = all_1303_0 | (
% 260.41/41.55 | ~ (v3 = v0) & c_Groups_Ozero__class_Ozero(v1) = v3 &
% 260.41/41.55 | $i(v3)))))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (583) implies:
% 260.41/41.55 | (584) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1303_0
% 260.41/41.55 | (585) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.55 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 260.41/41.55 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 260.41/41.55 | $i] : (( ~ (v2 = all_1303_0) | (v3 = v0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(v1) = v0)) & (v2 = all_1303_0 | (
% 260.41/41.55 | ~ (v3 = v0) & c_Groups_Ozero__class_Ozero(v1) = v3 &
% 260.41/41.55 | $i(v3)))))
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (73) with fresh symbols all_1311_0, all_1311_1 gives:
% 260.41/41.55 | (586) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1311_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1311_1 &
% 260.41/41.55 | $i(all_1311_0) & $i(all_1311_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.55 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v2) =
% 260.41/41.55 | v4) | ~ (hAPP(v3, v1) = v5) | ~ (hAPP(all_1311_0, v0) = v3) |
% 260.41/41.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1311_1, v0) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (586) implies:
% 260.41/41.55 | (587) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1311_1
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (4) with fresh symbol all_1326_0 gives:
% 260.41/41.55 | (588) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1326_0 &
% 260.41/41.55 | $i(all_1326_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.55 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 260.41/41.55 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 260.41/41.55 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.55 | v2, all_1326_0) | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1)
% 260.41/41.55 | = v0)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.55 | v2, all_1326_0) | ( ~ (v3 = v0) &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3)))))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (588) implies:
% 260.41/41.55 | (589) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1326_0
% 260.41/41.55 | (590) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.55 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 260.41/41.55 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 260.41/41.55 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.55 | v2, all_1326_0) | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1)
% 260.41/41.55 | = v0)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.55 | v2, all_1326_0) | ( ~ (v3 = v0) &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3)))))
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (137) with fresh symbols all_1329_0, all_1329_1 gives:
% 260.41/41.55 | (591) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1329_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1329_1 &
% 260.41/41.55 | $i(all_1329_0) & $i(all_1329_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.55 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 260.41/41.55 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1329_0, v2) = v3) |
% 260.41/41.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1329_1, v2) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (591) implies:
% 260.41/41.55 | (592) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1329_1
% 260.41/41.55 | (593) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1329_0
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (169) with fresh symbols all_1338_0, all_1338_1 gives:
% 260.41/41.55 | (594) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1338_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1338_1 &
% 260.41/41.55 | $i(all_1338_0) & $i(all_1338_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.41/41.55 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1338_1, v0) |
% 260.41/41.55 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1338_0,
% 260.41/41.55 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.55 | all_1338_1, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.41/41.55 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1338_1, v0) |
% 260.41/41.55 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1338_1,
% 260.41/41.55 | v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.55 | all_1338_0, v0))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (594) implies:
% 260.41/41.55 | (595) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1338_1
% 260.41/41.55 | (596) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1338_0
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (152) with fresh symbol all_1341_0 gives:
% 260.41/41.55 | (597) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1341_0 &
% 260.41/41.55 | $i(all_1341_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 260.41/41.55 | | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1341_0, v1) |
% 260.41/41.55 | ~ class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v0)
% 260.41/41.55 | | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 260.41/41.55 | (c_RealVector_Onorm__class_Onorm(v2, v4) = v5 & hAPP(v0, v3) = v4 &
% 260.41/41.55 | $i(v5) & $i(v4) & $i(v3) & ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1)))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (597) implies:
% 260.41/41.55 | (598) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1341_0
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (165) with fresh symbols all_1350_0, all_1350_1 gives:
% 260.41/41.55 | (599) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1350_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1350_1 &
% 260.41/41.55 | $i(all_1350_0) & $i(all_1350_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.41/41.55 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_1350_1) |
% 260.41/41.55 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1350_1, v0) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1350_0)) &
% 260.41/41.55 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Transcendental_Oln(v0) = v1) | ~
% 260.41/41.55 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.41/41.55 | all_1350_0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.41/41.55 | all_1350_1, v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.41/41.55 | v1, all_1350_1))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (599) implies:
% 260.41/41.55 | (600) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1350_1
% 260.41/41.55 | (601) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1350_0
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (163) with fresh symbols all_1353_0, all_1353_1 gives:
% 260.41/41.55 | (602) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1353_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1353_1 &
% 260.41/41.55 | $i(all_1353_0) & $i(all_1353_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.41/41.55 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1353_0, v0) |
% 260.41/41.55 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1353_1, v0) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1353_1, v1)) &
% 260.41/41.55 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Transcendental_Oln(v0) = v1) | ~
% 260.41/41.55 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.41/41.55 | all_1353_1, v1) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1353_1, v0) |
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1353_0, v0))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (602) implies:
% 260.41/41.55 | (603) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1353_1
% 260.41/41.55 | (604) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1353_0
% 260.41/41.55 |
% 260.41/41.55 | DELTA: instantiating (213) with fresh symbols all_1356_0, all_1356_1 gives:
% 260.41/41.55 | (605) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1356_0 &
% 260.41/41.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1356_1 &
% 260.41/41.55 | $i(all_1356_0) & $i(all_1356_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.55 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.41/41.55 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v4, v5) = v6) | ~
% 260.41/41.55 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1356_0,
% 260.41/41.55 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1356_1, v2) |
% 260.41/41.55 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v6 & $i(v6)))
% 260.41/41.55 |
% 260.41/41.55 | ALPHA: (605) implies:
% 260.41/41.56 | (606) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1356_1
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (35) with fresh symbols all_1362_0, all_1362_1 gives:
% 260.41/41.56 | (607) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1362_0 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1362_1 &
% 260.41/41.56 | $i(all_1362_0) & $i(all_1362_1) & ! [v0: $i] : ! [v1: any] : !
% 260.41/41.56 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 260.41/41.56 | (v1 = all_1362_1 | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,
% 260.41/41.56 | v1) = v3) | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0)
% 260.41/41.56 | = v5) | ~ (hAPP(v4, v5) = v6) | ~ (hAPP(all_1362_0, v2) = v4) |
% 260.41/41.56 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v6) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 260.41/41.56 | all_1362_1))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (607) implies:
% 260.41/41.56 | (608) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1362_1
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (135) with fresh symbol all_1365_0 gives:
% 260.41/41.56 | (609) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1365_0 &
% 260.41/41.56 | $i(all_1365_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.56 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 260.41/41.56 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) |
% 260.41/41.56 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1365_0, v0) | ~
% 260.41/41.56 | class_Rings_Olinordered__semidom(v2) | ? [v6: $i] :
% 260.41/41.56 | (c_Groups_Oone__class_Oone(v2) = v6 & $i(v6) & ( ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless(v2, v6, v1) |
% 260.41/41.56 | c_Orderings_Oord__class_Oless(v2, v6, v5))))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (609) implies:
% 260.41/41.56 | (610) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1365_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (72) with fresh symbols all_1383_0, all_1383_1 gives:
% 260.41/41.56 | (611) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1383_0 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1383_1 &
% 260.41/41.56 | $i(all_1383_0) & $i(all_1383_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.56 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.41/41.56 | (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1383_0,
% 260.41/41.56 | v2) = v3) | ~ (hAPP(all_1383_0, v1) = v5) | ~ $i(v2) | ~
% 260.41/41.56 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.56 | v2, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.56 | all_1383_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4,
% 260.41/41.56 | v6))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (611) implies:
% 260.41/41.56 | (612) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1383_1
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (87) with fresh symbols all_1386_0, all_1386_1,
% 260.41/41.56 | all_1386_2 gives:
% 260.41/41.56 | (613) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1386_0 &
% 260.41/41.56 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1386_1 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1386_2 &
% 260.41/41.56 | $i(all_1386_0) & $i(all_1386_1) & $i(all_1386_2) & ! [v0: $i] : !
% 260.41/41.56 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 260.41/41.56 | all_1386_1) = v1) | ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1386_2, v0)
% 260.41/41.56 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatfloor(v1) = v2 &
% 260.41/41.56 | c_RComplete_Onatfloor(v0) = v3 &
% 260.41/41.56 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1386_0) = v2 &
% 260.41/41.56 | $i(v3) & $i(v2)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (613) implies:
% 260.41/41.56 | (614) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1386_2
% 260.41/41.56 | (615) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1386_1
% 260.41/41.56 | (616) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1386_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (79) with fresh symbols all_1389_0, all_1389_1,
% 260.41/41.56 | all_1389_2 gives:
% 260.41/41.56 | (617) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1389_0 &
% 260.41/41.56 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1389_1 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1389_2 &
% 260.41/41.56 | $i(all_1389_0) & $i(all_1389_1) & $i(all_1389_2) & ! [v0: $i] : !
% 260.41/41.56 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 260.41/41.56 | all_1389_1) = v1) | ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1389_2, v0)
% 260.41/41.56 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatceiling(v1) = v2 &
% 260.41/41.56 | c_RComplete_Onatceiling(v0) = v3 &
% 260.41/41.56 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1389_0) = v2 &
% 260.41/41.56 | $i(v3) & $i(v2)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (617) implies:
% 260.41/41.56 | (618) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1389_2
% 260.41/41.56 | (619) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1389_1
% 260.41/41.56 | (620) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1389_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (221) with fresh symbols all_1395_0, all_1395_1 gives:
% 260.41/41.56 | (621) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1395_1 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1395_0 &
% 260.41/41.56 | $i(all_1395_0) & $i(all_1395_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.56 | $i] : ! [v3: $i] : ( ~
% 260.41/41.56 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v2) = v3) |
% 260.41/41.56 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.56 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1395_0, v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1395_1, v1)
% 260.41/41.56 | | ? [v4: $i] : ? [v5: $i] :
% 260.41/41.56 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v0) = v4 &
% 260.41/41.56 | c_RComplete_Onatfloor(v3) = v4 & c_RComplete_Onatfloor(v1) = v5 &
% 260.41/41.56 | $i(v5) & $i(v4)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (621) implies:
% 260.41/41.56 | (622) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1395_0
% 260.41/41.56 | (623) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1395_1
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (215) with fresh symbol all_1398_0 gives:
% 260.41/41.56 | (624) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1398_0 &
% 260.41/41.56 | $i(all_1398_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.56 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) |
% 260.41/41.56 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~
% 260.41/41.56 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.56 | all_1398_0, v1) | ? [v4: any] : ? [v5: int] : (( ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | (v4 =
% 260.41/41.56 | all_1398_0 & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1)
% 260.41/41.56 | = all_1398_0)) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.56 | v0, v1) | (v5 = v4 & c_Divides_Odiv__class_Odiv(tc_Nat_Onat,
% 260.41/41.56 | v0, v1) = v4 & c_Nat_OSuc(v3) = v4 & $i(v4)))))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (624) implies:
% 260.41/41.56 | (625) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1398_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (138) with fresh symbols all_1401_0, all_1401_1 gives:
% 260.41/41.56 | (626) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1401_1 &
% 260.41/41.56 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1401_0 &
% 260.41/41.56 | $i(all_1401_0) & $i(all_1401_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.56 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 260.41/41.56 | v1) = v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1401_0, v2) =
% 260.41/41.56 | v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 260.41/41.56 | (c_RealDef_Oreal(tc_Nat_Onat, v6) = v4 & hAPP(v5, v0) = v6 &
% 260.41/41.56 | hAPP(all_1401_1, v1) = v5 & $i(v6) & $i(v5) & $i(v4)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (626) implies:
% 260.41/41.56 | (627) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1401_1
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (117) with fresh symbols all_1404_0, all_1404_1 gives:
% 260.41/41.56 | (628) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1404_0 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1404_1 &
% 260.41/41.56 | $i(all_1404_0) & $i(all_1404_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1404_1, v0)
% 260.41/41.56 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 260.41/41.56 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 260.41/41.56 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 &
% 260.41/41.56 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1404_0) = v2 &
% 260.41/41.56 | $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) &
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (628) implies:
% 260.41/41.56 | (629) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1404_1
% 260.41/41.56 | (630) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1404_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (202) with fresh symbols all_1407_0, all_1407_1 gives:
% 260.41/41.56 | (631) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1407_0 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1407_1 &
% 260.41/41.56 | $i(all_1407_0) & $i(all_1407_1) & ! [v0: $i] : ! [v1: any] : !
% 260.41/41.56 | [v2: $i] : ! [v3: $i] : (v1 = all_1407_1 | ~
% 260.41/41.56 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1407_0) = v2) |
% 260.41/41.56 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v0) = v3) | ~
% 260.41/41.56 | $i(v1) | ~ $i(v0) | ? [v4: $i] : (c_Nat_OSuc(v3) = v4 &
% 260.41/41.56 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v4 & $i(v4)))
% 260.41/41.56 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 260.41/41.56 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1407_1, v0) = v1) |
% 260.41/41.56 | ~ $i(v0))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (631) implies:
% 260.41/41.56 | (632) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1407_1
% 260.41/41.56 | (633) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1407_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (95) with fresh symbol all_1410_0 gives:
% 260.41/41.56 | (634) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1410_0 &
% 260.41/41.56 | $i(all_1410_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.56 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v2) | ~ $i(v1) | ~
% 260.41/41.56 | $i(v0) | ? [v3: $i] : ($i(v3) &
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1410_0, v3) &
% 260.41/41.56 | ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ $i(v4) |
% 260.41/41.56 | ? [v6: $i] : ? [v7: $i] :
% 260.41/41.56 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7
% 260.41/41.56 | & $i(v7) &
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 260.41/41.56 | v3)) |
% 260.41/41.56 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) =
% 260.41/41.56 | v6 & $i(v6) & ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 260.41/41.56 | v0))))))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (634) implies:
% 260.41/41.56 | (635) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1410_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (127) with fresh symbols all_1418_0, all_1418_1 gives:
% 260.41/41.56 | (636) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1418_0 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1418_1 &
% 260.41/41.56 | $i(all_1418_0) & $i(all_1418_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 260.41/41.56 | $i(v1) | ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1418_1, v1) |
% 260.41/41.56 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 260.41/41.56 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & hAPP(v4, v1) = v5 &
% 260.41/41.56 | hAPP(all_1418_0, v3) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (636) implies:
% 260.41/41.56 | (637) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1418_1
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (154) with fresh symbols all_1420_0, all_1420_1,
% 260.41/41.56 | all_1420_2 gives:
% 260.41/41.56 | (638) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1420_0 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1420_2 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1420_1 &
% 260.41/41.56 | $i(all_1420_0) & $i(all_1420_1) & $i(all_1420_2) & ! [v0: $i] : !
% 260.41/41.56 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1420_2, v1) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1420_1, v0) |
% 260.41/41.56 | ? [v2: $i] : ? [v3: $i] : (hAPP(v3, v1) = v0 & hAPP(all_1420_0,
% 260.41/41.56 | v2) = v3 & $i(v3) & $i(v2) &
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1420_1, v2)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (638) implies:
% 260.41/41.56 | (639) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1420_1
% 260.41/41.56 | (640) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1420_2
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (94) with fresh symbols all_1432_0, all_1432_1 gives:
% 260.41/41.56 | (641) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1432_0 &
% 260.41/41.56 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1432_1 &
% 260.41/41.56 | $i(all_1432_0) & $i(all_1432_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.56 | $i] : ! [v3: $i] : (v3 = v2 | ~ (c_RComplete_Onatceiling(v0) =
% 260.41/41.56 | v2) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1,
% 260.41/41.56 | all_1432_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ?
% 260.41/41.56 | [v5: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 & $i(v4) & ( ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0) |
% 260.41/41.56 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, all_1432_1)
% 260.41/41.56 | = v5 & $i(v5) & ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.41/41.56 | v5)))))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (641) implies:
% 260.41/41.56 | (642) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1432_1
% 260.41/41.56 | (643) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1432_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (139) with fresh symbols all_1438_0, all_1438_1 gives:
% 260.41/41.56 | (644) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1438_0 &
% 260.41/41.56 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1438_1 &
% 260.41/41.56 | $i(all_1438_0) & $i(all_1438_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.56 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 260.41/41.56 | v1) = v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1438_1, v2) =
% 260.41/41.56 | v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 260.41/41.56 | (c_RealDef_Oreal(tc_Nat_Onat, v6) = v4 & hAPP(v5, v0) = v6 &
% 260.41/41.56 | hAPP(all_1438_0, v1) = v5 & $i(v6) & $i(v5) & $i(v4)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (644) implies:
% 260.41/41.56 | (645) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1438_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (12) with fresh symbols all_1447_0, all_1447_1 gives:
% 260.41/41.56 | (646) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1447_0 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1447_1 &
% 260.41/41.56 | $i(all_1447_0) & $i(all_1447_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.56 | $i] : ! [v3: $i] : ( ~ (c_Groups_Osgn__class_Osgn(v1, v0) = v2) |
% 260.41/41.56 | ~ (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~
% 260.41/41.56 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4:
% 260.41/41.56 | $i] : ((v3 = all_1447_0 | (v4 = v0 &
% 260.41/41.56 | c_Groups_Ozero__class_Ozero(v1) = v0)) & (v3 = all_1447_1 | (
% 260.41/41.56 | ~ (v4 = v0) & c_Groups_Ozero__class_Ozero(v1) = v4 &
% 260.41/41.56 | $i(v4)))))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (646) implies:
% 260.41/41.56 | (647) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1447_1
% 260.41/41.56 | (648) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1447_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (108) with fresh symbol all_1450_0 gives:
% 260.41/41.56 | (649) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1450_0 &
% 260.41/41.56 | $i(all_1450_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.56 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 260.41/41.56 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1450_0, v1)
% 260.41/41.56 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)) & !
% 260.41/41.56 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.56 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 260.41/41.56 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ~
% 260.41/41.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1450_0, v1)
% 260.41/41.56 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (649) implies:
% 260.41/41.56 | (650) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1450_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (223) with fresh symbol all_1456_0 gives:
% 260.41/41.56 | (651) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1456_0 &
% 260.41/41.56 | $i(all_1456_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.56 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 260.41/41.56 | [v8: $i] : ( ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v6,
% 260.41/41.56 | v2) = v7) | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, v1)
% 260.41/41.56 | = v5) | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v3)
% 260.41/41.56 | | ~ (c_RealDef_Oreal(tc_Nat_Onat, v5) = v6) | ~
% 260.41/41.56 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4) | ~
% 260.41/41.56 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.56 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v7) = v8) | ~
% 260.41/41.56 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.56 | all_1456_0, v1) | ? [v9: $i] :
% 260.41/41.56 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v9, v2) = v8 &
% 260.41/41.56 | c_RealDef_Oreal(tc_Nat_Onat, v0) = v9 & $i(v9) & $i(v8)))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (651) implies:
% 260.41/41.56 | (652) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1456_0
% 260.41/41.56 |
% 260.41/41.56 | DELTA: instantiating (14) with fresh symbols all_1468_0, all_1468_1,
% 260.41/41.56 | all_1468_2, all_1468_3 gives:
% 260.41/41.56 | (653) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1468_1) = all_1468_0 &
% 260.41/41.56 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) =
% 260.41/41.56 | all_1468_1 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____,
% 260.41/41.56 | all_1468_3) = all_1468_2 &
% 260.41/41.56 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____) =
% 260.41/41.56 | all_1468_3 & $i(all_1468_0) & $i(all_1468_1) & $i(all_1468_2) &
% 260.41/41.56 | $i(all_1468_3) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1468_0,
% 260.41/41.56 | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] :
% 260.41/41.56 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 &
% 260.41/41.56 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.56 | all_1468_2, v3)) |
% 260.41/41.56 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 &
% 260.41/41.56 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.56 | v_r____, v2))))
% 260.41/41.56 |
% 260.41/41.56 | ALPHA: (653) implies:
% 260.41/41.57 | (654) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____) =
% 260.41/41.57 | all_1468_3
% 260.41/41.57 | (655) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, all_1468_3) =
% 260.41/41.57 | all_1468_2
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (33) with fresh symbols all_1477_0, all_1477_1 gives:
% 260.41/41.57 | (656) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1477_0 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1477_1 &
% 260.41/41.57 | $i(all_1477_0) & $i(all_1477_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.57 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 260.41/41.57 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v1) = v4) | ~
% 260.41/41.57 | (c_RealVector_Onorm__class_Onorm(v3, v0) = v6) | ~ (hAPP(v5, v6) =
% 260.41/41.57 | v7) | ~ (hAPP(all_1477_0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 260.41/41.57 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v3)
% 260.41/41.57 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v7) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 260.41/41.57 | all_1477_1) | c_Groups_Ozero__class_Ozero(v3) = v1)
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (656) implies:
% 260.41/41.57 | (657) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1477_1
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (109) with fresh symbol all_1486_0 gives:
% 260.41/41.57 | (658) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1486_0 &
% 260.41/41.57 | $i(all_1486_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.57 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 260.41/41.57 | (c_RComplete_Onatceiling(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1486_0, v1)
% 260.41/41.57 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)) & !
% 260.41/41.57 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.57 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 260.41/41.57 | (c_RComplete_Onatceiling(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1486_0, v1)
% 260.41/41.57 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (658) implies:
% 260.41/41.57 | (659) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1486_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (11) with fresh symbol all_1501_0 gives:
% 260.41/41.57 | (660) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1501_0 &
% 260.41/41.57 | $i(all_1501_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.57 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v2) |
% 260.41/41.57 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Ozero(v1) | ? [v3: $i] : ?
% 260.41/41.57 | [v4: $i] : (( ~ (v2 = all_1501_0) | (v4 = v0 &
% 260.41/41.57 | tc_Polynomial_Opoly(v1) = v3 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(v3) = v0 & $i(v3))) & (v2 =
% 260.41/41.57 | all_1501_0 | ( ~ (v4 = v0) & tc_Polynomial_Opoly(v1) = v3 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(v3) = v4 & $i(v4) & $i(v3)))))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (660) implies:
% 260.41/41.57 | (661) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1501_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (32) with fresh symbols all_1504_0, all_1504_1,
% 260.41/41.57 | all_1504_2, all_1504_3, all_1504_4 gives:
% 260.41/41.57 | (662) c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1504_2) = all_1504_1 &
% 260.41/41.57 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) =
% 260.41/41.57 | all_1504_2 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____,
% 260.41/41.57 | all_1504_4) = all_1504_3 &
% 260.41/41.57 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____) =
% 260.41/41.57 | all_1504_4 & $i(all_1504_0) & $i(all_1504_1) & $i(all_1504_2) &
% 260.41/41.57 | $i(all_1504_3) & $i(all_1504_4) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.41/41.57 | (hAPP(all_1504_1, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i]
% 260.41/41.57 | : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 &
% 260.41/41.57 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.57 | all_1504_3, v3)) |
% 260.41/41.57 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 &
% 260.41/41.57 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.57 | all_1504_0, v2))))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (662) implies:
% 260.41/41.57 | (663) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____) =
% 260.41/41.57 | all_1504_4
% 260.41/41.57 | (664) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, all_1504_4) =
% 260.41/41.57 | all_1504_3
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (40) with fresh symbols all_1507_0, all_1507_1 gives:
% 260.41/41.57 | (665) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1507_0 &
% 260.41/41.57 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1507_1 & $i(all_1507_0)
% 260.41/41.57 | & $i(all_1507_1) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 =
% 260.41/41.57 | all_1507_1 | ~ (hAPP(v2, v0) = all_1507_1) | ~ (hAPP(all_1507_0,
% 260.41/41.57 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i]
% 260.41/41.57 | : ! [v2: $i] : (v0 = all_1507_1 | ~ (hAPP(v2, v0) = all_1507_1) |
% 260.41/41.57 | ~ (hAPP(all_1507_0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0:
% 260.41/41.57 | $i] : ! [v1: int] : (v1 = all_1507_1 | ~ (hAPP(v0, all_1507_1) =
% 260.41/41.57 | v1) | ~ (hAPP(all_1507_0, all_1507_1) = v0))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (665) implies:
% 260.41/41.57 | (666) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1507_1
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (170) with fresh symbols all_1516_0, all_1516_1 gives:
% 260.41/41.57 | (667) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1516_0 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1516_1 &
% 260.41/41.57 | $i(all_1516_0) & $i(all_1516_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.57 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v1) =
% 260.41/41.57 | v2) | ~ (c_Transcendental_Oln(v0) = v3) | ~
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 260.41/41.57 | $i(v1) | ~ $i(v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1516_1, v1) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1516_1, v0) |
% 260.41/41.57 | ? [v5: $i] : ? [v6: $i] : (c_Transcendental_Oln(v6) = v4 &
% 260.41/41.57 | hAPP(v5, v0) = v6 & hAPP(all_1516_0, v1) = v5 & $i(v6) & $i(v5) &
% 260.41/41.57 | $i(v4)))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (667) implies:
% 260.41/41.57 | (668) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1516_1
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (42) with fresh symbols all_1525_0, all_1525_1 gives:
% 260.41/41.57 | (669) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1525_1 &
% 260.41/41.57 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1525_0 & $i(all_1525_0)
% 260.41/41.57 | & $i(all_1525_1) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 =
% 260.41/41.57 | all_1525_0 | ~ (hAPP(v2, v0) = all_1525_0) | ~ (hAPP(all_1525_1,
% 260.41/41.57 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i]
% 260.41/41.57 | : ! [v2: $i] : (v0 = all_1525_0 | ~ (hAPP(v2, v0) = all_1525_0) |
% 260.41/41.57 | ~ (hAPP(all_1525_1, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0:
% 260.41/41.57 | $i] : ! [v1: int] : (v1 = all_1525_0 | ~ (hAPP(v0, all_1525_0) =
% 260.41/41.57 | v1) | ~ (hAPP(all_1525_1, all_1525_0) = v0))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (669) implies:
% 260.41/41.57 | (670) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1525_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (160) with fresh symbol all_1534_0 gives:
% 260.41/41.57 | (671) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1534_0 &
% 260.41/41.57 | $i(all_1534_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.57 | $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~
% 260.41/41.57 | (c_Transcendental_Oln(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1534_0, v1) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1534_0, v0) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3) |
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 260.41/41.57 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.57 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 260.41/41.57 | v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1534_0, v1) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1534_0, v0) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (671) implies:
% 260.41/41.57 | (672) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1534_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (222) with fresh symbols all_1537_0, all_1537_1 gives:
% 260.41/41.57 | (673) c_Nat_OSuc(all_1537_1) = all_1537_0 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1537_1 &
% 260.41/41.57 | $i(all_1537_0) & $i(all_1537_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.57 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 260.41/41.57 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 260.41/41.57 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v5) | ~
% 260.41/41.57 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, all_1537_0, v0) = v6) | ~
% 260.41/41.57 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v0) = v8) | ~
% 260.41/41.57 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v2) | ~
% 260.41/41.57 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, all_1537_0, v0) = v3) | ~
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v6) = v7) | ~
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v8) = v9) | ~
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v1)
% 260.41/41.57 | | ~ $i(v0) | ? [v10: $i] :
% 260.41/41.57 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v10, v0) = v9 &
% 260.41/41.57 | c_Nat_OSuc(v1) = v10 & $i(v10) & $i(v9)))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (673) implies:
% 260.41/41.57 | (674) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1537_1
% 260.41/41.57 | (675) c_Nat_OSuc(all_1537_1) = all_1537_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (132) with fresh symbols all_1540_0, all_1540_1 gives:
% 260.41/41.57 | (676) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1540_0 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1540_1 &
% 260.41/41.57 | $i(all_1540_0) & $i(all_1540_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.57 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 260.41/41.57 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 260.41/41.57 | (c_Power_Opower__class_Opower(v2) = v4) | ~
% 260.41/41.57 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1540_0) = v6) |
% 260.41/41.57 | ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v8, v0) =
% 260.41/41.57 | v9) | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v4, v0) = v5) | ~
% 260.41/41.57 | (hAPP(v3, v7) = v8) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.57 | class_Groups_Omonoid__mult(v2) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1540_1, v1) |
% 260.41/41.57 | (hAPP(v5, v1) = v9 & $i(v9)))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (676) implies:
% 260.41/41.57 | (677) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1540_1
% 260.41/41.57 | (678) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1540_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (134) with fresh symbol all_1543_0 gives:
% 260.41/41.57 | (679) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1543_0 &
% 260.41/41.57 | $i(all_1543_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.57 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 260.41/41.57 | [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7,
% 260.41/41.57 | v0) = v8) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v2) = v5) |
% 260.41/41.57 | ~ (hAPP(v4, v1) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 260.41/41.57 | $i(v0) | ~ c_Orderings_Oord__class_Oless(v3, v2, v1) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1543_0, v0) | ~
% 260.41/41.57 | class_Rings_Olinordered__semidom(v3) |
% 260.41/41.57 | c_Orderings_Oord__class_Oless(v3, v6, v8) | ? [v9: $i] :
% 260.41/41.57 | (c_Groups_Ozero__class_Ozero(v3) = v9 & $i(v9) & ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(v3, v9, v2)))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (679) implies:
% 260.41/41.57 | (680) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1543_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (55) with fresh symbols all_1549_0, all_1549_1 gives:
% 260.41/41.57 | (681) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1549_1 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1549_0 &
% 260.41/41.57 | $i(all_1549_0) & $i(all_1549_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.57 | int] : (v2 = all_1549_0 | ~ (hAPP(v1, v0) = v2) | ~
% 260.41/41.57 | (hAPP(all_1549_1, all_1549_0) = v1) | ~ $i(v0)) & ! [v0: $i] : !
% 260.41/41.57 | [v1: $i] : ! [v2: int] : (v2 = all_1549_0 | ~ (hAPP(v1, all_1549_0)
% 260.41/41.57 | = v2) | ~ (hAPP(all_1549_1, v0) = v1) | ~ $i(v0)) & ! [v0:
% 260.41/41.57 | any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1549_0 | v0 =
% 260.41/41.57 | all_1549_0 | ~ (hAPP(v2, v0) = all_1549_0) | ~ (hAPP(all_1549_1,
% 260.41/41.57 | v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (681) implies:
% 260.41/41.57 | (682) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1549_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (158) with fresh symbol all_1552_0 gives:
% 260.41/41.57 | (683) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1552_0 &
% 260.41/41.57 | $i(all_1552_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.57 | $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~
% 260.41/41.57 | (c_Transcendental_Oln(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1552_0, v1) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1552_0, v0) |
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0:
% 260.41/41.57 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.57 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 260.41/41.57 | v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1552_0, v1) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1552_0, v0) |
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (683) implies:
% 260.41/41.57 | (684) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1552_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (75) with fresh symbols all_1555_0, all_1555_1 gives:
% 260.41/41.57 | (685) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1555_1 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1555_0 &
% 260.41/41.57 | $i(all_1555_0) & $i(all_1555_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.57 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3)
% 260.41/41.57 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1555_1, all_1555_0) = v2) |
% 260.41/41.57 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] :
% 260.41/41.57 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1555_0 | v1 = v0 | ~ (hAPP(v3,
% 260.41/41.57 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1555_1, v2) =
% 260.41/41.57 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (685) implies:
% 260.41/41.57 | (686) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1555_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (64) with fresh symbol all_1558_0 gives:
% 260.41/41.57 | (687) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1558_0 &
% 260.41/41.57 | $i(all_1558_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)
% 260.41/41.57 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.57 | all_1558_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.57 | all_1558_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.57 | all_1558_0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)
% 260.41/41.57 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.57 | all_1558_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.57 | all_1558_0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)
% 260.41/41.57 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.57 | all_1558_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.41/41.57 | all_1558_0, v2))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (687) implies:
% 260.41/41.57 | (688) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1558_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (146) with fresh symbol all_1561_0 gives:
% 260.41/41.57 | (689) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1561_0 &
% 260.41/41.57 | $i(all_1561_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.57 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v2 =
% 260.41/41.57 | v0 | ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7, v1)
% 260.41/41.57 | = v6) | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~
% 260.41/41.57 | (hAPP(v4, v0) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 260.41/41.57 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1561_0, v1) |
% 260.41/41.57 | ~ class_Rings_Olinordered__semidom(v3) | ? [v8: $i] :
% 260.41/41.57 | (c_Groups_Ozero__class_Ozero(v3) = v8 & $i(v8) & ( ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(v3, v8, v2) | ~
% 260.41/41.57 | c_Orderings_Oord__class_Oless__eq(v3, v8, v0))))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (689) implies:
% 260.41/41.57 | (690) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1561_0
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (106) with fresh symbol all_1564_0 gives:
% 260.41/41.57 | (691) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1564_0 &
% 260.41/41.57 | $i(all_1564_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.57 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.57 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i]
% 260.41/41.57 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1564_0) =
% 260.41/41.57 | v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.57 | v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.57 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.57 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] :
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1564_0) = v4
% 260.41/41.57 | & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.57 | v4, v3)))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (691) implies:
% 260.41/41.57 | (692) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1564_0
% 260.41/41.57 | (693) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.57 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.57 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] :
% 260.41/41.57 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1564_0) = v4
% 260.41/41.57 | & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.57 | v4, v3)))
% 260.41/41.57 | (694) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.57 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.57 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.57 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i]
% 260.41/41.57 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1564_0) =
% 260.41/41.57 | v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.41/41.57 | v4, v3)))
% 260.41/41.57 |
% 260.41/41.57 | DELTA: instantiating (75) with fresh symbols all_1570_0, all_1570_1 gives:
% 260.41/41.57 | (695) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1570_1 &
% 260.41/41.57 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1570_0 &
% 260.41/41.57 | $i(all_1570_0) & $i(all_1570_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.57 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3)
% 260.41/41.57 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1570_1, all_1570_0) = v2) |
% 260.41/41.57 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] :
% 260.41/41.57 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1570_0 | v1 = v0 | ~ (hAPP(v3,
% 260.41/41.57 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1570_1, v2) =
% 260.41/41.57 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 260.41/41.57 |
% 260.41/41.57 | ALPHA: (695) implies:
% 260.41/41.57 | (696) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1570_0
% 260.41/41.57 |
% 260.41/41.58 | DELTA: instantiating (107) with fresh symbol all_1579_0 gives:
% 260.41/41.58 | (697) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1579_0 &
% 260.41/41.58 | $i(all_1579_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.41/41.58 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.58 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.58 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 260.41/41.58 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 260.41/41.58 | all_1579_0) = v4 & $i(v4) &
% 260.41/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) & !
% 260.41/41.58 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.58 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.58 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.58 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 260.41/41.58 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 260.41/41.58 | all_1579_0) = v4 & $i(v4) & ~
% 260.41/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4)))
% 260.41/41.58 |
% 260.41/41.58 | ALPHA: (697) implies:
% 260.41/41.58 | (698) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1579_0
% 260.41/41.58 | (699) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.58 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.58 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.58 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 260.41/41.58 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 260.41/41.58 | all_1579_0) = v4 & $i(v4) & ~
% 260.41/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4)))
% 260.41/41.58 | (700) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.41/41.58 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 260.41/41.58 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 260.41/41.58 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 260.41/41.58 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 260.41/41.58 | all_1579_0) = v4 & $i(v4) &
% 260.41/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4)))
% 260.41/41.58 |
% 260.41/41.58 | DELTA: instantiating (140) with fresh symbols all_1585_0, all_1585_1 gives:
% 260.41/41.58 | (701) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1585_0 &
% 260.41/41.58 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1585_1 &
% 260.41/41.58 | $i(all_1585_0) & $i(all_1585_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.41/41.58 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RComplete_Onatfloor(v1) =
% 260.41/41.58 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1585_0, v2) = v3) |
% 260.41/41.58 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 260.41/41.58 | [v8: $i] : ((v8 = v4 & c_RComplete_Onatfloor(v7) = v4 & hAPP(v6,
% 260.41/41.58 | v0) = v7 & hAPP(all_1585_1, v1) = v6 & $i(v7) & $i(v6) &
% 260.41/41.58 | $i(v4)) | ( ~ (v5 = v1) & c_RealDef_Oreal(tc_Nat_Onat, v2) = v5
% 260.41/41.58 | & $i(v5))))
% 260.41/41.58 |
% 260.41/41.58 | ALPHA: (701) implies:
% 260.41/41.58 | (702) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1585_0
% 260.41/41.58 |
% 260.41/41.58 | DELTA: instantiating (155) with fresh symbols all_1588_0, all_1588_1,
% 260.41/41.58 | all_1588_2 gives:
% 260.41/41.58 | (703) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1588_1 &
% 260.41/41.58 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1588_0 &
% 260.41/41.58 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1588_2 &
% 260.56/41.58 | $i(all_1588_0) & $i(all_1588_1) & $i(all_1588_2) & ! [v0: $i] : !
% 260.56/41.58 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 260.56/41.58 | ~ (c_Transcendental_Oln(v1) = v4) | ~
% 260.56/41.58 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ (hAPP(v3, v4) = v5) |
% 260.56/41.58 | ~ (hAPP(all_1588_0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1588_2, v1) |
% 260.56/41.58 | ? [v6: $i] : ? [v7: $i] : (c_Transcendental_Oln(v7) = v5 &
% 260.56/41.58 | hAPP(v6, v0) = v7 & hAPP(all_1588_1, v1) = v6 & $i(v7) & $i(v6) &
% 260.56/41.58 | $i(v5)))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (703) implies:
% 260.56/41.58 | (704) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1588_2
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (176) with fresh symbols all_1594_0, all_1594_1,
% 260.56/41.58 | all_1594_2 gives:
% 260.56/41.58 | (705) c_Nat_OSuc(all_1594_1) = all_1594_0 &
% 260.56/41.58 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1594_2 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1594_1 &
% 260.56/41.58 | $i(all_1594_0) & $i(all_1594_1) & $i(all_1594_2) & ! [v0: $i] : !
% 260.56/41.58 | [v1: any] : ! [v2: $i] : (v1 = all_1594_0 | ~ (hAPP(v2, v0) =
% 260.56/41.58 | all_1594_0) | ~ (hAPP(all_1594_2, v1) = v2) | ~ $i(v1) | ~
% 260.56/41.58 | $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 =
% 260.56/41.58 | all_1594_0 | ~ (hAPP(v2, v0) = all_1594_0) | ~ (hAPP(all_1594_2,
% 260.56/41.58 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int]
% 260.56/41.58 | : (v1 = all_1594_0 | ~ (hAPP(v0, all_1594_0) = v1) | ~
% 260.56/41.58 | (hAPP(all_1594_2, all_1594_0) = v0))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (705) implies:
% 260.56/41.58 | (706) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1594_1
% 260.56/41.58 | (707) c_Nat_OSuc(all_1594_1) = all_1594_0
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (205) with fresh symbols all_1608_0, all_1608_1,
% 260.56/41.58 | all_1608_2, all_1608_3 gives:
% 260.56/41.58 | (708) c_Nat_OSuc(all_1608_3) = all_1608_0 &
% 260.56/41.58 | c_Power_Opower__class_Opower(tc_Int_Oint) = all_1608_1 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1608_2 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1608_3 &
% 260.56/41.58 | $i(all_1608_0) & $i(all_1608_1) & $i(all_1608_2) & $i(all_1608_3) &
% 260.56/41.58 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 260.56/41.58 | ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1608_0) = v3)
% 260.56/41.58 | | ~ (hAPP(v2, v3) = v4) | ~ (hAPP(all_1608_1, v0) = v2) | ~
% 260.56/41.58 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 260.56/41.58 | all_1608_2, v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.56/41.58 | all_1608_3, v1) | ? [v5: $i] :
% 260.56/41.58 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5, v0) = v4 & hAPP(v2,
% 260.56/41.58 | v1) = v5 & $i(v5) & $i(v4)))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (708) implies:
% 260.56/41.58 | (709) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1608_3
% 260.56/41.58 | (710) c_Nat_OSuc(all_1608_3) = all_1608_0
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (224) with fresh symbols all_1611_0, all_1611_1 gives:
% 260.56/41.58 | (711) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1611_0 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1611_1 &
% 260.56/41.58 | $i(all_1611_0) & $i(all_1611_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.58 | int] : (v2 = all_1611_1 | ~
% 260.56/41.58 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)
% 260.56/41.58 | | ~ $i(v0) | ? [v3: $i] : (hAPP(all_1611_0, v0) = v3 & $i(v3) &
% 260.56/41.58 | ! [v4: $i] : ( ~ (hAPP(v3, v4) = v1) | ~ $i(v4)))) & ! [v0: $i]
% 260.56/41.58 | : ! [v1: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0)
% 260.56/41.58 | = all_1611_1) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i]
% 260.56/41.58 | : (hAPP(v2, v3) = v1 & hAPP(all_1611_0, v0) = v2 & $i(v3) &
% 260.56/41.58 | $i(v2)))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (711) implies:
% 260.56/41.58 | (712) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1611_1
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (186) with fresh symbol all_1614_0 gives:
% 260.56/41.58 | (713) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1614_0 &
% 260.56/41.58 | $i(all_1614_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.58 | $i] : ( ~ (c_Nat_OSuc(v3) = v1) | ~ (c_Nat_OSuc(v0) = v2) | ~
% 260.56/41.58 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0) |
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)) & ! [v0: $i] :
% 260.56/41.58 | ! [v1: any] : ! [v2: $i] : (v1 = all_1614_0 | ~ (c_Nat_OSuc(v0) =
% 260.56/41.58 | v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v3: $i] :
% 260.56/41.58 | (c_Nat_OSuc(v3) = v1 & $i(v3) &
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))) & ! [v0:
% 260.56/41.58 | $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1614_0, v1))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (713) implies:
% 260.56/41.58 | (714) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1614_0
% 260.56/41.58 | (715) ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = all_1614_0 | ~
% 260.56/41.58 | (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v3: $i] :
% 260.56/41.58 | (c_Nat_OSuc(v3) = v1 & $i(v3) &
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0)))
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (153) with fresh symbols all_1620_0, all_1620_1,
% 260.56/41.58 | all_1620_2 gives:
% 260.56/41.58 | (716) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1620_0 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1620_2 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1620_1 &
% 260.56/41.58 | $i(all_1620_0) & $i(all_1620_1) & $i(all_1620_2) & ! [v0: $i] : !
% 260.56/41.58 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1620_2, v1) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1620_1, v0) |
% 260.56/41.58 | ? [v2: $i] : ? [v3: $i] : (hAPP(v3, v1) = v0 & hAPP(all_1620_0,
% 260.56/41.58 | v2) = v3 & $i(v3) & $i(v2) &
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1620_1, v2) &
% 260.56/41.58 | ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v1) = v0) |
% 260.56/41.58 | ~ (hAPP(all_1620_0, v4) = v5) | ~ $i(v4) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1620_1,
% 260.56/41.58 | v4))))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (716) implies:
% 260.56/41.58 | (717) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1620_1
% 260.56/41.58 | (718) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1620_2
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (80) with fresh symbols all_1626_0, all_1626_1 gives:
% 260.56/41.58 | (719) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1626_0 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1626_1 &
% 260.56/41.58 | $i(all_1626_0) & $i(all_1626_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.58 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) |
% 260.56/41.58 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4)
% 260.56/41.58 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1626_1, v4)
% 260.56/41.58 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 260.56/41.58 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7,
% 260.56/41.58 | v4) = v8) | ~ (hAPP(all_1626_0, v6) = v7) | ~ $i(v5) | ?
% 260.56/41.58 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 260.56/41.58 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) &
% 260.56/41.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 260.56/41.58 | v8)))))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (719) implies:
% 260.56/41.58 | (720) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1626_1
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (121) with fresh symbols all_1629_0, all_1629_1 gives:
% 260.56/41.58 | (721) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1629_0 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1629_1 &
% 260.56/41.58 | $i(all_1629_0) & $i(all_1629_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.58 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) |
% 260.56/41.58 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4)
% 260.56/41.58 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1629_1,
% 260.56/41.58 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (
% 260.56/41.58 | ~ (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7,
% 260.56/41.58 | v4) = v8) | ~ (hAPP(all_1629_0, v6) = v7) | ~ $i(v5) | ?
% 260.56/41.58 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 260.56/41.58 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) &
% 260.56/41.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 260.56/41.58 | v8)))))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (721) implies:
% 260.56/41.58 | (722) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1629_1
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (189) with fresh symbols all_1632_0, all_1632_1,
% 260.56/41.58 | all_1632_2 gives:
% 260.56/41.58 | (723) c_Nat_OSuc(all_1632_1) = all_1632_0 &
% 260.56/41.58 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1632_2 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1632_1 &
% 260.56/41.58 | $i(all_1632_0) & $i(all_1632_1) & $i(all_1632_2) & ! [v0: $i] : !
% 260.56/41.58 | [v1: $i] : ! [v2: int] : (v2 = all_1632_0 | ~ (hAPP(v1, v0) = v2) |
% 260.56/41.58 | ~ (hAPP(all_1632_2, all_1632_0) = v1) | ~ $i(v0)) & ! [v0: $i] :
% 260.56/41.58 | ! [v1: $i] : ! [v2: int] : (v2 = all_1632_0 | ~ (hAPP(v1,
% 260.56/41.58 | all_1632_1) = v2) | ~ (hAPP(all_1632_2, v0) = v1) | ~ $i(v0))
% 260.56/41.58 | & ! [v0: any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1632_0 | v0 =
% 260.56/41.58 | all_1632_1 | ~ (hAPP(v2, v0) = all_1632_0) | ~ (hAPP(all_1632_2,
% 260.56/41.58 | v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (723) implies:
% 260.56/41.58 | (724) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1632_1
% 260.56/41.58 | (725) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1632_2
% 260.56/41.58 | (726) c_Nat_OSuc(all_1632_1) = all_1632_0
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (143) with fresh symbol all_1635_0 gives:
% 260.56/41.58 | (727) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1635_0 &
% 260.56/41.58 | $i(all_1635_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.58 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.58 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) |
% 260.56/41.58 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | class_Power_Opower(v2) | ~ class_Rings_Ono__zero__divisors(v2) |
% 260.56/41.58 | ~ class_Rings_Omult__zero(v2) | ~ class_Rings_Ozero__neq__one(v2)
% 260.56/41.58 | | ? [v6: $i] : (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & (
% 260.56/41.58 | ~ (v6 = v5) | (v5 = v1 & ~ (v0 = all_1635_0))) & ( ~ (v6 = v1)
% 260.56/41.58 | | v5 = v1 | v0 = all_1635_0)))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (727) implies:
% 260.56/41.58 | (728) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1635_0
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (56) with fresh symbols all_1641_0, all_1641_1 gives:
% 260.56/41.58 | (729) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1641_1 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1641_0 &
% 260.56/41.58 | $i(all_1641_0) & $i(all_1641_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.58 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 260.56/41.58 | (hAPP(v4, all_1641_0) = v5) | ~ (hAPP(v2, all_1641_0) = v3) | ~
% 260.56/41.58 | (hAPP(all_1641_1, v1) = v2) | ~ (hAPP(all_1641_1, v0) = v4) | ~
% 260.56/41.58 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : !
% 260.56/41.58 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | v1 = all_1641_0 |
% 260.56/41.58 | ~ (hAPP(v5, v1) = v4) | ~ (hAPP(v3, v1) = v4) | ~
% 260.56/41.58 | (hAPP(all_1641_1, v2) = v3) | ~ (hAPP(all_1641_1, v0) = v5) | ~
% 260.56/41.58 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (729) implies:
% 260.56/41.58 | (730) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1641_0
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (148) with fresh symbols all_1647_0, all_1647_1 gives:
% 260.56/41.58 | (731) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1647_0 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1647_1 &
% 260.56/41.58 | $i(all_1647_0) & $i(all_1647_1) & ! [v0: any] : ! [v1: $i] : !
% 260.56/41.58 | [v2: $i] : ! [v3: $i] : (v0 = all_1647_1 | ~ (hAPP(v2, v0) = v3) |
% 260.56/41.58 | ~ (hAPP(all_1647_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1647_1, v3) |
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1647_1, v1)) & !
% 260.56/41.58 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2,
% 260.56/41.58 | v0) = v3) | ~ (hAPP(all_1647_0, v1) = v2) | ~ $i(v1) | ~
% 260.56/41.58 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1647_1,
% 260.56/41.58 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1647_1, v3))
% 260.56/41.58 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1647_1)
% 260.56/41.58 | = v2) | ~ (hAPP(all_1647_0, v0) = v1) | ~ $i(v0) |
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1647_1, v2))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (731) implies:
% 260.56/41.58 | (732) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1647_1
% 260.56/41.58 | (733) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1647_0
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (148) with fresh symbols all_1653_0, all_1653_1 gives:
% 260.56/41.58 | (734) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1653_0 &
% 260.56/41.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1653_1 &
% 260.56/41.58 | $i(all_1653_0) & $i(all_1653_1) & ! [v0: any] : ! [v1: $i] : !
% 260.56/41.58 | [v2: $i] : ! [v3: $i] : (v0 = all_1653_1 | ~ (hAPP(v2, v0) = v3) |
% 260.56/41.58 | ~ (hAPP(all_1653_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1653_1, v3) |
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1653_1, v1)) & !
% 260.56/41.58 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2,
% 260.56/41.58 | v0) = v3) | ~ (hAPP(all_1653_0, v1) = v2) | ~ $i(v1) | ~
% 260.56/41.58 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1653_1,
% 260.56/41.58 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1653_1, v3))
% 260.56/41.58 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1653_1)
% 260.56/41.58 | = v2) | ~ (hAPP(all_1653_0, v0) = v1) | ~ $i(v0) |
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1653_1, v2))
% 260.56/41.58 |
% 260.56/41.58 | ALPHA: (734) implies:
% 260.56/41.58 | (735) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1653_1
% 260.56/41.58 | (736) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1653_0
% 260.56/41.58 |
% 260.56/41.58 | DELTA: instantiating (125) with fresh symbol all_1656_0 gives:
% 260.56/41.58 | (737) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1656_0 &
% 260.56/41.58 | $i(all_1656_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 260.56/41.58 | | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 260.56/41.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ? [v3:
% 260.56/41.58 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.56/41.58 | all_1656_0, v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.58 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5)
% 260.56/41.58 | | ~ $i(v4) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.56/41.59 | v4, v0) | ? [v6: $i] :
% 260.56/41.59 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) = v6 & $i(v6)
% 260.56/41.59 | & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 260.56/41.59 | v3))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.59 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5)
% 260.56/41.59 | | ~ $i(v4) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.56/41.59 | v2, v4) | ? [v6: $i] :
% 260.56/41.59 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) = v6 & $i(v6)
% 260.56/41.59 | & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 260.56/41.59 | v3)))))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (737) implies:
% 260.56/41.59 | (738) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1656_0
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (93) with fresh symbols all_1659_0, all_1659_1,
% 260.56/41.59 | all_1659_2 gives:
% 260.56/41.59 | (739) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1659_1 &
% 260.56/41.59 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1659_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1659_2 &
% 260.56/41.59 | $i(all_1659_0) & $i(all_1659_1) & $i(all_1659_2) & ! [v0: $i] : !
% 260.56/41.59 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 260.56/41.59 | ~ (c_RComplete_Onatfloor(v1) = v2) | ~ (c_RComplete_Onatfloor(v0)
% 260.56/41.59 | = v4) | ~ (hAPP(v3, v4) = v5) | ~ (hAPP(all_1659_1, v2) = v3) |
% 260.56/41.59 | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1659_2, v1)
% 260.56/41.59 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.56/41.59 | all_1659_2, v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 260.56/41.59 | (c_RComplete_Onatfloor(v7) = v8 & hAPP(v6, v0) = v7 &
% 260.56/41.59 | hAPP(all_1659_0, v1) = v6 & $i(v8) & $i(v7) & $i(v6) &
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v8)))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (739) implies:
% 260.56/41.59 | (740) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1659_2
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (209) with fresh symbols all_1662_0, all_1662_1 gives:
% 260.56/41.59 | (741) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1662_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1662_1 &
% 260.56/41.59 | $i(all_1662_0) & $i(all_1662_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2
% 260.56/41.59 | = all_1662_1 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v4, v5)
% 260.56/41.59 | = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 260.56/41.59 | (hAPP(all_1662_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.59 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v6 & $i(v6))) &
% 260.56/41.59 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 260.56/41.59 | ! [v5: int] : (v5 = all_1662_1 | ~
% 260.56/41.59 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v4) = v5) | ~
% 260.56/41.59 | (hAPP(v2, v1) = v3) | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1662_0,
% 260.56/41.59 | all_1662_1) = v2) | ~ $i(v1) | ~ $i(v0))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (741) implies:
% 260.56/41.59 | (742) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1662_1
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (122) with fresh symbols all_1665_0, all_1665_1 gives:
% 260.56/41.59 | (743) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1665_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1665_1 &
% 260.56/41.59 | $i(all_1665_0) & $i(all_1665_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~
% 260.56/41.59 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3:
% 260.56/41.59 | $i] : ($i(v3) &
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1665_1,
% 260.56/41.59 | v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (
% 260.56/41.59 | ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v6,
% 260.56/41.59 | v3) = v7) | ~ (hAPP(all_1665_0, v5) = v6) | ~ $i(v4) | ?
% 260.56/41.59 | [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 260.56/41.59 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) =
% 260.56/41.59 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 260.56/41.59 | v7)))))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (743) implies:
% 260.56/41.59 | (744) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1665_1
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (145) with fresh symbol all_1673_0 gives:
% 260.56/41.59 | (745) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1673_0 &
% 260.56/41.59 | $i(all_1673_0) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.59 | $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | v0 = all_1673_0 | ~
% 260.56/41.59 | (c_Power_Opower__class_Opower(v1) = v2) | ~
% 260.56/41.59 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) |
% 260.56/41.59 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.59 | class_Rings_Osemiring__0(v1) | ~ class_Power_Opower(v1)) & ! [v0:
% 260.56/41.59 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.56/41.59 | (c_Power_Opower__class_Opower(v0) = v1) | ~
% 260.56/41.59 | (c_Groups_Ozero__class_Ozero(v0) = v2) | ~ (hAPP(v3, all_1673_0) =
% 260.56/41.59 | v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v0) | ~
% 260.56/41.59 | class_Rings_Osemiring__0(v0) | ~ class_Power_Opower(v0) |
% 260.56/41.59 | (c_Groups_Oone__class_Oone(v0) = v4 & $i(v4)))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (745) implies:
% 260.56/41.59 | (746) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1673_0
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (81) with fresh symbols all_1676_0, all_1676_1 gives:
% 260.56/41.59 | (747) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1676_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1676_1 &
% 260.56/41.59 | $i(all_1676_0) & $i(all_1676_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~
% 260.56/41.59 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3:
% 260.56/41.59 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.56/41.59 | all_1676_1, v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 260.56/41.59 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) |
% 260.56/41.59 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(all_1676_0, v5) = v6) | ~
% 260.56/41.59 | $i(v4) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 260.56/41.59 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) =
% 260.56/41.59 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 260.56/41.59 | v7)))))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (747) implies:
% 260.56/41.59 | (748) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1676_1
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (34) with fresh symbols all_1681_0, all_1681_1,
% 260.56/41.59 | all_1681_2 gives:
% 260.56/41.59 | (749) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1681_1 &
% 260.56/41.59 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1681_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1681_2 &
% 260.56/41.59 | $i(all_1681_0) & $i(all_1681_1) & $i(all_1681_2) & ! [v0: $i] : !
% 260.56/41.59 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 260.56/41.59 | (v1 = all_1681_2 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1,
% 260.56/41.59 | all_1681_0) = v2) | ~
% 260.56/41.59 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v4) = v5) | ~
% 260.56/41.59 | (hAPP(v3, v0) = v4) | ~ (hAPP(all_1681_1, v2) = v3) | ~ $i(v1) |
% 260.56/41.59 | ~ $i(v0) | ? [v6: $i] : (hAPP(v6, v0) = v5 & hAPP(all_1681_1, v1)
% 260.56/41.59 | = v6 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | int] : (v2 = all_1681_2 | ~ (hAPP(v1, v0) = v2) | ~
% 260.56/41.59 | (hAPP(all_1681_1, all_1681_2) = v1) | ~ $i(v0))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (749) implies:
% 260.56/41.59 | (750) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1681_2
% 260.56/41.59 | (751) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1681_0
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (118) with fresh symbol all_1684_0 gives:
% 260.56/41.59 | (752) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1684_0 &
% 260.56/41.59 | $i(all_1684_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 260.56/41.59 | | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ? [v3:
% 260.56/41.59 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.56/41.59 | all_1684_0, v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.59 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5)
% 260.56/41.59 | | ~ $i(v4) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) |
% 260.56/41.59 | ? [v6: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) =
% 260.56/41.59 | v6 & $i(v6) & ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v3))) &
% 260.56/41.59 | ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.59 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5)
% 260.56/41.59 | | ~ $i(v4) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) |
% 260.56/41.59 | ? [v6: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) =
% 260.56/41.59 | v6 & $i(v6) & ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v3)))))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (752) implies:
% 260.56/41.59 | (753) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1684_0
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (76) with fresh symbols all_1687_0, all_1687_1 gives:
% 260.56/41.59 | (754) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1687_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1687_1 &
% 260.56/41.59 | $i(all_1687_0) & $i(all_1687_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 260.56/41.59 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1687_0, v2) = v3) |
% 260.56/41.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1687_1, v2) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] :
% 260.56/41.59 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 260.56/41.59 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 260.56/41.59 | (hAPP(all_1687_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.59 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1687_1, v2) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (754) implies:
% 260.56/41.59 | (755) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1687_1
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (124) with fresh symbol all_1693_0 gives:
% 260.56/41.59 | (756) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1693_0 &
% 260.56/41.59 | $i(all_1693_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.59 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 260.56/41.59 | v0) = v3) | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 260.56/41.59 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.56/41.59 | all_1693_0, v2) | ? [v5: $i] : ($i(v5) &
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1693_0, v5) &
% 260.56/41.59 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 260.56/41.59 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v7, v4) =
% 260.56/41.59 | v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v6) | ? [v9: $i] : ?
% 260.56/41.59 | [v10: $i] : ? [v11: $i] :
% 260.56/41.59 | ((c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v6, v1) =
% 260.56/41.59 | v9 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 260.56/41.59 | v9) = v10 & $i(v10) & $i(v9) & ( ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10, v5)
% 260.56/41.59 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.56/41.59 | all_1693_0, v10))) |
% 260.56/41.59 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) =
% 260.56/41.59 | v11 & $i(v11) &
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 260.56/41.59 | v2))))))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (756) implies:
% 260.56/41.59 | (757) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1693_0
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (226) with fresh symbol all_1699_0 gives:
% 260.56/41.59 | (758) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1699_0 &
% 260.56/41.59 | $i(all_1699_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.59 | int] : (v3 = all_1699_0 | ~
% 260.56/41.59 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v0) = v3) | ~
% 260.56/41.59 | (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ?
% 260.56/41.59 | [v5: $i] : ( ~ (v5 = v0) & c_Divides_Odiv__class_Omod(tc_Nat_Onat,
% 260.56/41.59 | v1, v0) = v4 & c_Nat_OSuc(v4) = v5 & $i(v5) & $i(v4))) & !
% 260.56/41.59 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.56/41.59 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v0) = v3) | ~
% 260.56/41.59 | (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ?
% 260.56/41.59 | [v5: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v4 &
% 260.56/41.59 | c_Nat_OSuc(v4) = v5 & $i(v5) & $i(v4) & (v5 = v3 | v5 = v0)))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (758) implies:
% 260.56/41.59 | (759) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1699_0
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (119) with fresh symbols all_1702_0, all_1702_1 gives:
% 260.56/41.59 | (760) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1702_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1702_1 &
% 260.56/41.59 | $i(all_1702_0) & $i(all_1702_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | $i] : ( ~ (hAPP(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.59 | hBOOL(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 260.56/41.59 | ($i(v4) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4,
% 260.56/41.59 | all_1702_0) = v5 & hAPP(v1, v5) = v6 & $i(v6) & $i(v5) &
% 260.56/41.59 | hBOOL(v6) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4,
% 260.56/41.59 | v0) & ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v1, v7) = v8) |
% 260.56/41.59 | ~ $i(v7) | ~ hBOOL(v8) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v7, v4))) |
% 260.56/41.59 | (hAPP(v1, all_1702_1) = v3 & $i(v3) & hBOOL(v3)))))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (760) implies:
% 260.56/41.59 | (761) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1702_1
% 260.56/41.59 | (762) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1702_0
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (141) with fresh symbols all_1705_0, all_1705_1,
% 260.56/41.59 | all_1705_2, all_1705_3 gives:
% 260.56/41.59 | (763) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1705_2 &
% 260.56/41.59 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1705_0 &
% 260.56/41.59 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1705_1 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1705_3 &
% 260.56/41.59 | $i(all_1705_0) & $i(all_1705_1) & $i(all_1705_2) & $i(all_1705_3) &
% 260.56/41.59 | ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 260.56/41.59 | ! [v5: $i] : ! [v6: $i] : (v1 = all_1705_3 | ~
% 260.56/41.59 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1705_1) = v4) |
% 260.56/41.59 | ~ (hAPP(v3, v5) = v6) | ~ (hAPP(v2, v4) = v5) | ~
% 260.56/41.59 | (hAPP(all_1705_0, v0) = v3) | ~ (hAPP(all_1705_2, v0) = v2) | ~
% 260.56/41.59 | $i(v1) | ~ $i(v0) | (hAPP(v2, v1) = v6 & $i(v6))) & ! [v0: $i] :
% 260.56/41.59 | ! [v1: $i] : ! [v2: int] : (v2 = all_1705_1 | ~ (hAPP(v1,
% 260.56/41.59 | all_1705_3) = v2) | ~ (hAPP(all_1705_2, v0) = v1) | ~ $i(v0))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (763) implies:
% 260.56/41.59 | (764) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1705_3
% 260.56/41.59 | (765) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1705_1
% 260.56/41.59 | (766) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1705_2
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (218) with fresh symbols all_1708_0, all_1708_1 gives:
% 260.56/41.59 | (767) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1708_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1708_1 &
% 260.56/41.59 | $i(all_1708_0) & $i(all_1708_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.56/41.59 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v2) = v6) | ~
% 260.56/41.59 | (c_Nat_OSuc(v1) = v4) | ~ (hAPP(v3, v4) = v5) | ~
% 260.56/41.59 | (hAPP(all_1708_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.59 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1708_1, v2) | ?
% 260.56/41.59 | [v7: $i] : (( ~ (v6 = v1) | (hAPP(v3, v1) = v7 & $i(v7) &
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) &
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v7, v0))) &
% 260.56/41.59 | (v6 = v1 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)
% 260.56/41.59 | | (hAPP(v3, v1) = v7 & $i(v7) & ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v7, v0)))))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (767) implies:
% 260.56/41.59 | (768) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1708_1
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (78) with fresh symbols all_1711_0, all_1711_1 gives:
% 260.56/41.59 | (769) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1711_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1711_1 &
% 260.56/41.59 | $i(all_1711_0) & $i(all_1711_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 260.56/41.59 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1711_0, v2) = v3) |
% 260.56/41.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1711_1, v2) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0:
% 260.56/41.59 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.59 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 260.56/41.59 | (hAPP(all_1711_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.59 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1711_1, v2) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (769) implies:
% 260.56/41.59 | (770) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1711_1
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (18) with fresh symbols all_1714_0, all_1714_1 gives:
% 260.56/41.59 | (771) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1714_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1714_1 &
% 260.56/41.59 | $i(all_1714_0) & $i(all_1714_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 260.56/41.59 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1714_0, v2) = v3) |
% 260.56/41.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1714_1, v2) |
% 260.56/41.59 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 260.56/41.59 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.59 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 260.56/41.59 | (hAPP(all_1714_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.59 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1714_1, v2) |
% 260.56/41.59 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (771) implies:
% 260.56/41.59 | (772) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1714_1
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (65) with fresh symbols all_1720_0, all_1720_1 gives:
% 260.56/41.59 | (773) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1720_0 &
% 260.56/41.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1720_1 &
% 260.56/41.59 | $i(all_1720_0) & $i(all_1720_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.59 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1720_0,
% 260.56/41.59 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1720_1, v3) |
% 260.56/41.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1720_1, v1)) & !
% 260.56/41.59 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2,
% 260.56/41.59 | v0) = v3) | ~ (hAPP(all_1720_0, v1) = v2) | ~ $i(v1) | ~
% 260.56/41.59 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1720_1,
% 260.56/41.59 | v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1720_1, v0))
% 260.56/41.59 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.56/41.59 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1720_0, v1) = v2) | ~ $i(v1) |
% 260.56/41.59 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.56/41.59 | all_1720_1, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.56/41.59 | all_1720_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.56/41.59 | all_1720_1, v3))
% 260.56/41.59 |
% 260.56/41.59 | ALPHA: (773) implies:
% 260.56/41.59 | (774) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1720_1
% 260.56/41.59 |
% 260.56/41.59 | DELTA: instantiating (128) with fresh symbols all_1723_0, all_1723_1,
% 260.56/41.59 | all_1723_2, all_1723_3 gives:
% 260.56/41.60 | (775) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1723_0 &
% 260.56/41.60 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1723_2 &
% 260.56/41.60 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1723_1 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1723_3 &
% 260.56/41.60 | $i(all_1723_0) & $i(all_1723_1) & $i(all_1723_2) & $i(all_1723_3) &
% 260.56/41.60 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 260.56/41.60 | ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1723_1) =
% 260.56/41.60 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1723_0, v2) = v3) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1723_3, v1)
% 260.56/41.60 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 260.56/41.60 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v5 &
% 260.56/41.60 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, all_1723_1) =
% 260.56/41.60 | v8 & hAPP(v6, v1) = v7 & hAPP(all_1723_2, v5) = v6 & $i(v8) &
% 260.56/41.60 | $i(v7) & $i(v6) & $i(v5) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v4)))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (775) implies:
% 260.56/41.60 | (776) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1723_3
% 260.56/41.60 | (777) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1723_1
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (120) with fresh symbols all_1729_0, all_1729_1 gives:
% 260.56/41.60 | (778) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1729_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1729_1 &
% 260.56/41.60 | $i(all_1729_0) & $i(all_1729_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.56/41.60 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~
% 260.56/41.60 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2)
% 260.56/41.60 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1729_1,
% 260.56/41.60 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 260.56/41.60 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9,
% 260.56/41.60 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1729_0,
% 260.56/41.60 | v8) = v9) | ~ (hAPP(all_1729_0, v5) = v6) | ~ $i(v4) | ~
% 260.56/41.60 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4)
% 260.56/41.60 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 260.56/41.60 | v10)))))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (778) implies:
% 260.56/41.60 | (779) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1729_1
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (19) with fresh symbols all_1732_0, all_1732_1 gives:
% 260.56/41.60 | (780) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1732_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1732_1 &
% 260.56/41.60 | $i(all_1732_0) & $i(all_1732_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.60 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.56/41.60 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1732_0,
% 260.56/41.60 | v1) = v3) | ~ (hAPP(all_1732_0, v0) = v5) | ~ $i(v2) | ~
% 260.56/41.60 | $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1732_1, v2) |
% 260.56/41.60 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6) |
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 260.56/41.60 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.60 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) =
% 260.56/41.60 | v4) | ~ (hAPP(all_1732_0, v1) = v3) | ~ (hAPP(all_1732_0, v0) =
% 260.56/41.60 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1732_1, v2) |
% 260.56/41.60 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (780) implies:
% 260.56/41.60 | (781) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1732_1
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (27) with fresh symbols all_1735_0, all_1735_1 gives:
% 260.56/41.60 | (782) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1735_1 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1735_0 &
% 260.56/41.60 | $i(all_1735_0) & $i(all_1735_1) & ! [v0: $i] : ! [v1: any] : !
% 260.56/41.60 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = all_1735_0
% 260.56/41.60 | | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) =
% 260.56/41.60 | all_1735_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) |
% 260.56/41.60 | ~ (hAPP(all_1735_1, v1) = v2) | ~ (hAPP(all_1735_1, v0) = v4) | ~
% 260.56/41.60 | $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : !
% 260.56/41.60 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v0 = all_1735_0 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) =
% 260.56/41.60 | all_1735_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) |
% 260.56/41.60 | ~ (hAPP(all_1735_1, v1) = v2) | ~ (hAPP(all_1735_1, v0) = v4) | ~
% 260.56/41.60 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 260.56/41.60 | (v2 = all_1735_0 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.56/41.60 | v1, v1) = v2) | ~ (hAPP(v0, all_1735_0) = v1) | ~
% 260.56/41.60 | (hAPP(all_1735_1, all_1735_0) = v0))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (782) implies:
% 260.56/41.60 | (783) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1735_0
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (17) with fresh symbols all_1738_0, all_1738_1 gives:
% 260.56/41.60 | (784) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1738_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1738_1 &
% 260.56/41.60 | $i(all_1738_0) & $i(all_1738_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.60 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.56/41.60 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1738_0,
% 260.56/41.60 | v1) = v3) | ~ (hAPP(all_1738_0, v0) = v5) | ~ $i(v2) | ~
% 260.56/41.60 | $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1738_1, v2) |
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0:
% 260.56/41.60 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.60 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) =
% 260.56/41.60 | v4) | ~ (hAPP(all_1738_0, v1) = v3) | ~ (hAPP(all_1738_0, v0) =
% 260.56/41.60 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1738_1, v2) |
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (784) implies:
% 260.56/41.60 | (785) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1738_1
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (136) with fresh symbols all_1741_0, all_1741_1,
% 260.56/41.60 | all_1741_2 gives:
% 260.56/41.60 | (786) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1741_1 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1741_2 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1741_0 &
% 260.56/41.60 | $i(all_1741_0) & $i(all_1741_1) & $i(all_1741_2) & ! [v0: $i] : !
% 260.56/41.60 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 =
% 260.56/41.60 | all_1741_2 | ~ (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v1) = v2) |
% 260.56/41.60 | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1741_1, v2) = v3) | ~ $i(v1)
% 260.56/41.60 | | ~ $i(v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 260.56/41.60 | all_1741_2, v4)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : !
% 260.56/41.60 | [v3: $i] : (v0 = all_1741_0 | ~
% 260.56/41.60 | (c_Groups_Oabs__class_Oabs(tc_Int_Oint, all_1741_2) = v1) | ~
% 260.56/41.60 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1741_1, v1) = v2) | ~ $i(v0) |
% 260.56/41.60 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1741_2, v3)) & !
% 260.56/41.60 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 260.56/41.60 | (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v0) = v1) | ~ (hAPP(v2,
% 260.56/41.60 | all_1741_0) = v3) | ~ (hAPP(all_1741_1, v1) = v2) | ~ $i(v0)
% 260.56/41.60 | | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1741_2, v3))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (786) implies:
% 260.56/41.60 | (787) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1741_0
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (129) with fresh symbol all_1744_0 gives:
% 260.56/41.60 | (788) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1744_0 &
% 260.56/41.60 | $i(all_1744_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 260.56/41.60 | | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1744_0, v2) |
% 260.56/41.60 | ~ class_RealVector_Oreal__normed__vector(v1) | c_SEQ_OBseq(v1, v0)
% 260.56/41.60 | | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5 & hAPP(v0, v3) = v4 &
% 260.56/41.60 | $i(v5) & $i(v4) & $i(v3) & ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))) &
% 260.56/41.60 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 260.56/41.60 | | ? [v2: $i] : ($i(v2) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1744_0, v2) &
% 260.56/41.60 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v0,
% 260.56/41.60 | v3) = v4) | ~ $i(v3) |
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (788) implies:
% 260.56/41.60 | (789) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1744_0
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (38) with fresh symbols all_1747_0, all_1747_1 gives:
% 260.56/41.60 | (790) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1747_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1747_1 &
% 260.56/41.60 | $i(all_1747_0) & $i(all_1747_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.56/41.60 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~
% 260.56/41.60 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2)
% 260.56/41.60 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1747_1, v2)
% 260.56/41.60 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 260.56/41.60 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9,
% 260.56/41.60 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1747_0,
% 260.56/41.60 | v8) = v9) | ~ (hAPP(all_1747_0, v5) = v6) | ~ $i(v4) | ~
% 260.56/41.60 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4)
% 260.56/41.60 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 260.56/41.60 | v10)))))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (790) implies:
% 260.56/41.60 | (791) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1747_1
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (133) with fresh symbols all_1750_0, all_1750_1 gives:
% 260.56/41.60 | (792) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1750_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1750_1 &
% 260.56/41.60 | $i(all_1750_0) & $i(all_1750_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.60 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 260.56/41.60 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 260.56/41.60 | (c_Power_Opower__class_Opower(v2) = v3) | ~
% 260.56/41.60 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1750_0) = v7) |
% 260.56/41.60 | ~ (c_Groups_Otimes__class_Otimes(v2) = v5) | ~ (hAPP(v6, v8) =
% 260.56/41.60 | v9) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v7) = v8) | ~
% 260.56/41.60 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | class_Power_Opower(v2) | ? [v10: $i] : ? [v11: $i] : (( ~ (v1 =
% 260.56/41.60 | all_1750_1) | (v11 = v10 & c_Groups_Oone__class_Oone(v2) =
% 260.56/41.60 | v10 & hAPP(v4, all_1750_1) = v10 & $i(v10))) & (v1 =
% 260.56/41.60 | all_1750_1 | (v10 = v9 & hAPP(v4, v1) = v9 & $i(v9)))))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (792) implies:
% 260.56/41.60 | (793) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1750_1
% 260.56/41.60 | (794) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1750_0
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (204) with fresh symbols all_1753_0, all_1753_1 gives:
% 260.56/41.60 | (795) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1753_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1753_1 &
% 260.56/41.60 | $i(all_1753_0) & $i(all_1753_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.56/41.60 | $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1753_1, v1) |
% 260.56/41.60 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1753_1,
% 260.56/41.60 | v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 260.56/41.60 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 260.56/41.60 | (c_Nat_OSuc(v2) = v6 & c_RealDef_Oreal(tc_Nat_Onat, v6) = v7 &
% 260.56/41.60 | c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & hAPP(v8, v1) = v9 &
% 260.56/41.60 | hAPP(v4, v1) = v5 & hAPP(all_1753_0, v7) = v8 & hAPP(all_1753_0,
% 260.56/41.60 | v3) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4)
% 260.56/41.60 | & $i(v3) & $i(v2) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v9) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v0)))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (795) implies:
% 260.56/41.60 | (796) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1753_1
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (196) with fresh symbols all_1762_0, all_1762_1,
% 260.56/41.60 | all_1762_2 gives:
% 260.56/41.60 | (797) c_Nat_OSuc(all_1762_2) = all_1762_1 &
% 260.56/41.60 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1762_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1762_2 &
% 260.56/41.60 | $i(all_1762_0) & $i(all_1762_1) & $i(all_1762_2) & ! [v0: $i] : !
% 260.56/41.60 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~
% 260.56/41.60 | (hAPP(all_1762_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1762_1, v3) |
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1762_1, v1)) &
% 260.56/41.60 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2,
% 260.56/41.60 | v0) = v3) | ~ (hAPP(all_1762_0, v1) = v2) | ~ $i(v1) | ~
% 260.56/41.60 | $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.56/41.60 | all_1762_1, v3) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.56/41.60 | all_1762_1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 260.56/41.60 | [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1762_0, v1) = v2) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1762_1, v1) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1762_1, v0) |
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1762_1, v3))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (797) implies:
% 260.56/41.60 | (798) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1762_2
% 260.56/41.60 | (799) c_Nat_OSuc(all_1762_2) = all_1762_1
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (126) with fresh symbol all_1765_0 gives:
% 260.56/41.60 | (800) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1765_0 &
% 260.56/41.60 | $i(all_1765_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.60 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ (hAPP(v0, v1) =
% 260.56/41.60 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.60 | class_RealVector_Oreal__normed__vector(v3) | ~
% 260.56/41.60 | class_Orderings_Oord(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 260.56/41.60 | : ? [v9: $i] : ? [v10: $i] : ($i(v7) &
% 260.56/41.60 | ((c_Groups_Ominus__class_Ominus(v3, v4, v8) = v9 &
% 260.56/41.60 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & hAPP(v0, v7)
% 260.56/41.60 | = v8 & $i(v10) & $i(v9) & $i(v8) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(v2, v1, v7) & ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10,
% 260.56/41.60 | all_1765_0)) |
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1765_0, v5)
% 260.56/41.60 | = v6 & $i(v6) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] :
% 260.56/41.60 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~
% 260.56/41.60 | (hAPP(v0, v11) = v12) | ~ $i(v11) | ~
% 260.56/41.60 | c_Orderings_Oord__class_Oless__eq(v2, v1, v11) |
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13,
% 260.56/41.60 | v6))))))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (800) implies:
% 260.56/41.60 | (801) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1765_0
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (203) with fresh symbols all_1768_0, all_1768_1,
% 260.56/41.60 | all_1768_2 gives:
% 260.56/41.60 | (802) c_Nat_OSuc(all_1768_1) = all_1768_0 & c_Nat_OSuc(all_1768_2) =
% 260.56/41.60 | all_1768_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1768_2 &
% 260.56/41.60 | $i(all_1768_0) & $i(all_1768_1) & $i(all_1768_2) & ! [v0: $i] : !
% 260.56/41.60 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 260.56/41.60 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 260.56/41.60 | (c_Power_Opower__class_Opower(v2) = v3) | ~
% 260.56/41.60 | (c_Groups_Ominus__class_Ominus(v2, v5, v7) = v8) | ~ (hAPP(v6,
% 260.56/41.60 | all_1768_0) = v7) | ~ (hAPP(v4, all_1768_0) = v5) | ~
% 260.56/41.60 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v6) | ~ $i(v2) | ~
% 260.56/41.60 | $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__ring__1(v2) | ? [v9:
% 260.56/41.60 | $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 260.56/41.60 | (c_Groups_Ominus__class_Ominus(v2, v1, v0) = v10 &
% 260.56/41.60 | c_Groups_Otimes__class_Otimes(v2) = v9 &
% 260.56/41.60 | c_Groups_Oplus__class_Oplus(v2, v1, v0) = v12 & hAPP(v11, v12) =
% 260.56/41.60 | v8 & hAPP(v9, v10) = v11 & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 260.56/41.60 | $i(v8)))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (802) implies:
% 260.56/41.60 | (803) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1768_2
% 260.56/41.60 | (804) c_Nat_OSuc(all_1768_2) = all_1768_1
% 260.56/41.60 | (805) c_Nat_OSuc(all_1768_1) = all_1768_0
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (123) with fresh symbols all_1777_0, all_1777_1 gives:
% 260.56/41.60 | (806) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1777_1 &
% 260.56/41.60 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1777_0 &
% 260.56/41.60 | $i(all_1777_0) & $i(all_1777_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 260.56/41.60 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v0, all_1777_0)
% 260.56/41.60 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ?
% 260.56/41.60 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 260.56/41.60 | (( ~ (v2 = all_1777_1) &
% 260.56/41.60 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 &
% 260.56/41.60 | $i(v2)) | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,
% 260.56/41.60 | v0, c_Complex_Oii) = v8 &
% 260.56/41.60 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9 &
% 260.56/41.60 | $i(v9) & $i(v8) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9,
% 260.56/41.60 | all_1777_1)) |
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v0, all_1777_0)
% 260.56/41.60 | = v3 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3)
% 260.56/41.60 | = v4 & $i(v4) & $i(v3) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4,
% 260.56/41.60 | all_1777_1)) |
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v0,
% 260.56/41.60 | c_Complex_Oii) = v6 &
% 260.56/41.60 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) = v7 &
% 260.56/41.60 | $i(v7) & $i(v6) &
% 260.56/41.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 260.56/41.60 | all_1777_1)) |
% 260.56/41.60 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v5 &
% 260.56/41.60 | $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v5,
% 260.56/41.60 | all_1777_1))))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (806) implies:
% 260.56/41.60 | (807) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1777_1
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (184) with fresh symbols all_1780_0, all_1780_1 gives:
% 260.56/41.60 | (808) c_Nat_OSuc(all_1780_1) = all_1780_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1780_1 &
% 260.56/41.60 | $i(all_1780_0) & $i(all_1780_1) & ! [v0: $i] : ! [v1: any] : (v1 =
% 260.56/41.60 | all_1780_0 | v1 = all_1780_1 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1780_0) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 =
% 260.56/41.60 | all_1780_0 | v0 = all_1780_0 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1780_0) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 =
% 260.56/41.60 | all_1780_1 | v0 = all_1780_1 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1780_0) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 =
% 260.56/41.60 | all_1780_0 | v0 = all_1780_1 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1780_0) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1780_0 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1780_0, all_1780_1) =
% 260.56/41.60 | v0)) & ! [v0: int] : (v0 = all_1780_0 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1780_1, all_1780_0) =
% 260.56/41.60 | v0))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (808) implies:
% 260.56/41.60 | (809) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1780_1
% 260.56/41.60 | (810) c_Nat_OSuc(all_1780_1) = all_1780_0
% 260.56/41.60 |
% 260.56/41.60 | DELTA: instantiating (184) with fresh symbols all_1783_0, all_1783_1 gives:
% 260.56/41.60 | (811) c_Nat_OSuc(all_1783_1) = all_1783_0 &
% 260.56/41.60 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1783_1 &
% 260.56/41.60 | $i(all_1783_0) & $i(all_1783_1) & ! [v0: $i] : ! [v1: any] : (v1 =
% 260.56/41.60 | all_1783_0 | v1 = all_1783_1 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1783_0) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 =
% 260.56/41.60 | all_1783_0 | v0 = all_1783_0 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1783_0) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 =
% 260.56/41.60 | all_1783_1 | v0 = all_1783_1 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1783_0) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 =
% 260.56/41.60 | all_1783_0 | v0 = all_1783_1 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1783_0) |
% 260.56/41.60 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1783_0 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1783_0, all_1783_1) =
% 260.56/41.60 | v0)) & ! [v0: int] : (v0 = all_1783_0 | ~
% 260.56/41.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1783_1, all_1783_0) =
% 260.56/41.60 | v0))
% 260.56/41.60 |
% 260.56/41.60 | ALPHA: (811) implies:
% 260.56/41.60 | (812) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1783_1
% 260.56/41.61 | (813) c_Nat_OSuc(all_1783_1) = all_1783_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (37) with fresh symbol all_1786_0 gives:
% 260.56/41.61 | (814) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1786_0 &
% 260.56/41.61 | $i(all_1786_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.61 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(v2, v1) = v3) | ~
% 260.56/41.61 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 260.56/41.61 | ? [v8: any] : (((v8 = all_1786_0 & ~ (v7 = v1) &
% 260.56/41.61 | c_Polynomial_Oorder(v2, v0, v1) = all_1786_0 &
% 260.56/41.61 | tc_Polynomial_Opoly(v2) = v6 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6)) | (v5
% 260.56/41.61 | = v4 & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) & ((v7
% 260.56/41.61 | = v1 & tc_Polynomial_Opoly(v2) = v6 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(v6) = v1 & $i(v6)) | ( ~ (v8 =
% 260.56/41.61 | all_1786_0) & c_Polynomial_Oorder(v2, v0, v1) = v8 &
% 260.56/41.61 | $i(v8)) | ( ~ (v5 = v4) & c_Groups_Ozero__class_Ozero(v2) =
% 260.56/41.61 | v5 & $i(v5)))))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (814) implies:
% 260.56/41.61 | (815) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1786_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (147) with fresh symbols all_1789_0, all_1789_1,
% 260.56/41.61 | all_1789_2, all_1789_3, all_1789_4, all_1789_5 gives:
% 260.56/41.61 | (816) c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = all_1789_1 &
% 260.56/41.61 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1789_2 &
% 260.56/41.61 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1789_0 &
% 260.56/41.61 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1789_3 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1789_4 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1789_5 &
% 260.56/41.61 | $i(all_1789_0) & $i(all_1789_1) & $i(all_1789_2) & $i(all_1789_3) &
% 260.56/41.61 | $i(all_1789_4) & $i(all_1789_5) & ? [v0: any] : ! [v1: any] : !
% 260.56/41.61 | [v2: $i] : (v1 = all_1789_5 | v0 = all_1789_4 | ~ (hAPP(all_1789_2,
% 260.56/41.61 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 260.56/41.61 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 260.56/41.61 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, all_1789_3, v6) =
% 260.56/41.61 | v7 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v7) =
% 260.56/41.61 | v8 & hAPP(v4, v0) = v5 & hAPP(v2, v5) = v6 & hAPP(all_1789_1, v3)
% 260.56/41.61 | = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, all_1789_0)))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (816) implies:
% 260.56/41.61 | (817) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1789_4
% 260.56/41.61 | (818) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1789_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (68) with fresh symbols all_1791_0, all_1791_1 gives:
% 260.56/41.61 | (819) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1791_1 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1791_0 &
% 260.56/41.61 | $i(all_1791_0) & $i(all_1791_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.61 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 260.56/41.61 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1791_1, v2) = v3) |
% 260.56/41.61 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1791_0, v2) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0:
% 260.56/41.61 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.61 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 260.56/41.61 | (hAPP(all_1791_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.61 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)) & ! [v0:
% 260.56/41.61 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.61 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 260.56/41.61 | (hAPP(all_1791_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1791_0, v2) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (819) implies:
% 260.56/41.61 | (820) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1791_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (66) with fresh symbols all_1794_0, all_1794_1 gives:
% 260.56/41.61 | (821) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1794_1 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1794_0 &
% 260.56/41.61 | $i(all_1794_0) & $i(all_1794_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.61 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 260.56/41.61 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1794_1, v2) = v3) |
% 260.56/41.61 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] :
% 260.56/41.61 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 260.56/41.61 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 260.56/41.61 | (hAPP(all_1794_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.61 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1794_0, v2)) & !
% 260.56/41.61 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.61 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 260.56/41.61 | (hAPP(all_1794_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.61 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1794_0, v2) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (821) implies:
% 260.56/41.61 | (822) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1794_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (172) with fresh symbols all_1803_0, all_1803_1,
% 260.56/41.61 | all_1803_2 gives:
% 260.56/41.61 | (823) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1803_1 &
% 260.56/41.61 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1803_2 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1803_0 &
% 260.56/41.61 | $i(all_1803_0) & $i(all_1803_1) & $i(all_1803_2) & ! [v0: $i] : !
% 260.56/41.61 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~
% 260.56/41.61 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) | ? [v4:
% 260.56/41.61 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 260.56/41.61 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ($i(v7) &
% 260.56/41.61 | $i(v5) & ((v6 = v0 & hAPP(v1, v5) = v0 &
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v2)) |
% 260.56/41.61 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v9, v10) = v11 &
% 260.56/41.61 | c_Groups_Oabs__class_Oabs(tc_Int_Oint, v11) = v12 &
% 260.56/41.61 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, all_1803_2) = v8
% 260.56/41.61 | & hAPP(v1, v8) = v9 & hAPP(v1, v7) = v10 & $i(v12) & $i(v11)
% 260.56/41.61 | & $i(v10) & $i(v9) & $i(v8) &
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v7, v2) & ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v12,
% 260.56/41.61 | all_1803_1)) | (hAPP(v1, all_1803_0) = v4 & $i(v4) & ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v0)))))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (823) implies:
% 260.56/41.61 | (824) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1803_0
% 260.56/41.61 | (825) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1803_2
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (172) with fresh symbols all_1815_0, all_1815_1,
% 260.56/41.61 | all_1815_2 gives:
% 260.56/41.61 | (826) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1815_1 &
% 260.56/41.61 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1815_2 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1815_0 &
% 260.56/41.61 | $i(all_1815_0) & $i(all_1815_1) & $i(all_1815_2) & ! [v0: $i] : !
% 260.56/41.61 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~
% 260.56/41.61 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) | ? [v4:
% 260.56/41.61 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 260.56/41.61 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ($i(v7) &
% 260.56/41.61 | $i(v5) & ((v6 = v0 & hAPP(v1, v5) = v0 &
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v2)) |
% 260.56/41.61 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v9, v10) = v11 &
% 260.56/41.61 | c_Groups_Oabs__class_Oabs(tc_Int_Oint, v11) = v12 &
% 260.56/41.61 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, all_1815_2) = v8
% 260.56/41.61 | & hAPP(v1, v8) = v9 & hAPP(v1, v7) = v10 & $i(v12) & $i(v11)
% 260.56/41.61 | & $i(v10) & $i(v9) & $i(v8) &
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v7, v2) & ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v12,
% 260.56/41.61 | all_1815_1)) | (hAPP(v1, all_1815_0) = v4 & $i(v4) & ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v0)))))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (826) implies:
% 260.56/41.61 | (827) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1815_0
% 260.56/41.61 | (828) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1815_2
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (67) with fresh symbols all_1821_0, all_1821_1 gives:
% 260.56/41.61 | (829) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1821_1 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1821_0 &
% 260.56/41.61 | $i(all_1821_0) & $i(all_1821_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.61 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.56/41.61 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1821_1,
% 260.56/41.61 | v2) = v3) | ~ (hAPP(all_1821_1, v0) = v5) | ~ $i(v2) | ~
% 260.56/41.61 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.56/41.61 | v4, v6) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0)) &
% 260.56/41.61 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 260.56/41.61 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1)
% 260.56/41.61 | = v4) | ~ (hAPP(all_1821_1, v2) = v3) | ~ (hAPP(all_1821_1, v0)
% 260.56/41.61 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1821_0, v1)) & !
% 260.56/41.61 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.61 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) =
% 260.56/41.61 | v4) | ~ (hAPP(all_1821_1, v2) = v3) | ~ (hAPP(all_1821_1, v0) =
% 260.56/41.61 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1821_0, v1) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (829) implies:
% 260.56/41.61 | (830) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1821_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (69) with fresh symbols all_1824_0, all_1824_1 gives:
% 260.56/41.61 | (831) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1824_1 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1824_0 &
% 260.56/41.61 | $i(all_1824_0) & $i(all_1824_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.61 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 260.56/41.61 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1824_1,
% 260.56/41.61 | v2) = v3) | ~ (hAPP(all_1824_1, v0) = v5) | ~ $i(v2) | ~
% 260.56/41.61 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.56/41.61 | all_1824_0, v1) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0)) & ! [v0:
% 260.56/41.61 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.61 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) =
% 260.56/41.61 | v4) | ~ (hAPP(all_1824_1, v2) = v3) | ~ (hAPP(all_1824_1, v0) =
% 260.56/41.61 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6)) & ! [v0:
% 260.56/41.61 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 260.56/41.61 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) =
% 260.56/41.61 | v4) | ~ (hAPP(all_1824_1, v2) = v3) | ~ (hAPP(all_1824_1, v0) =
% 260.56/41.61 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1824_0, v1) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (831) implies:
% 260.56/41.61 | (832) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1824_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (174) with fresh symbol all_1827_0 gives:
% 260.56/41.61 | (833) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1827_0 &
% 260.56/41.61 | $i(all_1827_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.61 | $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 260.56/41.61 | | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ?
% 260.56/41.61 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 260.56/41.61 | $i(v4) & ((c_RealDef_Oreal(tc_Nat_Onat, v3) = v5 &
% 260.56/41.61 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6) =
% 260.56/41.61 | v7 & $i(v8) & $i(v7) & $i(v5) & ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v5)) |
% 260.56/41.61 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1827_0,
% 260.56/41.61 | v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 260.56/41.61 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~
% 260.56/41.61 | (hAPP(v0, v9) = v10) | ~ $i(v9) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11,
% 260.56/41.61 | v4)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.56/41.61 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1827_0, v2) |
% 260.56/41.61 | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3: $i] : ?
% 260.56/41.61 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 260.56/41.61 | ($i(v6) & $i(v3) & ((c_Nat_OSuc(v3) = v4 &
% 260.56/41.61 | c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & $i(v5) & $i(v4) & !
% 260.56/41.61 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 260.56/41.61 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~
% 260.56/41.61 | (hAPP(v0, v9) = v10) | ~ $i(v9) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v5)))
% 260.56/41.61 | | (c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6)
% 260.56/41.61 | = v7 & $i(v8) & $i(v7) & ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 260.56/41.61 | v2)))))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (833) implies:
% 260.56/41.61 | (834) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1827_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (173) with fresh symbol all_1832_0 gives:
% 260.56/41.61 | (835) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1832_0 &
% 260.56/41.61 | $i(all_1832_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.61 | $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 260.56/41.61 | | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ?
% 260.56/41.61 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 260.56/41.61 | $i(v4) & ((c_RealDef_Oreal(tc_Nat_Onat, v3) = v5 &
% 260.56/41.61 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6) =
% 260.56/41.61 | v7 & $i(v8) & $i(v7) & $i(v5) & ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v5))
% 260.56/41.61 | | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1832_0,
% 260.56/41.61 | v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 260.56/41.61 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~
% 260.56/41.61 | (hAPP(v0, v9) = v10) | ~ $i(v9) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11,
% 260.56/41.61 | v4)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 260.56/41.61 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1832_0, v2) |
% 260.56/41.61 | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3: $i] : ?
% 260.56/41.61 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 260.56/41.61 | ($i(v6) & $i(v3) & ((c_Nat_OSuc(v3) = v4 &
% 260.56/41.61 | c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & $i(v5) & $i(v4) & !
% 260.56/41.61 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 260.56/41.61 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~
% 260.56/41.61 | (hAPP(v0, v9) = v10) | ~ $i(v9) |
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11,
% 260.56/41.61 | v5))) | (c_RealVector_Onorm__class_Onorm(v1, v7) = v8 &
% 260.56/41.61 | hAPP(v0, v6) = v7 & $i(v8) & $i(v7) & ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 260.56/41.61 | v2)))))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (835) implies:
% 260.56/41.61 | (836) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1832_0
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (217) with fresh symbols all_1846_0, all_1846_1 gives:
% 260.56/41.61 | (837) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1846_0 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1846_1 &
% 260.56/41.61 | $i(all_1846_0) & $i(all_1846_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.61 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.56/41.61 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.61 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : (( ~ (v0 = all_1846_1) |
% 260.56/41.61 | (hAPP(v2, all_1846_1) = v5 & $i(v5) & hBOOL(v5))) & (v0 =
% 260.56/41.61 | all_1846_1 | (hAPP(all_1846_0, v0) = v6 & $i(v6) & ! [v7: $i]
% 260.56/41.61 | : ! [v8: $i] : ! [v9: $i] : ( ~
% 260.56/41.61 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v9, v8) = v1) |
% 260.56/41.61 | ~ (hAPP(v6, v7) = v9) | ~ $i(v8) | ~ $i(v7) | ~
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v8, v0) | ?
% 260.56/41.61 | [v10: $i] : (hAPP(v2, v7) = v10 & $i(v10) &
% 260.56/41.61 | hBOOL(v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.61 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.56/41.61 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.61 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 260.56/41.61 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 260.56/41.61 | $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & $i(v7) & ((v10 = v1
% 260.56/41.61 | & ~ (v0 = all_1846_1) &
% 260.56/41.61 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v9, v8) = v1 &
% 260.56/41.61 | hAPP(v6, v7) = v9 & hAPP(v2, v7) = v11 & hAPP(all_1846_0, v0)
% 260.56/41.61 | = v6 & $i(v11) & $i(v9) & $i(v6) &
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v8, v0) & ~
% 260.56/41.61 | hBOOL(v11)) | (v0 = all_1846_1 & hAPP(v2, all_1846_1) = v5 &
% 260.56/41.61 | $i(v5) & ~ hBOOL(v5)))))
% 260.56/41.61 |
% 260.56/41.61 | ALPHA: (837) implies:
% 260.56/41.61 | (838) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1846_1
% 260.56/41.61 |
% 260.56/41.61 | DELTA: instantiating (219) with fresh symbols all_1849_0, all_1849_1 gives:
% 260.56/41.61 | (839) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1849_0 &
% 260.56/41.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1849_1 &
% 260.56/41.61 | $i(all_1849_0) & $i(all_1849_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 260.56/41.61 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.56/41.61 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.61 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 260.56/41.61 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 260.56/41.61 | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v7) & ((v0 =
% 260.56/41.61 | all_1849_1 & hAPP(v2, all_1849_1) = v5 & $i(v5) & hBOOL(v5))
% 260.56/41.61 | | (c_Nat_OSuc(v7) = v9 & hAPP(v6, v9) = v10 & hAPP(v6, v7) = v8
% 260.56/41.61 | & hAPP(v2, v7) = v11 & hAPP(all_1849_0, v0) = v6 & $i(v11) &
% 260.56/41.61 | $i(v10) & $i(v9) & $i(v8) & $i(v6) & hBOOL(v11) &
% 260.56/41.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v10) &
% 260.56/41.61 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v1))))) &
% 260.56/41.61 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 260.56/41.61 | ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.61 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 260.56/41.61 | | ? [v5: $i] : ? [v6: $i] : (hAPP(all_1849_0, v0) = v6 & $i(v6) &
% 260.56/41.61 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (c_Nat_OSuc(v7) =
% 260.56/41.61 | v8) | ~ (hAPP(v6, v8) = v9) | ~ $i(v7) | ~
% 260.56/41.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v9) | ? [v10:
% 260.56/41.62 | $i] : ? [v11: $i] : ((hAPP(v6, v7) = v10 & $i(v10) & ~
% 260.56/41.62 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v10, v1)) |
% 260.56/41.62 | (hAPP(v2, v7) = v11 & $i(v11) & ~ hBOOL(v11)))) & ( ~ (v0 =
% 260.56/41.62 | all_1849_1) | (hAPP(v2, all_1849_1) = v5 & $i(v5) & ~
% 260.56/41.62 | hBOOL(v5)))))
% 260.56/41.62 |
% 260.56/41.62 | ALPHA: (839) implies:
% 260.56/41.62 | (840) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1849_1
% 260.56/41.62 |
% 260.56/41.62 | DELTA: instantiating (62) with fresh symbol all_1852_0 gives:
% 260.56/41.62 | (841) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1852_0 &
% 260.56/41.62 | $i(all_1852_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.62 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.62 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.62 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1) | ~
% 260.56/41.62 | (hAPP(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 260.56/41.62 | | ~ hBOOL(v4) | ? [v6: $i] : (hAPP(v2, v5) = v6 & $i(v6) &
% 260.56/41.62 | hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.62 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,
% 260.56/41.62 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 260.56/41.62 | | ~ $i(v0) | ~ hBOOL(v4) | ~
% 260.56/41.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i] :
% 260.56/41.62 | (hAPP(v2, all_1852_0) = v5 & $i(v5) & hBOOL(v5))) & ! [v0: $i] :
% 260.56/41.62 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.56/41.62 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.62 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 260.56/41.62 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i]
% 260.56/41.62 | : ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) =
% 260.56/41.62 | v1 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) & ~ hBOOL(v6))) & !
% 260.56/41.62 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 260.56/41.62 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.62 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 260.56/41.62 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 260.56/41.62 | ((v7 = v1 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v6) = v1
% 260.56/41.62 | & hAPP(v2, v6) = v8 & $i(v8) & ~ hBOOL(v8)) | (hAPP(v2,
% 260.56/41.62 | all_1852_0) = v5 & $i(v5) & ~ hBOOL(v5)))))
% 260.56/41.62 |
% 260.56/41.62 | ALPHA: (841) implies:
% 260.56/41.62 | (842) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1852_0
% 260.56/41.62 |
% 260.56/41.62 | DELTA: instantiating (62) with fresh symbol all_1855_0 gives:
% 260.56/41.62 | (843) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1855_0 &
% 260.56/41.62 | $i(all_1855_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.62 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 260.56/41.62 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.62 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1) | ~
% 260.56/41.62 | (hAPP(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 260.56/41.62 | | ~ hBOOL(v4) | ? [v6: $i] : (hAPP(v2, v5) = v6 & $i(v6) &
% 260.56/41.62 | hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 260.56/41.62 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,
% 260.56/41.62 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 260.56/41.62 | | ~ $i(v0) | ~ hBOOL(v4) | ~
% 260.56/41.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i] :
% 260.56/41.62 | (hAPP(v2, all_1855_0) = v5 & $i(v5) & hBOOL(v5))) & ! [v0: $i] :
% 260.56/41.62 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 260.56/41.62 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.62 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 260.56/41.62 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i]
% 260.56/41.62 | : ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) =
% 260.56/41.62 | v1 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) & ~ hBOOL(v6))) & !
% 260.56/41.62 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 260.56/41.62 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 260.56/41.62 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 260.56/41.62 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 260.56/41.62 | ((v7 = v1 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v6) = v1
% 260.56/41.62 | & hAPP(v2, v6) = v8 & $i(v8) & ~ hBOOL(v8)) | (hAPP(v2,
% 260.56/41.62 | all_1855_0) = v5 & $i(v5) & ~ hBOOL(v5)))))
% 260.56/41.62 |
% 260.56/41.62 | ALPHA: (843) implies:
% 260.56/41.62 | (844) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1855_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_755_1, all_759_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (323), (327) gives:
% 260.56/41.62 | (845) all_759_0 = all_755_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_759_0, all_780_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (327), (340) gives:
% 260.56/41.62 | (846) all_780_0 = all_759_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_780_0, all_815_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (340), (356) gives:
% 260.56/41.62 | (847) all_815_0 = all_780_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_735_0, all_845_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (318), (367) gives:
% 260.56/41.62 | (848) all_845_0 = all_735_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_815_0, all_856_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (356), (372) gives:
% 260.56/41.62 | (849) all_856_1 = all_815_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_713_1, all_856_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (295), (372) gives:
% 260.56/41.62 | (850) all_856_1 = all_713_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_845_0, all_959_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (367), (422) gives:
% 260.56/41.62 | (851) all_959_1 = all_845_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_959_1, all_965_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (422), (428) gives:
% 260.56/41.62 | (852) all_965_1 = all_959_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_911_0, all_1003_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (398), (440) gives:
% 260.56/41.62 | (853) all_1003_1 = all_911_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_856_1, all_1003_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (372), (440) gives:
% 260.56/41.62 | (854) all_1003_1 = all_856_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_965_1, all_1016_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (428), (451) gives:
% 260.56/41.62 | (855) all_1016_1 = all_965_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1003_1, all_1027_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (440), (466) gives:
% 260.56/41.62 | (856) all_1027_1 = all_1003_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_962_0, all_1045_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (425), (478) gives:
% 260.56/41.62 | (857) all_1045_0 = all_962_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1045_0, all_1075_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (478), (493) gives:
% 260.56/41.62 | (858) all_1075_1 = all_1045_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1075_1, all_1159_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (493), (519) gives:
% 260.56/41.62 | (859) all_1159_1 = all_1075_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1159_1, all_1165_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (519), (524) gives:
% 260.56/41.62 | (860) all_1165_1 = all_1159_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_974_0, all_1192_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (431), (538) gives:
% 260.56/41.62 | (861) all_1192_1 = all_974_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_962_0, all_1192_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (425), (538) gives:
% 260.56/41.62 | (862) all_1192_1 = all_962_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_911_0, all_1192_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (398), (538) gives:
% 260.56/41.62 | (863) all_1192_1 = all_911_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1192_1, all_1229_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (538), (553) gives:
% 260.56/41.62 | (864) all_1229_0 = all_1192_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1123_1, all_1229_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (507), (553) gives:
% 260.56/41.62 | (865) all_1229_0 = all_1123_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_935_0, all_1229_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (413), (553) gives:
% 260.56/41.62 | (866) all_1229_0 = all_935_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1209_1, all_1232_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (546), (555) gives:
% 260.56/41.62 | (867) all_1232_0 = all_1209_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1232_0, all_1250_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (555), (564) gives:
% 260.56/41.62 | (868) all_1250_0 = all_1232_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1016_1, all_1253_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (451), (566) gives:
% 260.56/41.62 | (869) all_1253_0 = all_1016_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1192_1, all_1259_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (538), (572) gives:
% 260.56/41.62 | (870) all_1259_1 = all_1192_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1030_1, all_1259_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (469), (572) gives:
% 260.56/41.62 | (871) all_1259_1 = all_1030_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1209_1, all_1282_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (546), (580) gives:
% 260.56/41.62 | (872) all_1282_0 = all_1209_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1165_1, all_1282_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (524), (580) gives:
% 260.56/41.62 | (873) all_1282_0 = all_1165_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1282_0, all_1303_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (580), (584) gives:
% 260.56/41.62 | (874) all_1303_0 = all_1282_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1250_0, all_1326_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (564), (589) gives:
% 260.56/41.62 | (875) all_1326_0 = all_1250_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1024_1, all_1338_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (463), (595) gives:
% 260.56/41.62 | (876) all_1338_1 = all_1024_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_974_0, all_1338_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (431), (595) gives:
% 260.56/41.62 | (877) all_1338_1 = all_974_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_926_1, all_1338_1, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (406), (595) gives:
% 260.56/41.62 | (878) all_1338_1 = all_926_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_755_1, all_1341_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (323), (598) gives:
% 260.56/41.62 | (879) all_1341_0 = all_755_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_742_0, all_1341_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (320), (598) gives:
% 260.56/41.62 | (880) all_1341_0 = all_742_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_735_0, all_1341_0, tc_RealDef_Oreal,
% 260.56/41.62 | simplifying with (318), (598) gives:
% 260.56/41.62 | (881) all_1341_0 = all_735_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1303_0, all_1350_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (584), (600) gives:
% 260.56/41.62 | (882) all_1350_1 = all_1303_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1341_0, all_1353_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (598), (603) gives:
% 260.56/41.62 | (883) all_1353_1 = all_1341_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1303_0, all_1362_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (584), (608) gives:
% 260.56/41.62 | (884) all_1362_1 = all_1303_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1326_0, all_1386_2,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (589), (614) gives:
% 260.56/41.62 | (885) all_1386_2 = all_1326_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1386_2, all_1389_2,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (614), (618) gives:
% 260.56/41.62 | (886) all_1389_2 = all_1386_2
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1389_2, all_1404_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (618), (629) gives:
% 260.56/41.62 | (887) all_1404_1 = all_1389_2
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1404_1, all_1410_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (629), (635) gives:
% 260.56/41.62 | (888) all_1410_0 = all_1404_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1350_1, all_1418_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (600), (637) gives:
% 260.56/41.62 | (889) all_1418_1 = all_1350_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1418_1, all_1420_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (637), (639) gives:
% 260.56/41.62 | (890) all_1420_1 = all_1418_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1410_0, all_1447_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (635), (647) gives:
% 260.56/41.62 | (891) all_1447_1 = all_1410_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1447_1, all_1450_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (647), (650) gives:
% 260.56/41.62 | (892) all_1450_0 = all_1447_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1450_0, all_1477_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (650), (657) gives:
% 260.56/41.62 | (893) all_1477_1 = all_1450_0
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1420_1, all_1486_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (639), (659) gives:
% 260.56/41.62 | (894) all_1486_0 = all_1420_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1477_1, all_1516_1,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (657), (668) gives:
% 260.56/41.62 | (895) all_1516_1 = all_1477_1
% 260.56/41.62 |
% 260.56/41.62 | GROUND_INST: instantiating (248) with all_1516_1, all_1534_0,
% 260.56/41.62 | tc_RealDef_Oreal, simplifying with (668), (672) gives:
% 260.56/41.62 | (896) all_1534_0 = all_1516_1
% 260.56/41.62 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1362_1, all_1552_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (608), (684) gives:
% 260.56/41.63 | (897) all_1552_0 = all_1362_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1486_0, all_1588_2,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (659), (704) gives:
% 260.56/41.63 | (898) all_1588_2 = all_1486_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1588_2, all_1620_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (704), (717) gives:
% 260.56/41.63 | (899) all_1620_1 = all_1588_2
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1534_0, all_1626_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (672), (720) gives:
% 260.56/41.63 | (900) all_1626_1 = all_1534_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1620_1, all_1629_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (717), (722) gives:
% 260.56/41.63 | (901) all_1629_1 = all_1620_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1552_0, all_1656_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (684), (738) gives:
% 260.56/41.63 | (902) all_1656_0 = all_1552_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1629_1, all_1659_2,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (722), (740) gives:
% 260.56/41.63 | (903) all_1659_2 = all_1629_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1659_2, all_1676_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (740), (748) gives:
% 260.56/41.63 | (904) all_1676_1 = all_1659_2
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1626_1, all_1684_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (720), (753) gives:
% 260.56/41.63 | (905) all_1684_0 = all_1626_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1676_1, all_1693_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (748), (757) gives:
% 260.56/41.63 | (906) all_1693_0 = all_1676_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1353_1, all_1714_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (603), (772) gives:
% 260.56/41.63 | (907) all_1714_1 = all_1353_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1214_1, all_1714_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (549), (772) gives:
% 260.56/41.63 | (908) all_1714_1 = all_1214_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1656_0, all_1723_3,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (738), (776) gives:
% 260.56/41.63 | (909) all_1723_3 = all_1656_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1027_1, all_1729_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (466), (779) gives:
% 260.56/41.63 | (910) all_1729_1 = all_1027_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_893_0, all_1729_1, tc_RealDef_Oreal,
% 260.56/41.63 | simplifying with (393), (779) gives:
% 260.56/41.63 | (911) all_1729_1 = all_893_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1714_1, all_1732_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (772), (781) gives:
% 260.56/41.63 | (912) all_1732_1 = all_1714_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1665_1, all_1732_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (744), (781) gives:
% 260.56/41.63 | (913) all_1732_1 = all_1665_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1684_0, all_1735_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (753), (783) gives:
% 260.56/41.63 | (914) all_1735_0 = all_1684_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_832_0, all_1735_0, tc_RealDef_Oreal,
% 260.56/41.63 | simplifying with (362), (783) gives:
% 260.56/41.63 | (915) all_1735_0 = all_832_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1192_1, all_1738_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (538), (785) gives:
% 260.56/41.63 | (916) all_1738_1 = all_1192_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1006_0, all_1738_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (444), (785) gives:
% 260.56/41.63 | (917) all_1738_1 = all_1006_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1253_0, all_1744_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (566), (789) gives:
% 260.56/41.63 | (918) all_1744_0 = all_1253_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_733_1, all_1744_0, tc_RealDef_Oreal,
% 260.56/41.63 | simplifying with (314), (789) gives:
% 260.56/41.63 | (919) all_1744_0 = all_733_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1723_3, all_1753_1,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (776), (796) gives:
% 260.56/41.63 | (920) all_1753_1 = all_1723_3
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1747_1, all_1827_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (791), (834) gives:
% 260.56/41.63 | (921) all_1827_0 = all_1747_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1693_0, all_1827_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (757), (834) gives:
% 260.56/41.63 | (922) all_1827_0 = all_1693_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1288_1, all_1827_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (582), (834) gives:
% 260.56/41.63 | (923) all_1827_0 = all_1288_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1753_1, all_1832_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (796), (836) gives:
% 260.56/41.63 | (924) all_1832_0 = all_1753_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1204_0, all_1832_0,
% 260.56/41.63 | tc_RealDef_Oreal, simplifying with (544), (836) gives:
% 260.56/41.63 | (925) all_1832_0 = all_1204_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_659_0, all_661_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (262), (264) gives:
% 260.56/41.63 | (926) all_661_0 = all_659_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_667_0, all_673_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (268), (272) gives:
% 260.56/41.63 | (927) all_673_0 = all_667_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_673_0, all_686_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (272), (280) gives:
% 260.56/41.63 | (928) all_686_0 = all_673_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_670_0, all_686_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (270), (280) gives:
% 260.56/41.63 | (929) all_686_0 = all_670_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_692_0, all_695_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (282), (284) gives:
% 260.56/41.63 | (930) all_695_0 = all_692_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_700_0, all_724_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (288), (307) gives:
% 260.56/41.63 | (931) all_724_0 = all_700_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_724_0, all_727_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (307), (309) gives:
% 260.56/41.63 | (932) all_727_0 = all_724_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_679_0, all_770_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (276), (329) gives:
% 260.56/41.63 | (933) all_770_0 = all_679_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_733_0, all_772_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (315), (333) gives:
% 260.56/41.63 | (934) all_772_0 = all_733_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_780_1, all_786_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (341), (345) gives:
% 260.56/41.63 | (935) all_786_0 = all_780_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_770_0, all_809_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (329), (352) gives:
% 260.56/41.63 | (936) all_809_0 = all_770_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_692_0, all_809_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (282), (352) gives:
% 260.56/41.63 | (937) all_809_0 = all_692_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_667_0, all_827_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (268), (360) gives:
% 260.56/41.63 | (938) all_827_0 = all_667_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_661_0, all_827_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (264), (360) gives:
% 260.56/41.63 | (939) all_827_0 = all_661_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_842_0, all_861_2, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (365), (375) gives:
% 260.56/41.63 | (940) all_861_2 = all_842_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_861_2, all_875_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (375), (380) gives:
% 260.56/41.63 | (941) all_875_0 = all_861_2
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_875_0, all_878_1, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (380), (382) gives:
% 260.56/41.63 | (942) all_878_1 = all_875_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_700_0, all_884_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (288), (387) gives:
% 260.56/41.63 | (943) all_884_0 = all_700_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_698_0, all_884_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (286), (387) gives:
% 260.56/41.63 | (944) all_884_0 = all_698_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_695_0, all_884_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (284), (387) gives:
% 260.56/41.63 | (945) all_884_0 = all_695_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_809_0, all_887_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (352), (389) gives:
% 260.56/41.63 | (946) all_887_0 = all_809_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_673_0, all_887_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (272), (389) gives:
% 260.56/41.63 | (947) all_887_0 = all_673_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_878_1, all_920_1, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (382), (400) gives:
% 260.56/41.63 | (948) all_920_1 = all_878_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_920_1, all_923_1, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (400), (403) gives:
% 260.56/41.63 | (949) all_923_1 = all_920_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_923_1, all_926_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (403), (407) gives:
% 260.56/41.63 | (950) all_926_0 = all_923_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_809_0, all_929_1, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (352), (410) gives:
% 260.56/41.63 | (951) all_929_1 = all_809_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_686_0, all_994_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (280), (434) gives:
% 260.56/41.63 | (952) all_994_0 = all_686_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1027_0, all_1042_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (467), (476) gives:
% 260.56/41.63 | (953) all_1042_0 = all_1027_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_926_0, all_1042_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (407), (476) gives:
% 260.56/41.63 | (954) all_1042_0 = all_926_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_994_0, all_1051_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (434), (483) gives:
% 260.56/41.63 | (955) all_1051_0 = all_994_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1027_0, all_1063_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (467), (486) gives:
% 260.56/41.63 | (956) all_1063_0 = all_1027_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1075_0, all_1090_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (494), (496) gives:
% 260.56/41.63 | (957) all_1090_0 = all_1075_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_788_0, all_1093_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (348), (498) gives:
% 260.56/41.63 | (958) all_1093_0 = all_788_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1090_0, all_1120_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (496), (505) gives:
% 260.56/41.63 | (959) all_1120_0 = all_1090_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1120_0, all_1138_1, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (505), (510) gives:
% 260.56/41.63 | (960) all_1138_1 = all_1120_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_887_0, all_1144_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (389), (512) gives:
% 260.56/41.63 | (961) all_1144_0 = all_887_0
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1138_1, all_1153_2, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (510), (515) gives:
% 260.56/41.63 | (962) all_1153_2 = all_1138_1
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1153_2, all_1174_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (515), (526) gives:
% 260.56/41.63 | (963) all_1174_0 = all_1153_2
% 260.56/41.63 |
% 260.56/41.63 | GROUND_INST: instantiating (248) with all_1174_0, all_1177_0, tc_Nat_Onat,
% 260.56/41.63 | simplifying with (526), (528) gives:
% 260.56/41.63 | (964) all_1177_0 = all_1174_0
% 260.56/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_1093_0, all_1180_1, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (498), (530) gives:
% 260.81/41.63 | (965) all_1180_1 = all_1093_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_786_0, all_1180_1, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (345), (530) gives:
% 260.81/41.63 | (966) all_1180_1 = all_786_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_1177_0, all_1198_1, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (528), (540) gives:
% 260.81/41.63 | (967) all_1198_1 = all_1177_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_1198_1, all_1201_0, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (540), (542) gives:
% 260.81/41.63 | (968) all_1201_0 = all_1198_1
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_1144_0, all_1209_0, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (512), (547) gives:
% 260.81/41.63 | (969) all_1209_0 = all_1144_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_1201_0, all_1220_0, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (542), (551) gives:
% 260.81/41.63 | (970) all_1220_0 = all_1201_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_1209_0, all_1247_2, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (547), (560) gives:
% 260.81/41.63 | (971) all_1247_2 = all_1209_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_1235_0, all_1270_2, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (557), (574) gives:
% 260.81/41.63 | (972) all_1270_2 = all_1235_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_1063_0, all_1270_2, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (486), (574) gives:
% 260.81/41.63 | (973) all_1270_2 = all_1063_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_780_1, all_1329_1, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (341), (592) gives:
% 260.81/41.63 | (974) all_1329_1 = all_780_1
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_775_0, all_1329_1, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (335), (592) gives:
% 260.81/41.63 | (975) all_1329_1 = all_775_0
% 260.81/41.63 |
% 260.81/41.63 | GROUND_INST: instantiating (248) with all_772_0, all_1329_1, tc_Nat_Onat,
% 260.81/41.63 | simplifying with (333), (592) gives:
% 260.81/41.63 | (976) all_1329_1 = all_772_0
% 260.81/41.63 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1311_1, all_1356_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (587), (606) gives:
% 260.81/41.64 | (977) all_1356_1 = all_1311_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1256_2, all_1356_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (569), (606) gives:
% 260.81/41.64 | (978) all_1356_1 = all_1256_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1220_0, all_1356_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (551), (606) gives:
% 260.81/41.64 | (979) all_1356_1 = all_1220_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1311_1, all_1365_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (587), (610) gives:
% 260.81/41.64 | (980) all_1365_0 = all_1311_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1365_0, all_1383_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (610), (612) gives:
% 260.81/41.64 | (981) all_1383_1 = all_1365_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1180_1, all_1395_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (530), (622) gives:
% 260.81/41.64 | (982) all_1395_0 = all_1180_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_842_0, all_1395_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (365), (622) gives:
% 260.81/41.64 | (983) all_1395_0 = all_842_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_824_0, all_1395_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (358), (622) gives:
% 260.81/41.64 | (984) all_1395_0 = all_824_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1383_1, all_1398_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (612), (625) gives:
% 260.81/41.64 | (985) all_1398_0 = all_1383_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_733_0, all_1407_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (315), (632) gives:
% 260.81/41.64 | (986) all_1407_1 = all_733_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_727_0, all_1407_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (309), (632) gives:
% 260.81/41.64 | (987) all_1407_1 = all_727_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_950_1, all_1420_2, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (419), (640) gives:
% 260.81/41.64 | (988) all_1420_2 = all_950_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_947_0, all_1420_2, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (417), (640) gives:
% 260.81/41.64 | (989) all_1420_2 = all_947_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_929_1, all_1420_2, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (410), (640) gives:
% 260.81/41.64 | (990) all_1420_2 = all_929_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_950_1, all_1456_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (419), (652) gives:
% 260.81/41.64 | (991) all_1456_0 = all_950_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1456_0, all_1501_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (652), (661) gives:
% 260.81/41.64 | (992) all_1501_0 = all_1456_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1543_0, all_1549_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (680), (682) gives:
% 260.81/41.64 | (993) all_1549_0 = all_1543_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1549_0, all_1558_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (682), (688) gives:
% 260.81/41.64 | (994) all_1558_0 = all_1549_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1558_0, all_1561_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (688), (690) gives:
% 260.81/41.64 | (995) all_1561_0 = all_1558_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1180_1, all_1570_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (530), (696) gives:
% 260.81/41.64 | (996) all_1570_0 = all_1180_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_902_1, all_1570_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (395), (696) gives:
% 260.81/41.64 | (997) all_1570_0 = all_902_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1555_0, all_1594_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (686), (706) gives:
% 260.81/41.64 | (998) all_1594_1 = all_1555_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1540_1, all_1594_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (677), (706) gives:
% 260.81/41.64 | (999) all_1594_1 = all_1540_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1279_2, all_1594_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (577), (706) gives:
% 260.81/41.64 | (1000) all_1594_1 = all_1279_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1270_2, all_1594_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (574), (706) gives:
% 260.81/41.64 | (1001) all_1594_1 = all_1270_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_724_0, all_1608_3, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (307), (709) gives:
% 260.81/41.64 | (1002) all_1608_3 = all_724_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1561_0, all_1611_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (690), (712) gives:
% 260.81/41.64 | (1003) all_1611_1 = all_1561_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1611_1, all_1614_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (712), (714) gives:
% 260.81/41.64 | (1004) all_1614_0 = all_1611_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1420_2, all_1620_2, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (640), (718) gives:
% 260.81/41.64 | (1005) all_1620_2 = all_1420_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1013_1, all_1620_2, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (449), (718) gives:
% 260.81/41.64 | (1006) all_1620_2 = all_1013_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1501_0, all_1632_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (661), (724) gives:
% 260.81/41.64 | (1007) all_1632_1 = all_1501_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1632_1, all_1635_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (724), (728) gives:
% 260.81/41.64 | (1008) all_1635_0 = all_1632_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1051_0, all_1647_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (483), (732) gives:
% 260.81/41.64 | (1009) all_1647_1 = all_1051_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1635_0, all_1653_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (728), (735) gives:
% 260.81/41.64 | (1010) all_1653_1 = all_1635_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1647_1, all_1662_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (732), (742) gives:
% 260.81/41.64 | (1011) all_1662_1 = all_1647_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1662_1, all_1673_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (742), (746) gives:
% 260.81/41.64 | (1012) all_1673_0 = all_1662_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1540_1, all_1681_2, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (677), (750) gives:
% 260.81/41.64 | (1013) all_1681_2 = all_1540_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1543_0, all_1687_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (680), (755) gives:
% 260.81/41.64 | (1014) all_1687_1 = all_1543_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1537_1, all_1687_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (674), (755) gives:
% 260.81/41.64 | (1015) all_1687_1 = all_1537_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1398_0, all_1687_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (625), (755) gives:
% 260.81/41.64 | (1016) all_1687_1 = all_1398_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1608_3, all_1699_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (709), (759) gives:
% 260.81/41.64 | (1017) all_1699_0 = all_1608_3
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_710_0, all_1699_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (292), (759) gives:
% 260.81/41.64 | (1018) all_1699_0 = all_710_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1673_0, all_1702_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (746), (761) gives:
% 260.81/41.64 | (1019) all_1702_1 = all_1673_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1614_0, all_1705_3, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (714), (764) gives:
% 260.81/41.64 | (1020) all_1705_3 = all_1614_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1042_0, all_1708_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (476), (768) gives:
% 260.81/41.64 | (1021) all_1708_1 = all_1042_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_959_0, all_1708_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (423), (768) gives:
% 260.81/41.64 | (1022) all_1708_1 = all_959_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1641_0, all_1711_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (730), (770) gives:
% 260.81/41.64 | (1023) all_1711_1 = all_1641_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1407_1, all_1711_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (632), (770) gives:
% 260.81/41.64 | (1024) all_1711_1 = all_1407_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_730_0, all_1711_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (311), (770) gives:
% 260.81/41.64 | (1025) all_1711_1 = all_730_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1653_1, all_1720_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (735), (774) gives:
% 260.81/41.64 | (1026) all_1720_1 = all_1653_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1702_1, all_1741_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (761), (787) gives:
% 260.81/41.64 | (1027) all_1741_0 = all_1702_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_827_0, all_1750_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (360), (793) gives:
% 260.81/41.64 | (1028) all_1750_1 = all_827_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1705_3, all_1762_2, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (764), (798) gives:
% 260.81/41.64 | (1029) all_1762_2 = all_1705_3
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1762_2, all_1768_2, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (798), (803) gives:
% 260.81/41.64 | (1030) all_1768_2 = all_1762_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1075_0, all_1783_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (494), (812) gives:
% 260.81/41.64 | (1031) all_1783_1 = all_1075_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1066_2, all_1783_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (489), (812) gives:
% 260.81/41.64 | (1032) all_1783_1 = all_1066_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1063_0, all_1783_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (486), (812) gives:
% 260.81/41.64 | (1033) all_1783_1 = all_1063_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1768_2, all_1786_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (803), (815) gives:
% 260.81/41.64 | (1034) all_1786_0 = all_1768_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1786_0, all_1789_4, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (815), (817) gives:
% 260.81/41.64 | (1035) all_1789_4 = all_1786_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1750_1, all_1794_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (793), (822) gives:
% 260.81/41.64 | (1036) all_1794_0 = all_1750_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_664_0, all_1794_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (266), (822) gives:
% 260.81/41.64 | (1037) all_1794_0 = all_664_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1791_0, all_1803_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (820), (824) gives:
% 260.81/41.64 | (1038) all_1803_0 = all_1791_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1789_4, all_1803_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (817), (824) gives:
% 260.81/41.64 | (1039) all_1803_0 = all_1789_4
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1741_0, all_1815_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (787), (827) gives:
% 260.81/41.64 | (1040) all_1815_0 = all_1741_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_682_0, all_1815_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (278), (827) gives:
% 260.81/41.64 | (1041) all_1815_0 = all_682_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1780_1, all_1821_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (809), (830) gives:
% 260.81/41.64 | (1042) all_1821_0 = all_1780_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1681_2, all_1821_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (750), (830) gives:
% 260.81/41.64 | (1043) all_1821_0 = all_1681_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1821_0, all_1824_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (830), (832) gives:
% 260.81/41.64 | (1044) all_1824_0 = all_1821_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1033_0, all_1824_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (472), (832) gives:
% 260.81/41.64 | (1045) all_1824_0 = all_1033_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1846_1, all_1849_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (838), (840) gives:
% 260.81/41.64 | (1046) all_1849_1 = all_1846_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1720_1, all_1849_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (774), (840) gives:
% 260.81/41.64 | (1047) all_1849_1 = all_1720_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_755_0, all_1849_1, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (324), (840) gives:
% 260.81/41.64 | (1048) all_1849_1 = all_755_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1803_0, all_1852_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (824), (842) gives:
% 260.81/41.64 | (1049) all_1852_0 = all_1803_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_650_0, all_1852_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (259), (842) gives:
% 260.81/41.64 | (1050) all_1852_0 = all_650_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_1247_2, all_1855_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (560), (844) gives:
% 260.81/41.64 | (1051) all_1855_0 = all_1247_2
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (248) with all_676_0, all_1855_0, tc_Nat_Onat,
% 260.81/41.64 | simplifying with (274), (844) gives:
% 260.81/41.64 | (1052) all_1855_0 = all_676_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (252) with all_648_0, all_1022_0, v_z____,
% 260.81/41.64 | tc_Complex_Ocomplex, simplifying with (257), (458) gives:
% 260.81/41.64 | (1053) all_1022_0 = all_648_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (252) with all_1468_3, all_1504_4, v_aa____,
% 260.81/41.64 | tc_Complex_Ocomplex, simplifying with (654), (663) gives:
% 260.81/41.64 | (1054) all_1504_4 = all_1468_3
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_861_0, all_890_0, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (376), (391) gives:
% 260.81/41.64 | (1055) all_890_0 = all_861_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_890_0, all_962_1, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (391), (426) gives:
% 260.81/41.64 | (1056) all_962_1 = all_890_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_962_1, all_965_0, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (426), (429) gives:
% 260.81/41.64 | (1057) all_965_0 = all_962_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_965_0, all_974_1, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (429), (432) gives:
% 260.81/41.64 | (1058) all_974_1 = all_965_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_974_1, all_1016_0, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (432), (452) gives:
% 260.81/41.64 | (1059) all_1016_0 = all_974_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1016_0, all_1022_3,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (452), (461) gives:
% 260.81/41.64 | (1060) all_1022_3 = all_1016_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1022_3, all_1024_0,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (461), (464) gives:
% 260.81/41.64 | (1061) all_1024_0 = all_1022_3
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1024_0, all_1036_1,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (464), (474) gives:
% 260.81/41.64 | (1062) all_1036_1 = all_1024_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1036_1, all_1048_0,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (474), (480) gives:
% 260.81/41.64 | (1063) all_1048_0 = all_1036_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1048_0, all_1123_0,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (480), (508) gives:
% 260.81/41.64 | (1064) all_1123_0 = all_1048_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1159_0, all_1162_0,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (520), (522) gives:
% 260.81/41.64 | (1065) all_1162_0 = all_1159_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1123_0, all_1186_0,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (508), (532) gives:
% 260.81/41.64 | (1066) all_1186_0 = all_1123_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_861_0, all_1189_0, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (376), (535) gives:
% 260.81/41.64 | (1067) all_1189_0 = all_861_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_722_1, all_1189_0, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (303), (535) gives:
% 260.81/41.64 | (1068) all_1189_0 = all_722_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1162_0, all_1338_0,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (522), (596) gives:
% 260.81/41.64 | (1069) all_1338_0 = all_1162_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_713_0, all_1338_0, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (296), (596) gives:
% 260.81/41.64 | (1070) all_1338_0 = all_713_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1189_0, all_1353_0,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (535), (604) gives:
% 260.81/41.64 | (1071) all_1353_0 = all_1189_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1186_0, all_1386_1,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (532), (615) gives:
% 260.81/41.64 | (1072) all_1386_1 = all_1186_0
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_742_1, all_1386_1, tc_RealDef_Oreal,
% 260.81/41.64 | simplifying with (321), (615) gives:
% 260.81/41.64 | (1073) all_1386_1 = all_742_1
% 260.81/41.64 |
% 260.81/41.64 | GROUND_INST: instantiating (249) with all_1159_0, all_1389_1,
% 260.81/41.64 | tc_RealDef_Oreal, simplifying with (520), (619) gives:
% 260.81/41.65 | (1074) all_1389_1 = all_1159_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1030_0, all_1389_1,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (470), (619) gives:
% 260.81/41.65 | (1075) all_1389_1 = all_1030_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1019_0, all_1389_1,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (454), (619) gives:
% 260.81/41.65 | (1076) all_1389_1 = all_1019_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1447_0, all_1564_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (648), (692) gives:
% 260.81/41.65 | (1077) all_1564_0 = all_1447_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1432_1, all_1564_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (642), (692) gives:
% 260.81/41.65 | (1078) all_1564_0 = all_1432_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1395_1, all_1564_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (623), (692) gives:
% 260.81/41.65 | (1079) all_1564_0 = all_1395_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1350_0, all_1564_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (601), (692) gives:
% 260.81/41.65 | (1080) all_1564_0 = all_1350_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1019_0, all_1564_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (454), (692) gives:
% 260.81/41.65 | (1081) all_1564_0 = all_1019_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1009_0, all_1564_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (446), (692) gives:
% 260.81/41.65 | (1082) all_1564_0 = all_1009_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1395_1, all_1579_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (623), (698) gives:
% 260.81/41.65 | (1083) all_1579_0 = all_1395_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1395_1, all_1723_1,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (623), (777) gives:
% 260.81/41.65 | (1084) all_1723_1 = all_1395_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1189_0, all_1723_1,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (535), (777) gives:
% 260.81/41.65 | (1085) all_1723_1 = all_1189_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_778_0, all_1723_1, tc_RealDef_Oreal,
% 260.81/41.65 | simplifying with (337), (777) gives:
% 260.81/41.65 | (1086) all_1723_1 = all_778_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_722_1, all_1765_0, tc_RealDef_Oreal,
% 260.81/41.65 | simplifying with (303), (801) gives:
% 260.81/41.65 | (1087) all_1765_0 = all_722_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_720_1, all_1765_0, tc_RealDef_Oreal,
% 260.81/41.65 | simplifying with (299), (801) gives:
% 260.81/41.65 | (1088) all_1765_0 = all_720_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1353_0, all_1777_1,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (604), (807) gives:
% 260.81/41.65 | (1089) all_1777_1 = all_1353_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_853_0, all_1777_1, tc_RealDef_Oreal,
% 260.81/41.65 | simplifying with (369), (807) gives:
% 260.81/41.65 | (1090) all_1777_1 = all_853_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1579_0, all_1789_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (698), (818) gives:
% 260.81/41.65 | (1091) all_1789_0 = all_1579_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1003_0, all_1789_0,
% 260.81/41.65 | tc_RealDef_Oreal, simplifying with (441), (818) gives:
% 260.81/41.65 | (1092) all_1789_0 = all_1003_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_722_0, all_770_1, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (304), (330) gives:
% 260.81/41.65 | (1093) all_770_1 = all_722_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_770_1, all_797_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (330), (350) gives:
% 260.81/41.65 | (1094) all_797_0 = all_770_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_881_0, all_923_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (385), (404) gives:
% 260.81/41.65 | (1095) all_923_0 = all_881_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_881_0, all_997_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (385), (436) gives:
% 260.81/41.65 | (1096) all_997_0 = all_881_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_812_0, all_997_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (354), (436) gives:
% 260.81/41.65 | (1097) all_997_0 = all_812_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_797_0, all_997_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (350), (436) gives:
% 260.81/41.65 | (1098) all_997_0 = all_797_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_797_0, all_1093_1, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (350), (499) gives:
% 260.81/41.65 | (1099) all_1093_1 = all_797_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1093_1, all_1111_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (499), (501) gives:
% 260.81/41.65 | (1100) all_1111_0 = all_1093_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1111_0, all_1186_1, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (501), (533) gives:
% 260.81/41.65 | (1101) all_1186_1 = all_1111_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_778_1, all_1189_1, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (338), (536) gives:
% 260.81/41.65 | (1102) all_1189_1 = all_778_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_722_0, all_1235_1, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (304), (558) gives:
% 260.81/41.65 | (1103) all_1235_1 = all_722_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_950_0, all_1386_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (420), (616) gives:
% 260.81/41.65 | (1104) all_1386_0 = all_950_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_923_0, all_1386_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (404), (616) gives:
% 260.81/41.65 | (1105) all_1386_0 = all_923_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1404_0, all_1407_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (630), (633) gives:
% 260.81/41.65 | (1106) all_1407_0 = all_1404_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1186_1, all_1407_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (533), (633) gives:
% 260.81/41.65 | (1107) all_1407_0 = all_1186_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1404_0, all_1432_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (630), (643) gives:
% 260.81/41.65 | (1108) all_1432_0 = all_1404_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1386_0, all_1507_1, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (616), (666) gives:
% 260.81/41.65 | (1109) all_1507_1 = all_1386_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_941_0, all_1507_1, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (415), (666) gives:
% 260.81/41.65 | (1110) all_1507_1 = all_941_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1407_0, all_1525_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (633), (670) gives:
% 260.81/41.65 | (1111) all_1525_0 = all_1407_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1389_0, all_1525_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (620), (670) gives:
% 260.81/41.65 | (1112) all_1525_0 = all_1389_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1432_0, all_1540_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (643), (678) gives:
% 260.81/41.65 | (1113) all_1540_0 = all_1432_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1235_1, all_1702_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (558), (762) gives:
% 260.81/41.65 | (1114) all_1702_0 = all_1235_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_705_0, all_1702_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (290), (762) gives:
% 260.81/41.65 | (1115) all_1702_0 = all_705_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1540_0, all_1705_1, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (678), (765) gives:
% 260.81/41.65 | (1116) all_1705_1 = all_1540_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1705_1, all_1750_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (765), (794) gives:
% 260.81/41.65 | (1117) all_1750_0 = all_1705_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1000_1, all_1750_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (438), (794) gives:
% 260.81/41.65 | (1118) all_1750_0 = all_1000_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1681_0, all_1803_2, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (751), (825) gives:
% 260.81/41.65 | (1119) all_1803_2 = all_1681_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1189_1, all_1803_2, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (536), (825) gives:
% 260.81/41.65 | (1120) all_1803_2 = all_1189_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1114_0, all_1803_2, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (503), (825) gives:
% 260.81/41.65 | (1121) all_1803_2 = all_1114_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_950_0, all_1803_2, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (420), (825) gives:
% 260.81/41.65 | (1122) all_1803_2 = all_950_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_1093_1, all_1815_2, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (499), (828) gives:
% 260.81/41.65 | (1123) all_1815_2 = all_1093_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (249) with all_720_0, all_1815_2, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (300), (828) gives:
% 260.81/41.65 | (1124) all_1815_2 = all_720_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1401_1, all_1438_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (627), (645) gives:
% 260.81/41.65 | (1125) all_1438_0 = all_1401_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1438_0, all_1585_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (645), (702) gives:
% 260.81/41.65 | (1126) all_1585_0 = all_1438_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1632_2, all_1647_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (725), (733) gives:
% 260.81/41.65 | (1127) all_1647_0 = all_1632_2
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1401_1, all_1647_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (627), (733) gives:
% 260.81/41.65 | (1128) all_1647_0 = all_1401_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1153_3, all_1647_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (516), (733) gives:
% 260.81/41.65 | (1129) all_1647_0 = all_1153_3
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1585_0, all_1653_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (702), (736) gives:
% 260.81/41.65 | (1130) all_1653_0 = all_1585_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1329_0, all_1653_0, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (593), (736) gives:
% 260.81/41.65 | (1131) all_1653_0 = all_1329_0
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1401_1, all_1705_2, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (627), (766) gives:
% 260.81/41.65 | (1132) all_1705_2 = all_1401_1
% 260.81/41.65 |
% 260.81/41.65 | GROUND_INST: instantiating (250) with all_1247_0, all_1705_2, tc_Nat_Onat,
% 260.81/41.65 | simplifying with (561), (766) gives:
% 260.81/41.65 | (1133) all_1705_2 = all_1247_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1051), (1052) imply:
% 260.81/41.65 | (1134) all_1247_2 = all_676_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1134) implies:
% 260.81/41.65 | (1135) all_1247_2 = all_676_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1049), (1050) imply:
% 260.81/41.65 | (1136) all_1803_0 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1136) implies:
% 260.81/41.65 | (1137) all_1803_0 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1046), (1047) imply:
% 260.81/41.65 | (1138) all_1846_1 = all_1720_1
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1046), (1048) imply:
% 260.81/41.65 | (1139) all_1846_1 = all_755_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1138), (1139) imply:
% 260.81/41.65 | (1140) all_1720_1 = all_755_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1140) implies:
% 260.81/41.65 | (1141) all_1720_1 = all_755_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (924), (925) imply:
% 260.81/41.65 | (1142) all_1753_1 = all_1204_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1142) implies:
% 260.81/41.65 | (1143) all_1753_1 = all_1204_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (921), (922) imply:
% 260.81/41.65 | (1144) all_1747_1 = all_1693_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (921), (923) imply:
% 260.81/41.65 | (1145) all_1747_1 = all_1288_1
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1044), (1045) imply:
% 260.81/41.65 | (1146) all_1821_0 = all_1033_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1146) implies:
% 260.81/41.65 | (1147) all_1821_0 = all_1033_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1042), (1043) imply:
% 260.81/41.65 | (1148) all_1780_1 = all_1681_2
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1042), (1147) imply:
% 260.81/41.65 | (1149) all_1780_1 = all_1033_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1040), (1041) imply:
% 260.81/41.65 | (1150) all_1741_0 = all_682_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1150) implies:
% 260.81/41.65 | (1151) all_1741_0 = all_682_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1123), (1124) imply:
% 260.81/41.65 | (1152) all_1093_1 = all_720_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1152) implies:
% 260.81/41.65 | (1153) all_1093_1 = all_720_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1038), (1137) imply:
% 260.81/41.65 | (1154) all_1791_0 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1038), (1039) imply:
% 260.81/41.65 | (1155) all_1791_0 = all_1789_4
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1119), (1122) imply:
% 260.81/41.65 | (1156) all_1681_0 = all_950_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1119), (1121) imply:
% 260.81/41.65 | (1157) all_1681_0 = all_1114_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1119), (1120) imply:
% 260.81/41.65 | (1158) all_1681_0 = all_1189_1
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1036), (1037) imply:
% 260.81/41.65 | (1159) all_1750_1 = all_664_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1159) implies:
% 260.81/41.65 | (1160) all_1750_1 = all_664_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1154), (1155) imply:
% 260.81/41.65 | (1161) all_1789_4 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1161) implies:
% 260.81/41.65 | (1162) all_1789_4 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1091), (1092) imply:
% 260.81/41.65 | (1163) all_1579_0 = all_1003_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1163) implies:
% 260.81/41.65 | (1164) all_1579_0 = all_1003_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1035), (1162) imply:
% 260.81/41.65 | (1165) all_1786_0 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1165) implies:
% 260.81/41.65 | (1166) all_1786_0 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1034), (1166) imply:
% 260.81/41.65 | (1167) all_1768_2 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1167) implies:
% 260.81/41.65 | (1168) all_1768_2 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1031), (1032) imply:
% 260.81/41.65 | (1169) all_1075_0 = all_1066_2
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1169) implies:
% 260.81/41.65 | (1170) all_1075_0 = all_1066_2
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1032), (1033) imply:
% 260.81/41.65 | (1171) all_1066_2 = all_1063_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1148), (1149) imply:
% 260.81/41.65 | (1172) all_1681_2 = all_1033_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1172) implies:
% 260.81/41.65 | (1173) all_1681_2 = all_1033_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1089), (1090) imply:
% 260.81/41.65 | (1174) all_1353_0 = all_853_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1174) implies:
% 260.81/41.65 | (1175) all_1353_0 = all_853_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1030), (1168) imply:
% 260.81/41.65 | (1176) all_1762_2 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1176) implies:
% 260.81/41.65 | (1177) all_1762_2 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1087), (1088) imply:
% 260.81/41.65 | (1178) all_722_1 = all_720_1
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1178) implies:
% 260.81/41.65 | (1179) all_722_1 = all_720_1
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1029), (1177) imply:
% 260.81/41.65 | (1180) all_1705_3 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1180) implies:
% 260.81/41.65 | (1181) all_1705_3 = all_650_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (920), (1143) imply:
% 260.81/41.65 | (1182) all_1723_3 = all_1204_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1182) implies:
% 260.81/41.65 | (1183) all_1723_3 = all_1204_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1117), (1118) imply:
% 260.81/41.65 | (1184) all_1705_1 = all_1000_1
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1184) implies:
% 260.81/41.65 | (1185) all_1705_1 = all_1000_1
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1028), (1160) imply:
% 260.81/41.65 | (1186) all_827_0 = all_664_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1186) implies:
% 260.81/41.65 | (1187) all_827_0 = all_664_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1144), (1145) imply:
% 260.81/41.65 | (1188) all_1693_0 = all_1288_1
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1188) implies:
% 260.81/41.65 | (1189) all_1693_0 = all_1288_1
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (918), (919) imply:
% 260.81/41.65 | (1190) all_1253_0 = all_733_1
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1190) implies:
% 260.81/41.65 | (1191) all_1253_0 = all_733_1
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (1027), (1151) imply:
% 260.81/41.65 | (1192) all_1702_1 = all_682_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1192) implies:
% 260.81/41.65 | (1193) all_1702_1 = all_682_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (916), (917) imply:
% 260.81/41.65 | (1194) all_1192_1 = all_1006_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1194) implies:
% 260.81/41.65 | (1195) all_1192_1 = all_1006_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (914), (915) imply:
% 260.81/41.65 | (1196) all_1684_0 = all_832_0
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1196) implies:
% 260.81/41.65 | (1197) all_1684_0 = all_832_0
% 260.81/41.65 |
% 260.81/41.65 | COMBINE_EQS: (912), (913) imply:
% 260.81/41.65 | (1198) all_1714_1 = all_1665_1
% 260.81/41.65 |
% 260.81/41.65 | SIMP: (1198) implies:
% 260.81/41.65 | (1199) all_1714_1 = all_1665_1
% 260.81/41.65 |
% 260.90/41.65 | COMBINE_EQS: (910), (911) imply:
% 260.90/41.65 | (1200) all_1027_1 = all_893_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1200) implies:
% 260.90/41.65 | (1201) all_1027_1 = all_893_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1084), (1086) imply:
% 260.90/41.65 | (1202) all_1395_1 = all_778_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1202) implies:
% 260.90/41.65 | (1203) all_1395_1 = all_778_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1085), (1086) imply:
% 260.90/41.65 | (1204) all_1189_0 = all_778_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1204) implies:
% 260.90/41.65 | (1205) all_1189_0 = all_778_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (909), (1183) imply:
% 260.90/41.65 | (1206) all_1656_0 = all_1204_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1206) implies:
% 260.90/41.65 | (1207) all_1656_0 = all_1204_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1026), (1141) imply:
% 260.90/41.65 | (1208) all_1653_1 = all_755_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1208) implies:
% 260.90/41.65 | (1209) all_1653_1 = all_755_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (907), (1199) imply:
% 260.90/41.65 | (1210) all_1665_1 = all_1353_1
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (908), (1199) imply:
% 260.90/41.65 | (1211) all_1665_1 = all_1214_1
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1023), (1024) imply:
% 260.90/41.65 | (1212) all_1641_0 = all_1407_1
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1023), (1025) imply:
% 260.90/41.65 | (1213) all_1641_0 = all_730_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1021), (1022) imply:
% 260.90/41.65 | (1214) all_1042_0 = all_959_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1214) implies:
% 260.90/41.65 | (1215) all_1042_0 = all_959_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1116), (1185) imply:
% 260.90/41.65 | (1216) all_1540_0 = all_1000_1
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1216) implies:
% 260.90/41.65 | (1217) all_1540_0 = all_1000_1
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1132), (1133) imply:
% 260.90/41.65 | (1218) all_1401_1 = all_1247_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1218) implies:
% 260.90/41.65 | (1219) all_1401_1 = all_1247_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1020), (1181) imply:
% 260.90/41.65 | (1220) all_1614_0 = all_650_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1220) implies:
% 260.90/41.65 | (1221) all_1614_0 = all_650_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1114), (1115) imply:
% 260.90/41.65 | (1222) all_1235_1 = all_705_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1222) implies:
% 260.90/41.65 | (1223) all_1235_1 = all_705_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1019), (1193) imply:
% 260.90/41.65 | (1224) all_1673_0 = all_682_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1224) implies:
% 260.90/41.65 | (1225) all_1673_0 = all_682_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1017), (1018) imply:
% 260.90/41.65 | (1226) all_1608_3 = all_710_0
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1226) implies:
% 260.90/41.65 | (1227) all_1608_3 = all_710_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (906), (1189) imply:
% 260.90/41.65 | (1228) all_1676_1 = all_1288_1
% 260.90/41.65 |
% 260.90/41.65 | SIMP: (1228) implies:
% 260.90/41.65 | (1229) all_1676_1 = all_1288_1
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1015), (1016) imply:
% 260.90/41.65 | (1230) all_1537_1 = all_1398_0
% 260.90/41.65 |
% 260.90/41.65 | COMBINE_EQS: (1014), (1015) imply:
% 260.90/41.65 | (1231) all_1543_0 = all_1537_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1231) implies:
% 260.90/41.66 | (1232) all_1543_0 = all_1537_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (905), (1197) imply:
% 260.90/41.66 | (1233) all_1626_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1233) implies:
% 260.90/41.66 | (1234) all_1626_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1156), (1157) imply:
% 260.90/41.66 | (1235) all_1114_0 = all_950_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1157), (1158) imply:
% 260.90/41.66 | (1236) all_1189_1 = all_1114_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1236) implies:
% 260.90/41.66 | (1237) all_1189_1 = all_1114_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1013), (1173) imply:
% 260.90/41.66 | (1238) all_1540_1 = all_1033_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1238) implies:
% 260.90/41.66 | (1239) all_1540_1 = all_1033_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (904), (1229) imply:
% 260.90/41.66 | (1240) all_1659_2 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1240) implies:
% 260.90/41.66 | (1241) all_1659_2 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1012), (1225) imply:
% 260.90/41.66 | (1242) all_1662_1 = all_682_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1242) implies:
% 260.90/41.66 | (1243) all_1662_1 = all_682_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1210), (1211) imply:
% 260.90/41.66 | (1244) all_1353_1 = all_1214_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1244) implies:
% 260.90/41.66 | (1245) all_1353_1 = all_1214_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1011), (1243) imply:
% 260.90/41.66 | (1246) all_1647_1 = all_682_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1246) implies:
% 260.90/41.66 | (1247) all_1647_1 = all_682_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (903), (1241) imply:
% 260.90/41.66 | (1248) all_1629_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1248) implies:
% 260.90/41.66 | (1249) all_1629_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (902), (1207) imply:
% 260.90/41.66 | (1250) all_1552_0 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1250) implies:
% 260.90/41.66 | (1251) all_1552_0 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1130), (1131) imply:
% 260.90/41.66 | (1252) all_1585_0 = all_1329_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1252) implies:
% 260.90/41.66 | (1253) all_1585_0 = all_1329_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1010), (1209) imply:
% 260.90/41.66 | (1254) all_1635_0 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1254) implies:
% 260.90/41.66 | (1255) all_1635_0 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1127), (1129) imply:
% 260.90/41.66 | (1256) all_1632_2 = all_1153_3
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1127), (1128) imply:
% 260.90/41.66 | (1257) all_1632_2 = all_1401_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1009), (1247) imply:
% 260.90/41.66 | (1258) all_1051_0 = all_682_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1258) implies:
% 260.90/41.66 | (1259) all_1051_0 = all_682_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1212), (1213) imply:
% 260.90/41.66 | (1260) all_1407_1 = all_730_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1260) implies:
% 260.90/41.66 | (1261) all_1407_1 = all_730_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1008), (1255) imply:
% 260.90/41.66 | (1262) all_1632_1 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1262) implies:
% 260.90/41.66 | (1263) all_1632_1 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1007), (1263) imply:
% 260.90/41.66 | (1264) all_1501_0 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1264) implies:
% 260.90/41.66 | (1265) all_1501_0 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1256), (1257) imply:
% 260.90/41.66 | (1266) all_1401_1 = all_1153_3
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1266) implies:
% 260.90/41.66 | (1267) all_1401_1 = all_1153_3
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (901), (1249) imply:
% 260.90/41.66 | (1268) all_1620_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1268) implies:
% 260.90/41.66 | (1269) all_1620_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (900), (1234) imply:
% 260.90/41.66 | (1270) all_1534_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1270) implies:
% 260.90/41.66 | (1271) all_1534_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (899), (1269) imply:
% 260.90/41.66 | (1272) all_1588_2 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1272) implies:
% 260.90/41.66 | (1273) all_1588_2 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1005), (1006) imply:
% 260.90/41.66 | (1274) all_1420_2 = all_1013_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1274) implies:
% 260.90/41.66 | (1275) all_1420_2 = all_1013_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1004), (1221) imply:
% 260.90/41.66 | (1276) all_1611_1 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1276) implies:
% 260.90/41.66 | (1277) all_1611_1 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1003), (1277) imply:
% 260.90/41.66 | (1278) all_1561_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1278) implies:
% 260.90/41.66 | (1279) all_1561_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1002), (1227) imply:
% 260.90/41.66 | (1280) all_724_0 = all_710_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1280) implies:
% 260.90/41.66 | (1281) all_724_0 = all_710_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (998), (1000) imply:
% 260.90/41.66 | (1282) all_1555_0 = all_1279_2
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (998), (999) imply:
% 260.90/41.66 | (1283) all_1555_0 = all_1540_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (998), (1001) imply:
% 260.90/41.66 | (1284) all_1555_0 = all_1270_2
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (898), (1273) imply:
% 260.90/41.66 | (1285) all_1486_0 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1285) implies:
% 260.90/41.66 | (1286) all_1486_0 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1126), (1253) imply:
% 260.90/41.66 | (1287) all_1438_0 = all_1329_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1287) implies:
% 260.90/41.66 | (1288) all_1438_0 = all_1329_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1083), (1164) imply:
% 260.90/41.66 | (1289) all_1395_1 = all_1003_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1289) implies:
% 260.90/41.66 | (1290) all_1395_1 = all_1003_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (996), (997) imply:
% 260.90/41.66 | (1291) all_1180_1 = all_902_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1291) implies:
% 260.90/41.66 | (1292) all_1180_1 = all_902_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1077), (1080) imply:
% 260.90/41.66 | (1293) all_1447_0 = all_1350_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1077), (1078) imply:
% 260.90/41.66 | (1294) all_1447_0 = all_1432_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1077), (1079) imply:
% 260.90/41.66 | (1295) all_1447_0 = all_1395_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1077), (1082) imply:
% 260.90/41.66 | (1296) all_1447_0 = all_1009_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1077), (1081) imply:
% 260.90/41.66 | (1297) all_1447_0 = all_1019_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (995), (1279) imply:
% 260.90/41.66 | (1298) all_1558_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1298) implies:
% 260.90/41.66 | (1299) all_1558_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (994), (1299) imply:
% 260.90/41.66 | (1300) all_1549_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1300) implies:
% 260.90/41.66 | (1301) all_1549_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1282), (1283) imply:
% 260.90/41.66 | (1302) all_1540_1 = all_1279_2
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1302) implies:
% 260.90/41.66 | (1303) all_1540_1 = all_1279_2
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1282), (1284) imply:
% 260.90/41.66 | (1304) all_1279_2 = all_1270_2
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (897), (1251) imply:
% 260.90/41.66 | (1305) all_1362_1 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1305) implies:
% 260.90/41.66 | (1306) all_1362_1 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (993), (1301) imply:
% 260.90/41.66 | (1307) all_1543_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1307) implies:
% 260.90/41.66 | (1308) all_1543_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1232), (1308) imply:
% 260.90/41.66 | (1309) all_1537_1 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1309) implies:
% 260.90/41.66 | (1310) all_1537_1 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1113), (1217) imply:
% 260.90/41.66 | (1311) all_1432_0 = all_1000_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1311) implies:
% 260.90/41.66 | (1312) all_1432_0 = all_1000_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1239), (1303) imply:
% 260.90/41.66 | (1313) all_1279_2 = all_1033_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1313) implies:
% 260.90/41.66 | (1314) all_1279_2 = all_1033_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1230), (1310) imply:
% 260.90/41.66 | (1315) all_1398_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1315) implies:
% 260.90/41.66 | (1316) all_1398_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (896), (1271) imply:
% 260.90/41.66 | (1317) all_1516_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1317) implies:
% 260.90/41.66 | (1318) all_1516_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1111), (1112) imply:
% 260.90/41.66 | (1319) all_1407_0 = all_1389_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1319) implies:
% 260.90/41.66 | (1320) all_1407_0 = all_1389_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (895), (1318) imply:
% 260.90/41.66 | (1321) all_1477_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1321) implies:
% 260.90/41.66 | (1322) all_1477_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1109), (1110) imply:
% 260.90/41.66 | (1323) all_1386_0 = all_941_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1323) implies:
% 260.90/41.66 | (1324) all_1386_0 = all_941_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (992), (1265) imply:
% 260.90/41.66 | (1325) all_1456_0 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1325) implies:
% 260.90/41.66 | (1326) all_1456_0 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (894), (1286) imply:
% 260.90/41.66 | (1327) all_1420_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1327) implies:
% 260.90/41.66 | (1328) all_1420_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (893), (1322) imply:
% 260.90/41.66 | (1329) all_1450_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1329) implies:
% 260.90/41.66 | (1330) all_1450_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (991), (1326) imply:
% 260.90/41.66 | (1331) all_950_1 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1331) implies:
% 260.90/41.66 | (1332) all_950_1 = all_755_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (892), (1330) imply:
% 260.90/41.66 | (1333) all_1447_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1333) implies:
% 260.90/41.66 | (1334) all_1447_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1294), (1295) imply:
% 260.90/41.66 | (1335) all_1432_1 = all_1395_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1293), (1294) imply:
% 260.90/41.66 | (1336) all_1432_1 = all_1350_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1294), (1297) imply:
% 260.90/41.66 | (1337) all_1432_1 = all_1019_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1294), (1296) imply:
% 260.90/41.66 | (1338) all_1432_1 = all_1009_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (891), (1334) imply:
% 260.90/41.66 | (1339) all_1410_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1339) implies:
% 260.90/41.66 | (1340) all_1410_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1125), (1288) imply:
% 260.90/41.66 | (1341) all_1401_1 = all_1329_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1341) implies:
% 260.90/41.66 | (1342) all_1401_1 = all_1329_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1108), (1312) imply:
% 260.90/41.66 | (1343) all_1404_0 = all_1000_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1343) implies:
% 260.90/41.66 | (1344) all_1404_0 = all_1000_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1335), (1336) imply:
% 260.90/41.66 | (1345) all_1395_1 = all_1350_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1345) implies:
% 260.90/41.66 | (1346) all_1395_1 = all_1350_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1336), (1338) imply:
% 260.90/41.66 | (1347) all_1350_0 = all_1009_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1336), (1337) imply:
% 260.90/41.66 | (1348) all_1350_0 = all_1019_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (890), (1328) imply:
% 260.90/41.66 | (1349) all_1418_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1349) implies:
% 260.90/41.66 | (1350) all_1418_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (990), (1275) imply:
% 260.90/41.66 | (1351) all_1013_1 = all_929_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (989), (1275) imply:
% 260.90/41.66 | (1352) all_1013_1 = all_947_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (988), (1275) imply:
% 260.90/41.66 | (1353) all_1013_1 = all_950_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (889), (1350) imply:
% 260.90/41.66 | (1354) all_1350_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1354) implies:
% 260.90/41.66 | (1355) all_1350_1 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (888), (1340) imply:
% 260.90/41.66 | (1356) all_1404_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1356) implies:
% 260.90/41.66 | (1357) all_1404_1 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1107), (1320) imply:
% 260.90/41.66 | (1358) all_1389_0 = all_1186_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1106), (1320) imply:
% 260.90/41.66 | (1359) all_1404_0 = all_1389_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1359) implies:
% 260.90/41.66 | (1360) all_1404_0 = all_1389_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (987), (1261) imply:
% 260.90/41.66 | (1361) all_730_0 = all_727_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (986), (1261) imply:
% 260.90/41.66 | (1362) all_733_0 = all_730_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1362) implies:
% 260.90/41.66 | (1363) all_733_0 = all_730_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1344), (1360) imply:
% 260.90/41.66 | (1364) all_1389_0 = all_1000_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1364) implies:
% 260.90/41.66 | (1365) all_1389_0 = all_1000_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (887), (1357) imply:
% 260.90/41.66 | (1366) all_1389_2 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1366) implies:
% 260.90/41.66 | (1367) all_1389_2 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1267), (1342) imply:
% 260.90/41.66 | (1368) all_1329_0 = all_1153_3
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1219), (1342) imply:
% 260.90/41.66 | (1369) all_1329_0 = all_1247_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (985), (1316) imply:
% 260.90/41.66 | (1370) all_1383_1 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1370) implies:
% 260.90/41.66 | (1371) all_1383_1 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (983), (984) imply:
% 260.90/41.66 | (1372) all_842_0 = all_824_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1372) implies:
% 260.90/41.66 | (1373) all_842_0 = all_824_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (982), (984) imply:
% 260.90/41.66 | (1374) all_1180_1 = all_824_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1374) implies:
% 260.90/41.66 | (1375) all_1180_1 = all_824_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1290), (1346) imply:
% 260.90/41.66 | (1376) all_1350_0 = all_1003_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1376) implies:
% 260.90/41.66 | (1377) all_1350_0 = all_1003_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1203), (1290) imply:
% 260.90/41.66 | (1378) all_1003_0 = all_778_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1358), (1365) imply:
% 260.90/41.66 | (1379) all_1186_1 = all_1000_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1379) implies:
% 260.90/41.66 | (1380) all_1186_1 = all_1000_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1074), (1075) imply:
% 260.90/41.66 | (1381) all_1159_0 = all_1030_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1381) implies:
% 260.90/41.66 | (1382) all_1159_0 = all_1030_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1075), (1076) imply:
% 260.90/41.66 | (1383) all_1030_0 = all_1019_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (886), (1367) imply:
% 260.90/41.66 | (1384) all_1386_2 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1384) implies:
% 260.90/41.66 | (1385) all_1386_2 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1104), (1324) imply:
% 260.90/41.66 | (1386) all_950_0 = all_941_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1386) implies:
% 260.90/41.66 | (1387) all_950_0 = all_941_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1105), (1324) imply:
% 260.90/41.66 | (1388) all_941_0 = all_923_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1072), (1073) imply:
% 260.90/41.66 | (1389) all_1186_0 = all_742_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1389) implies:
% 260.90/41.66 | (1390) all_1186_0 = all_742_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (885), (1385) imply:
% 260.90/41.66 | (1391) all_1326_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1391) implies:
% 260.90/41.66 | (1392) all_1326_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (981), (1371) imply:
% 260.90/41.66 | (1393) all_1365_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1393) implies:
% 260.90/41.66 | (1394) all_1365_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (980), (1394) imply:
% 260.90/41.66 | (1395) all_1311_1 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1395) implies:
% 260.90/41.66 | (1396) all_1311_1 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (884), (1306) imply:
% 260.90/41.66 | (1397) all_1303_0 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1397) implies:
% 260.90/41.66 | (1398) all_1303_0 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (977), (978) imply:
% 260.90/41.66 | (1399) all_1311_1 = all_1256_2
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1399) implies:
% 260.90/41.66 | (1400) all_1311_1 = all_1256_2
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (978), (979) imply:
% 260.90/41.66 | (1401) all_1256_2 = all_1220_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1071), (1175) imply:
% 260.90/41.66 | (1402) all_1189_0 = all_853_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1402) implies:
% 260.90/41.66 | (1403) all_1189_0 = all_853_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (883), (1245) imply:
% 260.90/41.66 | (1404) all_1341_0 = all_1214_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1404) implies:
% 260.90/41.66 | (1405) all_1341_0 = all_1214_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1347), (1348) imply:
% 260.90/41.66 | (1406) all_1019_0 = all_1009_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1406) implies:
% 260.90/41.66 | (1407) all_1019_0 = all_1009_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1347), (1377) imply:
% 260.90/41.66 | (1408) all_1009_0 = all_1003_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (882), (1355) imply:
% 260.90/41.66 | (1409) all_1303_0 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1409) implies:
% 260.90/41.66 | (1410) all_1303_0 = all_1288_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (879), (1405) imply:
% 260.90/41.66 | (1411) all_1214_1 = all_755_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (881), (1405) imply:
% 260.90/41.66 | (1412) all_1214_1 = all_735_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (880), (1405) imply:
% 260.90/41.66 | (1413) all_1214_1 = all_742_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1069), (1070) imply:
% 260.90/41.66 | (1414) all_1162_0 = all_713_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1414) implies:
% 260.90/41.66 | (1415) all_1162_0 = all_713_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (876), (878) imply:
% 260.90/41.66 | (1416) all_1024_1 = all_926_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (876), (877) imply:
% 260.90/41.66 | (1417) all_1024_1 = all_974_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1368), (1369) imply:
% 260.90/41.66 | (1418) all_1247_0 = all_1153_3
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (974), (975) imply:
% 260.90/41.66 | (1419) all_780_1 = all_775_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1419) implies:
% 260.90/41.66 | (1420) all_780_1 = all_775_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (975), (976) imply:
% 260.90/41.66 | (1421) all_775_0 = all_772_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (875), (1392) imply:
% 260.90/41.66 | (1422) all_1250_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1422) implies:
% 260.90/41.66 | (1423) all_1250_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1396), (1400) imply:
% 260.90/41.66 | (1424) all_1256_2 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1424) implies:
% 260.90/41.66 | (1425) all_1256_2 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (874), (1410) imply:
% 260.90/41.66 | (1426) all_1288_1 = all_1282_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1398), (1410) imply:
% 260.90/41.66 | (1427) all_1288_1 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1426), (1427) imply:
% 260.90/41.66 | (1428) all_1282_0 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1428) implies:
% 260.90/41.66 | (1429) all_1282_0 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (873), (1429) imply:
% 260.90/41.66 | (1430) all_1204_0 = all_1165_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (872), (1429) imply:
% 260.90/41.66 | (1431) all_1209_1 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1431) implies:
% 260.90/41.66 | (1432) all_1209_1 = all_1204_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1304), (1314) imply:
% 260.90/41.66 | (1433) all_1270_2 = all_1033_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1433) implies:
% 260.90/41.66 | (1434) all_1270_2 = all_1033_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (972), (973) imply:
% 260.90/41.66 | (1435) all_1235_0 = all_1063_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (972), (1434) imply:
% 260.90/41.66 | (1436) all_1235_0 = all_1033_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (870), (871) imply:
% 260.90/41.66 | (1437) all_1192_1 = all_1030_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1437) implies:
% 260.90/41.66 | (1438) all_1192_1 = all_1030_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1401), (1425) imply:
% 260.90/41.66 | (1439) all_1220_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1439) implies:
% 260.90/41.66 | (1440) all_1220_0 = all_650_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (869), (1191) imply:
% 260.90/41.66 | (1441) all_1016_1 = all_733_1
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1441) implies:
% 260.90/41.66 | (1442) all_1016_1 = all_733_1
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (868), (1423) imply:
% 260.90/41.66 | (1443) all_1232_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1443) implies:
% 260.90/41.66 | (1444) all_1232_0 = all_832_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (971), (1135) imply:
% 260.90/41.66 | (1445) all_1209_0 = all_676_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1445) implies:
% 260.90/41.66 | (1446) all_1209_0 = all_676_0
% 260.90/41.66 |
% 260.90/41.66 | COMBINE_EQS: (1435), (1436) imply:
% 260.90/41.66 | (1447) all_1063_0 = all_1033_0
% 260.90/41.66 |
% 260.90/41.66 | SIMP: (1447) implies:
% 260.90/41.67 | (1448) all_1063_0 = all_1033_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1103), (1223) imply:
% 260.90/41.67 | (1449) all_722_0 = all_705_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1449) implies:
% 260.90/41.67 | (1450) all_722_0 = all_705_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (867), (1444) imply:
% 260.90/41.67 | (1451) all_1209_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1451) implies:
% 260.90/41.67 | (1452) all_1209_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (864), (865) imply:
% 260.90/41.67 | (1453) all_1192_1 = all_1123_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1453) implies:
% 260.90/41.67 | (1454) all_1192_1 = all_1123_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (865), (866) imply:
% 260.90/41.67 | (1455) all_1123_1 = all_935_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (970), (1440) imply:
% 260.90/41.67 | (1456) all_1201_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1456) implies:
% 260.90/41.67 | (1457) all_1201_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1411), (1413) imply:
% 260.90/41.67 | (1458) all_755_1 = all_742_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1458) implies:
% 260.90/41.67 | (1459) all_755_1 = all_742_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1412), (1413) imply:
% 260.90/41.67 | (1460) all_742_0 = all_735_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (969), (1446) imply:
% 260.90/41.67 | (1461) all_1144_0 = all_676_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1461) implies:
% 260.90/41.67 | (1462) all_1144_0 = all_676_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1432), (1452) imply:
% 260.90/41.67 | (1463) all_1204_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1463) implies:
% 260.90/41.67 | (1464) all_1204_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1430), (1464) imply:
% 260.90/41.67 | (1465) all_1165_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1465) implies:
% 260.90/41.67 | (1466) all_1165_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (968), (1457) imply:
% 260.90/41.67 | (1467) all_1198_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1467) implies:
% 260.90/41.67 | (1468) all_1198_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (967), (1468) imply:
% 260.90/41.67 | (1469) all_1177_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1469) implies:
% 260.90/41.67 | (1470) all_1177_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1438), (1454) imply:
% 260.90/41.67 | (1471) all_1123_1 = all_1030_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1471) implies:
% 260.90/41.67 | (1472) all_1123_1 = all_1030_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (861), (1438) imply:
% 260.90/41.67 | (1473) all_1030_1 = all_974_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (862), (1438) imply:
% 260.90/41.67 | (1474) all_1030_1 = all_962_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (863), (1438) imply:
% 260.90/41.67 | (1475) all_1030_1 = all_911_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1195), (1438) imply:
% 260.90/41.67 | (1476) all_1030_1 = all_1006_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1068), (1403) imply:
% 260.90/41.67 | (1477) all_853_0 = all_722_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1205), (1403) imply:
% 260.90/41.67 | (1478) all_853_0 = all_778_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1067), (1403) imply:
% 260.90/41.67 | (1479) all_861_0 = all_853_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1479) implies:
% 260.90/41.67 | (1480) all_861_0 = all_853_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1102), (1237) imply:
% 260.90/41.67 | (1481) all_1114_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1481) implies:
% 260.90/41.67 | (1482) all_1114_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1066), (1390) imply:
% 260.90/41.67 | (1483) all_1123_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1483) implies:
% 260.90/41.67 | (1484) all_1123_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1101), (1380) imply:
% 260.90/41.67 | (1485) all_1111_0 = all_1000_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1485) implies:
% 260.90/41.67 | (1486) all_1111_0 = all_1000_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (965), (1292) imply:
% 260.90/41.67 | (1487) all_1093_0 = all_902_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1487) implies:
% 260.90/41.67 | (1488) all_1093_0 = all_902_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (966), (1292) imply:
% 260.90/41.67 | (1489) all_902_1 = all_786_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1292), (1375) imply:
% 260.90/41.67 | (1490) all_902_1 = all_824_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (964), (1470) imply:
% 260.90/41.67 | (1491) all_1174_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1491) implies:
% 260.90/41.67 | (1492) all_1174_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (963), (1492) imply:
% 260.90/41.67 | (1493) all_1153_2 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1493) implies:
% 260.90/41.67 | (1494) all_1153_2 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (860), (1466) imply:
% 260.90/41.67 | (1495) all_1159_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1495) implies:
% 260.90/41.67 | (1496) all_1159_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1065), (1415) imply:
% 260.90/41.67 | (1497) all_1159_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1497) implies:
% 260.90/41.67 | (1498) all_1159_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1382), (1498) imply:
% 260.90/41.67 | (1499) all_1030_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1499) implies:
% 260.90/41.67 | (1500) all_1030_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (859), (1496) imply:
% 260.90/41.67 | (1501) all_1075_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1501) implies:
% 260.90/41.67 | (1502) all_1075_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (962), (1494) imply:
% 260.90/41.67 | (1503) all_1138_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1503) implies:
% 260.90/41.67 | (1504) all_1138_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (961), (1462) imply:
% 260.90/41.67 | (1505) all_887_0 = all_676_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1505) implies:
% 260.90/41.67 | (1506) all_887_0 = all_676_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (960), (1504) imply:
% 260.90/41.67 | (1507) all_1120_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1507) implies:
% 260.90/41.67 | (1508) all_1120_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1064), (1484) imply:
% 260.90/41.67 | (1509) all_1048_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1509) implies:
% 260.90/41.67 | (1510) all_1048_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1455), (1472) imply:
% 260.90/41.67 | (1511) all_1030_1 = all_935_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1511) implies:
% 260.90/41.67 | (1512) all_1030_1 = all_935_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (959), (1508) imply:
% 260.90/41.67 | (1513) all_1090_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1513) implies:
% 260.90/41.67 | (1514) all_1090_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1235), (1482) imply:
% 260.90/41.67 | (1515) all_950_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1515) implies:
% 260.90/41.67 | (1516) all_950_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1100), (1486) imply:
% 260.90/41.67 | (1517) all_1093_1 = all_1000_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1517) implies:
% 260.90/41.67 | (1518) all_1093_1 = all_1000_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (958), (1488) imply:
% 260.90/41.67 | (1519) all_902_1 = all_788_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1519) implies:
% 260.90/41.67 | (1520) all_902_1 = all_788_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1099), (1518) imply:
% 260.90/41.67 | (1521) all_1000_1 = all_797_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1153), (1518) imply:
% 260.90/41.67 | (1522) all_1000_1 = all_720_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (957), (1514) imply:
% 260.90/41.67 | (1523) all_1075_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1523) implies:
% 260.90/41.67 | (1524) all_1075_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1170), (1524) imply:
% 260.90/41.67 | (1525) all_1066_2 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1525) implies:
% 260.90/41.67 | (1526) all_1066_2 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (858), (1502) imply:
% 260.90/41.67 | (1527) all_1045_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1527) implies:
% 260.90/41.67 | (1528) all_1045_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1171), (1526) imply:
% 260.90/41.67 | (1529) all_1063_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1529) implies:
% 260.90/41.67 | (1530) all_1063_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (956), (1448) imply:
% 260.90/41.67 | (1531) all_1033_0 = all_1027_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1448), (1530) imply:
% 260.90/41.67 | (1532) all_1033_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (955), (1259) imply:
% 260.90/41.67 | (1533) all_994_0 = all_682_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1533) implies:
% 260.90/41.67 | (1534) all_994_0 = all_682_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1063), (1510) imply:
% 260.90/41.67 | (1535) all_1036_1 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1535) implies:
% 260.90/41.67 | (1536) all_1036_1 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (857), (1528) imply:
% 260.90/41.67 | (1537) all_962_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1537) implies:
% 260.90/41.67 | (1538) all_962_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (953), (1215) imply:
% 260.90/41.67 | (1539) all_1027_0 = all_959_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1539) implies:
% 260.90/41.67 | (1540) all_1027_0 = all_959_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (954), (1215) imply:
% 260.90/41.67 | (1541) all_959_0 = all_926_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1062), (1536) imply:
% 260.90/41.67 | (1542) all_1024_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1542) implies:
% 260.90/41.67 | (1543) all_1024_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1531), (1532) imply:
% 260.90/41.67 | (1544) all_1027_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1544) implies:
% 260.90/41.67 | (1545) all_1027_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1383), (1500) imply:
% 260.90/41.67 | (1546) all_1019_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1546) implies:
% 260.90/41.67 | (1547) all_1019_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1475), (1476) imply:
% 260.90/41.67 | (1548) all_1006_0 = all_911_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1473), (1476) imply:
% 260.90/41.67 | (1549) all_1006_0 = all_974_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1474), (1476) imply:
% 260.90/41.67 | (1550) all_1006_0 = all_962_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1476), (1512) imply:
% 260.90/41.67 | (1551) all_1006_0 = all_935_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1540), (1545) imply:
% 260.90/41.67 | (1552) all_959_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1552) implies:
% 260.90/41.67 | (1553) all_959_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (856), (1201) imply:
% 260.90/41.67 | (1554) all_1003_1 = all_893_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1554) implies:
% 260.90/41.67 | (1555) all_1003_1 = all_893_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1061), (1543) imply:
% 260.90/41.67 | (1556) all_1022_3 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1556) implies:
% 260.90/41.67 | (1557) all_1022_3 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1416), (1417) imply:
% 260.90/41.67 | (1558) all_974_0 = all_926_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1558) implies:
% 260.90/41.67 | (1559) all_974_0 = all_926_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1060), (1557) imply:
% 260.90/41.67 | (1560) all_1016_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1560) implies:
% 260.90/41.67 | (1561) all_1016_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1407), (1547) imply:
% 260.90/41.67 | (1562) all_1009_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1562) implies:
% 260.90/41.67 | (1563) all_1009_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1059), (1561) imply:
% 260.90/41.67 | (1564) all_974_1 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1564) implies:
% 260.90/41.67 | (1565) all_974_1 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (855), (1442) imply:
% 260.90/41.67 | (1566) all_965_1 = all_733_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1566) implies:
% 260.90/41.67 | (1567) all_965_1 = all_733_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1351), (1352) imply:
% 260.90/41.67 | (1568) all_947_0 = all_929_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1352), (1353) imply:
% 260.90/41.67 | (1569) all_950_1 = all_947_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1569) implies:
% 260.90/41.67 | (1570) all_950_1 = all_947_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1408), (1563) imply:
% 260.90/41.67 | (1571) all_1003_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1571) implies:
% 260.90/41.67 | (1572) all_1003_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1550), (1551) imply:
% 260.90/41.67 | (1573) all_962_0 = all_935_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1573) implies:
% 260.90/41.67 | (1574) all_962_0 = all_935_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1548), (1551) imply:
% 260.90/41.67 | (1575) all_935_0 = all_911_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1549), (1551) imply:
% 260.90/41.67 | (1576) all_974_0 = all_935_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1576) implies:
% 260.90/41.67 | (1577) all_974_0 = all_935_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1378), (1572) imply:
% 260.90/41.67 | (1578) all_778_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1578) implies:
% 260.90/41.67 | (1579) all_778_0 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (853), (1555) imply:
% 260.90/41.67 | (1580) all_911_0 = all_893_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1580) implies:
% 260.90/41.67 | (1581) all_911_0 = all_893_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (854), (1555) imply:
% 260.90/41.67 | (1582) all_893_0 = all_856_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1521), (1522) imply:
% 260.90/41.67 | (1583) all_797_0 = all_720_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1583) implies:
% 260.90/41.67 | (1584) all_797_0 = all_720_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1096), (1097) imply:
% 260.90/41.67 | (1585) all_881_0 = all_812_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1585) implies:
% 260.90/41.67 | (1586) all_881_0 = all_812_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1097), (1098) imply:
% 260.90/41.67 | (1587) all_812_0 = all_797_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (952), (1534) imply:
% 260.90/41.67 | (1588) all_686_0 = all_682_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1588) implies:
% 260.90/41.67 | (1589) all_686_0 = all_682_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1559), (1577) imply:
% 260.90/41.67 | (1590) all_935_0 = all_926_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1590) implies:
% 260.90/41.67 | (1591) all_935_0 = all_926_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1058), (1565) imply:
% 260.90/41.67 | (1592) all_965_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1592) implies:
% 260.90/41.67 | (1593) all_965_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1057), (1593) imply:
% 260.90/41.67 | (1594) all_962_1 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1594) implies:
% 260.90/41.67 | (1595) all_962_1 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (852), (1567) imply:
% 260.90/41.67 | (1596) all_959_1 = all_733_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1596) implies:
% 260.90/41.67 | (1597) all_959_1 = all_733_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1538), (1574) imply:
% 260.90/41.67 | (1598) all_935_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1598) implies:
% 260.90/41.67 | (1599) all_935_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1056), (1595) imply:
% 260.90/41.67 | (1600) all_890_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1600) implies:
% 260.90/41.67 | (1601) all_890_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1541), (1553) imply:
% 260.90/41.67 | (1602) all_926_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1602) implies:
% 260.90/41.67 | (1603) all_926_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (851), (1597) imply:
% 260.90/41.67 | (1604) all_845_0 = all_733_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1604) implies:
% 260.90/41.67 | (1605) all_845_0 = all_733_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1387), (1516) imply:
% 260.90/41.67 | (1606) all_941_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1606) implies:
% 260.90/41.67 | (1607) all_941_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1332), (1570) imply:
% 260.90/41.67 | (1608) all_947_0 = all_755_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1608) implies:
% 260.90/41.67 | (1609) all_947_0 = all_755_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1568), (1609) imply:
% 260.90/41.67 | (1610) all_929_1 = all_755_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1610) implies:
% 260.90/41.67 | (1611) all_929_1 = all_755_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1388), (1607) imply:
% 260.90/41.67 | (1612) all_923_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1612) implies:
% 260.90/41.67 | (1613) all_923_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1575), (1591) imply:
% 260.90/41.67 | (1614) all_926_1 = all_911_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1591), (1599) imply:
% 260.90/41.67 | (1615) all_926_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (951), (1611) imply:
% 260.90/41.67 | (1616) all_809_0 = all_755_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1616) implies:
% 260.90/41.67 | (1617) all_809_0 = all_755_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (950), (1603) imply:
% 260.90/41.67 | (1618) all_923_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1618) implies:
% 260.90/41.67 | (1619) all_923_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1614), (1615) imply:
% 260.90/41.67 | (1620) all_911_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1620) implies:
% 260.90/41.67 | (1621) all_911_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1095), (1613) imply:
% 260.90/41.67 | (1622) all_881_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1622) implies:
% 260.90/41.67 | (1623) all_881_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (949), (1619) imply:
% 260.90/41.67 | (1624) all_920_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1624) implies:
% 260.90/41.67 | (1625) all_920_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (948), (1625) imply:
% 260.90/41.67 | (1626) all_878_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1626) implies:
% 260.90/41.67 | (1627) all_878_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1581), (1621) imply:
% 260.90/41.67 | (1628) all_893_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1628) implies:
% 260.90/41.67 | (1629) all_893_0 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1489), (1520) imply:
% 260.90/41.67 | (1630) all_788_0 = all_786_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1490), (1520) imply:
% 260.90/41.67 | (1631) all_824_0 = all_788_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1631) implies:
% 260.90/41.67 | (1632) all_824_0 = all_788_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1582), (1629) imply:
% 260.90/41.67 | (1633) all_856_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1633) implies:
% 260.90/41.67 | (1634) all_856_1 = all_832_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1055), (1601) imply:
% 260.90/41.67 | (1635) all_861_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1635) implies:
% 260.90/41.67 | (1636) all_861_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (946), (1506) imply:
% 260.90/41.67 | (1637) all_809_0 = all_676_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1637) implies:
% 260.90/41.67 | (1638) all_809_0 = all_676_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (947), (1506) imply:
% 260.90/41.67 | (1639) all_676_0 = all_673_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (943), (944) imply:
% 260.90/41.67 | (1640) all_700_0 = all_698_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1640) implies:
% 260.90/41.67 | (1641) all_700_0 = all_698_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (944), (945) imply:
% 260.90/41.67 | (1642) all_698_0 = all_695_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1586), (1623) imply:
% 260.90/41.67 | (1643) all_812_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1643) implies:
% 260.90/41.67 | (1644) all_812_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (942), (1627) imply:
% 260.90/41.67 | (1645) all_875_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1645) implies:
% 260.90/41.67 | (1646) all_875_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (941), (1646) imply:
% 260.90/41.67 | (1647) all_861_2 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1647) implies:
% 260.90/41.67 | (1648) all_861_2 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1480), (1636) imply:
% 260.90/41.67 | (1649) all_853_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1649) implies:
% 260.90/41.67 | (1650) all_853_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (940), (1648) imply:
% 260.90/41.67 | (1651) all_842_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1651) implies:
% 260.90/41.67 | (1652) all_842_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (850), (1634) imply:
% 260.90/41.67 | (1653) all_832_0 = all_713_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (849), (1634) imply:
% 260.90/41.67 | (1654) all_832_0 = all_815_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1478), (1650) imply:
% 260.90/41.67 | (1655) all_778_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1655) implies:
% 260.90/41.67 | (1656) all_778_0 = all_742_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1477), (1650) imply:
% 260.90/41.67 | (1657) all_742_1 = all_722_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (848), (1605) imply:
% 260.90/41.67 | (1658) all_735_0 = all_733_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1658) implies:
% 260.90/41.67 | (1659) all_735_0 = all_733_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1373), (1652) imply:
% 260.90/41.67 | (1660) all_824_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1660) implies:
% 260.90/41.67 | (1661) all_824_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1653), (1654) imply:
% 260.90/41.67 | (1662) all_815_0 = all_713_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1662) implies:
% 260.90/41.67 | (1663) all_815_0 = all_713_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (938), (1187) imply:
% 260.90/41.67 | (1664) all_667_0 = all_664_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1664) implies:
% 260.90/41.67 | (1665) all_667_0 = all_664_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (939), (1187) imply:
% 260.90/41.67 | (1666) all_664_0 = all_661_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1632), (1661) imply:
% 260.90/41.67 | (1667) all_788_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1667) implies:
% 260.90/41.67 | (1668) all_788_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (847), (1663) imply:
% 260.90/41.67 | (1669) all_780_0 = all_713_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1669) implies:
% 260.90/41.67 | (1670) all_780_0 = all_713_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1587), (1644) imply:
% 260.90/41.67 | (1671) all_797_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1671) implies:
% 260.90/41.67 | (1672) all_797_0 = all_778_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (936), (1617) imply:
% 260.90/41.67 | (1673) all_770_0 = all_755_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1673) implies:
% 260.90/41.67 | (1674) all_770_0 = all_755_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (937), (1617) imply:
% 260.90/41.67 | (1675) all_755_0 = all_692_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1617), (1638) imply:
% 260.90/41.67 | (1676) all_755_0 = all_676_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1094), (1672) imply:
% 260.90/41.67 | (1677) all_778_1 = all_770_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1584), (1672) imply:
% 260.90/41.67 | (1678) all_778_1 = all_720_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1630), (1668) imply:
% 260.90/41.67 | (1679) all_786_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1679) implies:
% 260.90/41.67 | (1680) all_786_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (935), (1680) imply:
% 260.90/41.67 | (1681) all_780_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1681) implies:
% 260.90/41.67 | (1682) all_780_1 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (846), (1670) imply:
% 260.90/41.67 | (1683) all_759_0 = all_713_1
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1683) implies:
% 260.90/41.67 | (1684) all_759_0 = all_713_1
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1420), (1682) imply:
% 260.90/41.67 | (1685) all_775_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1685) implies:
% 260.90/41.67 | (1686) all_775_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1579), (1656) imply:
% 260.90/41.67 | (1687) all_742_1 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1687) implies:
% 260.90/41.67 | (1688) all_742_1 = all_713_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1677), (1678) imply:
% 260.90/41.67 | (1689) all_770_1 = all_720_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1689) implies:
% 260.90/41.67 | (1690) all_770_1 = all_720_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (1421), (1686) imply:
% 260.90/41.67 | (1691) all_772_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1691) implies:
% 260.90/41.67 | (1692) all_772_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (934), (1692) imply:
% 260.90/41.67 | (1693) all_733_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1693) implies:
% 260.90/41.67 | (1694) all_733_0 = all_650_0
% 260.90/41.67 |
% 260.90/41.67 | COMBINE_EQS: (933), (1674) imply:
% 260.90/41.67 | (1695) all_755_0 = all_679_0
% 260.90/41.67 |
% 260.90/41.67 | SIMP: (1695) implies:
% 260.90/41.67 | (1696) all_755_0 = all_679_0
% 260.90/41.67 |
% 260.90/41.68 | COMBINE_EQS: (1093), (1690) imply:
% 260.90/41.68 | (1697) all_722_0 = all_720_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1697) implies:
% 260.90/41.68 | (1698) all_722_0 = all_720_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (845), (1684) imply:
% 260.90/41.68 | (1699) all_755_1 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1699) implies:
% 260.90/41.68 | (1700) all_755_1 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1675), (1696) imply:
% 260.90/41.68 | (1701) all_692_0 = all_679_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1701) implies:
% 260.90/41.68 | (1702) all_692_0 = all_679_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1676), (1696) imply:
% 260.90/41.68 | (1703) all_679_0 = all_676_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1459), (1700) imply:
% 260.90/41.68 | (1704) all_742_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1704) implies:
% 260.90/41.68 | (1705) all_742_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1460), (1705) imply:
% 260.90/41.68 | (1706) all_735_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1706) implies:
% 260.90/41.68 | (1707) all_735_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1657), (1688) imply:
% 260.90/41.68 | (1708) all_722_1 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1708) implies:
% 260.90/41.68 | (1709) all_722_1 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1659), (1707) imply:
% 260.90/41.68 | (1710) all_733_1 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1710) implies:
% 260.90/41.68 | (1711) all_733_1 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1363), (1694) imply:
% 260.90/41.68 | (1712) all_730_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1712) implies:
% 260.90/41.68 | (1713) all_730_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1361), (1713) imply:
% 260.90/41.68 | (1714) all_727_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1714) implies:
% 260.90/41.68 | (1715) all_727_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (932), (1715) imply:
% 260.90/41.68 | (1716) all_724_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1716) implies:
% 260.90/41.68 | (1717) all_724_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (931), (1281) imply:
% 260.90/41.68 | (1718) all_710_0 = all_700_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1281), (1717) imply:
% 260.90/41.68 | (1719) all_710_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1450), (1698) imply:
% 260.90/41.68 | (1720) all_720_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1179), (1709) imply:
% 260.90/41.68 | (1721) all_720_1 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1721) implies:
% 260.90/41.68 | (1722) all_720_1 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1718), (1719) imply:
% 260.90/41.68 | (1723) all_700_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1723) implies:
% 260.90/41.68 | (1724) all_700_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1641), (1724) imply:
% 260.90/41.68 | (1725) all_698_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1725) implies:
% 260.90/41.68 | (1726) all_698_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1642), (1726) imply:
% 260.90/41.68 | (1727) all_695_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1727) implies:
% 260.90/41.68 | (1728) all_695_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (930), (1728) imply:
% 260.90/41.68 | (1729) all_692_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1729) implies:
% 260.90/41.68 | (1730) all_692_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1702), (1730) imply:
% 260.90/41.68 | (1731) all_679_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1731) implies:
% 260.90/41.68 | (1732) all_679_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (929), (1589) imply:
% 260.90/41.68 | (1733) all_682_0 = all_670_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (928), (1589) imply:
% 260.90/41.68 | (1734) all_682_0 = all_673_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1733), (1734) imply:
% 260.90/41.68 | (1735) all_673_0 = all_670_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1735) implies:
% 260.90/41.68 | (1736) all_673_0 = all_670_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1703), (1732) imply:
% 260.90/41.68 | (1737) all_676_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1737) implies:
% 260.90/41.68 | (1738) all_676_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1639), (1738) imply:
% 260.90/41.68 | (1739) all_673_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1739) implies:
% 260.90/41.68 | (1740) all_673_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (927), (1736) imply:
% 260.90/41.68 | (1741) all_670_0 = all_667_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1736), (1740) imply:
% 260.90/41.68 | (1742) all_670_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1741), (1742) imply:
% 260.90/41.68 | (1743) all_667_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1743) implies:
% 260.90/41.68 | (1744) all_667_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1665), (1744) imply:
% 260.90/41.68 | (1745) all_664_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1745) implies:
% 260.90/41.68 | (1746) all_664_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1666), (1746) imply:
% 260.90/41.68 | (1747) all_661_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1747) implies:
% 260.90/41.68 | (1748) all_661_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (926), (1748) imply:
% 260.90/41.68 | (1749) all_659_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1749) implies:
% 260.90/41.68 | (1750) all_659_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1696), (1732) imply:
% 260.90/41.68 | (1751) all_755_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1690), (1720) imply:
% 260.90/41.68 | (1752) all_770_1 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (933), (1732) imply:
% 260.90/41.68 | (1753) all_770_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1650), (1688) imply:
% 260.90/41.68 | (1754) all_853_0 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1636), (1688) imply:
% 260.90/41.68 | (1755) all_861_0 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1629), (1653) imply:
% 260.90/41.68 | (1756) all_893_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1520), (1668) imply:
% 260.90/41.68 | (1757) all_902_1 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1611), (1751) imply:
% 260.90/41.68 | (1758) all_929_1 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1555), (1756) imply:
% 260.90/41.68 | (1759) all_1003_1 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1557), (1688) imply:
% 260.90/41.68 | (1760) all_1022_3 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1510), (1688) imply:
% 260.90/41.68 | (1761) all_1048_0 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1464), (1653) imply:
% 260.90/41.68 | (1762) all_1204_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1436), (1532) imply:
% 260.90/41.68 | (1763) all_1235_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1135), (1738) imply:
% 260.90/41.68 | (1764) all_1247_2 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1191), (1711) imply:
% 260.90/41.68 | (1765) all_1253_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (972), (1763) imply:
% 260.90/41.68 | (1766) all_1270_2 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1314), (1532) imply:
% 260.90/41.68 | (1767) all_1279_2 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1427), (1762) imply:
% 260.90/41.68 | (1768) all_1288_1 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1410), (1768) imply:
% 260.90/41.68 | (1769) all_1303_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1392), (1653) imply:
% 260.90/41.68 | (1770) all_1326_0 = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1347), (1563) imply:
% 260.90/41.68 | (1771) all_1350_0 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1336), (1771) imply:
% 260.90/41.68 | (1772) all_1432_1 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1294), (1772) imply:
% 260.90/41.68 | (1773) all_1447_0 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1282), (1767) imply:
% 260.90/41.68 | (1774) all_1555_0 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1077), (1773) imply:
% 260.90/41.68 | (1775) all_1564_0 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1164), (1572) imply:
% 260.90/41.68 | (1776) all_1579_0 = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (998), (1774) imply:
% 260.90/41.68 | (1777) all_1594_1 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1227), (1719) imply:
% 260.90/41.68 | (1778) all_1608_3 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1263), (1751) imply:
% 260.90/41.68 | (1779) all_1632_1 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1149), (1532) imply:
% 260.90/41.68 | (1780) all_1780_1 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1032), (1526) imply:
% 260.90/41.68 | (1781) all_1783_1 = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (813), (1781) imply:
% 260.90/41.68 | (1782) c_Nat_OSuc(all_650_0) = all_1783_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (810), (1780) imply:
% 260.90/41.68 | (1783) c_Nat_OSuc(all_650_0) = all_1780_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (804), (1168) imply:
% 260.90/41.68 | (1784) c_Nat_OSuc(all_650_0) = all_1768_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (799), (1177) imply:
% 260.90/41.68 | (1785) c_Nat_OSuc(all_650_0) = all_1762_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (726), (1779) imply:
% 260.90/41.68 | (1786) c_Nat_OSuc(all_650_0) = all_1632_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (710), (1778) imply:
% 260.90/41.68 | (1787) c_Nat_OSuc(all_650_0) = all_1608_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (707), (1777) imply:
% 260.90/41.68 | (1788) c_Nat_OSuc(all_650_0) = all_1594_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (675), (1310) imply:
% 260.90/41.68 | (1789) c_Nat_OSuc(all_650_0) = all_1537_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (578), (1767) imply:
% 260.90/41.68 | (1790) c_Nat_OSuc(all_650_0) = all_1279_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (575), (1766) imply:
% 260.90/41.68 | (1791) c_Nat_OSuc(all_650_0) = all_1270_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (570), (1425) imply:
% 260.90/41.68 | (1792) c_Nat_OSuc(all_650_0) = all_1256_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (562), (1764) imply:
% 260.90/41.68 | (1793) c_Nat_OSuc(all_650_0) = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (517), (1494) imply:
% 260.90/41.68 | (1794) c_Nat_OSuc(all_650_0) = all_1153_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (490), (1526) imply:
% 260.90/41.68 | (1795) c_Nat_OSuc(all_650_0) = all_1066_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (411), (1758) imply:
% 260.90/41.68 | (1796) c_Nat_OSuc(all_650_0) = all_929_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (401), (1625) imply:
% 260.90/41.68 | (1797) c_Nat_OSuc(all_650_0) = all_920_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (396), (1757) imply:
% 260.90/41.68 | (1798) c_Nat_OSuc(all_650_0) = all_902_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (383), (1627) imply:
% 260.90/41.68 | (1799) c_Nat_OSuc(all_650_0) = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (378), (1648) imply:
% 260.90/41.68 | (1800) c_Nat_OSuc(all_650_0) = all_861_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (331), (1752), (1753) imply:
% 260.90/41.68 | (1801) c_Nat_OSuc(all_650_0) = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (377), (1755) imply:
% 260.90/41.68 | (1802) c_RealDef_Oreal(tc_Nat_Onat, all_861_1) = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (342), (1670), (1682) imply:
% 260.90/41.68 | (1803) c_RealDef_Oreal(tc_Nat_Onat, all_650_0) = all_713_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (316), (1694), (1711) imply:
% 260.90/41.68 | (1804) c_RComplete_Onatfloor(all_713_1) = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (305), (1450), (1709) imply:
% 260.90/41.68 | (1805) c_RComplete_Onatfloor(all_713_0) = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (325), (1700), (1751) imply:
% 260.90/41.68 | (1806) c_RComplete_Onatceiling(all_713_1) = all_650_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (301), (1720), (1722) imply:
% 260.90/41.68 | (1807) c_RComplete_Onatceiling(all_713_0) = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (459), (1760) imply:
% 260.90/41.68 | (1808) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0, all_1022_2)
% 260.90/41.68 | = all_1022_1
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (664), (1054) imply:
% 260.90/41.68 | (1809) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, all_1468_3)
% 260.90/41.68 | = all_1504_3
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (313), (1711) imply:
% 260.90/41.68 | (1810) $i(all_713_1)
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (298), (1722) imply:
% 260.90/41.68 | (1811) $i(all_713_0)
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (261), (1750) imply:
% 260.90/41.68 | (1812) $i(all_650_0)
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (409), (1758) imply:
% 260.90/41.68 | (1813) c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_650_0, all_929_0)
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (347), (1668) imply:
% 260.90/41.68 | (1814) c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_650_0, all_650_0)
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (456), (1053) imply:
% 260.90/41.68 | (1815) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_1,
% 260.90/41.68 | all_648_0)
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (344), (1680) imply:
% 260.90/41.68 | (1816) ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_650_0, all_650_0)
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (254) with all_1468_2, all_1504_3, all_1468_3,
% 260.90/41.68 | v_da____, tc_RealDef_Oreal, simplifying with (655), (1809) gives:
% 260.90/41.68 | (1817) all_1504_3 = all_1468_2
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_929_0, all_1066_1, all_650_0,
% 260.90/41.68 | simplifying with (1795), (1796) gives:
% 260.90/41.68 | (1818) all_1066_1 = all_929_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1066_1, all_1270_1, all_650_0,
% 260.90/41.68 | simplifying with (1791), (1795) gives:
% 260.90/41.68 | (1819) all_1270_1 = all_1066_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_920_0, all_1270_1, all_650_0,
% 260.90/41.68 | simplifying with (1791), (1797) gives:
% 260.90/41.68 | (1820) all_1270_1 = all_920_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1256_1, all_1279_1, all_650_0,
% 260.90/41.68 | simplifying with (1790), (1792) gives:
% 260.90/41.68 | (1821) all_1279_1 = all_1256_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1256_1, all_1537_0, all_650_0,
% 260.90/41.68 | simplifying with (1789), (1792) gives:
% 260.90/41.68 | (1822) all_1537_0 = all_1256_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_929_0, all_1537_0, all_650_0,
% 260.90/41.68 | simplifying with (1789), (1796) gives:
% 260.90/41.68 | (1823) all_1537_0 = all_929_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1153_1, all_1594_0, all_650_0,
% 260.90/41.68 | simplifying with (1788), (1794) gives:
% 260.90/41.68 | (1824) all_1594_0 = all_1153_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1066_1, all_1594_0, all_650_0,
% 260.90/41.68 | simplifying with (1788), (1795) gives:
% 260.90/41.68 | (1825) all_1594_0 = all_1066_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_902_0, all_1594_0, all_650_0,
% 260.90/41.68 | simplifying with (1788), (1798) gives:
% 260.90/41.68 | (1826) all_1594_0 = all_902_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_861_1, all_1594_0, all_650_0,
% 260.90/41.68 | simplifying with (1788), (1800) gives:
% 260.90/41.68 | (1827) all_1594_0 = all_861_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1537_0, all_1608_0, all_650_0,
% 260.90/41.68 | simplifying with (1787), (1789) gives:
% 260.90/41.68 | (1828) all_1608_0 = all_1537_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1153_1, all_1632_0, all_650_0,
% 260.90/41.68 | simplifying with (1786), (1794) gives:
% 260.90/41.68 | (1829) all_1632_0 = all_1153_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1279_1, all_1762_1, all_650_0,
% 260.90/41.68 | simplifying with (1785), (1790) gives:
% 260.90/41.68 | (1830) all_1762_1 = all_1279_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_878_0, all_1762_1, all_650_0,
% 260.90/41.68 | simplifying with (1785), (1799) gives:
% 260.90/41.68 | (1831) all_1762_1 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1768_1, all_1780_0, all_650_0,
% 260.90/41.68 | simplifying with (1783), (1784) gives:
% 260.90/41.68 | (1832) all_1780_0 = all_1768_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1608_0, all_1780_0, all_650_0,
% 260.90/41.68 | simplifying with (1783), (1787) gives:
% 260.90/41.68 | (1833) all_1780_0 = all_1608_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1247_1, all_1780_0, all_650_0,
% 260.90/41.68 | simplifying with (1783), (1793) gives:
% 260.90/41.68 | (1834) all_1780_0 = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1632_0, all_1783_0, all_650_0,
% 260.90/41.68 | simplifying with (1782), (1786) gives:
% 260.90/41.68 | (1835) all_1783_0 = all_1632_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_705_0, all_1783_0, all_650_0,
% 260.90/41.68 | simplifying with (1782), (1801) gives:
% 260.90/41.68 | (1836) all_1783_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1835), (1836) imply:
% 260.90/41.68 | (1837) all_1632_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1837) implies:
% 260.90/41.68 | (1838) all_1632_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1832), (1834) imply:
% 260.90/41.68 | (1839) all_1768_1 = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1832), (1833) imply:
% 260.90/41.68 | (1840) all_1768_1 = all_1608_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1839), (1840) imply:
% 260.90/41.68 | (1841) all_1608_0 = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1841) implies:
% 260.90/41.68 | (1842) all_1608_0 = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1830), (1831) imply:
% 260.90/41.68 | (1843) all_1279_1 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1843) implies:
% 260.90/41.68 | (1844) all_1279_1 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1829), (1838) imply:
% 260.90/41.68 | (1845) all_1153_1 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1845) implies:
% 260.90/41.68 | (1846) all_1153_1 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1828), (1842) imply:
% 260.90/41.68 | (1847) all_1537_0 = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1847) implies:
% 260.90/41.68 | (1848) all_1537_0 = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1825), (1826) imply:
% 260.90/41.68 | (1849) all_1066_1 = all_902_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1849) implies:
% 260.90/41.68 | (1850) all_1066_1 = all_902_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1824), (1826) imply:
% 260.90/41.68 | (1851) all_1153_1 = all_902_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1851) implies:
% 260.90/41.68 | (1852) all_1153_1 = all_902_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1826), (1827) imply:
% 260.90/41.68 | (1853) all_902_0 = all_861_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1823), (1848) imply:
% 260.90/41.68 | (1854) all_1247_1 = all_929_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1822), (1848) imply:
% 260.90/41.68 | (1855) all_1256_1 = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1855) implies:
% 260.90/41.68 | (1856) all_1256_1 = all_1247_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1821), (1844) imply:
% 260.90/41.68 | (1857) all_1256_1 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1857) implies:
% 260.90/41.68 | (1858) all_1256_1 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1819), (1820) imply:
% 260.90/41.68 | (1859) all_1066_1 = all_920_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1859) implies:
% 260.90/41.68 | (1860) all_1066_1 = all_920_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1856), (1858) imply:
% 260.90/41.68 | (1861) all_1247_1 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1861) implies:
% 260.90/41.68 | (1862) all_1247_1 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1854), (1862) imply:
% 260.90/41.68 | (1863) all_929_0 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1863) implies:
% 260.90/41.68 | (1864) all_929_0 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1846), (1852) imply:
% 260.90/41.68 | (1865) all_902_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1865) implies:
% 260.90/41.68 | (1866) all_902_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1850), (1860) imply:
% 260.90/41.68 | (1867) all_920_0 = all_902_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1818), (1860) imply:
% 260.90/41.68 | (1868) all_929_0 = all_920_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1868) implies:
% 260.90/41.68 | (1869) all_929_0 = all_920_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1864), (1869) imply:
% 260.90/41.68 | (1870) all_920_0 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1870) implies:
% 260.90/41.68 | (1871) all_920_0 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1867), (1871) imply:
% 260.90/41.68 | (1872) all_902_0 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | SIMP: (1872) implies:
% 260.90/41.68 | (1873) all_902_0 = all_878_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1853), (1873) imply:
% 260.90/41.68 | (1874) all_878_0 = all_861_1
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1866), (1873) imply:
% 260.90/41.68 | (1875) all_878_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1874), (1875) imply:
% 260.90/41.68 | (1876) all_861_1 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1871), (1875) imply:
% 260.90/41.68 | (1877) all_920_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1864), (1875) imply:
% 260.90/41.68 | (1878) all_929_0 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1860), (1877) imply:
% 260.90/41.68 | (1879) all_1066_1 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1862), (1875) imply:
% 260.90/41.68 | (1880) all_1247_1 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | COMBINE_EQS: (1839), (1880) imply:
% 260.90/41.68 | (1881) all_1768_1 = all_705_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (805), (1881) imply:
% 260.90/41.68 | (1882) c_Nat_OSuc(all_705_0) = all_1768_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (491), (1879) imply:
% 260.90/41.68 | (1883) c_Nat_OSuc(all_705_0) = all_1066_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (1802), (1876) imply:
% 260.90/41.68 | (1884) c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = all_713_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (514), (1846) imply:
% 260.90/41.68 | (1885) hAPP(all_1153_3, all_705_0) = all_1153_0
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (374), (1876) imply:
% 260.90/41.68 | (1886) $i(all_705_0)
% 260.90/41.68 |
% 260.90/41.68 | REDUCE: (1813), (1878) imply:
% 260.90/41.68 | (1887) c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_650_0, all_705_0)
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (251) with all_1066_0, all_1768_0, all_705_0,
% 260.90/41.68 | simplifying with (1882), (1883) gives:
% 260.90/41.68 | (1888) all_1768_0 = all_1066_0
% 260.90/41.68 |
% 260.90/41.68 | GROUND_INST: instantiating (10) with v_z____, tc_Complex_Ocomplex, all_648_0,
% 260.90/41.68 | simplifying with (242), (243), (246), (257) gives:
% 260.90/41.68 | (1889) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_648_0) = all_648_0 &
% 260.90/41.68 | $i(all_648_0)
% 260.90/41.68 |
% 260.90/41.68 | ALPHA: (1889) implies:
% 260.90/41.69 | (1890) $i(all_648_0)
% 260.90/41.69 | (1891) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_648_0) = all_648_0
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (10) with v_aa____, tc_Complex_Ocomplex,
% 260.90/41.69 | all_1468_3, simplifying with (31), (242), (243), (654) gives:
% 260.90/41.69 | (1892) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1468_3) = all_1468_3
% 260.90/41.69 | & $i(all_1468_3)
% 260.90/41.69 |
% 260.90/41.69 | ALPHA: (1892) implies:
% 260.90/41.69 | (1893) $i(all_1468_3)
% 260.90/41.69 | (1894) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1468_3) = all_1468_3
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__pos__pos) with all_1468_3, v_da____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1468_2, simplifying with (30), (236),
% 260.90/41.69 | (244), (655), (1893) gives:
% 260.90/41.69 | (1895) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1468_3) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v_da____) |
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1468_2)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__pos__nonneg) with all_1468_3, v_da____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1468_2, simplifying with (30), (236),
% 260.90/41.69 | (244), (655), (1893) gives:
% 260.90/41.69 | (1896) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | v_da____) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1468_3) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | v0, all_1468_2)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonneg__pos) with all_1468_3, v_da____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1468_2, simplifying with (30), (236),
% 260.90/41.69 | (244), (655), (1893) gives:
% 260.90/41.69 | (1897) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1468_3) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | v_da____) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | v0, all_1468_2)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__neg__neg) with all_1468_3, v_da____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1468_2, simplifying with (30), (236),
% 260.90/41.69 | (244), (655), (1893) gives:
% 260.90/41.69 | (1898) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1468_3, v0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, v0) |
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1468_2,
% 260.90/41.69 | v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__neg__nonpos) with all_1468_3, v_da____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1468_2, simplifying with (30), (236),
% 260.90/41.69 | (244), (655), (1893) gives:
% 260.90/41.69 | (1899) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | v_da____, v0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1468_3,
% 260.90/41.69 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1468_2, v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonpos__neg) with all_1468_3, v_da____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1468_2, simplifying with (30), (236),
% 260.90/41.69 | (244), (655), (1893) gives:
% 260.90/41.69 | (1900) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1468_3, v0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____,
% 260.90/41.69 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1468_2, v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonneg__nonneg) with all_1468_3,
% 260.90/41.69 | v_da____, tc_RealDef_Oreal, all_1468_2, simplifying with (30),
% 260.90/41.69 | (236), (244), (655), (1893) gives:
% 260.90/41.69 | (1901) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | v0, all_1468_3) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | v_da____) |
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1468_2)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonneg__eq__0__iff) with all_1468_3,
% 260.90/41.69 | v_da____, tc_RealDef_Oreal, all_1468_2, simplifying with (30),
% 260.90/41.69 | (236), (244), (655), (1893) gives:
% 260.90/41.69 | (1902) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | v0, all_1468_3) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | v_da____) | (( ~ (v0 = all_1468_2) | (all_1468_2 = v_da____ &
% 260.90/41.69 | all_1468_3 = v_da____)) & ( ~ (v0 = v_da____) | ~
% 260.90/41.69 | (all_1468_3 = v_da____) | all_1468_2 = v_da____))))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonpos__nonpos) with all_1468_3,
% 260.90/41.69 | v_da____, tc_RealDef_Oreal, all_1468_2, simplifying with (30),
% 260.90/41.69 | (236), (244), (655), (1893) gives:
% 260.90/41.69 | (1903) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | all_1468_3, v0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____,
% 260.90/41.69 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | all_1468_2, v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating
% 260.90/41.69 | (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)
% 260.90/41.69 | with v_da____, all_1468_3, tc_RealDef_Oreal, all_1468_2,
% 260.90/41.69 | simplifying with (30), (241), (244), (655), (1893) gives:
% 260.90/41.69 | (1904) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1468_3, v_da____)
% 260.90/41.69 | = all_1468_2 & $i(all_1468_2)
% 260.90/41.69 |
% 260.90/41.69 | ALPHA: (1904) implies:
% 260.90/41.69 | (1905) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1468_3, v_da____)
% 260.90/41.69 | = all_1468_2
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__pos__pos) with all_1022_2, all_713_0,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_1, simplifying with (236), (244),
% 260.90/41.69 | (457), (1808), (1811) gives:
% 260.90/41.69 | (1906) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1022_2) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_713_0) |
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1022_1)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__pos__nonneg) with all_1022_2, all_713_0,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_1, simplifying with (236), (244),
% 260.90/41.69 | (457), (1808), (1811) gives:
% 260.90/41.69 | (1907) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_713_0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1022_2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | v0, all_1022_1)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonneg__pos) with all_1022_2, all_713_0,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_1, simplifying with (236), (244),
% 260.90/41.69 | (457), (1808), (1811) gives:
% 260.90/41.69 | (1908) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1022_2) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_713_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | v0, all_1022_1)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__neg__neg) with all_1022_2, all_713_0,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_1, simplifying with (236), (244),
% 260.90/41.69 | (457), (1808), (1811) gives:
% 260.90/41.69 | (1909) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_2, v0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_0, v0) |
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1022_1,
% 260.90/41.69 | v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__neg__nonpos) with all_1022_2, all_713_0,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_1, simplifying with (236), (244),
% 260.90/41.69 | (457), (1808), (1811) gives:
% 260.90/41.69 | (1910) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_713_0, v0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_2,
% 260.90/41.69 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_1, v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonpos__neg) with all_1022_2, all_713_0,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_1, simplifying with (236), (244),
% 260.90/41.69 | (457), (1808), (1811) gives:
% 260.90/41.69 | (1911) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_2, v0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_0,
% 260.90/41.69 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_1, v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonneg__nonneg) with all_1022_2,
% 260.90/41.69 | all_713_0, tc_RealDef_Oreal, all_1022_1, simplifying with (236),
% 260.90/41.69 | (244), (457), (1808), (1811) gives:
% 260.90/41.69 | (1912) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | v0, all_1022_2) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_713_0) |
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1022_1)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonneg__eq__0__iff) with all_1022_2,
% 260.90/41.69 | all_713_0, tc_RealDef_Oreal, all_1022_1, simplifying with (236),
% 260.90/41.69 | (244), (457), (1808), (1811) gives:
% 260.90/41.69 | (1913) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | v0, all_1022_2) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_713_0) | (( ~ (v0 = all_1022_1) | (all_1022_1 = all_713_0
% 260.90/41.69 | & all_1022_2 = all_713_0)) & ( ~ (v0 = all_713_0) | ~
% 260.90/41.69 | (all_1022_2 = all_713_0) | all_1022_1 = all_713_0))))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__nonpos__nonpos) with all_1022_2,
% 260.90/41.69 | all_713_0, tc_RealDef_Oreal, all_1022_1, simplifying with (236),
% 260.90/41.69 | (244), (457), (1808), (1811) gives:
% 260.90/41.69 | (1914) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_2, v0) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_0,
% 260.90/41.69 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_1, v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_add__0__iff) with all_1022_2, all_713_0,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_1, simplifying with (234), (244),
% 260.90/41.69 | (457), (1808), (1811) gives:
% 260.90/41.69 | (1915) ? [v0: any] : (( ~ (all_1022_1 = all_713_0) | (v0 = all_1022_2 &
% 260.90/41.69 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1022_2)) &
% 260.90/41.69 | (all_1022_1 = all_713_0 | ( ~ (v0 = all_1022_2) &
% 260.90/41.69 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0))))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating
% 260.90/41.69 | (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)
% 260.90/41.69 | with all_713_0, all_1022_2, tc_RealDef_Oreal, all_1022_1,
% 260.90/41.69 | simplifying with (241), (244), (457), (1808), (1811) gives:
% 260.90/41.69 | (1916) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1022_2, all_713_0)
% 260.90/41.69 | = all_1022_1 & $i(all_1022_1)
% 260.90/41.69 |
% 260.90/41.69 | ALPHA: (1916) implies:
% 260.90/41.69 | (1917) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1022_2, all_713_0)
% 260.90/41.69 | = all_1022_1
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_abs__ge__self) with v_r____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_2, simplifying with (235), (244),
% 260.90/41.69 | (245), (460) gives:
% 260.90/41.69 | (1918) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r____,
% 260.90/41.69 | all_1022_2)
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_abs__ge__zero) with v_r____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_2, simplifying with (235), (244),
% 260.90/41.69 | (245), (460) gives:
% 260.90/41.69 | (1919) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1022_2))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_abs__not__less__zero) with v_r____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_2, simplifying with (235), (244),
% 260.90/41.69 | (245), (460) gives:
% 260.90/41.69 | (1920) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_2, v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_abs__eq__0) with v_r____, tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_2, simplifying with (235), (244), (245), (460) gives:
% 260.90/41.69 | (1921) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ (v0 = all_1022_2) | all_1022_2 = v_r____) & ( ~ (v0 =
% 260.90/41.69 | v_r____) | all_1022_2 = v_r____))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_zero__less__abs__iff) with v_r____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_2, simplifying with (235), (244),
% 260.90/41.69 | (245), (460) gives:
% 260.90/41.69 | (1922) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ (v0 = v_r____) | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_r____,
% 260.90/41.69 | all_1022_2)) & (v0 = v_r____ |
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1022_2)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_abs__le__zero__iff) with v_r____,
% 260.90/41.69 | tc_RealDef_Oreal, all_1022_2, simplifying with (235), (244),
% 260.90/41.69 | (245), (460) gives:
% 260.90/41.69 | (1923) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ( ~ (v0 = v_r____) |
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_2,
% 260.90/41.69 | v_r____)) & (v0 = v_r____ | ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_2,
% 260.90/41.69 | v0)))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (370) with v_r____, all_1022_2, simplifying with
% 260.90/41.69 | (245), (460) gives:
% 260.90/41.69 | (1924) ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.90/41.69 | all_1022_2, all_853_0) = v0 & $i(v0) & ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v_r____))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (442) with v_r____, all_1022_2, simplifying with
% 260.90/41.69 | (245), (460) gives:
% 260.90/41.69 | (1925) ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.90/41.69 | all_1003_0, all_1022_2) = v0 & $i(v0) &
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1003_1, v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (5) with v_r____, all_1022_2, simplifying with
% 260.90/41.69 | (245), (460) gives:
% 260.90/41.69 | (1926) c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v_r____) =
% 260.90/41.69 | all_1022_2 & $i(all_1022_2)
% 260.90/41.69 |
% 260.90/41.69 | ALPHA: (1926) implies:
% 260.90/41.69 | (1927) c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v_r____) =
% 260.90/41.69 | all_1022_2
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_zero__less__one) with tc_RealDef_Oreal,
% 260.90/41.69 | all_713_0, simplifying with (239), (244), (296) gives:
% 260.90/41.69 | (1928) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_713_0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_zero__le__one) with tc_RealDef_Oreal,
% 260.90/41.69 | all_713_0, simplifying with (239), (244), (296) gives:
% 260.90/41.69 | (1929) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_713_0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_RealDef_Oreal,
% 260.90/41.69 | all_713_0, simplifying with (239), (244), (296) gives:
% 260.90/41.69 | (1930) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.69 | all_713_0, v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_not__one__le__zero) with tc_RealDef_Oreal,
% 260.90/41.69 | all_713_0, simplifying with (239), (244), (296) gives:
% 260.90/41.69 | (1931) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 260.90/41.69 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.69 | all_713_0, v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_zero__neq__one) with tc_Nat_Onat, all_705_0,
% 260.90/41.69 | simplifying with (231), (233), (290) gives:
% 260.90/41.69 | (1932) ? [v0: any] : ( ~ (v0 = all_705_0) &
% 260.90/41.69 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_zero__le__one) with tc_Nat_Onat, all_705_0,
% 260.90/41.69 | simplifying with (229), (233), (290) gives:
% 260.90/41.69 | (1933) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 260.90/41.69 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 260.90/41.69 | all_705_0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_Nat_Onat,
% 260.90/41.69 | all_705_0, simplifying with (229), (233), (290) gives:
% 260.90/41.69 | (1934) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 260.90/41.69 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_705_0,
% 260.90/41.69 | v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (fact_not__one__le__zero) with tc_Nat_Onat,
% 260.90/41.69 | all_705_0, simplifying with (229), (233), (290) gives:
% 260.90/41.69 | (1935) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 260.90/41.69 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.90/41.69 | all_705_0, v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (102) with all_713_1, all_650_0, simplifying with
% 260.90/41.69 | (1806), (1810) gives:
% 260.90/41.69 | (1936) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_650_0) = v0 & $i(v0)
% 260.90/41.69 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_1,
% 260.90/41.69 | v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (102) with all_713_0, all_705_0, simplifying with
% 260.90/41.69 | (1807), (1811) gives:
% 260.90/41.69 | (1937) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = v0 & $i(v0)
% 260.90/41.69 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_0,
% 260.90/41.69 | v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (447) with all_713_1, all_650_0, simplifying with
% 260.90/41.69 | (1804), (1810) gives:
% 260.90/41.69 | (1938) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_650_0)
% 260.90/41.69 | = v0 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1009_0) = v1 & $i(v1) & $i(v0) &
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_1, v1))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (447) with all_713_0, all_705_0, simplifying with
% 260.90/41.69 | (1805), (1811) gives:
% 260.90/41.69 | (1939) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_705_0)
% 260.90/41.69 | = v0 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_1009_0) = v1 & $i(v1) & $i(v0) &
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_0, v1))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (700) with all_650_0, all_650_0, all_713_1,
% 260.90/41.69 | all_713_1, simplifying with (1803), (1812), (1814) gives:
% 260.90/41.69 | (1940) ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.90/41.69 | all_713_1, all_1579_0) = v0 & $i(v0) &
% 260.90/41.69 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_1, v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (693) with all_650_0, all_650_0, all_713_1,
% 260.90/41.69 | all_713_1, simplifying with (1803), (1812), (1816) gives:
% 260.90/41.69 | (1941) ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.90/41.69 | all_713_1, all_1564_0) = v0 & $i(v0) & ~
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.69 | all_713_1))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (481) with all_650_0, all_713_1, simplifying with
% 260.90/41.69 | (1803), (1812) gives:
% 260.90/41.69 | (1942) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(all_650_0) = v0 &
% 260.90/41.69 | c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 260.90/41.69 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 260.90/41.69 | all_1048_0) = v1 & $i(v1) & $i(v0))
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (97) with all_650_0, all_713_1, simplifying with
% 260.90/41.69 | (1803), (1812) gives:
% 260.90/41.69 | (1943) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_713_1) = all_713_1 &
% 260.90/41.69 | $i(all_713_1)
% 260.90/41.69 |
% 260.90/41.69 | ALPHA: (1943) implies:
% 260.90/41.69 | (1944) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_713_1) = all_713_1
% 260.90/41.69 |
% 260.90/41.69 | GROUND_INST: instantiating (694) with all_705_0, all_650_0, all_713_1,
% 260.90/41.69 | all_713_0, simplifying with (1803), (1812), (1884), (1886),
% 260.90/41.69 | (1887) gives:
% 260.90/41.69 | (1945) ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.90/41.69 | all_713_1, all_1564_0) = v0 & $i(v0) &
% 260.90/41.69 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.70 | all_713_0))
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (693) with all_650_0, all_705_0, all_713_0,
% 260.90/41.70 | all_713_1, simplifying with (1803), (1812), (1884), (1886) gives:
% 260.90/41.70 | (1946) c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_705_0, all_650_0) |
% 260.90/41.70 | ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.90/41.70 | all_713_0, all_1564_0) = v0 & $i(v0) & ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 260.90/41.70 | all_713_1))
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (699) with all_650_0, all_705_0, all_713_0,
% 260.90/41.70 | all_713_1, simplifying with (1803), (1812), (1884), (1886) gives:
% 260.90/41.70 | (1947) c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_705_0, all_650_0)
% 260.90/41.70 | | ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 260.90/41.70 | all_713_1, all_1579_0) = v0 & $i(v0) & ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_0, v0))
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (481) with all_705_0, all_713_0, simplifying with
% 260.90/41.70 | (1884), (1886) gives:
% 260.90/41.70 | (1948) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(all_705_0) = v0 &
% 260.90/41.70 | c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 260.90/41.70 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 260.90/41.70 | all_1048_0) = v1 & $i(v1) & $i(v0))
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (97) with all_705_0, all_713_0, simplifying with
% 260.90/41.70 | (1884), (1886) gives:
% 260.90/41.70 | (1949) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_713_0) = all_713_0 &
% 260.90/41.70 | $i(all_713_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1949) implies:
% 260.90/41.70 | (1950) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_713_0) = all_713_0
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (487) with all_705_0, tc_Nat_Onat, all_1153_3,
% 260.90/41.70 | all_1153_0, simplifying with (232), (233), (516), (1885), (1886)
% 260.90/41.70 | gives:
% 260.90/41.70 | (1951) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 260.90/41.70 | hAPP(all_1153_0, all_1063_0) = v0 & $i(v0))
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (484) with all_705_0, tc_Nat_Onat, all_1153_3,
% 260.90/41.70 | all_1153_0, simplifying with (230), (233), (516), (1885), (1886)
% 260.90/41.70 | gives:
% 260.90/41.70 | (1952) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 260.90/41.70 | hAPP(all_1153_0, all_1051_0) = v0 & $i(v0))
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (363) with all_650_0, all_705_0, simplifying with
% 260.90/41.70 | (1801), (1812) gives:
% 260.90/41.70 | (1953) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = v0 & $i(v0)
% 260.90/41.70 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_832_0, v0))
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (183) with all_705_0, all_1066_0, simplifying with
% 260.90/41.70 | (1883), (1886) gives:
% 260.90/41.70 | (1954) c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_705_0, all_1066_0)
% 260.90/41.70 |
% 260.90/41.70 | GROUND_INST: instantiating (363) with all_705_0, all_1066_0, simplifying with
% 260.90/41.70 | (1883), (1886) gives:
% 260.90/41.70 | (1955) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_1066_0) = v0 &
% 260.90/41.70 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_832_0, v0))
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1941) with fresh symbol all_1912_0 gives:
% 260.90/41.70 | (1956) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_1564_0)
% 260.90/41.70 | = all_1912_0 & $i(all_1912_0) & ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1912_0,
% 260.90/41.70 | all_713_1)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1956) implies:
% 260.90/41.70 | (1957) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_1564_0)
% 260.90/41.70 | = all_1912_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1940) with fresh symbol all_1914_0 gives:
% 260.90/41.70 | (1958) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_1579_0)
% 260.90/41.70 | = all_1914_0 & $i(all_1914_0) &
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_1,
% 260.90/41.70 | all_1914_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1958) implies:
% 260.90/41.70 | (1959) $i(all_1914_0)
% 260.90/41.70 | (1960) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_1579_0)
% 260.90/41.70 | = all_1914_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1937) with fresh symbol all_1916_0 gives:
% 260.90/41.70 | (1961) c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = all_1916_0 &
% 260.90/41.70 | $i(all_1916_0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.70 | all_713_0, all_1916_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1961) implies:
% 260.90/41.70 | (1962) c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = all_1916_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1953) with fresh symbol all_1918_0 gives:
% 260.90/41.70 | (1963) c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = all_1918_0 &
% 260.90/41.70 | $i(all_1918_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_832_0, all_1918_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1963) implies:
% 260.90/41.70 | (1964) c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = all_1918_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1936) with fresh symbol all_1920_0 gives:
% 260.90/41.70 | (1965) c_RealDef_Oreal(tc_Nat_Onat, all_650_0) = all_1920_0 &
% 260.90/41.70 | $i(all_1920_0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.70 | all_713_1, all_1920_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1965) implies:
% 260.90/41.70 | (1966) $i(all_1920_0)
% 260.90/41.70 | (1967) c_RealDef_Oreal(tc_Nat_Onat, all_650_0) = all_1920_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1919) with fresh symbol all_1922_0 gives:
% 260.90/41.70 | (1968) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1922_0 &
% 260.90/41.70 | $i(all_1922_0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.70 | all_1922_0, all_1022_2)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1968) implies:
% 260.90/41.70 | (1969) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1922_0,
% 260.90/41.70 | all_1022_2)
% 260.90/41.70 | (1970) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1922_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1952) with fresh symbol all_1926_0 gives:
% 260.90/41.70 | (1971) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1926_0 &
% 260.90/41.70 | hAPP(all_1153_0, all_1051_0) = all_1926_0 & $i(all_1926_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1971) implies:
% 260.90/41.70 | (1972) $i(all_1926_0)
% 260.90/41.70 | (1973) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1926_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1935) with fresh symbol all_1932_0 gives:
% 260.90/41.70 | (1974) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1932_0 &
% 260.90/41.70 | $i(all_1932_0) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.90/41.70 | all_705_0, all_1932_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1974) implies:
% 260.90/41.70 | (1975) ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_705_0,
% 260.90/41.70 | all_1932_0)
% 260.90/41.70 | (1976) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1932_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1933) with fresh symbol all_1934_0 gives:
% 260.90/41.70 | (1977) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1934_0 &
% 260.90/41.70 | $i(all_1934_0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 260.90/41.70 | all_1934_0, all_705_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1977) implies:
% 260.90/41.70 | (1978) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1934_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1932) with fresh symbol all_1936_0 gives:
% 260.90/41.70 | (1979) ~ (all_1936_0 = all_705_0) &
% 260.90/41.70 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1936_0 &
% 260.90/41.70 | $i(all_1936_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1979) implies:
% 260.90/41.70 | (1980) ~ (all_1936_0 = all_705_0)
% 260.90/41.70 | (1981) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1936_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1925) with fresh symbol all_1938_0 gives:
% 260.90/41.70 | (1982) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1003_0,
% 260.90/41.70 | all_1022_2) = all_1938_0 & $i(all_1938_0) &
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1003_1,
% 260.90/41.70 | all_1938_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1982) implies:
% 260.90/41.70 | (1983) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1003_1,
% 260.90/41.70 | all_1938_0)
% 260.90/41.70 | (1984) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1003_0,
% 260.90/41.70 | all_1022_2) = all_1938_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1934) with fresh symbol all_1940_0 gives:
% 260.90/41.70 | (1985) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1940_0 &
% 260.90/41.70 | $i(all_1940_0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 260.90/41.70 | all_705_0, all_1940_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1985) implies:
% 260.90/41.70 | (1986) ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_705_0, all_1940_0)
% 260.90/41.70 | (1987) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1940_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1924) with fresh symbol all_1942_0 gives:
% 260.90/41.70 | (1988) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1022_2, all_853_0)
% 260.90/41.70 | = all_1942_0 & $i(all_1942_0) & ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1942_0, v_r____)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1988) implies:
% 260.90/41.70 | (1989) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1022_2, all_853_0)
% 260.90/41.70 | = all_1942_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1920) with fresh symbol all_1944_0 gives:
% 260.90/41.70 | (1990) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1944_0 &
% 260.90/41.70 | $i(all_1944_0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1022_2, all_1944_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1990) implies:
% 260.90/41.70 | (1991) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1944_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1951) with fresh symbol all_1946_0 gives:
% 260.90/41.70 | (1992) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1946_0 &
% 260.90/41.70 | hAPP(all_1153_0, all_1063_0) = all_1946_0 & $i(all_1946_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1992) implies:
% 260.90/41.70 | (1993) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1946_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1945) with fresh symbol all_1948_0 gives:
% 260.90/41.70 | (1994) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_1564_0)
% 260.90/41.70 | = all_1948_0 & $i(all_1948_0) &
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1948_0,
% 260.90/41.70 | all_713_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1994) implies:
% 260.90/41.70 | (1995) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1948_0,
% 260.90/41.70 | all_713_0)
% 260.90/41.70 | (1996) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_1564_0)
% 260.90/41.70 | = all_1948_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1955) with fresh symbol all_1950_0 gives:
% 260.90/41.70 | (1997) c_RealDef_Oreal(tc_Nat_Onat, all_1066_0) = all_1950_0 &
% 260.90/41.70 | $i(all_1950_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_832_0, all_1950_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1997) implies:
% 260.90/41.70 | (1998) c_RealDef_Oreal(tc_Nat_Onat, all_1066_0) = all_1950_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1931) with fresh symbol all_1952_0 gives:
% 260.90/41.70 | (1999) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1952_0 &
% 260.90/41.70 | $i(all_1952_0) & ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_0,
% 260.90/41.70 | all_1952_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (1999) implies:
% 260.90/41.70 | (2000) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1952_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1930) with fresh symbol all_1954_0 gives:
% 260.90/41.70 | (2001) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1954_0 &
% 260.90/41.70 | $i(all_1954_0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_713_0, all_1954_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2001) implies:
% 260.90/41.70 | (2002) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1954_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1929) with fresh symbol all_1956_0 gives:
% 260.90/41.70 | (2003) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1956_0 &
% 260.90/41.70 | $i(all_1956_0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.70 | all_1956_0, all_713_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2003) implies:
% 260.90/41.70 | (2004) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1956_0,
% 260.90/41.70 | all_713_0)
% 260.90/41.70 | (2005) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1956_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1928) with fresh symbol all_1958_0 gives:
% 260.90/41.70 | (2006) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1958_0 &
% 260.90/41.70 | $i(all_1958_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1958_0, all_713_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2006) implies:
% 260.90/41.70 | (2007) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1958_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1939) with fresh symbols all_1962_0, all_1962_1 gives:
% 260.90/41.70 | (2008) c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = all_1962_1 &
% 260.90/41.70 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1962_1,
% 260.90/41.70 | all_1009_0) = all_1962_0 & $i(all_1962_0) & $i(all_1962_1) &
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_0,
% 260.90/41.70 | all_1962_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2008) implies:
% 260.90/41.70 | (2009) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_0,
% 260.90/41.70 | all_1962_0)
% 260.90/41.70 | (2010) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1962_1,
% 260.90/41.70 | all_1009_0) = all_1962_0
% 260.90/41.70 | (2011) c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = all_1962_1
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1912) with fresh symbol all_1964_0 gives:
% 260.90/41.70 | (2012) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1964_0 &
% 260.90/41.70 | $i(all_1964_0) & ( ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1964_0,
% 260.90/41.70 | all_1022_2) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1964_0,
% 260.90/41.70 | all_713_0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.70 | all_1964_0, all_1022_1))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2012) implies:
% 260.90/41.70 | (2013) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1964_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1911) with fresh symbol all_1966_0 gives:
% 260.90/41.70 | (2014) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1966_0 &
% 260.90/41.70 | $i(all_1966_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1022_2, all_1966_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_0,
% 260.90/41.70 | all_1966_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1022_1, all_1966_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2014) implies:
% 260.90/41.70 | (2015) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1966_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1910) with fresh symbol all_1968_0 gives:
% 260.90/41.70 | (2016) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1968_0 &
% 260.90/41.70 | $i(all_1968_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_713_0, all_1968_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_2,
% 260.90/41.70 | all_1968_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1022_1, all_1968_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2016) implies:
% 260.90/41.70 | (2017) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1968_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1909) with fresh symbol all_1970_0 gives:
% 260.90/41.70 | (2018) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1970_0 &
% 260.90/41.70 | $i(all_1970_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1022_2, all_1970_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_0,
% 260.90/41.70 | all_1970_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1022_1, all_1970_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2018) implies:
% 260.90/41.70 | (2019) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1970_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1908) with fresh symbol all_1972_0 gives:
% 260.90/41.70 | (2020) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1972_0 &
% 260.90/41.70 | $i(all_1972_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1972_0, all_1022_2) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1972_0,
% 260.90/41.70 | all_713_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1972_0, all_1022_1))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2020) implies:
% 260.90/41.70 | (2021) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1972_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1942) with fresh symbols all_1974_0, all_1974_1 gives:
% 260.90/41.70 | (2022) c_Nat_OSuc(all_650_0) = all_1974_1 & c_RealDef_Oreal(tc_Nat_Onat,
% 260.90/41.70 | all_1974_1) = all_1974_0 &
% 260.90/41.70 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_1048_0)
% 260.90/41.70 | = all_1974_0 & $i(all_1974_0) & $i(all_1974_1)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2022) implies:
% 260.90/41.70 | (2023) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_1048_0)
% 260.90/41.70 | = all_1974_0
% 260.90/41.70 | (2024) c_RealDef_Oreal(tc_Nat_Onat, all_1974_1) = all_1974_0
% 260.90/41.70 | (2025) c_Nat_OSuc(all_650_0) = all_1974_1
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1948) with fresh symbols all_1976_0, all_1976_1 gives:
% 260.90/41.70 | (2026) c_Nat_OSuc(all_705_0) = all_1976_1 & c_RealDef_Oreal(tc_Nat_Onat,
% 260.90/41.70 | all_1976_1) = all_1976_0 &
% 260.90/41.70 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0, all_1048_0)
% 260.90/41.70 | = all_1976_0 & $i(all_1976_0) & $i(all_1976_1)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2026) implies:
% 260.90/41.70 | (2027) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0, all_1048_0)
% 260.90/41.70 | = all_1976_0
% 260.90/41.70 | (2028) c_RealDef_Oreal(tc_Nat_Onat, all_1976_1) = all_1976_0
% 260.90/41.70 | (2029) c_Nat_OSuc(all_705_0) = all_1976_1
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1938) with fresh symbols all_1978_0, all_1978_1 gives:
% 260.90/41.70 | (2030) c_RealDef_Oreal(tc_Nat_Onat, all_650_0) = all_1978_1 &
% 260.90/41.70 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1978_1,
% 260.90/41.70 | all_1009_0) = all_1978_0 & $i(all_1978_0) & $i(all_1978_1) &
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_1,
% 260.90/41.70 | all_1978_0)
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2030) implies:
% 260.90/41.70 | (2031) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1978_1,
% 260.90/41.70 | all_1009_0) = all_1978_0
% 260.90/41.70 | (2032) c_RealDef_Oreal(tc_Nat_Onat, all_650_0) = all_1978_1
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1907) with fresh symbol all_1980_0 gives:
% 260.90/41.70 | (2033) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1980_0 &
% 260.90/41.70 | $i(all_1980_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1980_0, all_713_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1980_0,
% 260.90/41.70 | all_1022_2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1980_0, all_1022_1))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2033) implies:
% 260.90/41.70 | (2034) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1980_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1914) with fresh symbol all_1982_0 gives:
% 260.90/41.70 | (2035) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1982_0 &
% 260.90/41.70 | $i(all_1982_0) & ( ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_2,
% 260.90/41.70 | all_1982_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_0,
% 260.90/41.70 | all_1982_0) |
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_1,
% 260.90/41.70 | all_1982_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2035) implies:
% 260.90/41.70 | (2036) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1982_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1903) with fresh symbol all_1984_0 gives:
% 260.90/41.70 | (2037) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1984_0 &
% 260.90/41.70 | $i(all_1984_0) & ( ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1468_3,
% 260.90/41.70 | all_1984_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____,
% 260.90/41.70 | all_1984_0) |
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1468_2,
% 260.90/41.70 | all_1984_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2037) implies:
% 260.90/41.70 | (2038) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1984_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1900) with fresh symbol all_1986_0 gives:
% 260.90/41.70 | (2039) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1986_0 &
% 260.90/41.70 | $i(all_1986_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1468_3, all_1986_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____,
% 260.90/41.70 | all_1986_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1468_2, all_1986_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2039) implies:
% 260.90/41.70 | (2040) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1986_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1899) with fresh symbol all_1988_0 gives:
% 260.90/41.70 | (2041) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1988_0 &
% 260.90/41.70 | $i(all_1988_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | v_da____, all_1988_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1468_3,
% 260.90/41.70 | all_1988_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1468_2, all_1988_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2041) implies:
% 260.90/41.70 | (2042) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1988_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1898) with fresh symbol all_1990_0 gives:
% 260.90/41.70 | (2043) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1990_0 &
% 260.90/41.70 | $i(all_1990_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1468_3, all_1990_0) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____,
% 260.90/41.70 | all_1990_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1468_2, all_1990_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2043) implies:
% 260.90/41.70 | (2044) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1990_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1906) with fresh symbol all_1992_0 gives:
% 260.90/41.70 | (2045) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1992_0 &
% 260.90/41.70 | $i(all_1992_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1992_0, all_1022_2) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1992_0,
% 260.90/41.70 | all_713_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1992_0, all_1022_1))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2045) implies:
% 260.90/41.70 | (2046) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1992_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1897) with fresh symbol all_1994_0 gives:
% 260.90/41.70 | (2047) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1994_0 &
% 260.90/41.70 | $i(all_1994_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1994_0, all_1468_3) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1994_0,
% 260.90/41.70 | v_da____) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1994_0, all_1468_2))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2047) implies:
% 260.90/41.70 | (2048) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1994_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1901) with fresh symbol all_1996_0 gives:
% 260.90/41.70 | (2049) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1996_0 &
% 260.90/41.70 | $i(all_1996_0) & ( ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1996_0,
% 260.90/41.70 | all_1468_3) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1996_0,
% 260.90/41.70 | v_da____) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 260.90/41.70 | all_1996_0, all_1468_2))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2049) implies:
% 260.90/41.70 | (2050) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1996_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1896) with fresh symbol all_1998_0 gives:
% 260.90/41.70 | (2051) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1998_0 &
% 260.90/41.70 | $i(all_1998_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1998_0, v_da____) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1998_0,
% 260.90/41.70 | all_1468_3) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_1998_0, all_1468_2))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2051) implies:
% 260.90/41.70 | (2052) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1998_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1895) with fresh symbol all_2000_0 gives:
% 260.90/41.70 | (2053) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2000_0 &
% 260.90/41.70 | $i(all_2000_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_2000_0, all_1468_3) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_2000_0,
% 260.90/41.70 | v_da____) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 260.90/41.70 | all_2000_0, all_1468_2))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2053) implies:
% 260.90/41.70 | (2054) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2000_0
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1923) with fresh symbol all_2002_0 gives:
% 260.90/41.70 | (2055) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2002_0 &
% 260.90/41.70 | $i(all_2002_0) & ( ~ (all_2002_0 = v_r____) |
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_2,
% 260.90/41.70 | v_r____)) & (all_2002_0 = v_r____ | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_2,
% 260.90/41.70 | all_2002_0))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2055) implies:
% 260.90/41.70 | (2056) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2002_0
% 260.90/41.70 | (2057) all_2002_0 = v_r____ | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1022_2,
% 260.90/41.70 | all_2002_0)
% 260.90/41.70 |
% 260.90/41.70 | DELTA: instantiating (1922) with fresh symbol all_2004_0 gives:
% 260.90/41.70 | (2058) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2004_0 &
% 260.90/41.70 | $i(all_2004_0) & ( ~ (all_2004_0 = v_r____) | ~
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_r____,
% 260.90/41.70 | all_1022_2)) & (all_2004_0 = v_r____ |
% 260.90/41.70 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_2004_0,
% 260.90/41.70 | all_1022_2))
% 260.90/41.70 |
% 260.90/41.70 | ALPHA: (2058) implies:
% 260.90/41.71 | (2059) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2004_0
% 260.90/41.71 | (2060) ~ (all_2004_0 = v_r____) | ~
% 260.90/41.71 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_r____, all_1022_2)
% 260.90/41.71 |
% 260.90/41.71 | DELTA: instantiating (1921) with fresh symbol all_2006_0 gives:
% 260.90/41.71 | (2061) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2006_0 &
% 260.90/41.71 | $i(all_2006_0) & ( ~ (all_2006_0 = all_1022_2) | all_1022_2 =
% 260.90/41.71 | v_r____) & ( ~ (all_2006_0 = v_r____) | all_1022_2 = v_r____)
% 260.90/41.71 |
% 260.90/41.71 | ALPHA: (2061) implies:
% 260.90/41.71 | (2062) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2006_0
% 260.90/41.71 |
% 260.90/41.71 | DELTA: instantiating (1915) with fresh symbol all_2009_0 gives:
% 260.90/41.71 | (2063) ( ~ (all_1022_1 = all_713_0) | (all_2009_0 = all_1022_2 &
% 260.90/41.71 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1022_2)) &
% 260.90/41.71 | (all_1022_1 = all_713_0 | ( ~ (all_2009_0 = all_1022_2) &
% 260.90/41.71 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2009_0 &
% 260.90/41.71 | $i(all_2009_0)))
% 260.90/41.71 |
% 260.90/41.71 | ALPHA: (2063) implies:
% 260.90/41.71 | (2064) all_1022_1 = all_713_0 | ( ~ (all_2009_0 = all_1022_2) &
% 260.90/41.71 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2009_0 &
% 260.90/41.71 | $i(all_2009_0))
% 260.90/41.71 | (2065) ~ (all_1022_1 = all_713_0) | (all_2009_0 = all_1022_2 &
% 260.90/41.71 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1022_2)
% 260.90/41.71 |
% 260.90/41.71 | DELTA: instantiating (1913) with fresh symbol all_2016_0 gives:
% 260.90/41.71 | (2066) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2016_0 &
% 260.90/41.71 | $i(all_2016_0) & ( ~
% 260.90/41.71 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2016_0,
% 260.90/41.71 | all_1022_2) | ~
% 260.90/41.71 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2016_0,
% 260.90/41.71 | all_713_0) | (( ~ (all_2016_0 = all_1022_1) | (all_1022_1 =
% 260.90/41.71 | all_713_0 & all_1022_2 = all_713_0)) & ( ~ (all_2016_0 =
% 260.90/41.71 | all_713_0) | ~ (all_1022_2 = all_713_0) | all_1022_1 =
% 260.90/41.71 | all_713_0)))
% 260.90/41.71 |
% 260.90/41.71 | ALPHA: (2066) implies:
% 260.90/41.71 | (2067) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2016_0
% 260.90/41.71 | (2068) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2016_0,
% 260.90/41.71 | all_1022_2) | ~
% 260.90/41.71 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2016_0,
% 260.90/41.71 | all_713_0) | (( ~ (all_2016_0 = all_1022_1) | (all_1022_1 =
% 260.90/41.71 | all_713_0 & all_1022_2 = all_713_0)) & ( ~ (all_2016_0 =
% 260.90/41.71 | all_713_0) | ~ (all_1022_2 = all_713_0) | all_1022_1 =
% 260.90/41.71 | all_713_0))
% 260.90/41.71 |
% 260.90/41.71 | DELTA: instantiating (1902) with fresh symbol all_2018_0 gives:
% 260.90/41.71 | (2069) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2018_0 &
% 260.90/41.71 | $i(all_2018_0) & ( ~
% 260.90/41.71 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2018_0,
% 260.90/41.71 | all_1468_3) | ~
% 260.90/41.71 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2018_0,
% 260.90/41.71 | v_da____) | (( ~ (all_2018_0 = all_1468_2) | (all_1468_2 =
% 260.90/41.71 | v_da____ & all_1468_3 = v_da____)) & ( ~ (all_2018_0 =
% 260.90/41.71 | v_da____) | ~ (all_1468_3 = v_da____) | all_1468_2 =
% 260.90/41.71 | v_da____)))
% 260.90/41.71 |
% 260.90/41.71 | ALPHA: (2069) implies:
% 260.90/41.71 | (2070) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2018_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1563), (2031) imply:
% 260.90/41.71 | (2071) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1978_1, all_713_0)
% 260.90/41.71 | = all_1978_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1563), (2010) imply:
% 260.90/41.71 | (2072) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1962_1, all_713_0)
% 260.90/41.71 | = all_1962_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1754), (1989) imply:
% 260.90/41.71 | (2073) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1022_2, all_713_0)
% 260.90/41.71 | = all_1942_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1572), (1984) imply:
% 260.90/41.71 | (2074) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0, all_1022_2)
% 260.90/41.71 | = all_1938_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1761), (2027) imply:
% 260.90/41.71 | (2075) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0, all_713_0)
% 260.90/41.71 | = all_1976_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1776), (1960) imply:
% 260.90/41.71 | (2076) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_713_0)
% 260.90/41.71 | = all_1914_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1775), (1996) imply:
% 260.90/41.71 | (2077) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_713_0)
% 260.90/41.71 | = all_1948_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1775), (1957) imply:
% 260.90/41.71 | (2078) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_713_0)
% 260.90/41.71 | = all_1912_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1761), (2023) imply:
% 260.90/41.71 | (2079) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_713_0)
% 260.90/41.71 | = all_1974_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1759), (1983) imply:
% 260.90/41.71 | (2080) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_1,
% 260.90/41.71 | all_1938_0)
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1958_0, all_1964_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2007), (2013) gives:
% 260.90/41.71 | (2081) all_1964_0 = all_1958_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1964_0, all_1966_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2013), (2015) gives:
% 260.90/41.71 | (2082) all_1966_0 = all_1964_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1966_0, all_1968_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2015), (2017) gives:
% 260.90/41.71 | (2083) all_1968_0 = all_1966_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1968_0, all_1970_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2017), (2019) gives:
% 260.90/41.71 | (2084) all_1970_0 = all_1968_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_713_1, all_1984_0, tc_RealDef_Oreal,
% 260.90/41.71 | simplifying with (295), (2038) gives:
% 260.90/41.71 | (2085) all_1984_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1944_0, all_1984_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (1991), (2038) gives:
% 260.90/41.71 | (2086) all_1984_0 = all_1944_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1986_0, all_1988_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2040), (2042) gives:
% 260.90/41.71 | (2087) all_1988_0 = all_1986_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1986_0, all_1990_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2040), (2044) gives:
% 260.90/41.71 | (2088) all_1990_0 = all_1986_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1980_0, all_1990_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2034), (2044) gives:
% 260.90/41.71 | (2089) all_1990_0 = all_1980_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1970_0, all_1990_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2019), (2044) gives:
% 260.90/41.71 | (2090) all_1990_0 = all_1970_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1988_0, all_1992_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2042), (2046) gives:
% 260.90/41.71 | (2091) all_1992_0 = all_1988_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1990_0, all_1994_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2044), (2048) gives:
% 260.90/41.71 | (2092) all_1994_0 = all_1990_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1980_0, all_1996_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2034), (2050) gives:
% 260.90/41.71 | (2093) all_1996_0 = all_1980_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1954_0, all_1998_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2002), (2052) gives:
% 260.90/41.71 | (2094) all_1998_0 = all_1954_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1952_0, all_1998_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2000), (2052) gives:
% 260.90/41.71 | (2095) all_1998_0 = all_1952_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1944_0, all_1998_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (1991), (2052) gives:
% 260.90/41.71 | (2096) all_1998_0 = all_1944_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1996_0, all_2000_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2050), (2054) gives:
% 260.90/41.71 | (2097) all_2000_0 = all_1996_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1922_0, all_2000_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (1970), (2054) gives:
% 260.90/41.71 | (2098) all_2000_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1994_0, all_2002_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2048), (2056) gives:
% 260.90/41.71 | (2099) all_2002_0 = all_1994_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_2002_0, all_2004_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2056), (2059) gives:
% 260.90/41.71 | (2100) all_2004_0 = all_2002_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1992_0, all_2006_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2046), (2062) gives:
% 260.90/41.71 | (2101) all_2006_0 = all_1992_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1972_0, all_2006_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2021), (2062) gives:
% 260.90/41.71 | (2102) all_2006_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1958_0, all_2016_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2007), (2067) gives:
% 260.90/41.71 | (2103) all_2016_0 = all_1958_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1956_0, all_2016_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2005), (2067) gives:
% 260.90/41.71 | (2104) all_2016_0 = all_1956_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1954_0, all_2016_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2002), (2067) gives:
% 260.90/41.71 | (2105) all_2016_0 = all_1954_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_2004_0, all_2018_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2059), (2070) gives:
% 260.90/41.71 | (2106) all_2018_0 = all_2004_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1982_0, all_2018_0,
% 260.90/41.71 | tc_RealDef_Oreal, simplifying with (2036), (2070) gives:
% 260.90/41.71 | (2107) all_2018_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_650_0, all_1934_0, tc_Nat_Onat,
% 260.90/41.71 | simplifying with (259), (1978) gives:
% 260.90/41.71 | (2108) all_1934_0 = all_650_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1936_0, all_1940_0, tc_Nat_Onat,
% 260.90/41.71 | simplifying with (1981), (1987) gives:
% 260.90/41.71 | (2109) all_1940_0 = all_1936_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1934_0, all_1940_0, tc_Nat_Onat,
% 260.90/41.71 | simplifying with (1978), (1987) gives:
% 260.90/41.71 | (2110) all_1940_0 = all_1934_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (248) with all_1932_0, all_1940_0, tc_Nat_Onat,
% 260.90/41.71 | simplifying with (1976), (1987) gives:
% 260.90/41.71 | (2111) all_1940_0 = all_1932_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (254) with all_1914_0, all_1948_0, all_713_0,
% 260.90/41.71 | all_713_1, tc_RealDef_Oreal, simplifying with (2076), (2077)
% 260.90/41.71 | gives:
% 260.90/41.71 | (2112) all_1948_0 = all_1914_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (254) with all_1948_0, all_1974_0, all_713_0,
% 260.90/41.71 | all_713_1, tc_RealDef_Oreal, simplifying with (2077), (2079)
% 260.90/41.71 | gives:
% 260.90/41.71 | (2113) all_1974_0 = all_1948_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (254) with all_1912_0, all_1974_0, all_713_0,
% 260.90/41.71 | all_713_1, tc_RealDef_Oreal, simplifying with (2078), (2079)
% 260.90/41.71 | gives:
% 260.90/41.71 | (2114) all_1974_0 = all_1912_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (254) with all_1022_1, all_1938_0, all_1022_2,
% 260.90/41.71 | all_713_0, tc_RealDef_Oreal, simplifying with (1808), (2074)
% 260.90/41.71 | gives:
% 260.90/41.71 | (2115) all_1938_0 = all_1022_1
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (254) with all_1022_1, all_1942_0, all_713_0,
% 260.90/41.71 | all_1022_2, tc_RealDef_Oreal, simplifying with (1917), (2073)
% 260.90/41.71 | gives:
% 260.90/41.71 | (2116) all_1942_0 = all_1022_1
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (249) with all_705_0, all_1946_0, tc_Nat_Onat,
% 260.90/41.71 | simplifying with (290), (1993) gives:
% 260.90/41.71 | (2117) all_1946_0 = all_705_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (249) with all_1926_0, all_1946_0, tc_Nat_Onat,
% 260.90/41.71 | simplifying with (1973), (1993) gives:
% 260.90/41.71 | (2118) all_1946_0 = all_1926_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (253) with all_713_1, all_1978_1, all_650_0,
% 260.90/41.71 | tc_Nat_Onat, simplifying with (1803), (2032) gives:
% 260.90/41.71 | (2119) all_1978_1 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (253) with all_1920_0, all_1978_1, all_650_0,
% 260.90/41.71 | tc_Nat_Onat, simplifying with (1967), (2032) gives:
% 260.90/41.71 | (2120) all_1978_1 = all_1920_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (253) with all_713_0, all_1962_1, all_705_0,
% 260.90/41.71 | tc_Nat_Onat, simplifying with (1884), (2011) gives:
% 260.90/41.71 | (2121) all_1962_1 = all_713_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (253) with all_1918_0, all_1962_1, all_705_0,
% 260.90/41.71 | tc_Nat_Onat, simplifying with (1964), (2011) gives:
% 260.90/41.71 | (2122) all_1962_1 = all_1918_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (253) with all_1916_0, all_1962_1, all_705_0,
% 260.90/41.71 | tc_Nat_Onat, simplifying with (1962), (2011) gives:
% 260.90/41.71 | (2123) all_1962_1 = all_1916_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (251) with all_705_0, all_1974_1, all_650_0,
% 260.90/41.71 | simplifying with (1801), (2025) gives:
% 260.90/41.71 | (2124) all_1974_1 = all_705_0
% 260.90/41.71 |
% 260.90/41.71 | GROUND_INST: instantiating (251) with all_1066_0, all_1976_1, all_705_0,
% 260.90/41.71 | simplifying with (1883), (2029) gives:
% 260.90/41.71 | (2125) all_1976_1 = all_1066_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2106), (2107) imply:
% 260.90/41.71 | (2126) all_2004_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2126) implies:
% 260.90/41.71 | (2127) all_2004_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2104), (2105) imply:
% 260.90/41.71 | (2128) all_1956_0 = all_1954_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2103), (2104) imply:
% 260.90/41.71 | (2129) all_1958_0 = all_1956_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2129) implies:
% 260.90/41.71 | (2130) all_1958_0 = all_1956_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2101), (2102) imply:
% 260.90/41.71 | (2131) all_1992_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2131) implies:
% 260.90/41.71 | (2132) all_1992_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2100), (2127) imply:
% 260.90/41.71 | (2133) all_2002_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2133) implies:
% 260.90/41.71 | (2134) all_2002_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2099), (2134) imply:
% 260.90/41.71 | (2135) all_1994_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2135) implies:
% 260.90/41.71 | (2136) all_1994_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2097), (2098) imply:
% 260.90/41.71 | (2137) all_1996_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2137) implies:
% 260.90/41.71 | (2138) all_1996_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2095), (2096) imply:
% 260.90/41.71 | (2139) all_1952_0 = all_1944_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2094), (2095) imply:
% 260.90/41.71 | (2140) all_1954_0 = all_1952_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2140) implies:
% 260.90/41.71 | (2141) all_1954_0 = all_1952_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2093), (2138) imply:
% 260.90/41.71 | (2142) all_1980_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2142) implies:
% 260.90/41.71 | (2143) all_1980_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2092), (2136) imply:
% 260.90/41.71 | (2144) all_1990_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2144) implies:
% 260.90/41.71 | (2145) all_1990_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2091), (2132) imply:
% 260.90/41.71 | (2146) all_1988_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2146) implies:
% 260.90/41.71 | (2147) all_1988_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2089), (2145) imply:
% 260.90/41.71 | (2148) all_1982_0 = all_1980_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2088), (2145) imply:
% 260.90/41.71 | (2149) all_1986_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2149) implies:
% 260.90/41.71 | (2150) all_1986_0 = all_1982_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2090), (2145) imply:
% 260.90/41.71 | (2151) all_1982_0 = all_1970_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2087), (2147) imply:
% 260.90/41.71 | (2152) all_1986_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2152) implies:
% 260.90/41.71 | (2153) all_1986_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2150), (2153) imply:
% 260.90/41.71 | (2154) all_1982_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2154) implies:
% 260.90/41.71 | (2155) all_1982_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2085), (2086) imply:
% 260.90/41.71 | (2156) all_1944_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2156) implies:
% 260.90/41.71 | (2157) all_1944_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2148), (2155) imply:
% 260.90/41.71 | (2158) all_1980_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2158) implies:
% 260.90/41.71 | (2159) all_1980_0 = all_1972_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2151), (2155) imply:
% 260.90/41.71 | (2160) all_1972_0 = all_1970_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2143), (2159) imply:
% 260.90/41.71 | (2161) all_1972_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2161) implies:
% 260.90/41.71 | (2162) all_1972_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2119), (2120) imply:
% 260.90/41.71 | (2163) all_1920_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2113), (2114) imply:
% 260.90/41.71 | (2164) all_1948_0 = all_1912_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2164) implies:
% 260.90/41.71 | (2165) all_1948_0 = all_1912_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2160), (2162) imply:
% 260.90/41.71 | (2166) all_1970_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2166) implies:
% 260.90/41.71 | (2167) all_1970_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2084), (2167) imply:
% 260.90/41.71 | (2168) all_1968_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2168) implies:
% 260.90/41.71 | (2169) all_1968_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2083), (2169) imply:
% 260.90/41.71 | (2170) all_1966_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2170) implies:
% 260.90/41.71 | (2171) all_1966_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2082), (2171) imply:
% 260.90/41.71 | (2172) all_1964_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2172) implies:
% 260.90/41.71 | (2173) all_1964_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2081), (2173) imply:
% 260.90/41.71 | (2174) all_1958_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2174) implies:
% 260.90/41.71 | (2175) all_1958_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2121), (2122) imply:
% 260.90/41.71 | (2176) all_1918_0 = all_713_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2122), (2123) imply:
% 260.90/41.71 | (2177) all_1918_0 = all_1916_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2130), (2175) imply:
% 260.90/41.71 | (2178) all_1956_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2178) implies:
% 260.90/41.71 | (2179) all_1956_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2128), (2179) imply:
% 260.90/41.71 | (2180) all_1954_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2180) implies:
% 260.90/41.71 | (2181) all_1954_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2141), (2181) imply:
% 260.90/41.71 | (2182) all_1952_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2182) implies:
% 260.90/41.71 | (2183) all_1952_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2139), (2183) imply:
% 260.90/41.71 | (2184) all_1944_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2184) implies:
% 260.90/41.71 | (2185) all_1944_0 = all_1922_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2112), (2165) imply:
% 260.90/41.71 | (2186) all_1914_0 = all_1912_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2117), (2118) imply:
% 260.90/41.71 | (2187) all_1926_0 = all_705_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2157), (2185) imply:
% 260.90/41.71 | (2188) all_1922_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2109), (2110) imply:
% 260.90/41.71 | (2189) all_1936_0 = all_1934_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2109), (2111) imply:
% 260.90/41.71 | (2190) all_1936_0 = all_1932_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2189), (2190) imply:
% 260.90/41.71 | (2191) all_1934_0 = all_1932_0
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2191) implies:
% 260.90/41.71 | (2192) all_1934_0 = all_1932_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2108), (2192) imply:
% 260.90/41.71 | (2193) all_1932_0 = all_650_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2176), (2177) imply:
% 260.90/41.71 | (2194) all_1916_0 = all_713_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2190), (2193) imply:
% 260.90/41.71 | (2195) all_1936_0 = all_650_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2109), (2195) imply:
% 260.90/41.71 | (2196) all_1940_0 = all_650_0
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2179), (2188) imply:
% 260.90/41.71 | (2197) all_1956_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2162), (2188) imply:
% 260.90/41.71 | (2198) all_1972_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2155), (2198) imply:
% 260.90/41.71 | (2199) all_1982_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2134), (2199) imply:
% 260.90/41.71 | (2200) all_2002_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2127), (2199) imply:
% 260.90/41.71 | (2201) all_2004_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | COMBINE_EQS: (2104), (2197) imply:
% 260.90/41.71 | (2202) all_2016_0 = all_713_1
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1980), (2195) imply:
% 260.90/41.71 | (2203) ~ (all_705_0 = all_650_0)
% 260.90/41.71 |
% 260.90/41.71 | SIMP: (2203) implies:
% 260.90/41.71 | (2204) ~ (all_705_0 = all_650_0)
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (2028), (2125) imply:
% 260.90/41.71 | (2205) c_RealDef_Oreal(tc_Nat_Onat, all_1066_0) = all_1976_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (2024), (2114), (2124) imply:
% 260.90/41.71 | (2206) c_RealDef_Oreal(tc_Nat_Onat, all_705_0) = all_1912_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (2071), (2119) imply:
% 260.90/41.71 | (2207) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1, all_713_0)
% 260.90/41.71 | = all_1978_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (2072), (2121) imply:
% 260.90/41.71 | (2208) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0, all_713_0)
% 260.90/41.71 | = all_1962_0
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1959), (2186) imply:
% 260.90/41.71 | (2209) $i(all_1912_0)
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (2080), (2115) imply:
% 260.90/41.71 | (2210) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_1,
% 260.90/41.71 | all_1022_1)
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (2004), (2197) imply:
% 260.90/41.71 | (2211) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_1,
% 260.90/41.71 | all_713_0)
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1995), (2165) imply:
% 260.90/41.71 | (2212) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1912_0,
% 260.90/41.71 | all_713_0)
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1969), (2188) imply:
% 260.90/41.71 | (2213) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_1,
% 260.90/41.71 | all_1022_2)
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1986), (2196) imply:
% 260.90/41.71 | (2214) ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_705_0, all_650_0)
% 260.90/41.71 |
% 260.90/41.71 | REDUCE: (1975), (2193) imply:
% 260.90/41.71 | (2215) ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_705_0,
% 260.90/41.71 | all_650_0)
% 260.90/41.71 |
% 260.90/41.71 | BETA: splitting (2068) gives:
% 260.90/41.71 |
% 260.90/41.71 | Case 1:
% 260.90/41.71 | |
% 260.90/41.72 | | (2216) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2016_0,
% 260.90/41.72 | | all_1022_2)
% 260.90/41.72 | |
% 260.90/41.72 | | REDUCE: (2202), (2216) imply:
% 260.90/41.72 | | (2217) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_713_1,
% 260.90/41.72 | | all_1022_2)
% 260.90/41.72 | |
% 260.90/41.72 | | PRED_UNIFY: (2213), (2217) imply:
% 260.90/41.72 | | (2218) $false
% 260.90/41.72 | |
% 260.90/41.72 | | CLOSE: (2218) is inconsistent.
% 260.90/41.72 | |
% 261.16/41.72 | Case 2:
% 261.16/41.72 | |
% 261.16/41.72 | | (2219) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2016_0,
% 261.16/41.72 | | all_713_0) | (( ~ (all_2016_0 = all_1022_1) | (all_1022_1 =
% 261.16/41.72 | | all_713_0 & all_1022_2 = all_713_0)) & ( ~ (all_2016_0 =
% 261.16/41.72 | | all_713_0) | ~ (all_1022_2 = all_713_0) | all_1022_1 =
% 261.16/41.72 | | all_713_0))
% 261.16/41.72 | |
% 261.16/41.72 | | BETA: splitting (2219) gives:
% 261.16/41.72 | |
% 261.16/41.72 | | Case 1:
% 261.16/41.72 | | |
% 261.16/41.72 | | | (2220) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.72 | | | all_2016_0, all_713_0)
% 261.16/41.72 | | |
% 261.16/41.72 | | | REDUCE: (2202), (2220) imply:
% 261.16/41.72 | | | (2221) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.72 | | | all_713_1, all_713_0)
% 261.16/41.72 | | |
% 261.16/41.72 | | | PRED_UNIFY: (2211), (2221) imply:
% 261.16/41.72 | | | (2222) $false
% 261.16/41.72 | | |
% 261.16/41.72 | | | CLOSE: (2222) is inconsistent.
% 261.16/41.72 | | |
% 261.16/41.72 | | Case 2:
% 261.16/41.72 | | |
% 261.16/41.72 | | | (2223) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2016_0,
% 261.16/41.72 | | | all_713_0)
% 261.16/41.72 | | | (2224) ( ~ (all_2016_0 = all_1022_1) | (all_1022_1 = all_713_0 &
% 261.16/41.72 | | | all_1022_2 = all_713_0)) & ( ~ (all_2016_0 = all_713_0) | ~
% 261.16/41.72 | | | (all_1022_2 = all_713_0) | all_1022_1 = all_713_0)
% 261.16/41.72 | | |
% 261.16/41.72 | | | ALPHA: (2224) implies:
% 261.16/41.72 | | | (2225) ~ (all_2016_0 = all_1022_1) | (all_1022_1 = all_713_0 &
% 261.16/41.72 | | | all_1022_2 = all_713_0)
% 261.16/41.72 | | |
% 261.16/41.72 | | | BETA: splitting (2225) gives:
% 261.16/41.72 | | |
% 261.16/41.72 | | | Case 1:
% 261.16/41.72 | | | |
% 261.16/41.72 | | | | (2226) ~ (all_2016_0 = all_1022_1)
% 261.16/41.72 | | | |
% 261.16/41.72 | | | | REDUCE: (2202), (2226) imply:
% 261.16/41.72 | | | | (2227) ~ (all_1022_1 = all_713_1)
% 261.16/41.72 | | | |
% 261.16/41.72 | | | | SIMP: (2227) implies:
% 261.16/41.72 | | | | (2228) ~ (all_1022_1 = all_713_1)
% 261.16/41.72 | | | |
% 261.16/41.72 | | | | BETA: splitting (1946) gives:
% 261.16/41.72 | | | |
% 261.16/41.72 | | | | Case 1:
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | (2229) c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_705_0,
% 261.16/41.72 | | | | | all_650_0)
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | PRED_UNIFY: (2214), (2229) imply:
% 261.16/41.72 | | | | | (2230) $false
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | CLOSE: (2230) is inconsistent.
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | Case 2:
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | (2231) ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 261.16/41.72 | | | | | all_713_0, all_1564_0) = v0 & $i(v0) & ~
% 261.16/41.72 | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 261.16/41.72 | | | | | all_713_1))
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | DELTA: instantiating (2231) with fresh symbol all_2071_0 gives:
% 261.16/41.72 | | | | | (2232) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.72 | | | | | all_1564_0) = all_2071_0 & $i(all_2071_0) & ~
% 261.16/41.72 | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.72 | | | | | all_2071_0, all_713_1)
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | ALPHA: (2232) implies:
% 261.16/41.72 | | | | | (2233) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.72 | | | | | all_1564_0) = all_2071_0
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | REDUCE: (1775), (2233) imply:
% 261.16/41.72 | | | | | (2234) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.72 | | | | | all_713_0) = all_2071_0
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | BETA: splitting (1947) gives:
% 261.16/41.72 | | | | |
% 261.16/41.72 | | | | | Case 1:
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | (2235) c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_705_0,
% 261.16/41.72 | | | | | | all_650_0)
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | PRED_UNIFY: (2215), (2235) imply:
% 261.16/41.72 | | | | | | (2236) $false
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | CLOSE: (2236) is inconsistent.
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | Case 2:
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | (2237) ? [v0: $i] :
% 261.16/41.72 | | | | | | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.72 | | | | | | all_1579_0) = v0 & $i(v0) & ~
% 261.16/41.72 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_713_0, v0))
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | DELTA: instantiating (2237) with fresh symbol all_2085_0 gives:
% 261.16/41.72 | | | | | | (2238) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.72 | | | | | | all_1579_0) = all_2085_0 & $i(all_2085_0) & ~
% 261.16/41.72 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_0,
% 261.16/41.72 | | | | | | all_2085_0)
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | ALPHA: (2238) implies:
% 261.16/41.72 | | | | | | (2239) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_713_0, all_2085_0)
% 261.16/41.72 | | | | | | (2240) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.72 | | | | | | all_1579_0) = all_2085_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | REDUCE: (1776), (2240) imply:
% 261.16/41.72 | | | | | | (2241) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.72 | | | | | | all_713_0) = all_2085_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (254) with all_1912_0, all_2085_0,
% 261.16/41.72 | | | | | | all_713_0, all_713_1, tc_RealDef_Oreal, simplifying
% 261.16/41.72 | | | | | | with (2078), (2241) gives:
% 261.16/41.72 | | | | | | (2242) all_2085_0 = all_1912_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (254) with all_1978_0, all_2085_0,
% 261.16/41.72 | | | | | | all_713_0, all_713_1, tc_RealDef_Oreal, simplifying
% 261.16/41.72 | | | | | | with (2207), (2241) gives:
% 261.16/41.72 | | | | | | (2243) all_2085_0 = all_1978_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (254) with all_1976_0, all_2071_0,
% 261.16/41.72 | | | | | | all_713_0, all_713_0, tc_RealDef_Oreal, simplifying
% 261.16/41.72 | | | | | | with (2075), (2234) gives:
% 261.16/41.72 | | | | | | (2244) all_2071_0 = all_1976_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (254) with all_1962_0, all_2071_0,
% 261.16/41.72 | | | | | | all_713_0, all_713_0, tc_RealDef_Oreal, simplifying
% 261.16/41.72 | | | | | | with (2208), (2234) gives:
% 261.16/41.72 | | | | | | (2245) all_2071_0 = all_1962_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (253) with all_713_0, all_1912_0,
% 261.16/41.72 | | | | | | all_705_0, tc_Nat_Onat, simplifying with (1884), (2206)
% 261.16/41.72 | | | | | | gives:
% 261.16/41.72 | | | | | | (2246) all_1912_0 = all_713_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (253) with all_1950_0, all_1976_0,
% 261.16/41.72 | | | | | | all_1066_0, tc_Nat_Onat, simplifying with (1998),
% 261.16/41.72 | | | | | | (2205) gives:
% 261.16/41.72 | | | | | | (2247) all_1976_0 = all_1950_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | COMBINE_EQS: (2242), (2243) imply:
% 261.16/41.72 | | | | | | (2248) all_1978_0 = all_1912_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | COMBINE_EQS: (2244), (2245) imply:
% 261.16/41.72 | | | | | | (2249) all_1976_0 = all_1962_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | COMBINE_EQS: (2247), (2249) imply:
% 261.16/41.72 | | | | | | (2250) all_1962_0 = all_1950_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | COMBINE_EQS: (2246), (2248) imply:
% 261.16/41.72 | | | | | | (2251) all_1978_0 = all_713_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | COMBINE_EQS: (2243), (2251) imply:
% 261.16/41.72 | | | | | | (2252) all_2085_0 = all_713_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | REDUCE: (2208), (2250) imply:
% 261.16/41.72 | | | | | | (2253) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.72 | | | | | | all_713_0) = all_1950_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | REDUCE: (2078), (2246) imply:
% 261.16/41.72 | | | | | | (2254) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.72 | | | | | | all_713_0) = all_713_0
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | REDUCE: (2009), (2250) imply:
% 261.16/41.72 | | | | | | (2255) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_0,
% 261.16/41.72 | | | | | | all_1950_0)
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | REDUCE: (2212), (2246) imply:
% 261.16/41.72 | | | | | | (2256) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_713_0, all_713_0)
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | REDUCE: (2239), (2252) imply:
% 261.16/41.72 | | | | | | (2257) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_713_0, all_713_0)
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (fact_add__strict__increasing) with
% 261.16/41.72 | | | | | | all_1022_2, v_r____, all_713_0, tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_1022_1, simplifying with (236), (244), (245),
% 261.16/41.72 | | | | | | (457), (1808), (1811), (1918) gives:
% 261.16/41.72 | | | | | | (2258) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_r____,
% 261.16/41.72 | | | | | | all_1022_1) | ? [v0: $i] :
% 261.16/41.72 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.72 | | | | | | $i(v0) & ~
% 261.16/41.72 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 261.16/41.72 | | | | | | all_713_0))
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (23) with all_1022_2, v_r____,
% 261.16/41.72 | | | | | | simplifying with (245), (457), (1918) gives:
% 261.16/41.72 | | | | | | (2259) all_1022_2 = v_r____ |
% 261.16/41.72 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_r____,
% 261.16/41.72 | | | | | | all_1022_2)
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (715) with all_705_0, all_705_0,
% 261.16/41.72 | | | | | | all_1066_0, simplifying with (1883), (1886), (1954)
% 261.16/41.72 | | | | | | gives:
% 261.16/41.72 | | | | | | (2260) all_1614_0 = all_705_0 | ? [v0: $i] : (c_Nat_OSuc(v0) =
% 261.16/41.72 | | | | | | all_705_0 & $i(v0) &
% 261.16/41.72 | | | | | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 261.16/41.72 | | | | | | all_705_0))
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (585) with v_r____, tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_1022_2, simplifying with (238), (244), (245),
% 261.16/41.72 | | | | | | (1927) gives:
% 261.16/41.72 | | | | | | (2261) ? [v0: $i] : (( ~ (all_1303_0 = all_1022_2) | (v0 =
% 261.16/41.72 | | | | | | v_r____ &
% 261.16/41.72 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.72 | | | | | | v_r____)) & (all_1303_0 = all_1022_2 | ( ~ (v0 =
% 261.16/41.72 | | | | | | v_r____) &
% 261.16/41.72 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.72 | | | | | | $i(v0))))
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (567) with v_r____, tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_1022_2, simplifying with (238), (244), (245),
% 261.16/41.72 | | | | | | (1927) gives:
% 261.16/41.72 | | | | | | (2262) ? [v0: $i] : (( ~
% 261.16/41.72 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_1253_0, all_1022_2) | ( ~ (v0 = v_r____) &
% 261.16/41.72 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.72 | | | | | | $i(v0))) &
% 261.16/41.72 | | | | | | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_1253_0, all_1022_2) | (v0 = v_r____ &
% 261.16/41.72 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.72 | | | | | | v_r____)))
% 261.16/41.72 | | | | | |
% 261.16/41.72 | | | | | | GROUND_INST: instantiating (590) with v_r____, tc_RealDef_Oreal,
% 261.16/41.72 | | | | | | all_1022_2, simplifying with (238), (244), (245),
% 261.16/41.72 | | | | | | (1927) gives:
% 261.16/41.73 | | | | | | (2263) ? [v0: $i] : (( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1022_2, all_1326_0) | (v0 = v_r____ &
% 261.16/41.73 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.73 | | | | | | v_r____)) &
% 261.16/41.73 | | | | | | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1022_2, all_1326_0) | ( ~ (v0 = v_r____) &
% 261.16/41.73 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0))))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (10) with v_r____, tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1022_2, simplifying with (238), (244), (245),
% 261.16/41.73 | | | | | | (1927) gives:
% 261.16/41.73 | | | | | | (2264) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1022_2) =
% 261.16/41.73 | | | | | | all_1022_2 & $i(all_1022_2)
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating
% 261.16/41.73 | | | | | | (fact_ab__semigroup__add__class_Oadd__ac_I1_J) with
% 261.16/41.73 | | | | | | all_1022_2, all_713_0, all_713_1, tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_713_0, all_1022_1, simplifying with (240), (244),
% 261.16/41.73 | | | | | | (457), (1808), (1810), (1811), (2254) gives:
% 261.16/41.73 | | | | | | (2265) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.73 | | | | | | all_1022_2) = v0 &
% 261.16/41.73 | | | | | | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.73 | | | | | | v0) = all_1022_1 & $i(v0) & $i(all_1022_1))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_add__strict__increasing) with
% 261.16/41.73 | | | | | | all_713_0, all_713_0, all_713_1, tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_713_0, simplifying with (236), (244), (1810),
% 261.16/41.73 | | | | | | (1811), (2254), (2256), (2257) gives:
% 261.16/41.73 | | | | | | (2266) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 261.16/41.73 | | | | | | all_713_1))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating
% 261.16/41.73 | | | | | | (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)
% 261.16/41.73 | | | | | | with all_713_0, all_713_0, all_713_1, all_713_1,
% 261.16/41.73 | | | | | | tc_RealDef_Oreal, all_713_0, all_713_0, all_1950_0,
% 261.16/41.73 | | | | | | simplifying with (241), (244), (1810), (1811), (2253),
% 261.16/41.73 | | | | | | (2254) gives:
% 261.16/41.73 | | | | | | (2267) ? [v0: $i] : ? [v1: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v1) =
% 261.16/41.73 | | | | | | all_1950_0 &
% 261.16/41.73 | | | | | | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.73 | | | | | | all_713_0) = v1 &
% 261.16/41.73 | | | | | | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.73 | | | | | | all_713_1) = v0 & $i(v1) & $i(v0) & $i(all_1950_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_add__nonneg__nonneg) with
% 261.16/41.73 | | | | | | all_713_0, all_713_0, tc_RealDef_Oreal, all_1950_0,
% 261.16/41.73 | | | | | | simplifying with (236), (244), (1811), (2253) gives:
% 261.16/41.73 | | | | | | (2268) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v0, all_713_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v0, all_1950_0)))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_add__nonneg__eq__0__iff) with
% 261.16/41.73 | | | | | | all_713_0, all_713_0, tc_RealDef_Oreal, all_1950_0,
% 261.16/41.73 | | | | | | simplifying with (236), (244), (1811), (2253) gives:
% 261.16/41.73 | | | | | | (2269) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v0, all_713_0) | (( ~ (v0 = all_1950_0) | all_1950_0
% 261.16/41.73 | | | | | | = all_713_0) & ( ~ (v0 = all_713_0) | all_1950_0 =
% 261.16/41.73 | | | | | | all_713_0))))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_add__0__iff) with all_713_0,
% 261.16/41.73 | | | | | | all_713_0, tc_RealDef_Oreal, all_1950_0, simplifying
% 261.16/41.73 | | | | | | with (234), (244), (1811), (2253) gives:
% 261.16/41.73 | | | | | | (2270) ? [v0: any] : (( ~ (all_1950_0 = all_713_0) | (v0 =
% 261.16/41.73 | | | | | | all_713_0 &
% 261.16/41.73 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.73 | | | | | | all_713_0)) & (all_1950_0 = all_713_0 | ( ~ (v0 =
% 261.16/41.73 | | | | | | all_713_0) &
% 261.16/41.73 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0))))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_double__zero__sym) with all_713_0,
% 261.16/41.73 | | | | | | tc_RealDef_Oreal, all_1950_0, simplifying with (237),
% 261.16/41.73 | | | | | | (244), (1811), (2253) gives:
% 261.16/41.73 | | | | | | (2271) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~ (v0 = all_1950_0) | all_1950_0 = all_713_0)
% 261.16/41.73 | | | | | | & ( ~ (v0 = all_713_0) | all_1950_0 = all_713_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating
% 261.16/41.73 | | | | | | (fact_double__add__less__zero__iff__single__add__less__zero)
% 261.16/41.73 | | | | | | with all_713_0, tc_RealDef_Oreal, all_1950_0,
% 261.16/41.73 | | | | | | simplifying with (237), (244), (1811), (2253) gives:
% 261.16/41.73 | | | | | | (2272) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1950_0, v0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_713_0, v0)) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_713_0, v0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1950_0, v0)))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating
% 261.16/41.73 | | | | | | (fact_zero__le__double__add__iff__zero__le__single__add)
% 261.16/41.73 | | | | | | with all_713_0, tc_RealDef_Oreal, all_1950_0,
% 261.16/41.73 | | | | | | simplifying with (237), (244), (1811), (2253) gives:
% 261.16/41.73 | | | | | | (2273) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v0, all_1950_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v0, all_713_0)) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v0, all_713_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v0, all_1950_0)))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_add__increasing2) with all_1022_2,
% 261.16/41.73 | | | | | | v_r____, all_713_0, tc_RealDef_Oreal, all_1022_1,
% 261.16/41.73 | | | | | | simplifying with (236), (244), (245), (457), (1811),
% 261.16/41.73 | | | | | | (1917), (1918) gives:
% 261.16/41.73 | | | | | | (2274) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v_r____, all_1022_1) | ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 261.16/41.73 | | | | | | all_713_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_less__add__one) with all_1022_2,
% 261.16/41.73 | | | | | | tc_RealDef_Oreal, all_713_0, all_1022_1, simplifying
% 261.16/41.73 | | | | | | with (239), (244), (296), (457), (1917) gives:
% 261.16/41.73 | | | | | | (2275) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1022_2, all_1022_1)
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_add__0__iff) with all_713_0,
% 261.16/41.73 | | | | | | all_1022_2, tc_RealDef_Oreal, all_1022_1, simplifying
% 261.16/41.73 | | | | | | with (234), (244), (457), (1811), (1917) gives:
% 261.16/41.73 | | | | | | (2276) ? [v0: any] : (( ~ (all_1022_1 = all_1022_2) | (v0 =
% 261.16/41.73 | | | | | | all_713_0 &
% 261.16/41.73 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.73 | | | | | | all_713_0)) & (all_1022_1 = all_1022_2 | ( ~ (v0 =
% 261.16/41.73 | | | | | | all_713_0) &
% 261.16/41.73 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0))))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_abs__not__less__zero) with
% 261.16/41.73 | | | | | | all_648_0, tc_RealDef_Oreal, all_648_0, simplifying
% 261.16/41.73 | | | | | | with (235), (244), (1890), (1891) gives:
% 261.16/41.73 | | | | | | (2277) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_648_0, v0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_zero__less__abs__iff) with
% 261.16/41.73 | | | | | | all_648_0, tc_RealDef_Oreal, all_648_0, simplifying
% 261.16/41.73 | | | | | | with (235), (244), (1890), (1891) gives:
% 261.16/41.73 | | | | | | (2278) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~ (v0 = all_648_0) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_648_0, all_648_0)) & (v0 = all_648_0 |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 261.16/41.73 | | | | | | all_648_0)))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_abs__le__zero__iff) with all_648_0,
% 261.16/41.73 | | | | | | tc_RealDef_Oreal, all_648_0, simplifying with (235),
% 261.16/41.73 | | | | | | (244), (1890), (1891) gives:
% 261.16/41.73 | | | | | | (2279) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~ (v0 = all_648_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_648_0, all_648_0)) & (v0 = all_648_0 | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_648_0, v0)))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_abs__not__less__zero) with
% 261.16/41.73 | | | | | | all_713_1, tc_RealDef_Oreal, all_713_1, simplifying
% 261.16/41.73 | | | | | | with (235), (244), (1810), (1944) gives:
% 261.16/41.73 | | | | | | (2280) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_713_1, v0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_zero__less__abs__iff) with
% 261.16/41.73 | | | | | | all_713_1, tc_RealDef_Oreal, all_713_1, simplifying
% 261.16/41.73 | | | | | | with (235), (244), (1810), (1944) gives:
% 261.16/41.73 | | | | | | (2281) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~ (v0 = all_713_1) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_713_1, all_713_1)) & (v0 = all_713_1 |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 261.16/41.73 | | | | | | all_713_1)))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (370) with all_713_0, all_713_0,
% 261.16/41.73 | | | | | | simplifying with (1811), (1950) gives:
% 261.16/41.73 | | | | | | (2282) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.73 | | | | | | all_853_0) = v0 & $i(v0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 261.16/41.73 | | | | | | all_713_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_abs__not__less__zero) with
% 261.16/41.73 | | | | | | all_1468_3, tc_RealDef_Oreal, all_1468_3, simplifying
% 261.16/41.73 | | | | | | with (235), (244), (1893), (1894) gives:
% 261.16/41.73 | | | | | | (2283) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, v0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_zero__less__abs__iff) with
% 261.16/41.73 | | | | | | all_1468_3, tc_RealDef_Oreal, all_1468_3, simplifying
% 261.16/41.73 | | | | | | with (235), (244), (1893), (1894) gives:
% 261.16/41.73 | | | | | | (2284) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~ (v0 = all_1468_3) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, all_1468_3)) & (v0 = all_1468_3 |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 261.16/41.73 | | | | | | all_1468_3)))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | GROUND_INST: instantiating (fact_abs__le__zero__iff) with
% 261.16/41.73 | | | | | | all_1468_3, tc_RealDef_Oreal, all_1468_3, simplifying
% 261.16/41.73 | | | | | | with (235), (244), (1893), (1894) gives:
% 261.16/41.73 | | | | | | (2285) ? [v0: $i] :
% 261.16/41.73 | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 261.16/41.73 | | | | | | $i(v0) & ( ~ (v0 = all_1468_3) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, all_1468_3)) & (v0 = all_1468_3 | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, v0)))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (2266) with fresh symbol all_2205_0 gives:
% 261.16/41.73 | | | | | | (2286) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2205_0
% 261.16/41.73 | | | | | | & $i(all_2205_0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2205_0, all_713_1)
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2286) implies:
% 261.16/41.73 | | | | | | (2287) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2205_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (2280) with fresh symbol all_2213_0 gives:
% 261.16/41.73 | | | | | | (2288) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2213_0
% 261.16/41.73 | | | | | | & $i(all_2213_0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_713_1,
% 261.16/41.73 | | | | | | all_2213_0)
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2288) implies:
% 261.16/41.73 | | | | | | (2289) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2213_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (2283) with fresh symbol all_2219_0 gives:
% 261.16/41.73 | | | | | | (2290) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2219_0
% 261.16/41.73 | | | | | | & $i(all_2219_0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, all_2219_0)
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2290) implies:
% 261.16/41.73 | | | | | | (2291) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2219_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (2277) with fresh symbol all_2227_0 gives:
% 261.16/41.73 | | | | | | (2292) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2227_0
% 261.16/41.73 | | | | | | & $i(all_2227_0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_648_0,
% 261.16/41.73 | | | | | | all_2227_0)
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2292) implies:
% 261.16/41.73 | | | | | | (2293) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2227_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (2282) with fresh symbol all_2235_0 gives:
% 261.16/41.73 | | | | | | (2294) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.73 | | | | | | all_853_0) = all_2235_0 & $i(all_2235_0) & ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2235_0, all_713_0)
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2294) implies:
% 261.16/41.73 | | | | | | (2295) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2235_0, all_713_0)
% 261.16/41.73 | | | | | | (2296) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.73 | | | | | | all_853_0) = all_2235_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (2268) with fresh symbol all_2273_0 gives:
% 261.16/41.73 | | | | | | (2297) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2273_0
% 261.16/41.73 | | | | | | & $i(all_2273_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2273_0, all_713_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2273_0, all_1950_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2297) implies:
% 261.16/41.73 | | | | | | (2298) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2273_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (2265) with fresh symbol all_2275_0 gives:
% 261.16/41.73 | | | | | | (2299) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.73 | | | | | | all_1022_2) = all_2275_0 &
% 261.16/41.73 | | | | | | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.73 | | | | | | all_2275_0) = all_1022_1 & $i(all_2275_0) &
% 261.16/41.73 | | | | | | $i(all_1022_1)
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2299) implies:
% 261.16/41.73 | | | | | | (2300) $i(all_2275_0)
% 261.16/41.73 | | | | | | (2301) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.73 | | | | | | all_1022_2) = all_2275_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (1896) with fresh symbol all_2287_0 gives:
% 261.16/41.73 | | | | | | (2302) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2287_0
% 261.16/41.73 | | | | | | & $i(all_2287_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2287_0, v_da____) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2287_0, all_1468_3) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2287_0, all_1468_2))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2302) implies:
% 261.16/41.73 | | | | | | (2303) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2287_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (1897) with fresh symbol all_2289_0 gives:
% 261.16/41.73 | | | | | | (2304) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2289_0
% 261.16/41.73 | | | | | | & $i(all_2289_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2289_0, all_1468_3) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2289_0, v_da____) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2289_0, all_1468_2))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2304) implies:
% 261.16/41.73 | | | | | | (2305) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2289_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (1895) with fresh symbol all_2293_0 gives:
% 261.16/41.73 | | | | | | (2306) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2293_0
% 261.16/41.73 | | | | | | & $i(all_2293_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2293_0, all_1468_3) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2293_0, v_da____) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2293_0, all_1468_2))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2306) implies:
% 261.16/41.73 | | | | | | (2307) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2293_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (1903) with fresh symbol all_2313_0 gives:
% 261.16/41.73 | | | | | | (2308) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2313_0
% 261.16/41.73 | | | | | | & $i(all_2313_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, all_2313_0) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v_da____, all_2313_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_2, all_2313_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2308) implies:
% 261.16/41.73 | | | | | | (2309) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2313_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (1901) with fresh symbol all_2319_0 gives:
% 261.16/41.73 | | | | | | (2310) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2319_0
% 261.16/41.73 | | | | | | & $i(all_2319_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2319_0, all_1468_3) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2319_0, v_da____) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2319_0, all_1468_2))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2310) implies:
% 261.16/41.73 | | | | | | (2311) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2319_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (1900) with fresh symbol all_2321_0 gives:
% 261.16/41.73 | | | | | | (2312) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2321_0
% 261.16/41.73 | | | | | | & $i(all_2321_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, all_2321_0) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v_da____, all_2321_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_2, all_2321_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2312) implies:
% 261.16/41.73 | | | | | | (2313) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2321_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (1898) with fresh symbol all_2323_0 gives:
% 261.16/41.73 | | | | | | (2314) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2323_0
% 261.16/41.73 | | | | | | & $i(all_2323_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, all_2323_0) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v_da____, all_2323_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_2, all_2323_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2314) implies:
% 261.16/41.73 | | | | | | (2315) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2323_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (1899) with fresh symbol all_2329_0 gives:
% 261.16/41.73 | | | | | | (2316) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2329_0
% 261.16/41.73 | | | | | | & $i(all_2329_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | v_da____, all_2329_0) | ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_3, all_2329_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_1468_2, all_2329_0))
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | ALPHA: (2316) implies:
% 261.16/41.73 | | | | | | (2317) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2329_0
% 261.16/41.73 | | | | | |
% 261.16/41.73 | | | | | | DELTA: instantiating (2273) with fresh symbol all_2339_0 gives:
% 261.16/41.73 | | | | | | (2318) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2339_0
% 261.16/41.73 | | | | | | & $i(all_2339_0) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2339_0, all_1950_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2339_0, all_713_0)) & ( ~
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.73 | | | | | | all_2339_0, all_713_0) |
% 261.16/41.73 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_2339_0, all_1950_0))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2318) implies:
% 261.16/41.74 | | | | | | (2319) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2339_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2272) with fresh symbol all_2343_0 gives:
% 261.16/41.74 | | | | | | (2320) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2343_0
% 261.16/41.74 | | | | | | & $i(all_2343_0) & ( ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1950_0, all_2343_0) |
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_713_0, all_2343_0)) & ( ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_713_0, all_2343_0) |
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1950_0, all_2343_0))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2320) implies:
% 261.16/41.74 | | | | | | (2321) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2343_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2267) with fresh symbols all_2345_0,
% 261.16/41.74 | | | | | | all_2345_1 gives:
% 261.16/41.74 | | | | | | (2322) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_2345_1,
% 261.16/41.74 | | | | | | all_2345_0) = all_1950_0 &
% 261.16/41.74 | | | | | | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.74 | | | | | | all_713_0) = all_2345_0 &
% 261.16/41.74 | | | | | | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_1,
% 261.16/41.74 | | | | | | all_713_1) = all_2345_1 & $i(all_2345_0) &
% 261.16/41.74 | | | | | | $i(all_2345_1) & $i(all_1950_0)
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2322) implies:
% 261.16/41.74 | | | | | | (2323) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.74 | | | | | | all_713_0) = all_2345_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2281) with fresh symbol all_2347_0 gives:
% 261.16/41.74 | | | | | | (2324) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2347_0
% 261.16/41.74 | | | | | | & $i(all_2347_0) & ( ~ (all_2347_0 = all_713_1) | ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_713_1, all_713_1)) & (all_2347_0 = all_713_1 |
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_2347_0, all_713_1))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2324) implies:
% 261.16/41.74 | | | | | | (2325) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2347_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2284) with fresh symbol all_2349_0 gives:
% 261.16/41.74 | | | | | | (2326) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2349_0
% 261.16/41.74 | | | | | | & $i(all_2349_0) & ( ~ (all_2349_0 = all_1468_3) | ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1468_3, all_1468_3)) & (all_2349_0 = all_1468_3 |
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_2349_0, all_1468_3))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2326) implies:
% 261.16/41.74 | | | | | | (2327) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2349_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2278) with fresh symbol all_2351_0 gives:
% 261.16/41.74 | | | | | | (2328) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2351_0
% 261.16/41.74 | | | | | | & $i(all_2351_0) & ( ~ (all_2351_0 = all_648_0) | ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_648_0, all_648_0)) & (all_2351_0 = all_648_0 |
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_2351_0, all_648_0))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2328) implies:
% 261.16/41.74 | | | | | | (2329) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2351_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2271) with fresh symbol all_2353_0 gives:
% 261.16/41.74 | | | | | | (2330) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2353_0
% 261.16/41.74 | | | | | | & $i(all_2353_0) & ( ~ (all_2353_0 = all_1950_0) |
% 261.16/41.74 | | | | | | all_1950_0 = all_713_0) & ( ~ (all_2353_0 = all_713_0) |
% 261.16/41.74 | | | | | | all_1950_0 = all_713_0)
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2330) implies:
% 261.16/41.74 | | | | | | (2331) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2353_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2285) with fresh symbol all_2355_0 gives:
% 261.16/41.74 | | | | | | (2332) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2355_0
% 261.16/41.74 | | | | | | & $i(all_2355_0) & ( ~ (all_2355_0 = all_1468_3) |
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1468_3, all_1468_3)) & (all_2355_0 = all_1468_3 |
% 261.16/41.74 | | | | | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1468_3, all_2355_0))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2332) implies:
% 261.16/41.74 | | | | | | (2333) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2355_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2279) with fresh symbol all_2357_0 gives:
% 261.16/41.74 | | | | | | (2334) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2357_0
% 261.16/41.74 | | | | | | & $i(all_2357_0) & ( ~ (all_2357_0 = all_648_0) |
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_648_0, all_648_0)) & (all_2357_0 = all_648_0 | ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_648_0, all_2357_0))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2334) implies:
% 261.16/41.74 | | | | | | (2335) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2357_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2276) with fresh symbol all_2359_0 gives:
% 261.16/41.74 | | | | | | (2336) ( ~ (all_1022_1 = all_1022_2) | (all_2359_0 = all_713_0 &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_713_0)) & (all_1022_1 = all_1022_2 | ( ~
% 261.16/41.74 | | | | | | (all_2359_0 = all_713_0) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2359_0 & $i(all_2359_0)))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2336) implies:
% 261.16/41.74 | | | | | | (2337) all_1022_1 = all_1022_2 | ( ~ (all_2359_0 = all_713_0) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2359_0 & $i(all_2359_0))
% 261.16/41.74 | | | | | | (2338) ~ (all_1022_1 = all_1022_2) | (all_2359_0 = all_713_0 &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_713_0)
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2263) with fresh symbol all_2365_0 gives:
% 261.16/41.74 | | | | | | (2339) ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1022_2, all_1326_0) | (all_2365_0 = v_r____ &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | v_r____)) &
% 261.16/41.74 | | | | | | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1022_2, all_1326_0) | ( ~ (all_2365_0 = v_r____) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2365_0 & $i(all_2365_0)))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2339) implies:
% 261.16/41.74 | | | | | | (2340) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1022_2, all_1326_0) | ( ~ (all_2365_0 = v_r____) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2365_0 & $i(all_2365_0))
% 261.16/41.74 | | | | | | (2341) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1022_2, all_1326_0) | (all_2365_0 = v_r____ &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r____)
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2270) with fresh symbol all_2366_0 gives:
% 261.16/41.74 | | | | | | (2342) ( ~ (all_1950_0 = all_713_0) | (all_2366_0 = all_713_0 &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_713_0)) & (all_1950_0 = all_713_0 | ( ~
% 261.16/41.74 | | | | | | (all_2366_0 = all_713_0) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2366_0 & $i(all_2366_0)))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2342) implies:
% 261.16/41.74 | | | | | | (2343) all_1950_0 = all_713_0 | ( ~ (all_2366_0 = all_713_0) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2366_0 & $i(all_2366_0))
% 261.16/41.74 | | | | | | (2344) ~ (all_1950_0 = all_713_0) | (all_2366_0 = all_713_0 &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_713_0)
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2269) with fresh symbol all_2367_0 gives:
% 261.16/41.74 | | | | | | (2345) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2367_0
% 261.16/41.74 | | | | | | & $i(all_2367_0) & ( ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_2367_0, all_713_0) | (( ~ (all_2367_0 =
% 261.16/41.74 | | | | | | all_1950_0) | all_1950_0 = all_713_0) & ( ~
% 261.16/41.74 | | | | | | (all_2367_0 = all_713_0) | all_1950_0 = all_713_0)))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2345) implies:
% 261.16/41.74 | | | | | | (2346) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2367_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2261) with fresh symbol all_2369_0 gives:
% 261.16/41.74 | | | | | | (2347) ( ~ (all_1303_0 = all_1022_2) | (all_2369_0 = v_r____ &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | v_r____)) & (all_1303_0 = all_1022_2 | ( ~ (all_2369_0
% 261.16/41.74 | | | | | | = v_r____) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2369_0 & $i(all_2369_0)))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2347) implies:
% 261.16/41.74 | | | | | | (2348) all_1303_0 = all_1022_2 | ( ~ (all_2369_0 = v_r____) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2369_0 & $i(all_2369_0))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (2262) with fresh symbol all_2370_0 gives:
% 261.16/41.74 | | | | | | (2349) ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1253_0, all_1022_2) | ( ~ (all_2370_0 = v_r____) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2370_0 & $i(all_2370_0))) &
% 261.16/41.74 | | | | | | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1253_0, all_1022_2) | (all_2370_0 = v_r____ &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | v_r____))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2349) implies:
% 261.16/41.74 | | | | | | (2350) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_1253_0, all_1022_2) | ( ~ (all_2370_0 = v_r____) &
% 261.16/41.74 | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.74 | | | | | | all_2370_0 & $i(all_2370_0))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | DELTA: instantiating (1902) with fresh symbol all_2373_0 gives:
% 261.16/41.74 | | | | | | (2351) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2373_0
% 261.16/41.74 | | | | | | & $i(all_2373_0) & ( ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_2373_0, all_1468_3) | ~
% 261.16/41.74 | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.74 | | | | | | all_2373_0, v_da____) | (( ~ (all_2373_0 = all_1468_2)
% 261.16/41.74 | | | | | | | (all_1468_2 = v_da____ & all_1468_3 = v_da____)) &
% 261.16/41.74 | | | | | | ( ~ (all_2373_0 = v_da____) | ~ (all_1468_3 =
% 261.16/41.74 | | | | | | v_da____) | all_1468_2 = v_da____)))
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | ALPHA: (2351) implies:
% 261.16/41.74 | | | | | | (2352) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2373_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | REDUCE: (1754), (2296) imply:
% 261.16/41.74 | | | | | | (2353) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_713_0,
% 261.16/41.74 | | | | | | all_713_0) = all_2235_0
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | BETA: splitting (2260) gives:
% 261.16/41.74 | | | | | |
% 261.16/41.74 | | | | | | Case 1:
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | (2354) all_1614_0 = all_705_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (1221), (2354) imply:
% 261.16/41.74 | | | | | | | (2355) all_705_0 = all_650_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | REDUCE: (2204), (2355) imply:
% 261.16/41.74 | | | | | | | (2356) $false
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | CLOSE: (2356) is inconsistent.
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | Case 2:
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2219_0, all_2227_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2291), (2293)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2357) all_2227_0 = all_2219_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2273_0, all_2289_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2298), (2305)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2358) all_2289_0 = all_2273_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2227_0, all_2289_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2293), (2305)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2359) all_2289_0 = all_2227_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_713_1, all_2319_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (295), (2311)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2360) all_2319_0 = all_713_1
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2227_0, all_2319_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2293), (2311)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2361) all_2319_0 = all_2227_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2293_0, all_2329_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2307), (2317)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2362) all_2329_0 = all_2293_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2289_0, all_2329_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2305), (2317)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2363) all_2329_0 = all_2289_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2287_0, all_2329_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2303), (2317)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2364) all_2329_0 = all_2287_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2313_0, all_2339_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2309), (2319)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2365) all_2339_0 = all_2313_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2339_0, all_2351_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2319), (2329)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2366) all_2351_0 = all_2339_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2323_0, all_2351_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2315), (2329)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2367) all_2351_0 = all_2323_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2321_0, all_2351_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2313), (2329)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2368) all_2351_0 = all_2321_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2293_0, all_2351_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2307), (2329)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2369) all_2351_0 = all_2293_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2213_0, all_2353_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2289), (2331)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2370) all_2353_0 = all_2213_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2353_0, all_2355_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2331), (2333)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2371) all_2355_0 = all_2353_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2343_0, all_2355_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2321), (2333)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2372) all_2355_0 = all_2343_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2319_0, all_2355_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2311), (2333)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2373) all_2355_0 = all_2319_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2349_0, all_2357_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2327), (2335)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2374) all_2357_0 = all_2349_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2205_0, all_2357_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2287), (2335)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2375) all_2357_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2367_0, all_2373_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2346), (2352)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2376) all_2373_0 = all_2367_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2349_0, all_2373_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2327), (2352)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2377) all_2373_0 = all_2349_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2347_0, all_2373_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2325), (2352)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2378) all_2373_0 = all_2347_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (248) with all_2321_0, all_2373_0,
% 261.16/41.74 | | | | | | | tc_RealDef_Oreal, simplifying with (2313), (2352)
% 261.16/41.74 | | | | | | | gives:
% 261.16/41.74 | | | | | | | (2379) all_2373_0 = all_2321_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (254) with all_1950_0, all_2345_0,
% 261.16/41.74 | | | | | | | all_713_0, all_713_0, tc_RealDef_Oreal, simplifying
% 261.16/41.74 | | | | | | | with (2253), (2323) gives:
% 261.16/41.74 | | | | | | | (2380) all_2345_0 = all_1950_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (254) with all_2235_0, all_2345_0,
% 261.16/41.74 | | | | | | | all_713_0, all_713_0, tc_RealDef_Oreal, simplifying
% 261.16/41.74 | | | | | | | with (2323), (2353) gives:
% 261.16/41.74 | | | | | | | (2381) all_2345_0 = all_2235_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | GROUND_INST: instantiating (254) with all_1022_1, all_2275_0,
% 261.16/41.74 | | | | | | | all_1022_2, all_713_0, tc_RealDef_Oreal, simplifying
% 261.16/41.74 | | | | | | | with (1808), (2301) gives:
% 261.16/41.74 | | | | | | | (2382) all_2275_0 = all_1022_1
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2376), (2379) imply:
% 261.16/41.74 | | | | | | | (2383) all_2367_0 = all_2321_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2376), (2378) imply:
% 261.16/41.74 | | | | | | | (2384) all_2367_0 = all_2347_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2376), (2377) imply:
% 261.16/41.74 | | | | | | | (2385) all_2367_0 = all_2349_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2383), (2384) imply:
% 261.16/41.74 | | | | | | | (2386) all_2347_0 = all_2321_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2384), (2385) imply:
% 261.16/41.74 | | | | | | | (2387) all_2349_0 = all_2347_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2387) implies:
% 261.16/41.74 | | | | | | | (2388) all_2349_0 = all_2347_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2374), (2375) imply:
% 261.16/41.74 | | | | | | | (2389) all_2349_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2389) implies:
% 261.16/41.74 | | | | | | | (2390) all_2349_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2372), (2373) imply:
% 261.16/41.74 | | | | | | | (2391) all_2343_0 = all_2319_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2371), (2372) imply:
% 261.16/41.74 | | | | | | | (2392) all_2353_0 = all_2343_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2392) implies:
% 261.16/41.74 | | | | | | | (2393) all_2353_0 = all_2343_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2370), (2393) imply:
% 261.16/41.74 | | | | | | | (2394) all_2343_0 = all_2213_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2394) implies:
% 261.16/41.74 | | | | | | | (2395) all_2343_0 = all_2213_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2367), (2369) imply:
% 261.16/41.74 | | | | | | | (2396) all_2323_0 = all_2293_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2366), (2367) imply:
% 261.16/41.74 | | | | | | | (2397) all_2339_0 = all_2323_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2397) implies:
% 261.16/41.74 | | | | | | | (2398) all_2339_0 = all_2323_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2367), (2368) imply:
% 261.16/41.74 | | | | | | | (2399) all_2323_0 = all_2321_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2388), (2390) imply:
% 261.16/41.74 | | | | | | | (2400) all_2347_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2400) implies:
% 261.16/41.74 | | | | | | | (2401) all_2347_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2386), (2401) imply:
% 261.16/41.74 | | | | | | | (2402) all_2321_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2402) implies:
% 261.16/41.74 | | | | | | | (2403) all_2321_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2380), (2381) imply:
% 261.16/41.74 | | | | | | | (2404) all_2235_0 = all_1950_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2391), (2395) imply:
% 261.16/41.74 | | | | | | | (2405) all_2319_0 = all_2213_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2405) implies:
% 261.16/41.74 | | | | | | | (2406) all_2319_0 = all_2213_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2365), (2398) imply:
% 261.16/41.74 | | | | | | | (2407) all_2323_0 = all_2313_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2407) implies:
% 261.16/41.74 | | | | | | | (2408) all_2323_0 = all_2313_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2363), (2364) imply:
% 261.16/41.74 | | | | | | | (2409) all_2289_0 = all_2287_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2409) implies:
% 261.16/41.74 | | | | | | | (2410) all_2289_0 = all_2287_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2362), (2364) imply:
% 261.16/41.74 | | | | | | | (2411) all_2293_0 = all_2287_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2411) implies:
% 261.16/41.74 | | | | | | | (2412) all_2293_0 = all_2287_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2399), (2408) imply:
% 261.16/41.74 | | | | | | | (2413) all_2321_0 = all_2313_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2413) implies:
% 261.16/41.74 | | | | | | | (2414) all_2321_0 = all_2313_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2396), (2408) imply:
% 261.16/41.74 | | | | | | | (2415) all_2313_0 = all_2293_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2403), (2414) imply:
% 261.16/41.74 | | | | | | | (2416) all_2313_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2416) implies:
% 261.16/41.74 | | | | | | | (2417) all_2313_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2360), (2406) imply:
% 261.16/41.74 | | | | | | | (2418) all_2213_0 = all_713_1
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2361), (2406) imply:
% 261.16/41.74 | | | | | | | (2419) all_2227_0 = all_2213_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2419) implies:
% 261.16/41.74 | | | | | | | (2420) all_2227_0 = all_2213_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2415), (2417) imply:
% 261.16/41.74 | | | | | | | (2421) all_2293_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2421) implies:
% 261.16/41.74 | | | | | | | (2422) all_2293_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2412), (2422) imply:
% 261.16/41.74 | | | | | | | (2423) all_2287_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | SIMP: (2423) implies:
% 261.16/41.74 | | | | | | | (2424) all_2287_0 = all_2205_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2358), (2359) imply:
% 261.16/41.74 | | | | | | | (2425) all_2273_0 = all_2227_0
% 261.16/41.74 | | | | | | |
% 261.16/41.74 | | | | | | | COMBINE_EQS: (2358), (2410) imply:
% 261.16/41.75 | | | | | | | (2426) all_2287_0 = all_2273_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | SIMP: (2426) implies:
% 261.16/41.75 | | | | | | | (2427) all_2287_0 = all_2273_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | COMBINE_EQS: (2424), (2427) imply:
% 261.16/41.75 | | | | | | | (2428) all_2273_0 = all_2205_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | SIMP: (2428) implies:
% 261.16/41.75 | | | | | | | (2429) all_2273_0 = all_2205_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | COMBINE_EQS: (2425), (2429) imply:
% 261.16/41.75 | | | | | | | (2430) all_2227_0 = all_2205_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | SIMP: (2430) implies:
% 261.16/41.75 | | | | | | | (2431) all_2227_0 = all_2205_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | COMBINE_EQS: (2357), (2420) imply:
% 261.16/41.75 | | | | | | | (2432) all_2219_0 = all_2213_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | COMBINE_EQS: (2357), (2431) imply:
% 261.16/41.75 | | | | | | | (2433) all_2219_0 = all_2205_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | COMBINE_EQS: (2432), (2433) imply:
% 261.16/41.75 | | | | | | | (2434) all_2213_0 = all_2205_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | SIMP: (2434) implies:
% 261.16/41.75 | | | | | | | (2435) all_2213_0 = all_2205_0
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | COMBINE_EQS: (2418), (2435) imply:
% 261.16/41.75 | | | | | | | (2436) all_2205_0 = all_713_1
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | REDUCE: (2300), (2382) imply:
% 261.16/41.75 | | | | | | | (2437) $i(all_1022_1)
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | REDUCE: (2295), (2404) imply:
% 261.16/41.75 | | | | | | | (2438) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | all_1950_0, all_713_0)
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | BETA: splitting (2338) gives:
% 261.16/41.75 | | | | | | |
% 261.16/41.75 | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | (2439) ~ (all_1022_1 = all_1022_2)
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | BETA: splitting (2344) gives:
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | (2440) ~ (all_1950_0 = all_713_0)
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | BETA: splitting (2274) gives:
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | (2441) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | v_r____, all_1022_1)
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | GROUND_INST: instantiating (2) with all_648_0, all_1022_1,
% 261.16/41.75 | | | | | | | | | | v_r____, simplifying with (245), (256), (1815),
% 261.16/41.75 | | | | | | | | | | (1890), (2437), (2441) gives:
% 261.16/41.75 | | | | | | | | | | (2442) $false
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | CLOSE: (2442) is inconsistent.
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | (2443) ? [v0: $i] :
% 261.16/41.75 | | | | | | | | | | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | v0 & $i(v0) & ~
% 261.16/41.75 | | | | | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | v0, all_713_0))
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | DELTA: instantiating (2443) with fresh symbol all_2449_0
% 261.16/41.75 | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | (2444) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | all_2449_0 & $i(all_2449_0) & ~
% 261.16/41.75 | | | | | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | all_2449_0, all_713_0)
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | ALPHA: (2444) implies:
% 261.16/41.75 | | | | | | | | | | (2445) ~
% 261.16/41.75 | | | | | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | all_2449_0, all_713_0)
% 261.16/41.75 | | | | | | | | | | (2446) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | all_2449_0
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | BETA: splitting (2337) gives:
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | (2447) all_1022_1 = all_1022_2
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | REDUCE: (2439), (2447) imply:
% 261.16/41.75 | | | | | | | | | | | (2448) $false
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | CLOSE: (2448) is inconsistent.
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | (2449) ~ (all_2359_0 = all_713_0) &
% 261.16/41.75 | | | | | | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | all_2359_0 & $i(all_2359_0)
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | ALPHA: (2449) implies:
% 261.16/41.75 | | | | | | | | | | | (2450) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | all_2359_0
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | BETA: splitting (2343) gives:
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | (2451) all_1950_0 = all_713_0
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | REDUCE: (2440), (2451) imply:
% 261.16/41.75 | | | | | | | | | | | | (2452) $false
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | CLOSE: (2452) is inconsistent.
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | (2453) ~ (all_2366_0 = all_713_0) &
% 261.16/41.75 | | | | | | | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | all_2366_0 & $i(all_2366_0)
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | ALPHA: (2453) implies:
% 261.16/41.75 | | | | | | | | | | | | (2454) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | all_2366_0
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_713_1, all_2449_0,
% 261.16/41.75 | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (295), (2446)
% 261.16/41.75 | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | (2455) all_2449_0 = all_713_1
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_2366_0, all_2449_0,
% 261.16/41.75 | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (2446), (2454)
% 261.16/41.75 | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | (2456) all_2449_0 = all_2366_0
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_2359_0, all_2449_0,
% 261.16/41.75 | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (2446), (2450)
% 261.16/41.75 | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | (2457) all_2449_0 = all_2359_0
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | COMBINE_EQS: (2456), (2457) imply:
% 261.16/41.75 | | | | | | | | | | | | (2458) all_2366_0 = all_2359_0
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | COMBINE_EQS: (2455), (2456) imply:
% 261.16/41.75 | | | | | | | | | | | | (2459) all_2366_0 = all_713_1
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | COMBINE_EQS: (2458), (2459) imply:
% 261.16/41.75 | | | | | | | | | | | | (2460) all_2359_0 = all_713_1
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | REDUCE: (2445), (2455) imply:
% 261.16/41.75 | | | | | | | | | | | | (2461) ~
% 261.16/41.75 | | | | | | | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | all_713_1, all_713_0)
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | PRED_UNIFY: (2211), (2461) imply:
% 261.16/41.75 | | | | | | | | | | | | (2462) $false
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | CLOSE: (2462) is inconsistent.
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | End of split
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | End of split
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | End of split
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | (2463) all_1950_0 = all_713_0
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | REDUCE: (2255), (2463) imply:
% 261.16/41.75 | | | | | | | | | (2464) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | all_713_0, all_713_0)
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | PRED_UNIFY: (2257), (2464) imply:
% 261.16/41.75 | | | | | | | | | (2465) $false
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | CLOSE: (2465) is inconsistent.
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | End of split
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | (2466) all_1022_1 = all_1022_2
% 261.16/41.75 | | | | | | | | (2467) all_2359_0 = all_713_0 &
% 261.16/41.75 | | | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | all_713_0
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | ALPHA: (2467) implies:
% 261.16/41.75 | | | | | | | | (2468) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | all_713_0
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | REDUCE: (2228), (2466) imply:
% 261.16/41.75 | | | | | | | | (2469) ~ (all_1022_2 = all_713_1)
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | REDUCE: (2275), (2466) imply:
% 261.16/41.75 | | | | | | | | (2470) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | all_1022_2, all_1022_2)
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | REDUCE: (2210), (2466) imply:
% 261.16/41.75 | | | | | | | | (2471) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | all_713_1, all_1022_2)
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | BETA: splitting (2065) gives:
% 261.16/41.75 | | | | | | | |
% 261.16/41.75 | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | (2472) ~ (all_1022_1 = all_713_0)
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | REDUCE: (2466), (2472) imply:
% 261.16/41.75 | | | | | | | | | (2473) ~ (all_1022_2 = all_713_0)
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | BETA: splitting (2348) gives:
% 261.16/41.75 | | | | | | | | |
% 261.16/41.75 | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | (2474) all_1303_0 = all_1022_2
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | COMBINE_EQS: (1769), (2474) imply:
% 261.16/41.75 | | | | | | | | | | (2475) all_1022_2 = all_713_1
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | REDUCE: (2469), (2475) imply:
% 261.16/41.75 | | | | | | | | | | (2476) $false
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | CLOSE: (2476) is inconsistent.
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | (2477) ~ (all_2369_0 = v_r____) &
% 261.16/41.75 | | | | | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | all_2369_0 & $i(all_2369_0)
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | ALPHA: (2477) implies:
% 261.16/41.75 | | | | | | | | | | (2478) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | all_2369_0
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | BETA: splitting (2344) gives:
% 261.16/41.75 | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | (2479) ~ (all_1950_0 = all_713_0)
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | BETA: splitting (2064) gives:
% 261.16/41.75 | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | (2480) all_1022_1 = all_713_0
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | COMBINE_EQS: (2466), (2480) imply:
% 261.16/41.75 | | | | | | | | | | | | (2481) all_1022_2 = all_713_0
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | REDUCE: (2473), (2481) imply:
% 261.16/41.75 | | | | | | | | | | | | (2482) $false
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | CLOSE: (2482) is inconsistent.
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | (2483) ~ (all_2009_0 = all_1022_2) &
% 261.16/41.75 | | | | | | | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | all_2009_0 & $i(all_2009_0)
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | ALPHA: (2483) implies:
% 261.16/41.75 | | | | | | | | | | | | (2484) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | all_2009_0
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | BETA: splitting (2343) gives:
% 261.16/41.75 | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | (2485) all_1950_0 = all_713_0
% 261.16/41.75 | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | REDUCE: (2479), (2485) imply:
% 261.16/41.75 | | | | | | | | | | | | | (2486) $false
% 261.16/41.75 | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | CLOSE: (2486) is inconsistent.
% 261.16/41.75 | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | (2487) ~ (all_2366_0 = all_713_0) &
% 261.16/41.75 | | | | | | | | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | | all_2366_0 & $i(all_2366_0)
% 261.16/41.75 | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | ALPHA: (2487) implies:
% 261.16/41.75 | | | | | | | | | | | | | (2488) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | | all_2366_0
% 261.16/41.75 | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | BETA: splitting (2258) gives:
% 261.16/41.75 | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | (2489) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | v_r____, all_1022_1)
% 261.16/41.75 | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | REDUCE: (2466), (2489) imply:
% 261.16/41.75 | | | | | | | | | | | | | | (2490) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | v_r____, all_1022_2)
% 261.16/41.75 | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | BETA: splitting (2060) gives:
% 261.16/41.75 | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | (2491) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | | v_r____, all_1022_2)
% 261.16/41.75 | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | PRED_UNIFY: (2490), (2491) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | (2492) $false
% 261.16/41.75 | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | CLOSE: (2492) is inconsistent.
% 261.16/41.75 | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | (2493) ~ (all_2004_0 = v_r____)
% 261.16/41.75 | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | REDUCE: (2201), (2493) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | (2494) ~ (all_713_1 = v_r____)
% 261.16/41.75 | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | BETA: splitting (2341) gives:
% 261.16/41.75 | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | (2495) ~
% 261.16/41.75 | | | | | | | | | | | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | | | all_1022_2, all_1326_0)
% 261.16/41.75 | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | REDUCE: (1770), (2495) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | | (2496) ~
% 261.16/41.75 | | | | | | | | | | | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | | | all_1022_2, all_713_1)
% 261.16/41.75 | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | BETA: splitting (2350) gives:
% 261.16/41.75 | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | (2497) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | | | | all_1253_0, all_1022_2)
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | REDUCE: (1765), (2497) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | | | (2498) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | | | | all_713_1, all_1022_2)
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2471), (2498) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | | | (2499) $false
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | CLOSE: (2499) is inconsistent.
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | (2500) ~ (all_2370_0 = v_r____) &
% 261.16/41.75 | | | | | | | | | | | | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | | | | | | all_2370_0 & $i(all_2370_0)
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | ALPHA: (2500) implies:
% 261.16/41.75 | | | | | | | | | | | | | | | | | (2501) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | | | | | | all_2370_0
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | BETA: splitting (2340) gives:
% 261.16/41.75 | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | Case 1:
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2502) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | | | | | all_1022_2, all_1326_0)
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | REDUCE: (1770), (2502) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2503) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.75 | | | | | | | | | | | | | | | | | | all_1022_2, all_713_1)
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2496), (2503) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2504) $false
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | CLOSE: (2504) is inconsistent.
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | Case 2:
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2505) ~ (all_2365_0 = v_r____) &
% 261.16/41.75 | | | | | | | | | | | | | | | | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | | | | | | | all_2365_0 & $i(all_2365_0)
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | ALPHA: (2505) implies:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2506) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 261.16/41.75 | | | | | | | | | | | | | | | | | | all_2365_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_713_1, all_2009_0,
% 261.16/41.75 | | | | | | | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (295), (2484)
% 261.16/41.75 | | | | | | | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2507) all_2009_0 = all_713_1
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_2009_0, all_2365_0,
% 261.16/41.75 | | | | | | | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (2484), (2506)
% 261.16/41.75 | | | | | | | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2508) all_2365_0 = all_2009_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_2365_0, all_2366_0,
% 261.16/41.75 | | | | | | | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (2488), (2506)
% 261.16/41.75 | | | | | | | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2509) all_2366_0 = all_2365_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_2366_0, all_2369_0,
% 261.16/41.75 | | | | | | | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (2478), (2488)
% 261.16/41.75 | | | | | | | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2510) all_2369_0 = all_2366_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_2369_0, all_2370_0,
% 261.16/41.75 | | | | | | | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (2478), (2501)
% 261.16/41.75 | | | | | | | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2511) all_2370_0 = all_2369_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (248) with all_713_0, all_2370_0,
% 261.16/41.75 | | | | | | | | | | | | | | | | | | tc_RealDef_Oreal, simplifying with (2468), (2501)
% 261.16/41.75 | | | | | | | | | | | | | | | | | | gives:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2512) all_2370_0 = all_713_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2511), (2512) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2513) all_2369_0 = all_713_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | SIMP: (2513) implies:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2514) all_2369_0 = all_713_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2510), (2514) imply:
% 261.16/41.75 | | | | | | | | | | | | | | | | | | (2515) all_2366_0 = all_713_0
% 261.16/41.75 | | | | | | | | | | | | | | | | | |
% 261.16/41.75 | | | | | | | | | | | | | | | | | | SIMP: (2515) implies:
% 261.16/41.76 | | | | | | | | | | | | | | | | | | (2516) all_2366_0 = all_713_0
% 261.16/41.76 | | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2509), (2516) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | | | (2517) all_2365_0 = all_713_0
% 261.16/41.76 | | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | | SIMP: (2517) implies:
% 261.16/41.76 | | | | | | | | | | | | | | | | | | (2518) all_2365_0 = all_713_0
% 261.16/41.76 | | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2508), (2518) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | | | (2519) all_2009_0 = all_713_0
% 261.16/41.76 | | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | | SIMP: (2519) implies:
% 261.16/41.76 | | | | | | | | | | | | | | | | | | (2520) all_2009_0 = all_713_0
% 261.16/41.76 | | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2507), (2520) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | | | (2521) all_713_0 = all_713_1
% 261.16/41.76 | | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | | REDUCE: (294), (2521) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | | | (2522) $false
% 261.16/41.76 | | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | | CLOSE: (2522) is inconsistent.
% 261.16/41.76 | | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | Case 2:
% 261.16/41.76 | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | (2523) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | | | all_1022_2, all_1326_0)
% 261.16/41.76 | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | REDUCE: (1770), (2523) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | (2524) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | | | all_1022_2, all_713_1)
% 261.16/41.76 | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | BETA: splitting (2057) gives:
% 261.16/41.76 | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | Case 1:
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | (2525) ~
% 261.16/41.76 | | | | | | | | | | | | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | | | | all_1022_2, all_2002_0)
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | REDUCE: (2200), (2525) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | | (2526) ~
% 261.16/41.76 | | | | | | | | | | | | | | | | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | | | | all_1022_2, all_713_1)
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2524), (2526) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | | (2527) $false
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | CLOSE: (2527) is inconsistent.
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | Case 2:
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | (2528) all_2002_0 = v_r____
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2200), (2528) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | | (2529) all_713_1 = v_r____
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | REDUCE: (2494), (2529) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | | | (2530) $false
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | | CLOSE: (2530) is inconsistent.
% 261.16/41.76 | | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | Case 2:
% 261.16/41.76 | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | (2531) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | v_r____, all_1022_1)
% 261.16/41.76 | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | REDUCE: (2466), (2531) imply:
% 261.16/41.76 | | | | | | | | | | | | | | (2532) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | v_r____, all_1022_2)
% 261.16/41.76 | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | BETA: splitting (2259) gives:
% 261.16/41.76 | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | Case 1:
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | (2533) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | | v_r____, all_1022_2)
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | PRED_UNIFY: (2532), (2533) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | (2534) $false
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | CLOSE: (2534) is inconsistent.
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | Case 2:
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | (2535) all_1022_2 = v_r____
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | REDUCE: (2470), (2535) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | (2536) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | | v_r____, v_r____)
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | REDUCE: (2532), (2535) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | (2537) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | | | | | v_r____, v_r____)
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | PRED_UNIFY: (2536), (2537) imply:
% 261.16/41.76 | | | | | | | | | | | | | | | (2538) $false
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | | CLOSE: (2538) is inconsistent.
% 261.16/41.76 | | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | Case 2:
% 261.16/41.76 | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | (2539) all_1950_0 = all_713_0
% 261.16/41.76 | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | REDUCE: (2255), (2539) imply:
% 261.16/41.76 | | | | | | | | | | | (2540) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | | | all_713_0, all_713_0)
% 261.16/41.76 | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | PRED_UNIFY: (2257), (2540) imply:
% 261.16/41.76 | | | | | | | | | | | (2541) $false
% 261.16/41.76 | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | | CLOSE: (2541) is inconsistent.
% 261.16/41.76 | | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | | |
% 261.16/41.76 | | | | | | | | | End of split
% 261.16/41.76 | | | | | | | | |
% 261.16/41.76 | | | | | | | | Case 2:
% 261.16/41.76 | | | | | | | | |
% 261.16/41.76 | | | | | | | | | (2542) all_1022_1 = all_713_0
% 261.16/41.76 | | | | | | | | |
% 261.16/41.76 | | | | | | | | | COMBINE_EQS: (2466), (2542) imply:
% 261.16/41.76 | | | | | | | | | (2543) all_1022_2 = all_713_0
% 261.16/41.76 | | | | | | | | |
% 261.16/41.76 | | | | | | | | | REDUCE: (2470), (2543) imply:
% 261.16/41.76 | | | | | | | | | (2544) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 261.16/41.76 | | | | | | | | | all_713_0, all_713_0)
% 261.16/41.76 | | | | | | | | |
% 261.16/41.76 | | | | | | | | | PRED_UNIFY: (2257), (2544) imply:
% 261.16/41.76 | | | | | | | | | (2545) $false
% 261.16/41.76 | | | | | | | | |
% 261.16/41.76 | | | | | | | | | CLOSE: (2545) is inconsistent.
% 261.16/41.76 | | | | | | | | |
% 261.37/41.76 | | | | | | | | End of split
% 261.37/41.76 | | | | | | | |
% 261.37/41.76 | | | | | | | End of split
% 261.37/41.76 | | | | | | |
% 261.37/41.76 | | | | | | End of split
% 261.37/41.76 | | | | | |
% 261.37/41.77 | | | | | End of split
% 261.37/41.77 | | | | |
% 261.37/41.77 | | | | End of split
% 261.37/41.77 | | | |
% 261.37/41.77 | | | Case 2:
% 261.37/41.77 | | | |
% 261.37/41.77 | | | | (2546) all_2016_0 = all_1022_1
% 261.37/41.77 | | | | (2547) all_1022_1 = all_713_0 & all_1022_2 = all_713_0
% 261.37/41.77 | | | |
% 261.37/41.77 | | | | ALPHA: (2547) implies:
% 261.37/41.77 | | | | (2548) all_1022_1 = all_713_0
% 261.37/41.77 | | | |
% 261.37/41.77 | | | | COMBINE_EQS: (2202), (2546) imply:
% 261.37/41.77 | | | | (2549) all_1022_1 = all_713_1
% 261.37/41.77 | | | |
% 261.37/41.77 | | | | COMBINE_EQS: (2548), (2549) imply:
% 261.37/41.77 | | | | (2550) all_713_0 = all_713_1
% 261.37/41.77 | | | |
% 261.37/41.77 | | | | REDUCE: (294), (2550) imply:
% 261.37/41.77 | | | | (2551) $false
% 261.37/41.77 | | | |
% 261.37/41.77 | | | | CLOSE: (2551) is inconsistent.
% 261.37/41.77 | | | |
% 261.37/41.77 | | | End of split
% 261.37/41.77 | | |
% 261.37/41.77 | | End of split
% 261.37/41.77 | |
% 261.37/41.77 | End of split
% 261.37/41.77 |
% 261.37/41.77 End of proof
% 261.37/41.77 % SZS output end Proof for theBenchmark
% 261.37/41.77
% 261.37/41.77 41168ms
%------------------------------------------------------------------------------