TSTP Solution File: SWW275+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW275+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:49:40 EDT 2023
% Result : Theorem 83.08s 11.79s
% Output : Proof 222.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW275+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun Aug 27 18:30:30 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.51 ________ _____
% 0.14/0.51 ___ __ \_________(_)________________________________
% 0.14/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.51
% 0.14/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.51 (2023-06-19)
% 0.14/0.51
% 0.14/0.51 (c) Philipp Rümmer, 2009-2023
% 0.14/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.51 Amanda Stjerna.
% 0.14/0.51 Free software under BSD-3-Clause.
% 0.14/0.51
% 0.14/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.51
% 0.14/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.52 Running up to 7 provers in parallel.
% 0.14/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 17.65/3.10 Prover 6: Preprocessing ...
% 17.65/3.11 Prover 0: Preprocessing ...
% 18.65/3.21 Prover 5: Preprocessing ...
% 19.03/3.26 Prover 3: Preprocessing ...
% 19.03/3.28 Prover 2: Preprocessing ...
% 19.03/3.35 Prover 4: Preprocessing ...
% 19.03/3.38 Prover 1: Preprocessing ...
% 54.00/7.92 Prover 1: Warning: ignoring some quantifiers
% 54.00/7.95 Prover 3: Warning: ignoring some quantifiers
% 55.15/8.10 Prover 3: Constructing countermodel ...
% 55.80/8.15 Prover 1: Constructing countermodel ...
% 56.28/8.21 Prover 6: Proving ...
% 64.38/9.30 Prover 4: Warning: ignoring some quantifiers
% 66.71/9.61 Prover 4: Constructing countermodel ...
% 71.10/10.20 Prover 5: Proving ...
% 72.33/10.35 Prover 0: Proving ...
% 77.69/11.09 Prover 2: Proving ...
% 78.89/11.25 Prover 2: stopped
% 78.89/11.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 83.08/11.79 Prover 3: proved (11258ms)
% 83.08/11.79
% 83.08/11.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 83.08/11.79
% 83.08/11.79 Prover 6: stopped
% 83.08/11.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 83.08/11.80 Prover 5: stopped
% 83.08/11.81 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 83.08/11.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 83.70/11.87 Prover 0: stopped
% 84.07/11.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 88.66/12.51 Prover 7: Preprocessing ...
% 92.52/13.05 Prover 8: Preprocessing ...
% 94.26/13.26 Prover 10: Preprocessing ...
% 94.26/13.27 Prover 11: Preprocessing ...
% 94.26/13.31 Prover 13: Preprocessing ...
% 104.24/14.56 Prover 7: Warning: ignoring some quantifiers
% 104.74/14.62 Prover 10: Warning: ignoring some quantifiers
% 105.21/14.74 Prover 8: Warning: ignoring some quantifiers
% 107.63/15.02 Prover 10: Constructing countermodel ...
% 107.63/15.04 Prover 7: Constructing countermodel ...
% 108.80/15.14 Prover 8: Constructing countermodel ...
% 111.94/15.68 Prover 13: Warning: ignoring some quantifiers
% 114.22/15.88 Prover 1: stopped
% 114.52/15.89 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 114.94/15.99 Prover 13: Constructing countermodel ...
% 116.82/16.26 Prover 11: Warning: ignoring some quantifiers
% 121.89/16.94 Prover 11: Constructing countermodel ...
% 124.20/17.21 Prover 16: Preprocessing ...
% 137.14/18.90 Prover 16: Warning: ignoring some quantifiers
% 137.94/19.03 Prover 16: Constructing countermodel ...
% 147.90/20.42 Prover 13: stopped
% 147.90/20.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 149.25/20.71 Prover 16: stopped
% 152.01/21.01 Prover 19: Preprocessing ...
% 162.38/22.41 Prover 19: Warning: ignoring some quantifiers
% 163.54/22.59 Prover 19: Constructing countermodel ...
% 170.03/23.45 Prover 19: stopped
% 200.82/27.86 Prover 4: stopped
% 215.27/30.27 Prover 10: Found proof (size 2186)
% 215.27/30.27 Prover 10: proved (18465ms)
% 215.27/30.28 Prover 11: stopped
% 215.27/30.28 Prover 8: stopped
% 216.26/30.56 Prover 7: stopped
% 216.26/30.56
% 216.26/30.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 216.26/30.56
% 219.96/33.99 % SZS output start Proof for theBenchmark
% 219.96/34.01 Assumptions after simplification:
% 219.96/34.01 ---------------------------------
% 219.96/34.01
% 219.96/34.01 (arity_Complex__Ocomplex__Groups_Ogroup__add)
% 219.96/34.02 $i(tc_Complex_Ocomplex) & class_Groups_Ogroup__add(tc_Complex_Ocomplex)
% 219.96/34.02
% 219.96/34.02 (arity_Complex__Ocomplex__Groups_Ozero)
% 219.96/34.02 $i(tc_Complex_Ocomplex) & class_Groups_Ozero(tc_Complex_Ocomplex)
% 219.96/34.02
% 219.96/34.02 (arity_Complex__Ocomplex__Int_Oring__char__0)
% 219.96/34.02 $i(tc_Complex_Ocomplex) & class_Int_Oring__char__0(tc_Complex_Ocomplex)
% 219.96/34.02
% 219.96/34.02 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1)
% 219.96/34.02 $i(tc_Complex_Ocomplex) & class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
% 219.96/34.02
% 219.96/34.02 (arity_Complex__Ocomplex__Rings_Oidom)
% 219.96/34.02 $i(tc_Complex_Ocomplex) & class_Rings_Oidom(tc_Complex_Ocomplex)
% 219.96/34.02
% 219.96/34.02 (arity_Complex__Ocomplex__Rings_Ozero__neq__one)
% 219.96/34.02 $i(tc_Complex_Ocomplex) & class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
% 219.96/34.02
% 219.96/34.02 (arity_Int__Oint__Groups_Ogroup__add)
% 219.96/34.02 $i(tc_Int_Oint) & class_Groups_Ogroup__add(tc_Int_Oint)
% 219.96/34.02
% 219.96/34.02 (arity_Int__Oint__Groups_Oordered__ab__group__add)
% 219.96/34.02 $i(tc_Int_Oint) & class_Groups_Oordered__ab__group__add(tc_Int_Oint)
% 219.96/34.02
% 219.96/34.02 (arity_Int__Oint__Rings_Odvd)
% 219.96/34.02 $i(tc_Int_Oint) & class_Rings_Odvd(tc_Int_Oint)
% 219.96/34.02
% 219.96/34.02 (arity_Int__Oint__Rings_Olinordered__semidom)
% 219.96/34.02 $i(tc_Int_Oint) & class_Rings_Olinordered__semidom(tc_Int_Oint)
% 219.96/34.02
% 219.96/34.02 (arity_Nat__Onat__Power_Opower)
% 219.96/34.02 $i(tc_Nat_Onat) & class_Power_Opower(tc_Nat_Onat)
% 219.96/34.02
% 219.96/34.02 (arity_Nat__Onat__Rings_Ocomm__semiring__1)
% 219.96/34.02 $i(tc_Nat_Onat) & class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
% 219.96/34.02
% 219.96/34.02 (arity_Nat__Onat__Rings_Olinordered__semidom)
% 219.96/34.02 $i(tc_Nat_Onat) & class_Rings_Olinordered__semidom(tc_Nat_Onat)
% 219.96/34.02
% 219.96/34.02 (arity_Nat__Onat__Rings_Ozero__neq__one)
% 219.96/34.02 $i(tc_Nat_Onat) & class_Rings_Ozero__neq__one(tc_Nat_Onat)
% 219.96/34.02
% 219.96/34.02 (arity_Polynomial__Opoly__Groups_Omonoid__mult)
% 219.96/34.04 ! [v0: $i] : ! [v1: $i] : ( ~ (tc_Polynomial_Opoly(v0) = v1) | ~ $i(v0) |
% 219.96/34.04 ~ class_Rings_Ocomm__semiring__1(v0) | class_Groups_Omonoid__mult(v1))
% 219.96/34.04
% 219.96/34.04 (conj_0)
% 219.96/34.05 $i(v_r____) & $i(v_pa____) & $i(v_a____) & $i(tc_Complex_Ocomplex) &
% 219.96/34.05 $i(v_na____) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 219.96/34.05 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 219.96/34.05 : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 219.96/34.05 [v14: $i] : ? [v15: $i] : ? [v16: $i] : ( ~ (v16 = v9) &
% 219.96/34.05 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, v11) = v14 &
% 219.96/34.05 c_Groups_Otimes__class_Otimes(v0) = v10 & c_Power_Opower__class_Opower(v0) =
% 219.96/34.05 v3 & c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v4 &
% 219.96/34.05 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v5 &
% 219.96/34.05 c_Polynomial_OpCons(tc_Complex_Ocomplex, v5, v1) = v6 &
% 219.96/34.05 c_Polynomial_OpCons(tc_Complex_Ocomplex, v4, v6) = v7 &
% 219.96/34.05 c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v11 &
% 219.96/34.05 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 219.96/34.05 c_Groups_Ozero__class_Ozero(v0) = v1 & hAPP(v13, v15) = v16 & hAPP(v10, v12)
% 219.96/34.05 = v13 & hAPP(v8, v14) = v15 & hAPP(v8, v11) = v12 & hAPP(v8, v_na____) = v9
% 219.96/34.05 & hAPP(v3, v7) = v8 & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 219.96/34.05 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 219.96/34.05 $i(v3) & $i(v1) & $i(v0) & ( ~ (v1 = v_r____) |
% 219.96/34.05 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & ~
% 219.96/34.05 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v_na____))))
% 219.96/34.05
% 219.96/34.05 (fact_Divides_Otransfer__nat__int__function__closures_I1_J)
% 219.96/34.05 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 219.96/34.05 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 219.96/34.05 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 219.96/34.05 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ~
% 219.96/34.05 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) |
% 219.96/34.05 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 219.96/34.05
% 219.96/34.05 (fact_IH)
% 219.96/34.05 $i(tc_Complex_Ocomplex) & $i(v_na____) & $i(tc_Nat_Onat) & ? [v0: $i] : ?
% 219.96/34.05 [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(v2) = v3
% 219.96/34.05 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v2 &
% 219.96/34.05 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 219.96/34.05 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v3) & $i(v2) & $i(v1) &
% 219.96/34.05 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 219.96/34.05 : ! [v9: $i] : (v4 = v1 | ~ (c_Polynomial_Opoly(tc_Complex_Ocomplex, v5) =
% 219.96/34.05 v7) | ~ (hAPP(v8, v4) = v9) | ~ (hAPP(v3, v6) = v8) | ~ $i(v6) | ~
% 219.96/34.05 $i(v5) | ~ $i(v4) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4,
% 219.96/34.05 v_na____) | c_Rings_Odvd__class_Odvd(v2, v5, v9) | ? [v10: $i] : ?
% 219.96/34.05 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ($i(v12) & ((v13
% 219.96/34.05 = v0 & ~ (v14 = v0) & c_Polynomial_Opoly(tc_Complex_Ocomplex, v6) =
% 219.96/34.05 v10 & hAPP(v10, v12) = v14 & hAPP(v7, v12) = v0 & $i(v14) & $i(v10))
% 219.96/34.05 | ( ~ (v11 = v4) & c_Polynomial_Odegree(tc_Complex_Ocomplex, v5) = v11
% 219.96/34.05 & $i(v11))))))
% 219.96/34.05
% 219.96/34.05 (fact_Nat_Oadd__0__right)
% 219.96/34.06 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 219.96/34.06 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 219.96/34.06 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)))
% 219.96/34.06
% 219.96/34.06 (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)
% 219.96/34.06 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 219.96/34.06 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 219.96/34.06 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 219.96/34.06 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ~
% 219.96/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) |
% 219.96/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 219.96/34.06
% 219.96/34.06 (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)
% 219.96/34.06 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 219.96/34.06 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 219.96/34.06 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 219.96/34.06 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) |
% 219.96/34.06 ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 219.96/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) | ~
% 219.96/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 219.96/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v5)))
% 219.96/34.06
% 219.96/34.06 (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J)
% 219.96/34.06 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 219.96/34.06 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 219.96/34.06 (c_Nat__Transfer_Otsub(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 219.96/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ~
% 219.96/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) |
% 219.96/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 219.96/34.06
% 219.96/34.06 (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J)
% 220.25/34.06 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.25/34.06 (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 &
% 220.25/34.06 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.25/34.06 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) |
% 220.25/34.06 ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.25/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) |
% 220.25/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v5)))
% 220.25/34.06
% 220.25/34.06 (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J)
% 220.25/34.06 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.25/34.06 & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v0))
% 220.25/34.06
% 220.25/34.06 (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)
% 220.25/34.06 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.25/34.06 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 220.25/34.06 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 220.25/34.06 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1))
% 220.25/34.06
% 220.25/34.06 (fact_One__nat__def)
% 220.25/34.07 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 &
% 220.25/34.07 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.25/34.07 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0))
% 220.25/34.07
% 220.25/34.07 (fact_Suc__diff__1)
% 220.25/34.07 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.25/34.07 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 220.25/34.07 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.25/34.07 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 220.25/34.07 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 220.25/34.07 v0, v2) | c_Nat_OSuc(v3) = v2))
% 220.25/34.07
% 220.25/34.07 (fact_Suc__eq__plus1)
% 220.25/34.07 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.25/34.07 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 220.25/34.07 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) |
% 220.25/34.07 (c_Nat_OSuc(v1) = v2 & $i(v2))))
% 220.25/34.07
% 220.25/34.07 (fact_Suc__eq__plus1__left)
% 220.25/34.07 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.25/34.07 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 220.25/34.07 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) |
% 220.25/34.07 (c_Nat_OSuc(v1) = v2 & $i(v2))))
% 220.25/34.07
% 220.25/34.07 (fact_Suc__neq__Zero)
% 220.25/34.07 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.25/34.07 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 220.25/34.07
% 220.25/34.07 (fact_Suc__not__Zero)
% 220.25/34.07 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.25/34.07 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 220.25/34.07
% 220.25/34.07 (fact_Suc__pred)
% 220.25/34.07 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 220.25/34.07 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.25/34.07 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 220.25/34.07 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 220.25/34.07 v0, v2) | c_Nat_OSuc(v3) = v2))
% 220.25/34.07
% 220.25/34.07 (fact_Suc__pred_H)
% 220.25/34.07 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.25/34.07 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 220.25/34.07 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.25/34.07 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 220.25/34.07 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 220.25/34.07 v0, v2) | c_Nat_OSuc(v3) = v2))
% 220.25/34.07
% 220.25/34.07 (fact_Zero__neq__Suc)
% 220.25/34.08 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.25/34.08 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 220.25/34.08
% 220.25/34.08 (fact_Zero__not__Suc)
% 220.25/34.08 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.25/34.08 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 220.25/34.08
% 220.25/34.08 (fact__096EX_Ak_O_As_A_061_A_091_058k_058_093_096)
% 220.25/34.08 $i(v_s____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.25/34.08 $i] : (c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v1) = v_s____ &
% 220.25/34.08 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.25/34.08 c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v2) & $i(v1) & $i(v0))
% 220.25/34.08
% 220.25/34.08 (fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096)
% 220.25/34.08 $i(v_a____) & $i(v_qa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 220.25/34.08 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 220.25/34.08 (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v1 &
% 220.25/34.08 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 &
% 220.25/34.08 c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v3) = v4 &
% 220.25/34.08 c_Polynomial_OpCons(tc_Complex_Ocomplex, v1, v4) = v5 &
% 220.25/34.08 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.25/34.08 c_Groups_Ozero__class_Ozero(v0) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 220.25/34.08 $i(v1) & $i(v0) & c_Rings_Odvd__class_Odvd(v0, v5, v_qa____))
% 220.25/34.08
% 220.25/34.08 (fact__096_B_Bthesis_O_A_I_B_Bk_O_As_A_061_A_091_058k_058_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 220.25/34.08 $i(v_s____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.25/34.08 $i] : (c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v1) = v_s____ &
% 220.25/34.08 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.25/34.08 c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v2) & $i(v1) & $i(v0))
% 220.25/34.08
% 220.25/34.08 (fact__096_B_Bthesis_O_A_I_B_Br_O_Aq_A_061_A_091_058_N_Aa_M_A1_058_093_A_K_Ar_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 220.25/34.08 $i(v_a____) & $i(v_qa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 220.25/34.08 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 220.25/34.08 ? [v7: $i] : ? [v8: $i] : (c_Groups_Otimes__class_Otimes(v0) = v1 &
% 220.25/34.08 c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v2 &
% 220.25/34.08 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 220.25/34.08 c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 220.25/34.08 c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 220.25/34.08 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.25/34.08 c_Groups_Ozero__class_Ozero(v0) = v4 & hAPP(v7, v8) = v_qa____ & hAPP(v1,
% 220.25/34.08 v6) = v7 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 220.25/34.08 $i(v1) & $i(v0))
% 220.25/34.08
% 220.25/34.08 (fact__096_B_Bthesis_O_A_I_B_Bs_O_Ap_A_061_A_091_058_N_Aa_M_A1_058_093_A_094_Aorder_Aa_Ap_A_K_As_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 220.25/34.09 $i(v_pa____) & $i(v_a____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 220.25/34.09 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 220.25/34.09 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 220.25/34.09 [v12: $i] : (c_Groups_Otimes__class_Otimes(v0) = v1 &
% 220.25/34.09 c_Power_Opower__class_Opower(v0) = v2 &
% 220.25/34.09 c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v3 &
% 220.25/34.09 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v4 &
% 220.25/34.09 c_Polynomial_OpCons(tc_Complex_Ocomplex, v4, v5) = v6 &
% 220.25/34.09 c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v6) = v7 &
% 220.25/34.09 c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v9 &
% 220.25/34.09 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.25/34.09 c_Groups_Ozero__class_Ozero(v0) = v5 & hAPP(v11, v12) = v_pa____ & hAPP(v8,
% 220.25/34.09 v9) = v10 & hAPP(v2, v7) = v8 & hAPP(v1, v10) = v11 & $i(v12) & $i(v11) &
% 220.25/34.09 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 220.25/34.09 $i(v2) & $i(v1) & $i(v0))
% 220.25/34.09
% 220.25/34.09 (fact__096order_Aa_Ap_A_060_061_An_096)
% 220.25/34.09 $i(v_pa____) & $i(v_a____) & $i(tc_Complex_Ocomplex) & $i(v_na____) &
% 220.25/34.09 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Polynomial_Oorder(tc_Complex_Ocomplex,
% 220.25/34.09 v_a____, v_pa____) = v0 & $i(v0) &
% 220.25/34.09 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v_na____))
% 220.25/34.09
% 220.25/34.09 (fact_a)
% 220.25/34.09 $i(v_pa____) & $i(v_a____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 220.25/34.09 $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 &
% 220.25/34.09 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & hAPP(v0, v_a____) =
% 220.25/34.09 v1 & $i(v1) & $i(v0))
% 220.25/34.09
% 220.25/34.09 (fact_add1__zle__eq)
% 220.25/34.09 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 &
% 220.25/34.09 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.25/34.09 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v0) = v3) | ~ $i(v2) | ~
% 220.25/34.09 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 220.25/34.09 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1)) & ! [v1: $i] : !
% 220.25/34.09 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2,
% 220.25/34.09 v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.25/34.09 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1) |
% 220.25/34.09 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)))
% 220.25/34.09
% 220.25/34.09 (fact_add__eq__if)
% 220.25/34.09 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.25/34.09 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 220.25/34.09 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.25/34.09 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | ~
% 220.25/34.09 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = v5) | ~
% 220.25/34.09 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ $i(v3) | ~
% 220.25/34.09 $i(v2) | ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) =
% 220.25/34.09 v6 & c_Nat_OSuc(v5) = v6 & $i(v6))) & ! [v2: $i] : ! [v3: $i] : (v3 =
% 220.25/34.09 v2 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = v3) | ~
% 220.25/34.09 $i(v2)))
% 220.25/34.09
% 220.25/34.09 (fact_add__eq__self__zero)
% 220.40/34.09 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.09 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 220.40/34.09 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ $i(v2) | ~
% 220.40/34.09 $i(v1)))
% 220.40/34.09
% 220.40/34.09 (fact_add__gr__0)
% 220.40/34.09 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.09 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.09 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.09 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 220.40/34.09 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 220.40/34.09 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i] : !
% 220.40/34.09 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2,
% 220.40/34.09 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.09 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 220.40/34.09 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : !
% 220.40/34.09 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2,
% 220.40/34.09 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.09 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) |
% 220.40/34.09 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 220.40/34.09
% 220.40/34.09 (fact_add__is__0)
% 220.40/34.10 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.10 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 220.40/34.10 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~
% 220.40/34.10 $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 220.40/34.10 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~
% 220.40/34.10 $i(v1)) & ! [v1: $i] : (v1 = v0 | ~
% 220.40/34.10 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1)))
% 220.40/34.10
% 220.40/34.10 (fact_add__is__1)
% 220.40/34.10 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 220.40/34.10 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.10 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 220.40/34.10 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 220.40/34.10 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~
% 220.40/34.10 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 220.40/34.10 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~
% 220.40/34.10 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 220.40/34.10 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~
% 220.40/34.10 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 220.40/34.10 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~
% 220.40/34.10 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] :
% 220.40/34.10 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2)))
% 220.40/34.10
% 220.40/34.10 (fact_ap_I1_J)
% 220.40/34.10 $i(v_pa____) & $i(v_a____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 220.40/34.10 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 220.40/34.10 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (c_Power_Opower__class_Opower(v0) =
% 220.40/34.10 v1 & c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v2 &
% 220.40/34.10 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 220.40/34.10 c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 220.40/34.10 c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 220.40/34.10 c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v8 &
% 220.40/34.10 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.40/34.10 c_Groups_Ozero__class_Ozero(v0) = v4 & hAPP(v7, v8) = v9 & hAPP(v1, v6) = v7
% 220.40/34.10 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 220.40/34.10 $i(v1) & $i(v0) & c_Rings_Odvd__class_Odvd(v0, v9, v_pa____))
% 220.40/34.10
% 220.40/34.10 (fact_ap_I2_J)
% 220.40/34.10 $i(v_pa____) & $i(v_a____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 220.40/34.10 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 220.40/34.10 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : (c_Nat_OSuc(v8) = v9 &
% 220.40/34.10 c_Power_Opower__class_Opower(v0) = v1 &
% 220.40/34.10 c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v2 &
% 220.40/34.10 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 220.40/34.10 c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 220.40/34.10 c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 220.40/34.10 c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v8 &
% 220.40/34.10 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.40/34.10 c_Groups_Ozero__class_Ozero(v0) = v4 & hAPP(v7, v9) = v10 & hAPP(v1, v6) =
% 220.40/34.10 v7 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 220.40/34.10 & $i(v2) & $i(v1) & $i(v0) & ~ c_Rings_Odvd__class_Odvd(v0, v10, v_pa____))
% 220.40/34.10
% 220.40/34.10 (fact_assms_I1_J)
% 220.40/34.10 $i(v_q) & $i(v_p) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ?
% 220.40/34.10 [v2: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q) = v2 &
% 220.40/34.10 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p) = v0 &
% 220.40/34.10 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v2) & $i(v1) &
% 220.40/34.10 $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v2, v3) = v4) | ~
% 220.40/34.10 $i(v3) | ? [v5: $i] : ( ~ (v5 = v1) & hAPP(v0, v3) = v5 & $i(v5))))
% 220.40/34.10
% 220.40/34.10 (fact_assms_I2_J)
% 220.40/34.10 c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v_n & $i(v_p) &
% 220.40/34.10 $i(tc_Complex_Ocomplex) & $i(v_n)
% 220.40/34.10
% 220.40/34.10 (fact_assms_I3_J)
% 220.40/34.10 $i(v_n) & $i(tc_Nat_Onat) & ? [v0: $i] : ( ~ (v0 = v_n) &
% 220.40/34.10 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0))
% 220.40/34.10
% 220.40/34.11 (fact_calculation)
% 220.40/34.11 $i(v_pa____) & $i(v_qa____) & $i(tc_Complex_Ocomplex) & $i(v_na____) & ? [v0:
% 220.40/34.11 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 220.40/34.11 (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & $i(v0) & (( ~ (v1 = v_qa____)
% 220.40/34.11 & c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1)) |
% 220.40/34.11 (c_Power_Opower__class_Opower(v0) = v2 & hAPP(v3, v_na____) = v4 &
% 220.40/34.11 hAPP(v2, v_qa____) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 220.40/34.11 c_Rings_Odvd__class_Odvd(v0, v_pa____, v4))))
% 220.40/34.11
% 220.40/34.11 (fact_coeff__1)
% 220.40/34.11 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.11 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.11 $i] : ! [v6: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v4) = v5) | ~
% 220.40/34.11 (c_Groups_Oone__class_Oone(v3) = v4) | ~ (tc_Polynomial_Opoly(v2) = v3) |
% 220.40/34.11 ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.11 class_Rings_Ocomm__semiring__1(v2) | ? [v7: $i] : ? [v8: $i] : (( ~ (v1
% 220.40/34.11 = v0) | (v7 = v6 & c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))) &
% 220.40/34.11 (v1 = v0 | (v8 = v6 & c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6))))))
% 220.40/34.11
% 220.40/34.11 (fact_coeff__pCons__0)
% 220.40/34.11 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.11 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.11 $i] : ( ~ (c_Polynomial_Ocoeff(v3, v4) = v5) | ~ (c_Polynomial_OpCons(v3,
% 220.40/34.11 v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.11 class_Groups_Ozero(v3) | hAPP(v5, v0) = v2))
% 220.40/34.11
% 220.40/34.11 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)
% 220.40/34.11 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.11 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.40/34.11 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 220.40/34.11 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | ? [v5: $i] :
% 220.40/34.11 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5))))
% 220.40/34.11
% 220.40/34.11 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)
% 220.40/34.11 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.40/34.11 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.40/34.11 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 220.40/34.11 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | hAPP(v4, v0)
% 220.40/34.11 = v1))
% 220.40/34.11
% 220.40/34.11 (fact_decr__mult__lemma)
% 220.40/34.11 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.11 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 220.40/34.11 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.11 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.11 : ! [v8: $i] : ! [v9: $i] : ( ~
% 220.40/34.11 (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v7, v6) = v8) | ~ (hAPP(v5,
% 220.40/34.11 v4) = v6) | ~ (hAPP(v3, v8) = v9) | ~ (hAPP(v1, v2) = v5) | ~
% 220.40/34.11 $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.11 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ~
% 220.40/34.11 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | hBOOL(v9) | ?
% 220.40/34.11 [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 220.40/34.11 ($i(v11) & ((c_Groups_Ominus__class_Ominus(tc_Int_Oint, v11, v4) = v13 &
% 220.40/34.11 hAPP(v3, v13) = v14 & hAPP(v3, v11) = v12 & $i(v14) & $i(v13) &
% 220.40/34.11 $i(v12) & hBOOL(v12) & ~ hBOOL(v14)) | (hAPP(v3, v7) = v10 &
% 220.40/34.11 $i(v10) & ~ hBOOL(v10))))))
% 220.40/34.11
% 220.40/34.11 (fact_degree__0)
% 220.40/34.12 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.12 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0
% 220.40/34.12 | ~ (c_Polynomial_Odegree(v1, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) =
% 220.40/34.12 v2) | ~ (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~
% 220.40/34.12 class_Groups_Ozero(v1)))
% 220.40/34.12
% 220.40/34.12 (fact_degree__1)
% 220.40/34.12 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.12 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0
% 220.40/34.12 | ~ (c_Polynomial_Odegree(v1, v3) = v4) | ~
% 220.40/34.12 (c_Groups_Oone__class_Oone(v2) = v3) | ~ (tc_Polynomial_Opoly(v1) = v2) |
% 220.40/34.12 ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v1)))
% 220.40/34.12
% 220.40/34.12 (fact_degree__pCons__0)
% 220.40/34.12 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.12 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.12 $i] : ! [v6: $i] : (v6 = v0 | ~ (c_Polynomial_Odegree(v2, v5) = v6) | ~
% 220.40/34.12 (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ (tc_Polynomial_Opoly(v2) = v3)
% 220.40/34.12 | ~ (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.12 class_Groups_Ozero(v2)))
% 220.40/34.12
% 220.40/34.12 (fact_degree__pCons__eq__if)
% 220.40/34.12 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.12 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.12 $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~
% 220.40/34.12 (c_Polynomial_OpCons(v3, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 220.40/34.12 | ~ class_Groups_Ozero(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 220.40/34.12 [v9: $i] : ((v5 = v0 | ( ~ (v7 = v2) & tc_Polynomial_Opoly(v3) = v6 &
% 220.40/34.12 c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6))) & ((v9 = v5
% 220.40/34.12 & c_Nat_OSuc(v8) = v5 & c_Polynomial_Odegree(v3, v2) = v8 & $i(v8) &
% 220.40/34.12 $i(v5)) | (v7 = v2 & tc_Polynomial_Opoly(v3) = v6 &
% 220.40/34.12 c_Groups_Ozero__class_Ozero(v6) = v2 & $i(v6))))))
% 220.40/34.12
% 220.40/34.12 (fact_degree__synthetic__div)
% 220.40/34.12 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.40/34.12 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 220.40/34.12 : ( ~ (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~
% 220.40/34.12 (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 220.40/34.12 ~ class_Rings_Ocomm__semiring__0(v3) | ? [v6: $i] :
% 220.40/34.12 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v0) = v5 &
% 220.40/34.12 c_Polynomial_Odegree(v3, v2) = v6 & $i(v6) & $i(v5))))
% 220.40/34.12
% 220.40/34.12 (fact_diff__0__eq__0)
% 220.40/34.12 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.12 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 220.40/34.12 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1)))
% 220.40/34.12
% 220.40/34.12 (fact_diff__Suc__1)
% 220.40/34.12 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.40/34.12 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) |
% 220.40/34.12 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v1))
% 220.40/34.12
% 220.40/34.12 (fact_diff__Suc__eq__diff__pred)
% 220.40/34.12 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.40/34.12 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.40/34.12 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~
% 220.40/34.12 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ $i(v2) | ~
% 220.40/34.12 $i(v1) | ? [v5: $i] : (c_Nat_OSuc(v1) = v5 &
% 220.40/34.12 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) = v4 & $i(v5) &
% 220.40/34.12 $i(v4))))
% 220.40/34.12
% 220.40/34.12 (fact_diff__Suc__less)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.40/34.13 (c_Nat_OSuc(v1) = v3) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 220.40/34.13 v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 220.40/34.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 220.40/34.13
% 220.40/34.13 (fact_diff__add__0)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0
% 220.40/34.13 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 220.40/34.13 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v2) | ~
% 220.40/34.13 $i(v1)))
% 220.40/34.13
% 220.40/34.13 (fact_diff__add__inverse)
% 220.40/34.13 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3
% 220.40/34.13 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~
% 220.40/34.13 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v1) | ~
% 220.40/34.13 $i(v0))
% 220.40/34.13
% 220.40/34.13 (fact_diff__is__0__eq)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 220.40/34.13 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.13 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & !
% 220.40/34.13 [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 220.40/34.13 v1) = v0) | ~ $i(v2) | ~ $i(v1) |
% 220.40/34.13 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 220.40/34.13
% 220.40/34.13 (fact_diff__is__0__eq_H)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 220.40/34.13 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.13 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 220.40/34.13
% 220.40/34.13 (fact_diff__less)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.13 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~
% 220.40/34.13 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 220.40/34.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) |
% 220.40/34.13 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1)))
% 220.40/34.13
% 220.40/34.13 (fact_diff__self__eq__0)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 220.40/34.13 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ $i(v1)))
% 220.40/34.13
% 220.40/34.13 (fact_diffs0__imp__equal)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 220.40/34.13 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ $i(v2) | ~
% 220.40/34.13 $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) &
% 220.40/34.13 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & $i(v3))))
% 220.40/34.13
% 220.40/34.13 (fact_div__1)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 220.40/34.13 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.13 $i] : ! [v3: $i] : (v3 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,
% 220.40/34.13 v2, v1) = v3) | ~ $i(v2)))
% 220.40/34.13
% 220.40/34.13 (fact_div__le__mono2)
% 220.40/34.13 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.13 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.13 $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v3) = v5) | ~
% 220.40/34.13 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v4) | ~ $i(v3) | ~
% 220.40/34.13 $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)
% 220.40/34.13 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 220.40/34.13 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)))
% 220.40/34.13
% 220.40/34.13 (fact_div__less__dividend)
% 220.40/34.14 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.14 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.40/34.14 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.14 $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.40/34.14 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v3) | ~
% 220.40/34.14 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~
% 220.40/34.14 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 220.40/34.14 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 220.40/34.14
% 220.40/34.14 (fact_div__mult__self1__is__m)
% 220.40/34.14 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.14 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.14 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.14 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 |
% 220.40/34.14 ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = v6) | ~ (hAPP(v4,
% 220.40/34.14 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.14 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 220.40/34.14
% 220.40/34.14 (fact_div__mult__self__is__m)
% 220.40/34.14 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.14 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.14 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.14 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 |
% 220.40/34.14 ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = v6) | ~ (hAPP(v4,
% 220.40/34.14 v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.14 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 220.40/34.14
% 220.40/34.14 (fact_div__neg__neg__trivial)
% 220.40/34.14 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.14 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 220.40/34.14 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.14 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) | ~
% 220.40/34.14 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0)))
% 220.40/34.14
% 220.40/34.14 (fact_div__neg__pos__less0)
% 220.40/34.14 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.14 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.14 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.14 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 220.40/34.14 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) |
% 220.40/34.14 c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)))
% 220.40/34.14
% 220.40/34.14 (fact_div__nonneg__neg__le0)
% 220.40/34.14 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.14 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.14 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.14 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) | ~
% 220.40/34.14 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 220.40/34.14 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v0)))
% 220.40/34.14
% 220.40/34.14 (fact_div__nonpos__pos__le0)
% 220.40/34.14 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.14 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.14 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.14 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) | ~
% 220.40/34.14 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0) |
% 220.40/34.14 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v0)))
% 220.40/34.14
% 220.40/34.14 (fact_div__pos__pos__trivial)
% 220.40/34.14 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.14 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 220.40/34.14 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.14 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) | ~
% 220.40/34.14 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)))
% 220.40/34.14
% 220.40/34.14 (fact_divmod__int__rel__div__eq)
% 220.40/34.15 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.15 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 220.40/34.15 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.15 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.15 : ! [v8: $i] : (v8 = v3 | v4 = v1 | ~
% 220.40/34.15 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5, v4) = v8) | ~
% 220.40/34.15 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v2) = v5) | ~ (hAPP(v6, v3)
% 220.40/34.15 = v7) | ~ (hAPP(v0, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.15 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v2) | ~
% 220.40/34.15 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v4) | ~
% 220.40/34.15 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) | ~
% 220.40/34.15 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2)) & ! [v2: $i] : !
% 220.40/34.15 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 220.40/34.15 $i] : (v8 = v3 | v4 = v1 | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5,
% 220.40/34.15 v4) = v8) | ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v2) = v5)
% 220.40/34.15 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v0, v4) = v6) | ~ $i(v5) | ~ $i(v4)
% 220.40/34.15 | ~ $i(v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 220.40/34.15 v4, v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 220.40/34.15 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4)) & ! [v2: $i] : !
% 220.40/34.15 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 220.40/34.15 $i] : (v8 = v3 | v4 = v1 | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5,
% 220.40/34.15 v4) = v8) | ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v2) = v5)
% 220.40/34.15 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v0, v4) = v6) | ~ $i(v5) | ~ $i(v4)
% 220.40/34.15 | ~ $i(v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 220.40/34.15 v2, v4) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 220.40/34.15 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2)))
% 220.40/34.15
% 220.40/34.15 (fact_ds0)
% 220.40/34.15 $i(v_s____) & $i(tc_Complex_Ocomplex) & $i(tc_Nat_Onat) & ? [v0: $i] :
% 220.40/34.15 (c_Polynomial_Odegree(tc_Complex_Ocomplex, v_s____) = v0 &
% 220.40/34.15 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0))
% 220.40/34.15
% 220.40/34.15 (fact_dvd__1__iff__1)
% 220.40/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 220.40/34.15 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 220.40/34.15 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v1) & ! [v2: $i] : (v2 = v1 | ~
% 220.40/34.15 $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1)))
% 220.40/34.15
% 220.40/34.15 (fact_dvd__1__left)
% 220.40/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 220.40/34.15 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ? [v2:
% 220.40/34.15 $i] : ( ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2)))
% 220.40/34.15
% 220.40/34.15 (fact_dvd__imp__le)
% 220.40/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.15 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.15 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 220.40/34.15 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1) |
% 220.40/34.15 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 220.40/34.15
% 220.40/34.15 (fact_dvd__mult__cancel)
% 220.40/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.15 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.15 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.15 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.15 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5)
% 220.40/34.15 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.15 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 220.40/34.15 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) |
% 220.40/34.15 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)))
% 220.40/34.15
% 220.40/34.15 (fact_dvd__mult__cancel1)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.40/34.16 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.16 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 220.40/34.16 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.16 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~
% 220.40/34.16 (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 220.40/34.16 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : ! [v4: $i]
% 220.40/34.16 : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3)
% 220.40/34.16 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 220.40/34.16 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 220.40/34.16
% 220.40/34.16 (fact_dvd__mult__cancel2)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.40/34.16 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.16 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 220.40/34.16 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.16 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~
% 220.40/34.16 (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 220.40/34.16 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : ! [v4: $i]
% 220.40/34.16 : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ $i(v3)
% 220.40/34.16 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 220.40/34.16 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 220.40/34.16
% 220.40/34.16 (fact_dvd__pos__nat)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 220.40/34.16 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) |
% 220.40/34.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)))
% 220.40/34.16
% 220.40/34.16 (fact_dvd__power)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.16 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~
% 220.40/34.16 (hAPP(v5, v2) = v6) | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.16 $i(v1) | ~ class_Rings_Ocomm__semiring__1(v3) | ~
% 220.40/34.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 220.40/34.16 c_Rings_Odvd__class_Odvd(v3, v1, v6)) & ! [v1: $i] : ! [v2: $i] : !
% 220.40/34.16 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 220.40/34.16 (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v2) = v6) | ~
% 220.40/34.16 (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.16 class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3, v1, v6)
% 220.40/34.16 | ? [v7: $i] : ( ~ (v7 = v1) & c_Groups_Oone__class_Oone(v3) = v7 &
% 220.40/34.16 $i(v7))))
% 220.40/34.16
% 220.40/34.16 (fact_expand__Suc)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.16 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 220.40/34.16 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.16 $i] : ! [v3: $i] : ( ~ (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2)
% 220.40/34.16 = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 220.40/34.16 v3) | ? [v4: $i] : (c_Nat_OSuc(v4) = v3 &
% 220.40/34.16 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & $i(v4) &
% 220.40/34.16 $i(v3))))
% 220.40/34.16
% 220.40/34.16 (fact_gcd__lcm__complete__lattice__nat_Obot__least)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.40/34.16 $i(v0) & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 220.40/34.16 v0, v1)))
% 220.40/34.16
% 220.40/34.16 (fact_gcd__lcm__complete__lattice__nat_Otop__greatest)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.16 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 220.40/34.16 v1, v0)))
% 220.40/34.16
% 220.40/34.16 (fact_gr0I)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.16 & $i(v0) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) |
% 220.40/34.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)))
% 220.40/34.16
% 220.40/34.16 (fact_gr0__conv__Suc)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.16 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2)
% 220.40/34.16 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & !
% 220.40/34.16 [v1: $i] : ( ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 220.40/34.16 v1) | ? [v2: $i] : (c_Nat_OSuc(v2) = v1 & $i(v2))))
% 220.40/34.16
% 220.40/34.16 (fact_gr__implies__not0)
% 220.40/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.16 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 220.40/34.16 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 220.40/34.16
% 220.40/34.16 (fact_incr__mult__lemma)
% 220.40/34.17 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.17 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 220.40/34.17 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.17 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.17 : ! [v8: $i] : ! [v9: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint,
% 220.40/34.17 v7, v6) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v3, v8) = v9) | ~
% 220.40/34.17 (hAPP(v1, v2) = v5) | ~ $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.17 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ~
% 220.40/34.17 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | hBOOL(v9) | ?
% 220.40/34.17 [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 220.40/34.17 ($i(v11) & ((c_Groups_Oplus__class_Oplus(tc_Int_Oint, v11, v4) = v13 &
% 220.40/34.17 hAPP(v3, v13) = v14 & hAPP(v3, v11) = v12 & $i(v14) & $i(v13) &
% 220.40/34.17 $i(v12) & hBOOL(v12) & ~ hBOOL(v14)) | (hAPP(v3, v7) = v10 &
% 220.40/34.17 $i(v10) & ~ hBOOL(v10))))))
% 220.40/34.17
% 220.40/34.17 (fact_int__0__less__1)
% 220.40/34.17 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.17 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 220.40/34.17 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 220.40/34.17 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1))
% 220.40/34.17
% 220.40/34.17 (fact_int__0__neq__1)
% 220.40/34.17 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 220.40/34.17 c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 220.40/34.17 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0))
% 220.40/34.17
% 220.40/34.17 (fact_int__div__less__self)
% 220.40/34.17 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.17 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 220.40/34.17 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.17 $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.40/34.17 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v4) | ~ $i(v3) | ~
% 220.40/34.17 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) | ~
% 220.40/34.17 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3) |
% 220.40/34.17 c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v3)))
% 220.40/34.17
% 220.40/34.17 (fact_int__one__le__iff__zero__less)
% 220.40/34.17 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.17 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 &
% 220.40/34.17 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.17 $i] : ( ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) |
% 220.40/34.17 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)) & ! [v2: $i] : (
% 220.40/34.17 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 220.40/34.17 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2)))
% 220.40/34.17
% 220.40/34.17 (fact_int__power__div__base)
% 220.40/34.17 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.40/34.17 ? [v3: $i] : (c_Nat_OSuc(v0) = v3 & c_Power_Opower__class_Opower(tc_Int_Oint)
% 220.40/34.17 = v2 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 &
% 220.40/34.17 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 220.40/34.17 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 220.40/34.17 : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v3) = v7) | ~
% 220.40/34.17 (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~
% 220.40/34.17 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 220.40/34.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v9: $i] :
% 220.40/34.17 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v9, v4) = v8 & hAPP(v6, v5) = v9
% 220.40/34.17 & $i(v9) & $i(v8))))
% 220.40/34.17
% 220.40/34.17 (fact_k)
% 220.40/34.17 $i(v_k____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ( ~ (v0 = v_k____) &
% 220.40/34.17 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v0))
% 220.40/34.17
% 220.40/34.17 (fact_kpn)
% 220.40/34.17 $i(v_s____) & $i(v_k____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 220.40/34.17 $i] : (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, v1) = v_s____ &
% 220.40/34.17 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.40/34.17 c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0))
% 220.40/34.17
% 220.40/34.17 (fact_le0)
% 220.40/34.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.17 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) |
% 220.40/34.17 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1)))
% 220.40/34.17
% 220.40/34.17 (fact_le__0__eq)
% 220.40/34.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.17 & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) & ! [v1:
% 220.40/34.17 $i] : (v1 = v0 | ~ $i(v1) | ~
% 220.40/34.17 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)))
% 220.40/34.17
% 220.40/34.17 (fact_le__Suc__ex__iff)
% 220.40/34.17 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.40/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v2) = v0) | ~ $i(v2) | ~
% 220.40/34.17 $i(v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 220.40/34.17 & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.17 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v2: $i] :
% 220.40/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v2) = v0 & $i(v2)))
% 220.40/34.17
% 220.40/34.17 (fact_le__iff__add)
% 220.40/34.18 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.40/34.18 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v2) = v0) | ~ $i(v2) | ~
% 220.40/34.18 $i(v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 220.40/34.18 & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.18 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v2: $i] :
% 220.40/34.18 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v2) = v0 & $i(v2)))
% 220.40/34.18
% 220.40/34.18 (fact_le__imp__0__less)
% 220.40/34.18 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.18 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 220.40/34.18 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.18 $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v2)
% 220.40/34.18 = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 220.40/34.18 v0, v2) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)))
% 220.40/34.18
% 220.40/34.18 (fact_less__Suc0)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 220.40/34.18 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] : (v2 = v0
% 220.40/34.18 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)))
% 220.40/34.18
% 220.40/34.18 (fact_less__Suc__eq)
% 220.40/34.18 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 220.40/34.18 (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! [v1:
% 220.40/34.18 $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) |
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)) & ! [v0: $i] : ! [v1:
% 220.40/34.18 $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))
% 220.40/34.18
% 220.40/34.18 (fact_less__Suc__eq__0__disj)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.18 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.40/34.18 (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~ $i(v2) |
% 220.40/34.18 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) |
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v1: $i] : !
% 220.40/34.18 [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v2) |
% 220.40/34.18 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4:
% 220.40/34.18 $i] : (c_Nat_OSuc(v4) = v2 & $i(v4) &
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1: $i] : !
% 220.40/34.18 [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) |
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)))
% 220.40/34.18
% 220.40/34.18 (fact_less__bin__lemma)
% 220.40/34.18 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.18 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.18 (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.18 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0) |
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)) & ! [v1: $i] : !
% 220.40/34.18 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v2,
% 220.40/34.18 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)))
% 220.40/34.18
% 220.40/34.18 (fact_less__eq__nat_Osimps_I1_J)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.18 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) |
% 220.40/34.18 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1)))
% 220.40/34.18
% 220.40/34.18 (fact_less__nat__zero__code)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.18 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 220.40/34.18
% 220.40/34.18 (fact_less__zeroE)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.18 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 220.40/34.18 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 220.40/34.18
% 220.40/34.18 (fact_minus__nat_Odiff__0)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.18 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 220.40/34.18 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)))
% 220.40/34.18
% 220.40/34.18 (fact_monom__0)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.18 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.18 $i] : ( ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~
% 220.40/34.18 (tc_Polynomial_Opoly(v2) = v3) | ~ (c_Groups_Ozero__class_Ozero(v3) = v4)
% 220.40/34.18 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) |
% 220.40/34.18 (c_Polynomial_Omonom(v2, v1, v0) = v5 & $i(v5))))
% 220.40/34.18
% 220.40/34.18 (fact_mult__0)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.40/34.18 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.18 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) &
% 220.40/34.18 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v2, v3) =
% 220.40/34.18 v4) | ~ $i(v3)))
% 220.40/34.18
% 220.40/34.18 (fact_mult__0__right)
% 220.40/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.18 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.18 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.18 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) =
% 220.40/34.18 v1))
% 220.40/34.18
% 220.40/34.18 (fact_mult__cancel1)
% 220.40/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.19 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.19 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 |
% 220.40/34.19 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) |
% 220.40/34.19 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.19 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~
% 220.40/34.19 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.19 $i(v2)))
% 220.40/34.19
% 220.40/34.19 (fact_mult__cancel2)
% 220.40/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.19 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.19 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.19 : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0,
% 220.40/34.19 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 220.40/34.19 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.19 : (v4 = v2 | v3 = v1 | ~ (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~
% 220.40/34.19 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.19 $i(v2)))
% 220.40/34.19
% 220.40/34.19 (fact_mult__eq__1__iff)
% 220.40/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 220.40/34.19 v2 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.19 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v3) = v2) |
% 220.40/34.19 ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4:
% 220.40/34.19 $i] : ! [v5: $i] : (v3 = v2 | ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) =
% 220.40/34.19 v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 220.40/34.19 (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v2) = v3)))
% 220.40/34.19
% 220.40/34.19 (fact_mult__eq__if)
% 220.40/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.40/34.19 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.19 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 220.40/34.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.19 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 220.40/34.19 $i] : (v4 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) =
% 220.40/34.19 v8) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~
% 220.40/34.19 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ?
% 220.40/34.19 [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & $i(v9) & $i(v8))) & !
% 220.40/34.19 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v0 | ~ (hAPP(v4, v3) = v5) |
% 220.40/34.19 ~ (hAPP(v1, v0) = v4) | ~ $i(v3)))
% 220.40/34.19
% 220.40/34.19 (fact_mult__eq__self__implies__10)
% 220.40/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.40/34.19 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.19 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 220.40/34.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.19 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5,
% 220.40/34.19 v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)))
% 220.40/34.19
% 220.40/34.19 (fact_mult__is__0)
% 220.40/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.19 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.19 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) = v4) | ~
% 220.40/34.19 (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 220.40/34.19 : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v0, v2) = v3) | ~ $i(v2)) &
% 220.40/34.19 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4,
% 220.40/34.19 v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)))
% 220.40/34.19
% 220.40/34.19 (fact_mult__le__cancel1)
% 220.40/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.19 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.19 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.19 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.19 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5)
% 220.40/34.19 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.19 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 220.40/34.19 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) |
% 220.40/34.19 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 220.40/34.19 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 220.40/34.19 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 220.40/34.19 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.19 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 220.40/34.19 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : !
% 220.40/34.19 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 220.40/34.19 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 220.40/34.19 $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 220.40/34.19 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 220.40/34.19 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)))
% 220.40/34.19
% 220.40/34.19 (fact_mult__le__cancel2)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.20 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.20 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.20 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~
% 220.40/34.20 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.20 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) |
% 220.40/34.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : !
% 220.40/34.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 220.40/34.20 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 220.40/34.20 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) |
% 220.40/34.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)) & ! [v2: $i] : !
% 220.40/34.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 220.40/34.20 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 220.40/34.20 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 220.40/34.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)))
% 220.40/34.20
% 220.40/34.20 (fact_mult__less__cancel1)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.20 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.20 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.20 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5)
% 220.40/34.20 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 220.40/34.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 220.40/34.20 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 220.40/34.20 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i] : !
% 220.40/34.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 220.40/34.20 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 220.40/34.20 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 220.40/34.20
% 220.40/34.20 (fact_mult__less__cancel2)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.20 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.20 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.20 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~
% 220.40/34.20 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.20 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : !
% 220.40/34.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 220.40/34.20 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 220.40/34.20 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] : !
% 220.40/34.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 220.40/34.20 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4)
% 220.40/34.20 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 220.40/34.20
% 220.40/34.20 (fact_mult__less__mono1)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.20 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.20 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.20 : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5, v2) = v6) | ~
% 220.40/34.20 (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.20 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 220.40/34.20
% 220.40/34.20 (fact_mult__less__mono2)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.20 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.20 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.20 : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ (hAPP(v1, v2) = v5)
% 220.40/34.20 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 220.40/34.20
% 220.40/34.20 (fact_n0)
% 220.40/34.20 $i(v_na____) & $i(tc_Nat_Onat) & ? [v0: $i] : ( ~ (v0 = v_na____) &
% 220.40/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0))
% 220.40/34.20
% 220.40/34.20 (fact_n__less__m__mult__n)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 220.40/34.20 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 220.40/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.20 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) =
% 220.40/34.20 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)))
% 220.40/34.20
% 220.40/34.20 (fact_n__less__n__mult__m)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 220.40/34.20 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 220.40/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.20 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) =
% 220.40/34.20 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 220.40/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)))
% 220.40/34.20
% 220.40/34.20 (fact_nat_Osimps_I2_J)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.20 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 220.40/34.20
% 220.40/34.20 (fact_nat_Osimps_I3_J)
% 220.40/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.20 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 220.40/34.20
% 220.40/34.20 (fact_nat__0__less__mult__iff)
% 220.40/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.21 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.21 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.21 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) |
% 220.40/34.21 ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : !
% 220.40/34.21 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 220.40/34.21 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i] : !
% 220.40/34.21 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 220.40/34.21 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)))
% 220.40/34.21
% 220.40/34.21 (fact_nat__1__eq__mult__iff)
% 220.40/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.21 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.21 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i]
% 220.40/34.21 : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = v0) | ~
% 220.40/34.21 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 220.40/34.21 ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) |
% 220.40/34.21 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 220.40/34.21 (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2)))
% 220.40/34.21
% 220.40/34.21 (fact_nat__diff__split)
% 220.40/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.21 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.21 $i] : ! [v6: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6)
% 220.40/34.21 = v2) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) |
% 220.40/34.21 ~ (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.21 hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) & hBOOL(v7))) & !
% 220.40/34.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.40/34.21 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 220.40/34.21 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v5) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] :
% 220.40/34.21 (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! [v1: $i] : ! [v2: $i] : !
% 220.40/34.21 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.40/34.21 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 220.40/34.21 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) |
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] : ? [v7:
% 220.40/34.21 $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3,
% 220.40/34.21 v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : ! [v2:
% 220.40/34.21 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.40/34.21 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 220.40/34.21 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | ? [v6:
% 220.40/34.21 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ((v8 = v2 &
% 220.40/34.21 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v7) = v2 & hAPP(v3, v7)
% 220.40/34.21 = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, v0) = v6 & $i(v6) & ~
% 220.40/34.21 hBOOL(v6))))))
% 220.40/34.21
% 220.40/34.21 (fact_nat__diff__split__asm)
% 220.40/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.21 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.21 $i] : ! [v6: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6)
% 220.40/34.21 = v2) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) |
% 220.40/34.21 ~ (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.21 hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) & hBOOL(v7))) & !
% 220.40/34.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.40/34.21 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 220.40/34.21 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v5) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] :
% 220.40/34.21 (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! [v1: $i] : ! [v2: $i] : !
% 220.40/34.21 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.40/34.21 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 220.40/34.21 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) |
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] : ? [v7:
% 220.40/34.21 $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3,
% 220.40/34.21 v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : ! [v2:
% 220.40/34.21 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.40/34.21 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3,
% 220.40/34.21 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | ? [v6:
% 220.40/34.21 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ((v8 = v2 &
% 220.40/34.21 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v7) = v2 & hAPP(v3, v7)
% 220.40/34.21 = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, v0) = v6 & $i(v6) & ~
% 220.40/34.21 hBOOL(v6))))))
% 220.40/34.21
% 220.40/34.21 (fact_nat__dvd__1__iff__1)
% 220.40/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 220.40/34.21 $i(v0) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 =
% 220.40/34.21 v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)))
% 220.40/34.21
% 220.40/34.21 (fact_nat__dvd__not__less)
% 220.40/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.21 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 220.40/34.21 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2)))
% 220.40/34.21
% 220.40/34.21 (fact_nat__lt__two__imp__zero__or__one)
% 220.40/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 220.40/34.21 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 220.40/34.21 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ $i(v3) | ~
% 220.40/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 220.40/34.21
% 220.40/34.21 (fact_nat__mult__1)
% 220.40/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.40/34.22 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.22 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) &
% 220.40/34.22 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3) =
% 220.40/34.22 v4) | ~ $i(v3)))
% 220.40/34.22
% 220.40/34.22 (fact_nat__mult__1__right)
% 220.40/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.22 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.22 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 220.40/34.22 : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = v2))
% 220.40/34.22
% 220.40/34.22 (fact_nat__mult__dvd__cancel1)
% 220.40/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.22 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.22 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.22 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5)
% 220.40/34.22 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 220.40/34.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) |
% 220.40/34.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i]
% 220.40/34.22 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3)
% 220.40/34.22 = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~
% 220.40/34.22 $i(v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)
% 220.40/34.22 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) |
% 220.40/34.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7)))
% 220.40/34.22
% 220.40/34.22 (fact_nat__mult__dvd__cancel__disj)
% 220.40/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.22 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.22 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.22 : (v4 = v1 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0,
% 220.40/34.22 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) |
% 220.40/34.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i]
% 220.40/34.22 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3)
% 220.40/34.22 = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~
% 220.40/34.22 $i(v3) | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) |
% 220.40/34.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : ! [v3: $i]
% 220.40/34.22 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, v3) = v5) | ~
% 220.40/34.22 (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 220.40/34.22 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v6)))
% 220.40/34.22
% 220.40/34.22 (fact_nat__mult__eq__1__iff)
% 220.40/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.22 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.22 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 220.40/34.22 : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = v1) | ~
% 220.40/34.22 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 220.40/34.22 ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) |
% 220.40/34.22 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 220.40/34.22 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 220.40/34.22
% 220.40/34.22 (fact_nat__mult__eq__cancel1)
% 220.40/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.22 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.22 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 |
% 220.40/34.22 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) |
% 220.40/34.22 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 220.40/34.22
% 220.40/34.22 (fact_nat__mult__eq__cancel__disj)
% 220.40/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.22 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 220.40/34.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.22 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 |
% 220.40/34.22 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) |
% 220.40/34.22 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.22 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~
% 220.40/34.22 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.22 $i(v2)))
% 220.40/34.22
% 220.40/34.22 (fact_nat__mult__le__cancel1)
% 220.40/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.22 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.22 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.22 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5)
% 220.40/34.22 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 220.40/34.22 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) |
% 220.40/34.22 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 220.40/34.22 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 220.40/34.22 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 220.40/34.22 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 220.40/34.22 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 220.40/34.22 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)))
% 220.40/34.22
% 220.40/34.22 (fact_nat__mult__less__cancel1)
% 220.40/34.23 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.23 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 220.40/34.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.23 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.23 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5)
% 220.40/34.23 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 220.40/34.23 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 220.40/34.23 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 220.40/34.23 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 220.40/34.23
% 220.40/34.23 (fact_nat__one__le__power)
% 220.40/34.23 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 220.40/34.23 v1 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 &
% 220.40/34.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.23 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) =
% 220.40/34.23 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) |
% 220.40/34.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)))
% 220.40/34.23
% 220.40/34.23 (fact_nat__power__eq__Suc__0__iff)
% 220.40/34.23 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 220.40/34.23 v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 220.40/34.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.23 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v3) = v5) |
% 220.40/34.23 ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.23 $i] : (v5 = v2 | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, v3) = v4) | ~
% 220.40/34.23 $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 |
% 220.40/34.23 ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)))
% 220.40/34.23
% 220.40/34.23 (fact_nat__power__less__imp__less)
% 220.40/34.23 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.23 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 220.40/34.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.23 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 220.40/34.23 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5)
% 220.40/34.23 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 220.40/34.23
% 220.40/34.23 (fact_nat__zero__less__power__iff)
% 220.40/34.23 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.23 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 220.40/34.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.23 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4,
% 220.40/34.23 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : !
% 220.40/34.23 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 220.40/34.23 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : !
% 220.40/34.23 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) |
% 220.40/34.23 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 220.40/34.23
% 220.40/34.23 (fact_neg__0__equal__iff__equal)
% 220.40/34.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.40/34.23 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.23 class_Groups_Ogroup__add(v1) | ? [v3: $i] :
% 220.40/34.23 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) &
% 220.40/34.23 ( ~ (v3 = v0) | v2 = v0)))
% 220.40/34.23
% 220.40/34.23 (fact_neg__0__le__iff__le)
% 220.40/34.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.40/34.23 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.23 class_Groups_Oordered__ab__group__add(v1) | ? [v3: $i] :
% 220.40/34.23 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~
% 220.40/34.23 c_Orderings_Oord__class_Oless__eq(v1, v3, v2) |
% 220.40/34.23 c_Orderings_Oord__class_Oless__eq(v1, v0, v3)) & ( ~
% 220.40/34.23 c_Orderings_Oord__class_Oless__eq(v1, v0, v3) |
% 220.40/34.23 c_Orderings_Oord__class_Oless__eq(v1, v3, v2))))
% 220.40/34.23
% 220.40/34.23 (fact_neg__0__less__iff__less)
% 220.40/34.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.40/34.23 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.23 class_Groups_Oordered__ab__group__add(v1) | ? [v3: $i] :
% 220.40/34.23 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(v1, v3, v2) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(v1, v0, v3)) & ( ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(v1, v0, v3) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(v1, v3, v2))))
% 220.40/34.23
% 220.40/34.23 (fact_neg__equal__0__iff__equal)
% 220.40/34.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.40/34.23 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.23 class_Groups_Ogroup__add(v1) | ? [v3: $i] :
% 220.40/34.23 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) &
% 220.40/34.23 ( ~ (v3 = v0) | v2 = v0)))
% 220.40/34.23
% 220.40/34.23 (fact_neg__imp__zdiv__neg__iff)
% 220.40/34.23 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.23 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.23 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~ $i(v2) | ~
% 220.40/34.23 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1)) & ! [v1: $i] : !
% 220.40/34.23 [v2: $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1,
% 220.40/34.23 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) |
% 220.40/34.23 c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)))
% 220.40/34.23
% 220.40/34.23 (fact_neg__imp__zdiv__nonneg__iff)
% 220.40/34.24 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.24 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.24 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~ $i(v2) | ~
% 220.40/34.24 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0) |
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)) & ! [v1: $i] : !
% 220.40/34.24 [v2: $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1,
% 220.40/34.24 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) |
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0)))
% 220.40/34.24
% 220.40/34.24 (fact_neg__le__0__iff__le)
% 220.40/34.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.40/34.24 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.24 class_Groups_Oordered__ab__group__add(v1) | ? [v3: $i] :
% 220.40/34.24 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(v1, v3, v0) |
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(v1, v2, v3)) & ( ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(v1, v2, v3) |
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(v1, v3, v0))))
% 220.40/34.24
% 220.40/34.24 (fact_neg__less__0__iff__less)
% 220.40/34.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.40/34.24 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 220.40/34.24 class_Groups_Oordered__ab__group__add(v1) | ? [v3: $i] :
% 220.40/34.24 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~
% 220.40/34.24 c_Orderings_Oord__class_Oless(v1, v3, v0) |
% 220.40/34.24 c_Orderings_Oord__class_Oless(v1, v2, v3)) & ( ~
% 220.40/34.24 c_Orderings_Oord__class_Oless(v1, v2, v3) |
% 220.40/34.24 c_Orderings_Oord__class_Oless(v1, v3, v0))))
% 220.40/34.24
% 220.40/34.24 (fact_neq0__conv)
% 220.40/34.24 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.24 & $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1:
% 220.40/34.24 $i] : (v1 = v0 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 220.40/34.24 v0, v1)))
% 220.40/34.24
% 220.40/34.24 (fact_nonneg1__imp__zdiv__pos__iff)
% 220.40/34.24 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 220.40/34.24 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.40/34.24 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 220.40/34.24 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1)) & ! [v1: $i] : !
% 220.40/34.24 [v2: $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2,
% 220.40/34.24 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2)) & ! [v1: $i] : !
% 220.40/34.24 [v2: $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2,
% 220.40/34.24 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)))
% 220.40/34.24
% 220.40/34.24 (fact_not__less0)
% 220.40/34.24 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.24 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 220.40/34.24
% 220.40/34.24 (fact_not__one__le__zero)
% 220.40/34.24 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 220.40/34.24 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 220.40/34.24 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~
% 220.40/34.24 c_Orderings_Oord__class_Oless__eq(v0, v1, v2)))
% 220.40/34.24
% 220.40/34.24 (fact_not__one__less__zero)
% 220.40/34.24 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 220.40/34.24 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 220.40/34.24 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~
% 220.40/34.24 c_Orderings_Oord__class_Oless(v0, v1, v2)))
% 220.40/34.24
% 220.40/34.24 (fact_oa)
% 220.40/34.24 $i(v_pa____) & $i(v_a____) & $i(tc_Complex_Ocomplex) & $i(tc_Nat_Onat) & ?
% 220.40/34.24 [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 220.40/34.24 c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v0 &
% 220.40/34.24 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0))
% 220.40/34.24
% 220.40/34.24 (fact_odd__less__0)
% 220.40/34.24 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.24 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 &
% 220.40/34.24 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.24 $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.40/34.24 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v3, v2) = v4) | ~
% 220.40/34.24 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, v2) = v3) | ~ $i(v2) | ~
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v1) |
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)) & ! [v2: $i] : !
% 220.40/34.24 [v3: $i] : ! [v4: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v3,
% 220.40/34.24 v2) = v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, v2) = v3)
% 220.40/34.24 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 220.40/34.24 c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v1)))
% 220.40/34.24
% 220.40/34.24 (fact_odd__nonzero)
% 220.40/34.24 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 220.40/34.24 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 &
% 220.40/34.24 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.24 $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v3, v2)
% 220.40/34.24 = v1) | ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, v2) = v3) | ~
% 220.40/34.24 $i(v2)))
% 220.40/34.24
% 220.40/34.24 (fact_one__is__add)
% 220.40/34.24 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 220.40/34.24 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.40/34.24 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 220.40/34.24 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 220.40/34.24 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~
% 220.40/34.24 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 220.40/34.24 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~
% 220.40/34.24 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 220.40/34.24 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~
% 220.40/34.24 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~
% 220.40/34.24 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~
% 220.40/34.24 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] :
% 220.40/34.24 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2)))
% 220.40/34.24
% 220.40/34.24 (fact_one__le__mult__iff)
% 220.40/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 220.40/34.25 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 220.40/34.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.25 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) =
% 220.40/34.25 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) |
% 220.40/34.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)) & ! [v3: $i] : !
% 220.40/34.25 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = v6) | ~
% 220.40/34.25 (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) |
% 220.40/34.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) & ! [v3: $i] : !
% 220.40/34.25 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = v6) | ~
% 220.40/34.25 (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) | ~
% 220.40/34.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) |
% 220.40/34.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)))
% 220.40/34.25
% 220.40/34.25 (fact_one__less__mult)
% 220.40/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) =
% 220.40/34.25 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 220.40/34.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 220.40/34.25 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) =
% 220.40/34.25 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 220.40/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 220.40/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 220.40/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6)))
% 220.40/34.25
% 220.40/34.25 (fact_one__less__power)
% 220.40/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.25 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.25 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~
% 220.40/34.25 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 220.40/34.25 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 220.40/34.25 class_Rings_Olinordered__semidom(v3) | ? [v7: $i] :
% 220.40/34.25 (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~
% 220.40/34.25 c_Orderings_Oord__class_Oless(v3, v7, v2) |
% 220.40/34.25 c_Orderings_Oord__class_Oless(v3, v7, v6)))))
% 220.40/34.25
% 220.40/34.25 (fact_one__neq__zero)
% 220.40/34.25 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 220.40/34.25 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) &
% 220.40/34.25 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2)))
% 220.40/34.25
% 220.40/34.25 (fact_order__root)
% 220.40/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.40/34.25 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 220.40/34.25 $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~
% 220.40/34.25 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: $i] :
% 220.40/34.25 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) &
% 220.40/34.25 c_Polynomial_Oorder(v3, v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7
% 220.40/34.25 & c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | (v6 = v5
% 220.40/34.25 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & ((v8 = v2 &
% 220.40/34.25 tc_Polynomial_Opoly(v3) = v7 & c_Groups_Ozero__class_Ozero(v7) = v2
% 220.40/34.25 & $i(v7)) | ( ~ (v9 = v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 &
% 220.40/34.25 $i(v9)) | ( ~ (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 &
% 220.40/34.25 $i(v6))))))
% 220.40/34.25
% 220.40/34.25 (fact_pCons__eq__0__iff)
% 220.94/34.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.94/34.25 (c_Polynomial_OpCons(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 220.94/34.25 ~ class_Groups_Ozero(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 220.94/34.25 (tc_Polynomial_Opoly(v2) = v4 & c_Groups_Ozero__class_Ozero(v4) = v5 &
% 220.94/34.25 $i(v5) & $i(v4) & ( ~ (v5 = v3) | (v6 = v1 & v3 = v0 &
% 220.94/34.25 c_Groups_Ozero__class_Ozero(v2) = v1)) & ( ~ (v5 = v0) | v3 = v0 | ( ~
% 220.94/34.25 (v6 = v1) & c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6)))))
% 220.94/34.25
% 220.94/34.25 (fact_plus__nat_Oadd__0)
% 220.94/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 220.94/34.25 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 220.94/34.25 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1)))
% 220.94/34.25
% 220.94/34.25 (fact_pne)
% 220.94/34.25 $i(v_pa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 =
% 220.94/34.25 v_pa____) & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 220.94/34.25 c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0))
% 220.94/34.25
% 220.94/34.25 (fact_poly__eq__0__iff__dvd)
% 220.94/34.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.94/34.25 (c_Polynomial_Opoly(v2, v1) = v3) | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~
% 220.94/34.25 $i(v1) | ~ $i(v0) | ~ class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] :
% 220.94/34.25 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (((v5
% 220.94/34.25 = v4 & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4)) |
% 220.94/34.25 (c_Groups_Ouminus__class_Ouminus(v2, v0) = v7 &
% 220.94/34.25 c_Groups_Oone__class_Oone(v2) = v8 & c_Polynomial_OpCons(v2, v8, v9) =
% 220.94/34.25 v10 & c_Polynomial_OpCons(v2, v7, v10) = v11 & tc_Polynomial_Opoly(v2)
% 220.94/34.25 = v6 & c_Groups_Ozero__class_Ozero(v6) = v9 & $i(v11) & $i(v10) &
% 220.94/34.25 $i(v9) & $i(v8) & $i(v7) & $i(v6) & ~ c_Rings_Odvd__class_Odvd(v6,
% 220.94/34.25 v11, v1))) & (( ~ (v5 = v4) & c_Groups_Ozero__class_Ozero(v2) = v5 &
% 220.94/34.25 $i(v5)) | (c_Groups_Ouminus__class_Ouminus(v2, v0) = v7 &
% 220.94/34.25 c_Groups_Oone__class_Oone(v2) = v8 & c_Polynomial_OpCons(v2, v8, v9) =
% 220.94/34.25 v10 & c_Polynomial_OpCons(v2, v7, v10) = v11 & tc_Polynomial_Opoly(v2)
% 220.94/34.25 = v6 & c_Groups_Ozero__class_Ozero(v6) = v9 & $i(v11) & $i(v10) &
% 220.94/34.25 $i(v9) & $i(v8) & $i(v7) & $i(v6) & c_Rings_Odvd__class_Odvd(v6, v11,
% 220.94/34.25 v1)))))
% 220.94/34.25
% 220.94/34.25 (fact_poly__zero)
% 220.94/34.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Polynomial_Opoly(v1, v0) =
% 220.94/34.25 v2) | ~ $i(v1) | ~ $i(v0) | ~ class_Int_Oring__char__0(v1) | ~
% 220.94/34.25 class_Rings_Oidom(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 220.94/34.25 (tc_Polynomial_Opoly(v1) = v3 & c_Groups_Ozero__class_Ozero(v3) = v4 &
% 220.94/34.25 $i(v4) & $i(v3) & ( ~ (v4 = v0) | v5 = v2) & (v4 = v0 | ( ~ (v5 = v2) &
% 220.94/34.25 c_Polynomial_Opoly(v1, v4) = v5 & $i(v5)))))
% 220.94/34.25
% 220.94/34.25 (fact_pos__imp__zdiv__neg__iff)
% 221.16/34.25 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.25 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.25 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~ $i(v2) | ~
% 221.16/34.25 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0) | ~
% 221.16/34.25 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.16/34.25 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0)) & ! [v1: $i] : !
% 221.16/34.25 [v2: $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1,
% 221.16/34.25 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.25 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) | ~
% 221.16/34.25 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.16/34.25 c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)))
% 221.16/34.25
% 221.16/34.25 (fact_pos__imp__zdiv__nonneg__iff)
% 221.16/34.26 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.26 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.26 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~ $i(v2) | ~
% 221.16/34.26 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) |
% 221.16/34.26 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1)) & ! [v1: $i] : !
% 221.16/34.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1,
% 221.16/34.26 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) |
% 221.16/34.26 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 221.16/34.26
% 221.16/34.26 (fact_pos__imp__zdiv__pos__iff)
% 221.16/34.26 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.26 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.26 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~ $i(v2) | ~
% 221.16/34.26 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.16/34.26 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1)) & ! [v1: $i] : !
% 221.16/34.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1,
% 221.16/34.26 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.16/34.26 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)))
% 221.16/34.26
% 221.16/34.26 (fact_pos__zmult__eq__1__iff)
% 221.16/34.26 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.16/34.26 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.16/34.26 c_Groups_Oone__class_Oone(tc_Int_Oint) = v2 &
% 221.16/34.26 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 221.16/34.26 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v3) = v2) |
% 221.16/34.26 ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4)) & ! [v3: $i] : !
% 221.16/34.26 [v4: $i] : ! [v5: $i] : (v3 = v2 | ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v1,
% 221.16/34.26 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4)) & ! [v3: $i] : !
% 221.16/34.26 [v4: $i] : (v4 = v2 | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(v1, v2) = v3) | ~
% 221.16/34.26 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2)))
% 221.16/34.26
% 221.16/34.26 (fact_pow__divides__eq__int)
% 221.16/34.26 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.26 (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 &
% 221.16/34.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.26 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.26 : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) |
% 221.16/34.26 ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) |
% 221.16/34.26 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) |
% 221.16/34.26 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)) & ! [v2: $i] : ! [v3: $i]
% 221.16/34.26 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4
% 221.16/34.26 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3)
% 221.16/34.26 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.26 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2) |
% 221.16/34.26 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8)))
% 221.16/34.26
% 221.16/34.26 (fact_pow__divides__eq__nat)
% 221.16/34.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.26 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 221.16/34.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.26 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.26 : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) |
% 221.16/34.26 ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) |
% 221.16/34.26 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) |
% 221.16/34.26 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i]
% 221.16/34.26 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4
% 221.16/34.26 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3)
% 221.16/34.26 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.26 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) |
% 221.16/34.26 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8)))
% 221.16/34.26
% 221.16/34.26 (fact_pow__divides__pow__int)
% 221.16/34.26 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.26 (c_Power_Opower__class_Opower(tc_Int_Oint) = v0 &
% 221.16/34.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.26 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.26 : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) |
% 221.16/34.26 ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) |
% 221.16/34.26 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) |
% 221.16/34.26 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v2)))
% 221.16/34.26
% 221.16/34.26 (fact_pow__divides__pow__nat)
% 221.16/34.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.26 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 221.16/34.26 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.26 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.26 : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) |
% 221.16/34.26 ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) |
% 221.16/34.26 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) |
% 221.16/34.26 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v2)))
% 221.16/34.26
% 221.16/34.26 (fact_power_Opower_Opower__0)
% 221.16/34.26 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.26 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.26 $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | ~
% 221.16/34.26 (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 221.16/34.26 hAPP(v6, v0) = v3))
% 221.16/34.26
% 221.16/34.26 (fact_power__0)
% 221.16/34.26 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.26 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.16/34.26 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 221.16/34.26 $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] :
% 221.16/34.26 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5))))
% 221.16/34.26
% 221.16/34.26 (fact_power__0__left)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.27 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.27 $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~
% 221.16/34.27 (c_Power_Opower__class_Opower(v2) = v3) | ~
% 221.16/34.27 (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | ~
% 221.16/34.27 (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.27 class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2)) & ! [v1: $i] :
% 221.16/34.27 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 221.16/34.27 (c_Power_Opower__class_Opower(v1) = v2) | ~
% 221.16/34.27 (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | ~
% 221.16/34.27 (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ class_Rings_Osemiring__0(v1) | ~
% 221.16/34.27 class_Power_Opower(v1) | (c_Groups_Oone__class_Oone(v1) = v5 & $i(v5))))
% 221.16/34.27
% 221.16/34.27 (fact_power__0__left__number__of)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.27 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.27 $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v5 | v3 = v0 | ~
% 221.16/34.27 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v1) = v3) | ~
% 221.16/34.27 (c_Power_Opower__class_Opower(v2) = v4) | ~
% 221.16/34.27 (c_Groups_Ozero__class_Ozero(v2) = v5) | ~ (hAPP(v6, v3) = v7) | ~
% 221.16/34.27 (hAPP(v4, v5) = v6) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.27 class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2)) & ! [v1: $i] :
% 221.16/34.27 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.16/34.27 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v1) = v0) | ~
% 221.16/34.27 (c_Power_Opower__class_Opower(v2) = v3) | ~
% 221.16/34.27 (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v0) = v6) | ~
% 221.16/34.27 (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.27 class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2) |
% 221.16/34.27 (c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))))
% 221.16/34.27
% 221.16/34.27 (fact_power__Suc__0)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 221.16/34.27 (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 221.16/34.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 & $i(v3) &
% 221.16/34.27 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~
% 221.16/34.27 (hAPP(v3, v4) = v5) | ~ $i(v4)))
% 221.16/34.27
% 221.16/34.27 (fact_power__add)
% 221.16/34.27 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 221.16/34.27 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 221.16/34.27 : ! [v10: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v3) = v6) | ~
% 221.16/34.27 (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v8, v9) = v10) | ~
% 221.16/34.27 (hAPP(v6, v7) = v8) | ~ (hAPP(v5, v1) = v7) | ~ (hAPP(v5, v0) = v9) | ~
% 221.16/34.27 (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.16/34.27 class_Groups_Omonoid__mult(v3) | ? [v11: $i] :
% 221.16/34.27 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v11 & hAPP(v5, v11) =
% 221.16/34.27 v10 & $i(v11) & $i(v10)))
% 221.16/34.27
% 221.16/34.27 (fact_power__dvd__imp__le)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.27 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 221.16/34.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 221.16/34.27 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 221.16/34.27 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 221.16/34.27 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 221.16/34.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) |
% 221.16/34.27 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)))
% 221.16/34.27
% 221.16/34.27 (fact_power__eq__0__iff)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.27 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.27 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~
% 221.16/34.27 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.27 $i(v1) | ~ class_Rings_Ozero__neq__one(v3) | ~
% 221.16/34.27 class_Rings_Ono__zero__divisors(v3) | ~ class_Rings_Omult__zero(v3) | ~
% 221.16/34.27 class_Power_Opower(v3) | ? [v7: $i] : (c_Groups_Ozero__class_Ozero(v3) =
% 221.16/34.27 v7 & $i(v7) & ( ~ (v7 = v6) | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2)
% 221.16/34.27 | v6 = v2 | v1 = v0))))
% 221.16/34.27
% 221.16/34.27 (fact_power__eq__0__iff__number__of)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.27 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.27 $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 221.16/34.27 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v1) = v6) | ~
% 221.16/34.27 (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v6) = v7) | ~
% 221.16/34.27 (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.27 class_Rings_Ozero__neq__one(v3) | ~ class_Rings_Ono__zero__divisors(v3) |
% 221.16/34.27 ~ class_Rings_Omult__zero(v3) | ~ class_Power_Opower(v3) | ? [v8: $i] :
% 221.16/34.27 (c_Groups_Ozero__class_Ozero(v3) = v8 & $i(v8) & ( ~ (v8 = v7) | (v7 = v2
% 221.16/34.27 & ~ (v6 = v0))) & ( ~ (v8 = v2) | v7 = v2 | v6 = v0))))
% 221.16/34.27
% 221.16/34.27 (fact_power__eq__if)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 221.16/34.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 &
% 221.16/34.27 c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 221.16/34.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 221.16/34.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 221.16/34.27 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 221.16/34.27 : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~
% 221.16/34.27 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ (hAPP(v7,
% 221.16/34.27 v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = v7) | ~
% 221.16/34.27 (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, v5) = v10 &
% 221.16/34.27 $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | ~
% 221.16/34.27 (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4)))
% 221.16/34.27
% 221.16/34.27 (fact_power__eq__imp__eq__base)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.27 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.27 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~
% 221.16/34.27 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v2) = v7) | ~
% 221.16/34.27 (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v1) = v8) | ~
% 221.16/34.27 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 221.16/34.27 class_Rings_Olinordered__semidom(v4) | ? [v9: $i] :
% 221.16/34.27 (c_Groups_Ozero__class_Ozero(v4) = v9 & $i(v9) & ( ~
% 221.16/34.27 c_Orderings_Oord__class_Oless__eq(v4, v9, v3) | ~
% 221.16/34.27 c_Orderings_Oord__class_Oless__eq(v4, v9, v1)))))
% 221.16/34.27
% 221.16/34.27 (fact_power__one__right)
% 221.16/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 221.16/34.27 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.16/34.27 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 221.16/34.27 $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | hAPP(v4, v0) =
% 221.16/34.27 v1))
% 221.16/34.27
% 221.16/34.27 (fact_power__strict__mono)
% 221.16/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.28 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.28 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 221.16/34.28 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9) | ~
% 221.16/34.28 (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v8) | ~
% 221.16/34.28 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.28 c_Orderings_Oord__class_Oless(v4, v3, v2) | ~
% 221.16/34.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 221.16/34.28 class_Rings_Olinordered__semidom(v4) | c_Orderings_Oord__class_Oless(v4,
% 221.16/34.28 v7, v9) | ? [v10: $i] : (c_Groups_Ozero__class_Ozero(v4) = v10 &
% 221.16/34.28 $i(v10) & ~ c_Orderings_Oord__class_Oless__eq(v4, v10, v3))))
% 221.16/34.28
% 221.16/34.28 (fact_pq0)
% 221.16/34.28 $i(v_pa____) & $i(v_qa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1:
% 221.16/34.28 $i] : ? [v2: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0
% 221.16/34.28 & c_Polynomial_Opoly(tc_Complex_Ocomplex, v_qa____) = v2 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v2) & $i(v1) &
% 221.16/34.28 $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v2, v3) = v4) | ~
% 221.16/34.28 $i(v3) | ? [v5: $i] : ( ~ (v5 = v1) & hAPP(v0, v3) = v5 & $i(v5))))
% 221.16/34.28
% 221.16/34.28 (fact_psize__def)
% 221.16/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.28 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.28 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | ~
% 221.16/34.28 $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i] : ? [v5: $i]
% 221.16/34.28 : ? [v6: $i] : ? [v7: $i] : ((v3 = v0 | ( ~ (v5 = v1) &
% 221.16/34.28 tc_Polynomial_Opoly(v2) = v4 & c_Groups_Ozero__class_Ozero(v4) = v5
% 221.16/34.28 & $i(v5) & $i(v4))) & ((v7 = v3 & c_Nat_OSuc(v6) = v3 &
% 221.16/34.28 c_Polynomial_Odegree(v2, v1) = v6 & $i(v6) & $i(v3)) | (v5 = v1 &
% 221.16/34.28 tc_Polynomial_Opoly(v2) = v4 & c_Groups_Ozero__class_Ozero(v4) = v1
% 221.16/34.28 & $i(v4))))))
% 221.16/34.28
% 221.16/34.28 (fact_psize__eq__0__iff)
% 221.16/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.28 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.28 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | ~
% 221.16/34.28 $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i] : ? [v5: $i]
% 221.16/34.28 : (( ~ (v3 = v0) | (v5 = v1 & tc_Polynomial_Opoly(v2) = v4 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(v4) = v1 & $i(v4))) & (v3 = v0 | ( ~ (v5
% 221.16/34.28 = v1) & tc_Polynomial_Opoly(v2) = v4 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))))))
% 221.16/34.28
% 221.16/34.28 (fact_q0)
% 221.16/34.28 $i(v_qa____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 =
% 221.16/34.28 v_qa____) & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0))
% 221.16/34.28
% 221.16/34.28 (fact_q__neg__lemma)
% 221.16/34.28 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.28 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.28 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.28 : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v6, v2) = v7) | ~ (hAPP(v5,
% 221.16/34.28 v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 221.16/34.28 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v7, v1) | ~
% 221.16/34.28 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 221.16/34.28 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2) |
% 221.16/34.28 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1)))
% 221.16/34.28
% 221.16/34.28 (fact_q__pos__lemma)
% 221.16/34.28 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.28 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.28 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.28 : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v6, v2) = v7) | ~ (hAPP(v5,
% 221.16/34.28 v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 221.16/34.28 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v4) | ~
% 221.16/34.28 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ~
% 221.16/34.28 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v7) |
% 221.16/34.28 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 221.16/34.28
% 221.16/34.28 (fact_r)
% 221.16/34.28 $i(v_r____) & $i(v_a____) & $i(v_qa____) & $i(tc_Complex_Ocomplex) & ? [v0:
% 221.16/34.28 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 221.16/34.28 ? [v6: $i] : ? [v7: $i] : (c_Groups_Otimes__class_Otimes(v0) = v1 &
% 221.16/34.28 c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v2 &
% 221.16/34.28 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 221.16/34.28 c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 221.16/34.28 c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 221.16/34.28 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(v0) = v4 & hAPP(v7, v_r____) = v_qa____ &
% 221.16/34.28 hAPP(v1, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 221.16/34.28 $i(v1) & $i(v0))
% 221.16/34.28
% 221.16/34.28 (fact_realpow__minus__mult)
% 221.16/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.28 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.28 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.28 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 221.16/34.28 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~
% 221.16/34.28 (c_Groups_Otimes__class_Otimes(v4) = v5) | ~
% 221.16/34.28 (c_Power_Opower__class_Opower(v4) = v6) | ~ (hAPP(v10, v2) = v11) | ~
% 221.16/34.28 (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v9) = v10) |
% 221.16/34.28 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ class_Groups_Omonoid__mult(v4) | ~
% 221.16/34.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3) = v11 &
% 221.16/34.28 $i(v11))))
% 221.16/34.28
% 221.16/34.28 (fact_realpow__num__eq__if)
% 221.16/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.28 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 221.16/34.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.28 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.28 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 221.16/34.28 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~
% 221.16/34.28 (c_Groups_Otimes__class_Otimes(v4) = v7) | ~
% 221.16/34.28 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v10) = v11) | ~
% 221.16/34.28 (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ (hAPP(v5, v2) = v6) |
% 221.16/34.28 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ class_Power_Opower(v4) | ? [v12:
% 221.16/34.28 $i] : ? [v13: $i] : (( ~ (v3 = v0) | (v13 = v12 &
% 221.16/34.28 c_Groups_Oone__class_Oone(v4) = v12 & hAPP(v6, v0) = v12 & $i(v12)))
% 221.16/34.28 & (v3 = v0 | (v12 = v11 & hAPP(v6, v3) = v11 & $i(v11))))))
% 221.16/34.28
% 221.16/34.28 (fact_realpow__two__diff)
% 221.16/34.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 221.16/34.29 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 221.16/34.29 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 221.16/34.29 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 221.16/34.29 $i] : ( ~ (c_Groups_Ominus__class_Ominus(v5, v8, v10) = v11) | ~
% 221.16/34.29 (c_Power_Opower__class_Opower(v5) = v6) | ~ (hAPP(v9, v2) = v10) | ~
% 221.16/34.29 (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, v3) = v9) | ~
% 221.16/34.29 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ class_Rings_Ocomm__ring__1(v5) | ?
% 221.16/34.29 [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 221.16/34.29 (c_Groups_Oplus__class_Oplus(v5, v4, v3) = v15 &
% 221.16/34.29 c_Groups_Ominus__class_Ominus(v5, v4, v3) = v13 &
% 221.16/34.29 c_Groups_Otimes__class_Otimes(v5) = v12 & hAPP(v14, v15) = v11 &
% 221.16/34.29 hAPP(v12, v13) = v14 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 221.16/34.29 $i(v11))))
% 221.16/34.29
% 221.16/34.29 (fact_realpow__two__disj)
% 221.16/34.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) =
% 221.16/34.29 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 221.16/34.29 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 221.16/34.29 $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v5) =
% 221.16/34.29 v6) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~
% 221.16/34.29 $i(v4) | ~ $i(v3) | ~ class_Rings_Oidom(v5) | ? [v9: $i] : ? [v10: $i]
% 221.16/34.29 : ? [v11: $i] : ((v4 = v3 | (v11 = v4 &
% 221.16/34.29 c_Groups_Ouminus__class_Ouminus(v5, v3) = v4) | ( ~ (v10 = v9) &
% 221.16/34.29 hAPP(v8, v2) = v10 & hAPP(v7, v2) = v9 & $i(v10) & $i(v9))) & ((v10
% 221.16/34.29 = v9 & hAPP(v8, v2) = v9 & hAPP(v7, v2) = v9 & $i(v9)) | ( ~ (v11 =
% 221.16/34.29 v4) & ~ (v4 = v3) & c_Groups_Ouminus__class_Ouminus(v5, v3) = v11
% 221.16/34.29 & $i(v11))))))
% 221.16/34.29
% 221.16/34.29 (fact_s)
% 221.16/34.29 $i(v_s____) & $i(v_pa____) & $i(v_a____) & $i(tc_Complex_Ocomplex) & ? [v0:
% 221.16/34.29 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 221.16/34.29 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11:
% 221.16/34.29 $i] : (c_Groups_Otimes__class_Otimes(v0) = v1 &
% 221.16/34.29 c_Power_Opower__class_Opower(v0) = v2 &
% 221.16/34.29 c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v3 &
% 221.16/34.29 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v4 &
% 221.16/34.29 c_Polynomial_OpCons(tc_Complex_Ocomplex, v4, v5) = v6 &
% 221.16/34.29 c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v6) = v7 &
% 221.16/34.29 c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v9 &
% 221.16/34.29 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.16/34.29 c_Groups_Ozero__class_Ozero(v0) = v5 & hAPP(v11, v_s____) = v_pa____ &
% 221.16/34.29 hAPP(v8, v9) = v10 & hAPP(v2, v7) = v8 & hAPP(v1, v10) = v11 & $i(v11) &
% 221.16/34.29 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 221.16/34.29 $i(v2) & $i(v1) & $i(v0))
% 221.16/34.29
% 221.16/34.29 (fact_self__quotient__aux1)
% 221.16/34.29 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.16/34.29 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.16/34.29 c_Groups_Oone__class_Oone(tc_Int_Oint) = v2 &
% 221.16/34.29 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 221.16/34.29 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 221.16/34.29 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v4, v7) = v5) | ~ (hAPP(v6, v3)
% 221.16/34.29 = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.16/34.29 c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v5) | ~
% 221.16/34.29 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v5) |
% 221.16/34.29 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v3)))
% 221.16/34.29
% 221.16/34.29 (fact_self__quotient__aux2)
% 221.16/34.29 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.16/34.29 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.16/34.29 c_Groups_Oone__class_Oone(tc_Int_Oint) = v2 &
% 221.16/34.29 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 221.16/34.29 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 221.16/34.29 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v4, v7) = v5) | ~ (hAPP(v6, v3)
% 221.16/34.29 = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.16/34.29 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v5) | ~
% 221.16/34.29 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v4) |
% 221.16/34.29 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v2)))
% 221.16/34.29
% 221.16/34.29 (fact_sne)
% 221.16/34.29 $i(v_s____) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 =
% 221.16/34.29 v_s____) & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.16/34.29 c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0))
% 221.16/34.29
% 221.16/34.29 (fact_split__zdiv)
% 221.16/34.29 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.29 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.16/34.29 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.16/34.29 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v5) | ~ (hAPP(v4, v5)
% 221.16/34.29 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ? [v7: $i] :
% 221.16/34.29 ? [v8: $i] : (( ~ (v2 = v0) | (hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7))) &
% 221.16/34.29 ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | (hAPP(v1, v2) =
% 221.16/34.29 v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 221.16/34.29 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v11) = v3) | ~
% 221.16/34.29 (hAPP(v8, v9) = v10) | ~ $i(v11) | ~ $i(v9) | ~
% 221.16/34.29 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v11) | ~
% 221.16/34.29 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v11, v0) | ? [v12:
% 221.16/34.29 $i] : (hAPP(v4, v9) = v12 & $i(v12) & hBOOL(v12))))) & ( ~
% 221.16/34.29 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | (hAPP(v1, v2) =
% 221.16/34.29 v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 221.16/34.29 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v11) = v3) | ~
% 221.16/34.29 (hAPP(v8, v9) = v10) | ~ $i(v11) | ~ $i(v9) | ~
% 221.16/34.29 c_Orderings_Oord__class_Oless(tc_Int_Oint, v11, v2) | ~
% 221.16/34.29 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v11) | ? [v12:
% 221.16/34.29 $i] : (hAPP(v4, v9) = v12 & $i(v12) & hBOOL(v12))))))) & ! [v2:
% 221.16/34.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.16/34.29 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v5) | ~ (hAPP(v4, v5)
% 221.16/34.29 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | hBOOL(v6) | ? [v7: $i] : ?
% 221.16/34.29 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 221.16/34.29 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 221.16/34.29 [v18: $i] : ($i(v17) & $i(v14) & $i(v12) & $i(v9) & ((v18 = v3 &
% 221.16/34.29 c_Groups_Oplus__class_Oplus(tc_Int_Oint, v15, v17) = v3 & hAPP(v8,
% 221.16/34.29 v14) = v15 & hAPP(v4, v14) = v16 & hAPP(v1, v2) = v8 & $i(v16) &
% 221.16/34.29 $i(v15) & $i(v8) & c_Orderings_Oord__class_Oless(tc_Int_Oint, v17,
% 221.16/34.29 v2) & c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) &
% 221.16/34.29 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v17) & ~
% 221.16/34.29 hBOOL(v16)) | (v13 = v3 & c_Groups_Oplus__class_Oplus(tc_Int_Oint,
% 221.16/34.29 v10, v12) = v3 & hAPP(v8, v9) = v10 & hAPP(v4, v9) = v11 &
% 221.16/34.29 hAPP(v1, v2) = v8 & $i(v11) & $i(v10) & $i(v8) &
% 221.16/34.29 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v12) &
% 221.16/34.29 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) &
% 221.16/34.29 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v12, v0) & ~
% 221.16/34.29 hBOOL(v11)) | (v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & ~
% 221.16/34.29 hBOOL(v7))))))
% 221.16/34.29
% 221.16/34.29 (fact_synthetic__div__eq__0__iff)
% 221.16/34.30 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.16/34.30 (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 221.16/34.30 ~ $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? [v5: $i] : ? [v6:
% 221.16/34.30 $i] : ? [v7: $i] : (((v7 = v0 & c_Polynomial_Odegree(v3, v2) = v0) | (
% 221.16/34.30 ~ (v6 = v4) & tc_Polynomial_Opoly(v3) = v5 &
% 221.16/34.30 c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) & ((v6 = v4
% 221.16/34.30 & tc_Polynomial_Opoly(v3) = v5 & c_Groups_Ozero__class_Ozero(v5) =
% 221.16/34.30 v4 & $i(v5) & $i(v4)) | ( ~ (v7 = v0) & c_Polynomial_Odegree(v3, v2)
% 221.16/34.30 = v7 & $i(v7))))))
% 221.16/34.30
% 221.16/34.30 (fact_tsub__def)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.16/34.30 (c_Nat__Transfer_Otsub(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1)) & ! [v1: $i] : !
% 221.16/34.30 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v1,
% 221.16/34.30 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.16/34.30 (c_Nat__Transfer_Otsub(v1, v2) = v3 & $i(v3))))
% 221.16/34.30
% 221.16/34.30 (fact_unique__quotient__lemma)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.30 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.16/34.30 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.30 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.30 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 221.16/34.30 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v2) = v11) | ~
% 221.16/34.30 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v8, v4) = v9) | ~ (hAPP(v7, v5)
% 221.16/34.30 = v8) | ~ (hAPP(v7, v3) = v10) | ~ (hAPP(v0, v6) = v7) | ~ $i(v6) |
% 221.16/34.30 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v6) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v6) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v9, v11) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v4) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v5, v3)))
% 221.16/34.30
% 221.16/34.30 (fact_unique__quotient__lemma__neg)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.30 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.16/34.30 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.30 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.30 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 221.16/34.30 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v2) = v11) | ~
% 221.16/34.30 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v8, v4) = v9) | ~ (hAPP(v7, v5)
% 221.16/34.30 = v8) | ~ (hAPP(v7, v3) = v10) | ~ (hAPP(v0, v6) = v7) | ~ $i(v6) |
% 221.16/34.30 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless(tc_Int_Oint, v6, v4) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless(tc_Int_Oint, v6, v2) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v9, v11) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v5)))
% 221.16/34.30
% 221.16/34.30 (fact_z3div__def)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v3) = v4) | ~
% 221.16/34.30 (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v2) = v3) | ~ $i(v2) | ~
% 221.16/34.30 $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ? [v5:
% 221.16/34.30 $i] : (c_SMT_Oz3div(v1, v2) = v5 &
% 221.16/34.30 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v4) = v5 & $i(v5))) & !
% 221.16/34.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~ $i(v2) | ~
% 221.16/34.30 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.16/34.30 (c_SMT_Oz3div(v1, v2) = v3 & $i(v3))))
% 221.16/34.30
% 221.16/34.30 (fact_zadd__0)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 221.16/34.30 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)))
% 221.16/34.30
% 221.16/34.30 (fact_zadd__0__right)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 221.16/34.30 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)))
% 221.16/34.30
% 221.16/34.30 (fact_zadd__zminus__inverse2)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.16/34.30 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v1) = v3) | ~
% 221.16/34.30 (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v1) = v2) | ~ $i(v1)))
% 221.16/34.30
% 221.16/34.30 (fact_zdiv__eq__0__iff)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 221.16/34.30 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)) & ! [v1: $i] : !
% 221.16/34.30 [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~ $i(v2) | ~
% 221.16/34.30 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0)) & ! [v1: $i] : !
% 221.16/34.30 [v2: $i] : (v2 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) =
% 221.16/34.30 v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v0) | ~ $i(v2) | ~
% 221.16/34.30 $i(v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.16/34.30 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2)) & ! [v1: $i] : !
% 221.16/34.30 [v2: $i] : (v1 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) =
% 221.16/34.30 v0) | ~ $i(v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.16/34.30 v2, v1) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0)) & !
% 221.16/34.30 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v0) | ~ $i(v2) | ~
% 221.16/34.30 $i(v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)) & ! [v1: $i] : !
% 221.16/34.30 [v2: $i] : (v1 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) =
% 221.16/34.30 v0) | ~ $i(v2) | ~ $i(v1) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)))
% 221.16/34.30
% 221.16/34.30 (fact_zdiv__mono1)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.30 $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v1) = v4) | ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v5) | ~ $i(v3) | ~
% 221.16/34.30 $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1)
% 221.16/34.30 | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v2) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v5)))
% 221.16/34.30
% 221.16/34.30 (fact_zdiv__mono1__neg)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.30 $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v1) = v5) | ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v4) | ~ $i(v3) | ~
% 221.16/34.30 $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0)
% 221.16/34.30 | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v2) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v5)))
% 221.16/34.30
% 221.16/34.30 (fact_zdiv__mono2)
% 221.16/34.30 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.30 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.30 $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v5) | ~
% 221.16/34.30 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v1) = v4) | ~ $i(v3) | ~
% 221.16/34.30 $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2)
% 221.16/34.30 | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) | ~
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) |
% 221.16/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v5)))
% 221.16/34.30
% 221.16/34.30 (fact_zdiv__mono2__lemma)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.31 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : (
% 221.16/34.31 ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v12, v2) = v10) | ~
% 221.16/34.31 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v9, v5) = v10) | ~ (hAPP(v11,
% 221.16/34.31 v3) = v12) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v0, v7) = v8) | ~
% 221.16/34.31 (hAPP(v0, v4) = v11) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 221.16/34.31 $i(v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v4)
% 221.16/34.31 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v7) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v10) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v5) |
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v6, v3)))
% 221.16/34.31
% 221.16/34.31 (fact_zdiv__mono2__neg)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.31 $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v4) | ~
% 221.16/34.31 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v1) = v5) | ~ $i(v3) | ~
% 221.16/34.31 $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)
% 221.16/34.31 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v5)))
% 221.16/34.31
% 221.16/34.31 (fact_zdiv__mono2__neg__lemma)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.31 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : (
% 221.16/34.31 ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v12, v2) = v10) | ~
% 221.16/34.31 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v9, v5) = v10) | ~ (hAPP(v11,
% 221.16/34.31 v3) = v12) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v0, v7) = v8) | ~
% 221.16/34.31 (hAPP(v0, v4) = v11) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 221.16/34.31 $i(v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v10,
% 221.16/34.31 v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v5, v7) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v7) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2) |
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v6)))
% 221.16/34.31
% 221.16/34.31 (fact_zdiv__self)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : (v3 = v1 | v2 = v0 | ~
% 221.16/34.31 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v2) = v3) | ~ $i(v2)))
% 221.16/34.31
% 221.16/34.31 (fact_zdiv__zero)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 221.16/34.31 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)))
% 221.16/34.31
% 221.16/34.31 (fact_zdiv__zmult2__eq)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.31 : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v6) = v7) | ~ (hAPP(v5,
% 221.16/34.31 v4) = v6) | ~ (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 221.16/34.31 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ? [v8: $i] :
% 221.16/34.31 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v8, v4) = v7 &
% 221.16/34.31 c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v8 & $i(v8) &
% 221.16/34.31 $i(v7))))
% 221.16/34.31
% 221.16/34.31 (fact_zdvd__antisym__nonneg)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.31 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v2, v1) | ~
% 221.16/34.31 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v2) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1)))
% 221.16/34.31
% 221.16/34.31 (fact_zdvd__imp__le)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) | ~
% 221.16/34.31 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v2, v1) |
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1)))
% 221.16/34.31
% 221.16/34.31 (fact_zdvd__mono)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.31 : (v4 = v0 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1,
% 221.16/34.31 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.31 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v7) |
% 221.16/34.31 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)) & ! [v2: $i] : ! [v3: $i]
% 221.16/34.31 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v0 | ~
% 221.16/34.31 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 221.16/34.31 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,
% 221.16/34.31 v3, v2) | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v7)))
% 221.16/34.31
% 221.16/34.31 (fact_zdvd__mult__cancel)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.31 : (v4 = v1 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0,
% 221.16/34.31 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.31 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v7) |
% 221.16/34.31 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)))
% 221.16/34.31
% 221.16/34.31 (fact_zdvd__not__zless)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0
% 221.16/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.16/34.31 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v2)))
% 221.16/34.31
% 221.16/34.31 (fact_zero__le__one)
% 221.16/34.31 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 221.16/34.31 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 221.16/34.31 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) &
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(v0, v2, v1)))
% 221.16/34.31
% 221.16/34.31 (fact_zero__less__Suc)
% 221.16/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1)
% 221.16/34.31 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)))
% 221.16/34.31
% 221.16/34.31 (fact_zero__less__diff)
% 221.16/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.16/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.31 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~
% 221.16/34.31 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : !
% 221.16/34.31 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2,
% 221.16/34.31 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 221.16/34.31
% 221.16/34.31 (fact_zero__less__power__nat__eq)
% 221.16/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4,
% 221.16/34.31 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : !
% 221.16/34.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 221.16/34.31 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : !
% 221.16/34.31 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) |
% 221.16/34.31 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 221.16/34.31
% 221.16/34.31 (fact_zero__less__power__nat__eq__number__of)
% 221.16/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v5 = v0 |
% 221.16/34.31 ~ (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v5) | ~ (hAPP(v4,
% 221.16/34.31 v5) = v6) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v6) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : !
% 221.16/34.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.16/34.31 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v4) | ~ (hAPP(v5,
% 221.16/34.31 v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v6)) & ! [v2: $i] : !
% 221.16/34.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 221.16/34.31 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v0) | ~ (hAPP(v4,
% 221.16/34.31 v0) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)))
% 221.16/34.31
% 221.16/34.31 (fact_zero__neq__one)
% 221.16/34.31 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 221.16/34.31 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2)))
% 221.16/34.31
% 221.16/34.31 (fact_zle__add1__eq__le)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 &
% 221.16/34.31 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.31 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v3) | ~ $i(v2) | ~
% 221.16/34.31 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v3) |
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1)) & ! [v1: $i] : !
% 221.16/34.31 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1,
% 221.16/34.31 v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v3)))
% 221.16/34.31
% 221.16/34.31 (fact_zle__diff1__eq)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 &
% 221.16/34.31 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.31 (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v1, v0) = v3) | ~ $i(v2) | ~
% 221.16/34.31 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v3)) & ! [v1: $i] : !
% 221.16/34.31 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v1,
% 221.16/34.31 v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v3) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)))
% 221.16/34.31
% 221.16/34.31 (fact_zless__add1__eq)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 &
% 221.16/34.31 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 221.16/34.31 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v3) | ~ $i(v2) | ~
% 221.16/34.31 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v3) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)) & ! [v1: $i] : !
% 221.16/34.31 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1,
% 221.16/34.31 v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v3)) & ! [v1: $i] : !
% 221.16/34.31 [v2: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v2) | ~
% 221.16/34.31 $i(v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2)))
% 221.16/34.31
% 221.16/34.31 (fact_zless__imp__add1__zle)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 &
% 221.16/34.31 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.16/34.31 (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v0) = v3) | ~ $i(v2) | ~
% 221.16/34.31 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.16/34.31 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1)))
% 221.16/34.31
% 221.16/34.31 (fact_zminus__0)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,
% 221.16/34.31 v0) = v0 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0))
% 221.16/34.31
% 221.16/34.31 (fact_zmult__1)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.16/34.31 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.16/34.31 c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 & hAPP(v0, v1) = v2 & $i(v2) &
% 221.16/34.31 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3) =
% 221.16/34.31 v4) | ~ $i(v3)))
% 221.16/34.31
% 221.16/34.31 (fact_zmult__1__right)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.16/34.31 c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 221.16/34.31 : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = v2))
% 221.16/34.31
% 221.16/34.31 (fact_zmult__zless__mono2)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] :
% 221.16/34.31 (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) & ! [v2:
% 221.16/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 221.16/34.31 : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ (hAPP(v1, v2) = v5)
% 221.16/34.31 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v3) | ~
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v6, v7)))
% 221.16/34.31
% 221.16/34.31 (fact_zsgn__def)
% 221.16/34.31 $i(tc_Int_Oint) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.16/34.31 (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v1) = v2 &
% 221.16/34.31 c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 221.16/34.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 221.16/34.31 ! [v3: $i] : ! [v4: $i] : (v4 = v2 | v3 = v0 | ~
% 221.16/34.31 (c_Groups_Osgn__class_Osgn(tc_Int_Oint, v3) = v4) | ~ $i(v3) |
% 221.16/34.31 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)) & ! [v3: $i] : !
% 221.16/34.31 [v4: $i] : (v4 = v1 | v3 = v0 | ~ (c_Groups_Osgn__class_Osgn(tc_Int_Oint,
% 221.16/34.31 v3) = v4) | ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.16/34.31 v0, v3)) & ! [v3: $i] : (v3 = v0 | ~
% 221.16/34.31 (c_Groups_Osgn__class_Osgn(tc_Int_Oint, v0) = v3)))
% 221.16/34.31
% 221.16/34.31 (function-axioms)
% 221.16/34.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.16/34.32 $i] : ! [v6: $i] : (v1 = v0 | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3,
% 221.16/34.32 v2) = v1) | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, v2) = v0)) & !
% 221.16/34.32 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 221.16/34.32 : (v1 = v0 | ~ (c_If(v5, v4, v3, v2) = v1) | ~ (c_If(v5, v4, v3, v2) = v0))
% 221.16/34.32 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 =
% 221.16/34.32 v0 | ~ (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~
% 221.16/34.32 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 221.16/34.32 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 221.16/34.32 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 221.16/34.32 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 221.16/34.32 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 221.16/34.32 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v1) | ~
% 221.16/34.32 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 221.16/34.32 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 221.16/34.32 (c_Polynomial_Omonom(v4, v3, v2) = v1) | ~ (c_Polynomial_Omonom(v4, v3, v2)
% 221.16/34.32 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 221.16/34.32 $i] : (v1 = v0 | ~ (c_Polynomial_Opcompose(v4, v3, v2) = v1) | ~
% 221.16/34.32 (c_Polynomial_Opcompose(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 221.16/34.32 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 221.16/34.32 (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ (c_Power_Opower_Opower(v4, v3,
% 221.16/34.32 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 221.16/34.32 [v4: $i] : (v1 = v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 221.16/34.32 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 221.16/34.32 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 221.16/34.32 (c_Polynomial_OpCons(v4, v3, v2) = v1) | ~ (c_Polynomial_OpCons(v4, v3, v2)
% 221.16/34.32 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 221.16/34.32 $i] : (v1 = v0 | ~ (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~
% 221.16/34.32 (c_Polynomial_Oorder(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 221.16/34.32 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_SMT_Oz3div(v3, v2) = v1) | ~
% 221.16/34.32 (c_SMT_Oz3div(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 221.16/34.32 [v3: $i] : (v1 = v0 | ~ (c_Int_Onumber__class_Onumber__of(v3, v2) = v1) | ~
% 221.16/34.32 (c_Int_Onumber__class_Onumber__of(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 221.16/34.32 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Polynomial_Ocoeff(v3, v2) = v1)
% 221.16/34.32 | ~ (c_Polynomial_Ocoeff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 221.16/34.32 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_fequal(v3, v2) = v1) | ~
% 221.16/34.32 (c_fequal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.16/34.32 $i] : (v1 = v0 | ~ (c_Groups_Osgn__class_Osgn(v3, v2) = v1) | ~
% 221.16/34.32 (c_Groups_Osgn__class_Osgn(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 221.16/34.32 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Nat__Transfer_Otsub(v3, v2) = v1) |
% 221.16/34.32 ~ (c_Nat__Transfer_Otsub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 221.16/34.32 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3,
% 221.16/34.32 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 221.16/34.32 = v0 | ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v1) |
% 221.16/34.32 ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v0)) & !
% 221.16/34.32 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 221.16/34.32 (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, v2) =
% 221.16/34.32 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 221.16/34.32 ~ (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) = v0))
% 221.16/34.32 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 221.16/34.32 (c_Groups_Ouminus__class_Ouminus(v3, v2) = v1) | ~
% 221.16/34.32 (c_Groups_Ouminus__class_Ouminus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 221.16/34.32 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3,
% 221.16/34.32 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.16/34.32 (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0)) & ! [v0: $i] : ! [v1:
% 221.16/34.32 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Groups_Otimes__class_Otimes(v2) = v1) |
% 221.16/34.32 ~ (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 221.16/34.32 ! [v2: $i] : (v1 = v0 | ~ (c_Power_Opower__class_Opower(v2) = v1) | ~
% 221.16/34.32 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 221.16/34.32 [v2: $i] : (v1 = v0 | ~ (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 221.16/34.32 (c_Groups_Oone__class_Oone(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.16/34.32 $i] : (v1 = v0 | ~ (tc_Polynomial_Opoly(v2) = v1) | ~
% 221.16/34.32 (tc_Polynomial_Opoly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 221.16/34.32 (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 221.16/34.32 (c_Groups_Ozero__class_Ozero(v2) = v0))
% 221.16/34.32
% 221.16/34.32 Further assumptions not needed in the proof:
% 221.16/34.32 --------------------------------------------
% 221.16/34.32 arity_Complex__Ocomplex__Fields_Ofield,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Oab__group__add,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Oab__semigroup__add,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Ominus,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Omonoid__add,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Omonoid__mult,
% 221.16/34.32 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ouminus,
% 221.16/34.32 arity_Complex__Ocomplex__Int_Onumber,
% 221.16/34.32 arity_Complex__Ocomplex__Int_Onumber__ring,
% 221.16/34.32 arity_Complex__Ocomplex__Power_Opower,
% 221.16/34.32 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
% 221.16/34.32 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
% 221.16/34.32 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
% 221.16/34.32 arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Ocomm__ring,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Ocomm__ring__1,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Ocomm__semiring,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Odvd, arity_Complex__Ocomplex__Rings_Omult__zero,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Ono__zero__divisors,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Osemiring,
% 221.16/34.32 arity_Complex__Ocomplex__Rings_Osemiring__0,
% 221.16/34.32 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 221.16/34.32 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Groups_Ouminus,
% 221.16/34.32 arity_HOL__Obool__Lattices_Oboolean__algebra, arity_HOL__Obool__Orderings_Oord,
% 221.16/34.32 arity_HOL__Obool__Orderings_Oorder, arity_HOL__Obool__Orderings_Opreorder,
% 221.16/34.32 arity_Int__Oint__Divides_Oring__div, arity_Int__Oint__Divides_Osemiring__div,
% 221.16/34.32 arity_Int__Oint__Groups_Oab__group__add,
% 221.16/34.32 arity_Int__Oint__Groups_Oab__semigroup__add,
% 221.16/34.32 arity_Int__Oint__Groups_Oab__semigroup__mult,
% 221.16/34.32 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,
% 221.16/34.32 arity_Int__Oint__Groups_Ocancel__comm__monoid__add,
% 221.16/34.32 arity_Int__Oint__Groups_Ocancel__semigroup__add,
% 221.16/34.32 arity_Int__Oint__Groups_Ocomm__monoid__add,
% 221.16/34.32 arity_Int__Oint__Groups_Ocomm__monoid__mult,
% 221.16/34.32 arity_Int__Oint__Groups_Olinordered__ab__group__add,
% 221.16/34.32 arity_Int__Oint__Groups_Ominus, arity_Int__Oint__Groups_Omonoid__add,
% 221.16/34.32 arity_Int__Oint__Groups_Omonoid__mult, arity_Int__Oint__Groups_Oone,
% 221.16/34.32 arity_Int__Oint__Groups_Oordered__ab__semigroup__add,
% 221.16/34.32 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,
% 221.16/34.32 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,
% 221.16/34.32 arity_Int__Oint__Groups_Oordered__comm__monoid__add,
% 221.16/34.32 arity_Int__Oint__Groups_Osgn__if, arity_Int__Oint__Groups_Ouminus,
% 221.16/34.32 arity_Int__Oint__Groups_Ozero, arity_Int__Oint__Int_Onumber,
% 221.16/34.32 arity_Int__Oint__Int_Onumber__ring, arity_Int__Oint__Int_Oring__char__0,
% 221.16/34.32 arity_Int__Oint__Orderings_Olinorder, arity_Int__Oint__Orderings_Oord,
% 221.16/34.32 arity_Int__Oint__Orderings_Oorder, arity_Int__Oint__Orderings_Opreorder,
% 221.16/34.32 arity_Int__Oint__Power_Opower, arity_Int__Oint__Rings_Ocomm__ring,
% 221.16/34.32 arity_Int__Oint__Rings_Ocomm__ring__1, arity_Int__Oint__Rings_Ocomm__semiring,
% 221.16/34.32 arity_Int__Oint__Rings_Ocomm__semiring__0,
% 221.16/34.32 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Oidom,
% 221.16/34.32 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,
% 221.16/34.32 arity_Int__Oint__Rings_Olinordered__idom,
% 221.16/34.32 arity_Int__Oint__Rings_Olinordered__ring,
% 221.16/34.32 arity_Int__Oint__Rings_Olinordered__ring__strict,
% 221.16/34.32 arity_Int__Oint__Rings_Olinordered__semiring,
% 221.16/34.32 arity_Int__Oint__Rings_Olinordered__semiring__1,
% 221.16/34.32 arity_Int__Oint__Rings_Olinordered__semiring__1__strict,
% 221.16/34.32 arity_Int__Oint__Rings_Olinordered__semiring__strict,
% 221.16/34.32 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors,
% 221.16/34.32 arity_Int__Oint__Rings_Oordered__cancel__semiring,
% 221.16/34.32 arity_Int__Oint__Rings_Oordered__comm__semiring,
% 221.16/34.32 arity_Int__Oint__Rings_Oordered__ring,
% 221.16/34.32 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring,
% 221.16/34.32 arity_Int__Oint__Rings_Oring__1,
% 221.16/34.32 arity_Int__Oint__Rings_Oring__1__no__zero__divisors,
% 221.16/34.32 arity_Int__Oint__Rings_Oring__no__zero__divisors,
% 221.16/34.32 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0,
% 221.16/34.32 arity_Int__Oint__Rings_Ozero__neq__one,
% 221.16/34.32 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 221.16/34.32 arity_Nat__Onat__Divides_Osemiring__div,
% 221.16/34.32 arity_Nat__Onat__Groups_Oab__semigroup__add,
% 221.16/34.32 arity_Nat__Onat__Groups_Oab__semigroup__mult,
% 221.16/34.32 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,
% 221.16/34.32 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,
% 221.16/34.32 arity_Nat__Onat__Groups_Ocancel__semigroup__add,
% 221.16/34.32 arity_Nat__Onat__Groups_Ocomm__monoid__add,
% 221.16/34.32 arity_Nat__Onat__Groups_Ocomm__monoid__mult, arity_Nat__Onat__Groups_Ominus,
% 221.16/34.32 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult,
% 221.16/34.32 arity_Nat__Onat__Groups_Oone,
% 221.16/34.32 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,
% 221.16/34.32 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,
% 221.16/34.32 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,
% 221.16/34.32 arity_Nat__Onat__Groups_Oordered__comm__monoid__add,
% 221.16/34.32 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Int_Onumber,
% 221.16/34.32 arity_Nat__Onat__Orderings_Olinorder, arity_Nat__Onat__Orderings_Oord,
% 221.16/34.32 arity_Nat__Onat__Orderings_Oorder, arity_Nat__Onat__Orderings_Opreorder,
% 221.16/34.32 arity_Nat__Onat__Rings_Ocomm__semiring,
% 221.16/34.32 arity_Nat__Onat__Rings_Ocomm__semiring__0, arity_Nat__Onat__Rings_Odvd,
% 221.16/34.32 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,
% 221.16/34.32 arity_Nat__Onat__Rings_Olinordered__semiring,
% 221.16/34.32 arity_Nat__Onat__Rings_Olinordered__semiring__strict,
% 221.16/34.32 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors,
% 221.16/34.32 arity_Nat__Onat__Rings_Oordered__cancel__semiring,
% 221.16/34.32 arity_Nat__Onat__Rings_Oordered__comm__semiring,
% 221.16/34.32 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring,
% 221.16/34.32 arity_Nat__Onat__Rings_Osemiring__0,
% 221.16/34.32 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 221.16/34.32 arity_Polynomial__Opoly__Divides_Oring__div,
% 221.16/34.32 arity_Polynomial__Opoly__Divides_Osemiring__div,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oab__group__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oab__semigroup__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Ogroup__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Ominus,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Omonoid__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oone,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Osgn__if,
% 221.16/34.32 arity_Polynomial__Opoly__Groups_Ouminus, arity_Polynomial__Opoly__Groups_Ozero,
% 221.16/34.32 arity_Polynomial__Opoly__Int_Onumber,
% 221.16/34.32 arity_Polynomial__Opoly__Int_Onumber__ring,
% 221.16/34.32 arity_Polynomial__Opoly__Int_Oring__char__0,
% 221.16/34.32 arity_Polynomial__Opoly__Orderings_Olinorder,
% 221.16/34.32 arity_Polynomial__Opoly__Orderings_Oord,
% 221.16/34.32 arity_Polynomial__Opoly__Orderings_Oorder,
% 221.16/34.32 arity_Polynomial__Opoly__Orderings_Opreorder,
% 221.16/34.32 arity_Polynomial__Opoly__Power_Opower,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Ocomm__ring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Ocomm__ring__1,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Ocomm__semiring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Oidom,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__idom,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__ring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__semidom,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__semiring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Omult__zero,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Ono__zero__divisors,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Oordered__ring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Oordered__semiring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Osemiring,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Osemiring__0,
% 221.16/34.32 arity_Polynomial__Opoly__Rings_Ozero__neq__one,
% 221.16/34.32 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 221.16/34.32 arity_fun__Groups_Ominus, arity_fun__Groups_Ouminus,
% 221.16/34.32 arity_fun__Lattices_Oboolean__algebra, arity_fun__Orderings_Oord,
% 221.16/34.32 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder,
% 221.16/34.32 fact_Deriv_Oadd__diff__add, fact_Limits_Ominus__diff__minus,
% 221.16/34.32 fact_Nat_Odiff__diff__eq, fact_Suc__diff__diff, fact_Suc__diff__le,
% 221.16/34.32 fact_Suc__inject, fact_Suc__leD, fact_Suc__leI, fact_Suc__le__eq,
% 221.16/34.32 fact_Suc__le__lessD, fact_Suc__le__mono, fact_Suc__lessD, fact_Suc__lessI,
% 221.16/34.32 fact_Suc__less__SucD, fact_Suc__less__eq, fact_Suc__mono,
% 221.16/34.32 fact_Suc__mult__cancel1, fact_Suc__mult__le__cancel1,
% 221.16/34.32 fact_Suc__mult__less__cancel1, fact_Suc__n__not__le__n, fact_Suc__n__not__n,
% 221.16/34.32 fact_ab__diff__minus, fact_ab__left__minus,
% 221.16/34.32 fact_ab__semigroup__add__class_Oadd__ac_I1_J,
% 221.16/34.32 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_add_Ocomm__neutral,
% 221.16/34.32 fact_add__0, fact_add__0__iff, fact_add__0__left, fact_add__0__right,
% 221.16/34.32 fact_add__Suc, fact_add__Suc__right, fact_add__Suc__shift,
% 221.16/34.32 fact_add__diff__assoc, fact_add__diff__assoc2, fact_add__diff__cancel,
% 221.16/34.32 fact_add__diff__inverse, fact_add__eq__0__iff, fact_add__imp__eq,
% 221.16/34.32 fact_add__increasing, fact_add__increasing2, fact_add__leD1, fact_add__leD2,
% 221.16/34.32 fact_add__leE, fact_add__le__cancel__left, fact_add__le__cancel__right,
% 221.16/34.32 fact_add__le__imp__le__left, fact_add__le__imp__le__right,
% 221.16/34.32 fact_add__le__less__mono, fact_add__le__mono, fact_add__le__mono1,
% 221.16/34.32 fact_add__left__cancel, fact_add__left__imp__eq, fact_add__left__mono,
% 221.16/34.32 fact_add__lessD1, fact_add__less__cancel__left, fact_add__less__cancel__right,
% 221.16/34.32 fact_add__less__imp__less__left, fact_add__less__imp__less__right,
% 221.16/34.32 fact_add__less__le__mono, fact_add__less__mono, fact_add__less__mono1,
% 221.16/34.32 fact_add__minus__cancel, fact_add__mono, fact_add__monom,
% 221.16/34.32 fact_add__mult__distrib, fact_add__mult__distrib2, fact_add__neg__neg,
% 221.16/34.32 fact_add__neg__nonpos, fact_add__nonneg__eq__0__iff, fact_add__nonneg__nonneg,
% 221.16/34.32 fact_add__nonneg__pos, fact_add__nonpos__neg, fact_add__nonpos__nonpos,
% 221.16/34.32 fact_add__number__of__diff1, fact_add__number__of__diff2,
% 221.16/34.32 fact_add__number__of__eq, fact_add__number__of__left, fact_add__pCons,
% 221.16/34.32 fact_add__poly__code_I1_J, fact_add__poly__code_I2_J, fact_add__pos__nonneg,
% 221.16/34.32 fact_add__pos__pos, fact_add__right__cancel, fact_add__right__imp__eq,
% 221.16/34.32 fact_add__right__mono, fact_add__scale__eq__noteq, fact_add__strict__increasing,
% 221.16/34.32 fact_add__strict__increasing2, fact_add__strict__left__mono,
% 221.16/34.32 fact_add__strict__mono, fact_add__strict__right__mono, fact_arith__simps_I30_J,
% 221.16/34.32 fact_arith__simps_I32_J, fact_coeff__0, fact_coeff__add, fact_coeff__diff,
% 221.16/34.32 fact_coeff__eq__0, fact_coeff__inject, fact_coeff__linear__power,
% 221.16/34.32 fact_coeff__minus, fact_coeff__monom, fact_coeff__mult__degree__sum,
% 221.16/34.32 fact_coeff__pCons__Suc, fact_combine__common__factor,
% 221.16/34.32 fact_comm__mult__left__mono, fact_comm__mult__strict__left__mono,
% 221.16/34.32 fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,
% 221.16/34.32 fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,
% 221.16/34.32 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,
% 221.16/34.32 fact_comm__semiring__class_Odistrib, fact_compl__eq__compl__iff,
% 221.16/34.32 fact_compl__le__compl__iff, fact_compl__mono, fact_convex__bound__le,
% 221.16/34.32 fact_convex__bound__lt, fact_crossproduct__eq, fact_crossproduct__noteq,
% 221.16/34.32 fact_degree__add__eq__left, fact_degree__add__eq__right, fact_degree__add__le,
% 221.16/34.32 fact_degree__add__less, fact_degree__diff__le, fact_degree__diff__less,
% 221.16/34.32 fact_degree__le, fact_degree__linear__power, fact_degree__minus,
% 221.16/34.32 fact_degree__monom__eq, fact_degree__monom__le, fact_degree__mult__eq,
% 221.16/34.32 fact_degree__mult__le, fact_degree__pCons__eq, fact_degree__pCons__le,
% 221.16/34.32 fact_degree__pcompose__le, fact_degree__power__le, fact_diff__0,
% 221.16/34.32 fact_diff__0__right, fact_diff__Suc__Suc, fact_diff__Suc__diff__eq1,
% 221.16/34.32 fact_diff__Suc__diff__eq2, fact_diff__add__assoc, fact_diff__add__assoc2,
% 221.16/34.32 fact_diff__add__cancel, fact_diff__add__inverse2, fact_diff__cancel,
% 221.16/34.32 fact_diff__cancel2, fact_diff__commute, fact_diff__def, fact_diff__diff__cancel,
% 221.16/34.32 fact_diff__diff__left, fact_diff__diff__right, fact_diff__eq__diff__eq,
% 221.16/34.32 fact_diff__eq__diff__less, fact_diff__eq__diff__less__eq, fact_diff__int__def,
% 221.16/34.32 fact_diff__int__def__symmetric, fact_diff__le__mono, fact_diff__le__mono2,
% 221.16/34.32 fact_diff__le__self, fact_diff__less__Suc, fact_diff__less__mono,
% 221.16/34.32 fact_diff__less__mono2, fact_diff__minus__eq__add, fact_diff__monom,
% 221.16/34.32 fact_diff__mult__distrib, fact_diff__mult__distrib2, fact_diff__number__of__eq,
% 221.16/34.32 fact_diff__pCons, fact_diff__poly__code_I1_J, fact_diff__poly__code_I2_J,
% 221.16/34.32 fact_diff__self, fact_div__0, fact_div__add, fact_div__add__self1,
% 221.16/34.32 fact_div__add__self2, fact_div__by__0, fact_div__by__1, fact_div__dvd__div,
% 221.16/34.32 fact_div__mult2__eq, fact_div__mult__div__if__dvd, fact_div__mult__mult1,
% 221.16/34.32 fact_div__mult__mult1__if, fact_div__mult__mult2, fact_div__mult__self1,
% 221.16/34.32 fact_div__mult__self1__is__id, fact_div__mult__self2,
% 221.16/34.32 fact_div__mult__self2__is__id, fact_div__mult__swap, fact_div__power,
% 221.16/34.32 fact_div__self, fact_divisors__zero,
% 221.16/34.32 fact_double__add__le__zero__iff__single__add__le__zero,
% 221.16/34.32 fact_double__add__less__zero__iff__single__add__less__zero, fact_double__compl,
% 221.16/34.32 fact_double__eq__0__iff, fact_double__zero__sym, fact_dpn, fact_dvdI,
% 221.16/34.32 fact_dvd_Oantisym, fact_dvd_Oantisym__conv, fact_dvd_Oeq__iff,
% 221.16/34.32 fact_dvd_Oeq__refl, fact_dvd_Ole__imp__less__or__eq, fact_dvd_Ole__less,
% 221.16/34.32 fact_dvd_Ole__less__trans, fact_dvd_Ole__neq__trans, fact_dvd_Oless__asym,
% 221.16/34.32 fact_dvd_Oless__asym_H, fact_dvd_Oless__imp__le, fact_dvd_Oless__imp__neq,
% 221.16/34.32 fact_dvd_Oless__imp__not__eq, fact_dvd_Oless__imp__not__eq2,
% 221.16/34.32 fact_dvd_Oless__imp__not__less, fact_dvd_Oless__le, fact_dvd_Oless__le__trans,
% 221.16/34.32 fact_dvd_Oless__not__sym, fact_dvd_Oless__trans, fact_dvd_Oneq__le__trans,
% 221.16/34.32 fact_dvd_Oord__eq__le__trans, fact_dvd_Oord__eq__less__trans,
% 221.16/34.32 fact_dvd_Oord__le__eq__trans, fact_dvd_Oord__less__eq__trans,
% 221.16/34.32 fact_dvd_Oorder__refl, fact_dvd_Oorder__trans, fact_dvd__0__left,
% 221.16/34.32 fact_dvd__0__right, fact_dvd__add, fact_dvd__antisym, fact_dvd__diff,
% 221.16/34.32 fact_dvd__diffD, fact_dvd__diffD1, fact_dvd__diff__nat,
% 221.16/34.32 fact_dvd__div__div__eq__mult, fact_dvd__div__eq__mult, fact_dvd__div__mult,
% 221.16/34.32 fact_dvd__div__mult__self, fact_dvd__div__neg, fact_dvd__iff__poly__eq__0,
% 221.16/34.32 fact_dvd__imp__degree__le, fact_dvd__minus__iff, fact_dvd__mult,
% 221.16/34.32 fact_dvd__mult2, fact_dvd__mult__cancel__left, fact_dvd__mult__cancel__right,
% 221.16/34.32 fact_dvd__mult__div__cancel, fact_dvd__mult__left, fact_dvd__mult__right,
% 221.16/34.32 fact_dvd__neg__div, fact_dvd__power__le, fact_dvd__power__same,
% 221.16/34.32 fact_dvd__reduce, fact_dvd__refl, fact_dvd__trans, fact_dvd__triv__left,
% 221.16/34.32 fact_dvd__triv__right, fact_eq__add__iff1, fact_eq__add__iff2,
% 221.16/34.32 fact_eq__diff__iff, fact_eq__iff__diff__eq__0, fact_eq__imp__le,
% 221.16/34.32 fact_eq__neg__iff__add__eq__0, fact_eq__number__of,
% 221.16/34.32 fact_eq__zero__or__degree__less, fact_equal__neg__zero,
% 221.16/34.32 fact_equation__minus__iff, fact_even__less__0__iff, fact_expand__poly__eq,
% 221.16/34.32 fact_ext, fact_field__power__not__zero, fact_inf__period_I3_J,
% 221.16/34.32 fact_inf__period_I4_J, fact_leD, fact_leI, fact_le__SucE, fact_le__SucI,
% 221.16/34.32 fact_le__Suc__eq, fact_le__add1, fact_le__add2, fact_le__add__diff,
% 221.16/34.32 fact_le__add__diff__inverse, fact_le__add__diff__inverse2, fact_le__add__iff1,
% 221.16/34.32 fact_le__add__iff2, fact_le__antisym, fact_le__cube, fact_le__degree,
% 221.16/34.32 fact_le__diff__conv, fact_le__diff__conv2, fact_le__diff__iff,
% 221.16/34.32 fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE, fact_le__fun__def,
% 221.16/34.32 fact_le__iff__diff__le__0, fact_le__imp__diff__is__add, fact_le__imp__less__Suc,
% 221.16/34.32 fact_le__imp__neg__le, fact_le__imp__power__dvd, fact_le__less__Suc__eq,
% 221.16/34.32 fact_le__minus__iff, fact_le__minus__self__iff, fact_le__neq__implies__less,
% 221.16/34.32 fact_le__number__of, fact_le__number__of__eq__not__less, fact_le__refl,
% 221.16/34.32 fact_le__square, fact_le__trans, fact_leading__coeff__0__iff,
% 221.16/34.32 fact_leading__coeff__neq__0, fact_left__add__mult__distrib,
% 221.16/34.32 fact_left__diff__distrib__number__of, fact_left__distrib__number__of,
% 221.16/34.32 fact_left__minus, fact_lemma__realpow__diff, fact_lessI, fact_less__1__mult,
% 221.16/34.32 fact_less__SucE, fact_less__SucI, fact_less__Suc__eq__le, fact_less__add__Suc1,
% 221.16/34.32 fact_less__add__Suc2, fact_less__add__eq__less, fact_less__add__iff1,
% 221.16/34.32 fact_less__add__iff2, fact_less__add__one, fact_less__antisym,
% 221.16/34.32 fact_less__diff__conv, fact_less__diff__iff, fact_less__eq__Suc__le,
% 221.16/34.32 fact_less__eq__number__of__int__code, fact_less__eq__poly__def,
% 221.16/34.32 fact_less__fun__def, fact_less__iff__Suc__add, fact_less__iff__diff__less__0,
% 221.16/34.32 fact_less__imp__diff__less, fact_less__imp__le__nat, fact_less__imp__neq,
% 221.16/34.32 fact_less__irrefl__nat, fact_less__le__not__le, fact_less__minus__iff,
% 221.16/34.32 fact_less__minus__self__iff, fact_less__not__refl, fact_less__not__refl2,
% 221.16/34.32 fact_less__not__refl3, fact_less__number__of, fact_less__number__of__int__code,
% 221.16/34.32 fact_less__or__eq__imp__le, fact_less__poly__def, fact_less__trans__Suc,
% 221.16/34.32 fact_linorder__antisym__conv1, fact_linorder__antisym__conv2,
% 221.16/34.32 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases,
% 221.16/34.32 fact_linorder__le__less__linear, fact_linorder__less__linear,
% 221.16/34.32 fact_linorder__linear, fact_linorder__neqE,
% 221.16/34.32 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat,
% 221.16/34.32 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less,
% 221.16/34.32 fact_minus__add, fact_minus__add__cancel, fact_minus__add__distrib,
% 221.16/34.32 fact_minus__apply, fact_minus__diff__eq, fact_minus__dvd__iff,
% 221.16/34.32 fact_minus__equation__iff, fact_minus__le__iff, fact_minus__le__self__iff,
% 221.16/34.32 fact_minus__less__iff, fact_minus__minus, fact_minus__monom,
% 221.16/34.32 fact_minus__mult__commute, fact_minus__mult__left, fact_minus__mult__minus,
% 221.16/34.32 fact_minus__mult__right, fact_minus__number__of__mult,
% 221.16/34.32 fact_minus__numeral__code_I5_J, fact_minus__numeral__code_I6_J,
% 221.16/34.32 fact_minus__pCons, fact_minus__poly__code_I1_J, fact_minus__poly__code_I2_J,
% 221.16/34.32 fact_minus__unique, fact_minus__zero, fact_monom__Suc, fact_monom__eq__0,
% 221.16/34.32 fact_monom__eq__0__iff, fact_monom__eq__iff, fact_mult_Oadd__left,
% 221.16/34.32 fact_mult_Oadd__right, fact_mult_Ocomm__neutral, fact_mult_Odiff__left,
% 221.16/34.32 fact_mult_Odiff__right, fact_mult_Ominus__left, fact_mult_Ominus__right,
% 221.16/34.32 fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, fact_mult_Ozero__right,
% 221.16/34.32 fact_mult__1, fact_mult__1__left, fact_mult__1__right, fact_mult__Suc,
% 221.16/34.32 fact_mult__Suc__right, fact_mult__diff__mult, fact_mult__dvd__mono,
% 221.16/34.32 fact_mult__eq__0__iff, fact_mult__idem, fact_mult__le__0__iff,
% 221.16/34.32 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos,
% 221.16/34.32 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1,
% 221.16/34.32 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Odiff,
% 221.16/34.32 fact_mult__left_Ominus, fact_mult__left_Ozero, fact_mult__left__idem,
% 221.16/34.32 fact_mult__left__le__imp__le, fact_mult__left__le__one__le,
% 221.16/34.32 fact_mult__left__less__imp__less, fact_mult__left__mono,
% 221.16/34.32 fact_mult__left__mono__neg, fact_mult__less__cancel__left__disj,
% 221.16/34.32 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos,
% 221.16/34.32 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left,
% 221.16/34.32 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less,
% 221.16/34.32 fact_mult__mono, fact_mult__mono_H, fact_mult__monom, fact_mult__neg__neg,
% 221.16/34.32 fact_mult__neg__pos, fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos,
% 221.16/34.32 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg,
% 221.16/34.32 fact_mult__nonpos__nonpos, fact_mult__number__of__left,
% 221.16/34.32 fact_mult__poly__0__left, fact_mult__poly__0__right, fact_mult__poly__add__left,
% 221.16/34.32 fact_mult__pos__neg, fact_mult__pos__neg2, fact_mult__pos__pos,
% 221.16/34.32 fact_mult__right_Oadd, fact_mult__right_Odiff, fact_mult__right_Ominus,
% 221.16/34.32 fact_mult__right_Ozero, fact_mult__right__le__imp__le,
% 221.16/34.32 fact_mult__right__le__one__le, fact_mult__right__less__imp__less,
% 221.16/34.32 fact_mult__right__mono, fact_mult__right__mono__neg,
% 221.16/34.32 fact_mult__strict__left__mono, fact_mult__strict__left__mono__neg,
% 221.16/34.32 fact_mult__strict__mono, fact_mult__strict__mono_H,
% 221.16/34.32 fact_mult__strict__right__mono, fact_mult__strict__right__mono__neg,
% 221.16/34.32 fact_mult__zero__left, fact_mult__zero__right, fact_n__not__Suc__n,
% 221.16/34.32 fact_nat_Oinject, fact_nat__add__assoc, fact_nat__add__commute,
% 221.16/34.32 fact_nat__add__left__cancel, fact_nat__add__left__cancel__le,
% 221.16/34.32 fact_nat__add__left__cancel__less, fact_nat__add__left__commute,
% 221.16/34.32 fact_nat__add__right__cancel, fact_nat__diff__add__eq1,
% 221.16/34.32 fact_nat__diff__add__eq2, fact_nat__eq__add__iff1, fact_nat__eq__add__iff2,
% 221.16/34.32 fact_nat__le__add__iff1, fact_nat__le__add__iff2, fact_nat__le__linear,
% 221.16/34.32 fact_nat__less__add__iff1, fact_nat__less__add__iff2, fact_nat__less__cases,
% 221.16/34.32 fact_nat__less__le, fact_nat__mult__assoc, fact_nat__mult__commute,
% 221.16/34.32 fact_nat__neq__iff, fact_neg__equal__iff__equal, fact_neg__equal__zero,
% 221.16/34.32 fact_neg__le__iff__le, fact_neg__less__iff__less, fact_neg__less__nonneg,
% 221.16/34.32 fact_no__zero__divisors, fact_not__add__less1, fact_not__add__less2,
% 221.16/34.32 fact_not__leE, fact_not__less__eq, fact_not__less__eq__eq,
% 221.16/34.32 fact_not__less__iff__gr__or__eq, fact_not__less__less__Suc__eq,
% 221.16/34.32 fact_not__pos__poly__0, fact_not__square__less__zero,
% 221.16/34.32 fact_not__sum__squares__lt__zero, fact_number__of__add, fact_number__of__diff,
% 221.16/34.32 fact_number__of__is__id, fact_number__of__minus, fact_number__of__mult,
% 221.16/34.32 fact_number__of__reorient, fact_one__dvd, fact_one__le__power,
% 221.16/34.32 fact_one__poly__def, fact_one__reorient, fact_oop, fact_ord__eq__le__trans,
% 221.16/34.32 fact_ord__eq__less__trans, fact_ord__le__eq__trans, fact_ord__less__eq__trans,
% 221.16/34.32 fact_order, fact_order__1, fact_order__2, fact_order__antisym,
% 221.16/34.32 fact_order__antisym__conv, fact_order__degree, fact_order__eq__iff,
% 221.16/34.32 fact_order__eq__refl, fact_order__le__imp__less__or__eq, fact_order__le__less,
% 221.16/34.32 fact_order__le__less__trans, fact_order__le__neq__trans, fact_order__less__asym,
% 221.16/34.32 fact_order__less__asym_H, fact_order__less__imp__le,
% 221.16/34.32 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2,
% 221.16/34.32 fact_order__less__imp__not__less, fact_order__less__irrefl,
% 221.16/34.32 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym,
% 221.16/34.32 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl,
% 221.16/34.32 fact_order__trans, fact_pCons__0__0, fact_pCons__eq__iff, fact_pcompose__0,
% 221.16/34.32 fact_pcompose__pCons, fact_pdivmod__rel__0, fact_pdivmod__rel__0__iff,
% 221.16/34.32 fact_pdivmod__rel__by__0, fact_pdivmod__rel__by__0__iff, fact_pdivmod__rel__def,
% 221.16/34.32 fact_pdivmod__rel__mult, fact_pdivmod__rel__unique,
% 221.16/34.32 fact_pdivmod__rel__unique__div, fact_pdivmod__rel__unique__mod,
% 221.16/34.32 fact_plus__numeral__code_I9_J, fact_poly__0, fact_poly__1, fact_poly__add,
% 221.16/34.32 fact_poly__diff, fact_poly__dvd__antisym, fact_poly__eq__iff, fact_poly__minus,
% 221.16/34.32 fact_poly__monom, fact_poly__mult, fact_poly__pCons, fact_poly__pcompose,
% 221.16/34.32 fact_poly__power, fact_poly__rec_Osimps, fact_poly__rec__0,
% 221.16/34.32 fact_poly__rec__pCons, fact_poly__replicate__append, fact_pos__add__strict,
% 221.16/34.32 fact_pos__poly__add, fact_pos__poly__def, fact_pos__poly__mult,
% 221.16/34.32 fact_pos__poly__pCons, fact_pos__poly__total, fact_power_Opower_Opower__Suc,
% 221.16/34.32 fact_power__0__Suc, fact_power__Suc, fact_power__Suc2, fact_power__Suc__less,
% 221.16/34.32 fact_power__Suc__less__one, fact_power__commutes, fact_power__decreasing,
% 221.16/34.32 fact_power__gt1, fact_power__gt1__lemma, fact_power__increasing,
% 221.16/34.32 fact_power__increasing__iff, fact_power__inject__base, fact_power__inject__exp,
% 221.16/34.32 fact_power__le__dvd, fact_power__le__imp__le__base,
% 221.16/34.32 fact_power__le__imp__le__exp, fact_power__less__imp__less__base,
% 221.16/34.32 fact_power__less__imp__less__exp, fact_power__less__power__Suc,
% 221.16/34.32 fact_power__minus, fact_power__mono, fact_power__mult,
% 221.16/34.32 fact_power__mult__distrib, fact_power__one, fact_power__power__power,
% 221.16/34.32 fact_power__strict__decreasing, fact_power__strict__increasing,
% 221.16/34.32 fact_power__strict__increasing__iff, fact_real__squared__diff__one__factored,
% 221.16/34.32 fact_realpow__Suc__le__self, fact_right__diff__distrib__number__of,
% 221.16/34.32 fact_right__distrib__number__of, fact_right__minus, fact_right__minus__eq,
% 221.16/34.32 fact_sgn0, fact_sgn__0__0, fact_sgn__1__neg, fact_sgn__1__pos,
% 221.16/34.32 fact_sgn__greater, fact_sgn__if, fact_sgn__less, fact_sgn__minus,
% 221.16/34.32 fact_sgn__mult, fact_sgn__neg, fact_sgn__one, fact_sgn__poly__def,
% 221.16/34.32 fact_sgn__pos, fact_sgn__sgn, fact_sgn__times, fact_sgn__zero,
% 221.16/34.32 fact_sgn__zero__iff, fact_split__mult__neg__le, fact_split__mult__pos__le,
% 221.16/34.32 fact_square__eq__1__iff, fact_square__eq__iff, fact_sum__squares__eq__zero__iff,
% 221.16/34.32 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff,
% 221.16/34.32 fact_sum__squares__le__zero__iff, fact_synthetic__div__0,
% 221.16/34.32 fact_synthetic__div__correct_H, fact_synthetic__div__pCons,
% 221.16/34.32 fact_termination__basic__simps_I1_J, fact_termination__basic__simps_I2_J,
% 221.16/34.32 fact_termination__basic__simps_I3_J, fact_termination__basic__simps_I4_J,
% 221.16/34.32 fact_termination__basic__simps_I5_J, fact_times_Oidem,
% 221.16/34.32 fact_times__numeral__code_I5_J, fact_trans__le__add1, fact_trans__le__add2,
% 221.16/34.32 fact_trans__less__add1, fact_trans__less__add2, fact_tsub__eq,
% 221.16/34.32 fact_uminus__apply, fact_uminus__dvd__conv_I1_J, fact_uminus__dvd__conv_I2_J,
% 221.16/34.32 fact_unity__coeff__ex, fact_xt1_I10_J, fact_xt1_I11_J, fact_xt1_I12_J,
% 221.16/34.32 fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J, fact_xt1_I5_J,
% 221.16/34.32 fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J, fact_zadd__assoc,
% 221.16/34.32 fact_zadd__commute, fact_zadd__left__commute, fact_zadd__left__mono,
% 221.16/34.32 fact_zadd__strict__right__mono, fact_zadd__zless__mono,
% 221.16/34.32 fact_zadd__zmult__distrib, fact_zadd__zmult__distrib2,
% 221.16/34.32 fact_zdiff__zmult__distrib, fact_zdiff__zmult__distrib2, fact_zdiv__zminus2,
% 221.16/34.32 fact_zdiv__zminus__zminus, fact_zdvd__mult__div__cancel, fact_zdvd__period,
% 221.16/34.32 fact_zdvd__reduce, fact_zdvd__zdiffD,
% 221.16/34.32 fact_zero__le__double__add__iff__zero__le__single__add,
% 221.16/34.32 fact_zero__le__mult__iff, fact_zero__le__power, fact_zero__le__square,
% 221.16/34.32 fact_zero__less__double__add__iff__zero__less__single__add,
% 221.16/34.32 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, fact_zero__less__one,
% 221.16/34.32 fact_zero__less__power, fact_zero__less__two, fact_zero__reorient,
% 221.16/34.32 fact_zle__antisym, fact_zle__linear, fact_zle__refl, fact_zle__trans,
% 221.16/34.32 fact_zless__le, fact_zless__linear, fact_zminus__zadd__distrib,
% 221.16/34.32 fact_zminus__zminus, fact_zmult__assoc, fact_zmult__commute, fact_zmult__zminus,
% 221.16/34.32 fact_zpower__zadd__distrib, fact_zpower__zpower, help_c__fequal__1,
% 221.16/34.32 help_c__fequal__2
% 221.16/34.32
% 221.16/34.32 Those formulas are unsatisfiable:
% 221.16/34.32 ---------------------------------
% 221.16/34.32
% 221.16/34.32 Begin of proof
% 221.44/34.33 |
% 221.44/34.33 | ALPHA: (fact_assms_I3_J) implies:
% 221.44/34.33 | (1) ? [v0: $i] : ( ~ (v0 = v_n) & c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 221.44/34.33 | = v0 & $i(v0))
% 221.44/34.33 |
% 221.44/34.33 | ALPHA: (fact_n0) implies:
% 221.44/34.33 | (2) ? [v0: $i] : ( ~ (v0 = v_na____) &
% 221.44/34.33 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0))
% 221.44/34.33 |
% 221.44/34.33 | ALPHA: (fact_q0) implies:
% 221.44/34.33 | (3) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v_qa____) &
% 221.44/34.33 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.33 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0))
% 221.44/34.33 |
% 221.44/34.33 | ALPHA: (fact_oa) implies:
% 221.44/34.33 | (4) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 221.44/34.33 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v0 &
% 221.44/34.33 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0))
% 221.44/34.33 |
% 221.44/34.33 | ALPHA: (fact_pne) implies:
% 221.44/34.33 | (5) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v_pa____) &
% 221.44/34.33 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.33 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0))
% 221.44/34.33 |
% 221.44/34.33 | ALPHA: (fact_k) implies:
% 221.44/34.33 | (6) ? [v0: $i] : ( ~ (v0 = v_k____) &
% 221.44/34.33 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v0))
% 221.44/34.33 |
% 221.44/34.33 | ALPHA: (fact_kpn) implies:
% 221.44/34.34 | (7) ? [v0: $i] : ? [v1: $i] : (c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 221.44/34.34 | v_k____, v1) = v_s____ & tc_Polynomial_Opoly(tc_Complex_Ocomplex) =
% 221.44/34.34 | v0 & c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact__096order_Aa_Ap_A_060_061_An_096) implies:
% 221.44/34.34 | (8) ? [v0: $i] : (c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____,
% 221.44/34.34 | v_pa____) = v0 & $i(v0) &
% 221.44/34.34 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v_na____))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_s) implies:
% 221.44/34.34 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.44/34.34 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 221.44/34.34 | [v10: $i] : ? [v11: $i] : (c_Groups_Otimes__class_Otimes(v0) = v1 &
% 221.44/34.34 | c_Power_Opower__class_Opower(v0) = v2 &
% 221.44/34.34 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v3 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v4 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v4, v5) = v6 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v6) = v7 &
% 221.44/34.34 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v9 &
% 221.44/34.34 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(v0) = v5 & hAPP(v11, v_s____) = v_pa____
% 221.44/34.34 | & hAPP(v8, v9) = v10 & hAPP(v2, v7) = v8 & hAPP(v1, v10) = v11 &
% 221.44/34.34 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 221.44/34.34 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_r) implies:
% 221.44/34.34 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.44/34.34 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 221.44/34.34 | (c_Groups_Otimes__class_Otimes(v0) = v1 &
% 221.44/34.34 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v2 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 221.44/34.34 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(v0) = v4 & hAPP(v7, v_r____) = v_qa____
% 221.44/34.34 | & hAPP(v1, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 221.44/34.34 | $i(v2) & $i(v1) & $i(v0))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_a) implies:
% 221.44/34.34 | (11) ? [v0: $i] : ? [v1: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 221.44/34.34 | v_pa____) = v0 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 221.44/34.34 | = v1 & hAPP(v0, v_a____) = v1 & $i(v1) & $i(v0))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact__096_B_Bthesis_O_A_I_B_Bs_O_Ap_A_061_A_091_058_N_Aa_M_A1_058_093_A_094_Aorder_Aa_Ap_A_K_As_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 221.44/34.34 | implies:
% 221.44/34.34 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.44/34.34 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 221.44/34.34 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 221.44/34.34 | (c_Groups_Otimes__class_Otimes(v0) = v1 &
% 221.44/34.34 | c_Power_Opower__class_Opower(v0) = v2 &
% 221.44/34.34 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v3 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v4 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v4, v5) = v6 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v6) = v7 &
% 221.44/34.34 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v9 &
% 221.44/34.34 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(v0) = v5 & hAPP(v11, v12) = v_pa____ &
% 221.44/34.34 | hAPP(v8, v9) = v10 & hAPP(v2, v7) = v8 & hAPP(v1, v10) = v11 &
% 221.44/34.34 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 221.44/34.34 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_sne) implies:
% 221.44/34.34 | (13) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v_s____) &
% 221.44/34.34 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_ap_I1_J) implies:
% 221.44/34.34 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.44/34.34 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 221.44/34.34 | (c_Power_Opower__class_Opower(v0) = v1 &
% 221.44/34.34 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v2 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 221.44/34.34 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v8 &
% 221.44/34.34 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(v0) = v4 & hAPP(v7, v8) = v9 & hAPP(v1,
% 221.44/34.34 | v6) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 221.44/34.34 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & c_Rings_Odvd__class_Odvd(v0, v9,
% 221.44/34.34 | v_pa____))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_power__strict__mono) implies:
% 221.44/34.34 | (15) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.34 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.44/34.34 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 221.44/34.34 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9) |
% 221.44/34.34 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2)
% 221.44/34.34 | = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.44/34.34 | c_Orderings_Oord__class_Oless(v4, v3, v2) | ~
% 221.44/34.34 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 221.44/34.34 | class_Rings_Olinordered__semidom(v4) |
% 221.44/34.34 | c_Orderings_Oord__class_Oless(v4, v7, v9) | ? [v10: $i] :
% 221.44/34.34 | (c_Groups_Ozero__class_Ozero(v4) = v10 & $i(v10) & ~
% 221.44/34.34 | c_Orderings_Oord__class_Oless__eq(v4, v10, v3))))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_realpow__num__eq__if) implies:
% 221.44/34.34 | (16) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 221.44/34.34 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0)
% 221.44/34.34 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 221.44/34.34 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 221.44/34.34 | [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1)
% 221.44/34.34 | = v9) | ~ (c_Groups_Otimes__class_Otimes(v4) = v7) | ~
% 221.44/34.34 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v10) = v11)
% 221.44/34.34 | | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ (hAPP(v5,
% 221.44/34.34 | v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.34 | class_Power_Opower(v4) | ? [v12: $i] : ? [v13: $i] : (( ~ (v3 =
% 221.44/34.34 | v0) | (v13 = v12 & c_Groups_Oone__class_Oone(v4) = v12 &
% 221.44/34.34 | hAPP(v6, v0) = v12 & $i(v12))) & (v3 = v0 | (v12 = v11 &
% 221.44/34.34 | hAPP(v6, v3) = v11 & $i(v11))))))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_one__less__power) implies:
% 221.44/34.34 | (17) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.34 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.44/34.34 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) |
% 221.44/34.34 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~
% 221.44/34.34 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.44/34.34 | v0, v1) | ~ class_Rings_Olinordered__semidom(v3) | ? [v7: $i]
% 221.44/34.34 | : (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~
% 221.44/34.34 | c_Orderings_Oord__class_Oless(v3, v7, v2) |
% 221.44/34.34 | c_Orderings_Oord__class_Oless(v3, v7, v6)))))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_power__eq__imp__eq__base) implies:
% 221.44/34.34 | (18) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.34 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.44/34.34 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~
% 221.44/34.34 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v2) = v7) |
% 221.44/34.34 | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v1)
% 221.44/34.34 | = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.44/34.34 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 221.44/34.34 | class_Rings_Olinordered__semidom(v4) | ? [v9: $i] :
% 221.44/34.34 | (c_Groups_Ozero__class_Ozero(v4) = v9 & $i(v9) & ( ~
% 221.44/34.34 | c_Orderings_Oord__class_Oless__eq(v4, v9, v3) | ~
% 221.44/34.34 | c_Orderings_Oord__class_Oless__eq(v4, v9, v1)))))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_ds0) implies:
% 221.44/34.34 | (19) ? [v0: $i] : (c_Polynomial_Odegree(tc_Complex_Ocomplex, v_s____) = v0
% 221.44/34.34 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_assms_I1_J) implies:
% 221.44/34.34 | (20) $i(v_q)
% 221.44/34.34 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.44/34.34 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q) = v2 &
% 221.44/34.34 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p) = v0 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v2) &
% 221.44/34.34 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 221.44/34.34 | (hAPP(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ( ~ (v5 = v1) &
% 221.44/34.34 | hAPP(v0, v3) = v5 & $i(v5))))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_pq0) implies:
% 221.44/34.34 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.44/34.34 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = v0 &
% 221.44/34.34 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_qa____) = v2 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v2) &
% 221.44/34.34 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 221.44/34.34 | (hAPP(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ( ~ (v5 = v1) &
% 221.44/34.34 | hAPP(v0, v3) = v5 & $i(v5))))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_assms_I2_J) implies:
% 221.44/34.34 | (23) $i(v_p)
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096) implies:
% 221.44/34.34 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.44/34.34 | ? [v5: $i] : (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,
% 221.44/34.34 | v_a____) = v1 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 221.44/34.34 | v2 & c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v3) = v4 &
% 221.44/34.34 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v1, v4) = v5 &
% 221.44/34.34 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(v0) = v3 & $i(v5) & $i(v4) & $i(v3) &
% 221.44/34.34 | $i(v2) & $i(v1) & $i(v0) & c_Rings_Odvd__class_Odvd(v0, v5,
% 221.44/34.34 | v_qa____))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_calculation) implies:
% 221.44/34.34 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.44/34.34 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & $i(v0) & (( ~ (v1 =
% 221.44/34.34 | v_qa____) & c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1)) |
% 221.44/34.34 | (c_Power_Opower__class_Opower(v0) = v2 & hAPP(v3, v_na____) = v4 &
% 221.44/34.34 | hAPP(v2, v_qa____) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 221.44/34.34 | c_Rings_Odvd__class_Odvd(v0, v_pa____, v4))))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_IH) implies:
% 221.44/34.34 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 221.44/34.34 | (c_Power_Opower__class_Opower(v2) = v3 &
% 221.44/34.34 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v2 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v3) & $i(v2) &
% 221.44/34.34 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.44/34.34 | $i] : ! [v8: $i] : ! [v9: $i] : (v4 = v1 | ~
% 221.44/34.34 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v5) = v7) | ~ (hAPP(v8,
% 221.44/34.34 | v4) = v9) | ~ (hAPP(v3, v6) = v8) | ~ $i(v6) | ~ $i(v5) |
% 221.44/34.34 | ~ $i(v4) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4,
% 221.44/34.34 | v_na____) | c_Rings_Odvd__class_Odvd(v2, v5, v9) | ? [v10: $i]
% 221.44/34.34 | : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 221.44/34.34 | ($i(v12) & ((v13 = v0 & ~ (v14 = v0) &
% 221.44/34.34 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v6) = v10 &
% 221.44/34.34 | hAPP(v10, v12) = v14 & hAPP(v7, v12) = v0 & $i(v14) &
% 221.44/34.34 | $i(v10)) | ( ~ (v11 = v4) &
% 221.44/34.34 | c_Polynomial_Odegree(tc_Complex_Ocomplex, v5) = v11 &
% 221.44/34.34 | $i(v11))))))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_nat__mult__1) implies:
% 221.44/34.34 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.44/34.34 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 &
% 221.44/34.34 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 221.44/34.34 | (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_nat__1__eq__mult__iff) implies:
% 221.44/34.34 | (28) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.34 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 221.44/34.34 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) =
% 221.44/34.34 | v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 221.44/34.34 | $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) =
% 221.44/34.34 | v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 221.44/34.34 | $i] : ! [v3: $i] : (v3 = v0 | ~ (hAPP(v2, v0) = v3) | ~
% 221.44/34.34 | (hAPP(v1, v0) = v2)))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_nat__mult__1__right) implies:
% 221.44/34.34 | (29) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.34 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.34 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) |
% 221.44/34.34 | hAPP(v3, v1) = v2))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_nat__mult__eq__1__iff) implies:
% 221.44/34.34 | (30) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.34 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.34 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) =
% 221.44/34.34 | v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 221.44/34.34 | $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) =
% 221.44/34.34 | v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 221.44/34.34 | $i] : ! [v3: $i] : (v3 = v1 | ~ (hAPP(v2, v1) = v3) | ~
% 221.44/34.34 | (hAPP(v0, v1) = v2)))
% 221.44/34.34 |
% 221.44/34.34 | ALPHA: (fact_mult__eq__self__implies__10) implies:
% 221.44/34.34 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.44/34.34 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.34 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 221.44/34.34 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) &
% 221.44/34.34 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 =
% 221.44/34.34 | v1 | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) |
% 221.44/34.34 | ~ $i(v3)))
% 221.44/34.34 |
% 221.44/34.35 | ALPHA: (fact_mult__cancel2) implies:
% 221.44/34.35 | (32) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 221.44/34.35 | ! [v7: $i] : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) =
% 221.44/34.35 | v5) | ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~
% 221.44/34.35 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.44/34.35 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v2 | v3 = v1 | ~
% 221.44/34.35 | (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) =
% 221.44/34.35 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 221.44/34.35 | $i(v2)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__is__0) implies:
% 221.44/34.35 | (33) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) =
% 221.44/34.35 | v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : !
% 221.44/34.35 | [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~
% 221.44/34.35 | (hAPP(v0, v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : !
% 221.44/34.35 | [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~
% 221.44/34.35 | (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__0__right) implies:
% 221.44/34.35 | (34) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) |
% 221.44/34.35 | hAPP(v3, v1) = v1))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__0) implies:
% 221.44/34.35 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 &
% 221.44/34.35 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 221.44/34.35 | (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_power__one__right) implies:
% 221.44/34.35 | (36) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.44/34.35 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.44/34.35 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) |
% 221.44/34.35 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) |
% 221.44/34.35 | hAPP(v4, v0) = v1))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_nat__power__less__imp__less) implies:
% 221.44/34.35 | (37) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat)
% 221.44/34.35 | = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 221.44/34.35 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 221.44/34.35 | [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2)
% 221.44/34.35 | = v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.44/34.35 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 221.44/34.35 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__less__mono2) implies:
% 221.44/34.35 | (38) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 221.44/34.35 | ! [v7: $i] : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~
% 221.44/34.35 | (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__less__mono1) implies:
% 221.44/34.35 | (39) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 221.44/34.35 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5,
% 221.44/34.35 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) |
% 221.44/34.35 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__less__cancel2) implies:
% 221.44/34.35 | (40) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 221.44/34.35 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5,
% 221.44/34.35 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) |
% 221.44/34.35 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i]
% 221.44/34.35 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.44/34.35 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) =
% 221.44/34.35 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 221.44/34.35 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i]
% 221.44/34.35 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.44/34.35 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) =
% 221.44/34.35 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 221.44/34.35 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__less__cancel1) implies:
% 221.44/34.35 | (41) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 221.44/34.35 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.44/34.35 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i]
% 221.44/34.35 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.44/34.35 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.44/34.35 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i]
% 221.44/34.35 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.44/34.35 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.44/34.35 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_nat__0__less__mult__iff) implies:
% 221.44/34.35 | (42) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4,
% 221.44/34.35 | v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 221.44/34.35 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i]
% 221.44/34.35 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 221.44/34.35 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i]
% 221.44/34.35 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 221.44/34.35 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__le__cancel2) implies:
% 221.44/34.35 | (43) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 221.44/34.35 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5,
% 221.44/34.35 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) |
% 221.44/34.35 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2:
% 221.44/34.35 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.44/34.35 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3)
% 221.44/34.35 | = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 221.44/34.35 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)) & ! [v2:
% 221.44/34.35 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.44/34.35 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3)
% 221.44/34.35 | = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~
% 221.44/34.35 | $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_mult__le__cancel1) implies:
% 221.44/34.35 | (44) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.35 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.35 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.35 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 221.44/34.35 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.44/34.35 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2:
% 221.44/34.35 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.44/34.35 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.44/34.35 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)) & ! [v2:
% 221.44/34.35 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.44/34.35 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.44/34.35 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_dvd__power) implies:
% 221.44/34.35 | (45) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.44/34.35 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) |
% 221.44/34.35 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~
% 221.44/34.35 | $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v3) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 221.44/34.35 | c_Rings_Odvd__class_Odvd(v3, v1, v6)) & ! [v1: $i] : ! [v2: $i]
% 221.44/34.35 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.44/34.35 | (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v2) = v6) |
% 221.44/34.35 | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.44/34.35 | class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3,
% 221.44/34.35 | v1, v6) | ? [v7: $i] : ( ~ (v7 = v1) &
% 221.44/34.35 | c_Groups_Oone__class_Oone(v3) = v7 & $i(v7))))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_gr0I) implies:
% 221.44/34.35 | (46) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ? [v1: $i] : (v1 = v0 | ~ $i(v1) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_neq0__conv) implies:
% 221.44/34.35 | (47) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1:
% 221.44/34.35 | $i] : (v1 = v0 | ~ $i(v1) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_not__less0) implies:
% 221.44/34.35 | (48) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ! [v1: $i] : ( ~ $i(v1) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_le__0__eq) implies:
% 221.44/34.35 | (49) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) & ! [v1:
% 221.44/34.35 | $i] : (v1 = v0 | ~ $i(v1) | ~
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_less__eq__nat_Osimps_I1_J) implies:
% 221.44/34.35 | (50) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ? [v1: $i] : ( ~ $i(v1) |
% 221.44/34.35 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_diffs0__imp__equal) implies:
% 221.44/34.35 | (51) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 221.44/34.35 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~
% 221.44/34.35 | $i(v2) | ~ $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) &
% 221.44/34.35 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 &
% 221.44/34.35 | $i(v3))))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_diff__self__eq__0) implies:
% 221.44/34.35 | (52) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 221.44/34.35 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~
% 221.44/34.35 | $i(v1)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_minus__nat_Odiff__0) implies:
% 221.44/34.35 | (53) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 221.44/34.35 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~
% 221.44/34.35 | $i(v1)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_diff__0__eq__0) implies:
% 221.44/34.35 | (54) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 221.44/34.35 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~
% 221.44/34.35 | $i(v1)))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_power__eq__0__iff) implies:
% 221.44/34.35 | (55) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.44/34.35 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) |
% 221.44/34.35 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~
% 221.44/34.35 | $i(v2) | ~ $i(v1) | ~ class_Rings_Ozero__neq__one(v3) | ~
% 221.44/34.35 | class_Rings_Ono__zero__divisors(v3) | ~
% 221.44/34.35 | class_Rings_Omult__zero(v3) | ~ class_Power_Opower(v3) | ? [v7:
% 221.44/34.35 | $i] : (c_Groups_Ozero__class_Ozero(v3) = v7 & $i(v7) & ( ~ (v7 =
% 221.44/34.35 | v6) | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2) | v6 = v2 |
% 221.44/34.35 | v1 = v0))))
% 221.44/34.35 |
% 221.44/34.35 | ALPHA: (fact_power__0) implies:
% 221.44/34.35 | (56) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.35 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.44/34.36 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) |
% 221.44/34.36 | ~ $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] :
% 221.44/34.36 | (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 &
% 221.44/34.36 | $i(v5))))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_diff__less) implies:
% 221.44/34.36 | (57) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.44/34.36 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~
% 221.44/34.36 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.44/34.36 | v0, v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)
% 221.44/34.36 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_zero__less__diff) implies:
% 221.44/34.36 | (58) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.44/34.36 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.44/34.36 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.44/34.36 | v1, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) &
% 221.44/34.36 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.44/34.36 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.44/34.36 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.44/34.36 | v0, v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_diff__is__0__eq_H) implies:
% 221.44/34.36 | (59) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.44/34.36 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.44/34.36 | $i(v2) | ~ $i(v1) | ~
% 221.44/34.36 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_diff__is__0__eq) implies:
% 221.44/34.36 | (60) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.44/34.36 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.44/34.36 | $i(v2) | ~ $i(v1) | ~
% 221.44/34.36 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & ! [v1:
% 221.44/34.36 | $i] : ! [v2: $i] : ( ~
% 221.44/34.36 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v0) | ~
% 221.44/34.36 | $i(v2) | ~ $i(v1) |
% 221.44/34.36 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_power__0__left) implies:
% 221.44/34.36 | (61) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.44/34.36 | $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~
% 221.44/34.36 | (c_Power_Opower__class_Opower(v2) = v3) | ~
% 221.44/34.36 | (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) |
% 221.44/34.36 | ~ (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 221.44/34.36 | class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2)) & !
% 221.44/34.36 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 221.44/34.36 | ~ (c_Power_Opower__class_Opower(v1) = v2) | ~
% 221.44/34.36 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) |
% 221.44/34.36 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~
% 221.44/34.36 | class_Rings_Osemiring__0(v1) | ~ class_Power_Opower(v1) |
% 221.44/34.36 | (c_Groups_Oone__class_Oone(v1) = v5 & $i(v5))))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact__096_B_Bthesis_O_A_I_B_Br_O_Aq_A_061_A_091_058_N_Aa_M_A1_058_093_A_K_Ar_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 221.44/34.36 | implies:
% 221.44/34.36 | (62) $i(v_qa____)
% 221.44/34.36 | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.44/34.36 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 221.44/34.36 | (c_Groups_Otimes__class_Otimes(v0) = v1 &
% 221.44/34.36 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v2 &
% 221.44/34.36 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 221.44/34.36 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 221.44/34.36 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 221.44/34.36 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(v0) = v4 & hAPP(v7, v8) = v_qa____ &
% 221.44/34.36 | hAPP(v1, v6) = v7 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 221.44/34.36 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_ap_I2_J) implies:
% 221.44/34.36 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.44/34.36 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 221.44/34.36 | ? [v10: $i] : (c_Nat_OSuc(v8) = v9 & c_Power_Opower__class_Opower(v0)
% 221.44/34.36 | = v1 & c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____)
% 221.44/34.36 | = v2 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 221.44/34.36 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 221.44/34.36 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 221.44/34.36 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v8 &
% 221.44/34.36 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(v0) = v4 & hAPP(v7, v9) = v10 & hAPP(v1,
% 221.44/34.36 | v6) = v7 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 221.44/34.36 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 221.44/34.36 | c_Rings_Odvd__class_Odvd(v0, v10, v_pa____))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact__096_B_Bthesis_O_A_I_B_Bk_O_As_A_061_A_091_058k_058_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)
% 221.44/34.36 | implies:
% 221.44/34.36 | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.44/34.36 | (c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v1) = v_s____ &
% 221.44/34.36 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v2) & $i(v1) & $i(v0))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_realpow__minus__mult) implies:
% 221.44/34.36 | (66) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 221.44/34.36 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0)
% 221.44/34.36 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 221.44/34.36 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 221.44/34.36 | [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1)
% 221.44/34.36 | = v8) | ~ (c_Groups_Otimes__class_Otimes(v4) = v5) | ~
% 221.44/34.36 | (c_Power_Opower__class_Opower(v4) = v6) | ~ (hAPP(v10, v2) = v11)
% 221.44/34.36 | | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5,
% 221.44/34.36 | v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.36 | class_Groups_Omonoid__mult(v4) | ~
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3)
% 221.44/34.36 | = v11 & $i(v11))))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_order__root) implies:
% 221.44/34.36 | (67) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.44/34.36 | $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) =
% 221.44/34.36 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.44/34.36 | class_Rings_Oidom(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 221.44/34.36 | ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) & c_Polynomial_Oorder(v3,
% 221.44/34.36 | v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) |
% 221.44/34.36 | (v6 = v5 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) &
% 221.44/34.36 | ((v8 = v2 & tc_Polynomial_Opoly(v3) = v7 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(v7) = v2 & $i(v7)) | ( ~ (v9 =
% 221.44/34.36 | v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & $i(v9)) | ( ~
% 221.44/34.36 | (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 &
% 221.44/34.36 | $i(v6))))))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_dvd__1__left) implies:
% 221.44/34.36 | (68) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ?
% 221.44/34.36 | [v2: $i] : ( ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1,
% 221.44/34.36 | v2)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_zero__less__Suc) implies:
% 221.44/34.36 | (69) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1)
% 221.44/34.36 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_dvd__1__iff__1) implies:
% 221.44/34.36 | (70) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.44/34.36 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v1) & ! [v2: $i] : (v2 =
% 221.44/34.36 | v1 | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2,
% 221.44/34.36 | v1)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_nat_Osimps_I3_J) implies:
% 221.44/34.36 | (71) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_mult__eq__1__iff) implies:
% 221.44/34.36 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 221.44/34.36 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) &
% 221.44/34.36 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~
% 221.44/34.36 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~
% 221.44/34.36 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v2 | ~
% 221.44/34.36 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~
% 221.44/34.36 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (hAPP(v3, v2)
% 221.44/34.36 | = v4) | ~ (hAPP(v0, v2) = v3)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_nat__power__eq__Suc__0__iff) implies:
% 221.44/34.36 | (73) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 221.44/34.36 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) &
% 221.44/34.36 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~
% 221.44/34.36 | (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & !
% 221.44/34.36 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v1) =
% 221.44/34.36 | v5) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3)) & ! [v3: $i] : !
% 221.44/34.36 | [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3) = v2)
% 221.44/34.36 | | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_power__Suc__0) implies:
% 221.44/34.36 | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 221.44/34.36 | (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0
% 221.44/34.36 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3
% 221.44/34.36 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] :
% 221.44/34.36 | (v5 = v2 | ~ (hAPP(v3, v4) = v5) | ~ $i(v4)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_less__Suc__eq) implies:
% 221.44/34.36 | (75) ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_nat__dvd__1__iff__1) implies:
% 221.44/34.36 | (76) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.44/34.36 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 =
% 221.44/34.36 | v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1,
% 221.44/34.36 | v0)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_realpow__two__disj) implies:
% 221.44/34.36 | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 221.44/34.36 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.44/34.36 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 221.44/34.36 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 221.44/34.36 | (c_Power_Opower__class_Opower(v5) = v6) | ~ (hAPP(v6, v4) = v7) |
% 221.44/34.36 | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.44/34.36 | class_Rings_Oidom(v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i]
% 221.44/34.36 | : ((v4 = v3 | (v11 = v4 & c_Groups_Ouminus__class_Ouminus(v5, v3)
% 221.44/34.36 | = v4) | ( ~ (v10 = v9) & hAPP(v8, v2) = v10 & hAPP(v7, v2) =
% 221.44/34.36 | v9 & $i(v10) & $i(v9))) & ((v10 = v9 & hAPP(v8, v2) = v9 &
% 221.44/34.36 | hAPP(v7, v2) = v9 & $i(v9)) | ( ~ (v11 = v4) & ~ (v4 = v3)
% 221.44/34.36 | & c_Groups_Ouminus__class_Ouminus(v5, v3) = v11 &
% 221.44/34.36 | $i(v11))))))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_nat__dvd__not__less) implies:
% 221.44/34.36 | (78) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 221.44/34.36 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_dvd__mult__cancel) implies:
% 221.44/34.36 | (79) ? [v0: $i] : ? [v1: $i] :
% 221.44/34.36 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 221.44/34.36 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 221.44/34.36 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.44/34.36 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 221.44/34.36 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) |
% 221.44/34.36 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_gr0__conv__Suc) implies:
% 221.44/34.36 | (80) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2)
% 221.44/34.36 | | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))
% 221.44/34.36 | & ! [v1: $i] : ( ~ $i(v1) | ~
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v2: $i] :
% 221.44/34.36 | (c_Nat_OSuc(v2) = v1 & $i(v2))))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_less__Suc0) implies:
% 221.44/34.36 | (81) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] :
% 221.44/34.36 | (v2 = v0 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.44/34.36 | v2, v1)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_less__Suc__eq__0__disj) implies:
% 221.44/34.36 | (82) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.44/34.36 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.44/34.36 | (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~
% 221.44/34.36 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.44/34.36 | v4, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) &
% 221.44/34.36 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~
% 221.44/34.36 | (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4: $i] :
% 221.44/34.36 | (c_Nat_OSuc(v4) = v2 & $i(v4) &
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1:
% 221.44/34.36 | $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) |
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_n__less__m__mult__n) implies:
% 221.44/34.36 | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.44/34.36 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 221.44/34.36 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.44/34.36 | (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~
% 221.44/34.36 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 221.44/34.36 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_n__less__n__mult__m) implies:
% 221.44/34.36 | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.44/34.36 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 221.44/34.36 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 221.44/34.36 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.44/34.36 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~
% 221.44/34.36 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 221.44/34.36 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 221.44/34.36 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)))
% 221.44/34.36 |
% 221.44/34.36 | ALPHA: (fact_one__less__mult) implies:
% 221.44/34.37 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.44/34.37 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 221.44/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 221.44/34.37 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.44/34.37 | (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~
% 221.44/34.37 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 221.44/34.37 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) |
% 221.44/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6)))
% 221.44/34.37 |
% 221.44/34.37 | ALPHA: (fact_one__le__mult__iff) implies:
% 221.61/34.37 | (86) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.61/34.37 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 221.61/34.37 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.61/34.37 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~
% 221.61/34.37 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)
% 221.61/34.37 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)) & !
% 221.61/34.37 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5,
% 221.61/34.37 | v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 221.61/34.37 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) & ! [v3:
% 221.61/34.37 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3)
% 221.61/34.37 | = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_nat__one__le__power) implies:
% 221.61/34.37 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.61/34.37 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 221.61/34.37 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.61/34.37 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~
% 221.61/34.37 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)
% 221.61/34.37 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_One__nat__def) implies:
% 221.61/34.37 | (88) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 &
% 221.61/34.37 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_diff__Suc__1) implies:
% 221.61/34.37 | (89) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.61/34.37 | ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) |
% 221.61/34.37 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v1))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_degree__pCons__eq__if) implies:
% 221.61/34.37 | (90) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.37 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.37 | $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~
% 221.61/34.37 | (c_Polynomial_OpCons(v3, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) |
% 221.61/34.37 | ~ $i(v1) | ~ class_Groups_Ozero(v3) | ? [v6: $i] : ? [v7: $i] :
% 221.61/34.37 | ? [v8: $i] : ? [v9: $i] : ((v5 = v0 | ( ~ (v7 = v2) &
% 221.61/34.37 | tc_Polynomial_Opoly(v3) = v6 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6))) &
% 221.61/34.37 | ((v9 = v5 & c_Nat_OSuc(v8) = v5 & c_Polynomial_Odegree(v3, v2) =
% 221.61/34.37 | v8 & $i(v8) & $i(v5)) | (v7 = v2 & tc_Polynomial_Opoly(v3) =
% 221.61/34.37 | v6 & c_Groups_Ozero__class_Ozero(v6) = v2 & $i(v6))))))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_dvd__imp__le) implies:
% 221.61/34.37 | (91) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.37 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~
% 221.61/34.37 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_dvd__mult__cancel1) implies:
% 221.61/34.37 | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.61/34.37 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.37 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 221.61/34.37 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3
% 221.61/34.37 | = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4)
% 221.61/34.37 | | ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 221.61/34.37 | v4) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & !
% 221.61/34.37 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 221.61/34.37 | (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.61/34.37 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_dvd__mult__cancel2) implies:
% 221.61/34.37 | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.61/34.37 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.37 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 221.61/34.37 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3
% 221.61/34.37 | = v2 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4)
% 221.61/34.37 | | ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 221.61/34.37 | v4) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & !
% 221.61/34.37 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~
% 221.61/34.37 | (hAPP(v1, v2) = v4) | ~ $i(v3) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.61/34.37 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_Suc__pred) implies:
% 221.61/34.37 | (94) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 221.61/34.37 | [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.37 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.61/34.37 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 221.61/34.37 | c_Nat_OSuc(v3) = v2))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_diff__Suc__less) implies:
% 221.61/34.37 | (95) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.37 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.37 | (c_Nat_OSuc(v1) = v3) | ~
% 221.61/34.37 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~
% 221.61/34.37 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.61/34.37 | v0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_power__dvd__imp__le) implies:
% 221.61/34.37 | (96) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat)
% 221.61/34.37 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)
% 221.61/34.37 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 221.61/34.37 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 221.61/34.37 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 221.61/34.37 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~
% 221.61/34.37 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_degree__1) implies:
% 221.61/34.37 | (97) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.37 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 |
% 221.61/34.37 | ~ (c_Polynomial_Odegree(v1, v3) = v4) | ~
% 221.61/34.37 | (c_Groups_Oone__class_Oone(v2) = v3) | ~ (tc_Polynomial_Opoly(v1)
% 221.61/34.37 | = v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v1)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_degree__0) implies:
% 221.61/34.37 | (98) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.37 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 |
% 221.61/34.37 | ~ (c_Polynomial_Odegree(v1, v3) = v4) | ~
% 221.61/34.37 | (tc_Polynomial_Opoly(v1) = v2) | ~
% 221.61/34.37 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~
% 221.61/34.37 | class_Groups_Ozero(v1)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_degree__pCons__0) implies:
% 221.61/34.37 | (99) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.37 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.37 | $i] : ! [v6: $i] : (v6 = v0 | ~ (c_Polynomial_Odegree(v2, v5) =
% 221.61/34.37 | v6) | ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~
% 221.61/34.37 | (tc_Polynomial_Opoly(v2) = v3) | ~
% 221.61/34.37 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) |
% 221.61/34.37 | ~ class_Groups_Ozero(v2)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_power__eq__if) implies:
% 221.61/34.37 | (100) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 221.61/34.37 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 &
% 221.61/34.37 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 221.61/34.37 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) &
% 221.61/34.37 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.61/34.37 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~
% 221.61/34.37 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~
% 221.61/34.37 | (hAPP(v7, v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4)
% 221.61/34.37 | = v7) | ~ (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) |
% 221.61/34.37 | (hAPP(v6, v5) = v10 & $i(v10))) & ! [v4: $i] : ! [v5: $i] : !
% 221.61/34.37 | [v6: $i] : (v6 = v2 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) =
% 221.61/34.37 | v5) | ~ $i(v4)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_Suc__pred_H) implies:
% 221.61/34.37 | (101) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 221.61/34.37 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 221.61/34.37 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.37 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.61/34.37 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 221.61/34.37 | c_Nat_OSuc(v3) = v2))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_nat__mult__le__cancel1) implies:
% 221.61/34.37 | (102) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.37 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.37 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.37 | : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) |
% 221.61/34.37 | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2:
% 221.61/34.37 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.61/34.37 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.61/34.37 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_zero__less__power__nat__eq) implies:
% 221.61/34.37 | (103) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.37 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.37 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 |
% 221.61/34.37 | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 221.61/34.37 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i]
% 221.61/34.37 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 221.61/34.37 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i]
% 221.61/34.37 | : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~
% 221.61/34.37 | (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_diff__Suc__eq__diff__pred) implies:
% 221.61/34.37 | (104) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.61/34.37 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.37 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~
% 221.61/34.37 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~
% 221.61/34.37 | $i(v2) | ~ $i(v1) | ? [v5: $i] : (c_Nat_OSuc(v1) = v5 &
% 221.61/34.37 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) = v4 &
% 221.61/34.37 | $i(v5) & $i(v4))))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_nat__mult__dvd__cancel1) implies:
% 221.61/34.37 | (105) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.37 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.37 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.37 | : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) |
% 221.61/34.37 | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 221.61/34.37 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) |
% 221.61/34.37 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 221.61/34.37 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 221.61/34.37 | ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 221.61/34.37 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 221.61/34.37 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) |
% 221.61/34.37 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_nat__mult__eq__cancel1) implies:
% 221.61/34.37 | (106) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.37 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.37 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.37 | : (v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~
% 221.61/34.37 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_nat__mult__less__cancel1) implies:
% 221.61/34.37 | (107) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.37 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.37 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.37 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.37 | : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) |
% 221.61/34.37 | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i]
% 221.61/34.37 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.61/34.37 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.61/34.37 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 221.61/34.37 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_nat__lt__two__imp__zero__or__one) implies:
% 221.61/34.37 | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 221.61/34.37 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.61/34.37 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 221.61/34.37 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)))
% 221.61/34.37 |
% 221.61/34.37 | ALPHA: (fact_nat__mult__eq__cancel__disj) implies:
% 221.61/34.38 | (109) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.38 | : (v6 = v5 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~
% 221.61/34.38 | (hAPP(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : !
% 221.61/34.38 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | v3
% 221.61/34.38 | = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~
% 221.61/34.38 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_nat__mult__dvd__cancel__disj) implies:
% 221.61/34.38 | (110) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.38 | : ! [v7: $i] : (v4 = v1 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 221.61/34.38 | v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 221.61/34.38 | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 221.61/34.38 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 221.61/34.38 | ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4)
% 221.61/34.38 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : !
% 221.61/34.38 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4,
% 221.61/34.38 | v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) |
% 221.61/34.38 | ~ $i(v3) | ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5,
% 221.61/34.38 | v6)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_pow__divides__eq__nat) implies:
% 221.61/34.38 | (111) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.38 | : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) |
% 221.61/34.38 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2)
% 221.61/34.38 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : !
% 221.61/34.38 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 221.61/34.38 | ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) =
% 221.61/34.38 | v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~
% 221.61/34.38 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_pow__divides__pow__nat) implies:
% 221.61/34.38 | (112) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.38 | : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = v8) |
% 221.61/34.38 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2)
% 221.61/34.38 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v2)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_dvd__pos__nat) implies:
% 221.61/34.38 | (113) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)
% 221.61/34.38 | implies:
% 221.61/34.38 | (114) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.38 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 221.61/34.38 | | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) |
% 221.61/34.38 | ? [v5: $i] : (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0)
% 221.61/34.38 | = v5 & $i(v5))))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_pow__divides__pow__int) implies:
% 221.61/34.38 | (115) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Power_Opower__class_Opower(tc_Int_Oint) = v0 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.38 | : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = v8) |
% 221.61/34.38 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2)
% 221.61/34.38 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v2)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_pow__divides__eq__int) implies:
% 221.61/34.38 | (116) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.38 | : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) |
% 221.61/34.38 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2)
% 221.61/34.38 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)) & ! [v2: $i] : !
% 221.61/34.38 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 221.61/34.38 | ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) =
% 221.61/34.38 | v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~
% 221.61/34.38 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Otop__greatest) implies:
% 221.61/34.38 | (117) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.38 | & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 221.61/34.38 | v1, v0)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)
% 221.61/34.38 | implies:
% 221.61/34.38 | (118) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.61/34.38 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.38 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 221.61/34.38 | | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) |
% 221.61/34.38 | hAPP(v4, v0) = v1))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Obot__least) implies:
% 221.61/34.38 | (119) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.61/34.38 | ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 221.61/34.38 | v0, v1)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_psize__def) implies:
% 221.61/34.38 | (120) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.38 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3)
% 221.61/34.38 | | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i]
% 221.61/34.38 | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v3 = v0 | ( ~ (v5 =
% 221.61/34.38 | v1) & tc_Polynomial_Opoly(v2) = v4 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))) &
% 221.61/34.38 | ((v7 = v3 & c_Nat_OSuc(v6) = v3 & c_Polynomial_Odegree(v2, v1)
% 221.61/34.38 | = v6 & $i(v6) & $i(v3)) | (v5 = v1 &
% 221.61/34.38 | tc_Polynomial_Opoly(v2) = v4 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(v4) = v1 & $i(v4))))))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_power_Opower_Opower__0) implies:
% 221.61/34.38 | (121) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.38 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5)
% 221.61/34.38 | | ~ (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | $i(v1) | hAPP(v6, v0) = v3))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zdvd__antisym__nonneg) implies:
% 221.61/34.38 | (122) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v2, v1) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v2) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zdvd__not__zless) implies:
% 221.61/34.38 | (123) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v2)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zdvd__imp__le) implies:
% 221.61/34.38 | (124) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) | ~
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v2, v1) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zdvd__mult__cancel) implies:
% 221.61/34.38 | (125) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.38 | : ! [v7: $i] : (v4 = v1 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 221.61/34.38 | v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 221.61/34.38 | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v7) |
% 221.61/34.38 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_psize__eq__0__iff) implies:
% 221.61/34.38 | (126) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.38 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3)
% 221.61/34.38 | | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i]
% 221.61/34.38 | : ? [v5: $i] : (( ~ (v3 = v0) | (v5 = v1 &
% 221.61/34.38 | tc_Polynomial_Opoly(v2) = v4 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(v4) = v1 & $i(v4))) & (v3 = v0
% 221.61/34.38 | | ( ~ (v5 = v1) & tc_Polynomial_Opoly(v2) = v4 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))))))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_int__0__neq__1) implies:
% 221.61/34.38 | (127) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 221.61/34.38 | c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_int__0__less__1) implies:
% 221.61/34.38 | (128) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.38 | v1 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) &
% 221.61/34.38 | $i(v0) & c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zminus__0) implies:
% 221.61/34.38 | (129) ? [v0: $i] : (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v0) = v0
% 221.61/34.38 | & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zmult__1) implies:
% 221.61/34.38 | (130) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.61/34.38 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.38 | c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 & hAPP(v0, v1) = v2 &
% 221.61/34.38 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 |
% 221.61/34.38 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_int__one__le__iff__zero__less) implies:
% 221.61/34.38 | (131) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.38 | v0 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) &
% 221.61/34.38 | $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)) & ! [v2:
% 221.61/34.38 | $i] : ( ~ $i(v2) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zmult__1__right) implies:
% 221.61/34.38 | (132) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.38 | c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 & $i(v1) & $i(v0) & !
% 221.61/34.38 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) |
% 221.61/34.38 | hAPP(v3, v1) = v2))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_less__bin__lemma) implies:
% 221.61/34.38 | (133) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.38 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.38 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.38 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)) & ! [v1: $i]
% 221.61/34.38 | : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.38 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.38 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_pos__zmult__eq__1__iff) implies:
% 221.61/34.38 | (134) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.61/34.38 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.38 | c_Groups_Oone__class_Oone(tc_Int_Oint) = v2 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v2) & $i(v1) &
% 221.61/34.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~
% 221.61/34.38 | (hAPP(v5, v3) = v2) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~
% 221.61/34.38 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4)) &
% 221.61/34.38 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v2 | ~ (hAPP(v5,
% 221.61/34.38 | v3) = v2) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 221.61/34.38 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4)) & ! [v3:
% 221.61/34.38 | $i] : ! [v4: $i] : (v4 = v2 | ~ (hAPP(v3, v2) = v4) | ~
% 221.61/34.38 | (hAPP(v1, v2) = v3) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zmult__zless__mono2) implies:
% 221.61/34.38 | (135) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.38 | : ! [v7: $i] : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) |
% 221.61/34.38 | ~ (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v3) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v6, v7)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zle__diff1__eq) implies:
% 221.61/34.38 | (136) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 & $i(v0) &
% 221.61/34.38 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.38 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v1, v0) = v3) | ~
% 221.61/34.38 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v3)) & ! [v1:
% 221.61/34.38 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.38 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v1, v0) = v3) | ~
% 221.61/34.38 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.38 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v3) |
% 221.61/34.38 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J)
% 221.61/34.38 | implies:
% 221.61/34.38 | (137) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.38 | (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 &
% 221.61/34.38 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.38 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 221.61/34.38 | (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 221.61/34.38 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0,
% 221.61/34.38 | v3) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v5)))
% 221.61/34.38 |
% 221.61/34.38 | ALPHA: (fact_zdvd__mono) implies:
% 221.61/34.39 | (138) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.39 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.39 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.39 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.39 | : ! [v7: $i] : (v4 = v0 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 221.61/34.39 | v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 221.61/34.39 | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v7) |
% 221.61/34.39 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)) & ! [v2: $i] : !
% 221.61/34.39 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 221.61/34.39 | (v4 = v0 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 221.61/34.39 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.39 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2) |
% 221.61/34.39 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v7)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)
% 221.61/34.39 | implies:
% 221.61/34.39 | (139) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.39 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.39 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.39 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 221.61/34.39 | (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 221.61/34.39 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0,
% 221.61/34.39 | v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)
% 221.61/34.39 | | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v5)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J)
% 221.61/34.39 | implies:
% 221.61/34.39 | (140) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.39 | & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v0))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)
% 221.61/34.39 | implies:
% 221.61/34.39 | (141) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.39 | v1 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) &
% 221.61/34.39 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_tsub__def) implies:
% 221.61/34.39 | (142) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.61/34.39 | (c_Nat__Transfer_Otsub(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 221.61/34.39 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1)) & ! [v1:
% 221.61/34.39 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.39 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.39 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.39 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.61/34.39 | (c_Nat__Transfer_Otsub(v1, v2) = v3 & $i(v3))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J)
% 221.61/34.39 | implies:
% 221.61/34.39 | (143) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.39 | (c_Nat__Transfer_Otsub(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.39 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ~
% 221.61/34.39 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) |
% 221.61/34.39 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_decr__mult__lemma) implies:
% 221.61/34.39 | (144) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.39 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.39 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.39 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.39 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 221.61/34.39 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v7, v6) = v8) | ~
% 221.61/34.39 | (hAPP(v5, v4) = v6) | ~ (hAPP(v3, v8) = v9) | ~ (hAPP(v1, v2) =
% 221.61/34.39 | v5) | ~ $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.39 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ~
% 221.61/34.39 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.61/34.39 | hBOOL(v9) | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 221.61/34.39 | $i] : ? [v14: $i] : ($i(v11) &
% 221.61/34.39 | ((c_Groups_Ominus__class_Ominus(tc_Int_Oint, v11, v4) = v13 &
% 221.61/34.39 | hAPP(v3, v13) = v14 & hAPP(v3, v11) = v12 & $i(v14) &
% 221.61/34.39 | $i(v13) & $i(v12) & hBOOL(v12) & ~ hBOOL(v14)) | (hAPP(v3,
% 221.61/34.39 | v7) = v10 & $i(v10) & ~ hBOOL(v10))))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_monom__0) implies:
% 221.61/34.39 | (145) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.39 | $i] : ( ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~
% 221.61/34.39 | (tc_Polynomial_Opoly(v2) = v3) | ~
% 221.61/34.39 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) |
% 221.61/34.39 | ~ class_Groups_Ozero(v2) | (c_Polynomial_Omonom(v2, v1, v0) = v5
% 221.61/34.39 | & $i(v5))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_degree__synthetic__div) implies:
% 221.61/34.39 | (146) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.61/34.39 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 221.61/34.39 | : ( ~ (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~
% 221.61/34.39 | (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.39 | $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? [v6: $i] :
% 221.61/34.39 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v0) = v5 &
% 221.61/34.39 | c_Polynomial_Odegree(v3, v2) = v6 & $i(v6) & $i(v5))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_synthetic__div__eq__0__iff) implies:
% 221.61/34.39 | (147) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.39 | (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ $i(v3) | ~
% 221.61/34.39 | $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ?
% 221.61/34.39 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (((v7 = v0 &
% 221.61/34.39 | c_Polynomial_Odegree(v3, v2) = v0) | ( ~ (v6 = v4) &
% 221.61/34.39 | tc_Polynomial_Opoly(v3) = v5 &
% 221.61/34.39 | c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) &
% 221.61/34.39 | ((v6 = v4 & tc_Polynomial_Opoly(v3) = v5 &
% 221.61/34.39 | c_Groups_Ozero__class_Ozero(v5) = v4 & $i(v5) & $i(v4)) | (
% 221.61/34.39 | ~ (v7 = v0) & c_Polynomial_Odegree(v3, v2) = v7 &
% 221.61/34.39 | $i(v7))))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_zsgn__def) implies:
% 221.61/34.39 | (148) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.61/34.39 | (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v1) = v2 &
% 221.61/34.39 | c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 &
% 221.61/34.39 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v2) & $i(v1) &
% 221.61/34.39 | $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | v3 = v0 | ~
% 221.61/34.39 | (c_Groups_Osgn__class_Osgn(tc_Int_Oint, v3) = v4) | ~ $i(v3) |
% 221.61/34.39 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)) & ! [v3: $i]
% 221.61/34.39 | : ! [v4: $i] : (v4 = v1 | v3 = v0 | ~
% 221.61/34.39 | (c_Groups_Osgn__class_Osgn(tc_Int_Oint, v3) = v4) | ~ $i(v3) |
% 221.61/34.39 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)) & ! [v3:
% 221.61/34.39 | $i] : (v3 = v0 | ~ (c_Groups_Osgn__class_Osgn(tc_Int_Oint, v0) =
% 221.61/34.39 | v3)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_expand__Suc) implies:
% 221.61/34.39 | (149) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 221.61/34.39 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 221.61/34.39 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.39 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v3) | ~
% 221.61/34.39 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.61/34.39 | ? [v4: $i] : (c_Nat_OSuc(v4) = v3 &
% 221.61/34.39 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 &
% 221.61/34.39 | $i(v4) & $i(v3))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_coeff__pCons__0) implies:
% 221.61/34.39 | (150) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.39 | $i] : ( ~ (c_Polynomial_Ocoeff(v3, v4) = v5) | ~
% 221.61/34.39 | (c_Polynomial_OpCons(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 221.61/34.39 | ~ $i(v1) | ~ class_Groups_Ozero(v3) | hAPP(v5, v0) = v2))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_power__eq__0__iff__number__of) implies:
% 221.61/34.39 | (151) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.39 | $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 221.61/34.39 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v1) = v6) | ~
% 221.61/34.39 | (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v6) = v7)
% 221.61/34.39 | | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.39 | class_Rings_Ozero__neq__one(v3) | ~
% 221.61/34.39 | class_Rings_Ono__zero__divisors(v3) | ~
% 221.61/34.39 | class_Rings_Omult__zero(v3) | ~ class_Power_Opower(v3) | ? [v8:
% 221.61/34.39 | $i] : (c_Groups_Ozero__class_Ozero(v3) = v8 & $i(v8) & ( ~ (v8
% 221.61/34.39 | = v7) | (v7 = v2 & ~ (v6 = v0))) & ( ~ (v8 = v2) | v7 = v2
% 221.61/34.39 | | v6 = v0))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_zero__less__power__nat__eq__number__of) implies:
% 221.61/34.39 | (152) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.39 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 221.61/34.39 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.39 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.39 | : (v5 = v0 | ~ (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2)
% 221.61/34.39 | = v5) | ~ (hAPP(v4, v5) = v6) | ~ (hAPP(v1, v3) = v4) | ~
% 221.61/34.39 | $i(v3) | ~ $i(v2) | ~
% 221.61/34.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v6) |
% 221.61/34.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i]
% 221.61/34.39 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.61/34.39 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v4) | ~
% 221.61/34.39 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v3) | ~
% 221.61/34.39 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.61/34.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v6)) & ! [v2: $i]
% 221.61/34.39 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 221.61/34.39 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v0) | ~
% 221.61/34.39 | (hAPP(v4, v0) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 221.61/34.39 | $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_power__0__left__number__of) implies:
% 221.61/34.39 | (153) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.39 | $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v5 | v3 = v0 | ~
% 221.61/34.39 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v1) = v3) | ~
% 221.61/34.39 | (c_Power_Opower__class_Opower(v2) = v4) | ~
% 221.61/34.39 | (c_Groups_Ozero__class_Ozero(v2) = v5) | ~ (hAPP(v6, v3) = v7) |
% 221.61/34.39 | ~ (hAPP(v4, v5) = v6) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.39 | class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2)) & !
% 221.61/34.39 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 221.61/34.39 | ! [v6: $i] : ( ~ (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v1)
% 221.61/34.39 | = v0) | ~ (c_Power_Opower__class_Opower(v2) = v3) | ~
% 221.61/34.39 | (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v0) = v6) |
% 221.61/34.39 | ~ (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.39 | class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2) |
% 221.61/34.39 | (c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_coeff__1) implies:
% 221.61/34.39 | (154) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.39 | $i] : ! [v6: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v4) = v5) | ~
% 221.61/34.39 | (c_Groups_Oone__class_Oone(v3) = v4) | ~
% 221.61/34.39 | (tc_Polynomial_Opoly(v2) = v3) | ~ (hAPP(v5, v1) = v6) | ~
% 221.61/34.39 | $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | ?
% 221.61/34.39 | [v7: $i] : ? [v8: $i] : (( ~ (v1 = v0) | (v7 = v6 &
% 221.61/34.39 | c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))) & (v1 = v0 |
% 221.61/34.39 | (v8 = v6 & c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6))))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_realpow__two__diff) implies:
% 221.61/34.39 | (155) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 &
% 221.61/34.39 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0
% 221.61/34.39 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.39 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 221.61/34.39 | [v10: $i] : ! [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(v5,
% 221.61/34.39 | v8, v10) = v11) | ~ (c_Power_Opower__class_Opower(v5) = v6)
% 221.61/34.39 | | ~ (hAPP(v9, v2) = v10) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6,
% 221.61/34.39 | v4) = v7) | ~ (hAPP(v6, v3) = v9) | ~ $i(v5) | ~ $i(v4) |
% 221.61/34.39 | ~ $i(v3) | ~ class_Rings_Ocomm__ring__1(v5) | ? [v12: $i] : ?
% 221.61/34.39 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(v5, v4, v3) = v15 &
% 221.61/34.39 | c_Groups_Ominus__class_Ominus(v5, v4, v3) = v13 &
% 221.61/34.39 | c_Groups_Otimes__class_Otimes(v5) = v12 & hAPP(v14, v15) = v11
% 221.61/34.39 | & hAPP(v12, v13) = v14 & $i(v15) & $i(v14) & $i(v13) & $i(v12)
% 221.61/34.39 | & $i(v11))))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_zadd__0__right) implies:
% 221.61/34.39 | (156) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v2) | ~
% 221.61/34.39 | $i(v1)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_zadd__0) implies:
% 221.61/34.39 | (157) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, v1) = v2) | ~
% 221.61/34.39 | $i(v1)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_plus__nat_Oadd__0) implies:
% 221.61/34.39 | (158) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~
% 221.61/34.39 | $i(v1)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_Nat_Oadd__0__right) implies:
% 221.61/34.39 | (159) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~
% 221.61/34.39 | $i(v1)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_add__is__0) implies:
% 221.61/34.39 | (160) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~
% 221.61/34.39 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~
% 221.61/34.39 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : (v1 = v0 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_add__eq__self__zero) implies:
% 221.61/34.39 | (161) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.39 | & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~
% 221.61/34.39 | $i(v2) | ~ $i(v1)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_diff__add__inverse) implies:
% 221.61/34.39 | (162) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~
% 221.61/34.39 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.61/34.39 | $i(v1) | ~ $i(v0))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_power__add) implies:
% 221.61/34.39 | (163) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 221.61/34.39 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 221.61/34.39 | ! [v10: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v3) = v6) | ~
% 221.61/34.39 | (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v8, v9) = v10) |
% 221.61/34.39 | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v5, v1) = v7) | ~ (hAPP(v5, v0)
% 221.61/34.39 | = v9) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.39 | $i(v1) | ~ $i(v0) | ~ class_Groups_Omonoid__mult(v3) | ? [v11:
% 221.61/34.39 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v11 &
% 221.61/34.39 | hAPP(v5, v11) = v10 & $i(v11) & $i(v10)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_one__is__add) implies:
% 221.61/34.39 | (164) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.61/34.39 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.39 | ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~
% 221.61/34.39 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~
% 221.61/34.39 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 =
% 221.61/34.39 | v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) |
% 221.61/34.39 | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 |
% 221.61/34.39 | v2 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) =
% 221.61/34.39 | v1) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2
% 221.61/34.39 | = v1 | v2 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3,
% 221.61/34.39 | v2) = v1) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : (v2 = v1 |
% 221.61/34.39 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & !
% 221.61/34.39 | [v2: $i] : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 221.61/34.39 | v0, v1) = v2)))
% 221.61/34.39 |
% 221.61/34.39 | ALPHA: (fact_add__gr__0) implies:
% 221.61/34.40 | (165) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.40 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i]
% 221.61/34.40 | : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i]
% 221.61/34.40 | : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)
% 221.61/34.40 | implies:
% 221.61/34.40 | (166) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.40 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_odd__nonzero) implies:
% 221.61/34.40 | (167) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.40 | v0 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) &
% 221.61/34.40 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v3, v2) = v1) | ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, v2) = v3) | ~
% 221.61/34.40 | $i(v2)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_diff__add__0) implies:
% 221.61/34.40 | (168) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.40 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0
% 221.61/34.40 | | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.61/34.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_zless__add1__eq) implies:
% 221.61/34.40 | (169) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 & $i(v0) &
% 221.61/34.40 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v3) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)) & ! [v1: $i]
% 221.61/34.40 | : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v3)) & ! [v1: $i]
% 221.61/34.40 | : ! [v2: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1,
% 221.61/34.40 | v0) = v2) | ~ $i(v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_Suc__eq__plus1) implies:
% 221.61/34.40 | (170) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.61/34.40 | ! [v1: $i] : ! [v2: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~
% 221.61/34.40 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2))))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_Suc__eq__plus1__left) implies:
% 221.61/34.40 | (171) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 221.61/34.40 | ! [v1: $i] : ! [v2: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~
% 221.61/34.40 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2))))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_zadd__zminus__inverse2) implies:
% 221.61/34.40 | (172) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.40 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.40 | (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v1) = v2) | ~
% 221.61/34.40 | $i(v1)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_nat__diff__split__asm) implies:
% 221.61/34.40 | (173) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.40 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.40 | $i] : ! [v6: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 221.61/34.40 | v1, v6) = v2) | ~
% 221.61/34.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~
% 221.61/34.40 | (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.40 | $i(v1) | ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7)
% 221.61/34.40 | & hBOOL(v7))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 221.61/34.40 | [v4: $i] : ! [v5: $i] : ( ~
% 221.61/34.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~
% 221.61/34.40 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | hBOOL(v5) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)
% 221.61/34.40 | | ? [v6: $i] : (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & !
% 221.61/34.40 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 221.61/34.40 | ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~
% 221.61/34.40 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 221.61/34.40 | hBOOL(v5) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) |
% 221.61/34.40 | ? [v6: $i] : ? [v7: $i] :
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3,
% 221.61/34.40 | v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] :
% 221.61/34.40 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 221.61/34.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~
% 221.61/34.40 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 221.61/34.40 | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 221.61/34.40 | : ($i(v7) & ((v8 = v2 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 221.61/34.40 | v1, v7) = v2 & hAPP(v3, v7) = v9 & $i(v9) & ~ hBOOL(v9))
% 221.61/34.40 | | (hAPP(v3, v0) = v6 & $i(v6) & ~ hBOOL(v6))))))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_odd__less__0) implies:
% 221.61/34.40 | (174) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.40 | v0 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) &
% 221.61/34.40 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v3, v2) = v4) | ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, v2) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)) & ! [v2: $i]
% 221.61/34.40 | : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v3, v2) = v4) | ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, v2) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v1)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_zless__imp__add1__zle) implies:
% 221.61/34.40 | (175) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 & $i(v0) &
% 221.61/34.40 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v0) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_add1__zle__eq) implies:
% 221.61/34.40 | (176) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 & $i(v0) &
% 221.61/34.40 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v0) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1)) & ! [v1:
% 221.61/34.40 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v2, v0) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_zle__add1__eq__le) implies:
% 221.61/34.40 | (177) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) = v0 & $i(v0) &
% 221.61/34.40 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v3) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1)) & ! [v1:
% 221.61/34.40 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_le__imp__0__less) implies:
% 221.61/34.40 | (178) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.40 | v1 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) &
% 221.61/34.40 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.40 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0,
% 221.61/34.40 | v2) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_add__eq__if) implies:
% 221.61/34.40 | (179) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 221.61/34.40 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) &
% 221.61/34.40 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 221.61/34.40 | (v3 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) =
% 221.61/34.40 | v5) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) =
% 221.61/34.40 | v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: $i] :
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v6 &
% 221.61/34.40 | c_Nat_OSuc(v5) = v6 & $i(v6))) & ! [v2: $i] : ! [v3: $i] :
% 221.61/34.40 | (v3 = v2 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) =
% 221.61/34.40 | v3) | ~ $i(v2)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_mult__eq__if) implies:
% 221.61/34.40 | (180) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.40 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) &
% 221.61/34.40 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.61/34.40 | [v7: $i] : ! [v8: $i] : (v4 = v0 | ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~
% 221.61/34.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~
% 221.61/34.40 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~
% 221.61/34.40 | $i(v3) | ? [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 &
% 221.61/34.40 | $i(v9) & $i(v8))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 221.61/34.40 | (v5 = v0 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v0) = v4) | ~
% 221.61/34.40 | $i(v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_self__quotient__aux1) implies:
% 221.61/34.40 | (181) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.40 | c_Groups_Oone__class_Oone(tc_Int_Oint) = v2 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v2) & $i(v1) &
% 221.61/34.40 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.61/34.40 | [v7: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v4, v7) =
% 221.61/34.40 | v5) | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~
% 221.61/34.40 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v5) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v5) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_self__quotient__aux2) implies:
% 221.61/34.40 | (182) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.40 | c_Groups_Oone__class_Oone(tc_Int_Oint) = v2 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v2) & $i(v1) &
% 221.61/34.40 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.61/34.40 | [v7: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v4, v7) =
% 221.61/34.40 | v5) | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~
% 221.61/34.40 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v5) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v4) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v2)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_q__pos__lemma) implies:
% 221.61/34.40 | (183) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.40 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.40 | : ! [v7: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v6,
% 221.61/34.40 | v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) |
% 221.61/34.40 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v4) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v7) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_q__neg__lemma) implies:
% 221.61/34.40 | (184) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) &
% 221.61/34.40 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.40 | : ! [v7: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v6,
% 221.61/34.40 | v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) |
% 221.61/34.40 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v7, v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_unique__quotient__lemma) implies:
% 221.61/34.40 | (185) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) &
% 221.61/34.40 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.40 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 221.61/34.40 | $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v2) =
% 221.61/34.40 | v11) | ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v8, v4) =
% 221.61/34.40 | v9) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v7, v3) = v10) | ~
% 221.61/34.40 | (hAPP(v0, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 221.61/34.40 | $i(v3) | ~ $i(v2) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v6) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v6) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v9, v11) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v4) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v5, v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_zdiv__mono2__lemma) implies:
% 221.61/34.40 | (186) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) &
% 221.61/34.40 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.40 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 221.61/34.40 | $i] : ! [v12: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v12, v2) = v10) | ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v9, v5) = v10) | ~
% 221.61/34.40 | (hAPP(v11, v3) = v12) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v0, v7)
% 221.61/34.40 | = v8) | ~ (hAPP(v0, v4) = v11) | ~ $i(v7) | ~ $i(v6) | ~
% 221.61/34.40 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v4) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v7) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v10) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v5) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v6, v3)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_unique__quotient__lemma__neg) implies:
% 221.61/34.40 | (187) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) &
% 221.61/34.40 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.40 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 221.61/34.40 | $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v2) =
% 221.61/34.40 | v11) | ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v8, v4) =
% 221.61/34.40 | v9) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v7, v3) = v10) | ~
% 221.61/34.40 | (hAPP(v0, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 221.61/34.40 | $i(v3) | ~ $i(v2) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v6, v4) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v6, v2) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v9, v11) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v5)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_zdiv__mono2__neg__lemma) implies:
% 221.61/34.40 | (188) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.40 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.40 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) &
% 221.61/34.40 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.40 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 221.61/34.40 | $i] : ! [v12: $i] : ( ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v12, v2) = v10) | ~
% 221.61/34.40 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v9, v5) = v10) | ~
% 221.61/34.40 | (hAPP(v11, v3) = v12) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v0, v7)
% 221.61/34.40 | = v8) | ~ (hAPP(v0, v4) = v11) | ~ $i(v7) | ~ $i(v6) | ~
% 221.61/34.40 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v10, v1) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v5, v7) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v7) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2) |
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v6)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_le__iff__add) implies:
% 221.61/34.40 | (189) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 221.61/34.40 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v2:
% 221.61/34.40 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v2) = v0 &
% 221.61/34.40 | $i(v2)))
% 221.61/34.40 |
% 221.61/34.40 | ALPHA: (fact_int__power__div__base) implies:
% 221.61/34.41 | (190) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 221.61/34.41 | (c_Nat_OSuc(v0) = v3 & c_Power_Opower__class_Opower(tc_Int_Oint) = v2
% 221.61/34.41 | & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 &
% 221.61/34.41 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) &
% 221.61/34.41 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.61/34.41 | $i] : ! [v8: $i] : ( ~
% 221.61/34.41 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v3) = v7) | ~
% 221.61/34.41 | (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v4) = v6) | ~ $i(v5) | ~
% 221.61/34.41 | $i(v4) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) |
% 221.61/34.41 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v9:
% 221.61/34.41 | $i] : (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v9, v4) = v8 &
% 221.61/34.41 | hAPP(v6, v5) = v9 & $i(v9) & $i(v8))))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_zdiv__eq__0__iff) implies:
% 221.61/34.41 | (191) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)) & ! [v1:
% 221.61/34.41 | $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0)) & ! [v1:
% 221.61/34.41 | $i] : ! [v2: $i] : (v2 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~
% 221.61/34.41 | $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v0) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.61/34.41 | v2, v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2)) &
% 221.61/34.41 | ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v0) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.61/34.41 | v2, v1) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2,
% 221.61/34.41 | v0)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v0) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.61/34.41 | v1, v2) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0,
% 221.61/34.41 | v2)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v0) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_pos__imp__zdiv__nonneg__iff) implies:
% 221.61/34.41 | (192) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1)) & ! [v1:
% 221.61/34.41 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_pos__imp__zdiv__pos__iff) implies:
% 221.61/34.41 | (193) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1)) & ! [v1:
% 221.61/34.41 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_nonneg1__imp__zdiv__pos__iff) implies:
% 221.61/34.41 | (194) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1)) & ! [v1: $i]
% 221.61/34.41 | : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2)) & ! [v1:
% 221.61/34.41 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_zdiv__mono2) implies:
% 221.61/34.41 | (195) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.41 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v5)
% 221.61/34.41 | | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v1) = v4) | ~
% 221.61/34.41 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v5)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_div__nonneg__neg__le0) implies:
% 221.61/34.41 | (196) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v0)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_div__pos__pos__trivial) implies:
% 221.61/34.41 | (197) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_neg__imp__zdiv__nonneg__iff) implies:
% 221.61/34.41 | (198) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)) & ! [v1:
% 221.61/34.41 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_div__nonpos__pos__le0) implies:
% 221.61/34.41 | (199) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v0)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_zdiv__mono2__neg) implies:
% 221.61/34.41 | (200) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.41 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v4)
% 221.61/34.41 | | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v1) = v5) | ~
% 221.61/34.41 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v5)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_div__neg__neg__trivial) implies:
% 221.61/34.41 | (201) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_zdiv__mono1) implies:
% 221.61/34.41 | (202) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.41 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v1) = v4)
% 221.61/34.41 | | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v5) | ~
% 221.61/34.41 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v5)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_zdiv__mono1__neg) implies:
% 221.61/34.41 | (203) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.41 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v1) = v5)
% 221.61/34.41 | | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v4) | ~
% 221.61/34.41 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v5)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_int__div__less__self) implies:
% 221.61/34.41 | (204) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.41 | v1 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) &
% 221.61/34.41 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v4) | ~
% 221.61/34.41 | $i(v3) | ~ $i(v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v3) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v3)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_zdiv__zmult2__eq) implies:
% 221.61/34.41 | (205) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.41 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.41 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.41 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.41 | : ! [v7: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3,
% 221.61/34.41 | v6) = v7) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v2) = v5) |
% 221.61/34.41 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ? [v8: $i]
% 221.61/34.41 | : (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v8, v4) = v7 &
% 221.61/34.41 | c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v8 & $i(v8) &
% 221.61/34.41 | $i(v7))))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_zdiv__zero) implies:
% 221.61/34.41 | (206) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~
% 221.61/34.41 | $i(v1)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_zdiv__self) implies:
% 221.61/34.41 | (207) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.41 | v1 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) &
% 221.61/34.41 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v0 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v2) = v3) | ~
% 221.61/34.41 | $i(v2)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_div__neg__pos__less0) implies:
% 221.61/34.41 | (208) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_neg__imp__zdiv__neg__iff) implies:
% 221.61/34.41 | (209) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1)) & ! [v1: $i]
% 221.61/34.41 | : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_Divides_Otransfer__nat__int__function__closures_I1_J) implies:
% 221.61/34.41 | (210) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2, v1) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_pos__imp__zdiv__neg__iff) implies:
% 221.61/34.41 | (211) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.41 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0)) & ! [v1: $i]
% 221.61/34.41 | : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.41 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v0)))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_split__zdiv) implies:
% 221.61/34.41 | (212) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.41 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.41 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.41 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.41 | : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v5) | ~
% 221.61/34.41 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.41 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : (( ~ (v2 = v0) |
% 221.61/34.41 | (hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7))) & ( ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) |
% 221.61/34.41 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : !
% 221.61/34.41 | [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint,
% 221.61/34.41 | v10, v11) = v3) | ~ (hAPP(v8, v9) = v10) | ~
% 221.61/34.41 | $i(v11) | ~ $i(v9) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v11) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v11, v0) |
% 221.61/34.41 | ? [v12: $i] : (hAPP(v4, v9) = v12 & $i(v12) &
% 221.61/34.41 | hBOOL(v12))))) & ( ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) |
% 221.61/34.41 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : !
% 221.61/34.41 | [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint,
% 221.61/34.41 | v10, v11) = v3) | ~ (hAPP(v8, v9) = v10) | ~
% 221.61/34.41 | $i(v11) | ~ $i(v9) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v11, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v11) |
% 221.61/34.41 | ? [v12: $i] : (hAPP(v4, v9) = v12 & $i(v12) &
% 221.61/34.41 | hBOOL(v12))))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 221.61/34.41 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v5) | ~
% 221.61/34.41 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 221.61/34.41 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 221.61/34.41 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i]
% 221.61/34.41 | : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] :
% 221.61/34.41 | ($i(v17) & $i(v14) & $i(v12) & $i(v9) & ((v18 = v3 &
% 221.61/34.41 | c_Groups_Oplus__class_Oplus(tc_Int_Oint, v15, v17) = v3 &
% 221.61/34.41 | hAPP(v8, v14) = v15 & hAPP(v4, v14) = v16 & hAPP(v1, v2) =
% 221.61/34.41 | v8 & $i(v16) & $i(v15) & $i(v8) &
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v17, v2) &
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) &
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v17) &
% 221.61/34.41 | ~ hBOOL(v16)) | (v13 = v3 &
% 221.61/34.41 | c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v12) = v3 &
% 221.61/34.41 | hAPP(v8, v9) = v10 & hAPP(v4, v9) = v11 & hAPP(v1, v2) = v8
% 221.61/34.41 | & $i(v11) & $i(v10) & $i(v8) &
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v12) &
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) &
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v12, v0) &
% 221.61/34.41 | ~ hBOOL(v11)) | (v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & ~
% 221.61/34.41 | hBOOL(v7))))))
% 221.61/34.41 |
% 221.61/34.41 | ALPHA: (fact_divmod__int__rel__div__eq) implies:
% 221.61/34.41 | (213) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.41 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v0 &
% 221.61/34.41 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & $i(v1) & $i(v0) &
% 221.61/34.41 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.41 | : ! [v7: $i] : ! [v8: $i] : (v8 = v3 | v4 = v1 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5, v4) = v8) | ~
% 221.61/34.41 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v2) = v5) | ~
% 221.61/34.41 | (hAPP(v6, v3) = v7) | ~ (hAPP(v0, v4) = v6) | ~ $i(v5) | ~
% 221.61/34.41 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v4) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2)) & ! [v2:
% 221.61/34.41 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 221.61/34.41 | [v7: $i] : ! [v8: $i] : (v8 = v3 | v4 = v1 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5, v4) = v8) | ~
% 221.61/34.41 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v2) = v5) | ~
% 221.61/34.41 | (hAPP(v6, v3) = v7) | ~ (hAPP(v0, v4) = v6) | ~ $i(v5) | ~
% 221.61/34.41 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4)) & ! [v2: $i]
% 221.61/34.41 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 221.61/34.41 | $i] : ! [v8: $i] : (v8 = v3 | v4 = v1 | ~
% 221.61/34.41 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5, v4) = v8) | ~
% 221.61/34.41 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v2) = v5) | ~
% 221.61/34.41 | (hAPP(v6, v3) = v7) | ~ (hAPP(v0, v4) = v6) | ~ $i(v5) | ~
% 221.61/34.41 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v4) | ~
% 221.61/34.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2)))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (fact_z3div__def) implies:
% 221.61/34.42 | (214) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v0)
% 221.61/34.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.42 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v3) = v4) | ~
% 221.61/34.42 | (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v2) = v3) | ~
% 221.61/34.42 | $i(v2) | ~ $i(v1) |
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) | ? [v5:
% 221.61/34.42 | $i] : (c_SMT_Oz3div(v1, v2) = v5 &
% 221.61/34.42 | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v4) = v5 &
% 221.61/34.42 | $i(v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.61/34.42 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v2) = v3) | ~
% 221.61/34.42 | $i(v2) | ~ $i(v1) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.61/34.42 | (c_SMT_Oz3div(v1, v2) = v3 & $i(v3))))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (fact_incr__mult__lemma) implies:
% 221.61/34.42 | (215) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.42 | (c_Groups_Otimes__class_Otimes(tc_Int_Oint) = v1 &
% 221.61/34.42 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & $i(v1) & $i(v0) &
% 221.61/34.42 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.42 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 221.61/34.42 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v6) = v8) | ~
% 221.61/34.42 | (hAPP(v5, v4) = v6) | ~ (hAPP(v3, v8) = v9) | ~ (hAPP(v1, v2) =
% 221.61/34.42 | v5) | ~ $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v2) |
% 221.61/34.42 | hBOOL(v9) | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 221.61/34.42 | $i] : ? [v14: $i] : ($i(v11) &
% 221.61/34.42 | ((c_Groups_Oplus__class_Oplus(tc_Int_Oint, v11, v4) = v13 &
% 221.61/34.42 | hAPP(v3, v13) = v14 & hAPP(v3, v11) = v12 & $i(v14) &
% 221.61/34.42 | $i(v13) & $i(v12) & hBOOL(v12) & ~ hBOOL(v14)) | (hAPP(v3,
% 221.61/34.42 | v7) = v10 & $i(v10) & ~ hBOOL(v10))))))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (fact_div__le__mono2) implies:
% 221.61/34.42 | (216) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)
% 221.61/34.42 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 221.61/34.42 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v3) = v5)
% 221.61/34.42 | | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v4) | ~
% 221.61/34.42 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) |
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (fact_div__mult__self1__is__m) implies:
% 221.61/34.42 | (217) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.42 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.42 | : (v6 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) =
% 221.61/34.42 | v6) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~
% 221.61/34.42 | $i(v3) | ~ $i(v2) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (fact_div__mult__self__is__m) implies:
% 221.61/34.42 | (218) ? [v0: $i] : ? [v1: $i] :
% 221.61/34.42 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 221.61/34.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.42 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 221.61/34.42 | : (v6 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) =
% 221.61/34.42 | v6) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~
% 221.61/34.42 | $i(v3) | ~ $i(v2) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (fact_div__less__dividend) implies:
% 221.61/34.42 | (219) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 221.61/34.42 | v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) &
% 221.61/34.42 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 221.61/34.42 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~
% 221.61/34.42 | $i(v3) | ~ $i(v2) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (fact_div__1) implies:
% 221.61/34.42 | (220) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 &
% 221.61/34.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) &
% 221.61/34.42 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 221.61/34.42 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~
% 221.61/34.42 | $i(v2)))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Int__Oint__Groups_Oordered__ab__group__add) implies:
% 221.61/34.42 | (221) class_Groups_Oordered__ab__group__add(tc_Int_Oint)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Int__Oint__Rings_Olinordered__semidom) implies:
% 221.61/34.42 | (222) class_Rings_Olinordered__semidom(tc_Int_Oint)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Int__Oint__Groups_Ogroup__add) implies:
% 221.61/34.42 | (223) class_Groups_Ogroup__add(tc_Int_Oint)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Int__Oint__Rings_Odvd) implies:
% 221.61/34.42 | (224) $i(tc_Int_Oint)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Nat__Onat__Rings_Olinordered__semidom) implies:
% 221.61/34.42 | (225) class_Rings_Olinordered__semidom(tc_Nat_Onat)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Nat__Onat__Rings_Ocomm__semiring__1) implies:
% 221.61/34.42 | (226) class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Nat__Onat__Rings_Ozero__neq__one) implies:
% 221.61/34.42 | (227) class_Rings_Ozero__neq__one(tc_Nat_Onat)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Nat__Onat__Power_Opower) implies:
% 221.61/34.42 | (228) class_Power_Opower(tc_Nat_Onat)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) implies:
% 221.61/34.42 | (229) class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Complex__Ocomplex__Rings_Ozero__neq__one) implies:
% 221.61/34.42 | (230) class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Complex__Ocomplex__Groups_Ogroup__add) implies:
% 221.61/34.42 | (231) class_Groups_Ogroup__add(tc_Complex_Ocomplex)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Complex__Ocomplex__Int_Oring__char__0) implies:
% 221.61/34.42 | (232) class_Int_Oring__char__0(tc_Complex_Ocomplex)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Complex__Ocomplex__Groups_Ozero) implies:
% 221.61/34.42 | (233) class_Groups_Ozero(tc_Complex_Ocomplex)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (arity_Complex__Ocomplex__Rings_Oidom) implies:
% 221.61/34.42 | (234) class_Rings_Oidom(tc_Complex_Ocomplex)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (conj_0) implies:
% 221.61/34.42 | (235) $i(tc_Nat_Onat)
% 221.61/34.42 | (236) $i(v_na____)
% 221.61/34.42 | (237) $i(tc_Complex_Ocomplex)
% 221.61/34.42 | (238) $i(v_a____)
% 221.61/34.42 | (239) $i(v_pa____)
% 221.61/34.42 | (240) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 221.61/34.42 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 221.61/34.42 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 221.61/34.42 | $i] : ? [v15: $i] : ? [v16: $i] : ( ~ (v16 = v9) &
% 221.61/34.42 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, v11) = v14 &
% 221.61/34.42 | c_Groups_Otimes__class_Otimes(v0) = v10 &
% 221.61/34.42 | c_Power_Opower__class_Opower(v0) = v3 &
% 221.61/34.42 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) = v4
% 221.61/34.42 | & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v5 &
% 221.61/34.42 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v5, v1) = v6 &
% 221.61/34.42 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v4, v6) = v7 &
% 221.61/34.42 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = v11 &
% 221.61/34.42 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 221.61/34.42 | c_Groups_Ozero__class_Ozero(v0) = v1 & hAPP(v13, v15) = v16 &
% 221.61/34.42 | hAPP(v10, v12) = v13 & hAPP(v8, v14) = v15 & hAPP(v8, v11) = v12 &
% 221.61/34.42 | hAPP(v8, v_na____) = v9 & hAPP(v3, v7) = v8 & $i(v16) & $i(v15) &
% 221.61/34.42 | $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) &
% 221.61/34.42 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v1) & $i(v0) & ( ~
% 221.61/34.42 | (v1 = v_r____) | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 &
% 221.61/34.42 | $i(v2) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2,
% 221.61/34.42 | v_na____))))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (function-axioms) implies:
% 221.61/34.42 | (241) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.42 | (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 221.61/34.42 | (c_Groups_Ozero__class_Ozero(v2) = v0))
% 221.61/34.42 | (242) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.42 | (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0))
% 221.61/34.42 | (243) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.42 | (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 221.61/34.42 | (c_Groups_Oone__class_Oone(v2) = v0))
% 221.61/34.42 | (244) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.42 | (c_Power_Opower__class_Opower(v2) = v1) | ~
% 221.61/34.42 | (c_Power_Opower__class_Opower(v2) = v0))
% 221.61/34.42 | (245) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.42 | (c_Groups_Otimes__class_Otimes(v2) = v1) | ~
% 221.61/34.42 | (c_Groups_Otimes__class_Otimes(v2) = v0))
% 221.61/34.42 | (246) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 221.61/34.42 | (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0))
% 221.61/34.42 | (247) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 221.61/34.42 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0))
% 221.61/34.42 | (248) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 221.61/34.42 | (c_Groups_Ouminus__class_Ouminus(v3, v2) = v1) | ~
% 221.61/34.42 | (c_Groups_Ouminus__class_Ouminus(v3, v2) = v0))
% 221.61/34.42 | (249) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 221.61/34.42 | (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2)
% 221.61/34.42 | = v0))
% 221.61/34.42 | (250) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 221.61/34.42 | (v1 = v0 | ~ (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~
% 221.61/34.42 | (c_Polynomial_Oorder(v4, v3, v2) = v0))
% 221.61/34.42 | (251) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 221.61/34.42 | (v1 = v0 | ~ (c_Polynomial_OpCons(v4, v3, v2) = v1) | ~
% 221.61/34.42 | (c_Polynomial_OpCons(v4, v3, v2) = v0))
% 221.61/34.42 | (252) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 221.61/34.42 | (v1 = v0 | ~ (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 221.61/34.42 | (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0))
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (129) with fresh symbol all_742_0 gives:
% 221.61/34.42 | (253) c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, all_742_0) = all_742_0 &
% 221.61/34.42 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_742_0 & $i(all_742_0)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (253) implies:
% 221.61/34.42 | (254) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_742_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (8) with fresh symbol all_744_0 gives:
% 221.61/34.42 | (255) c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 221.61/34.42 | all_744_0 & $i(all_744_0) &
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_744_0, v_na____)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (255) implies:
% 221.61/34.42 | (256) c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_744_0, v_na____)
% 221.61/34.42 | (257) c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 221.61/34.42 | all_744_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (19) with fresh symbol all_746_0 gives:
% 221.61/34.42 | (258) c_Polynomial_Odegree(tc_Complex_Ocomplex, v_s____) = all_746_0 &
% 221.61/34.42 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_746_0 & $i(all_746_0)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (258) implies:
% 221.61/34.42 | (259) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_746_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (2) with fresh symbol all_748_0 gives:
% 221.61/34.42 | (260) ~ (all_748_0 = v_na____) & c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 221.61/34.42 | = all_748_0 & $i(all_748_0)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (260) implies:
% 221.61/34.42 | (261) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_748_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (140) with fresh symbol all_750_0 gives:
% 221.61/34.42 | (262) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_750_0 & $i(all_750_0)
% 221.61/34.42 | & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_750_0,
% 221.61/34.42 | all_750_0)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (262) implies:
% 221.61/34.42 | (263) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_750_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (6) with fresh symbol all_752_0 gives:
% 221.61/34.42 | (264) ~ (all_752_0 = v_k____) &
% 221.61/34.42 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_752_0 &
% 221.61/34.42 | $i(all_752_0)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (264) implies:
% 221.61/34.42 | (265) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_752_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (1) with fresh symbol all_754_0 gives:
% 221.61/34.42 | (266) ~ (all_754_0 = v_n) & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) =
% 221.61/34.42 | all_754_0 & $i(all_754_0)
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (266) implies:
% 221.61/34.42 | (267) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_754_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (48) with fresh symbol all_761_0 gives:
% 221.61/34.42 | (268) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_761_0 & $i(all_761_0)
% 221.61/34.42 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_761_0))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (268) implies:
% 221.61/34.42 | (269) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_761_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (71) with fresh symbol all_764_0 gives:
% 221.61/34.42 | (270) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_764_0 & $i(all_764_0)
% 221.61/34.42 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_764_0) | ~ $i(v0))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (270) implies:
% 221.61/34.42 | (271) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_764_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (117) with fresh symbol all_767_0 gives:
% 221.61/34.42 | (272) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_767_0 & $i(all_767_0)
% 221.61/34.42 | & ? [v0: $i] : ( ~ $i(v0) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 221.61/34.42 | v0, all_767_0))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (272) implies:
% 221.61/34.42 | (273) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_767_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (71) with fresh symbol all_769_0 gives:
% 221.61/34.42 | (274) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_769_0 & $i(all_769_0)
% 221.61/34.42 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_769_0) | ~ $i(v0))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (274) implies:
% 221.61/34.42 | (275) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_769_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (50) with fresh symbol all_778_0 gives:
% 221.61/34.42 | (276) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_778_0 & $i(all_778_0)
% 221.61/34.42 | & ? [v0: $i] : ( ~ $i(v0) |
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_778_0, v0))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (276) implies:
% 221.61/34.42 | (277) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_778_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (48) with fresh symbol all_780_0 gives:
% 221.61/34.42 | (278) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_780_0 & $i(all_780_0)
% 221.61/34.42 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 221.61/34.42 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_780_0))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (278) implies:
% 221.61/34.42 | (279) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_780_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (50) with fresh symbol all_783_0 gives:
% 221.61/34.42 | (280) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_783_0 & $i(all_783_0)
% 221.61/34.42 | & ? [v0: $i] : ( ~ $i(v0) |
% 221.61/34.42 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_783_0, v0))
% 221.61/34.42 |
% 221.61/34.42 | ALPHA: (280) implies:
% 221.61/34.42 | (281) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_783_0
% 221.61/34.42 |
% 221.61/34.42 | DELTA: instantiating (48) with fresh symbol all_785_0 gives:
% 221.61/34.43 | (282) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_785_0 & $i(all_785_0)
% 221.61/34.43 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 221.61/34.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_785_0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (282) implies:
% 221.61/34.43 | (283) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_785_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (71) with fresh symbol all_788_0 gives:
% 221.61/34.43 | (284) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_788_0 & $i(all_788_0)
% 221.61/34.43 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_788_0) | ~ $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (284) implies:
% 221.61/34.43 | (285) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_788_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (71) with fresh symbol all_791_0 gives:
% 221.61/34.43 | (286) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_791_0 & $i(all_791_0)
% 221.61/34.43 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_791_0) | ~ $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (286) implies:
% 221.61/34.43 | (287) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_791_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (119) with fresh symbol all_794_0 gives:
% 221.61/34.43 | (288) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_794_0 & $i(all_794_0) &
% 221.61/34.43 | ? [v0: $i] : ( ~ $i(v0) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 221.61/34.43 | all_794_0, v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (288) implies:
% 221.61/34.43 | (289) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_794_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (48) with fresh symbol all_796_0 gives:
% 221.61/34.43 | (290) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_796_0 & $i(all_796_0)
% 221.61/34.43 | & ! [v0: $i] : ( ~ $i(v0) | ~
% 221.61/34.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_796_0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (290) implies:
% 221.61/34.43 | (291) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_796_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (71) with fresh symbol all_799_0 gives:
% 221.61/34.43 | (292) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_799_0 & $i(all_799_0)
% 221.61/34.43 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_799_0) | ~ $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (292) implies:
% 221.61/34.43 | (293) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_799_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (71) with fresh symbol all_803_0 gives:
% 221.61/34.43 | (294) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_803_0 & $i(all_803_0)
% 221.61/34.43 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_803_0) | ~ $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (294) implies:
% 221.61/34.43 | (295) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_803_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (3) with fresh symbols all_806_0, all_806_1 gives:
% 221.61/34.43 | (296) ~ (all_806_0 = v_qa____) & tc_Polynomial_Opoly(tc_Complex_Ocomplex)
% 221.61/34.43 | = all_806_1 & c_Groups_Ozero__class_Ozero(all_806_1) = all_806_0 &
% 221.61/34.43 | $i(all_806_0) & $i(all_806_1)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (296) implies:
% 221.61/34.43 | (297) c_Groups_Ozero__class_Ozero(all_806_1) = all_806_0
% 221.61/34.43 | (298) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_806_1
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (5) with fresh symbols all_808_0, all_808_1 gives:
% 221.61/34.43 | (299) ~ (all_808_0 = v_pa____) & tc_Polynomial_Opoly(tc_Complex_Ocomplex)
% 221.61/34.43 | = all_808_1 & c_Groups_Ozero__class_Ozero(all_808_1) = all_808_0 &
% 221.61/34.43 | $i(all_808_0) & $i(all_808_1)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (299) implies:
% 221.61/34.43 | (300) $i(all_808_0)
% 221.61/34.43 | (301) c_Groups_Ozero__class_Ozero(all_808_1) = all_808_0
% 221.61/34.43 | (302) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_808_1
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (46) with fresh symbol all_812_0 gives:
% 221.61/34.43 | (303) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_812_0 & $i(all_812_0)
% 221.61/34.43 | & ? [v0: any] : (v0 = all_812_0 | ~ $i(v0) |
% 221.61/34.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_812_0, v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (303) implies:
% 221.61/34.43 | (304) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_812_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (54) with fresh symbol all_814_0 gives:
% 221.61/34.43 | (305) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_814_0 & $i(all_814_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: int] : (v1 = all_814_0 | ~
% 221.61/34.43 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, all_814_0, v0) = v1) |
% 221.61/34.43 | ~ $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (305) implies:
% 221.61/34.43 | (306) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_814_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (88) with fresh symbols all_817_0, all_817_1 gives:
% 221.61/34.43 | (307) c_Nat_OSuc(all_817_0) = all_817_1 &
% 221.61/34.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_817_1 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_817_0 & $i(all_817_0)
% 221.61/34.43 | & $i(all_817_1)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (307) implies:
% 221.61/34.43 | (308) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_817_0
% 221.61/34.43 | (309) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_817_1
% 221.61/34.43 | (310) c_Nat_OSuc(all_817_0) = all_817_1
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (69) with fresh symbol all_819_0 gives:
% 221.61/34.43 | (311) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_819_0 & $i(all_819_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 221.61/34.43 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_819_0, v1))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (311) implies:
% 221.61/34.43 | (312) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_819_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (52) with fresh symbol all_824_0 gives:
% 221.61/34.43 | (313) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_824_0 & $i(all_824_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: int] : (v1 = all_824_0 | ~
% 221.61/34.43 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v0) = v1) | ~
% 221.61/34.43 | $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (313) implies:
% 221.61/34.43 | (314) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_824_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (141) with fresh symbols all_830_0, all_830_1 gives:
% 221.61/34.43 | (315) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_830_0 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_830_1 & $i(all_830_0)
% 221.61/34.43 | & $i(all_830_1) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 221.61/34.43 | all_830_1, all_830_0)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (315) implies:
% 221.61/34.43 | (316) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_830_1
% 221.61/34.43 | (317) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_830_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (128) with fresh symbols all_832_0, all_832_1 gives:
% 221.61/34.43 | (318) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_832_0 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_832_1 & $i(all_832_0)
% 221.61/34.43 | & $i(all_832_1) & c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.61/34.43 | all_832_1, all_832_0)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (318) implies:
% 221.61/34.43 | (319) $i(all_832_0)
% 221.61/34.43 | (320) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_832_1
% 221.61/34.43 | (321) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_832_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (156) with fresh symbol all_835_0 gives:
% 221.61/34.43 | (322) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_835_0 & $i(all_835_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 221.61/34.43 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, all_835_0) = v1) | ~
% 221.61/34.43 | $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (322) implies:
% 221.61/34.43 | (323) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_835_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (53) with fresh symbol all_838_0 gives:
% 221.61/34.43 | (324) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_838_0 & $i(all_838_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 221.61/34.43 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_838_0) = v1) |
% 221.61/34.43 | ~ $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (324) implies:
% 221.61/34.43 | (325) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_838_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (13) with fresh symbols all_841_0, all_841_1 gives:
% 221.61/34.43 | (326) ~ (all_841_0 = v_s____) & tc_Polynomial_Opoly(tc_Complex_Ocomplex) =
% 221.61/34.43 | all_841_1 & c_Groups_Ozero__class_Ozero(all_841_1) = all_841_0 &
% 221.61/34.43 | $i(all_841_0) & $i(all_841_1)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (326) implies:
% 221.61/34.43 | (327) c_Groups_Ozero__class_Ozero(all_841_1) = all_841_0
% 221.61/34.43 | (328) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_841_1
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (159) with fresh symbol all_846_0 gives:
% 221.61/34.43 | (329) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_846_0 & $i(all_846_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 221.61/34.43 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_846_0) = v1) | ~
% 221.61/34.43 | $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (329) implies:
% 221.61/34.43 | (330) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_846_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (157) with fresh symbol all_849_0 gives:
% 221.61/34.43 | (331) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_849_0 & $i(all_849_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 221.61/34.43 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, all_849_0, v0) = v1) | ~
% 221.61/34.43 | $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (331) implies:
% 221.61/34.43 | (332) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_849_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (7) with fresh symbols all_852_0, all_852_1 gives:
% 221.61/34.43 | (333) c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, all_852_0) =
% 221.61/34.43 | v_s____ & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_852_1 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(all_852_1) = all_852_0 & $i(all_852_0) &
% 221.61/34.43 | $i(all_852_1)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (333) implies:
% 221.61/34.43 | (334) c_Groups_Ozero__class_Ozero(all_852_1) = all_852_0
% 221.61/34.43 | (335) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_852_1
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (11) with fresh symbols all_854_0, all_854_1 gives:
% 221.61/34.43 | (336) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_854_1 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_854_0 &
% 221.61/34.43 | hAPP(all_854_1, v_a____) = all_854_0 & $i(all_854_0) & $i(all_854_1)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (336) implies:
% 221.61/34.43 | (337) hAPP(all_854_1, v_a____) = all_854_0
% 221.61/34.43 | (338) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_854_0
% 221.61/34.43 | (339) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_854_1
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (4) with fresh symbols all_856_0, all_856_1 gives:
% 221.61/34.43 | (340) ~ (all_856_0 = all_856_1) & c_Polynomial_Oorder(tc_Complex_Ocomplex,
% 221.61/34.43 | v_a____, v_pa____) = all_856_1 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_856_0 & $i(all_856_0)
% 221.61/34.43 | & $i(all_856_1)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (340) implies:
% 221.61/34.43 | (341) $i(all_856_1)
% 221.61/34.43 | (342) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_856_0
% 221.61/34.43 | (343) c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 221.61/34.43 | all_856_1
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (206) with fresh symbol all_858_0 gives:
% 221.61/34.43 | (344) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_858_0 & $i(all_858_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: int] : (v1 = all_858_0 | ~
% 221.61/34.43 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, all_858_0, v0) = v1) | ~
% 221.61/34.43 | $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (344) implies:
% 221.61/34.43 | (345) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_858_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (127) with fresh symbols all_861_0, all_861_1 gives:
% 221.61/34.43 | (346) ~ (all_861_0 = all_861_1) & c_Groups_Oone__class_Oone(tc_Int_Oint) =
% 221.61/34.43 | all_861_0 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_861_1 &
% 221.61/34.43 | $i(all_861_0) & $i(all_861_1)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (346) implies:
% 221.61/34.43 | (347) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_861_1
% 221.61/34.43 | (348) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_861_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (89) with fresh symbol all_863_0 gives:
% 221.61/34.43 | (349) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_863_0 & $i(all_863_0) &
% 221.61/34.43 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 221.61/34.43 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_863_0) = v0)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (349) implies:
% 221.61/34.43 | (350) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_863_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (158) with fresh symbol all_868_0 gives:
% 221.61/34.43 | (351) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_868_0 & $i(all_868_0)
% 221.61/34.43 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 221.61/34.43 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_868_0, v0) = v1) | ~
% 221.61/34.43 | $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (351) implies:
% 221.61/34.43 | (352) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_868_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (68) with fresh symbols all_871_0, all_871_1 gives:
% 221.61/34.43 | (353) c_Nat_OSuc(all_871_1) = all_871_0 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_871_1 & $i(all_871_0)
% 221.61/34.43 | & $i(all_871_1) & ? [v0: $i] : ( ~ $i(v0) |
% 221.61/34.43 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_871_0, v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (353) implies:
% 221.61/34.43 | (354) $i(all_871_0)
% 221.61/34.43 | (355) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_871_1
% 221.61/34.43 | (356) c_Nat_OSuc(all_871_1) = all_871_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (161) with fresh symbol all_875_0 gives:
% 221.61/34.43 | (357) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_875_0 & $i(all_875_0)
% 221.61/34.43 | & ! [v0: any] : ! [v1: $i] : (v0 = all_875_0 | ~
% 221.61/34.43 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v1) | ~ $i(v1)
% 221.61/34.43 | | ~ $i(v0))
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (357) implies:
% 221.61/34.43 | (358) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_875_0
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (65) with fresh symbols all_880_0, all_880_1, all_880_2
% 221.61/34.43 | gives:
% 221.61/34.43 | (359) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_880_0, all_880_1) =
% 221.61/34.43 | v_s____ & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_880_2 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(all_880_2) = all_880_1 & $i(all_880_0) &
% 221.61/34.43 | $i(all_880_1) & $i(all_880_2)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (359) implies:
% 221.61/34.43 | (360) $i(all_880_0)
% 221.61/34.43 | (361) c_Groups_Ozero__class_Ozero(all_880_2) = all_880_1
% 221.61/34.43 | (362) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_880_2
% 221.61/34.43 | (363) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_880_0, all_880_1) =
% 221.61/34.43 | v_s____
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (65) with fresh symbols all_882_0, all_882_1, all_882_2
% 221.61/34.43 | gives:
% 221.61/34.43 | (364) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_882_0, all_882_1) =
% 221.61/34.43 | v_s____ & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_882_2 &
% 221.61/34.43 | c_Groups_Ozero__class_Ozero(all_882_2) = all_882_1 & $i(all_882_0) &
% 221.61/34.43 | $i(all_882_1) & $i(all_882_2)
% 221.61/34.43 |
% 221.61/34.43 | ALPHA: (364) implies:
% 221.61/34.43 | (365) $i(all_882_0)
% 221.61/34.43 | (366) c_Groups_Ozero__class_Ozero(all_882_2) = all_882_1
% 221.61/34.43 | (367) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_882_2
% 221.61/34.43 | (368) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_882_0, all_882_1) =
% 221.61/34.43 | v_s____
% 221.61/34.43 |
% 221.61/34.43 | DELTA: instantiating (47) with fresh symbol all_884_0 gives:
% 221.61/34.44 | (369) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_884_0 & $i(all_884_0)
% 221.61/34.44 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_884_0, all_884_0)
% 221.61/34.44 | & ? [v0: any] : (v0 = all_884_0 | ~ $i(v0) |
% 221.61/34.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_884_0, v0))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (369) implies:
% 221.61/34.44 | (370) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_884_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (170) with fresh symbol all_886_0 gives:
% 221.61/34.44 | (371) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_886_0 & $i(all_886_0) &
% 221.61/34.44 | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.61/34.44 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_886_0) = v1) | ~
% 221.61/34.44 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1)))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (371) implies:
% 221.61/34.44 | (372) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_886_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (76) with fresh symbol all_892_0 gives:
% 221.61/34.44 | (373) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_892_0 & $i(all_892_0) &
% 221.61/34.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_892_0, all_892_0) & ! [v0:
% 221.61/34.44 | any] : (v0 = all_892_0 | ~ $i(v0) | ~
% 221.61/34.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_892_0))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (373) implies:
% 221.61/34.44 | (374) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_892_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (49) with fresh symbol all_895_0 gives:
% 221.61/34.44 | (375) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_895_0 & $i(all_895_0)
% 221.61/34.44 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_895_0,
% 221.61/34.44 | all_895_0) & ! [v0: any] : (v0 = all_895_0 | ~ $i(v0) | ~
% 221.61/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, all_895_0))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (375) implies:
% 221.61/34.44 | (376) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_895_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (171) with fresh symbol all_898_0 gives:
% 221.61/34.44 | (377) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_898_0 & $i(all_898_0) &
% 221.61/34.44 | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.61/34.44 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_898_0, v0) = v1) | ~
% 221.61/34.44 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1)))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (377) implies:
% 221.61/34.44 | (378) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_898_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (172) with fresh symbol all_909_0 gives:
% 221.61/34.44 | (379) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_909_0 & $i(all_909_0)
% 221.61/34.44 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_909_0 | ~
% 221.61/34.44 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v2) | ~
% 221.61/34.44 | (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v0) = v1) | ~
% 221.61/34.44 | $i(v0))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (379) implies:
% 221.61/34.44 | (380) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_909_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (175) with fresh symbol all_914_0 gives:
% 221.61/34.44 | (381) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_914_0 & $i(all_914_0) &
% 221.61/34.44 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.61/34.44 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, all_914_0) = v2) | ~
% 221.61/34.44 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.61/34.44 | v1, v0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (381) implies:
% 221.61/34.44 | (382) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_914_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (34) with fresh symbols all_921_0, all_921_1 gives:
% 221.61/34.44 | (383) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_921_1 &
% 221.61/34.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_921_0 & $i(all_921_0)
% 221.61/34.44 | & $i(all_921_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_921_1,
% 221.61/34.44 | v0) = v1) | ~ $i(v0) | hAPP(v1, all_921_0) = all_921_0)
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (383) implies:
% 221.61/34.44 | (384) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_921_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (29) with fresh symbols all_929_0, all_929_1 gives:
% 221.61/34.44 | (385) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_929_1 &
% 221.61/34.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_929_0 & $i(all_929_0) &
% 221.61/34.44 | $i(all_929_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_929_1, v0)
% 221.61/34.44 | = v1) | ~ $i(v0) | hAPP(v1, all_929_0) = v0)
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (385) implies:
% 221.61/34.44 | (386) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_929_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (168) with fresh symbol all_932_0 gives:
% 221.61/34.44 | (387) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_932_0 & $i(all_932_0)
% 221.61/34.44 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 221.61/34.44 | all_932_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) =
% 221.61/34.44 | v2) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) =
% 221.61/34.44 | v3) | ~ $i(v1) | ~ $i(v0))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (387) implies:
% 221.61/34.44 | (388) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_932_0
% 221.61/34.44 |
% 221.61/34.44 | DELTA: instantiating (78) with fresh symbol all_935_0 gives:
% 221.61/34.44 | (389) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_935_0 & $i(all_935_0)
% 221.61/34.44 | & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 221.61/34.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~
% 221.61/34.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_935_0, v1) | ~
% 221.61/34.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v1))
% 221.61/34.44 |
% 221.61/34.44 | ALPHA: (389) implies:
% 221.61/34.44 | (390) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_935_0
% 221.61/34.44 |
% 221.92/34.44 | DELTA: instantiating (132) with fresh symbols all_938_0, all_938_1 gives:
% 221.92/34.44 | (391) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_938_1 &
% 221.92/34.44 | c_Groups_Oone__class_Oone(tc_Int_Oint) = all_938_0 & $i(all_938_0) &
% 221.92/34.44 | $i(all_938_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_938_1, v0)
% 221.92/34.44 | = v1) | ~ $i(v0) | hAPP(v1, all_938_0) = v0)
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (391) implies:
% 221.92/34.44 | (392) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_938_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (59) with fresh symbol all_941_0 gives:
% 221.92/34.44 | (393) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_941_0 & $i(all_941_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_941_0 | ~
% 221.92/34.44 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~
% 221.92/34.44 | $i(v1) | ~ $i(v0) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (393) implies:
% 221.92/34.44 | (394) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_941_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (91) with fresh symbol all_944_0 gives:
% 221.92/34.44 | (395) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_944_0 & $i(all_944_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_944_0, v0) | ~
% 221.92/34.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) |
% 221.92/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (395) implies:
% 221.92/34.44 | (396) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_944_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (167) with fresh symbols all_947_0, all_947_1 gives:
% 221.92/34.44 | (397) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_947_1 &
% 221.92/34.44 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_947_0 & $i(all_947_0)
% 221.92/34.44 | & $i(all_947_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 221.92/34.44 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = all_947_0) | ~
% 221.92/34.44 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, all_947_1, v0) = v1) | ~
% 221.92/34.44 | $i(v0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (397) implies:
% 221.92/34.44 | (398) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_947_0
% 221.92/34.44 | (399) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_947_1
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (123) with fresh symbol all_954_0 gives:
% 221.92/34.44 | (400) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_954_0 & $i(all_954_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_954_0, v1) | ~
% 221.92/34.44 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v0, v1))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (400) implies:
% 221.92/34.44 | (401) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_954_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (113) with fresh symbol all_957_0 gives:
% 221.92/34.44 | (402) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_957_0 & $i(all_957_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_957_0, v1) | ~
% 221.92/34.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v1) |
% 221.92/34.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_957_0, v0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (402) implies:
% 221.92/34.44 | (403) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_957_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (220) with fresh symbols all_960_0, all_960_1 gives:
% 221.92/34.44 | (404) c_Nat_OSuc(all_960_1) = all_960_0 &
% 221.92/34.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_960_1 & $i(all_960_0)
% 221.92/34.44 | & $i(all_960_1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 221.92/34.44 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, all_960_0) = v1) | ~
% 221.92/34.44 | $i(v0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (404) implies:
% 221.92/34.44 | (405) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_960_1
% 221.92/34.44 | (406) c_Nat_OSuc(all_960_1) = all_960_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (124) with fresh symbol all_965_0 gives:
% 221.92/34.44 | (407) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_965_0 & $i(all_965_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_965_0, v0) | ~
% 221.92/34.44 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0) |
% 221.92/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (407) implies:
% 221.92/34.44 | (408) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_965_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (201) with fresh symbol all_974_0 gives:
% 221.92/34.44 | (409) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_974_0 & $i(all_974_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_974_0 | ~
% 221.92/34.44 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 221.92/34.44 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1)
% 221.92/34.44 | | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, all_974_0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (409) implies:
% 221.92/34.44 | (410) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_974_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (207) with fresh symbols all_977_0, all_977_1 gives:
% 221.92/34.44 | (411) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_977_0 &
% 221.92/34.44 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_977_1 & $i(all_977_0)
% 221.92/34.44 | & $i(all_977_1) & ! [v0: any] : ! [v1: int] : (v1 = all_977_0 | v0
% 221.92/34.44 | = all_977_1 | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v0) =
% 221.92/34.44 | v1) | ~ $i(v0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (411) implies:
% 221.92/34.44 | (412) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_977_1
% 221.92/34.44 | (413) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_977_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (208) with fresh symbol all_980_0 gives:
% 221.92/34.44 | (414) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_980_0 & $i(all_980_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.44 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 221.92/34.44 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1,
% 221.92/34.44 | all_980_0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.92/34.44 | all_980_0, v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2,
% 221.92/34.44 | all_980_0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (414) implies:
% 221.92/34.44 | (415) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_980_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (101) with fresh symbols all_983_0, all_983_1 gives:
% 221.92/34.44 | (416) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_983_0 &
% 221.92/34.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_983_1 & $i(all_983_0)
% 221.92/34.44 | & $i(all_983_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 221.92/34.44 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_983_0) = v1) |
% 221.92/34.44 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_983_1,
% 221.92/34.44 | v0) | c_Nat_OSuc(v1) = v0)
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (416) implies:
% 221.92/34.44 | (417) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_983_1
% 221.92/34.44 | (418) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_983_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (143) with fresh symbol all_986_0 gives:
% 221.92/34.44 | (419) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_986_0 & $i(all_986_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.44 | (c_Nat__Transfer_Otsub(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_986_0, v1) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_986_0, v0) |
% 221.92/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_986_0, v2))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (419) implies:
% 221.92/34.44 | (420) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_986_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (196) with fresh symbol all_989_0 gives:
% 221.92/34.44 | (421) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_989_0 & $i(all_989_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.44 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 221.92/34.44 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 221.92/34.44 | all_989_0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 221.92/34.44 | all_989_0, v1) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 221.92/34.44 | v2, all_989_0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (421) implies:
% 221.92/34.44 | (422) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_989_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (81) with fresh symbols all_992_0, all_992_1 gives:
% 221.92/34.44 | (423) c_Nat_OSuc(all_992_1) = all_992_0 &
% 221.92/34.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_992_1 & $i(all_992_0)
% 221.92/34.44 | & $i(all_992_1) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.44 | all_992_1, all_992_0) & ! [v0: any] : (v0 = all_992_1 | ~ $i(v0)
% 221.92/34.44 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_992_0))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (423) implies:
% 221.92/34.44 | (424) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_992_1
% 221.92/34.44 | (425) c_Nat_OSuc(all_992_1) = all_992_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (197) with fresh symbol all_995_0 gives:
% 221.92/34.44 | (426) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_995_0 & $i(all_995_0)
% 221.92/34.44 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_995_0 | ~
% 221.92/34.44 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 221.92/34.44 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0)
% 221.92/34.44 | | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_995_0, v1))
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (426) implies:
% 221.92/34.44 | (427) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_995_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (36) with fresh symbol all_998_0 gives:
% 221.92/34.44 | (428) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_998_0 & $i(all_998_0) &
% 221.92/34.44 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.92/34.44 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 221.92/34.44 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Omonoid__mult(v1) | hAPP(v3,
% 221.92/34.44 | all_998_0) = v0)
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (428) implies:
% 221.92/34.44 | (429) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_998_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (94) with fresh symbols all_1001_0, all_1001_1 gives:
% 221.92/34.44 | (430) c_Nat_OSuc(all_1001_1) = all_1001_0 &
% 221.92/34.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1001_1 &
% 221.92/34.44 | $i(all_1001_0) & $i(all_1001_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 221.92/34.44 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_1001_0) = v1) |
% 221.92/34.44 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.44 | all_1001_1, v0) | c_Nat_OSuc(v1) = v0)
% 221.92/34.44 |
% 221.92/34.44 | ALPHA: (430) implies:
% 221.92/34.44 | (431) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1001_1
% 221.92/34.44 | (432) c_Nat_OSuc(all_1001_1) = all_1001_0
% 221.92/34.44 |
% 221.92/34.44 | DELTA: instantiating (210) with fresh symbol all_1004_0 gives:
% 221.92/34.44 | (433) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1004_0 &
% 221.92/34.44 | $i(all_1004_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.44 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 221.92/34.44 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 221.92/34.44 | all_1004_0, v1) | ~
% 221.92/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1004_0, v0) |
% 221.92/34.44 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1004_0, v2))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (433) implies:
% 221.92/34.45 | (434) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1004_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (70) with fresh symbols all_1007_0, all_1007_1 gives:
% 221.92/34.45 | (435) c_Nat_OSuc(all_1007_1) = all_1007_0 &
% 221.92/34.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1007_1 &
% 221.92/34.45 | $i(all_1007_0) & $i(all_1007_1) &
% 221.92/34.45 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_1007_0, all_1007_0) & !
% 221.92/34.45 | [v0: any] : (v0 = all_1007_0 | ~ $i(v0) | ~
% 221.92/34.45 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_1007_0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (435) implies:
% 221.92/34.45 | (436) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1007_1
% 221.92/34.45 | (437) c_Nat_OSuc(all_1007_1) = all_1007_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (101) with fresh symbols all_1010_0, all_1010_1 gives:
% 221.92/34.45 | (438) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1010_0 &
% 221.92/34.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1010_1 &
% 221.92/34.45 | $i(all_1010_0) & $i(all_1010_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 221.92/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_1010_0) = v1) |
% 221.92/34.45 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.45 | all_1010_1, v0) | c_Nat_OSuc(v1) = v0)
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (438) implies:
% 221.92/34.45 | (439) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1010_1
% 221.92/34.45 | (440) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1010_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (199) with fresh symbol all_1013_0 gives:
% 221.92/34.45 | (441) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1013_0 &
% 221.92/34.45 | $i(all_1013_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.45 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 221.92/34.45 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.92/34.45 | all_1013_0, v0) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, all_1013_0) |
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, all_1013_0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (441) implies:
% 221.92/34.45 | (442) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1013_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (57) with fresh symbol all_1016_0 gives:
% 221.92/34.45 | (443) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1016_0 &
% 221.92/34.45 | $i(all_1016_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~
% 221.92/34.45 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.45 | all_1016_0, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.45 | all_1016_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2,
% 221.92/34.45 | v0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (443) implies:
% 221.92/34.45 | (444) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1016_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (95) with fresh symbol all_1019_0 gives:
% 221.92/34.45 | (445) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1019_0 &
% 221.92/34.45 | $i(all_1019_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | $i] : ( ~ (c_Nat_OSuc(v0) = v2) | ~
% 221.92/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~
% 221.92/34.45 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.45 | all_1019_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3,
% 221.92/34.45 | v1))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (445) implies:
% 221.92/34.45 | (446) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1019_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (97) with fresh symbol all_1022_0 gives:
% 221.92/34.45 | (447) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1022_0 &
% 221.92/34.45 | $i(all_1022_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | int] : (v3 = all_1022_0 | ~ (c_Polynomial_Odegree(v0, v2) = v3) |
% 221.92/34.45 | ~ (c_Groups_Oone__class_Oone(v1) = v2) | ~
% 221.92/34.45 | (tc_Polynomial_Opoly(v0) = v1) | ~ $i(v0) | ~
% 221.92/34.45 | class_Rings_Ocomm__semiring__1(v0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (447) implies:
% 221.92/34.45 | (448) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1022_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (98) with fresh symbol all_1027_0 gives:
% 221.92/34.45 | (449) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1027_0 &
% 221.92/34.45 | $i(all_1027_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | int] : (v3 = all_1027_0 | ~ (c_Polynomial_Odegree(v0, v2) = v3) |
% 221.92/34.45 | ~ (tc_Polynomial_Opoly(v0) = v1) | ~
% 221.92/34.45 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v0) | ~
% 221.92/34.45 | class_Groups_Ozero(v0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (449) implies:
% 221.92/34.45 | (450) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1027_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (178) with fresh symbols all_1030_0, all_1030_1 gives:
% 221.92/34.45 | (451) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1030_0 &
% 221.92/34.45 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1030_1 &
% 221.92/34.45 | $i(all_1030_0) & $i(all_1030_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 221.92/34.45 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, all_1030_0, v0) = v1) |
% 221.92/34.45 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 221.92/34.45 | all_1030_1, v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.92/34.45 | all_1030_1, v1))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (451) implies:
% 221.92/34.45 | (452) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1030_1
% 221.92/34.45 | (453) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1030_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (118) with fresh symbol all_1033_0 gives:
% 221.92/34.45 | (454) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1033_0 & $i(all_1033_0)
% 221.92/34.45 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.92/34.45 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 221.92/34.45 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) |
% 221.92/34.45 | hAPP(v3, all_1033_0) = v0)
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (454) implies:
% 221.92/34.45 | (455) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1033_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (166) with fresh symbol all_1036_0 gives:
% 221.92/34.45 | (456) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1036_0 &
% 221.92/34.45 | $i(all_1036_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.45 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 221.92/34.45 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 221.92/34.45 | all_1036_0, v1) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1036_0, v0) |
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1036_0, v2))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (456) implies:
% 221.92/34.45 | (457) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1036_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (150) with fresh symbol all_1039_0 gives:
% 221.92/34.45 | (458) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1039_0 &
% 221.92/34.45 | $i(all_1039_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v3) = v4) | ~
% 221.92/34.45 | (c_Polynomial_OpCons(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 221.92/34.45 | $i(v0) | ~ class_Groups_Ozero(v2) | hAPP(v4, all_1039_0) = v1)
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (458) implies:
% 221.92/34.45 | (459) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1039_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (121) with fresh symbol all_1042_0 gives:
% 221.92/34.45 | (460) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1042_0 &
% 221.92/34.45 | $i(all_1042_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower_Opower(v3,
% 221.92/34.45 | v2, v1) = v4) | ~ (hAPP(v4, v0) = v5) | ~ $i(v3) | ~ $i(v2)
% 221.92/34.45 | | ~ $i(v1) | ~ $i(v0) | hAPP(v5, all_1042_0) = v2)
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (460) implies:
% 221.92/34.45 | (461) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1042_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (51) with fresh symbol all_1049_0 gives:
% 221.92/34.45 | (462) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1049_0 &
% 221.92/34.45 | $i(all_1049_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 221.92/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = all_1049_0) |
% 221.92/34.45 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = all_1049_0) &
% 221.92/34.45 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2 &
% 221.92/34.45 | $i(v2)))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (462) implies:
% 221.92/34.45 | (463) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1049_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (27) with fresh symbols all_1052_0, all_1052_1,
% 221.92/34.45 | all_1052_2 gives:
% 221.92/34.45 | (464) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1052_2 &
% 221.92/34.45 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1052_1 &
% 221.92/34.45 | hAPP(all_1052_2, all_1052_1) = all_1052_0 & $i(all_1052_0) &
% 221.92/34.45 | $i(all_1052_1) & $i(all_1052_2) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 221.92/34.45 | v0 | ~ (hAPP(all_1052_0, v0) = v1) | ~ $i(v0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (464) implies:
% 221.92/34.45 | (465) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1052_1
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (122) with fresh symbol all_1055_0 gives:
% 221.92/34.45 | (466) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1055_0 &
% 221.92/34.45 | $i(all_1055_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) |
% 221.92/34.45 | ~ $i(v0) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0) | ~
% 221.92/34.45 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v0, v1) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1055_0, v1) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1055_0, v0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (466) implies:
% 221.92/34.45 | (467) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1055_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (35) with fresh symbols all_1058_0, all_1058_1,
% 221.92/34.45 | all_1058_2 gives:
% 221.92/34.45 | (468) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1058_2 &
% 221.92/34.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1058_1 &
% 221.92/34.45 | hAPP(all_1058_2, all_1058_1) = all_1058_0 & $i(all_1058_0) &
% 221.92/34.45 | $i(all_1058_1) & $i(all_1058_2) & ! [v0: $i] : ! [v1: int] : (v1 =
% 221.92/34.45 | all_1058_1 | ~ (hAPP(all_1058_0, v0) = v1) | ~ $i(v0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (468) implies:
% 221.92/34.45 | (469) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1058_1
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (130) with fresh symbols all_1061_0, all_1061_1,
% 221.92/34.45 | all_1061_2 gives:
% 221.92/34.45 | (470) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1061_2 &
% 221.92/34.45 | c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1061_1 &
% 221.92/34.45 | hAPP(all_1061_2, all_1061_1) = all_1061_0 & $i(all_1061_0) &
% 221.92/34.45 | $i(all_1061_1) & $i(all_1061_2) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 221.92/34.45 | v0 | ~ (hAPP(all_1061_0, v0) = v1) | ~ $i(v0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (470) implies:
% 221.92/34.45 | (471) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1061_1
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (99) with fresh symbol all_1067_0 gives:
% 221.92/34.45 | (472) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1067_0 &
% 221.92/34.45 | $i(all_1067_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | $i] : ! [v4: $i] : ! [v5: int] : (v5 = all_1067_0 | ~
% 221.92/34.45 | (c_Polynomial_Odegree(v1, v4) = v5) | ~ (c_Polynomial_OpCons(v1,
% 221.92/34.45 | v0, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = v2) | ~
% 221.92/34.45 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.45 | class_Groups_Ozero(v1))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (472) implies:
% 221.92/34.45 | (473) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1067_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (137) with fresh symbols all_1073_0, all_1073_1 gives:
% 221.92/34.45 | (474) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1073_0 &
% 221.92/34.45 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1073_1 &
% 221.92/34.45 | $i(all_1073_0) & $i(all_1073_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.92/34.45 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1073_0,
% 221.92/34.45 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1073_1, v1) |
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1073_1, v3))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (474) implies:
% 221.92/34.45 | (475) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1073_1
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (131) with fresh symbols all_1079_0, all_1079_1 gives:
% 221.92/34.45 | (476) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1079_1 &
% 221.92/34.45 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1079_0 &
% 221.92/34.45 | $i(all_1079_0) & $i(all_1079_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1079_0, v0) |
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1079_1, v0)) &
% 221.92/34.45 | ! [v0: $i] : ( ~ $i(v0) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1079_1, v0) |
% 221.92/34.45 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1079_0, v0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (476) implies:
% 221.92/34.45 | (477) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1079_0
% 221.92/34.45 | (478) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1079_1
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (202) with fresh symbol all_1082_0 gives:
% 221.92/34.45 | (479) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1082_0 &
% 221.92/34.45 | $i(all_1082_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint,
% 221.92/34.45 | v2, v0) = v3) | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1,
% 221.92/34.45 | v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1082_0, v0) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v4))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (479) implies:
% 221.92/34.45 | (480) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1082_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (145) with fresh symbol all_1088_0 gives:
% 221.92/34.45 | (481) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1088_0 &
% 221.92/34.45 | $i(all_1088_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_OpCons(v1, v0, v3) = v4) | ~
% 221.92/34.45 | (tc_Polynomial_Opoly(v1) = v2) | ~
% 221.92/34.45 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.45 | class_Groups_Ozero(v1) | (c_Polynomial_Omonom(v1, v0, all_1088_0) =
% 221.92/34.45 | v4 & $i(v4)))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (481) implies:
% 221.92/34.45 | (482) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1088_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (108) with fresh symbols all_1091_0, all_1091_1,
% 221.92/34.45 | all_1091_2 gives:
% 221.92/34.45 | (483) c_Nat_OSuc(all_1091_1) = all_1091_0 & c_Nat_OSuc(all_1091_2) =
% 221.92/34.45 | all_1091_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1091_2 &
% 221.92/34.45 | $i(all_1091_0) & $i(all_1091_1) & $i(all_1091_2) & ! [v0: any] : (v0
% 221.92/34.45 | = all_1091_1 | v0 = all_1091_2 | ~ $i(v0) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1091_0))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (483) implies:
% 221.92/34.45 | (484) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1091_2
% 221.92/34.45 | (485) c_Nat_OSuc(all_1091_2) = all_1091_1
% 221.92/34.45 | (486) c_Nat_OSuc(all_1091_1) = all_1091_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (216) with fresh symbol all_1094_0 gives:
% 221.92/34.45 | (487) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1094_0 &
% 221.92/34.45 | $i(all_1094_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.45 | $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,
% 221.92/34.45 | v0, v2) = v4) | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0,
% 221.92/34.45 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1094_0, v2) | ~
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) |
% 221.92/34.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v4))
% 221.92/34.45 |
% 221.92/34.45 | ALPHA: (487) implies:
% 221.92/34.45 | (488) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1094_0
% 221.92/34.45 |
% 221.92/34.45 | DELTA: instantiating (204) with fresh symbols all_1097_0, all_1097_1 gives:
% 221.92/34.46 | (489) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1097_0 &
% 221.92/34.46 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1097_1 &
% 221.92/34.46 | $i(all_1097_0) & $i(all_1097_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.92/34.46 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1097_0, v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1097_1, v1) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (489) implies:
% 221.92/34.46 | (490) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1097_1
% 221.92/34.46 | (491) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1097_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (219) with fresh symbols all_1100_0, all_1100_1 gives:
% 221.92/34.46 | (492) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1100_1 &
% 221.92/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1100_0 &
% 221.92/34.46 | $i(all_1100_0) & $i(all_1100_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.92/34.46 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v2) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1100_0, v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1100_1, v1) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (492) implies:
% 221.92/34.46 | (493) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1100_0
% 221.92/34.46 | (494) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1100_1
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (114) with fresh symbol all_1103_0 gives:
% 221.92/34.46 | (495) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1103_0 &
% 221.92/34.46 | $i(all_1103_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.46 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2,
% 221.92/34.46 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | class_Rings_Ocomm__semiring__1(v1) | ? [v4: $i] :
% 221.92/34.46 | (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, all_1103_0) = v4 &
% 221.92/34.46 | $i(v4)))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (495) implies:
% 221.92/34.46 | (496) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1103_0
% 221.92/34.46 | (497) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.92/34.46 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | ?
% 221.92/34.46 | [v4: $i] : (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3,
% 221.92/34.46 | all_1103_0) = v4 & $i(v4)))
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (56) with fresh symbol all_1106_0 gives:
% 221.92/34.46 | (498) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1106_0 &
% 221.92/34.46 | $i(all_1106_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.46 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2,
% 221.92/34.46 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ class_Power_Opower(v1) |
% 221.92/34.46 | ? [v4: $i] : (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3,
% 221.92/34.46 | all_1106_0) = v4 & $i(v4)))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (498) implies:
% 221.92/34.46 | (499) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1106_0
% 221.92/34.46 | (500) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.92/34.46 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ~ class_Power_Opower(v1) | ? [v4: $i] :
% 221.92/34.46 | (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, all_1106_0) = v4 &
% 221.92/34.46 | $i(v4)))
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (203) with fresh symbol all_1109_0 gives:
% 221.92/34.46 | (501) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1109_0 &
% 221.92/34.46 | $i(all_1109_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.46 | $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint,
% 221.92/34.46 | v2, v0) = v4) | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1,
% 221.92/34.46 | v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, all_1109_0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v1) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v4))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (501) implies:
% 221.92/34.46 | (502) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1109_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (104) with fresh symbol all_1112_0 gives:
% 221.92/34.46 | (503) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1112_0 & $i(all_1112_0)
% 221.92/34.46 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 221.92/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~
% 221.92/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1112_0) = v2) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (c_Nat_OSuc(v0) = v4 &
% 221.92/34.46 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v4) = v3 & $i(v4)
% 221.92/34.46 | & $i(v3)))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (503) implies:
% 221.92/34.46 | (504) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1112_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (80) with fresh symbol all_1115_0 gives:
% 221.92/34.46 | (505) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1115_0 &
% 221.92/34.46 | $i(all_1115_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) =
% 221.92/34.46 | v0) | ~ $i(v1) | ~ $i(v0) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1115_0, v0)) & !
% 221.92/34.46 | [v0: $i] : ( ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.46 | all_1115_0, v0) | ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & $i(v1)))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (505) implies:
% 221.92/34.46 | (506) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1115_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (139) with fresh symbols all_1118_0, all_1118_1 gives:
% 221.92/34.46 | (507) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1118_0 &
% 221.92/34.46 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1118_1 &
% 221.92/34.46 | $i(all_1118_0) & $i(all_1118_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.92/34.46 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1118_0,
% 221.92/34.46 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1118_1, v1) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1118_1, v0) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1118_1, v3))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (507) implies:
% 221.92/34.46 | (508) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1118_1
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (60) with fresh symbol all_1121_0 gives:
% 221.92/34.46 | (509) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1121_0 &
% 221.92/34.46 | $i(all_1121_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 221.92/34.46 | all_1121_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0)
% 221.92/34.46 | = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0:
% 221.92/34.46 | $i] : ! [v1: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,
% 221.92/34.46 | v1, v0) = all_1121_0) | ~ $i(v1) | ~ $i(v0) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (509) implies:
% 221.92/34.46 | (510) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1121_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (217) with fresh symbols all_1124_0, all_1124_1 gives:
% 221.92/34.46 | (511) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1124_0 &
% 221.92/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1124_1 &
% 221.92/34.46 | $i(all_1124_0) & $i(all_1124_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.92/34.46 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~
% 221.92/34.46 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v1) = v4) | ~
% 221.92/34.46 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1124_0, v1) = v2) | ~ $i(v1) |
% 221.92/34.46 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.46 | all_1124_1, v1))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (511) implies:
% 221.92/34.46 | (512) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1124_1
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (74) with fresh symbols all_1130_0, all_1130_1,
% 221.92/34.46 | all_1130_2, all_1130_3 gives:
% 221.92/34.46 | (513) c_Nat_OSuc(all_1130_2) = all_1130_1 &
% 221.92/34.46 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1130_3 &
% 221.92/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1130_2 &
% 221.92/34.46 | hAPP(all_1130_3, all_1130_1) = all_1130_0 & $i(all_1130_0) &
% 221.92/34.46 | $i(all_1130_1) & $i(all_1130_2) & $i(all_1130_3) & ! [v0: $i] : !
% 221.92/34.46 | [v1: int] : (v1 = all_1130_1 | ~ (hAPP(all_1130_0, v0) = v1) | ~
% 221.92/34.46 | $i(v0))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (513) implies:
% 221.92/34.46 | (514) hAPP(all_1130_3, all_1130_1) = all_1130_0
% 221.92/34.46 | (515) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1130_2
% 221.92/34.46 | (516) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1130_3
% 221.92/34.46 | (517) c_Nat_OSuc(all_1130_2) = all_1130_1
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (149) with fresh symbols all_1133_0, all_1133_1 gives:
% 221.92/34.46 | (518) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1133_0 &
% 221.92/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1133_1 &
% 221.92/34.46 | $i(all_1133_0) & $i(all_1133_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 221.92/34.46 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0) = v1) | ~
% 221.92/34.46 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1133_1,
% 221.92/34.46 | v1) | ? [v2: $i] : (c_Nat_OSuc(v2) = v1 &
% 221.92/34.46 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1133_0) = v2 &
% 221.92/34.46 | $i(v2) & $i(v1)))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (518) implies:
% 221.92/34.46 | (519) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1133_1
% 221.92/34.46 | (520) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1133_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (218) with fresh symbols all_1139_0, all_1139_1 gives:
% 221.92/34.46 | (521) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1139_0 &
% 221.92/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1139_1 &
% 221.92/34.46 | $i(all_1139_0) & $i(all_1139_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.92/34.46 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~
% 221.92/34.46 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v1) = v4) | ~
% 221.92/34.46 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1139_0, v0) = v2) | ~ $i(v1) |
% 221.92/34.46 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.46 | all_1139_1, v1))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (521) implies:
% 221.92/34.46 | (522) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1139_1
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (200) with fresh symbol all_1142_0 gives:
% 221.92/34.46 | (523) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1142_0 &
% 221.92/34.46 | $i(all_1142_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.46 | $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint,
% 221.92/34.46 | v2, v1) = v3) | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2,
% 221.92/34.46 | v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, all_1142_0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1142_0, v1) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v4))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (523) implies:
% 221.92/34.46 | (524) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1142_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (195) with fresh symbol all_1145_0 gives:
% 221.92/34.46 | (525) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1145_0 &
% 221.92/34.46 | $i(all_1145_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 221.92/34.46 | $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint,
% 221.92/34.46 | v2, v1) = v4) | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v2,
% 221.92/34.46 | v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1145_0, v1) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1145_0, v2) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v4))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (525) implies:
% 221.92/34.46 | (526) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1145_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (176) with fresh symbol all_1148_0 gives:
% 221.92/34.46 | (527) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1148_0 & $i(all_1148_0)
% 221.92/34.46 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.46 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, all_1148_0) = v2) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0)) & ! [v0:
% 221.92/34.46 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.46 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, all_1148_0) = v2) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v0) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (527) implies:
% 221.92/34.46 | (528) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1148_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (21) with fresh symbols all_1151_0, all_1151_1,
% 221.92/34.46 | all_1151_2 gives:
% 221.92/34.46 | (529) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q) = all_1151_0 &
% 221.92/34.46 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p) = all_1151_2 &
% 221.92/34.46 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1151_1 &
% 221.92/34.46 | $i(all_1151_0) & $i(all_1151_1) & $i(all_1151_2) & ! [v0: $i] : !
% 221.92/34.46 | [v1: int] : (v1 = all_1151_1 | ~ (hAPP(all_1151_0, v0) = v1) | ~
% 221.92/34.46 | $i(v0) | ? [v2: any] : ( ~ (v2 = all_1151_1) & hAPP(all_1151_2,
% 221.92/34.46 | v0) = v2 & $i(v2)))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (529) implies:
% 221.92/34.46 | (530) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1151_1
% 221.92/34.46 | (531) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p) = all_1151_2
% 221.92/34.46 | (532) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q) = all_1151_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (136) with fresh symbol all_1154_0 gives:
% 221.92/34.46 | (533) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1154_0 & $i(all_1154_0)
% 221.92/34.46 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.46 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v0, all_1154_0) = v2) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2)) & ! [v0:
% 221.92/34.46 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.46 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v0, all_1154_0) = v2) |
% 221.92/34.46 | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v2) |
% 221.92/34.46 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (533) implies:
% 221.92/34.46 | (534) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1154_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (58) with fresh symbol all_1157_0 gives:
% 221.92/34.46 | (535) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1157_0 &
% 221.92/34.46 | $i(all_1157_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~
% 221.92/34.46 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.46 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1157_0,
% 221.92/34.46 | v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~
% 221.92/34.46 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 221.92/34.46 | all_1157_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 221.92/34.46 | v1))
% 221.92/34.46 |
% 221.92/34.46 | ALPHA: (535) implies:
% 221.92/34.46 | (536) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1157_0
% 221.92/34.46 |
% 221.92/34.46 | DELTA: instantiating (133) with fresh symbol all_1160_0 gives:
% 221.92/34.46 | (537) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1160_0 &
% 221.92/34.46 | $i(all_1160_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.46 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v1, v0) = v2) | ~
% 221.92/34.46 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.92/34.46 | v2, all_1160_0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1,
% 221.92/34.46 | v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.46 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v1, v0) = v2) | ~
% 221.92/34.47 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 221.92/34.47 | v1, v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2,
% 221.92/34.47 | all_1160_0))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (537) implies:
% 221.92/34.47 | (538) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1160_0
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (25) with fresh symbols all_1166_0, all_1166_1,
% 221.92/34.47 | all_1166_2, all_1166_3, all_1166_4 gives:
% 221.92/34.47 | (539) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1166_4 &
% 221.92/34.47 | $i(all_1166_4) & (( ~ (all_1166_3 = v_qa____) &
% 221.92/34.47 | c_Groups_Ozero__class_Ozero(all_1166_4) = all_1166_3 &
% 221.92/34.47 | $i(all_1166_3)) | (c_Power_Opower__class_Opower(all_1166_4) =
% 221.92/34.47 | all_1166_2 & hAPP(all_1166_1, v_na____) = all_1166_0 &
% 221.92/34.47 | hAPP(all_1166_2, v_qa____) = all_1166_1 & $i(all_1166_0) &
% 221.92/34.47 | $i(all_1166_1) & $i(all_1166_2) &
% 221.92/34.47 | c_Rings_Odvd__class_Odvd(all_1166_4, v_pa____, all_1166_0)))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (539) implies:
% 221.92/34.47 | (540) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1166_4
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (160) with fresh symbol all_1168_0 gives:
% 221.92/34.47 | (541) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1168_0 &
% 221.92/34.47 | $i(all_1168_0) & ! [v0: $i] : ! [v1: any] : (v1 = all_1168_0 | ~
% 221.92/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1168_0) |
% 221.92/34.47 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 =
% 221.92/34.47 | all_1168_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) =
% 221.92/34.47 | all_1168_0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 =
% 221.92/34.47 | all_1168_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 221.92/34.47 | all_1168_0, all_1168_0) = v0))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (541) implies:
% 221.92/34.47 | (542) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1168_0
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (106) with fresh symbols all_1171_0, all_1171_1 gives:
% 221.92/34.47 | (543) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1171_0 &
% 221.92/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1171_1 &
% 221.92/34.47 | $i(all_1171_0) & $i(all_1171_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.92/34.47 | $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (hAPP(v3, v1) = v4)
% 221.92/34.47 | | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1171_0, v2) = v3) | ~
% 221.92/34.47 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1171_1, v2))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (543) implies:
% 221.92/34.47 | (544) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1171_1
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (31) with fresh symbols all_1174_0, all_1174_1,
% 221.92/34.47 | all_1174_2 gives:
% 221.92/34.47 | (545) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1174_2 &
% 221.92/34.47 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1174_1 &
% 221.92/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1174_0 &
% 221.92/34.47 | $i(all_1174_0) & $i(all_1174_1) & $i(all_1174_2) & ! [v0: any] : !
% 221.92/34.47 | [v1: any] : ! [v2: $i] : (v1 = all_1174_0 | v0 = all_1174_1 | ~
% 221.92/34.47 | (hAPP(v2, v0) = v1) | ~ (hAPP(all_1174_2, v1) = v2) | ~ $i(v1) |
% 221.92/34.47 | ~ $i(v0))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (545) implies:
% 221.92/34.47 | (546) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1174_0
% 221.92/34.47 | (547) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1174_1
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (146) with fresh symbol all_1177_0 gives:
% 221.92/34.47 | (548) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1177_0 & $i(all_1177_0)
% 221.92/34.47 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 221.92/34.47 | : ( ~ (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3) | ~
% 221.92/34.47 | (c_Polynomial_Odegree(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 221.92/34.47 | $i(v0) | ~ class_Rings_Ocomm__semiring__0(v2) | ? [v5: $i] :
% 221.92/34.47 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, all_1177_0) = v4 &
% 221.92/34.47 | c_Polynomial_Odegree(v2, v1) = v5 & $i(v5) & $i(v4)))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (548) implies:
% 221.92/34.47 | (549) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1177_0
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (22) with fresh symbols all_1180_0, all_1180_1,
% 221.92/34.47 | all_1180_2 gives:
% 221.92/34.47 | (550) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1180_2 &
% 221.92/34.47 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_qa____) = all_1180_0 &
% 221.92/34.47 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1180_1 &
% 221.92/34.47 | $i(all_1180_0) & $i(all_1180_1) & $i(all_1180_2) & ! [v0: $i] : !
% 221.92/34.47 | [v1: int] : (v1 = all_1180_1 | ~ (hAPP(all_1180_0, v0) = v1) | ~
% 221.92/34.47 | $i(v0) | ? [v2: any] : ( ~ (v2 = all_1180_1) & hAPP(all_1180_2,
% 221.92/34.47 | v0) = v2 & $i(v2)))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (550) implies:
% 221.92/34.47 | (551) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1180_1
% 221.92/34.47 | (552) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_qa____) = all_1180_0
% 221.92/34.47 | (553) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____) = all_1180_2
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (177) with fresh symbol all_1183_0 gives:
% 221.92/34.47 | (554) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1183_0 & $i(all_1183_0)
% 221.92/34.47 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.47 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, all_1183_0) = v2) |
% 221.92/34.47 | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.47 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) |
% 221.92/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0)) & ! [v0:
% 221.92/34.47 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.92/34.47 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, all_1183_0) = v2) |
% 221.92/34.47 | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0) |
% 221.92/34.47 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (554) implies:
% 221.92/34.47 | (555) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1183_0
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (87) with fresh symbols all_1186_0, all_1186_1,
% 221.92/34.47 | all_1186_2 gives:
% 221.92/34.47 | (556) c_Nat_OSuc(all_1186_2) = all_1186_1 &
% 221.92/34.47 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1186_0 &
% 221.92/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_2 &
% 221.92/34.47 | $i(all_1186_0) & $i(all_1186_1) & $i(all_1186_2) & ! [v0: $i] : !
% 221.92/34.47 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~
% 221.92/34.47 | (hAPP(all_1186_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 221.92/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1186_1, v1) |
% 221.92/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1186_1, v3))
% 221.92/34.47 |
% 221.92/34.47 | ALPHA: (556) implies:
% 221.92/34.47 | (557) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_2
% 221.92/34.47 | (558) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1186_0
% 221.92/34.47 | (559) c_Nat_OSuc(all_1186_2) = all_1186_1
% 221.92/34.47 |
% 221.92/34.47 | DELTA: instantiating (135) with fresh symbols all_1192_0, all_1192_1 gives:
% 221.92/34.47 | (560) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1192_0 &
% 221.92/34.47 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1192_1 &
% 221.92/34.47 | $i(all_1192_0) & $i(all_1192_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 221.92/34.47 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v2) =
% 221.92/34.47 | v4) | ~ (hAPP(v3, v1) = v5) | ~ (hAPP(all_1192_0, v0) = v3) |
% 222.05/34.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v1) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1192_1, v0) |
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v5))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (560) implies:
% 222.05/34.47 | (561) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1192_1
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (38) with fresh symbols all_1201_0, all_1201_1 gives:
% 222.05/34.47 | (562) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1201_0 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1201_1 &
% 222.05/34.47 | $i(all_1201_0) & $i(all_1201_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.47 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v2) =
% 222.05/34.47 | v4) | ~ (hAPP(v3, v1) = v5) | ~ (hAPP(all_1201_0, v0) = v3) |
% 222.05/34.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1201_1, v0) |
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (562) implies:
% 222.05/34.47 | (563) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1201_1
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (83) with fresh symbols all_1204_0, all_1204_1,
% 222.05/34.47 | all_1204_2 gives:
% 222.05/34.47 | (564) c_Nat_OSuc(all_1204_2) = all_1204_1 &
% 222.05/34.47 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1204_0 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1204_2 &
% 222.05/34.47 | $i(all_1204_0) & $i(all_1204_1) & $i(all_1204_2) & ! [v0: $i] : !
% 222.05/34.47 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~
% 222.05/34.47 | (hAPP(all_1204_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1204_1, v1) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1204_1, v0) |
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (564) implies:
% 222.05/34.47 | (565) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1204_2
% 222.05/34.47 | (566) c_Nat_OSuc(all_1204_2) = all_1204_1
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (142) with fresh symbol all_1209_0 gives:
% 222.05/34.47 | (567) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1209_0 &
% 222.05/34.47 | $i(all_1209_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 222.05/34.47 | all_1209_0 | ~ (c_Nat__Transfer_Otsub(v0, v1) = v2) | ~ $i(v1) |
% 222.05/34.47 | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0))
% 222.05/34.47 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.47 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v0, v1) = v2) | ~
% 222.05/34.47 | $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0) |
% 222.05/34.47 | (c_Nat__Transfer_Otsub(v0, v1) = v2 & $i(v2)))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (567) implies:
% 222.05/34.47 | (568) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1209_0
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (37) with fresh symbols all_1212_0, all_1212_1 gives:
% 222.05/34.47 | (569) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1212_0 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1212_1 &
% 222.05/34.47 | $i(all_1212_0) & $i(all_1212_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.47 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 222.05/34.47 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1212_0, v2) = v3) |
% 222.05/34.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1212_1, v2) |
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (569) implies:
% 222.05/34.47 | (570) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1212_1
% 222.05/34.47 | (571) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1212_0
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (84) with fresh symbols all_1224_0, all_1224_1,
% 222.05/34.47 | all_1224_2 gives:
% 222.05/34.47 | (572) c_Nat_OSuc(all_1224_2) = all_1224_1 &
% 222.05/34.47 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1224_0 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1224_2 &
% 222.05/34.47 | $i(all_1224_0) & $i(all_1224_1) & $i(all_1224_2) & ! [v0: $i] : !
% 222.05/34.47 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~
% 222.05/34.47 | (hAPP(all_1224_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1224_1, v1) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1224_1, v0) |
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (572) implies:
% 222.05/34.47 | (573) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1224_2
% 222.05/34.47 | (574) c_Nat_OSuc(all_1224_2) = all_1224_1
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (85) with fresh symbols all_1230_0, all_1230_1,
% 222.05/34.47 | all_1230_2 gives:
% 222.05/34.47 | (575) c_Nat_OSuc(all_1230_2) = all_1230_1 &
% 222.05/34.47 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1230_0 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1230_2 &
% 222.05/34.47 | $i(all_1230_0) & $i(all_1230_1) & $i(all_1230_2) & ! [v0: $i] : !
% 222.05/34.47 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~
% 222.05/34.47 | (hAPP(all_1230_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1230_1, v1) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1230_1, v0) |
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1230_1, v3))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (575) implies:
% 222.05/34.47 | (576) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1230_2
% 222.05/34.47 | (577) c_Nat_OSuc(all_1230_2) = all_1230_1
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (125) with fresh symbols all_1233_0, all_1233_1 gives:
% 222.05/34.47 | (578) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1233_1 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1233_0 &
% 222.05/34.47 | $i(all_1233_0) & $i(all_1233_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.47 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1233_0 |
% 222.05/34.47 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.47 | (hAPP(all_1233_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.47 | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v5) |
% 222.05/34.47 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (578) implies:
% 222.05/34.47 | (579) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1233_0
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (96) with fresh symbols all_1236_0, all_1236_1 gives:
% 222.05/34.47 | (580) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1236_1 &
% 222.05/34.47 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1236_0 & $i(all_1236_0)
% 222.05/34.47 | & $i(all_1236_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.47 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~
% 222.05/34.47 | (hAPP(v3, v0) = v5) | ~ (hAPP(all_1236_1, v2) = v3) | ~ $i(v2) |
% 222.05/34.47 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1236_0, v2) | ~
% 222.05/34.47 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) |
% 222.05/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (580) implies:
% 222.05/34.47 | (581) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1236_0
% 222.05/34.47 | (582) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1236_1
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (79) with fresh symbols all_1239_0, all_1239_1 gives:
% 222.05/34.47 | (583) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1239_1 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1239_0 &
% 222.05/34.47 | $i(all_1239_0) & $i(all_1239_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.47 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 222.05/34.47 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1239_1, v2) = v3) |
% 222.05/34.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1239_0, v2) | ~
% 222.05/34.47 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) |
% 222.05/34.47 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (583) implies:
% 222.05/34.47 | (584) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1239_0
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (24) with fresh symbols all_1242_0, all_1242_1,
% 222.05/34.47 | all_1242_2, all_1242_3, all_1242_4, all_1242_5 gives:
% 222.05/34.47 | (585) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.47 | all_1242_4 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.05/34.47 | all_1242_3 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3,
% 222.05/34.47 | all_1242_2) = all_1242_1 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.05/34.47 | all_1242_4, all_1242_1) = all_1242_0 &
% 222.05/34.47 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1242_5 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(all_1242_5) = all_1242_2 & $i(all_1242_0)
% 222.05/34.47 | & $i(all_1242_1) & $i(all_1242_2) & $i(all_1242_3) & $i(all_1242_4) &
% 222.05/34.47 | $i(all_1242_5) & c_Rings_Odvd__class_Odvd(all_1242_5, all_1242_0,
% 222.05/34.47 | v_qa____)
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (585) implies:
% 222.05/34.47 | (586) c_Groups_Ozero__class_Ozero(all_1242_5) = all_1242_2
% 222.05/34.47 | (587) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1242_5
% 222.05/34.47 | (588) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1242_1) =
% 222.05/34.47 | all_1242_0
% 222.05/34.47 | (589) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_1242_2) =
% 222.05/34.47 | all_1242_1
% 222.05/34.47 | (590) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1242_3
% 222.05/34.47 | (591) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.47 | all_1242_4
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (115) with fresh symbols all_1244_0, all_1244_1 gives:
% 222.05/34.47 | (592) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1244_1 &
% 222.05/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1244_0 &
% 222.05/34.47 | $i(all_1244_0) & $i(all_1244_1) & ! [v0: $i] : ! [v1: any] : !
% 222.05/34.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 222.05/34.47 | (v1 = all_1244_0 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) |
% 222.05/34.47 | ~ (hAPP(all_1244_1, v2) = v3) | ~ (hAPP(all_1244_1, v0) = v5) | ~
% 222.05/34.47 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.47 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6) |
% 222.05/34.47 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v2, v0))
% 222.05/34.47 |
% 222.05/34.47 | ALPHA: (592) implies:
% 222.05/34.47 | (593) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1244_0
% 222.05/34.47 |
% 222.05/34.47 | DELTA: instantiating (112) with fresh symbols all_1247_0, all_1247_1 gives:
% 222.05/34.48 | (594) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1247_1 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1247_0 &
% 222.05/34.48 | $i(all_1247_0) & $i(all_1247_1) & ! [v0: $i] : ! [v1: any] : !
% 222.05/34.48 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 222.05/34.48 | (v1 = all_1247_0 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) |
% 222.05/34.48 | ~ (hAPP(all_1247_1, v2) = v3) | ~ (hAPP(all_1247_1, v0) = v5) | ~
% 222.05/34.48 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6) |
% 222.05/34.48 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (594) implies:
% 222.05/34.48 | (595) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1247_0
% 222.05/34.48 | (596) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1247_1
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (17) with fresh symbol all_1250_0 gives:
% 222.05/34.48 | (597) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1250_0 &
% 222.05/34.48 | $i(all_1250_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.48 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.05/34.48 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) |
% 222.05/34.48 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1250_0, v0) | ~
% 222.05/34.48 | class_Rings_Olinordered__semidom(v2) | ? [v6: $i] :
% 222.05/34.48 | (c_Groups_Oone__class_Oone(v2) = v6 & $i(v6) & ( ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(v2, v6, v1) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless(v2, v6, v5))))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (597) implies:
% 222.05/34.48 | (598) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1250_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (198) with fresh symbol all_1253_0 gives:
% 222.05/34.48 | (599) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1253_0 &
% 222.05/34.48 | $i(all_1253_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1,
% 222.05/34.48 | all_1253_0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.05/34.48 | v0, all_1253_0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.05/34.48 | all_1253_0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1,
% 222.05/34.48 | all_1253_0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.05/34.48 | all_1253_0, v2) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.05/34.48 | v0, all_1253_0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (599) implies:
% 222.05/34.48 | (600) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1253_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (211) with fresh symbol all_1256_0 gives:
% 222.05/34.48 | (601) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1256_0 &
% 222.05/34.48 | $i(all_1256_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2,
% 222.05/34.48 | all_1256_0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1256_0, v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 222.05/34.48 | all_1256_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 222.05/34.48 | all_1256_0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1256_0, v1) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2,
% 222.05/34.48 | all_1256_0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (601) implies:
% 222.05/34.48 | (602) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1256_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (39) with fresh symbols all_1259_0, all_1259_1 gives:
% 222.05/34.48 | (603) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1259_0 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1259_1 &
% 222.05/34.48 | $i(all_1259_0) & $i(all_1259_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.48 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 222.05/34.48 | (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1259_0,
% 222.05/34.48 | v2) = v3) | ~ (hAPP(all_1259_0, v1) = v5) | ~ $i(v2) | ~
% 222.05/34.48 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.48 | v2, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.48 | all_1259_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4,
% 222.05/34.48 | v6))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (603) implies:
% 222.05/34.48 | (604) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1259_1
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (183) with fresh symbols all_1262_0, all_1262_1 gives:
% 222.05/34.48 | (605) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1262_0 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1262_1 &
% 222.05/34.48 | $i(all_1262_0) & $i(all_1262_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.48 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v4, v0) = v5) | ~
% 222.05/34.48 | (hAPP(v3, v1) = v4) | ~ (hAPP(all_1262_0, v2) = v3) | ~ $i(v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1262_1, v2) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1262_1, v5) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1262_1, v1))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (605) implies:
% 222.05/34.48 | (606) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1262_1
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (192) with fresh symbol all_1265_0 gives:
% 222.05/34.48 | (607) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1265_0 &
% 222.05/34.48 | $i(all_1265_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1265_0, v1) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1265_0, v2) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1265_0, v0)) &
% 222.05/34.48 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1265_0, v1) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1265_0, v0) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1265_0, v2))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (607) implies:
% 222.05/34.48 | (608) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1265_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (174) with fresh symbols all_1268_0, all_1268_1 gives:
% 222.05/34.48 | (609) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1268_1 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1268_0 &
% 222.05/34.48 | $i(all_1268_0) & $i(all_1268_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.48 | $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v2) |
% 222.05/34.48 | ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, all_1268_1, v0) = v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2,
% 222.05/34.48 | all_1268_0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 222.05/34.48 | all_1268_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v0) = v2) | ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, all_1268_1, v0) = v1) |
% 222.05/34.48 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 222.05/34.48 | all_1268_0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2,
% 222.05/34.48 | all_1268_0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (609) implies:
% 222.05/34.48 | (610) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1268_0
% 222.05/34.48 | (611) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1268_1
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (184) with fresh symbols all_1271_0, all_1271_1 gives:
% 222.05/34.48 | (612) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1271_1 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1271_0 &
% 222.05/34.48 | $i(all_1271_0) & $i(all_1271_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.48 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v4, v0) = v5) | ~
% 222.05/34.48 | (hAPP(v3, v1) = v4) | ~ (hAPP(all_1271_1, v2) = v3) | ~ $i(v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v5, all_1271_0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1271_0, v2) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1271_0, v0) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, all_1271_0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (612) implies:
% 222.05/34.48 | (613) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1271_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (209) with fresh symbol all_1274_0 gives:
% 222.05/34.48 | (614) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1274_0 &
% 222.05/34.48 | $i(all_1274_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2,
% 222.05/34.48 | all_1274_0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1,
% 222.05/34.48 | all_1274_0) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1274_0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1,
% 222.05/34.48 | all_1274_0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1274_0, v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2,
% 222.05/34.48 | all_1274_0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (614) implies:
% 222.05/34.48 | (615) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1274_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (193) with fresh symbol all_1280_0 gives:
% 222.05/34.48 | (616) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1280_0 &
% 222.05/34.48 | $i(all_1280_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1280_0, v2) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1280_0, v1) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.05/34.48 | v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.48 | all_1280_0, v1) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v0) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1280_0, v2))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (616) implies:
% 222.05/34.48 | (617) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1280_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (181) with fresh symbols all_1289_0, all_1289_1,
% 222.05/34.48 | all_1289_2 gives:
% 222.05/34.48 | (618) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1289_1 &
% 222.05/34.48 | c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1289_0 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1289_2 &
% 222.05/34.48 | $i(all_1289_0) & $i(all_1289_1) & $i(all_1289_2) & ! [v0: $i] : !
% 222.05/34.48 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v4) = v2) | ~
% 222.05/34.48 | (hAPP(v3, v0) = v4) | ~ (hAPP(all_1289_1, v2) = v3) | ~ $i(v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1289_2, v2) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1289_0, v0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (618) implies:
% 222.05/34.48 | (619) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1289_2
% 222.05/34.48 | (620) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1289_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (182) with fresh symbols all_1309_0, all_1309_1,
% 222.05/34.48 | all_1309_2 gives:
% 222.05/34.48 | (621) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1309_1 &
% 222.05/34.48 | c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1309_0 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1309_2 &
% 222.05/34.48 | $i(all_1309_0) & $i(all_1309_1) & $i(all_1309_2) & ! [v0: $i] : !
% 222.05/34.48 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v1, v4) = v2) | ~
% 222.05/34.48 | (hAPP(v3, v0) = v4) | ~ (hAPP(all_1309_1, v2) = v3) | ~ $i(v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1309_2, v2) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1309_2, v1) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, all_1309_0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (621) implies:
% 222.05/34.48 | (622) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1309_2
% 222.05/34.48 | (623) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1309_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (179) with fresh symbols all_1312_0, all_1312_1 gives:
% 222.05/34.48 | (624) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1312_0 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1312_1 &
% 222.05/34.48 | $i(all_1312_0) & $i(all_1312_1) & ! [v0: $i] : ! [v1: any] : !
% 222.05/34.48 | [v2: $i] : ! [v3: $i] : (v1 = all_1312_1 | ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v0) = v3) | ~
% 222.05/34.48 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1312_0) = v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v4 &
% 222.05/34.48 | c_Nat_OSuc(v3) = v4 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : (v1
% 222.05/34.48 | = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1312_1, v0)
% 222.05/34.48 | = v1) | ~ $i(v0))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (624) implies:
% 222.05/34.48 | (625) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1312_1
% 222.05/34.48 | (626) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1312_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (205) with fresh symbols all_1315_0, all_1315_1 gives:
% 222.05/34.48 | (627) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1315_0 &
% 222.05/34.48 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1315_1 &
% 222.05/34.48 | $i(all_1315_0) & $i(all_1315_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.48 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v4) = v5) | ~
% 222.05/34.48 | (hAPP(v3, v2) = v4) | ~ (hAPP(all_1315_0, v0) = v3) | ~ $i(v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1315_1, v2) | ?
% 222.05/34.48 | [v6: $i] : (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v6, v2) = v5 &
% 222.05/34.48 | c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v6 & $i(v6) &
% 222.05/34.48 | $i(v5)))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (627) implies:
% 222.05/34.48 | (628) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1315_1
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (214) with fresh symbol all_1318_0 gives:
% 222.05/34.48 | (629) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1318_0 &
% 222.05/34.48 | $i(all_1318_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.48 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v2) = v3) |
% 222.05/34.48 | ~ (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v1) = v2) | ~
% 222.05/34.48 | $i(v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.05/34.48 | all_1318_0, v1) | ? [v4: $i] : (c_SMT_Oz3div(v0, v1) = v4 &
% 222.05/34.48 | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, v3) = v4 & $i(v4)))
% 222.05/34.48 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, v1) = v2) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.05/34.48 | all_1318_0, v1) | (c_SMT_Oz3div(v0, v1) = v2 & $i(v2)))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (629) implies:
% 222.05/34.48 | (630) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1318_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (169) with fresh symbol all_1324_0 gives:
% 222.05/34.48 | (631) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1324_0 & $i(all_1324_0)
% 222.05/34.48 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, all_1324_0) = v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0)) & ! [v0: $i] :
% 222.05/34.48 | ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0, all_1324_0) = v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v2)) & ! [v0: $i] :
% 222.05/34.48 | ! [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v0,
% 222.05/34.48 | all_1324_0) = v1) | ~ $i(v0) |
% 222.05/34.48 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (631) implies:
% 222.05/34.48 | (632) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1324_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (154) with fresh symbol all_1348_0 gives:
% 222.05/34.48 | (633) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1348_0 &
% 222.05/34.48 | $i(all_1348_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.48 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Polynomial_Ocoeff(v1, v3)
% 222.05/34.48 | = v4) | ~ (c_Groups_Oone__class_Oone(v2) = v3) | ~
% 222.05/34.48 | (tc_Polynomial_Opoly(v1) = v2) | ~ (hAPP(v4, v0) = v5) | ~ $i(v1)
% 222.05/34.48 | | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | ? [v6: $i] :
% 222.05/34.48 | ? [v7: $i] : (( ~ (v0 = all_1348_0) | (v6 = v5 &
% 222.05/34.48 | c_Groups_Oone__class_Oone(v1) = v5 & $i(v5))) & (v0 =
% 222.05/34.48 | all_1348_0 | (v7 = v5 & c_Groups_Ozero__class_Ozero(v1) = v5 &
% 222.05/34.48 | $i(v5)))))
% 222.05/34.48 |
% 222.05/34.48 | ALPHA: (633) implies:
% 222.05/34.48 | (634) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1348_0
% 222.05/34.48 |
% 222.05/34.48 | DELTA: instantiating (126) with fresh symbol all_1351_0 gives:
% 222.05/34.48 | (635) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1351_0 &
% 222.05/34.48 | $i(all_1351_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.48 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v2) |
% 222.05/34.48 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Ozero(v1) | ? [v3: $i] : ?
% 222.05/34.48 | [v4: $i] : (( ~ (v2 = all_1351_0) | (v4 = v0 &
% 222.05/34.49 | tc_Polynomial_Opoly(v1) = v3 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(v3) = v0 & $i(v3))) & (v2 =
% 222.05/34.49 | all_1351_0 | ( ~ (v4 = v0) & tc_Polynomial_Opoly(v1) = v3 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(v3) = v4 & $i(v4) & $i(v3)))))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (635) implies:
% 222.05/34.49 | (636) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1351_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (10) with fresh symbols all_1354_0, all_1354_1,
% 222.05/34.49 | all_1354_2, all_1354_3, all_1354_4, all_1354_5, all_1354_6, all_1354_7
% 222.05/34.49 | gives:
% 222.05/34.49 | (637) c_Groups_Otimes__class_Otimes(all_1354_7) = all_1354_6 &
% 222.05/34.49 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.49 | all_1354_5 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.05/34.49 | all_1354_4 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1354_4,
% 222.05/34.49 | all_1354_3) = all_1354_2 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.05/34.49 | all_1354_5, all_1354_2) = all_1354_1 &
% 222.05/34.49 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1354_7 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(all_1354_7) = all_1354_3 &
% 222.05/34.49 | hAPP(all_1354_0, v_r____) = v_qa____ & hAPP(all_1354_6, all_1354_1) =
% 222.05/34.49 | all_1354_0 & $i(all_1354_0) & $i(all_1354_1) & $i(all_1354_2) &
% 222.05/34.49 | $i(all_1354_3) & $i(all_1354_4) & $i(all_1354_5) & $i(all_1354_6) &
% 222.05/34.49 | $i(all_1354_7)
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (637) implies:
% 222.05/34.49 | (638) $i(all_1354_5)
% 222.05/34.49 | (639) $i(all_1354_4)
% 222.05/34.49 | (640) $i(all_1354_2)
% 222.05/34.49 | (641) c_Groups_Ozero__class_Ozero(all_1354_7) = all_1354_3
% 222.05/34.49 | (642) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1354_7
% 222.05/34.49 | (643) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1354_5, all_1354_2) =
% 222.05/34.49 | all_1354_1
% 222.05/34.49 | (644) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1354_4, all_1354_3) =
% 222.05/34.49 | all_1354_2
% 222.05/34.49 | (645) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1354_4
% 222.05/34.49 | (646) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.49 | all_1354_5
% 222.05/34.49 | (647) c_Groups_Otimes__class_Otimes(all_1354_7) = all_1354_6
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (30) with fresh symbols all_1356_0, all_1356_1 gives:
% 222.05/34.49 | (648) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1356_1 &
% 222.05/34.49 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1356_0 & $i(all_1356_0)
% 222.05/34.49 | & $i(all_1356_1) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 =
% 222.05/34.49 | all_1356_0 | ~ (hAPP(v2, v0) = all_1356_0) | ~ (hAPP(all_1356_1,
% 222.05/34.49 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i]
% 222.05/34.49 | : ! [v2: $i] : (v0 = all_1356_0 | ~ (hAPP(v2, v0) = all_1356_0) |
% 222.05/34.49 | ~ (hAPP(all_1356_1, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0:
% 222.05/34.49 | $i] : ! [v1: int] : (v1 = all_1356_0 | ~ (hAPP(v0, all_1356_0) =
% 222.05/34.49 | v1) | ~ (hAPP(all_1356_1, all_1356_0) = v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (648) implies:
% 222.05/34.49 | (649) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1356_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (28) with fresh symbols all_1359_0, all_1359_1 gives:
% 222.05/34.49 | (650) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1359_0 &
% 222.05/34.49 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1359_1 & $i(all_1359_0)
% 222.05/34.49 | & $i(all_1359_1) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 =
% 222.05/34.49 | all_1359_1 | ~ (hAPP(v2, v0) = all_1359_1) | ~ (hAPP(all_1359_0,
% 222.05/34.49 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i]
% 222.05/34.49 | : ! [v2: $i] : (v0 = all_1359_1 | ~ (hAPP(v2, v0) = all_1359_1) |
% 222.05/34.49 | ~ (hAPP(all_1359_0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0:
% 222.05/34.49 | $i] : ! [v1: int] : (v1 = all_1359_1 | ~ (hAPP(v0, all_1359_1) =
% 222.05/34.49 | v1) | ~ (hAPP(all_1359_0, all_1359_1) = v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (650) implies:
% 222.05/34.49 | (651) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1359_1
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (109) with fresh symbols all_1362_0, all_1362_1 gives:
% 222.05/34.49 | (652) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1362_1 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1362_0 &
% 222.05/34.49 | $i(all_1362_0) & $i(all_1362_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.49 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3)
% 222.05/34.49 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1362_1, all_1362_0) = v2) |
% 222.05/34.49 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] :
% 222.05/34.49 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1362_0 | v1 = v0 | ~ (hAPP(v3,
% 222.05/34.49 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1362_1, v2) =
% 222.05/34.49 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (652) implies:
% 222.05/34.49 | (653) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1362_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (93) with fresh symbols all_1365_0, all_1365_1,
% 222.05/34.49 | all_1365_2 gives:
% 222.05/34.49 | (654) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1365_1 &
% 222.05/34.49 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1365_0 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1365_2 &
% 222.05/34.49 | $i(all_1365_0) & $i(all_1365_1) & $i(all_1365_2) & ! [v0: any] : !
% 222.05/34.49 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = all_1365_0 | ~
% 222.05/34.49 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1365_1, v0) = v2) | ~ $i(v1) |
% 222.05/34.49 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1365_2, v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3,
% 222.05/34.49 | v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1,
% 222.05/34.49 | v0) = v2) | ~ (hAPP(all_1365_1, all_1365_0) = v1) | ~ $i(v0)
% 222.05/34.49 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1365_2, v0) |
% 222.05/34.49 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (654) implies:
% 222.05/34.49 | (655) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1365_2
% 222.05/34.49 | (656) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1365_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (15) with fresh symbol all_1368_0 gives:
% 222.05/34.49 | (657) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1368_0 &
% 222.05/34.49 | $i(all_1368_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.49 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 222.05/34.49 | [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7,
% 222.05/34.49 | v0) = v8) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v2) = v5) |
% 222.05/34.49 | ~ (hAPP(v4, v1) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 222.05/34.49 | $i(v0) | ~ c_Orderings_Oord__class_Oless(v3, v2, v1) | ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1368_0, v0) | ~
% 222.05/34.49 | class_Rings_Olinordered__semidom(v3) |
% 222.05/34.49 | c_Orderings_Oord__class_Oless(v3, v6, v8) | ? [v9: $i] :
% 222.05/34.49 | (c_Groups_Ozero__class_Ozero(v3) = v9 & $i(v9) & ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless__eq(v3, v9, v2)))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (657) implies:
% 222.05/34.49 | (658) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1368_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (109) with fresh symbols all_1371_0, all_1371_1 gives:
% 222.05/34.49 | (659) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1371_1 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1371_0 &
% 222.05/34.49 | $i(all_1371_0) & $i(all_1371_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.49 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3)
% 222.05/34.49 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1371_1, all_1371_0) = v2) |
% 222.05/34.49 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] :
% 222.05/34.49 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1371_0 | v1 = v0 | ~ (hAPP(v3,
% 222.05/34.49 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1371_1, v2) =
% 222.05/34.49 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (659) implies:
% 222.05/34.49 | (660) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1371_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (33) with fresh symbols all_1374_0, all_1374_1 gives:
% 222.05/34.49 | (661) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1374_1 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1374_0 &
% 222.05/34.49 | $i(all_1374_0) & $i(all_1374_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.49 | int] : (v2 = all_1374_0 | ~ (hAPP(v1, v0) = v2) | ~
% 222.05/34.49 | (hAPP(all_1374_1, all_1374_0) = v1) | ~ $i(v0)) & ! [v0: $i] : !
% 222.05/34.49 | [v1: $i] : ! [v2: int] : (v2 = all_1374_0 | ~ (hAPP(v1, all_1374_0)
% 222.05/34.49 | = v2) | ~ (hAPP(all_1374_1, v0) = v1) | ~ $i(v0)) & ! [v0:
% 222.05/34.49 | any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1374_0 | v0 =
% 222.05/34.49 | all_1374_0 | ~ (hAPP(v2, v0) = all_1374_0) | ~ (hAPP(all_1374_1,
% 222.05/34.49 | v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (661) implies:
% 222.05/34.49 | (662) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1374_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (66) with fresh symbols all_1377_0, all_1377_1 gives:
% 222.05/34.49 | (663) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1377_0 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1377_1 &
% 222.05/34.49 | $i(all_1377_0) & $i(all_1377_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.49 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 222.05/34.49 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 222.05/34.49 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1377_0) = v6) |
% 222.05/34.49 | ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 222.05/34.49 | (c_Power_Opower__class_Opower(v2) = v4) | ~ (hAPP(v8, v0) = v9) |
% 222.05/34.49 | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v3, v7) =
% 222.05/34.49 | v8) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.49 | class_Groups_Omonoid__mult(v2) | ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1377_1, v1) |
% 222.05/34.49 | (hAPP(v5, v1) = v9 & $i(v9)))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (663) implies:
% 222.05/34.49 | (664) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1377_1
% 222.05/34.49 | (665) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1377_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (18) with fresh symbol all_1383_0 gives:
% 222.05/34.49 | (666) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1383_0 &
% 222.05/34.49 | $i(all_1383_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.49 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v2 =
% 222.05/34.49 | v0 | ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7, v1)
% 222.05/34.49 | = v6) | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~
% 222.05/34.49 | (hAPP(v4, v0) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 222.05/34.49 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1383_0, v1) |
% 222.05/34.49 | ~ class_Rings_Olinordered__semidom(v3) | ? [v8: $i] :
% 222.05/34.49 | (c_Groups_Ozero__class_Ozero(v3) = v8 & $i(v8) & ( ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless__eq(v3, v8, v2) | ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless__eq(v3, v8, v0))))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (666) implies:
% 222.05/34.49 | (667) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1383_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (92) with fresh symbols all_1386_0, all_1386_1,
% 222.05/34.49 | all_1386_2 gives:
% 222.05/34.49 | (668) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1386_1 &
% 222.05/34.49 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1386_0 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1386_2 &
% 222.05/34.49 | $i(all_1386_0) & $i(all_1386_1) & $i(all_1386_2) & ! [v0: any] : !
% 222.05/34.49 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = all_1386_0 | ~
% 222.05/34.49 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1386_1, v1) = v2) | ~ $i(v1) |
% 222.05/34.49 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1386_2, v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3,
% 222.05/34.49 | v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1,
% 222.05/34.49 | all_1386_0) = v2) | ~ (hAPP(all_1386_1, v0) = v1) | ~ $i(v0)
% 222.05/34.49 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1386_2, v0) |
% 222.05/34.49 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (668) implies:
% 222.05/34.49 | (669) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1386_2
% 222.05/34.49 | (670) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1386_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (148) with fresh symbols all_1392_0, all_1392_1,
% 222.05/34.49 | all_1392_2 gives:
% 222.05/34.49 | (671) c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, all_1392_1) = all_1392_0
% 222.05/34.49 | & c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1392_1 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1392_2 &
% 222.05/34.49 | $i(all_1392_0) & $i(all_1392_1) & $i(all_1392_2) & ! [v0: any] : !
% 222.05/34.49 | [v1: int] : (v1 = all_1392_0 | v0 = all_1392_2 | ~
% 222.05/34.49 | (c_Groups_Osgn__class_Osgn(tc_Int_Oint, v0) = v1) | ~ $i(v0) |
% 222.05/34.49 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1392_2, v0)) & !
% 222.05/34.49 | [v0: any] : ! [v1: int] : (v1 = all_1392_1 | v0 = all_1392_2 | ~
% 222.05/34.49 | (c_Groups_Osgn__class_Osgn(tc_Int_Oint, v0) = v1) | ~ $i(v0) | ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1392_2, v0)) & !
% 222.05/34.49 | [v0: int] : (v0 = all_1392_2 | ~
% 222.05/34.49 | (c_Groups_Osgn__class_Osgn(tc_Int_Oint, all_1392_2) = v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (671) implies:
% 222.05/34.49 | (672) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1392_2
% 222.05/34.49 | (673) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1392_1
% 222.05/34.49 | (674) c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, all_1392_1) = all_1392_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (165) with fresh symbol all_1398_0 gives:
% 222.05/34.49 | (675) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1398_0 &
% 222.05/34.49 | $i(all_1398_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.49 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)
% 222.05/34.49 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1398_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1398_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1398_0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.49 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)
% 222.05/34.49 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1398_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1398_0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.49 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1)
% 222.05/34.49 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1398_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.49 | all_1398_0, v2))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (675) implies:
% 222.05/34.49 | (676) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1398_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (63) with fresh symbols all_1401_0, all_1401_1,
% 222.05/34.49 | all_1401_2, all_1401_3, all_1401_4, all_1401_5, all_1401_6, all_1401_7,
% 222.05/34.49 | all_1401_8 gives:
% 222.05/34.49 | (677) c_Groups_Otimes__class_Otimes(all_1401_8) = all_1401_7 &
% 222.05/34.49 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.49 | all_1401_6 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.05/34.49 | all_1401_5 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1401_5,
% 222.05/34.49 | all_1401_4) = all_1401_3 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.05/34.49 | all_1401_6, all_1401_3) = all_1401_2 &
% 222.05/34.49 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1401_8 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(all_1401_8) = all_1401_4 &
% 222.05/34.49 | hAPP(all_1401_1, all_1401_0) = v_qa____ & hAPP(all_1401_7,
% 222.05/34.49 | all_1401_2) = all_1401_1 & $i(all_1401_0) & $i(all_1401_1) &
% 222.05/34.49 | $i(all_1401_2) & $i(all_1401_3) & $i(all_1401_4) & $i(all_1401_5) &
% 222.05/34.49 | $i(all_1401_6) & $i(all_1401_7) & $i(all_1401_8)
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (677) implies:
% 222.05/34.49 | (678) c_Groups_Ozero__class_Ozero(all_1401_8) = all_1401_4
% 222.05/34.49 | (679) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1401_8
% 222.05/34.49 | (680) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1401_6, all_1401_3) =
% 222.05/34.49 | all_1401_2
% 222.05/34.49 | (681) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1401_5, all_1401_4) =
% 222.05/34.49 | all_1401_3
% 222.05/34.49 | (682) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1401_5
% 222.05/34.49 | (683) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.49 | all_1401_6
% 222.05/34.49 | (684) c_Groups_Otimes__class_Otimes(all_1401_8) = all_1401_7
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (72) with fresh symbols all_1406_0, all_1406_1,
% 222.05/34.49 | all_1406_2 gives:
% 222.05/34.49 | (685) c_Nat_OSuc(all_1406_1) = all_1406_0 &
% 222.05/34.49 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1406_2 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1406_1 &
% 222.05/34.49 | $i(all_1406_0) & $i(all_1406_1) & $i(all_1406_2) & ! [v0: $i] : !
% 222.05/34.49 | [v1: any] : ! [v2: $i] : (v1 = all_1406_0 | ~ (hAPP(v2, v0) =
% 222.05/34.49 | all_1406_0) | ~ (hAPP(all_1406_2, v1) = v2) | ~ $i(v1) | ~
% 222.05/34.49 | $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 =
% 222.05/34.49 | all_1406_0 | ~ (hAPP(v2, v0) = all_1406_0) | ~ (hAPP(all_1406_2,
% 222.05/34.49 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int]
% 222.05/34.49 | : (v1 = all_1406_0 | ~ (hAPP(v0, all_1406_0) = v1) | ~
% 222.05/34.49 | (hAPP(all_1406_2, all_1406_0) = v0))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (685) implies:
% 222.05/34.49 | (686) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1406_1
% 222.05/34.49 | (687) c_Nat_OSuc(all_1406_1) = all_1406_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (185) with fresh symbols all_1409_0, all_1409_1 gives:
% 222.05/34.49 | (688) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1409_1 &
% 222.05/34.49 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1409_0 &
% 222.05/34.49 | $i(all_1409_0) & $i(all_1409_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.49 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 222.05/34.49 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 222.05/34.49 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v8, v0) = v9) | ~
% 222.05/34.49 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v6, v2) = v7) | ~
% 222.05/34.49 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v1) = v8) | ~ (hAPP(all_1409_1,
% 222.05/34.49 | v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 222.05/34.49 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v4) | ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v4) | ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v7, v9) | ~
% 222.05/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1409_0, v2) |
% 222.05/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v1))
% 222.05/34.49 |
% 222.05/34.49 | ALPHA: (688) implies:
% 222.05/34.49 | (689) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1409_0
% 222.05/34.49 |
% 222.05/34.49 | DELTA: instantiating (187) with fresh symbols all_1412_0, all_1412_1 gives:
% 222.05/34.50 | (690) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1412_1 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1412_0 &
% 222.05/34.50 | $i(all_1412_0) & $i(all_1412_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.50 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 222.05/34.50 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 222.05/34.50 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v8, v0) = v9) | ~
% 222.05/34.50 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v6, v2) = v7) | ~
% 222.05/34.50 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v1) = v8) | ~ (hAPP(all_1412_1,
% 222.05/34.50 | v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 222.05/34.50 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v2) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v4, v0) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v7, v9) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, all_1412_0) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v3))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (690) implies:
% 222.05/34.50 | (691) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1412_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (190) with fresh symbols all_1415_0, all_1415_1,
% 222.05/34.50 | all_1415_2, all_1415_3 gives:
% 222.05/34.50 | (692) c_Nat_OSuc(all_1415_3) = all_1415_0 &
% 222.05/34.50 | c_Power_Opower__class_Opower(tc_Int_Oint) = all_1415_1 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1415_2 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1415_3 &
% 222.05/34.50 | $i(all_1415_0) & $i(all_1415_1) & $i(all_1415_2) & $i(all_1415_3) &
% 222.05/34.50 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 222.05/34.50 | ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1415_0) = v3)
% 222.05/34.50 | | ~ (hAPP(v2, v3) = v4) | ~ (hAPP(all_1415_1, v0) = v2) | ~
% 222.05/34.50 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.50 | all_1415_2, v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.50 | all_1415_3, v1) | ? [v5: $i] :
% 222.05/34.50 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5, v0) = v4 & hAPP(v2,
% 222.05/34.50 | v1) = v5 & $i(v5) & $i(v4)))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (692) implies:
% 222.05/34.50 | (693) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1415_3
% 222.05/34.50 | (694) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1415_2
% 222.05/34.50 | (695) c_Nat_OSuc(all_1415_3) = all_1415_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (82) with fresh symbol all_1421_0 gives:
% 222.05/34.50 | (696) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1421_0 &
% 222.05/34.50 | $i(all_1421_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.50 | $i] : ( ~ (c_Nat_OSuc(v3) = v1) | ~ (c_Nat_OSuc(v0) = v2) | ~
% 222.05/34.50 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)) & ! [v0: $i] :
% 222.05/34.50 | ! [v1: any] : ! [v2: $i] : (v1 = all_1421_0 | ~ (c_Nat_OSuc(v0) =
% 222.05/34.50 | v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v3: $i] :
% 222.05/34.50 | (c_Nat_OSuc(v3) = v1 & $i(v3) &
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))) & ! [v0:
% 222.05/34.50 | $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1421_0, v1))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (696) implies:
% 222.05/34.50 | (697) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1421_0
% 222.05/34.50 | (698) ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = all_1421_0 | ~
% 222.05/34.50 | (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v3: $i] :
% 222.05/34.50 | (c_Nat_OSuc(v3) = v1 & $i(v3) &
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0)))
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (32) with fresh symbols all_1427_0, all_1427_1 gives:
% 222.05/34.50 | (699) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1427_1 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1427_0 &
% 222.05/34.50 | $i(all_1427_0) & $i(all_1427_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.50 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~
% 222.05/34.50 | (hAPP(v4, all_1427_0) = v5) | ~ (hAPP(v2, all_1427_0) = v3) | ~
% 222.05/34.50 | (hAPP(all_1427_1, v1) = v2) | ~ (hAPP(all_1427_1, v0) = v4) | ~
% 222.05/34.50 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : !
% 222.05/34.50 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | v1 = all_1427_0 |
% 222.05/34.50 | ~ (hAPP(v5, v1) = v4) | ~ (hAPP(v3, v1) = v4) | ~
% 222.05/34.50 | (hAPP(all_1427_1, v2) = v3) | ~ (hAPP(all_1427_1, v0) = v5) | ~
% 222.05/34.50 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (699) implies:
% 222.05/34.50 | (700) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1427_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (73) with fresh symbols all_1430_0, all_1430_1,
% 222.05/34.50 | all_1430_2 gives:
% 222.05/34.50 | (701) c_Nat_OSuc(all_1430_1) = all_1430_0 &
% 222.05/34.50 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1430_2 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1430_1 &
% 222.05/34.50 | $i(all_1430_0) & $i(all_1430_1) & $i(all_1430_2) & ! [v0: $i] : !
% 222.05/34.50 | [v1: $i] : ! [v2: int] : (v2 = all_1430_0 | ~ (hAPP(v1, v0) = v2) |
% 222.05/34.50 | ~ (hAPP(all_1430_2, all_1430_0) = v1) | ~ $i(v0)) & ! [v0: $i] :
% 222.05/34.50 | ! [v1: $i] : ! [v2: int] : (v2 = all_1430_0 | ~ (hAPP(v1,
% 222.05/34.50 | all_1430_1) = v2) | ~ (hAPP(all_1430_2, v0) = v1) | ~ $i(v0))
% 222.05/34.50 | & ! [v0: any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1430_0 | v0 =
% 222.05/34.50 | all_1430_1 | ~ (hAPP(v2, v0) = all_1430_0) | ~ (hAPP(all_1430_2,
% 222.05/34.50 | v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (701) implies:
% 222.05/34.50 | (702) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1430_1
% 222.05/34.50 | (703) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1430_2
% 222.05/34.50 | (704) c_Nat_OSuc(all_1430_1) = all_1430_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (55) with fresh symbol all_1433_0 gives:
% 222.05/34.50 | (705) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1433_0 &
% 222.05/34.50 | $i(all_1433_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.50 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.05/34.50 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) |
% 222.05/34.50 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | class_Rings_Ozero__neq__one(v2) | ~
% 222.05/34.50 | class_Rings_Ono__zero__divisors(v2) | ~
% 222.05/34.50 | class_Rings_Omult__zero(v2) | ~ class_Power_Opower(v2) | ? [v6:
% 222.05/34.50 | $i] : (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 =
% 222.05/34.50 | v5) | (v5 = v1 & ~ (v0 = all_1433_0))) & ( ~ (v6 = v1) | v5
% 222.05/34.50 | = v1 | v0 = all_1433_0)))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (705) implies:
% 222.05/34.50 | (706) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1433_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (120) with fresh symbol all_1442_0 gives:
% 222.05/34.50 | (707) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1442_0 &
% 222.05/34.50 | $i(all_1442_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.50 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v2) |
% 222.05/34.50 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Ozero(v1) | ? [v3: $i] : ?
% 222.05/34.50 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v2 = all_1442_0 | ( ~ (v4
% 222.05/34.50 | = v0) & tc_Polynomial_Opoly(v1) = v3 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(v3) = v4 & $i(v4) & $i(v3))) &
% 222.05/34.50 | ((v6 = v2 & c_Nat_OSuc(v5) = v2 & c_Polynomial_Odegree(v1, v0) =
% 222.05/34.50 | v5 & $i(v5) & $i(v2)) | (v4 = v0 & tc_Polynomial_Opoly(v1) =
% 222.05/34.50 | v3 & c_Groups_Ozero__class_Ozero(v3) = v0 & $i(v3)))))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (707) implies:
% 222.05/34.50 | (708) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1442_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (194) with fresh symbol all_1445_0 gives:
% 222.05/34.50 | (709) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1445_0 &
% 222.05/34.50 | $i(all_1445_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.50 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 222.05/34.50 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.50 | all_1445_0, v2) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1445_0, v1) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1445_0, v0)) & !
% 222.05/34.50 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.50 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 222.05/34.50 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.50 | all_1445_0, v2) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1445_0, v1) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1)) & ! [v0:
% 222.05/34.50 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 222.05/34.50 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 222.05/34.50 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.50 | all_1445_0, v0) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v1) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1445_0, v1) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1445_0, v2))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (709) implies:
% 222.05/34.50 | (710) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1445_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (180) with fresh symbols all_1448_0, all_1448_1,
% 222.05/34.50 | all_1448_2 gives:
% 222.05/34.50 | (711) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1448_1 &
% 222.05/34.50 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1448_0 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1448_2 &
% 222.05/34.50 | $i(all_1448_0) & $i(all_1448_1) & $i(all_1448_2) & ! [v0: $i] : !
% 222.05/34.50 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 222.05/34.50 | (v1 = all_1448_2 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0,
% 222.05/34.50 | v4) = v5) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1,
% 222.05/34.50 | all_1448_0) = v2) | ~ (hAPP(v3, v0) = v4) | ~
% 222.05/34.50 | (hAPP(all_1448_1, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] :
% 222.05/34.50 | (hAPP(v6, v0) = v5 & hAPP(all_1448_1, v1) = v6 & $i(v6) & $i(v5)))
% 222.05/34.50 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_1448_2 | ~
% 222.05/34.50 | (hAPP(v1, v0) = v2) | ~ (hAPP(all_1448_1, all_1448_2) = v1) | ~
% 222.05/34.50 | $i(v0))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (711) implies:
% 222.05/34.50 | (712) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1448_2
% 222.05/34.50 | (713) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1448_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (103) with fresh symbols all_1451_0, all_1451_1 gives:
% 222.05/34.50 | (714) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1451_0 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1451_1 &
% 222.05/34.50 | $i(all_1451_0) & $i(all_1451_1) & ! [v0: any] : ! [v1: $i] : !
% 222.05/34.50 | [v2: $i] : ! [v3: $i] : (v0 = all_1451_1 | ~ (hAPP(v2, v0) = v3) |
% 222.05/34.50 | ~ (hAPP(all_1451_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1451_1, v3) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1451_1, v1)) & !
% 222.05/34.50 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2,
% 222.05/34.50 | v0) = v3) | ~ (hAPP(all_1451_0, v1) = v2) | ~ $i(v1) | ~
% 222.05/34.50 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1451_1,
% 222.05/34.50 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1451_1, v3))
% 222.05/34.50 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1451_1)
% 222.05/34.50 | = v2) | ~ (hAPP(all_1451_0, v0) = v1) | ~ $i(v0) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1451_1, v2))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (714) implies:
% 222.05/34.50 | (715) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1451_1
% 222.05/34.50 | (716) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1451_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (61) with fresh symbol all_1454_0 gives:
% 222.05/34.50 | (717) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1454_0 &
% 222.05/34.50 | $i(all_1454_0) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.50 | $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | v0 = all_1454_0 | ~
% 222.05/34.50 | (c_Power_Opower__class_Opower(v1) = v2) | ~
% 222.05/34.50 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) |
% 222.05/34.50 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | class_Rings_Osemiring__0(v1) | ~ class_Power_Opower(v1)) & ! [v0:
% 222.05/34.50 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 222.05/34.50 | (c_Power_Opower__class_Opower(v0) = v1) | ~
% 222.05/34.50 | (c_Groups_Ozero__class_Ozero(v0) = v2) | ~ (hAPP(v3, all_1454_0) =
% 222.05/34.50 | v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v0) | ~
% 222.05/34.50 | class_Rings_Osemiring__0(v0) | ~ class_Power_Opower(v0) |
% 222.05/34.50 | (c_Groups_Oone__class_Oone(v0) = v4 & $i(v4)))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (717) implies:
% 222.05/34.50 | (718) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1454_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (14) with fresh symbols all_1457_0, all_1457_1,
% 222.05/34.50 | all_1457_2, all_1457_3, all_1457_4, all_1457_5, all_1457_6, all_1457_7,
% 222.05/34.50 | all_1457_8, all_1457_9 gives:
% 222.05/34.50 | (719) c_Power_Opower__class_Opower(all_1457_9) = all_1457_8 &
% 222.05/34.50 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.50 | all_1457_7 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.05/34.50 | all_1457_6 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1457_6,
% 222.05/34.50 | all_1457_5) = all_1457_4 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.05/34.50 | all_1457_7, all_1457_4) = all_1457_3 &
% 222.05/34.50 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.05/34.50 | all_1457_1 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1457_9 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(all_1457_9) = all_1457_5 &
% 222.05/34.50 | hAPP(all_1457_2, all_1457_1) = all_1457_0 & hAPP(all_1457_8,
% 222.05/34.50 | all_1457_3) = all_1457_2 & $i(all_1457_0) & $i(all_1457_1) &
% 222.05/34.50 | $i(all_1457_2) & $i(all_1457_3) & $i(all_1457_4) & $i(all_1457_5) &
% 222.05/34.50 | $i(all_1457_6) & $i(all_1457_7) & $i(all_1457_8) & $i(all_1457_9) &
% 222.05/34.50 | c_Rings_Odvd__class_Odvd(all_1457_9, all_1457_0, v_pa____)
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (719) implies:
% 222.05/34.50 | (720) hAPP(all_1457_8, all_1457_3) = all_1457_2
% 222.05/34.50 | (721) hAPP(all_1457_2, all_1457_1) = all_1457_0
% 222.05/34.50 | (722) c_Groups_Ozero__class_Ozero(all_1457_9) = all_1457_5
% 222.05/34.50 | (723) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1457_9
% 222.05/34.50 | (724) c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.05/34.50 | all_1457_1
% 222.05/34.50 | (725) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1457_7, all_1457_4) =
% 222.05/34.50 | all_1457_3
% 222.05/34.50 | (726) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1457_6, all_1457_5) =
% 222.05/34.50 | all_1457_4
% 222.05/34.50 | (727) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1457_6
% 222.05/34.50 | (728) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.50 | all_1457_7
% 222.05/34.50 | (729) c_Power_Opower__class_Opower(all_1457_9) = all_1457_8
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (151) with fresh symbol all_1459_0 gives:
% 222.05/34.50 | (730) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1459_0 &
% 222.05/34.50 | $i(all_1459_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.50 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 222.05/34.50 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0) = v5) | ~
% 222.05/34.50 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v5) = v6) |
% 222.05/34.50 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | class_Rings_Ozero__neq__one(v2) | ~
% 222.05/34.50 | class_Rings_Ono__zero__divisors(v2) | ~
% 222.05/34.50 | class_Rings_Omult__zero(v2) | ~ class_Power_Opower(v2) | ? [v7:
% 222.05/34.50 | $i] : (c_Groups_Ozero__class_Ozero(v2) = v7 & $i(v7) & ( ~ (v7 =
% 222.05/34.50 | v6) | (v6 = v1 & ~ (v5 = all_1459_0))) & ( ~ (v7 = v1) | v6
% 222.05/34.50 | = v1 | v5 = all_1459_0)))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (730) implies:
% 222.05/34.50 | (731) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1459_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (103) with fresh symbols all_1462_0, all_1462_1 gives:
% 222.05/34.50 | (732) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1462_0 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1462_1 &
% 222.05/34.50 | $i(all_1462_0) & $i(all_1462_1) & ! [v0: any] : ! [v1: $i] : !
% 222.05/34.50 | [v2: $i] : ! [v3: $i] : (v0 = all_1462_1 | ~ (hAPP(v2, v0) = v3) |
% 222.05/34.50 | ~ (hAPP(all_1462_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1462_1, v3) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1462_1, v1)) & !
% 222.05/34.50 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2,
% 222.05/34.50 | v0) = v3) | ~ (hAPP(all_1462_0, v1) = v2) | ~ $i(v1) | ~
% 222.05/34.50 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1462_1,
% 222.05/34.50 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1462_1, v3))
% 222.05/34.50 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1462_1)
% 222.05/34.50 | = v2) | ~ (hAPP(all_1462_0, v0) = v1) | ~ $i(v0) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1462_1, v2))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (732) implies:
% 222.05/34.50 | (733) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1462_1
% 222.05/34.50 | (734) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1462_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (186) with fresh symbols all_1465_0, all_1465_1 gives:
% 222.05/34.50 | (735) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1465_1 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1465_0 &
% 222.05/34.50 | $i(all_1465_0) & $i(all_1465_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.50 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 222.05/34.50 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 222.05/34.50 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v0) = v8) | ~
% 222.05/34.50 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v3) = v8) | ~
% 222.05/34.50 | (hAPP(v9, v1) = v10) | ~ (hAPP(v6, v4) = v7) | ~
% 222.05/34.50 | (hAPP(all_1465_1, v5) = v6) | ~ (hAPP(all_1465_1, v2) = v9) | ~
% 222.05/34.50 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 222.05/34.50 | | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1465_0, v2) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v5) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1465_0, v8) | ~
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1465_0, v3) |
% 222.05/34.50 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v1))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (735) implies:
% 222.05/34.50 | (736) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1465_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (147) with fresh symbol all_1468_0 gives:
% 222.05/34.50 | (737) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1468_0 &
% 222.05/34.50 | $i(all_1468_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.50 | $i] : ( ~ (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3) | ~
% 222.05/34.50 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.50 | class_Rings_Ocomm__semiring__0(v2) | ? [v4: $i] : ? [v5: $i] : ?
% 222.05/34.50 | [v6: any] : (((v6 = all_1468_0 & c_Polynomial_Odegree(v2, v1) =
% 222.05/34.50 | all_1468_0) | ( ~ (v5 = v3) & tc_Polynomial_Opoly(v2) = v4 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))) &
% 222.05/34.50 | ((v5 = v3 & tc_Polynomial_Opoly(v2) = v4 &
% 222.05/34.50 | c_Groups_Ozero__class_Ozero(v4) = v3 & $i(v4) & $i(v3)) | ( ~
% 222.05/34.50 | (v6 = all_1468_0) & c_Polynomial_Odegree(v2, v1) = v6 &
% 222.05/34.50 | $i(v6)))))
% 222.05/34.50 |
% 222.05/34.50 | ALPHA: (737) implies:
% 222.05/34.50 | (738) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1468_0
% 222.05/34.50 |
% 222.05/34.50 | DELTA: instantiating (105) with fresh symbols all_1471_0, all_1471_1 gives:
% 222.05/34.51 | (739) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1471_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1471_1 &
% 222.05/34.51 | $i(all_1471_0) & $i(all_1471_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 222.05/34.51 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1471_0, v2) = v3) |
% 222.05/34.51 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1471_1, v2) | ~
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : !
% 222.05/34.51 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 222.05/34.51 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.51 | (hAPP(all_1471_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.51 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1471_1, v2) | ~
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (739) implies:
% 222.05/34.51 | (740) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1471_1
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (138) with fresh symbols all_1474_0, all_1474_1 gives:
% 222.05/34.51 | (741) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1474_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1474_1 &
% 222.05/34.51 | $i(all_1474_0) & $i(all_1474_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1474_1 |
% 222.05/34.51 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.51 | (hAPP(all_1474_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.51 | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v5) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0)) & ! [v0: $i] : !
% 222.05/34.51 | [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 222.05/34.51 | (v2 = all_1474_1 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) |
% 222.05/34.51 | ~ (hAPP(all_1474_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.51 | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v5))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (741) implies:
% 222.05/34.51 | (742) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1474_1
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (100) with fresh symbols all_1477_0, all_1477_1,
% 222.05/34.51 | all_1477_2, all_1477_3 gives:
% 222.05/34.51 | (743) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1477_0 &
% 222.05/34.51 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1477_2 &
% 222.05/34.51 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1477_1 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1477_3 &
% 222.05/34.51 | $i(all_1477_0) & $i(all_1477_1) & $i(all_1477_2) & $i(all_1477_3) &
% 222.05/34.51 | ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 222.05/34.51 | ! [v5: $i] : ! [v6: $i] : (v1 = all_1477_3 | ~
% 222.05/34.51 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1477_1) = v4) |
% 222.05/34.51 | ~ (hAPP(v3, v5) = v6) | ~ (hAPP(v2, v4) = v5) | ~
% 222.05/34.51 | (hAPP(all_1477_0, v0) = v3) | ~ (hAPP(all_1477_2, v0) = v2) | ~
% 222.05/34.51 | $i(v1) | ~ $i(v0) | (hAPP(v2, v1) = v6 & $i(v6))) & ! [v0: $i] :
% 222.05/34.51 | ! [v1: $i] : ! [v2: int] : (v2 = all_1477_1 | ~ (hAPP(v1,
% 222.05/34.51 | all_1477_3) = v2) | ~ (hAPP(all_1477_2, v0) = v1) | ~ $i(v0))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (743) implies:
% 222.05/34.51 | (744) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1477_3
% 222.05/34.51 | (745) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1477_1
% 222.05/34.51 | (746) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1477_2
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (102) with fresh symbols all_1480_0, all_1480_1 gives:
% 222.05/34.51 | (747) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1480_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1480_1 &
% 222.05/34.51 | $i(all_1480_0) & $i(all_1480_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 222.05/34.51 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1480_0, v2) = v3) |
% 222.05/34.51 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1480_1, v2) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) |
% 222.05/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0:
% 222.05/34.51 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.05/34.51 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.51 | (hAPP(all_1480_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.51 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1480_1, v2) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) |
% 222.05/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (747) implies:
% 222.05/34.51 | (748) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1480_1
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (45) with fresh symbol all_1483_0 gives:
% 222.05/34.51 | (749) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1483_0 &
% 222.05/34.51 | $i(all_1483_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.51 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.05/34.51 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v1) = v5) |
% 222.05/34.51 | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | class_Rings_Ocomm__semiring__1(v2) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1483_0, v1) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(v2, v0, v5)) & ! [v0: $i] : ! [v1: $i] :
% 222.05/34.51 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.05/34.51 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v1) = v5) |
% 222.05/34.51 | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | class_Rings_Ocomm__semiring__1(v2) | c_Rings_Odvd__class_Odvd(v2,
% 222.05/34.51 | v0, v5) | ? [v6: $i] : ( ~ (v6 = v0) &
% 222.05/34.51 | c_Groups_Oone__class_Oone(v2) = v6 & $i(v6)))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (749) implies:
% 222.05/34.51 | (750) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1483_0
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (134) with fresh symbols all_1486_0, all_1486_1,
% 222.05/34.51 | all_1486_2 gives:
% 222.05/34.51 | (751) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1486_1 &
% 222.05/34.51 | c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1486_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1486_2 &
% 222.05/34.51 | $i(all_1486_0) & $i(all_1486_1) & $i(all_1486_2) & ! [v0: $i] : !
% 222.05/34.51 | [v1: any] : ! [v2: $i] : (v1 = all_1486_0 | ~ (hAPP(v2, v0) =
% 222.05/34.51 | all_1486_0) | ~ (hAPP(all_1486_1, v1) = v2) | ~ $i(v1) | ~
% 222.05/34.51 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1486_2,
% 222.05/34.51 | v1)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 =
% 222.05/34.51 | all_1486_0 | ~ (hAPP(v2, v0) = all_1486_0) | ~ (hAPP(all_1486_1,
% 222.05/34.51 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1486_2, v1)) & !
% 222.05/34.51 | [v0: $i] : ! [v1: int] : (v1 = all_1486_0 | ~ (hAPP(v0, all_1486_0)
% 222.05/34.51 | = v1) | ~ (hAPP(all_1486_1, all_1486_0) = v0) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1486_2, all_1486_0))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (751) implies:
% 222.05/34.51 | (752) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1486_2
% 222.05/34.51 | (753) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1486_0
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (107) with fresh symbols all_1489_0, all_1489_1 gives:
% 222.05/34.51 | (754) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1489_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1489_1 &
% 222.05/34.51 | $i(all_1489_0) & $i(all_1489_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 222.05/34.51 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1489_0, v2) = v3) |
% 222.05/34.51 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1489_1, v2) |
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] :
% 222.05/34.51 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 222.05/34.51 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.51 | (hAPP(all_1489_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.51 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1489_1, v2) |
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (754) implies:
% 222.05/34.51 | (755) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1489_1
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (188) with fresh symbols all_1492_0, all_1492_1 gives:
% 222.05/34.51 | (756) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1492_1 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1492_0 &
% 222.05/34.51 | $i(all_1492_0) & $i(all_1492_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 222.05/34.51 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 222.05/34.51 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v10, v0) = v8) | ~
% 222.05/34.51 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v7, v3) = v8) | ~
% 222.05/34.51 | (hAPP(v9, v1) = v10) | ~ (hAPP(v6, v4) = v7) | ~
% 222.05/34.51 | (hAPP(all_1492_1, v5) = v6) | ~ (hAPP(all_1492_1, v2) = v9) | ~
% 222.05/34.51 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 222.05/34.51 | | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v8, all_1492_0) |
% 222.05/34.51 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v3, v5) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1492_0, v2) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v2, v5) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1492_0, v0) |
% 222.05/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1, v4))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (756) implies:
% 222.05/34.51 | (757) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1492_0
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (64) with fresh symbols all_1495_0, all_1495_1,
% 222.05/34.51 | all_1495_2, all_1495_3, all_1495_4, all_1495_5, all_1495_6, all_1495_7,
% 222.05/34.51 | all_1495_8, all_1495_9, all_1495_10 gives:
% 222.05/34.51 | (758) c_Nat_OSuc(all_1495_2) = all_1495_1 &
% 222.05/34.51 | c_Power_Opower__class_Opower(all_1495_10) = all_1495_9 &
% 222.05/34.51 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.51 | all_1495_8 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.05/34.51 | all_1495_7 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1495_7,
% 222.05/34.51 | all_1495_6) = all_1495_5 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.05/34.51 | all_1495_8, all_1495_5) = all_1495_4 &
% 222.05/34.51 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.05/34.51 | all_1495_2 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1495_10 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(all_1495_10) = all_1495_6 &
% 222.05/34.51 | hAPP(all_1495_3, all_1495_1) = all_1495_0 & hAPP(all_1495_9,
% 222.05/34.51 | all_1495_4) = all_1495_3 & $i(all_1495_0) & $i(all_1495_1) &
% 222.05/34.51 | $i(all_1495_2) & $i(all_1495_3) & $i(all_1495_4) & $i(all_1495_5) &
% 222.05/34.51 | $i(all_1495_6) & $i(all_1495_7) & $i(all_1495_8) & $i(all_1495_9) &
% 222.05/34.51 | $i(all_1495_10) & ~ c_Rings_Odvd__class_Odvd(all_1495_10,
% 222.05/34.51 | all_1495_0, v_pa____)
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (758) implies:
% 222.05/34.51 | (759) hAPP(all_1495_9, all_1495_4) = all_1495_3
% 222.05/34.51 | (760) c_Groups_Ozero__class_Ozero(all_1495_10) = all_1495_6
% 222.05/34.51 | (761) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1495_10
% 222.05/34.51 | (762) c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.05/34.51 | all_1495_2
% 222.05/34.51 | (763) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1495_8, all_1495_5) =
% 222.05/34.51 | all_1495_4
% 222.05/34.51 | (764) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1495_7, all_1495_6) =
% 222.05/34.51 | all_1495_5
% 222.05/34.51 | (765) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1495_7
% 222.05/34.51 | (766) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.51 | all_1495_8
% 222.05/34.51 | (767) c_Power_Opower__class_Opower(all_1495_10) = all_1495_9
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (90) with fresh symbol all_1497_0 gives:
% 222.05/34.51 | (768) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1497_0 &
% 222.05/34.51 | $i(all_1497_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.51 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Odegree(v2, v3) = v4) | ~
% 222.05/34.51 | (c_Polynomial_OpCons(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 222.05/34.51 | $i(v0) | ~ class_Groups_Ozero(v2) | ? [v5: $i] : ? [v6: $i] : ?
% 222.05/34.51 | [v7: $i] : ? [v8: $i] : ((v4 = all_1497_0 | ( ~ (v6 = v1) &
% 222.05/34.51 | tc_Polynomial_Opoly(v2) = v5 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) &
% 222.05/34.51 | ((v8 = v4 & c_Nat_OSuc(v7) = v4 & c_Polynomial_Odegree(v2, v1) =
% 222.05/34.51 | v7 & $i(v7) & $i(v4)) | (v6 = v1 & tc_Polynomial_Opoly(v2) =
% 222.05/34.51 | v5 & c_Groups_Ozero__class_Ozero(v5) = v1 & $i(v5)))))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (768) implies:
% 222.05/34.51 | (769) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1497_0
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (42) with fresh symbols all_1500_0, all_1500_1 gives:
% 222.05/34.51 | (770) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1500_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1500_1 &
% 222.05/34.51 | $i(all_1500_0) & $i(all_1500_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1500_0,
% 222.05/34.51 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1500_1, v3) |
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1500_1, v1)) & !
% 222.05/34.51 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2,
% 222.05/34.51 | v0) = v3) | ~ (hAPP(all_1500_0, v1) = v2) | ~ $i(v1) | ~
% 222.05/34.51 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1500_1,
% 222.05/34.51 | v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1500_1, v0))
% 222.05/34.51 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 222.05/34.51 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1500_0, v1) = v2) | ~ $i(v1) |
% 222.05/34.51 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.51 | all_1500_1, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.51 | all_1500_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.51 | all_1500_1, v3))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (770) implies:
% 222.05/34.51 | (771) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1500_1
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (16) with fresh symbols all_1503_0, all_1503_1 gives:
% 222.05/34.51 | (772) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1503_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1503_1 &
% 222.05/34.51 | $i(all_1503_0) & $i(all_1503_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 222.05/34.51 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 222.05/34.51 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1503_0) = v7) |
% 222.05/34.51 | ~ (c_Groups_Otimes__class_Otimes(v2) = v5) | ~
% 222.05/34.51 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v6, v8) = v9) |
% 222.05/34.51 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v7) = v8) | ~ (hAPP(v3, v0) =
% 222.05/34.51 | v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | class_Power_Opower(v2) | ? [v10: $i] : ? [v11: $i] : (( ~ (v1 =
% 222.05/34.51 | all_1503_1) | (v11 = v10 & c_Groups_Oone__class_Oone(v2) =
% 222.05/34.51 | v10 & hAPP(v4, all_1503_1) = v10 & $i(v10))) & (v1 =
% 222.05/34.51 | all_1503_1 | (v10 = v9 & hAPP(v4, v1) = v9 & $i(v9)))))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (772) implies:
% 222.05/34.51 | (773) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1503_1
% 222.05/34.51 | (774) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1503_0
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (111) with fresh symbols all_1506_0, all_1506_1 gives:
% 222.05/34.51 | (775) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1506_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1506_1 &
% 222.05/34.51 | $i(all_1506_0) & $i(all_1506_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2
% 222.05/34.51 | = all_1506_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~
% 222.05/34.51 | (hAPP(all_1506_0, v1) = v3) | ~ (hAPP(all_1506_0, v0) = v5) | ~
% 222.05/34.51 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : !
% 222.05/34.51 | [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 222.05/34.51 | ! [v6: $i] : (v2 = all_1506_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3,
% 222.05/34.51 | v2) = v4) | ~ (hAPP(all_1506_0, v1) = v3) | ~
% 222.05/34.51 | (hAPP(all_1506_0, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.51 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (775) implies:
% 222.05/34.51 | (776) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1506_1
% 222.05/34.51 | (777) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1506_0
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (153) with fresh symbol all_1509_0 gives:
% 222.05/34.51 | (778) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1509_0 &
% 222.05/34.51 | $i(all_1509_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ! [v3:
% 222.05/34.51 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v4 | v2 =
% 222.05/34.51 | all_1509_0 | ~ (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0)
% 222.05/34.51 | = v2) | ~ (c_Power_Opower__class_Opower(v1) = v3) | ~
% 222.05/34.51 | (c_Groups_Ozero__class_Ozero(v1) = v4) | ~ (hAPP(v5, v2) = v6) |
% 222.05/34.51 | ~ (hAPP(v3, v4) = v5) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | class_Rings_Osemiring__0(v1) | ~ class_Power_Opower(v1)) & ! [v0:
% 222.05/34.51 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.05/34.51 | [v5: $i] : ( ~ (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0) =
% 222.05/34.51 | all_1509_0) | ~ (c_Power_Opower__class_Opower(v1) = v2) | ~
% 222.05/34.51 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, all_1509_0) =
% 222.05/34.51 | v5) | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | class_Rings_Osemiring__0(v1) | ~ class_Power_Opower(v1) |
% 222.05/34.51 | (c_Groups_Oone__class_Oone(v1) = v5 & $i(v5)))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (778) implies:
% 222.05/34.51 | (779) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1509_0
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (116) with fresh symbols all_1512_0, all_1512_1 gives:
% 222.05/34.51 | (780) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1512_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1512_1 &
% 222.05/34.51 | $i(all_1512_0) & $i(all_1512_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2
% 222.05/34.51 | = all_1512_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~
% 222.05/34.51 | (hAPP(all_1512_0, v1) = v3) | ~ (hAPP(all_1512_0, v0) = v5) | ~
% 222.05/34.51 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0)) & ! [v0: $i] : !
% 222.05/34.51 | [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 222.05/34.51 | ! [v6: $i] : (v2 = all_1512_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3,
% 222.05/34.51 | v2) = v4) | ~ (hAPP(all_1512_0, v1) = v3) | ~
% 222.05/34.51 | (hAPP(all_1512_0, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.51 | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0) |
% 222.05/34.51 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (780) implies:
% 222.05/34.51 | (781) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1512_1
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (152) with fresh symbols all_1521_0, all_1521_1 gives:
% 222.05/34.51 | (782) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1521_0 &
% 222.05/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1521_1 &
% 222.05/34.51 | $i(all_1521_0) & $i(all_1521_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.51 | $i] : ! [v3: any] : ! [v4: $i] : (v3 = all_1521_1 | ~
% 222.05/34.51 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0) = v3) | ~
% 222.05/34.51 | (hAPP(v2, v3) = v4) | ~ (hAPP(all_1521_0, v1) = v2) | ~ $i(v1) |
% 222.05/34.51 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.51 | all_1521_1, v4) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.51 | all_1521_1, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 222.05/34.51 | [v3: $i] : ! [v4: $i] : ( ~
% 222.05/34.51 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0) = v2) | ~
% 222.05/34.51 | (hAPP(v3, v2) = v4) | ~ (hAPP(all_1521_0, v1) = v3) | ~ $i(v1) |
% 222.05/34.51 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.51 | all_1521_1, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.51 | all_1521_1, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 222.05/34.51 | [v3: $i] : ( ~ (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0) =
% 222.05/34.51 | all_1521_1) | ~ (hAPP(v2, all_1521_1) = v3) | ~
% 222.05/34.51 | (hAPP(all_1521_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1521_1, v3))
% 222.05/34.51 |
% 222.05/34.51 | ALPHA: (782) implies:
% 222.05/34.51 | (783) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1521_1
% 222.05/34.51 | (784) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1521_0
% 222.05/34.51 |
% 222.05/34.51 | DELTA: instantiating (86) with fresh symbols all_1524_0, all_1524_1,
% 222.05/34.51 | all_1524_2 gives:
% 222.05/34.51 | (785) c_Nat_OSuc(all_1524_2) = all_1524_1 &
% 222.05/34.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1524_0 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1524_2 &
% 222.05/34.52 | $i(all_1524_0) & $i(all_1524_1) & $i(all_1524_2) & ! [v0: $i] : !
% 222.05/34.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~
% 222.05/34.52 | (hAPP(all_1524_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.52 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1524_1, v3) |
% 222.05/34.52 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1524_1, v1)) &
% 222.05/34.52 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2,
% 222.05/34.52 | v0) = v3) | ~ (hAPP(all_1524_0, v1) = v2) | ~ $i(v1) | ~
% 222.05/34.52 | $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 222.05/34.52 | all_1524_1, v3) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 222.05/34.52 | all_1524_1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 222.05/34.52 | [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1524_0, v1) = v2) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.52 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1524_1, v1) | ~
% 222.05/34.52 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1524_1, v0) |
% 222.05/34.52 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1524_1, v3))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (785) implies:
% 222.05/34.52 | (786) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1524_2
% 222.05/34.52 | (787) c_Nat_OSuc(all_1524_2) = all_1524_1
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (9) with fresh symbols all_1527_0, all_1527_1,
% 222.05/34.52 | all_1527_2, all_1527_3, all_1527_4, all_1527_5, all_1527_6, all_1527_7,
% 222.05/34.52 | all_1527_8, all_1527_9, all_1527_10, all_1527_11 gives:
% 222.05/34.52 | (788) c_Groups_Otimes__class_Otimes(all_1527_11) = all_1527_10 &
% 222.05/34.52 | c_Power_Opower__class_Opower(all_1527_11) = all_1527_9 &
% 222.05/34.52 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.52 | all_1527_8 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.05/34.52 | all_1527_7 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1527_7,
% 222.05/34.52 | all_1527_6) = all_1527_5 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.05/34.52 | all_1527_8, all_1527_5) = all_1527_4 &
% 222.05/34.52 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.05/34.52 | all_1527_2 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1527_11 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(all_1527_11) = all_1527_6 &
% 222.05/34.52 | hAPP(all_1527_0, v_s____) = v_pa____ & hAPP(all_1527_3, all_1527_2) =
% 222.05/34.52 | all_1527_1 & hAPP(all_1527_9, all_1527_4) = all_1527_3 &
% 222.05/34.52 | hAPP(all_1527_10, all_1527_1) = all_1527_0 & $i(all_1527_0) &
% 222.05/34.52 | $i(all_1527_1) & $i(all_1527_2) & $i(all_1527_3) & $i(all_1527_4) &
% 222.05/34.52 | $i(all_1527_5) & $i(all_1527_6) & $i(all_1527_7) & $i(all_1527_8) &
% 222.05/34.52 | $i(all_1527_9) & $i(all_1527_10) & $i(all_1527_11)
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (788) implies:
% 222.05/34.52 | (789) hAPP(all_1527_10, all_1527_1) = all_1527_0
% 222.05/34.52 | (790) hAPP(all_1527_9, all_1527_4) = all_1527_3
% 222.05/34.52 | (791) hAPP(all_1527_3, all_1527_2) = all_1527_1
% 222.05/34.52 | (792) c_Groups_Ozero__class_Ozero(all_1527_11) = all_1527_6
% 222.05/34.52 | (793) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1527_11
% 222.05/34.52 | (794) c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.05/34.52 | all_1527_2
% 222.05/34.52 | (795) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1527_8, all_1527_5) =
% 222.05/34.52 | all_1527_4
% 222.05/34.52 | (796) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1527_7, all_1527_6) =
% 222.05/34.52 | all_1527_5
% 222.05/34.52 | (797) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1527_7
% 222.05/34.52 | (798) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.52 | all_1527_8
% 222.05/34.52 | (799) c_Power_Opower__class_Opower(all_1527_11) = all_1527_9
% 222.05/34.52 | (800) c_Groups_Otimes__class_Otimes(all_1527_11) = all_1527_10
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (155) with fresh symbols all_1532_0, all_1532_1,
% 222.05/34.52 | all_1532_2 gives:
% 222.05/34.52 | (801) c_Nat_OSuc(all_1532_1) = all_1532_0 & c_Nat_OSuc(all_1532_2) =
% 222.05/34.52 | all_1532_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1532_2 &
% 222.05/34.52 | $i(all_1532_0) & $i(all_1532_1) & $i(all_1532_2) & ! [v0: $i] : !
% 222.05/34.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 222.05/34.52 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 222.05/34.52 | (c_Groups_Ominus__class_Ominus(v2, v5, v7) = v8) | ~
% 222.05/34.52 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v6, all_1532_0)
% 222.05/34.52 | = v7) | ~ (hAPP(v4, all_1532_0) = v5) | ~ (hAPP(v3, v1) = v4) |
% 222.05/34.52 | ~ (hAPP(v3, v0) = v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.52 | class_Rings_Ocomm__ring__1(v2) | ? [v9: $i] : ? [v10: $i] : ?
% 222.05/34.52 | [v11: $i] : ? [v12: $i] : (c_Groups_Oplus__class_Oplus(v2, v1, v0)
% 222.05/34.52 | = v12 & c_Groups_Ominus__class_Ominus(v2, v1, v0) = v10 &
% 222.05/34.52 | c_Groups_Otimes__class_Otimes(v2) = v9 & hAPP(v11, v12) = v8 &
% 222.05/34.52 | hAPP(v9, v10) = v11 & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 222.05/34.52 | $i(v8)))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (801) implies:
% 222.05/34.52 | (802) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1532_2
% 222.05/34.52 | (803) c_Nat_OSuc(all_1532_2) = all_1532_1
% 222.05/34.52 | (804) c_Nat_OSuc(all_1532_1) = all_1532_0
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (12) with fresh symbols all_1535_0, all_1535_1,
% 222.05/34.52 | all_1535_2, all_1535_3, all_1535_4, all_1535_5, all_1535_6, all_1535_7,
% 222.05/34.52 | all_1535_8, all_1535_9, all_1535_10, all_1535_11, all_1535_12 gives:
% 222.05/34.52 | (805) c_Groups_Otimes__class_Otimes(all_1535_12) = all_1535_11 &
% 222.05/34.52 | c_Power_Opower__class_Opower(all_1535_12) = all_1535_10 &
% 222.05/34.52 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.52 | all_1535_9 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.05/34.52 | all_1535_8 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1535_8,
% 222.05/34.52 | all_1535_7) = all_1535_6 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.05/34.52 | all_1535_9, all_1535_6) = all_1535_5 &
% 222.05/34.52 | c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.05/34.52 | all_1535_3 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1535_12 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(all_1535_12) = all_1535_7 &
% 222.05/34.52 | hAPP(all_1535_1, all_1535_0) = v_pa____ & hAPP(all_1535_4,
% 222.05/34.52 | all_1535_3) = all_1535_2 & hAPP(all_1535_10, all_1535_5) =
% 222.05/34.52 | all_1535_4 & hAPP(all_1535_11, all_1535_2) = all_1535_1 &
% 222.05/34.52 | $i(all_1535_0) & $i(all_1535_1) & $i(all_1535_2) & $i(all_1535_3) &
% 222.05/34.52 | $i(all_1535_4) & $i(all_1535_5) & $i(all_1535_6) & $i(all_1535_7) &
% 222.05/34.52 | $i(all_1535_8) & $i(all_1535_9) & $i(all_1535_10) & $i(all_1535_11) &
% 222.05/34.52 | $i(all_1535_12)
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (805) implies:
% 222.05/34.52 | (806) hAPP(all_1535_11, all_1535_2) = all_1535_1
% 222.05/34.52 | (807) hAPP(all_1535_10, all_1535_5) = all_1535_4
% 222.05/34.52 | (808) hAPP(all_1535_4, all_1535_3) = all_1535_2
% 222.05/34.52 | (809) c_Groups_Ozero__class_Ozero(all_1535_12) = all_1535_7
% 222.05/34.52 | (810) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1535_12
% 222.05/34.52 | (811) c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.05/34.52 | all_1535_3
% 222.05/34.52 | (812) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1535_9, all_1535_6) =
% 222.05/34.52 | all_1535_5
% 222.05/34.52 | (813) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1535_8, all_1535_7) =
% 222.05/34.52 | all_1535_6
% 222.05/34.52 | (814) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1535_8
% 222.05/34.52 | (815) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.52 | all_1535_9
% 222.05/34.52 | (816) c_Power_Opower__class_Opower(all_1535_12) = all_1535_10
% 222.05/34.52 | (817) c_Groups_Otimes__class_Otimes(all_1535_12) = all_1535_11
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (144) with fresh symbols all_1537_0, all_1537_1 gives:
% 222.05/34.52 | (818) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1537_0 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1537_1 &
% 222.05/34.52 | $i(all_1537_0) & $i(all_1537_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.52 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 222.05/34.52 | [v7: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v5, v4) =
% 222.05/34.52 | v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(v1, v6) = v7) | ~
% 222.05/34.52 | (hAPP(all_1537_0, v0) = v3) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) |
% 222.05/34.52 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.52 | all_1537_1, v2) | ~
% 222.05/34.52 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1537_1, v0) |
% 222.05/34.52 | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i]
% 222.05/34.52 | : ? [v12: $i] : ($i(v9) &
% 222.05/34.52 | ((c_Groups_Ominus__class_Ominus(tc_Int_Oint, v9, v2) = v11 &
% 222.05/34.52 | hAPP(v1, v11) = v12 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11)
% 222.05/34.52 | & $i(v10) & hBOOL(v10) & ~ hBOOL(v12)) | (hAPP(v1, v5) = v8
% 222.05/34.52 | & $i(v8) & ~ hBOOL(v8)))))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (818) implies:
% 222.05/34.52 | (819) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1537_1
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (110) with fresh symbols all_1540_0, all_1540_1 gives:
% 222.05/34.52 | (820) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1540_1 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1540_0 &
% 222.05/34.52 | $i(all_1540_0) & $i(all_1540_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.52 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1540_0 |
% 222.05/34.52 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.52 | (hAPP(all_1540_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.52 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) |
% 222.05/34.52 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : !
% 222.05/34.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 222.05/34.52 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.52 | (hAPP(all_1540_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.52 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) |
% 222.05/34.52 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5)) & ! [v0: $i] : !
% 222.05/34.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v2,
% 222.05/34.52 | v1) = v3) | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1540_1,
% 222.05/34.52 | all_1540_0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.52 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v4))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (820) implies:
% 222.05/34.52 | (821) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1540_0
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (215) with fresh symbols all_1543_0, all_1543_1 gives:
% 222.05/34.52 | (822) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1543_0 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1543_1 &
% 222.05/34.52 | $i(all_1543_0) & $i(all_1543_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.52 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 222.05/34.52 | [v7: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v5, v4) =
% 222.05/34.52 | v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(v1, v6) = v7) | ~
% 222.05/34.52 | (hAPP(all_1543_0, v0) = v3) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) |
% 222.05/34.52 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.05/34.52 | all_1543_1, v2) | ~
% 222.05/34.52 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1543_1, v0) |
% 222.05/34.52 | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i]
% 222.05/34.52 | : ? [v12: $i] : ($i(v9) &
% 222.05/34.52 | ((c_Groups_Oplus__class_Oplus(tc_Int_Oint, v9, v2) = v11 &
% 222.05/34.52 | hAPP(v1, v11) = v12 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11)
% 222.05/34.52 | & $i(v10) & hBOOL(v10) & ~ hBOOL(v12)) | (hAPP(v1, v5) = v8
% 222.05/34.52 | & $i(v8) & ~ hBOOL(v8)))))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (822) implies:
% 222.05/34.52 | (823) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1543_1
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (26) with fresh symbols all_1546_0, all_1546_1,
% 222.05/34.52 | all_1546_2, all_1546_3 gives:
% 222.05/34.52 | (824) c_Power_Opower__class_Opower(all_1546_1) = all_1546_0 &
% 222.05/34.52 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1546_1 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1546_3 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1546_2 &
% 222.05/34.52 | $i(all_1546_0) & $i(all_1546_1) & $i(all_1546_2) & $i(all_1546_3) &
% 222.05/34.52 | ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 222.05/34.52 | ! [v5: $i] : (v0 = all_1546_2 | ~
% 222.05/34.52 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v3) | ~ (hAPP(v4,
% 222.05/34.52 | v0) = v5) | ~ (hAPP(all_1546_0, v2) = v4) | ~ $i(v2) | ~
% 222.05/34.52 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.52 | v0, v_na____) | c_Rings_Odvd__class_Odvd(all_1546_1, v1, v5) | ?
% 222.05/34.52 | [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : ? [v10:
% 222.05/34.52 | any] : ($i(v8) & ((v9 = all_1546_3 & ~ (v10 = all_1546_3) &
% 222.05/34.52 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v6 & hAPP(v6,
% 222.05/34.52 | v8) = v10 & hAPP(v3, v8) = all_1546_3 & $i(v10) & $i(v6)) |
% 222.05/34.52 | ( ~ (v7 = v0) & c_Polynomial_Odegree(tc_Complex_Ocomplex, v1) =
% 222.05/34.52 | v7 & $i(v7)))))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (824) implies:
% 222.05/34.52 | (825) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1546_2
% 222.05/34.52 | (826) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1546_3
% 222.05/34.52 | (827) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1546_1
% 222.05/34.52 | (828) c_Power_Opower__class_Opower(all_1546_1) = all_1546_0
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (67) with fresh symbol all_1549_0 gives:
% 222.05/34.52 | (829) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1549_0 &
% 222.05/34.52 | $i(all_1549_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.05/34.52 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(v2, v1) = v3) | ~
% 222.05/34.52 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.52 | class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 222.05/34.52 | ? [v8: any] : (((v8 = all_1549_0 & ~ (v7 = v1) &
% 222.05/34.52 | c_Polynomial_Oorder(v2, v0, v1) = all_1549_0 &
% 222.05/34.52 | tc_Polynomial_Opoly(v2) = v6 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6)) | (v5
% 222.05/34.52 | = v4 & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) & ((v7
% 222.05/34.52 | = v1 & tc_Polynomial_Opoly(v2) = v6 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(v6) = v1 & $i(v6)) | ( ~ (v8 =
% 222.05/34.52 | all_1549_0) & c_Polynomial_Oorder(v2, v0, v1) = v8 &
% 222.05/34.52 | $i(v8)) | ( ~ (v5 = v4) & c_Groups_Ozero__class_Ozero(v2) =
% 222.05/34.52 | v5 & $i(v5)))))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (829) implies:
% 222.05/34.52 | (830) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1549_0
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (164) with fresh symbols all_1552_0, all_1552_1 gives:
% 222.05/34.52 | (831) c_Nat_OSuc(all_1552_1) = all_1552_0 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1552_1 &
% 222.05/34.52 | $i(all_1552_0) & $i(all_1552_1) & ! [v0: $i] : ! [v1: any] : (v1 =
% 222.05/34.52 | all_1552_0 | v1 = all_1552_1 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1552_0) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 =
% 222.05/34.52 | all_1552_0 | v0 = all_1552_0 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1552_0) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 =
% 222.05/34.52 | all_1552_1 | v0 = all_1552_1 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1552_0) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 =
% 222.05/34.52 | all_1552_0 | v0 = all_1552_1 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1552_0) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1552_0 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1552_0, all_1552_1) =
% 222.05/34.52 | v0)) & ! [v0: int] : (v0 = all_1552_0 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1552_1, all_1552_0) =
% 222.05/34.52 | v0))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (831) implies:
% 222.05/34.52 | (832) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1552_1
% 222.05/34.52 | (833) c_Nat_OSuc(all_1552_1) = all_1552_0
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (164) with fresh symbols all_1555_0, all_1555_1 gives:
% 222.05/34.52 | (834) c_Nat_OSuc(all_1555_1) = all_1555_0 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1555_1 &
% 222.05/34.52 | $i(all_1555_0) & $i(all_1555_1) & ! [v0: $i] : ! [v1: any] : (v1 =
% 222.05/34.52 | all_1555_0 | v1 = all_1555_1 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1555_0) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 =
% 222.05/34.52 | all_1555_0 | v0 = all_1555_0 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1555_0) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 =
% 222.05/34.52 | all_1555_1 | v0 = all_1555_1 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1555_0) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 =
% 222.05/34.52 | all_1555_0 | v0 = all_1555_1 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1555_0) |
% 222.05/34.52 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1555_0 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1555_0, all_1555_1) =
% 222.05/34.52 | v0)) & ! [v0: int] : (v0 = all_1555_0 | ~
% 222.05/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1555_1, all_1555_0) =
% 222.05/34.52 | v0))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (834) implies:
% 222.05/34.52 | (835) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1555_1
% 222.05/34.52 | (836) c_Nat_OSuc(all_1555_1) = all_1555_0
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (41) with fresh symbols all_1558_0, all_1558_1 gives:
% 222.05/34.52 | (837) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1558_1 &
% 222.05/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1558_0 &
% 222.05/34.52 | $i(all_1558_0) & $i(all_1558_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.52 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 222.05/34.52 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1558_1, v2) = v3) |
% 222.05/34.52 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) |
% 222.05/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] :
% 222.05/34.52 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 222.05/34.52 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.52 | (hAPP(all_1558_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.52 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) |
% 222.05/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1558_0, v2)) & !
% 222.05/34.52 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.05/34.52 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.52 | (hAPP(all_1558_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.52 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~
% 222.05/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1558_0, v2) |
% 222.05/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (837) implies:
% 222.05/34.52 | (838) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1558_0
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (77) with fresh symbols all_1561_0, all_1561_1,
% 222.05/34.52 | all_1561_2 gives:
% 222.05/34.52 | (839) c_Nat_OSuc(all_1561_1) = all_1561_0 & c_Nat_OSuc(all_1561_2) =
% 222.05/34.52 | all_1561_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1561_2 &
% 222.05/34.52 | $i(all_1561_0) & $i(all_1561_1) & $i(all_1561_2) & ! [v0: $i] : !
% 222.05/34.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 222.05/34.52 | ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4)
% 222.05/34.52 | | ~ (hAPP(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.52 | class_Rings_Oidom(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 222.05/34.52 | ((v1 = v0 | (v8 = v1 & c_Groups_Ouminus__class_Ouminus(v2, v0) =
% 222.05/34.52 | v1) | ( ~ (v7 = v6) & hAPP(v5, all_1561_0) = v7 & hAPP(v4,
% 222.05/34.52 | all_1561_0) = v6 & $i(v7) & $i(v6))) & ((v7 = v6 & hAPP(v5,
% 222.05/34.52 | all_1561_0) = v6 & hAPP(v4, all_1561_0) = v6 & $i(v6)) | (
% 222.05/34.52 | ~ (v8 = v1) & ~ (v1 = v0) &
% 222.05/34.52 | c_Groups_Ouminus__class_Ouminus(v2, v0) = v8 & $i(v8)))))
% 222.05/34.52 |
% 222.05/34.52 | ALPHA: (839) implies:
% 222.05/34.52 | (840) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1561_2
% 222.05/34.52 | (841) c_Nat_OSuc(all_1561_2) = all_1561_1
% 222.05/34.52 | (842) c_Nat_OSuc(all_1561_1) = all_1561_0
% 222.05/34.52 |
% 222.05/34.52 | DELTA: instantiating (44) with fresh symbols all_1564_0, all_1564_1 gives:
% 222.05/34.53 | (843) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1564_1 &
% 222.05/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1564_0 &
% 222.05/34.53 | $i(all_1564_0) & $i(all_1564_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.53 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 222.05/34.53 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1564_1, v2) = v3) |
% 222.05/34.53 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1564_0, v2) | ~
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0:
% 222.05/34.53 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.05/34.53 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.53 | (hAPP(all_1564_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.53 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)) & ! [v0:
% 222.05/34.53 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.05/34.53 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 222.05/34.53 | (hAPP(all_1564_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1564_0, v2) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5))
% 222.05/34.53 |
% 222.05/34.53 | ALPHA: (843) implies:
% 222.05/34.53 | (844) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1564_0
% 222.05/34.53 |
% 222.05/34.53 | DELTA: instantiating (40) with fresh symbols all_1585_0, all_1585_1 gives:
% 222.05/34.53 | (845) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1585_1 &
% 222.05/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1585_0 &
% 222.05/34.53 | $i(all_1585_0) & $i(all_1585_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.53 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 222.05/34.53 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1585_1,
% 222.05/34.53 | v2) = v3) | ~ (hAPP(all_1585_1, v0) = v5) | ~ $i(v2) | ~
% 222.05/34.53 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.53 | v4, v6) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0)) &
% 222.05/34.53 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 222.05/34.53 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1)
% 222.05/34.53 | = v4) | ~ (hAPP(all_1585_1, v2) = v3) | ~ (hAPP(all_1585_1, v0)
% 222.05/34.53 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1585_0, v1)) & !
% 222.05/34.53 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.05/34.53 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) =
% 222.05/34.53 | v4) | ~ (hAPP(all_1585_1, v2) = v3) | ~ (hAPP(all_1585_1, v0) =
% 222.05/34.53 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0) | ~
% 222.05/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1585_0, v1) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))
% 222.05/34.53 |
% 222.05/34.53 | ALPHA: (845) implies:
% 222.05/34.53 | (846) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1585_0
% 222.05/34.53 |
% 222.05/34.53 | DELTA: instantiating (43) with fresh symbols all_1588_0, all_1588_1 gives:
% 222.05/34.53 | (847) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1588_1 &
% 222.05/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1588_0 &
% 222.05/34.53 | $i(all_1588_0) & $i(all_1588_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.05/34.53 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 222.05/34.53 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1588_1,
% 222.05/34.53 | v2) = v3) | ~ (hAPP(all_1588_1, v0) = v5) | ~ $i(v2) | ~
% 222.05/34.53 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.53 | all_1588_0, v1) | ~
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0)) & ! [v0:
% 222.05/34.53 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.05/34.53 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) =
% 222.05/34.53 | v4) | ~ (hAPP(all_1588_1, v2) = v3) | ~ (hAPP(all_1588_1, v0) =
% 222.05/34.53 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6)) & ! [v0:
% 222.05/34.53 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.05/34.53 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) =
% 222.05/34.53 | v4) | ~ (hAPP(all_1588_1, v2) = v3) | ~ (hAPP(all_1588_1, v0) =
% 222.05/34.53 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1588_0, v1) |
% 222.05/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6))
% 222.05/34.53 |
% 222.05/34.53 | ALPHA: (847) implies:
% 222.05/34.53 | (848) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1588_0
% 222.05/34.53 |
% 222.05/34.53 | DELTA: instantiating (240) with fresh symbols all_1593_0, all_1593_1,
% 222.05/34.53 | all_1593_2, all_1593_3, all_1593_4, all_1593_5, all_1593_6, all_1593_7,
% 222.05/34.53 | all_1593_8, all_1593_9, all_1593_10, all_1593_11, all_1593_12,
% 222.05/34.53 | all_1593_13, all_1593_14, all_1593_15, all_1593_16 gives:
% 222.05/34.53 | (849) ~ (all_1593_0 = all_1593_7) &
% 222.05/34.53 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, all_1593_5) =
% 222.05/34.53 | all_1593_2 & c_Groups_Otimes__class_Otimes(all_1593_16) = all_1593_6
% 222.05/34.53 | & c_Power_Opower__class_Opower(all_1593_16) = all_1593_13 &
% 222.05/34.53 | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.05/34.53 | all_1593_12 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.05/34.53 | all_1593_11 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1593_11,
% 222.05/34.53 | all_1593_15) = all_1593_10 &
% 222.05/34.53 | c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1593_12, all_1593_10) =
% 222.05/34.53 | all_1593_9 & c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____,
% 222.05/34.53 | v_pa____) = all_1593_5 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) =
% 222.05/34.53 | all_1593_16 & c_Groups_Ozero__class_Ozero(all_1593_16) = all_1593_15
% 222.05/34.53 | & hAPP(all_1593_3, all_1593_1) = all_1593_0 & hAPP(all_1593_6,
% 222.05/34.53 | all_1593_4) = all_1593_3 & hAPP(all_1593_8, all_1593_2) =
% 222.05/34.53 | all_1593_1 & hAPP(all_1593_8, all_1593_5) = all_1593_4 &
% 222.05/34.53 | hAPP(all_1593_8, v_na____) = all_1593_7 & hAPP(all_1593_13,
% 222.05/34.53 | all_1593_9) = all_1593_8 & $i(all_1593_0) & $i(all_1593_1) &
% 222.05/34.53 | $i(all_1593_2) & $i(all_1593_3) & $i(all_1593_4) & $i(all_1593_5) &
% 222.05/34.53 | $i(all_1593_6) & $i(all_1593_7) & $i(all_1593_8) & $i(all_1593_9) &
% 222.05/34.53 | $i(all_1593_10) & $i(all_1593_11) & $i(all_1593_12) & $i(all_1593_13)
% 222.05/34.53 | & $i(all_1593_15) & $i(all_1593_16) & ( ~ (all_1593_15 = v_r____) |
% 222.05/34.53 | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1593_14 &
% 222.05/34.53 | $i(all_1593_14) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.05/34.53 | all_1593_14, v_na____)))
% 222.05/34.53 |
% 222.05/34.53 | ALPHA: (849) implies:
% 222.29/34.53 | (850) ~ (all_1593_0 = all_1593_7)
% 222.29/34.53 | (851) $i(all_1593_2)
% 222.29/34.53 | (852) hAPP(all_1593_13, all_1593_9) = all_1593_8
% 222.29/34.53 | (853) hAPP(all_1593_8, v_na____) = all_1593_7
% 222.29/34.53 | (854) hAPP(all_1593_8, all_1593_5) = all_1593_4
% 222.29/34.53 | (855) hAPP(all_1593_8, all_1593_2) = all_1593_1
% 222.29/34.53 | (856) hAPP(all_1593_6, all_1593_4) = all_1593_3
% 222.29/34.53 | (857) hAPP(all_1593_3, all_1593_1) = all_1593_0
% 222.29/34.53 | (858) c_Groups_Ozero__class_Ozero(all_1593_16) = all_1593_15
% 222.29/34.53 | (859) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1593_16
% 222.29/34.53 | (860) c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) =
% 222.29/34.53 | all_1593_5
% 222.29/34.53 | (861) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1593_12, all_1593_10) =
% 222.29/34.53 | all_1593_9
% 222.29/34.53 | (862) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1593_11, all_1593_15) =
% 222.29/34.53 | all_1593_10
% 222.29/34.53 | (863) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1593_11
% 222.29/34.53 | (864) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.29/34.53 | all_1593_12
% 222.29/34.53 | (865) c_Power_Opower__class_Opower(all_1593_16) = all_1593_13
% 222.29/34.53 | (866) c_Groups_Otimes__class_Otimes(all_1593_16) = all_1593_6
% 222.29/34.53 | (867) c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, all_1593_5) =
% 222.29/34.53 | all_1593_2
% 222.29/34.53 |
% 222.29/34.53 | DELTA: instantiating (191) with fresh symbol all_1597_0 gives:
% 222.29/34.53 | (868) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1597_0 &
% 222.29/34.53 | $i(all_1597_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 222.29/34.53 | all_1597_0 | ~ (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) =
% 222.29/34.53 | v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v0) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1597_0, v1)) &
% 222.29/34.53 | ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_1597_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v2) | ~ $i(v1)
% 222.29/34.53 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1)
% 222.29/34.53 | | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1,
% 222.29/34.53 | all_1597_0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1597_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v0, all_1597_0) = v1) | ~
% 222.29/34.53 | $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = all_1597_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = all_1597_0) | ~
% 222.29/34.53 | $i(v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1,
% 222.29/34.53 | v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v1)) & !
% 222.29/34.53 | [v0: any] : ! [v1: $i] : (v0 = all_1597_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = all_1597_0) | ~
% 222.29/34.53 | $i(v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v1,
% 222.29/34.53 | v0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v1,
% 222.29/34.53 | all_1597_0)) & ! [v0: any] : ! [v1: $i] : (v0 = all_1597_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = all_1597_0) | ~
% 222.29/34.53 | $i(v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 222.29/34.53 | v1) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1597_0,
% 222.29/34.53 | v1)) & ! [v0: any] : ! [v1: $i] : (v0 = all_1597_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = all_1597_0) | ~
% 222.29/34.53 | $i(v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.29/34.53 | v1, all_1597_0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.29/34.53 | all_1597_0, v1))
% 222.29/34.53 |
% 222.29/34.53 | ALPHA: (868) implies:
% 222.29/34.53 | (869) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1597_0
% 222.29/34.53 |
% 222.29/34.53 | DELTA: instantiating (213) with fresh symbols all_1600_0, all_1600_1 gives:
% 222.29/34.53 | (870) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1600_1 &
% 222.29/34.53 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1600_0 &
% 222.29/34.53 | $i(all_1600_0) & $i(all_1600_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.29/34.53 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6
% 222.29/34.53 | = v1 | v2 = all_1600_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v6) | ~
% 222.29/34.53 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v5, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v4, v1) = v5) | ~ (hAPP(all_1600_1, v2) = v4) | ~ $i(v3) |
% 222.29/34.53 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, all_1600_0) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1600_0, v0)) &
% 222.29/34.53 | ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] :
% 222.29/34.53 | ! [v5: $i] : ! [v6: $i] : (v6 = v1 | v2 = all_1600_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v6) | ~
% 222.29/34.53 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v5, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v4, v1) = v5) | ~ (hAPP(all_1600_1, v2) = v4) | ~ $i(v3) |
% 222.29/34.53 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v2, v0) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, all_1600_0) |
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1600_0, v2)) & !
% 222.29/34.53 | [v0: $i] : ! [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] :
% 222.29/34.53 | ! [v5: $i] : ! [v6: $i] : (v6 = v1 | v2 = all_1600_0 | ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v3, v2) = v6) | ~
% 222.29/34.53 | (c_Groups_Oplus__class_Oplus(tc_Int_Oint, v5, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v4, v1) = v5) | ~ (hAPP(all_1600_1, v2) = v4) | ~ $i(v3) |
% 222.29/34.53 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v2) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1600_0, v2) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1600_0, v0))
% 222.29/34.53 |
% 222.29/34.53 | ALPHA: (870) implies:
% 222.29/34.53 | (871) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1600_0
% 222.29/34.53 |
% 222.29/34.53 | DELTA: instantiating (173) with fresh symbol all_1603_0 gives:
% 222.29/34.53 | (872) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1603_0 &
% 222.29/34.53 | $i(all_1603_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.29/34.53 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.29/34.53 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1) | ~
% 222.29/34.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 222.29/34.53 | | ~ hBOOL(v4) | ? [v6: $i] : (hAPP(v2, v5) = v6 & $i(v6) &
% 222.29/34.53 | hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.29/34.53 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,
% 222.29/34.53 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 222.29/34.53 | | ~ $i(v0) | ~ hBOOL(v4) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i] :
% 222.29/34.53 | (hAPP(v2, all_1603_0) = v5 & $i(v5) & hBOOL(v5))) & ! [v0: $i] :
% 222.29/34.53 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 222.29/34.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 222.29/34.53 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i]
% 222.29/34.53 | : ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) =
% 222.29/34.53 | v1 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) & ~ hBOOL(v6))) & !
% 222.29/34.53 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 222.29/34.53 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 222.29/34.53 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 222.29/34.53 | ((v7 = v1 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v6) = v1
% 222.29/34.53 | & hAPP(v2, v6) = v8 & $i(v8) & ~ hBOOL(v8)) | (hAPP(v2,
% 222.29/34.53 | all_1603_0) = v5 & $i(v5) & ~ hBOOL(v5)))))
% 222.29/34.53 |
% 222.29/34.53 | ALPHA: (872) implies:
% 222.29/34.53 | (873) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1603_0
% 222.29/34.53 |
% 222.29/34.53 | DELTA: instantiating (173) with fresh symbol all_1606_0 gives:
% 222.29/34.53 | (874) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1606_0 &
% 222.29/34.53 | $i(all_1606_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.29/34.53 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 222.29/34.53 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1) | ~
% 222.29/34.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 222.29/34.53 | | ~ hBOOL(v4) | ? [v6: $i] : (hAPP(v2, v5) = v6 & $i(v6) &
% 222.29/34.53 | hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 222.29/34.53 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,
% 222.29/34.53 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 222.29/34.53 | | ~ $i(v0) | ~ hBOOL(v4) | ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i] :
% 222.29/34.53 | (hAPP(v2, all_1606_0) = v5 & $i(v5) & hBOOL(v5))) & ! [v0: $i] :
% 222.29/34.53 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 222.29/34.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 222.29/34.53 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i]
% 222.29/34.53 | : ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) =
% 222.29/34.53 | v1 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) & ~ hBOOL(v6))) & !
% 222.29/34.53 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 222.29/34.53 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 222.29/34.53 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 222.29/34.53 | ((v7 = v1 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v6) = v1
% 222.29/34.53 | & hAPP(v2, v6) = v8 & $i(v8) & ~ hBOOL(v8)) | (hAPP(v2,
% 222.29/34.53 | all_1606_0) = v5 & $i(v5) & ~ hBOOL(v5)))))
% 222.29/34.53 |
% 222.29/34.53 | ALPHA: (874) implies:
% 222.29/34.53 | (875) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1606_0
% 222.29/34.53 |
% 222.29/34.53 | DELTA: instantiating (212) with fresh symbols all_1609_0, all_1609_1 gives:
% 222.29/34.53 | (876) c_Groups_Otimes__class_Otimes(tc_Int_Oint) = all_1609_0 &
% 222.29/34.53 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1609_1 &
% 222.29/34.53 | $i(all_1609_0) & $i(all_1609_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 222.29/34.53 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 222.29/34.53 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : (( ~ (v0 = all_1609_1) |
% 222.29/34.53 | (hAPP(v2, all_1609_1) = v5 & $i(v5) & hBOOL(v5))) & ( ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, all_1609_1) |
% 222.29/34.53 | (hAPP(all_1609_0, v0) = v6 & $i(v6) & ! [v7: $i] : ! [v8: $i]
% 222.29/34.53 | : ! [v9: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint,
% 222.29/34.53 | v8, v9) = v1) | ~ (hAPP(v6, v7) = v8) | ~ $i(v9) | ~
% 222.29/34.53 | $i(v7) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 222.29/34.53 | v9) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.29/34.53 | v9, all_1609_1) | ? [v10: $i] : (hAPP(v2, v7) = v10 &
% 222.29/34.53 | $i(v10) & hBOOL(v10))))) & ( ~
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1609_1, v0) |
% 222.29/34.53 | (hAPP(all_1609_0, v0) = v6 & $i(v6) & ! [v7: $i] : ! [v8: $i]
% 222.29/34.53 | : ! [v9: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Int_Oint,
% 222.29/34.53 | v8, v9) = v1) | ~ (hAPP(v6, v7) = v8) | ~ $i(v9) | ~
% 222.29/34.53 | $i(v7) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v9,
% 222.29/34.53 | v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.29/34.53 | all_1609_1, v9) | ? [v10: $i] : (hAPP(v2, v7) = v10 &
% 222.29/34.53 | $i(v10) & hBOOL(v10))))))) & ! [v0: $i] : ! [v1: $i] :
% 222.29/34.53 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 222.29/34.53 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v1, v0) = v3) | ~
% 222.29/34.53 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4)
% 222.29/34.53 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 222.29/34.53 | $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 222.29/34.53 | ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ($i(v15) & $i(v12) &
% 222.29/34.53 | $i(v10) & $i(v7) & ((v16 = v1 &
% 222.29/34.53 | c_Groups_Oplus__class_Oplus(tc_Int_Oint, v13, v15) = v1 &
% 222.29/34.53 | hAPP(v6, v12) = v13 & hAPP(v2, v12) = v14 & hAPP(all_1609_0,
% 222.29/34.53 | v0) = v6 & $i(v14) & $i(v13) & $i(v6) &
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v15, v0) &
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1609_1, v0) &
% 222.29/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1609_1,
% 222.29/34.53 | v15) & ~ hBOOL(v14)) | (v11 = v1 &
% 222.29/34.53 | c_Groups_Oplus__class_Oplus(tc_Int_Oint, v8, v10) = v1 &
% 222.29/34.53 | hAPP(v6, v7) = v8 & hAPP(v2, v7) = v9 & hAPP(all_1609_0, v0)
% 222.29/34.53 | = v6 & $i(v9) & $i(v8) & $i(v6) &
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v10) &
% 222.29/34.53 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, all_1609_1) &
% 222.29/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v10,
% 222.29/34.53 | all_1609_1) & ~ hBOOL(v9)) | (v0 = all_1609_1 & hAPP(v2,
% 222.29/34.53 | all_1609_1) = v5 & $i(v5) & ~ hBOOL(v5)))))
% 222.29/34.53 |
% 222.29/34.53 | ALPHA: (876) implies:
% 222.29/34.53 | (877) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1609_1
% 222.29/34.53 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_748_0, all_761_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (261), (269) gives:
% 222.29/34.54 | (878) all_761_0 = all_748_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_761_0, all_769_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (269), (275) gives:
% 222.29/34.54 | (879) all_769_0 = all_761_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_769_0, all_785_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (275), (283) gives:
% 222.29/34.54 | (880) all_785_0 = all_769_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_796_0, all_799_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (291), (293) gives:
% 222.29/34.54 | (881) all_799_0 = all_796_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_788_0, all_799_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (285), (293) gives:
% 222.29/34.54 | (882) all_799_0 = all_788_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_796_0, all_803_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (291), (295) gives:
% 222.29/34.54 | (883) all_803_0 = all_796_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_803_0, all_817_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (295), (308) gives:
% 222.29/34.54 | (884) all_817_0 = all_803_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_817_0, all_819_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (308), (312) gives:
% 222.29/34.54 | (885) all_819_0 = all_817_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_819_0, all_824_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (312), (314) gives:
% 222.29/34.54 | (886) all_824_0 = all_819_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_824_0, all_838_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (314), (325) gives:
% 222.29/34.54 | (887) all_838_0 = all_824_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_838_0, all_846_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (325), (330) gives:
% 222.29/34.54 | (888) all_846_0 = all_838_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_846_0, all_856_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (330), (342) gives:
% 222.29/34.54 | (889) all_856_0 = all_846_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_856_0, all_868_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (342), (352) gives:
% 222.29/34.54 | (890) all_868_0 = all_856_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_761_0, all_875_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (269), (358) gives:
% 222.29/34.54 | (891) all_875_0 = all_761_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_884_0, all_895_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (370), (376) gives:
% 222.29/34.54 | (892) all_895_0 = all_884_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_799_0, all_960_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (293), (405) gives:
% 222.29/34.54 | (893) all_960_1 = all_799_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_941_0, all_1007_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (394), (436) gives:
% 222.29/34.54 | (894) all_1007_1 = all_941_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1007_1, all_1010_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (436), (439) gives:
% 222.29/34.54 | (895) all_1010_1 = all_1007_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_983_1, all_1016_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (417), (444) gives:
% 222.29/34.54 | (896) all_1016_0 = all_983_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1010_1, all_1019_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (439), (446) gives:
% 222.29/34.54 | (897) all_1019_0 = all_1010_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_785_0, all_1022_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (283), (448) gives:
% 222.29/34.54 | (898) all_1022_0 = all_785_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_960_1, all_1027_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (405), (450) gives:
% 222.29/34.54 | (899) all_1027_0 = all_960_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_780_0, all_1039_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (279), (459) gives:
% 222.29/34.54 | (900) all_1039_0 = all_780_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_778_0, all_1039_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (277), (459) gives:
% 222.29/34.54 | (901) all_1039_0 = all_778_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1094_0, all_1103_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (488), (496) gives:
% 222.29/34.54 | (902) all_1103_0 = all_1094_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_983_1, all_1121_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (417), (510) gives:
% 222.29/34.54 | (903) all_1121_0 = all_983_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_817_0, all_1121_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (308), (510) gives:
% 222.29/34.54 | (904) all_1121_0 = all_817_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1016_0, all_1130_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (444), (515) gives:
% 222.29/34.54 | (905) all_1130_2 = all_1016_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1130_2, all_1133_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (515), (519) gives:
% 222.29/34.54 | (906) all_1133_1 = all_1130_2
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1100_0, all_1139_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (493), (522) gives:
% 222.29/34.54 | (907) all_1139_1 = all_1100_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1103_0, all_1171_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (496), (544) gives:
% 222.29/34.54 | (908) all_1171_1 = all_1103_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_884_0, all_1174_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (370), (546) gives:
% 222.29/34.54 | (909) all_1174_0 = all_884_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_868_0, all_1174_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (352), (546) gives:
% 222.29/34.54 | (910) all_1174_0 = all_868_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1115_0, all_1186_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (506), (557) gives:
% 222.29/34.54 | (911) all_1186_2 = all_1115_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1027_0, all_1186_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (450), (557) gives:
% 222.29/34.54 | (912) all_1186_2 = all_1027_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1094_0, all_1201_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (488), (563) gives:
% 222.29/34.54 | (913) all_1201_1 = all_1094_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1058_1, all_1201_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (469), (563) gives:
% 222.29/34.54 | (914) all_1201_1 = all_1058_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1124_1, all_1204_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (512), (565) gives:
% 222.29/34.54 | (915) all_1204_2 = all_1124_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_944_0, all_1204_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (396), (565) gives:
% 222.29/34.54 | (916) all_1204_2 = all_944_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_783_0, all_1204_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (281), (565) gives:
% 222.29/34.54 | (917) all_1204_2 = all_783_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1224_2, all_1230_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (573), (576) gives:
% 222.29/34.54 | (918) all_1230_2 = all_1224_2
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1212_1, all_1230_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (570), (576) gives:
% 222.29/34.54 | (919) all_1230_2 = all_1212_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1157_0, all_1239_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (536), (584) gives:
% 222.29/34.54 | (920) all_1239_0 = all_1157_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1121_0, all_1244_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (510), (593) gives:
% 222.29/34.54 | (921) all_1244_0 = all_1121_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1212_1, all_1247_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (570), (595) gives:
% 222.29/34.54 | (922) all_1247_0 = all_1212_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1091_2, all_1247_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (484), (595) gives:
% 222.29/34.54 | (923) all_1247_0 = all_1091_2
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1019_0, all_1247_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (446), (595) gives:
% 222.29/34.54 | (924) all_1247_0 = all_1019_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1171_1, all_1250_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (544), (598) gives:
% 222.29/34.54 | (925) all_1250_0 = all_1171_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1115_0, all_1259_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (506), (604) gives:
% 222.29/34.54 | (926) all_1259_1 = all_1115_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1133_1, all_1312_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (519), (625) gives:
% 222.29/34.54 | (927) all_1312_1 = all_1133_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1239_0, all_1351_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (584), (636) gives:
% 222.29/34.54 | (928) all_1351_0 = all_1239_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1042_0, all_1351_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (461), (636) gives:
% 222.29/34.54 | (929) all_1351_0 = all_1042_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1230_2, all_1368_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (576), (658) gives:
% 222.29/34.54 | (930) all_1368_0 = all_1230_2
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1259_1, all_1371_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (604), (660) gives:
% 222.29/34.54 | (931) all_1371_0 = all_1259_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1139_1, all_1383_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (522), (667) gives:
% 222.29/34.54 | (932) all_1383_0 = all_1139_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1100_0, all_1386_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (493), (669) gives:
% 222.29/34.54 | (933) all_1386_2 = all_1100_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_746_0, all_1386_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (259), (669) gives:
% 222.29/34.54 | (934) all_1386_2 = all_746_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1348_0, all_1406_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (634), (686) gives:
% 222.29/34.54 | (935) all_1406_1 = all_1348_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_941_0, all_1406_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (394), (686) gives:
% 222.29/34.54 | (936) all_1406_1 = all_941_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_935_0, all_1406_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (390), (686) gives:
% 222.29/34.54 | (937) all_1406_1 = all_935_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_895_0, all_1406_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (376), (686) gives:
% 222.29/34.54 | (938) all_1406_1 = all_895_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1244_0, all_1415_3, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (593), (693) gives:
% 222.29/34.54 | (939) all_1415_3 = all_1244_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_992_1, all_1415_3, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (424), (693) gives:
% 222.29/34.54 | (940) all_1415_3 = all_992_1
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1186_2, all_1421_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (557), (697) gives:
% 222.29/34.54 | (941) all_1421_0 = all_1186_2
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1383_0, all_1427_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (667), (700) gives:
% 222.29/34.54 | (942) all_1427_0 = all_1383_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1368_0, all_1430_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (658), (702) gives:
% 222.29/34.54 | (943) all_1430_1 = all_1368_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_778_0, all_1433_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (277), (706) gives:
% 222.29/34.54 | (944) all_1433_0 = all_778_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_769_0, all_1433_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (275), (706) gives:
% 222.29/34.54 | (945) all_1433_0 = all_769_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_767_0, all_1433_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (273), (706) gives:
% 222.29/34.54 | (946) all_1433_0 = all_767_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1374_0, all_1442_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (662), (708) gives:
% 222.29/34.54 | (947) all_1442_0 = all_1374_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1168_0, all_1442_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (542), (708) gives:
% 222.29/34.54 | (948) all_1442_0 = all_1168_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_814_0, all_1442_0, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (306), (708) gives:
% 222.29/34.54 | (949) all_1442_0 = all_814_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1022_0, all_1448_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (448), (712) gives:
% 222.29/34.54 | (950) all_1448_2 = all_1022_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_764_0, all_1448_2, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (271), (712) gives:
% 222.29/34.54 | (951) all_1448_2 = all_764_0
% 222.29/34.54 |
% 222.29/34.54 | GROUND_INST: instantiating (241) with all_1377_1, all_1451_1, tc_Nat_Onat,
% 222.29/34.54 | simplifying with (664), (715) gives:
% 222.29/34.54 | (952) all_1451_1 = all_1377_1
% 222.29/34.54 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1139_1, all_1451_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (522), (715) gives:
% 222.29/34.55 | (953) all_1451_1 = all_1139_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1001_1, all_1451_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (431), (715) gives:
% 222.29/34.55 | (954) all_1451_1 = all_1001_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_875_0, all_1451_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (358), (715) gives:
% 222.29/34.55 | (955) all_1451_1 = all_875_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1365_2, all_1454_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (655), (718) gives:
% 222.29/34.55 | (956) all_1454_0 = all_1365_2
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1312_1, all_1454_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (625), (718) gives:
% 222.29/34.55 | (957) all_1454_0 = all_1312_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1454_0, all_1459_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (718), (731) gives:
% 222.29/34.55 | (958) all_1459_0 = all_1454_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1406_1, all_1462_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (686), (733) gives:
% 222.29/34.55 | (959) all_1462_1 = all_1406_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1168_0, all_1462_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (542), (733) gives:
% 222.29/34.55 | (960) all_1462_1 = all_1168_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1106_0, all_1462_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (499), (733) gives:
% 222.29/34.55 | (961) all_1462_1 = all_1106_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1174_0, all_1468_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (546), (738) gives:
% 222.29/34.55 | (962) all_1468_0 = all_1174_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_871_1, all_1468_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (355), (738) gives:
% 222.29/34.55 | (963) all_1468_0 = all_871_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1371_0, all_1471_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (660), (740) gives:
% 222.29/34.55 | (964) all_1471_1 = all_1371_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1362_0, all_1480_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (653), (748) gives:
% 222.29/34.55 | (965) all_1480_1 = all_1362_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1250_0, all_1480_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (598), (748) gives:
% 222.29/34.55 | (966) all_1480_1 = all_1250_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_932_0, all_1480_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (388), (748) gives:
% 222.29/34.55 | (967) all_1480_1 = all_932_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1459_0, all_1483_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (731), (750) gives:
% 222.29/34.55 | (968) all_1483_0 = all_1459_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1454_0, all_1497_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (718), (769) gives:
% 222.29/34.55 | (969) all_1497_0 = all_1454_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1398_0, all_1497_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (676), (769) gives:
% 222.29/34.55 | (970) all_1497_0 = all_1398_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1430_1, all_1500_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (702), (771) gives:
% 222.29/34.55 | (971) all_1500_1 = all_1430_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1406_1, all_1503_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (686), (773) gives:
% 222.29/34.55 | (972) all_1503_1 = all_1406_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1157_0, all_1503_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (536), (773) gives:
% 222.29/34.55 | (973) all_1503_1 = all_1157_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1094_0, all_1503_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (488), (773) gives:
% 222.29/34.55 | (974) all_1503_1 = all_1094_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1049_0, all_1503_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (463), (773) gives:
% 222.29/34.55 | (975) all_1503_1 = all_1049_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1427_0, all_1506_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (700), (776) gives:
% 222.29/34.55 | (976) all_1506_1 = all_1427_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1483_0, all_1512_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (750), (781) gives:
% 222.29/34.55 | (977) all_1512_1 = all_1483_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1506_1, all_1521_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (776), (783) gives:
% 222.29/34.55 | (978) all_1521_1 = all_1506_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1521_1, all_1524_2, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (783), (786) gives:
% 222.29/34.55 | (979) all_1524_2 = all_1521_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1500_1, all_1532_2, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (771), (802) gives:
% 222.29/34.55 | (980) all_1532_2 = all_1500_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1512_1, all_1540_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (781), (821) gives:
% 222.29/34.55 | (981) all_1540_0 = all_1512_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_754_0, all_1540_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (267), (821) gives:
% 222.29/34.55 | (982) all_1540_0 = all_754_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1121_0, all_1546_2, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (510), (825) gives:
% 222.29/34.55 | (983) all_1546_2 = all_1121_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_957_0, all_1546_2, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (403), (825) gives:
% 222.29/34.55 | (984) all_1546_2 = all_957_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1524_2, all_1549_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (786), (830) gives:
% 222.29/34.55 | (985) all_1549_0 = all_1524_2
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1204_2, all_1552_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (565), (832) gives:
% 222.29/34.55 | (986) all_1552_1 = all_1204_2
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1039_0, all_1552_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (459), (832) gives:
% 222.29/34.55 | (987) all_1552_1 = all_1039_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_812_0, all_1552_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (304), (832) gives:
% 222.29/34.55 | (988) all_1552_1 = all_812_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_788_0, all_1552_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (285), (832) gives:
% 222.29/34.55 | (989) all_1552_1 = all_788_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1471_1, all_1555_1, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (740), (835) gives:
% 222.29/34.55 | (990) all_1555_1 = all_1471_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1532_2, all_1558_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (802), (838) gives:
% 222.29/34.55 | (991) all_1558_0 = all_1532_2
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1503_1, all_1561_2, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (773), (840) gives:
% 222.29/34.55 | (992) all_1561_2 = all_1503_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1489_1, all_1561_2, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (755), (840) gives:
% 222.29/34.55 | (993) all_1561_2 = all_1489_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1558_0, all_1564_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (838), (844) gives:
% 222.29/34.55 | (994) all_1564_0 = all_1558_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1564_0, all_1585_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (844), (846) gives:
% 222.29/34.55 | (995) all_1585_0 = all_1564_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_921_0, all_1585_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (384), (846) gives:
% 222.29/34.55 | (996) all_1585_0 = all_921_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1549_0, all_1588_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (830), (848) gives:
% 222.29/34.55 | (997) all_1588_0 = all_1549_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1088_0, all_1588_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (482), (848) gives:
% 222.29/34.55 | (998) all_1588_0 = all_1088_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1509_0, all_1603_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (779), (873) gives:
% 222.29/34.55 | (999) all_1603_0 = all_1509_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1477_3, all_1603_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (744), (873) gives:
% 222.29/34.55 | (1000) all_1603_0 = all_1477_3
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1421_0, all_1603_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (697), (873) gives:
% 222.29/34.55 | (1001) all_1603_0 = all_1421_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1067_0, all_1603_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (473), (873) gives:
% 222.29/34.55 | (1002) all_1603_0 = all_1067_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1555_1, all_1606_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (835), (875) gives:
% 222.29/34.55 | (1003) all_1606_0 = all_1555_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_791_0, all_1606_0, tc_Nat_Onat,
% 222.29/34.55 | simplifying with (287), (875) gives:
% 222.29/34.55 | (1004) all_1606_0 = all_791_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_752_0, all_1151_1,
% 222.29/34.55 | tc_Complex_Ocomplex, simplifying with (265), (530) gives:
% 222.29/34.55 | (1005) all_1151_1 = all_752_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1180_1, all_1546_3,
% 222.29/34.55 | tc_Complex_Ocomplex, simplifying with (551), (826) gives:
% 222.29/34.55 | (1006) all_1546_3 = all_1180_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1151_1, all_1546_3,
% 222.29/34.55 | tc_Complex_Ocomplex, simplifying with (530), (826) gives:
% 222.29/34.55 | (1007) all_1546_3 = all_1151_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_854_0, all_1546_3,
% 222.29/34.55 | tc_Complex_Ocomplex, simplifying with (338), (826) gives:
% 222.29/34.55 | (1008) all_1546_3 = all_854_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_750_0, all_832_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (263), (320) gives:
% 222.29/34.55 | (1009) all_832_1 = all_750_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_742_0, all_832_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (254), (320) gives:
% 222.29/34.55 | (1010) all_832_1 = all_742_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_832_1, all_835_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (320), (323) gives:
% 222.29/34.55 | (1011) all_835_0 = all_832_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_835_0, all_849_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (323), (332) gives:
% 222.29/34.55 | (1012) all_849_0 = all_835_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_849_0, all_858_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (332), (345) gives:
% 222.29/34.55 | (1013) all_858_0 = all_849_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_858_0, all_861_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (345), (347) gives:
% 222.29/34.55 | (1014) all_861_1 = all_858_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_861_1, all_909_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (347), (380) gives:
% 222.29/34.55 | (1015) all_909_0 = all_861_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_909_0, all_947_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (380), (398) gives:
% 222.29/34.55 | (1016) all_947_0 = all_909_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_947_0, all_954_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (398), (401) gives:
% 222.29/34.55 | (1017) all_954_0 = all_947_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_954_0, all_965_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (401), (408) gives:
% 222.29/34.55 | (1018) all_965_0 = all_954_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_965_0, all_974_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (408), (410) gives:
% 222.29/34.55 | (1019) all_974_0 = all_965_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_974_0, all_977_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (410), (412) gives:
% 222.29/34.55 | (1020) all_977_1 = all_974_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_977_1, all_980_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (412), (415) gives:
% 222.29/34.55 | (1021) all_980_0 = all_977_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_980_0, all_986_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (415), (420) gives:
% 222.29/34.55 | (1022) all_986_0 = all_980_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_986_0, all_989_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (420), (422) gives:
% 222.29/34.55 | (1023) all_989_0 = all_986_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_989_0, all_995_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (422), (427) gives:
% 222.29/34.55 | (1024) all_995_0 = all_989_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_995_0, all_1004_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (427), (434) gives:
% 222.29/34.55 | (1025) all_1004_0 = all_995_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1004_0, all_1013_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (434), (442) gives:
% 222.29/34.55 | (1026) all_1013_0 = all_1004_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1013_0, all_1030_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (442), (452) gives:
% 222.29/34.55 | (1027) all_1030_1 = all_1013_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1030_1, all_1036_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (452), (457) gives:
% 222.29/34.55 | (1028) all_1036_0 = all_1030_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1073_1, all_1079_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (475), (477) gives:
% 222.29/34.55 | (1029) all_1079_0 = all_1073_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1079_0, all_1082_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (477), (480) gives:
% 222.29/34.55 | (1030) all_1082_0 = all_1079_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1082_0, all_1097_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (480), (490) gives:
% 222.29/34.55 | (1031) all_1097_1 = all_1082_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1097_1, all_1109_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (490), (502) gives:
% 222.29/34.55 | (1032) all_1109_0 = all_1097_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1073_1, all_1118_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (475), (508) gives:
% 222.29/34.55 | (1033) all_1118_1 = all_1073_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1036_0, all_1118_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (457), (508) gives:
% 222.29/34.55 | (1034) all_1118_1 = all_1036_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1109_0, all_1142_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (502), (524) gives:
% 222.29/34.55 | (1035) all_1142_0 = all_1109_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1118_1, all_1145_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (508), (526) gives:
% 222.29/34.55 | (1036) all_1145_0 = all_1118_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1145_0, all_1160_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (526), (538) gives:
% 222.29/34.55 | (1037) all_1160_0 = all_1145_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1142_0, all_1192_1, tc_Int_Oint,
% 222.29/34.55 | simplifying with (524), (561) gives:
% 222.29/34.55 | (1038) all_1192_1 = all_1142_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1192_1, all_1209_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (561), (568) gives:
% 222.29/34.55 | (1039) all_1209_0 = all_1192_1
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1160_0, all_1233_0, tc_Int_Oint,
% 222.29/34.55 | simplifying with (538), (579) gives:
% 222.29/34.55 | (1040) all_1233_0 = all_1160_0
% 222.29/34.55 |
% 222.29/34.55 | GROUND_INST: instantiating (241) with all_1233_0, all_1253_0, tc_Int_Oint,
% 222.29/34.56 | simplifying with (579), (600) gives:
% 222.41/34.56 | (1041) all_1253_0 = all_1233_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1253_0, all_1256_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (600), (602) gives:
% 222.41/34.56 | (1042) all_1256_0 = all_1253_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1256_0, all_1262_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (602), (606) gives:
% 222.41/34.56 | (1043) all_1262_1 = all_1256_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1262_1, all_1265_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (606), (608) gives:
% 222.41/34.56 | (1044) all_1265_0 = all_1262_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1265_0, all_1268_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (608), (610) gives:
% 222.41/34.56 | (1045) all_1268_0 = all_1265_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1274_0, all_1280_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (615), (617) gives:
% 222.41/34.56 | (1046) all_1280_0 = all_1274_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1274_0, all_1289_2, tc_Int_Oint,
% 222.41/34.56 | simplifying with (615), (619) gives:
% 222.41/34.56 | (1047) all_1289_2 = all_1274_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1209_0, all_1289_2, tc_Int_Oint,
% 222.41/34.56 | simplifying with (568), (619) gives:
% 222.41/34.56 | (1048) all_1289_2 = all_1209_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1280_0, all_1309_2, tc_Int_Oint,
% 222.41/34.56 | simplifying with (617), (622) gives:
% 222.41/34.56 | (1049) all_1309_2 = all_1280_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1309_2, all_1315_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (622), (628) gives:
% 222.41/34.56 | (1050) all_1315_1 = all_1309_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1315_1, all_1318_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (628), (630) gives:
% 222.41/34.56 | (1051) all_1318_0 = all_1315_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1318_0, all_1392_2, tc_Int_Oint,
% 222.41/34.56 | simplifying with (630), (672) gives:
% 222.41/34.56 | (1052) all_1392_2 = all_1318_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1392_2, all_1409_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (672), (689) gives:
% 222.41/34.56 | (1053) all_1409_0 = all_1392_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1409_0, all_1412_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (689), (691) gives:
% 222.41/34.56 | (1054) all_1412_0 = all_1409_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1412_0, all_1415_2, tc_Int_Oint,
% 222.41/34.56 | simplifying with (691), (694) gives:
% 222.41/34.56 | (1055) all_1415_2 = all_1412_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1415_2, all_1445_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (694), (710) gives:
% 222.41/34.56 | (1056) all_1445_0 = all_1415_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1445_0, all_1465_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (710), (736) gives:
% 222.41/34.56 | (1057) all_1465_0 = all_1445_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1465_0, all_1474_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (736), (742) gives:
% 222.41/34.56 | (1058) all_1474_1 = all_1465_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1289_2, all_1492_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (619), (757) gives:
% 222.41/34.56 | (1059) all_1492_0 = all_1289_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1271_0, all_1492_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (613), (757) gives:
% 222.41/34.56 | (1060) all_1492_0 = all_1271_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1474_1, all_1537_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (742), (819) gives:
% 222.41/34.56 | (1061) all_1537_1 = all_1474_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1537_1, all_1543_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (819), (823) gives:
% 222.41/34.56 | (1062) all_1543_1 = all_1537_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1492_0, all_1597_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (757), (869) gives:
% 222.41/34.56 | (1063) all_1597_0 = all_1492_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1486_2, all_1597_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (752), (869) gives:
% 222.41/34.56 | (1064) all_1597_0 = all_1486_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1543_1, all_1600_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (823), (871) gives:
% 222.41/34.56 | (1065) all_1600_0 = all_1543_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_830_1, all_1600_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (316), (871) gives:
% 222.41/34.56 | (1066) all_1600_0 = all_830_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1268_0, all_1609_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (610), (877) gives:
% 222.41/34.56 | (1067) all_1609_1 = all_1268_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (241) with all_1055_0, all_1609_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (467), (877) gives:
% 222.41/34.56 | (1068) all_1609_1 = all_1055_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_808_1, all_841_1,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (302), (328) gives:
% 222.41/34.56 | (1069) all_841_1 = all_808_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_841_1, all_852_1,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (328), (335) gives:
% 222.41/34.56 | (1070) all_852_1 = all_841_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_852_1, all_880_2,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (335), (362) gives:
% 222.41/34.56 | (1071) all_880_2 = all_852_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_880_2, all_882_2,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (362), (367) gives:
% 222.41/34.56 | (1072) all_882_2 = all_880_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_882_2, all_1166_4,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (367), (540) gives:
% 222.41/34.56 | (1073) all_1166_4 = all_882_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1166_4, all_1242_5,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (540), (587) gives:
% 222.41/34.56 | (1074) all_1242_5 = all_1166_4
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1242_5, all_1354_7,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (587), (642) gives:
% 222.41/34.56 | (1075) all_1354_7 = all_1242_5
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1354_7, all_1401_8,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (642), (679) gives:
% 222.41/34.56 | (1076) all_1401_8 = all_1354_7
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1401_8, all_1457_9,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (679), (723) gives:
% 222.41/34.56 | (1077) all_1457_9 = all_1401_8
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1457_9, all_1495_10,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (723), (761) gives:
% 222.41/34.56 | (1078) all_1495_10 = all_1457_9
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1495_10, all_1527_11,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (761), (793) gives:
% 222.41/34.56 | (1079) all_1527_11 = all_1495_10
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1527_11, all_1535_12,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (793), (810) gives:
% 222.41/34.56 | (1080) all_1535_12 = all_1527_11
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1535_12, all_1546_1,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (810), (827) gives:
% 222.41/34.56 | (1081) all_1546_1 = all_1535_12
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_1546_1, all_1593_16,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (827), (859) gives:
% 222.41/34.56 | (1082) all_1593_16 = all_1546_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (242) with all_806_1, all_1593_16,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (298), (859) gives:
% 222.41/34.56 | (1083) all_1593_16 = all_806_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (250) with all_856_1, all_1457_1, v_pa____,
% 222.41/34.56 | v_a____, tc_Complex_Ocomplex, simplifying with (343), (724)
% 222.41/34.56 | gives:
% 222.41/34.56 | (1084) all_1457_1 = all_856_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (250) with all_1457_1, all_1495_2, v_pa____,
% 222.41/34.56 | v_a____, tc_Complex_Ocomplex, simplifying with (724), (762)
% 222.41/34.56 | gives:
% 222.41/34.56 | (1085) all_1495_2 = all_1457_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (250) with all_1495_2, all_1527_2, v_pa____,
% 222.41/34.56 | v_a____, tc_Complex_Ocomplex, simplifying with (762), (794)
% 222.41/34.56 | gives:
% 222.41/34.56 | (1086) all_1527_2 = all_1495_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (250) with all_1527_2, all_1535_3, v_pa____,
% 222.41/34.56 | v_a____, tc_Complex_Ocomplex, simplifying with (794), (811)
% 222.41/34.56 | gives:
% 222.41/34.56 | (1087) all_1535_3 = all_1527_2
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (250) with all_1535_3, all_1593_5, v_pa____,
% 222.41/34.56 | v_a____, tc_Complex_Ocomplex, simplifying with (811), (860)
% 222.41/34.56 | gives:
% 222.41/34.56 | (1088) all_1593_5 = all_1535_3
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (250) with all_744_0, all_1593_5, v_pa____,
% 222.41/34.56 | v_a____, tc_Complex_Ocomplex, simplifying with (257), (860)
% 222.41/34.56 | gives:
% 222.41/34.56 | (1089) all_1593_5 = all_744_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_886_0, all_898_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (372), (378) gives:
% 222.41/34.56 | (1090) all_898_0 = all_886_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_817_1, all_898_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (309), (378) gives:
% 222.41/34.56 | (1091) all_898_0 = all_817_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_898_0, all_929_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (378), (386) gives:
% 222.41/34.56 | (1092) all_929_0 = all_898_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_929_0, all_983_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (386), (418) gives:
% 222.41/34.56 | (1093) all_983_0 = all_929_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_983_0, all_998_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (418), (429) gives:
% 222.41/34.56 | (1094) all_998_0 = all_983_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_998_0, all_1010_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (429), (440) gives:
% 222.41/34.56 | (1095) all_1010_0 = all_998_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1010_0, all_1033_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (440), (455) gives:
% 222.41/34.56 | (1096) all_1033_0 = all_1010_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1033_0, all_1052_1, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (455), (465) gives:
% 222.41/34.56 | (1097) all_1052_1 = all_1033_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1052_1, all_1100_1, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (465), (494) gives:
% 222.41/34.56 | (1098) all_1100_1 = all_1052_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1100_1, all_1112_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (494), (504) gives:
% 222.41/34.56 | (1099) all_1112_0 = all_1100_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1112_0, all_1133_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (504), (520) gives:
% 222.41/34.56 | (1100) all_1133_0 = all_1112_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1133_0, all_1174_1, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (520), (547) gives:
% 222.41/34.56 | (1101) all_1174_1 = all_1133_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1174_1, all_1177_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (547), (549) gives:
% 222.41/34.56 | (1102) all_1177_0 = all_1174_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1177_0, all_1236_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (549), (581) gives:
% 222.41/34.56 | (1103) all_1236_0 = all_1177_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1236_0, all_1312_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (581), (626) gives:
% 222.41/34.56 | (1104) all_1312_0 = all_1236_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1312_0, all_1356_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (626), (649) gives:
% 222.41/34.56 | (1105) all_1356_0 = all_1312_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_886_0, all_1359_1, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (372), (651) gives:
% 222.41/34.56 | (1106) all_1359_1 = all_886_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_794_0, all_1359_1, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (289), (651) gives:
% 222.41/34.56 | (1107) all_1359_1 = all_794_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1356_0, all_1365_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (649), (656) gives:
% 222.41/34.56 | (1108) all_1365_0 = all_1356_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1365_0, all_1377_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (656), (665) gives:
% 222.41/34.56 | (1109) all_1377_0 = all_1365_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1377_0, all_1386_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (665), (670) gives:
% 222.41/34.56 | (1110) all_1386_0 = all_1377_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1386_0, all_1448_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (670), (713) gives:
% 222.41/34.56 | (1111) all_1448_0 = all_1386_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_886_0, all_1477_1, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (372), (745) gives:
% 222.41/34.56 | (1112) all_1477_1 = all_886_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_863_0, all_1477_1, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (350), (745) gives:
% 222.41/34.56 | (1113) all_1477_1 = all_863_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1448_0, all_1503_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (713), (774) gives:
% 222.41/34.56 | (1114) all_1503_0 = all_1448_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_892_0, all_1503_0, tc_Nat_Onat,
% 222.41/34.56 | simplifying with (374), (774) gives:
% 222.41/34.56 | (1115) all_1503_0 = all_892_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1401_5, all_1457_6,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (682), (727) gives:
% 222.41/34.56 | (1116) all_1457_6 = all_1401_5
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1457_6, all_1495_7,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (727), (765) gives:
% 222.41/34.56 | (1117) all_1495_7 = all_1457_6
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1495_7, all_1527_7,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (765), (797) gives:
% 222.41/34.56 | (1118) all_1527_7 = all_1495_7
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1401_5, all_1535_8,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (682), (814) gives:
% 222.41/34.56 | (1119) all_1535_8 = all_1401_5
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1354_4, all_1535_8,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (645), (814) gives:
% 222.41/34.56 | (1120) all_1535_8 = all_1354_4
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1527_7, all_1593_11,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (797), (863) gives:
% 222.41/34.56 | (1121) all_1593_11 = all_1527_7
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1242_3, all_1593_11,
% 222.41/34.56 | tc_Complex_Ocomplex, simplifying with (590), (863) gives:
% 222.41/34.56 | (1122) all_1593_11 = all_1242_3
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_938_0, all_947_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (392), (399) gives:
% 222.41/34.56 | (1123) all_947_1 = all_938_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_938_0, all_977_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (392), (413) gives:
% 222.41/34.56 | (1124) all_977_0 = all_938_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_947_1, all_1030_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (399), (453) gives:
% 222.41/34.56 | (1125) all_1030_0 = all_947_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_947_1, all_1061_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (399), (471) gives:
% 222.41/34.56 | (1126) all_1061_1 = all_947_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_977_0, all_1079_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (413), (478) gives:
% 222.41/34.56 | (1127) all_1079_1 = all_977_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1030_0, all_1097_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (453), (491) gives:
% 222.41/34.56 | (1128) all_1097_0 = all_1030_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1061_1, all_1148_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (471), (528) gives:
% 222.41/34.56 | (1129) all_1148_0 = all_1061_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1097_0, all_1154_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (491), (534) gives:
% 222.41/34.56 | (1130) all_1154_0 = all_1097_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1154_0, all_1183_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (534), (555) gives:
% 222.41/34.56 | (1131) all_1183_0 = all_1154_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1061_1, all_1268_1, tc_Int_Oint,
% 222.41/34.56 | simplifying with (471), (611) gives:
% 222.41/34.56 | (1132) all_1268_1 = all_1061_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1079_1, all_1289_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (478), (620) gives:
% 222.41/34.56 | (1133) all_1289_0 = all_1079_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1289_0, all_1309_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (620), (623) gives:
% 222.41/34.56 | (1134) all_1309_0 = all_1289_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_830_0, all_1309_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (317), (623) gives:
% 222.41/34.56 | (1135) all_1309_0 = all_830_0
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_1268_1, all_1324_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (611), (632) gives:
% 222.41/34.56 | (1136) all_1324_0 = all_1268_1
% 222.41/34.56 |
% 222.41/34.56 | GROUND_INST: instantiating (243) with all_832_0, all_1324_0, tc_Int_Oint,
% 222.41/34.56 | simplifying with (321), (632) gives:
% 222.41/34.56 | (1137) all_1324_0 = all_832_0
% 222.41/34.56 |
% 222.41/34.57 | GROUND_INST: instantiating (243) with all_1183_0, all_1392_1, tc_Int_Oint,
% 222.41/34.57 | simplifying with (555), (673) gives:
% 222.41/34.57 | (1138) all_1392_1 = all_1183_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (243) with all_914_0, all_1392_1, tc_Int_Oint,
% 222.41/34.57 | simplifying with (382), (673) gives:
% 222.41/34.57 | (1139) all_1392_1 = all_914_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (243) with all_1148_0, all_1486_0, tc_Int_Oint,
% 222.41/34.57 | simplifying with (528), (753) gives:
% 222.41/34.57 | (1140) all_1486_0 = all_1148_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (243) with all_861_0, all_1486_0, tc_Int_Oint,
% 222.41/34.57 | simplifying with (348), (753) gives:
% 222.41/34.57 | (1141) all_1486_0 = all_861_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (248) with all_1242_4, all_1495_8, v_a____,
% 222.41/34.57 | tc_Complex_Ocomplex, simplifying with (591), (766) gives:
% 222.41/34.57 | (1142) all_1495_8 = all_1242_4
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (248) with all_1457_7, all_1527_8, v_a____,
% 222.41/34.57 | tc_Complex_Ocomplex, simplifying with (728), (798) gives:
% 222.41/34.57 | (1143) all_1527_8 = all_1457_7
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (248) with all_1527_8, all_1535_9, v_a____,
% 222.41/34.57 | tc_Complex_Ocomplex, simplifying with (798), (815) gives:
% 222.41/34.57 | (1144) all_1535_9 = all_1527_8
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (248) with all_1354_5, all_1535_9, v_a____,
% 222.41/34.57 | tc_Complex_Ocomplex, simplifying with (646), (815) gives:
% 222.41/34.57 | (1145) all_1535_9 = all_1354_5
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (248) with all_1495_8, all_1593_12, v_a____,
% 222.41/34.57 | tc_Complex_Ocomplex, simplifying with (766), (864) gives:
% 222.41/34.57 | (1146) all_1593_12 = all_1495_8
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (248) with all_1457_7, all_1593_12, v_a____,
% 222.41/34.57 | tc_Complex_Ocomplex, simplifying with (728), (864) gives:
% 222.41/34.57 | (1147) all_1593_12 = all_1457_7
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (248) with all_1401_6, all_1593_12, v_a____,
% 222.41/34.57 | tc_Complex_Ocomplex, simplifying with (683), (864) gives:
% 222.41/34.57 | (1148) all_1593_12 = all_1401_6
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1186_0, all_1212_0, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (558), (571) gives:
% 222.41/34.57 | (1149) all_1212_0 = all_1186_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1212_0, all_1236_1, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (571), (582) gives:
% 222.41/34.57 | (1150) all_1236_1 = all_1212_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1236_1, all_1247_1, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (582), (596) gives:
% 222.41/34.57 | (1151) all_1247_1 = all_1236_1
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1462_0, all_1477_2, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (734), (746) gives:
% 222.41/34.57 | (1152) all_1477_2 = all_1462_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1451_0, all_1477_2, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (716), (746) gives:
% 222.41/34.57 | (1153) all_1477_2 = all_1451_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1430_2, all_1477_2, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (703), (746) gives:
% 222.41/34.57 | (1154) all_1477_2 = all_1430_2
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1247_1, all_1477_2, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (596), (746) gives:
% 222.41/34.57 | (1155) all_1477_2 = all_1247_1
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1462_0, all_1506_0, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (734), (777) gives:
% 222.41/34.57 | (1156) all_1506_0 = all_1462_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1506_0, all_1521_0, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (777), (784) gives:
% 222.41/34.57 | (1157) all_1521_0 = all_1506_0
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (244) with all_1130_3, all_1521_0, tc_Nat_Onat,
% 222.41/34.57 | simplifying with (516), (784) gives:
% 222.41/34.57 | (1158) all_1521_0 = all_1130_3
% 222.41/34.57 |
% 222.41/34.57 | GROUND_INST: instantiating (249) with all_854_1, all_1180_2, v_pa____,
% 222.41/34.57 | tc_Complex_Ocomplex, simplifying with (339), (553) gives:
% 222.41/34.57 | (1159) all_1180_2 = all_854_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1067), (1068) imply:
% 222.41/34.57 | (1160) all_1268_0 = all_1055_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1160) implies:
% 222.41/34.57 | (1161) all_1268_0 = all_1055_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1003), (1004) imply:
% 222.41/34.57 | (1162) all_1555_1 = all_791_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1162) implies:
% 222.41/34.57 | (1163) all_1555_1 = all_791_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (999), (1002) imply:
% 222.41/34.57 | (1164) all_1509_0 = all_1067_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (999), (1000) imply:
% 222.41/34.57 | (1165) all_1509_0 = all_1477_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (999), (1001) imply:
% 222.41/34.57 | (1166) all_1509_0 = all_1421_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1065), (1066) imply:
% 222.41/34.57 | (1167) all_1543_1 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1167) implies:
% 222.41/34.57 | (1168) all_1543_1 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1063), (1064) imply:
% 222.41/34.57 | (1169) all_1492_0 = all_1486_2
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1169) implies:
% 222.41/34.57 | (1170) all_1492_0 = all_1486_2
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1088), (1089) imply:
% 222.41/34.57 | (1171) all_1535_3 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1171) implies:
% 222.41/34.57 | (1172) all_1535_3 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1121), (1122) imply:
% 222.41/34.57 | (1173) all_1527_7 = all_1242_3
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1173) implies:
% 222.41/34.57 | (1174) all_1527_7 = all_1242_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1147), (1148) imply:
% 222.41/34.57 | (1175) all_1457_7 = all_1401_6
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1175) implies:
% 222.41/34.57 | (1176) all_1457_7 = all_1401_6
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1146), (1148) imply:
% 222.41/34.57 | (1177) all_1495_8 = all_1401_6
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1177) implies:
% 222.41/34.57 | (1178) all_1495_8 = all_1401_6
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1082), (1083) imply:
% 222.41/34.57 | (1179) all_1546_1 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1179) implies:
% 222.41/34.57 | (1180) all_1546_1 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (997), (998) imply:
% 222.41/34.57 | (1181) all_1549_0 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1181) implies:
% 222.41/34.57 | (1182) all_1549_0 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (995), (996) imply:
% 222.41/34.57 | (1183) all_1564_0 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1183) implies:
% 222.41/34.57 | (1184) all_1564_0 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (994), (1184) imply:
% 222.41/34.57 | (1185) all_1558_0 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1185) implies:
% 222.41/34.57 | (1186) all_1558_0 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (992), (993) imply:
% 222.41/34.57 | (1187) all_1503_1 = all_1489_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1187) implies:
% 222.41/34.57 | (1188) all_1503_1 = all_1489_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (991), (1186) imply:
% 222.41/34.57 | (1189) all_1532_2 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1189) implies:
% 222.41/34.57 | (1190) all_1532_2 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (990), (1163) imply:
% 222.41/34.57 | (1191) all_1471_1 = all_791_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1191) implies:
% 222.41/34.57 | (1192) all_1471_1 = all_791_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (986), (988) imply:
% 222.41/34.57 | (1193) all_1204_2 = all_812_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1193) implies:
% 222.41/34.57 | (1194) all_1204_2 = all_812_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (988), (989) imply:
% 222.41/34.57 | (1195) all_812_0 = all_788_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (987), (988) imply:
% 222.41/34.57 | (1196) all_1039_0 = all_812_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1196) implies:
% 222.41/34.57 | (1197) all_1039_0 = all_812_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (985), (1182) imply:
% 222.41/34.57 | (1198) all_1524_2 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1198) implies:
% 222.41/34.57 | (1199) all_1524_2 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1081), (1180) imply:
% 222.41/34.57 | (1200) all_1535_12 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1200) implies:
% 222.41/34.57 | (1201) all_1535_12 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (983), (984) imply:
% 222.41/34.57 | (1202) all_1121_0 = all_957_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1202) implies:
% 222.41/34.57 | (1203) all_1121_0 = all_957_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1006), (1007) imply:
% 222.41/34.57 | (1204) all_1180_1 = all_1151_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1006), (1008) imply:
% 222.41/34.57 | (1205) all_1180_1 = all_854_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1062), (1168) imply:
% 222.41/34.57 | (1206) all_1537_1 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1206) implies:
% 222.41/34.57 | (1207) all_1537_1 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (981), (982) imply:
% 222.41/34.57 | (1208) all_1512_1 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1208) implies:
% 222.41/34.57 | (1209) all_1512_1 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1061), (1207) imply:
% 222.41/34.57 | (1210) all_1474_1 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1210) implies:
% 222.41/34.57 | (1211) all_1474_1 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1087), (1172) imply:
% 222.41/34.57 | (1212) all_1527_2 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1212) implies:
% 222.41/34.57 | (1213) all_1527_2 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1119), (1120) imply:
% 222.41/34.57 | (1214) all_1401_5 = all_1354_4
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1214) implies:
% 222.41/34.57 | (1215) all_1401_5 = all_1354_4
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1144), (1145) imply:
% 222.41/34.57 | (1216) all_1527_8 = all_1354_5
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1216) implies:
% 222.41/34.57 | (1217) all_1527_8 = all_1354_5
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1080), (1201) imply:
% 222.41/34.57 | (1218) all_1527_11 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1218) implies:
% 222.41/34.57 | (1219) all_1527_11 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (980), (1190) imply:
% 222.41/34.57 | (1220) all_1500_1 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1220) implies:
% 222.41/34.57 | (1221) all_1500_1 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1086), (1213) imply:
% 222.41/34.57 | (1222) all_1495_2 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1222) implies:
% 222.41/34.57 | (1223) all_1495_2 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1118), (1174) imply:
% 222.41/34.57 | (1224) all_1495_7 = all_1242_3
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1224) implies:
% 222.41/34.57 | (1225) all_1495_7 = all_1242_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1143), (1217) imply:
% 222.41/34.57 | (1226) all_1457_7 = all_1354_5
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1226) implies:
% 222.41/34.57 | (1227) all_1457_7 = all_1354_5
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1079), (1219) imply:
% 222.41/34.57 | (1228) all_1495_10 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1228) implies:
% 222.41/34.57 | (1229) all_1495_10 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (979), (1199) imply:
% 222.41/34.57 | (1230) all_1521_1 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1230) implies:
% 222.41/34.57 | (1231) all_1521_1 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1157), (1158) imply:
% 222.41/34.57 | (1232) all_1506_0 = all_1130_3
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1232) implies:
% 222.41/34.57 | (1233) all_1506_0 = all_1130_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (978), (1231) imply:
% 222.41/34.57 | (1234) all_1506_1 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1234) implies:
% 222.41/34.57 | (1235) all_1506_1 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (977), (1209) imply:
% 222.41/34.57 | (1236) all_1483_0 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1236) implies:
% 222.41/34.57 | (1237) all_1483_0 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1165), (1166) imply:
% 222.41/34.57 | (1238) all_1477_3 = all_1421_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1164), (1165) imply:
% 222.41/34.57 | (1239) all_1477_3 = all_1067_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1156), (1233) imply:
% 222.41/34.57 | (1240) all_1462_0 = all_1130_3
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1240) implies:
% 222.41/34.57 | (1241) all_1462_0 = all_1130_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (976), (1235) imply:
% 222.41/34.57 | (1242) all_1427_0 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1242) implies:
% 222.41/34.57 | (1243) all_1427_0 = all_1088_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1114), (1115) imply:
% 222.41/34.57 | (1244) all_1448_0 = all_892_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1244) implies:
% 222.41/34.57 | (1245) all_1448_0 = all_892_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (974), (1188) imply:
% 222.41/34.57 | (1246) all_1489_1 = all_1094_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (973), (1188) imply:
% 222.41/34.57 | (1247) all_1489_1 = all_1157_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (975), (1188) imply:
% 222.41/34.57 | (1248) all_1489_1 = all_1049_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (972), (1188) imply:
% 222.41/34.57 | (1249) all_1489_1 = all_1406_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (971), (1221) imply:
% 222.41/34.57 | (1250) all_1430_1 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1250) implies:
% 222.41/34.57 | (1251) all_1430_1 = all_921_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (969), (970) imply:
% 222.41/34.57 | (1252) all_1454_0 = all_1398_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1252) implies:
% 222.41/34.57 | (1253) all_1454_0 = all_1398_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1085), (1223) imply:
% 222.41/34.57 | (1254) all_1457_1 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1254) implies:
% 222.41/34.57 | (1255) all_1457_1 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1117), (1225) imply:
% 222.41/34.57 | (1256) all_1457_6 = all_1242_3
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1256) implies:
% 222.41/34.57 | (1257) all_1457_6 = all_1242_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1142), (1178) imply:
% 222.41/34.57 | (1258) all_1401_6 = all_1242_4
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1258) implies:
% 222.41/34.57 | (1259) all_1401_6 = all_1242_4
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1078), (1229) imply:
% 222.41/34.57 | (1260) all_1457_9 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1260) implies:
% 222.41/34.57 | (1261) all_1457_9 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1059), (1170) imply:
% 222.41/34.57 | (1262) all_1486_2 = all_1289_2
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1060), (1170) imply:
% 222.41/34.57 | (1263) all_1486_2 = all_1271_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1246), (1248) imply:
% 222.41/34.57 | (1264) all_1094_0 = all_1049_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1264) implies:
% 222.41/34.57 | (1265) all_1094_0 = all_1049_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1247), (1248) imply:
% 222.41/34.57 | (1266) all_1157_0 = all_1049_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1266) implies:
% 222.41/34.57 | (1267) all_1157_0 = all_1049_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1248), (1249) imply:
% 222.41/34.57 | (1268) all_1406_1 = all_1049_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1268) implies:
% 222.41/34.57 | (1269) all_1406_1 = all_1049_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1140), (1141) imply:
% 222.41/34.57 | (1270) all_1148_0 = all_861_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1270) implies:
% 222.41/34.57 | (1271) all_1148_0 = all_861_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1262), (1263) imply:
% 222.41/34.57 | (1272) all_1289_2 = all_1271_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1272) implies:
% 222.41/34.57 | (1273) all_1289_2 = all_1271_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (968), (1237) imply:
% 222.41/34.57 | (1274) all_1459_0 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1274) implies:
% 222.41/34.57 | (1275) all_1459_0 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (965), (967) imply:
% 222.41/34.57 | (1276) all_1362_0 = all_932_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (965), (966) imply:
% 222.41/34.57 | (1277) all_1362_0 = all_1250_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1112), (1113) imply:
% 222.41/34.57 | (1278) all_886_0 = all_863_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1278) implies:
% 222.41/34.57 | (1279) all_886_0 = all_863_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1152), (1153) imply:
% 222.41/34.57 | (1280) all_1462_0 = all_1451_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1280) implies:
% 222.41/34.57 | (1281) all_1462_0 = all_1451_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1153), (1155) imply:
% 222.41/34.57 | (1282) all_1451_0 = all_1247_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1153), (1154) imply:
% 222.41/34.57 | (1283) all_1451_0 = all_1430_2
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1238), (1239) imply:
% 222.41/34.57 | (1284) all_1421_0 = all_1067_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1284) implies:
% 222.41/34.57 | (1285) all_1421_0 = all_1067_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1058), (1211) imply:
% 222.41/34.57 | (1286) all_1465_0 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1286) implies:
% 222.41/34.57 | (1287) all_1465_0 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (964), (1192) imply:
% 222.41/34.57 | (1288) all_1371_0 = all_791_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1288) implies:
% 222.41/34.57 | (1289) all_1371_0 = all_791_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (962), (963) imply:
% 222.41/34.57 | (1290) all_1174_0 = all_871_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1290) implies:
% 222.41/34.57 | (1291) all_1174_0 = all_871_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1057), (1287) imply:
% 222.41/34.57 | (1292) all_1445_0 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1292) implies:
% 222.41/34.57 | (1293) all_1445_0 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1241), (1281) imply:
% 222.41/34.57 | (1294) all_1451_0 = all_1130_3
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1294) implies:
% 222.41/34.57 | (1295) all_1451_0 = all_1130_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (960), (961) imply:
% 222.41/34.57 | (1296) all_1168_0 = all_1106_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1296) implies:
% 222.41/34.57 | (1297) all_1168_0 = all_1106_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (959), (961) imply:
% 222.41/34.57 | (1298) all_1406_1 = all_1106_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1298) implies:
% 222.41/34.57 | (1299) all_1406_1 = all_1106_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (958), (1275) imply:
% 222.41/34.57 | (1300) all_1454_0 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1300) implies:
% 222.41/34.57 | (1301) all_1454_0 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1084), (1255) imply:
% 222.41/34.57 | (1302) all_856_1 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1302) implies:
% 222.41/34.57 | (1303) all_856_1 = all_744_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1116), (1257) imply:
% 222.41/34.57 | (1304) all_1401_5 = all_1242_3
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1304) implies:
% 222.41/34.57 | (1305) all_1401_5 = all_1242_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1176), (1227) imply:
% 222.41/34.57 | (1306) all_1401_6 = all_1354_5
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1306) implies:
% 222.41/34.57 | (1307) all_1401_6 = all_1354_5
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1077), (1261) imply:
% 222.41/34.57 | (1308) all_1401_8 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1308) implies:
% 222.41/34.57 | (1309) all_1401_8 = all_806_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1253), (1301) imply:
% 222.41/34.57 | (1310) all_1398_0 = all_754_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (957), (1253) imply:
% 222.41/34.57 | (1311) all_1398_0 = all_1312_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (956), (1253) imply:
% 222.41/34.57 | (1312) all_1398_0 = all_1365_2
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1282), (1283) imply:
% 222.41/34.57 | (1313) all_1430_2 = all_1247_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1283), (1295) imply:
% 222.41/34.57 | (1314) all_1430_2 = all_1130_3
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (952), (953) imply:
% 222.41/34.57 | (1315) all_1377_1 = all_1139_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (952), (955) imply:
% 222.41/34.57 | (1316) all_1377_1 = all_875_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (952), (954) imply:
% 222.41/34.57 | (1317) all_1377_1 = all_1001_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1111), (1245) imply:
% 222.41/34.57 | (1318) all_1386_0 = all_892_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1318) implies:
% 222.41/34.57 | (1319) all_1386_0 = all_892_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (950), (951) imply:
% 222.41/34.57 | (1320) all_1022_0 = all_764_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1320) implies:
% 222.41/34.57 | (1321) all_1022_0 = all_764_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (1056), (1293) imply:
% 222.41/34.57 | (1322) all_1415_2 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1322) implies:
% 222.41/34.57 | (1323) all_1415_2 = all_830_1
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (947), (948) imply:
% 222.41/34.57 | (1324) all_1374_0 = all_1168_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (947), (949) imply:
% 222.41/34.57 | (1325) all_1374_0 = all_814_0
% 222.41/34.57 |
% 222.41/34.57 | COMBINE_EQS: (945), (946) imply:
% 222.41/34.57 | (1326) all_769_0 = all_767_0
% 222.41/34.57 |
% 222.41/34.57 | SIMP: (1326) implies:
% 222.41/34.57 | (1327) all_769_0 = all_767_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (944), (946) imply:
% 222.41/34.58 | (1328) all_778_0 = all_767_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1328) implies:
% 222.41/34.58 | (1329) all_778_0 = all_767_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (943), (1251) imply:
% 222.41/34.58 | (1330) all_1368_0 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1330) implies:
% 222.41/34.58 | (1331) all_1368_0 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1313), (1314) imply:
% 222.41/34.58 | (1332) all_1247_1 = all_1130_3
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1332) implies:
% 222.41/34.58 | (1333) all_1247_1 = all_1130_3
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (942), (1243) imply:
% 222.41/34.58 | (1334) all_1383_0 = all_1088_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1334) implies:
% 222.41/34.58 | (1335) all_1383_0 = all_1088_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (941), (1285) imply:
% 222.41/34.58 | (1336) all_1186_2 = all_1067_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1336) implies:
% 222.41/34.58 | (1337) all_1186_2 = all_1067_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1055), (1323) imply:
% 222.41/34.58 | (1338) all_1412_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1338) implies:
% 222.41/34.58 | (1339) all_1412_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (939), (940) imply:
% 222.41/34.58 | (1340) all_1244_0 = all_992_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1340) implies:
% 222.41/34.58 | (1341) all_1244_0 = all_992_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1054), (1339) imply:
% 222.41/34.58 | (1342) all_1409_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1342) implies:
% 222.41/34.58 | (1343) all_1409_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1053), (1343) imply:
% 222.41/34.58 | (1344) all_1392_2 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1344) implies:
% 222.41/34.58 | (1345) all_1392_2 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (935), (937) imply:
% 222.41/34.58 | (1346) all_1348_0 = all_935_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (935), (936) imply:
% 222.41/34.58 | (1347) all_1348_0 = all_941_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (935), (1299) imply:
% 222.41/34.58 | (1348) all_1348_0 = all_1106_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (935), (938) imply:
% 222.41/34.58 | (1349) all_1348_0 = all_895_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (935), (1269) imply:
% 222.41/34.58 | (1350) all_1348_0 = all_1049_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1215), (1305) imply:
% 222.41/34.58 | (1351) all_1354_4 = all_1242_3
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1351) implies:
% 222.41/34.58 | (1352) all_1354_4 = all_1242_3
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1259), (1307) imply:
% 222.41/34.58 | (1353) all_1354_5 = all_1242_4
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1076), (1309) imply:
% 222.41/34.58 | (1354) all_1354_7 = all_806_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1354) implies:
% 222.41/34.58 | (1355) all_1354_7 = all_806_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1311), (1312) imply:
% 222.41/34.58 | (1356) all_1365_2 = all_1312_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1310), (1312) imply:
% 222.41/34.58 | (1357) all_1365_2 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1138), (1139) imply:
% 222.41/34.58 | (1358) all_1183_0 = all_914_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1358) implies:
% 222.41/34.58 | (1359) all_1183_0 = all_914_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1052), (1345) imply:
% 222.41/34.58 | (1360) all_1318_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1360) implies:
% 222.41/34.58 | (1361) all_1318_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1110), (1319) imply:
% 222.41/34.58 | (1362) all_1377_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1362) implies:
% 222.41/34.58 | (1363) all_1377_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (933), (934) imply:
% 222.41/34.58 | (1364) all_1100_0 = all_746_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1364) implies:
% 222.41/34.58 | (1365) all_1100_0 = all_746_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (932), (1335) imply:
% 222.41/34.58 | (1366) all_1139_1 = all_1088_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1366) implies:
% 222.41/34.58 | (1367) all_1139_1 = all_1088_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1109), (1363) imply:
% 222.41/34.58 | (1368) all_1365_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1368) implies:
% 222.41/34.58 | (1369) all_1365_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1316), (1317) imply:
% 222.41/34.58 | (1370) all_1001_1 = all_875_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1315), (1317) imply:
% 222.41/34.58 | (1371) all_1139_1 = all_1001_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1371) implies:
% 222.41/34.58 | (1372) all_1139_1 = all_1001_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1324), (1325) imply:
% 222.41/34.58 | (1373) all_1168_0 = all_814_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1373) implies:
% 222.41/34.58 | (1374) all_1168_0 = all_814_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (931), (1289) imply:
% 222.41/34.58 | (1375) all_1259_1 = all_791_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1375) implies:
% 222.41/34.58 | (1376) all_1259_1 = all_791_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (930), (1331) imply:
% 222.41/34.58 | (1377) all_1230_2 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1377) implies:
% 222.41/34.58 | (1378) all_1230_2 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1108), (1369) imply:
% 222.41/34.58 | (1379) all_1356_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1379) implies:
% 222.41/34.58 | (1380) all_1356_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1356), (1357) imply:
% 222.41/34.58 | (1381) all_1312_1 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1381) implies:
% 222.41/34.58 | (1382) all_1312_1 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1276), (1277) imply:
% 222.41/34.58 | (1383) all_1250_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1383) implies:
% 222.41/34.58 | (1384) all_1250_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1106), (1107) imply:
% 222.41/34.58 | (1385) all_886_0 = all_794_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1385) implies:
% 222.41/34.58 | (1386) all_886_0 = all_794_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1105), (1380) imply:
% 222.41/34.58 | (1387) all_1312_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1387) implies:
% 222.41/34.58 | (1388) all_1312_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1075), (1355) imply:
% 222.41/34.58 | (1389) all_1242_5 = all_806_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1389) implies:
% 222.41/34.58 | (1390) all_1242_5 = all_806_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (928), (929) imply:
% 222.41/34.58 | (1391) all_1239_0 = all_1042_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1391) implies:
% 222.41/34.58 | (1392) all_1239_0 = all_1042_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1346), (1348) imply:
% 222.41/34.58 | (1393) all_1106_0 = all_935_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1393) implies:
% 222.41/34.58 | (1394) all_1106_0 = all_935_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1346), (1349) imply:
% 222.41/34.58 | (1395) all_935_0 = all_895_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1346), (1347) imply:
% 222.41/34.58 | (1396) all_941_0 = all_935_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1396) implies:
% 222.41/34.58 | (1397) all_941_0 = all_935_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1346), (1350) imply:
% 222.41/34.58 | (1398) all_1049_0 = all_935_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1398) implies:
% 222.41/34.58 | (1399) all_1049_0 = all_935_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1136), (1137) imply:
% 222.41/34.58 | (1400) all_1268_1 = all_832_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1400) implies:
% 222.41/34.58 | (1401) all_1268_1 = all_832_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1051), (1361) imply:
% 222.41/34.58 | (1402) all_1315_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1402) implies:
% 222.41/34.58 | (1403) all_1315_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1050), (1403) imply:
% 222.41/34.58 | (1404) all_1309_2 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1404) implies:
% 222.41/34.58 | (1405) all_1309_2 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1104), (1388) imply:
% 222.41/34.58 | (1406) all_1236_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1406) implies:
% 222.41/34.58 | (1407) all_1236_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (927), (1382) imply:
% 222.41/34.58 | (1408) all_1133_1 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1408) implies:
% 222.41/34.58 | (1409) all_1133_1 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1134), (1135) imply:
% 222.41/34.58 | (1410) all_1289_0 = all_830_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1410) implies:
% 222.41/34.58 | (1411) all_1289_0 = all_830_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1049), (1405) imply:
% 222.41/34.58 | (1412) all_1280_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1412) implies:
% 222.41/34.58 | (1413) all_1280_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1133), (1411) imply:
% 222.41/34.58 | (1414) all_1079_1 = all_830_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1414) implies:
% 222.41/34.58 | (1415) all_1079_1 = all_830_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1047), (1273) imply:
% 222.41/34.58 | (1416) all_1274_0 = all_1271_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1416) implies:
% 222.41/34.58 | (1417) all_1274_0 = all_1271_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1048), (1273) imply:
% 222.41/34.58 | (1418) all_1271_0 = all_1209_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1046), (1413) imply:
% 222.41/34.58 | (1419) all_1274_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1419) implies:
% 222.41/34.58 | (1420) all_1274_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1417), (1420) imply:
% 222.41/34.58 | (1421) all_1271_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1421) implies:
% 222.41/34.58 | (1422) all_1271_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1418), (1422) imply:
% 222.41/34.58 | (1423) all_1209_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1423) implies:
% 222.41/34.58 | (1424) all_1209_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1045), (1161) imply:
% 222.41/34.58 | (1425) all_1265_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1425) implies:
% 222.41/34.58 | (1426) all_1265_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1132), (1401) imply:
% 222.41/34.58 | (1427) all_1061_1 = all_832_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1427) implies:
% 222.41/34.58 | (1428) all_1061_1 = all_832_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1044), (1426) imply:
% 222.41/34.58 | (1429) all_1262_1 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1429) implies:
% 222.41/34.58 | (1430) all_1262_1 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1043), (1430) imply:
% 222.41/34.58 | (1431) all_1256_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1431) implies:
% 222.41/34.58 | (1432) all_1256_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (926), (1376) imply:
% 222.41/34.58 | (1433) all_1115_0 = all_791_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1433) implies:
% 222.41/34.58 | (1434) all_1115_0 = all_791_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1042), (1432) imply:
% 222.41/34.58 | (1435) all_1253_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1435) implies:
% 222.41/34.58 | (1436) all_1253_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1041), (1436) imply:
% 222.41/34.58 | (1437) all_1233_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1437) implies:
% 222.41/34.58 | (1438) all_1233_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (925), (1384) imply:
% 222.41/34.58 | (1439) all_1171_1 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1439) implies:
% 222.41/34.58 | (1440) all_1171_1 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (922), (923) imply:
% 222.41/34.58 | (1441) all_1212_1 = all_1091_2
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1441) implies:
% 222.41/34.58 | (1442) all_1212_1 = all_1091_2
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (923), (924) imply:
% 222.41/34.58 | (1443) all_1091_2 = all_1019_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1151), (1333) imply:
% 222.41/34.58 | (1444) all_1236_1 = all_1130_3
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1444) implies:
% 222.41/34.58 | (1445) all_1236_1 = all_1130_3
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (921), (1341) imply:
% 222.41/34.58 | (1446) all_1121_0 = all_992_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1446) implies:
% 222.41/34.58 | (1447) all_1121_0 = all_992_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1074), (1390) imply:
% 222.41/34.58 | (1448) all_1166_4 = all_806_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1448) implies:
% 222.41/34.58 | (1449) all_1166_4 = all_806_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (920), (1392) imply:
% 222.41/34.58 | (1450) all_1157_0 = all_1042_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1450) implies:
% 222.41/34.58 | (1451) all_1157_0 = all_1042_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1103), (1407) imply:
% 222.41/34.58 | (1452) all_1177_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1452) implies:
% 222.41/34.58 | (1453) all_1177_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1150), (1445) imply:
% 222.41/34.58 | (1454) all_1212_0 = all_1130_3
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1454) implies:
% 222.41/34.58 | (1455) all_1212_0 = all_1130_3
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1040), (1438) imply:
% 222.41/34.58 | (1456) all_1160_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1456) implies:
% 222.41/34.58 | (1457) all_1160_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (918), (919) imply:
% 222.41/34.58 | (1458) all_1224_2 = all_1212_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (918), (1378) imply:
% 222.41/34.58 | (1459) all_1224_2 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1458), (1459) imply:
% 222.41/34.58 | (1460) all_1212_1 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1460) implies:
% 222.41/34.58 | (1461) all_1212_1 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1149), (1455) imply:
% 222.41/34.58 | (1462) all_1186_0 = all_1130_3
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1462) implies:
% 222.41/34.58 | (1463) all_1186_0 = all_1130_3
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1442), (1461) imply:
% 222.41/34.58 | (1464) all_1091_2 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1464) implies:
% 222.41/34.58 | (1465) all_1091_2 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1039), (1424) imply:
% 222.41/34.58 | (1466) all_1192_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1466) implies:
% 222.41/34.58 | (1467) all_1192_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (915), (917) imply:
% 222.41/34.58 | (1468) all_1124_1 = all_783_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (915), (916) imply:
% 222.41/34.58 | (1469) all_1124_1 = all_944_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (915), (1194) imply:
% 222.41/34.58 | (1470) all_1124_1 = all_812_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (913), (914) imply:
% 222.41/34.58 | (1471) all_1094_0 = all_1058_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1471) implies:
% 222.41/34.58 | (1472) all_1094_0 = all_1058_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1038), (1467) imply:
% 222.41/34.58 | (1473) all_1142_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1473) implies:
% 222.41/34.58 | (1474) all_1142_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (912), (1337) imply:
% 222.41/34.58 | (1475) all_1067_0 = all_1027_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (911), (1337) imply:
% 222.41/34.58 | (1476) all_1115_0 = all_1067_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1476) implies:
% 222.41/34.58 | (1477) all_1115_0 = all_1067_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1131), (1359) imply:
% 222.41/34.58 | (1478) all_1154_0 = all_914_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1478) implies:
% 222.41/34.58 | (1479) all_1154_0 = all_914_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1204), (1205) imply:
% 222.41/34.58 | (1480) all_1151_1 = all_854_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1480) implies:
% 222.41/34.58 | (1481) all_1151_1 = all_854_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1102), (1453) imply:
% 222.41/34.58 | (1482) all_1174_1 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1482) implies:
% 222.41/34.58 | (1483) all_1174_1 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (909), (1291) imply:
% 222.41/34.58 | (1484) all_884_0 = all_871_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1484) implies:
% 222.41/34.58 | (1485) all_884_0 = all_871_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (910), (1291) imply:
% 222.41/34.58 | (1486) all_871_1 = all_868_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1101), (1483) imply:
% 222.41/34.58 | (1487) all_1133_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1487) implies:
% 222.41/34.58 | (1488) all_1133_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (908), (1440) imply:
% 222.41/34.58 | (1489) all_1103_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1489) implies:
% 222.41/34.58 | (1490) all_1103_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1297), (1374) imply:
% 222.41/34.58 | (1491) all_1106_0 = all_814_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1491) implies:
% 222.41/34.58 | (1492) all_1106_0 = all_814_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1073), (1449) imply:
% 222.41/34.58 | (1493) all_882_2 = all_806_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1493) implies:
% 222.41/34.58 | (1494) all_882_2 = all_806_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1037), (1457) imply:
% 222.41/34.58 | (1495) all_1145_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1495) implies:
% 222.41/34.58 | (1496) all_1145_0 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1267), (1451) imply:
% 222.41/34.58 | (1497) all_1049_0 = all_1042_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1497) implies:
% 222.41/34.58 | (1498) all_1049_0 = all_1042_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1130), (1479) imply:
% 222.41/34.58 | (1499) all_1097_0 = all_914_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1499) implies:
% 222.41/34.58 | (1500) all_1097_0 = all_914_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1005), (1481) imply:
% 222.41/34.58 | (1501) all_854_0 = all_752_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1501) implies:
% 222.41/34.58 | (1502) all_854_0 = all_752_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1129), (1271) imply:
% 222.41/34.58 | (1503) all_1061_1 = all_861_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1503) implies:
% 222.41/34.58 | (1504) all_1061_1 = all_861_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1036), (1496) imply:
% 222.41/34.58 | (1505) all_1118_1 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1505) implies:
% 222.41/34.58 | (1506) all_1118_1 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1035), (1474) imply:
% 222.41/34.58 | (1507) all_1109_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1507) implies:
% 222.41/34.58 | (1508) all_1109_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (907), (1367) imply:
% 222.41/34.58 | (1509) all_1100_0 = all_1088_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1509) implies:
% 222.41/34.58 | (1510) all_1100_0 = all_1088_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1367), (1372) imply:
% 222.41/34.58 | (1511) all_1088_0 = all_1001_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1100), (1488) imply:
% 222.41/34.58 | (1512) all_1112_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1512) implies:
% 222.41/34.58 | (1513) all_1112_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (906), (1409) imply:
% 222.41/34.58 | (1514) all_1130_2 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1514) implies:
% 222.41/34.58 | (1515) all_1130_2 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (905), (1515) imply:
% 222.41/34.58 | (1516) all_1016_0 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1516) implies:
% 222.41/34.58 | (1517) all_1016_0 = all_754_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1469), (1470) imply:
% 222.41/34.58 | (1518) all_944_0 = all_812_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1468), (1469) imply:
% 222.41/34.58 | (1519) all_944_0 = all_783_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (903), (1447) imply:
% 222.41/34.58 | (1520) all_992_1 = all_983_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1203), (1447) imply:
% 222.41/34.58 | (1521) all_992_1 = all_957_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (904), (1447) imply:
% 222.41/34.58 | (1522) all_992_1 = all_817_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1034), (1506) imply:
% 222.41/34.58 | (1523) all_1055_0 = all_1036_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1033), (1506) imply:
% 222.41/34.58 | (1524) all_1073_1 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1524) implies:
% 222.41/34.58 | (1525) all_1073_1 = all_1055_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1434), (1477) imply:
% 222.41/34.58 | (1526) all_1067_0 = all_791_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1526) implies:
% 222.41/34.58 | (1527) all_1067_0 = all_791_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1099), (1513) imply:
% 222.41/34.58 | (1528) all_1100_1 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1528) implies:
% 222.41/34.58 | (1529) all_1100_1 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1032), (1508) imply:
% 222.41/34.58 | (1530) all_1097_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1530) implies:
% 222.41/34.58 | (1531) all_1097_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1394), (1492) imply:
% 222.41/34.58 | (1532) all_935_0 = all_814_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1532) implies:
% 222.41/34.58 | (1533) all_935_0 = all_814_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (902), (1490) imply:
% 222.41/34.58 | (1534) all_1094_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1534) implies:
% 222.41/34.58 | (1535) all_1094_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1365), (1510) imply:
% 222.41/34.58 | (1536) all_1088_0 = all_746_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1536) implies:
% 222.41/34.58 | (1537) all_1088_0 = all_746_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1098), (1529) imply:
% 222.41/34.58 | (1538) all_1052_1 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1538) implies:
% 222.41/34.58 | (1539) all_1052_1 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1128), (1500) imply:
% 222.41/34.58 | (1540) all_1030_0 = all_914_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1540) implies:
% 222.41/34.58 | (1541) all_1030_0 = all_914_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1031), (1531) imply:
% 222.41/34.58 | (1542) all_1082_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1542) implies:
% 222.41/34.58 | (1543) all_1082_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1472), (1535) imply:
% 222.41/34.58 | (1544) all_1058_1 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1265), (1472) imply:
% 222.41/34.58 | (1545) all_1058_1 = all_1049_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1443), (1465) imply:
% 222.41/34.58 | (1546) all_1019_0 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1546) implies:
% 222.41/34.58 | (1547) all_1019_0 = all_921_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1511), (1537) imply:
% 222.41/34.58 | (1548) all_1001_1 = all_746_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1548) implies:
% 222.41/34.58 | (1549) all_1001_1 = all_746_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1030), (1543) imply:
% 222.41/34.58 | (1550) all_1079_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1550) implies:
% 222.41/34.58 | (1551) all_1079_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1029), (1551) imply:
% 222.41/34.58 | (1552) all_1073_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1552) implies:
% 222.41/34.58 | (1553) all_1073_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1127), (1415) imply:
% 222.41/34.58 | (1554) all_977_0 = all_830_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1554) implies:
% 222.41/34.58 | (1555) all_977_0 = all_830_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1525), (1553) imply:
% 222.41/34.58 | (1556) all_1055_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1556) implies:
% 222.41/34.58 | (1557) all_1055_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1475), (1527) imply:
% 222.41/34.58 | (1558) all_1027_0 = all_791_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1558) implies:
% 222.41/34.58 | (1559) all_1027_0 = all_791_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1126), (1504) imply:
% 222.41/34.58 | (1560) all_947_1 = all_861_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1560) implies:
% 222.41/34.58 | (1561) all_947_1 = all_861_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1428), (1504) imply:
% 222.41/34.58 | (1562) all_861_0 = all_832_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1544), (1545) imply:
% 222.41/34.58 | (1563) all_1049_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1563) implies:
% 222.41/34.58 | (1564) all_1049_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1523), (1557) imply:
% 222.41/34.58 | (1565) all_1036_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1565) implies:
% 222.41/34.58 | (1566) all_1036_0 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1097), (1539) imply:
% 222.41/34.58 | (1567) all_1033_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1567) implies:
% 222.41/34.58 | (1568) all_1033_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1399), (1498) imply:
% 222.41/34.58 | (1569) all_1042_0 = all_935_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1498), (1564) imply:
% 222.41/34.58 | (1570) all_1042_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1569), (1570) imply:
% 222.41/34.58 | (1571) all_935_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1571) implies:
% 222.41/34.58 | (1572) all_935_0 = all_932_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (900), (1197) imply:
% 222.41/34.58 | (1573) all_812_0 = all_780_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1573) implies:
% 222.41/34.58 | (1574) all_812_0 = all_780_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (900), (901) imply:
% 222.41/34.58 | (1575) all_780_0 = all_778_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1028), (1566) imply:
% 222.41/34.58 | (1576) all_1030_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1576) implies:
% 222.41/34.58 | (1577) all_1030_1 = all_830_1
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1096), (1568) imply:
% 222.41/34.58 | (1578) all_1010_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | SIMP: (1578) implies:
% 222.41/34.58 | (1579) all_1010_0 = all_892_0
% 222.41/34.58 |
% 222.41/34.58 | COMBINE_EQS: (1125), (1541) imply:
% 222.41/34.59 | (1580) all_947_1 = all_914_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1580) implies:
% 222.41/34.59 | (1581) all_947_1 = all_914_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1027), (1577) imply:
% 222.41/34.59 | (1582) all_1013_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1582) implies:
% 222.41/34.59 | (1583) all_1013_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (899), (1559) imply:
% 222.41/34.59 | (1584) all_960_1 = all_791_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1584) implies:
% 222.41/34.59 | (1585) all_960_1 = all_791_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (898), (1321) imply:
% 222.41/34.59 | (1586) all_785_0 = all_764_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1586) implies:
% 222.41/34.59 | (1587) all_785_0 = all_764_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (897), (1547) imply:
% 222.41/34.59 | (1588) all_1010_1 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1588) implies:
% 222.41/34.59 | (1589) all_1010_1 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (896), (1517) imply:
% 222.41/34.59 | (1590) all_983_1 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1590) implies:
% 222.41/34.59 | (1591) all_983_1 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1026), (1583) imply:
% 222.41/34.59 | (1592) all_1004_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1592) implies:
% 222.41/34.59 | (1593) all_1004_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1095), (1579) imply:
% 222.41/34.59 | (1594) all_998_0 = all_892_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1594) implies:
% 222.41/34.59 | (1595) all_998_0 = all_892_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (895), (1589) imply:
% 222.41/34.59 | (1596) all_1007_1 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1596) implies:
% 222.41/34.59 | (1597) all_1007_1 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (894), (1597) imply:
% 222.41/34.59 | (1598) all_941_0 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1598) implies:
% 222.41/34.59 | (1599) all_941_0 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1025), (1593) imply:
% 222.41/34.59 | (1600) all_995_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1600) implies:
% 222.41/34.59 | (1601) all_995_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1370), (1549) imply:
% 222.41/34.59 | (1602) all_875_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1602) implies:
% 222.41/34.59 | (1603) all_875_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1094), (1595) imply:
% 222.41/34.59 | (1604) all_983_0 = all_892_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1604) implies:
% 222.41/34.59 | (1605) all_983_0 = all_892_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1024), (1601) imply:
% 222.41/34.59 | (1606) all_989_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1606) implies:
% 222.41/34.59 | (1607) all_989_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1520), (1521) imply:
% 222.41/34.59 | (1608) all_983_1 = all_957_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1608) implies:
% 222.41/34.59 | (1609) all_983_1 = all_957_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1521), (1522) imply:
% 222.41/34.59 | (1610) all_957_0 = all_817_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1023), (1607) imply:
% 222.41/34.59 | (1611) all_986_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1611) implies:
% 222.41/34.59 | (1612) all_986_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1022), (1612) imply:
% 222.41/34.59 | (1613) all_980_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1613) implies:
% 222.41/34.59 | (1614) all_980_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1093), (1605) imply:
% 222.41/34.59 | (1615) all_929_0 = all_892_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1615) implies:
% 222.41/34.59 | (1616) all_929_0 = all_892_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1591), (1609) imply:
% 222.41/34.59 | (1617) all_957_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1617) implies:
% 222.41/34.59 | (1618) all_957_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1021), (1614) imply:
% 222.41/34.59 | (1619) all_977_1 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1619) implies:
% 222.41/34.59 | (1620) all_977_1 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1124), (1555) imply:
% 222.41/34.59 | (1621) all_938_0 = all_830_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1621) implies:
% 222.41/34.59 | (1622) all_938_0 = all_830_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1020), (1620) imply:
% 222.41/34.59 | (1623) all_974_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1623) implies:
% 222.41/34.59 | (1624) all_974_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1019), (1624) imply:
% 222.41/34.59 | (1625) all_965_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1625) implies:
% 222.41/34.59 | (1626) all_965_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1018), (1626) imply:
% 222.41/34.59 | (1627) all_954_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1627) implies:
% 222.41/34.59 | (1628) all_954_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (893), (1585) imply:
% 222.41/34.59 | (1629) all_799_0 = all_791_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1629) implies:
% 222.41/34.59 | (1630) all_799_0 = all_791_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1610), (1618) imply:
% 222.41/34.59 | (1631) all_817_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1631) implies:
% 222.41/34.59 | (1632) all_817_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1017), (1628) imply:
% 222.41/34.59 | (1633) all_947_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1633) implies:
% 222.41/34.59 | (1634) all_947_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1016), (1634) imply:
% 222.41/34.59 | (1635) all_909_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1635) implies:
% 222.41/34.59 | (1636) all_909_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1123), (1581) imply:
% 222.41/34.59 | (1637) all_938_0 = all_914_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1637) implies:
% 222.41/34.59 | (1638) all_938_0 = all_914_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1561), (1581) imply:
% 222.41/34.59 | (1639) all_914_0 = all_861_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1518), (1519) imply:
% 222.41/34.59 | (1640) all_812_0 = all_783_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1640) implies:
% 222.41/34.59 | (1641) all_812_0 = all_783_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1397), (1599) imply:
% 222.41/34.59 | (1642) all_935_0 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1642) implies:
% 222.41/34.59 | (1643) all_935_0 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1622), (1638) imply:
% 222.41/34.59 | (1644) all_914_0 = all_830_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1644) implies:
% 222.41/34.59 | (1645) all_914_0 = all_830_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1395), (1572) imply:
% 222.41/34.59 | (1646) all_932_0 = all_895_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1572), (1643) imply:
% 222.41/34.59 | (1647) all_932_0 = all_921_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1533), (1572) imply:
% 222.41/34.59 | (1648) all_932_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1646), (1647) imply:
% 222.41/34.59 | (1649) all_921_0 = all_895_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1647), (1648) imply:
% 222.41/34.59 | (1650) all_921_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1092), (1616) imply:
% 222.41/34.59 | (1651) all_898_0 = all_892_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1651) implies:
% 222.41/34.59 | (1652) all_898_0 = all_892_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1649), (1650) imply:
% 222.41/34.59 | (1653) all_895_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1653) implies:
% 222.41/34.59 | (1654) all_895_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1639), (1645) imply:
% 222.41/34.59 | (1655) all_861_0 = all_830_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1655) implies:
% 222.41/34.59 | (1656) all_861_0 = all_830_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1015), (1636) imply:
% 222.41/34.59 | (1657) all_861_1 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1657) implies:
% 222.41/34.59 | (1658) all_861_1 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1090), (1652) imply:
% 222.41/34.59 | (1659) all_892_0 = all_886_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1091), (1652) imply:
% 222.41/34.59 | (1660) all_892_0 = all_817_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (892), (1654) imply:
% 222.41/34.59 | (1661) all_884_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1661) implies:
% 222.41/34.59 | (1662) all_884_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1659), (1660) imply:
% 222.41/34.59 | (1663) all_886_0 = all_817_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1663) implies:
% 222.41/34.59 | (1664) all_886_0 = all_817_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1279), (1386) imply:
% 222.41/34.59 | (1665) all_863_0 = all_794_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1279), (1664) imply:
% 222.41/34.59 | (1666) all_863_0 = all_817_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1485), (1662) imply:
% 222.41/34.59 | (1667) all_871_1 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1667) implies:
% 222.41/34.59 | (1668) all_871_1 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1072), (1494) imply:
% 222.41/34.59 | (1669) all_880_2 = all_806_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1669) implies:
% 222.41/34.59 | (1670) all_880_2 = all_806_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1071), (1670) imply:
% 222.41/34.59 | (1671) all_852_1 = all_806_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1671) implies:
% 222.41/34.59 | (1672) all_852_1 = all_806_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (891), (1603) imply:
% 222.41/34.59 | (1673) all_761_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1673) implies:
% 222.41/34.59 | (1674) all_761_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1486), (1668) imply:
% 222.41/34.59 | (1675) all_868_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1675) implies:
% 222.41/34.59 | (1676) all_868_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (890), (1676) imply:
% 222.41/34.59 | (1677) all_856_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1677) implies:
% 222.41/34.59 | (1678) all_856_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1665), (1666) imply:
% 222.41/34.59 | (1679) all_817_1 = all_794_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1562), (1656) imply:
% 222.41/34.59 | (1680) all_832_0 = all_830_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1014), (1658) imply:
% 222.41/34.59 | (1681) all_858_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1681) implies:
% 222.41/34.59 | (1682) all_858_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1013), (1682) imply:
% 222.41/34.59 | (1683) all_849_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1683) implies:
% 222.41/34.59 | (1684) all_849_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (889), (1678) imply:
% 222.41/34.59 | (1685) all_846_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1685) implies:
% 222.41/34.59 | (1686) all_846_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1070), (1672) imply:
% 222.41/34.59 | (1687) all_841_1 = all_806_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1687) implies:
% 222.41/34.59 | (1688) all_841_1 = all_806_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1012), (1684) imply:
% 222.41/34.59 | (1689) all_835_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1689) implies:
% 222.41/34.59 | (1690) all_835_0 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (888), (1686) imply:
% 222.41/34.59 | (1691) all_838_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1691) implies:
% 222.41/34.59 | (1692) all_838_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1069), (1688) imply:
% 222.41/34.59 | (1693) all_808_1 = all_806_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1693) implies:
% 222.41/34.59 | (1694) all_808_1 = all_806_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (887), (1692) imply:
% 222.41/34.59 | (1695) all_824_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1695) implies:
% 222.41/34.59 | (1696) all_824_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1011), (1690) imply:
% 222.41/34.59 | (1697) all_832_1 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1697) implies:
% 222.41/34.59 | (1698) all_832_1 = all_830_1
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1010), (1698) imply:
% 222.41/34.59 | (1699) all_830_1 = all_742_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1009), (1698) imply:
% 222.41/34.59 | (1700) all_830_1 = all_750_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1699), (1700) imply:
% 222.41/34.59 | (1701) all_750_0 = all_742_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (886), (1696) imply:
% 222.41/34.59 | (1702) all_819_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1702) implies:
% 222.41/34.59 | (1703) all_819_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (885), (1703) imply:
% 222.41/34.59 | (1704) all_817_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1704) implies:
% 222.41/34.59 | (1705) all_817_0 = all_814_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (884), (1705) imply:
% 222.41/34.59 | (1706) all_814_0 = all_803_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1632), (1705) imply:
% 222.41/34.59 | (1707) all_814_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1706), (1707) imply:
% 222.41/34.59 | (1708) all_803_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1708) implies:
% 222.41/34.59 | (1709) all_803_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1195), (1641) imply:
% 222.41/34.59 | (1710) all_788_0 = all_783_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1710) implies:
% 222.41/34.59 | (1711) all_788_0 = all_783_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1574), (1641) imply:
% 222.41/34.59 | (1712) all_783_0 = all_780_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (883), (1709) imply:
% 222.41/34.59 | (1713) all_796_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1713) implies:
% 222.41/34.59 | (1714) all_796_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (881), (1630) imply:
% 222.41/34.59 | (1715) all_796_0 = all_791_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1715) implies:
% 222.41/34.59 | (1716) all_796_0 = all_791_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (882), (1630) imply:
% 222.41/34.59 | (1717) all_791_0 = all_788_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1714), (1716) imply:
% 222.41/34.59 | (1718) all_791_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1718) implies:
% 222.41/34.59 | (1719) all_791_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1717), (1719) imply:
% 222.41/34.59 | (1720) all_788_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1720) implies:
% 222.41/34.59 | (1721) all_788_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1711), (1721) imply:
% 222.41/34.59 | (1722) all_783_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1722) implies:
% 222.41/34.59 | (1723) all_783_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (880), (1587) imply:
% 222.41/34.59 | (1724) all_769_0 = all_764_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1724) implies:
% 222.41/34.59 | (1725) all_769_0 = all_764_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1712), (1723) imply:
% 222.41/34.59 | (1726) all_780_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1726) implies:
% 222.41/34.59 | (1727) all_780_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1575), (1727) imply:
% 222.41/34.59 | (1728) all_778_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1728) implies:
% 222.41/34.59 | (1729) all_778_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1329), (1729) imply:
% 222.41/34.59 | (1730) all_767_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1730) implies:
% 222.41/34.59 | (1731) all_767_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (879), (1725) imply:
% 222.41/34.59 | (1732) all_764_0 = all_761_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1327), (1725) imply:
% 222.41/34.59 | (1733) all_767_0 = all_764_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1733) implies:
% 222.41/34.59 | (1734) all_767_0 = all_764_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1731), (1734) imply:
% 222.41/34.59 | (1735) all_764_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1735) implies:
% 222.41/34.59 | (1736) all_764_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1732), (1736) imply:
% 222.41/34.59 | (1737) all_761_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | SIMP: (1737) implies:
% 222.41/34.59 | (1738) all_761_0 = all_754_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (878), (1738) imply:
% 222.41/34.59 | (1739) all_754_0 = all_748_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1674), (1738) imply:
% 222.41/34.59 | (1740) all_754_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1739), (1740) imply:
% 222.41/34.59 | (1741) all_748_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1723), (1740) imply:
% 222.41/34.59 | (1742) all_783_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1719), (1740) imply:
% 222.41/34.59 | (1743) all_791_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1641), (1742) imply:
% 222.41/34.59 | (1744) all_812_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1707), (1740) imply:
% 222.41/34.59 | (1745) all_814_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1705), (1745) imply:
% 222.41/34.59 | (1746) all_817_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1668), (1745) imply:
% 222.41/34.59 | (1747) all_871_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1650), (1745) imply:
% 222.41/34.59 | (1748) all_921_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1647), (1748) imply:
% 222.41/34.59 | (1749) all_932_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1572), (1749) imply:
% 222.41/34.59 | (1750) all_935_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1519), (1742) imply:
% 222.41/34.59 | (1751) all_944_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1618), (1740) imply:
% 222.41/34.59 | (1752) all_957_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1585), (1743) imply:
% 222.41/34.59 | (1753) all_960_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1521), (1752) imply:
% 222.41/34.59 | (1754) all_992_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1597), (1748) imply:
% 222.41/34.59 | (1755) all_1007_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1570), (1749) imply:
% 222.41/34.59 | (1756) all_1042_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1498), (1756) imply:
% 222.41/34.59 | (1757) all_1049_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1527), (1743) imply:
% 222.41/34.59 | (1758) all_1067_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1465), (1748) imply:
% 222.41/34.59 | (1759) all_1091_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1469), (1751) imply:
% 222.41/34.59 | (1760) all_1124_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1515), (1740) imply:
% 222.41/34.59 | (1761) all_1130_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1337), (1758) imply:
% 222.41/34.59 | (1762) all_1186_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (915), (1760) imply:
% 222.41/34.59 | (1763) all_1204_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1459), (1748) imply:
% 222.41/34.59 | (1764) all_1224_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (918), (1764) imply:
% 222.41/34.59 | (1765) all_1230_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1346), (1750) imply:
% 222.41/34.59 | (1766) all_1348_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1139), (1645) imply:
% 222.41/34.59 | (1767) all_1392_1 = all_830_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (935), (1766) imply:
% 222.41/34.59 | (1768) all_1406_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (940), (1754) imply:
% 222.41/34.59 | (1769) all_1415_3 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1285), (1758) imply:
% 222.41/34.59 | (1770) all_1421_0 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1251), (1748) imply:
% 222.41/34.59 | (1771) all_1430_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1227), (1353) imply:
% 222.41/34.59 | (1772) all_1457_7 = all_1242_4
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1248), (1757) imply:
% 222.41/34.59 | (1773) all_1489_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1199), (1537) imply:
% 222.41/34.59 | (1774) all_1524_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1217), (1353) imply:
% 222.41/34.59 | (1775) all_1527_8 = all_1242_4
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1190), (1748) imply:
% 222.41/34.59 | (1776) all_1532_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1145), (1353) imply:
% 222.41/34.59 | (1777) all_1535_9 = all_1242_4
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1120), (1352) imply:
% 222.41/34.59 | (1778) all_1535_8 = all_1242_3
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (988), (1744) imply:
% 222.41/34.59 | (1779) all_1552_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1163), (1743) imply:
% 222.41/34.59 | (1780) all_1555_1 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (993), (1773) imply:
% 222.41/34.59 | (1781) all_1561_2 = all_746_0
% 222.41/34.59 |
% 222.41/34.59 | COMBINE_EQS: (1148), (1259) imply:
% 222.41/34.59 | (1782) all_1593_12 = all_1242_4
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (841), (1781) imply:
% 222.41/34.59 | (1783) c_Nat_OSuc(all_746_0) = all_1561_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (836), (1780) imply:
% 222.41/34.59 | (1784) c_Nat_OSuc(all_746_0) = all_1555_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (833), (1779) imply:
% 222.41/34.59 | (1785) c_Nat_OSuc(all_746_0) = all_1552_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (803), (1776) imply:
% 222.41/34.59 | (1786) c_Nat_OSuc(all_746_0) = all_1532_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (787), (1774) imply:
% 222.41/34.59 | (1787) c_Nat_OSuc(all_746_0) = all_1524_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (704), (1771) imply:
% 222.41/34.59 | (1788) c_Nat_OSuc(all_746_0) = all_1430_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (695), (1769) imply:
% 222.41/34.59 | (1789) c_Nat_OSuc(all_746_0) = all_1415_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (687), (1768) imply:
% 222.41/34.59 | (1790) c_Nat_OSuc(all_746_0) = all_1406_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (577), (1765) imply:
% 222.41/34.59 | (1791) c_Nat_OSuc(all_746_0) = all_1230_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (574), (1764) imply:
% 222.41/34.59 | (1792) c_Nat_OSuc(all_746_0) = all_1224_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (566), (1763) imply:
% 222.41/34.59 | (1793) c_Nat_OSuc(all_746_0) = all_1204_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (559), (1762) imply:
% 222.41/34.59 | (1794) c_Nat_OSuc(all_746_0) = all_1186_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (517), (1761) imply:
% 222.41/34.59 | (1795) c_Nat_OSuc(all_746_0) = all_1130_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (485), (1759) imply:
% 222.41/34.59 | (1796) c_Nat_OSuc(all_746_0) = all_1091_1
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (437), (1755) imply:
% 222.41/34.59 | (1797) c_Nat_OSuc(all_746_0) = all_1007_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (432), (1549) imply:
% 222.41/34.59 | (1798) c_Nat_OSuc(all_746_0) = all_1001_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (425), (1754) imply:
% 222.41/34.59 | (1799) c_Nat_OSuc(all_746_0) = all_992_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (406), (1753) imply:
% 222.41/34.59 | (1800) c_Nat_OSuc(all_746_0) = all_960_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (356), (1747) imply:
% 222.41/34.59 | (1801) c_Nat_OSuc(all_746_0) = all_871_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (310), (1679), (1746) imply:
% 222.41/34.59 | (1802) c_Nat_OSuc(all_746_0) = all_794_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (867), (1089) imply:
% 222.41/34.59 | (1803) c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_na____, all_744_0) =
% 222.41/34.59 | all_1593_2
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (866), (1083) imply:
% 222.41/34.59 | (1804) c_Groups_Otimes__class_Otimes(all_806_1) = all_1593_6
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (817), (1201) imply:
% 222.41/34.59 | (1805) c_Groups_Otimes__class_Otimes(all_806_1) = all_1535_11
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (800), (1219) imply:
% 222.41/34.59 | (1806) c_Groups_Otimes__class_Otimes(all_806_1) = all_1527_10
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (684), (1309) imply:
% 222.41/34.59 | (1807) c_Groups_Otimes__class_Otimes(all_806_1) = all_1401_7
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (647), (1355) imply:
% 222.41/34.59 | (1808) c_Groups_Otimes__class_Otimes(all_806_1) = all_1354_6
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (865), (1083) imply:
% 222.41/34.59 | (1809) c_Power_Opower__class_Opower(all_806_1) = all_1593_13
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (828), (1180) imply:
% 222.41/34.59 | (1810) c_Power_Opower__class_Opower(all_806_1) = all_1546_0
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (816), (1201) imply:
% 222.41/34.59 | (1811) c_Power_Opower__class_Opower(all_806_1) = all_1535_10
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (799), (1219) imply:
% 222.41/34.59 | (1812) c_Power_Opower__class_Opower(all_806_1) = all_1527_9
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (767), (1229) imply:
% 222.41/34.59 | (1813) c_Power_Opower__class_Opower(all_806_1) = all_1495_9
% 222.41/34.59 |
% 222.41/34.59 | REDUCE: (729), (1261) imply:
% 222.41/34.59 | (1814) c_Power_Opower__class_Opower(all_806_1) = all_1457_8
% 222.41/34.59 |
% 222.41/34.60 | REDUCE: (674), (1767) imply:
% 222.41/34.60 | (1815) c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, all_830_0) = all_1392_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (862), (1122) imply:
% 222.41/34.60 | (1816) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_1593_15) =
% 222.41/34.60 | all_1593_10
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (861), (1782) imply:
% 222.41/34.60 | (1817) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1593_10) =
% 222.41/34.60 | all_1593_9
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (813), (1778) imply:
% 222.41/34.60 | (1818) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_1535_7) =
% 222.41/34.60 | all_1535_6
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (812), (1777) imply:
% 222.41/34.60 | (1819) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1535_6) =
% 222.41/34.60 | all_1535_5
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (796), (1174) imply:
% 222.41/34.60 | (1820) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_1527_6) =
% 222.41/34.60 | all_1527_5
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (795), (1775) imply:
% 222.41/34.60 | (1821) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1527_5) =
% 222.41/34.60 | all_1527_4
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (764), (1225) imply:
% 222.41/34.60 | (1822) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_1495_6) =
% 222.41/34.60 | all_1495_5
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (763), (1142) imply:
% 222.41/34.60 | (1823) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1495_5) =
% 222.41/34.60 | all_1495_4
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (726), (1257) imply:
% 222.41/34.60 | (1824) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_1457_5) =
% 222.41/34.60 | all_1457_4
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (725), (1772) imply:
% 222.41/34.60 | (1825) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1457_4) =
% 222.41/34.60 | all_1457_3
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (681), (1305) imply:
% 222.41/34.60 | (1826) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_1401_4) =
% 222.41/34.60 | all_1401_3
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (680), (1259) imply:
% 222.41/34.60 | (1827) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1401_3) =
% 222.41/34.60 | all_1401_2
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (644), (1352) imply:
% 222.41/34.60 | (1828) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_1354_3) =
% 222.41/34.60 | all_1354_2
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (643), (1353) imply:
% 222.41/34.60 | (1829) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1354_2) =
% 222.41/34.60 | all_1354_1
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (858), (1083) imply:
% 222.41/34.60 | (1830) c_Groups_Ozero__class_Ozero(all_806_1) = all_1593_15
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (809), (1201) imply:
% 222.41/34.60 | (1831) c_Groups_Ozero__class_Ozero(all_806_1) = all_1535_7
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (792), (1219) imply:
% 222.41/34.60 | (1832) c_Groups_Ozero__class_Ozero(all_806_1) = all_1527_6
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (760), (1229) imply:
% 222.41/34.60 | (1833) c_Groups_Ozero__class_Ozero(all_806_1) = all_1495_6
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (722), (1261) imply:
% 222.41/34.60 | (1834) c_Groups_Ozero__class_Ozero(all_806_1) = all_1457_5
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (678), (1309) imply:
% 222.41/34.60 | (1835) c_Groups_Ozero__class_Ozero(all_806_1) = all_1401_4
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (641), (1355) imply:
% 222.41/34.60 | (1836) c_Groups_Ozero__class_Ozero(all_806_1) = all_1354_3
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (586), (1390) imply:
% 222.41/34.60 | (1837) c_Groups_Ozero__class_Ozero(all_806_1) = all_1242_2
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (366), (1494) imply:
% 222.41/34.60 | (1838) c_Groups_Ozero__class_Ozero(all_806_1) = all_882_1
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (361), (1670) imply:
% 222.41/34.60 | (1839) c_Groups_Ozero__class_Ozero(all_806_1) = all_880_1
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (334), (1672) imply:
% 222.41/34.60 | (1840) c_Groups_Ozero__class_Ozero(all_806_1) = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (327), (1688) imply:
% 222.41/34.60 | (1841) c_Groups_Ozero__class_Ozero(all_806_1) = all_841_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (301), (1694) imply:
% 222.41/34.60 | (1842) c_Groups_Ozero__class_Ozero(all_806_1) = all_808_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (854), (1089) imply:
% 222.41/34.60 | (1843) hAPP(all_1593_8, all_744_0) = all_1593_4
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (808), (1172) imply:
% 222.41/34.60 | (1844) hAPP(all_1535_4, all_744_0) = all_1535_2
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (791), (1213) imply:
% 222.41/34.60 | (1845) hAPP(all_1527_3, all_744_0) = all_1527_1
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (721), (1255) imply:
% 222.41/34.60 | (1846) hAPP(all_1457_2, all_744_0) = all_1457_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (337), (1502) imply:
% 222.41/34.60 | (1847) hAPP(all_854_1, v_a____) = all_752_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (639), (1352) imply:
% 222.41/34.60 | (1848) $i(all_1242_3)
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (638), (1353) imply:
% 222.41/34.60 | (1849) $i(all_1242_4)
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (341), (1303) imply:
% 222.41/34.60 | (1850) $i(all_744_0)
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (319), (1680) imply:
% 222.41/34.60 | (1851) $i(all_830_0)
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_841_0, all_880_1, all_806_1,
% 222.41/34.60 | simplifying with (1839), (1841) gives:
% 222.41/34.60 | (1852) all_880_1 = all_841_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_806_0, all_1242_2, all_806_1,
% 222.41/34.60 | simplifying with (297), (1837) gives:
% 222.41/34.60 | (1853) all_1242_2 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_882_1, all_1242_2, all_806_1,
% 222.41/34.60 | simplifying with (1837), (1838) gives:
% 222.41/34.60 | (1854) all_1242_2 = all_882_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_1242_2, all_1354_3, all_806_1,
% 222.41/34.60 | simplifying with (1836), (1837) gives:
% 222.41/34.60 | (1855) all_1354_3 = all_1242_2
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_841_0, all_1354_3, all_806_1,
% 222.41/34.60 | simplifying with (1836), (1841) gives:
% 222.41/34.60 | (1856) all_1354_3 = all_841_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_880_1, all_1401_4, all_806_1,
% 222.41/34.60 | simplifying with (1835), (1839) gives:
% 222.41/34.60 | (1857) all_1401_4 = all_880_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_1401_4, all_1495_6, all_806_1,
% 222.41/34.60 | simplifying with (1833), (1835) gives:
% 222.41/34.60 | (1858) all_1495_6 = all_1401_4
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_808_0, all_1495_6, all_806_1,
% 222.41/34.60 | simplifying with (1833), (1842) gives:
% 222.41/34.60 | (1859) all_1495_6 = all_808_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_1457_5, all_1527_6, all_806_1,
% 222.41/34.60 | simplifying with (1832), (1834) gives:
% 222.41/34.60 | (1860) all_1527_6 = all_1457_5
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_1354_3, all_1527_6, all_806_1,
% 222.41/34.60 | simplifying with (1832), (1836) gives:
% 222.41/34.60 | (1861) all_1527_6 = all_1354_3
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_1535_7, all_1593_15, all_806_1,
% 222.41/34.60 | simplifying with (1830), (1831) gives:
% 222.41/34.60 | (1862) all_1593_15 = all_1535_7
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_1527_6, all_1593_15, all_806_1,
% 222.41/34.60 | simplifying with (1830), (1832) gives:
% 222.41/34.60 | (1863) all_1593_15 = all_1527_6
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (241) with all_852_0, all_1593_15, all_806_1,
% 222.41/34.60 | simplifying with (1830), (1840) gives:
% 222.41/34.60 | (1864) all_1593_15 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (244) with all_1495_9, all_1535_10, all_806_1,
% 222.41/34.60 | simplifying with (1811), (1813) gives:
% 222.41/34.60 | (1865) all_1535_10 = all_1495_9
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (244) with all_1457_8, all_1546_0, all_806_1,
% 222.41/34.60 | simplifying with (1810), (1814) gives:
% 222.41/34.60 | (1866) all_1546_0 = all_1457_8
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (244) with all_1546_0, all_1593_13, all_806_1,
% 222.41/34.60 | simplifying with (1809), (1810) gives:
% 222.41/34.60 | (1867) all_1593_13 = all_1546_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (244) with all_1535_10, all_1593_13, all_806_1,
% 222.41/34.60 | simplifying with (1809), (1811) gives:
% 222.41/34.60 | (1868) all_1593_13 = all_1535_10
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (244) with all_1527_9, all_1593_13, all_806_1,
% 222.41/34.60 | simplifying with (1809), (1812) gives:
% 222.41/34.60 | (1869) all_1593_13 = all_1527_9
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (245) with all_1401_7, all_1527_10, all_806_1,
% 222.41/34.60 | simplifying with (1806), (1807) gives:
% 222.41/34.60 | (1870) all_1527_10 = all_1401_7
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (245) with all_1527_10, all_1535_11, all_806_1,
% 222.41/34.60 | simplifying with (1805), (1806) gives:
% 222.41/34.60 | (1871) all_1535_11 = all_1527_10
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (245) with all_1535_11, all_1593_6, all_806_1,
% 222.41/34.60 | simplifying with (1804), (1805) gives:
% 222.41/34.60 | (1872) all_1593_6 = all_1535_11
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (245) with all_1354_6, all_1593_6, all_806_1,
% 222.41/34.60 | simplifying with (1804), (1808) gives:
% 222.41/34.60 | (1873) all_1593_6 = all_1354_6
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_871_0, all_992_0, all_746_0,
% 222.41/34.60 | simplifying with (1799), (1801) gives:
% 222.41/34.60 | (1874) all_992_0 = all_871_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_992_0, all_1001_0, all_746_0,
% 222.41/34.60 | simplifying with (1798), (1799) gives:
% 222.41/34.60 | (1875) all_1001_0 = all_992_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1001_0, all_1130_1, all_746_0,
% 222.41/34.60 | simplifying with (1795), (1798) gives:
% 222.41/34.60 | (1876) all_1130_1 = all_1001_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1130_1, all_1224_1, all_746_0,
% 222.41/34.60 | simplifying with (1792), (1795) gives:
% 222.41/34.60 | (1877) all_1224_1 = all_1130_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_960_0, all_1224_1, all_746_0,
% 222.41/34.60 | simplifying with (1792), (1800) gives:
% 222.41/34.60 | (1878) all_1224_1 = all_960_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1204_1, all_1406_0, all_746_0,
% 222.41/34.60 | simplifying with (1790), (1793) gives:
% 222.41/34.60 | (1879) all_1406_0 = all_1204_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1091_1, all_1406_0, all_746_0,
% 222.41/34.60 | simplifying with (1790), (1796) gives:
% 222.41/34.60 | (1880) all_1406_0 = all_1091_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_992_0, all_1406_0, all_746_0,
% 222.41/34.60 | simplifying with (1790), (1799) gives:
% 222.41/34.60 | (1881) all_1406_0 = all_992_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1230_1, all_1415_0, all_746_0,
% 222.41/34.60 | simplifying with (1789), (1791) gives:
% 222.41/34.60 | (1882) all_1415_0 = all_1230_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1186_1, all_1415_0, all_746_0,
% 222.41/34.60 | simplifying with (1789), (1794) gives:
% 222.41/34.60 | (1883) all_1415_0 = all_1186_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1091_1, all_1415_0, all_746_0,
% 222.41/34.60 | simplifying with (1789), (1796) gives:
% 222.41/34.60 | (1884) all_1415_0 = all_1091_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1406_0, all_1524_1, all_746_0,
% 222.41/34.60 | simplifying with (1787), (1790) gives:
% 222.41/34.60 | (1885) all_1524_1 = all_1406_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1007_0, all_1524_1, all_746_0,
% 222.41/34.60 | simplifying with (1787), (1797) gives:
% 222.41/34.60 | (1886) all_1524_1 = all_1007_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1430_0, all_1532_1, all_746_0,
% 222.41/34.60 | simplifying with (1786), (1788) gives:
% 222.41/34.60 | (1887) all_1532_1 = all_1430_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1230_1, all_1532_1, all_746_0,
% 222.41/34.60 | simplifying with (1786), (1791) gives:
% 222.41/34.60 | (1888) all_1532_1 = all_1230_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1532_1, all_1552_0, all_746_0,
% 222.41/34.60 | simplifying with (1785), (1786) gives:
% 222.41/34.60 | (1889) all_1552_0 = all_1532_1
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1552_0, all_1555_0, all_746_0,
% 222.41/34.60 | simplifying with (1784), (1785) gives:
% 222.41/34.60 | (1890) all_1555_0 = all_1552_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_1555_0, all_1561_1, all_746_0,
% 222.41/34.60 | simplifying with (1783), (1784) gives:
% 222.41/34.60 | (1891) all_1561_1 = all_1555_0
% 222.41/34.60 |
% 222.41/34.60 | GROUND_INST: instantiating (246) with all_794_0, all_1561_1, all_746_0,
% 222.41/34.60 | simplifying with (1783), (1802) gives:
% 222.41/34.60 | (1892) all_1561_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1872), (1873) imply:
% 222.41/34.60 | (1893) all_1535_11 = all_1354_6
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1893) implies:
% 222.41/34.60 | (1894) all_1535_11 = all_1354_6
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1867), (1869) imply:
% 222.41/34.60 | (1895) all_1546_0 = all_1527_9
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1895) implies:
% 222.41/34.60 | (1896) all_1546_0 = all_1527_9
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1868), (1869) imply:
% 222.41/34.60 | (1897) all_1535_10 = all_1527_9
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1897) implies:
% 222.41/34.60 | (1898) all_1535_10 = all_1527_9
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1862), (1863) imply:
% 222.41/34.60 | (1899) all_1535_7 = all_1527_6
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1862), (1864) imply:
% 222.41/34.60 | (1900) all_1535_7 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1891), (1892) imply:
% 222.41/34.60 | (1901) all_1555_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1901) implies:
% 222.41/34.60 | (1902) all_1555_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1890), (1902) imply:
% 222.41/34.60 | (1903) all_1552_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1903) implies:
% 222.41/34.60 | (1904) all_1552_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1889), (1904) imply:
% 222.41/34.60 | (1905) all_1532_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1905) implies:
% 222.41/34.60 | (1906) all_1532_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1866), (1896) imply:
% 222.41/34.60 | (1907) all_1527_9 = all_1457_8
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1907) implies:
% 222.41/34.60 | (1908) all_1527_9 = all_1457_8
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1899), (1900) imply:
% 222.41/34.60 | (1909) all_1527_6 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1909) implies:
% 222.41/34.60 | (1910) all_1527_6 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1865), (1898) imply:
% 222.41/34.60 | (1911) all_1527_9 = all_1495_9
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1911) implies:
% 222.41/34.60 | (1912) all_1527_9 = all_1495_9
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1871), (1894) imply:
% 222.41/34.60 | (1913) all_1527_10 = all_1354_6
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1913) implies:
% 222.41/34.60 | (1914) all_1527_10 = all_1354_6
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1887), (1906) imply:
% 222.41/34.60 | (1915) all_1430_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1887), (1888) imply:
% 222.41/34.60 | (1916) all_1430_0 = all_1230_1
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1860), (1910) imply:
% 222.41/34.60 | (1917) all_1457_5 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1860), (1861) imply:
% 222.41/34.60 | (1918) all_1457_5 = all_1354_3
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1908), (1912) imply:
% 222.41/34.60 | (1919) all_1495_9 = all_1457_8
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1919) implies:
% 222.41/34.60 | (1920) all_1495_9 = all_1457_8
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1870), (1914) imply:
% 222.41/34.60 | (1921) all_1401_7 = all_1354_6
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1921) implies:
% 222.41/34.60 | (1922) all_1401_7 = all_1354_6
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1885), (1886) imply:
% 222.41/34.60 | (1923) all_1406_0 = all_1007_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1923) implies:
% 222.41/34.60 | (1924) all_1406_0 = all_1007_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1858), (1859) imply:
% 222.41/34.60 | (1925) all_1401_4 = all_808_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1925) implies:
% 222.41/34.60 | (1926) all_1401_4 = all_808_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1917), (1918) imply:
% 222.41/34.60 | (1927) all_1354_3 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1927) implies:
% 222.41/34.60 | (1928) all_1354_3 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1915), (1916) imply:
% 222.41/34.60 | (1929) all_1230_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1929) implies:
% 222.41/34.60 | (1930) all_1230_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1882), (1883) imply:
% 222.41/34.60 | (1931) all_1230_1 = all_1186_1
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1931) implies:
% 222.41/34.60 | (1932) all_1230_1 = all_1186_1
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1883), (1884) imply:
% 222.41/34.60 | (1933) all_1186_1 = all_1091_1
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1879), (1924) imply:
% 222.41/34.60 | (1934) all_1204_1 = all_1007_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1879), (1881) imply:
% 222.41/34.60 | (1935) all_1204_1 = all_992_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1879), (1880) imply:
% 222.41/34.60 | (1936) all_1204_1 = all_1091_1
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1857), (1926) imply:
% 222.41/34.60 | (1937) all_880_1 = all_808_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1937) implies:
% 222.41/34.60 | (1938) all_880_1 = all_808_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1855), (1928) imply:
% 222.41/34.60 | (1939) all_1242_2 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1939) implies:
% 222.41/34.60 | (1940) all_1242_2 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1856), (1928) imply:
% 222.41/34.60 | (1941) all_852_0 = all_841_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1853), (1854) imply:
% 222.41/34.60 | (1942) all_882_1 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1854), (1940) imply:
% 222.41/34.60 | (1943) all_882_1 = all_852_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1930), (1932) imply:
% 222.41/34.60 | (1944) all_1186_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1944) implies:
% 222.41/34.60 | (1945) all_1186_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1877), (1878) imply:
% 222.41/34.60 | (1946) all_1130_1 = all_960_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1946) implies:
% 222.41/34.60 | (1947) all_1130_1 = all_960_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1934), (1936) imply:
% 222.41/34.60 | (1948) all_1091_1 = all_1007_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1948) implies:
% 222.41/34.60 | (1949) all_1091_1 = all_1007_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1934), (1935) imply:
% 222.41/34.60 | (1950) all_1007_0 = all_992_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1933), (1945) imply:
% 222.41/34.60 | (1951) all_1091_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1951) implies:
% 222.41/34.60 | (1952) all_1091_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1876), (1947) imply:
% 222.41/34.60 | (1953) all_1001_0 = all_960_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1953) implies:
% 222.41/34.60 | (1954) all_1001_0 = all_960_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1949), (1952) imply:
% 222.41/34.60 | (1955) all_1007_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1955) implies:
% 222.41/34.60 | (1956) all_1007_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1950), (1956) imply:
% 222.41/34.60 | (1957) all_992_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1957) implies:
% 222.41/34.60 | (1958) all_992_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1875), (1954) imply:
% 222.41/34.60 | (1959) all_992_0 = all_960_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1959) implies:
% 222.41/34.60 | (1960) all_992_0 = all_960_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1874), (1960) imply:
% 222.41/34.60 | (1961) all_960_0 = all_871_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1958), (1960) imply:
% 222.41/34.60 | (1962) all_960_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1961), (1962) imply:
% 222.41/34.60 | (1963) all_871_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1963) implies:
% 222.41/34.60 | (1964) all_871_0 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1942), (1943) imply:
% 222.41/34.60 | (1965) all_852_0 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1965) implies:
% 222.41/34.60 | (1966) all_852_0 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1852), (1938) imply:
% 222.41/34.60 | (1967) all_841_0 = all_808_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1967) implies:
% 222.41/34.60 | (1968) all_841_0 = all_808_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1941), (1966) imply:
% 222.41/34.60 | (1969) all_841_0 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | SIMP: (1969) implies:
% 222.41/34.60 | (1970) all_841_0 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1968), (1970) imply:
% 222.41/34.60 | (1971) all_808_0 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1938), (1971) imply:
% 222.41/34.60 | (1972) all_880_1 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1947), (1962) imply:
% 222.41/34.60 | (1973) all_1130_1 = all_794_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1928), (1966) imply:
% 222.41/34.60 | (1974) all_1354_3 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1926), (1971) imply:
% 222.41/34.60 | (1975) all_1401_4 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1917), (1966) imply:
% 222.41/34.60 | (1976) all_1457_5 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1859), (1971) imply:
% 222.41/34.60 | (1977) all_1495_6 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1860), (1976) imply:
% 222.41/34.60 | (1978) all_1527_6 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1865), (1920) imply:
% 222.41/34.60 | (1979) all_1535_10 = all_1457_8
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1900), (1966) imply:
% 222.41/34.60 | (1980) all_1535_7 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1862), (1980) imply:
% 222.41/34.60 | (1981) all_1593_15 = all_806_0
% 222.41/34.60 |
% 222.41/34.60 | COMBINE_EQS: (1869), (1908) imply:
% 222.41/34.60 | (1982) all_1593_13 = all_1457_8
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (842), (1892) imply:
% 222.41/34.60 | (1983) c_Nat_OSuc(all_794_0) = all_1561_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (804), (1906) imply:
% 222.41/34.60 | (1984) c_Nat_OSuc(all_794_0) = all_1532_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (486), (1952) imply:
% 222.41/34.60 | (1985) c_Nat_OSuc(all_794_0) = all_1091_0
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (1816), (1981) imply:
% 222.41/34.60 | (1986) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_806_0) =
% 222.41/34.60 | all_1593_10
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (1818), (1980) imply:
% 222.41/34.60 | (1987) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_806_0) =
% 222.41/34.60 | all_1535_6
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (1820), (1978) imply:
% 222.41/34.60 | (1988) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_806_0) =
% 222.41/34.60 | all_1527_5
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (1822), (1977) imply:
% 222.41/34.60 | (1989) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_806_0) =
% 222.41/34.60 | all_1495_5
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (1824), (1976) imply:
% 222.41/34.60 | (1990) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_806_0) =
% 222.41/34.60 | all_1457_4
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (1826), (1975) imply:
% 222.41/34.60 | (1991) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_806_0) =
% 222.41/34.60 | all_1401_3
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (1828), (1974) imply:
% 222.41/34.60 | (1992) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_806_0) =
% 222.41/34.60 | all_1354_2
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (589), (1853) imply:
% 222.41/34.60 | (1993) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3, all_806_0) =
% 222.41/34.60 | all_1242_1
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (368), (1942) imply:
% 222.41/34.60 | (1994) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_882_0, all_806_0) =
% 222.41/34.60 | v_s____
% 222.41/34.60 |
% 222.41/34.60 | REDUCE: (363), (1972) imply:
% 222.41/34.61 | (1995) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_880_0, all_806_0) =
% 222.41/34.61 | v_s____
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (856), (1873) imply:
% 222.41/34.61 | (1996) hAPP(all_1354_6, all_1593_4) = all_1593_3
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (852), (1982) imply:
% 222.41/34.61 | (1997) hAPP(all_1457_8, all_1593_9) = all_1593_8
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (807), (1979) imply:
% 222.41/34.61 | (1998) hAPP(all_1457_8, all_1535_5) = all_1535_4
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (806), (1894) imply:
% 222.41/34.61 | (1999) hAPP(all_1354_6, all_1535_2) = all_1535_1
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (790), (1908) imply:
% 222.41/34.61 | (2000) hAPP(all_1457_8, all_1527_4) = all_1527_3
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (789), (1914) imply:
% 222.41/34.61 | (2001) hAPP(all_1354_6, all_1527_1) = all_1527_0
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (759), (1920) imply:
% 222.41/34.61 | (2002) hAPP(all_1457_8, all_1495_4) = all_1495_3
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (514), (1973) imply:
% 222.41/34.61 | (2003) hAPP(all_1130_3, all_794_0) = all_1130_0
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (354), (1964) imply:
% 222.41/34.61 | (2004) $i(all_794_0)
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (300), (1971) imply:
% 222.41/34.61 | (2005) $i(all_806_0)
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1401_3, all_1457_4, all_806_0,
% 222.41/34.61 | all_1242_3, tc_Complex_Ocomplex, simplifying with (1990), (1991)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2006) all_1457_4 = all_1401_3
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1457_4, all_1527_5, all_806_0,
% 222.41/34.61 | all_1242_3, tc_Complex_Ocomplex, simplifying with (1988), (1990)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2007) all_1527_5 = all_1457_4
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1242_1, all_1527_5, all_806_0,
% 222.41/34.61 | all_1242_3, tc_Complex_Ocomplex, simplifying with (1988), (1993)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2008) all_1527_5 = all_1242_1
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1457_4, all_1535_6, all_806_0,
% 222.41/34.61 | all_1242_3, tc_Complex_Ocomplex, simplifying with (1987), (1990)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2009) all_1535_6 = all_1457_4
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1354_2, all_1535_6, all_806_0,
% 222.41/34.61 | all_1242_3, tc_Complex_Ocomplex, simplifying with (1987), (1992)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2010) all_1535_6 = all_1354_2
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1527_5, all_1593_10, all_806_0,
% 222.41/34.61 | all_1242_3, tc_Complex_Ocomplex, simplifying with (1986), (1988)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2011) all_1593_10 = all_1527_5
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1495_5, all_1593_10, all_806_0,
% 222.41/34.61 | all_1242_3, tc_Complex_Ocomplex, simplifying with (1986), (1989)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2012) all_1593_10 = all_1495_5
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (246) with all_1532_0, all_1561_0, all_794_0,
% 222.41/34.61 | simplifying with (1983), (1984) gives:
% 222.41/34.61 | (2013) all_1561_0 = all_1532_0
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (246) with all_1091_0, all_1561_0, all_794_0,
% 222.41/34.61 | simplifying with (1983), (1985) gives:
% 222.41/34.61 | (2014) all_1561_0 = all_1091_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2011), (2012) imply:
% 222.41/34.61 | (2015) all_1527_5 = all_1495_5
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2015) implies:
% 222.41/34.61 | (2016) all_1527_5 = all_1495_5
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2013), (2014) imply:
% 222.41/34.61 | (2017) all_1532_0 = all_1091_0
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2017) implies:
% 222.41/34.61 | (2018) all_1532_0 = all_1091_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2009), (2010) imply:
% 222.41/34.61 | (2019) all_1457_4 = all_1354_2
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2019) implies:
% 222.41/34.61 | (2020) all_1457_4 = all_1354_2
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2008), (2016) imply:
% 222.41/34.61 | (2021) all_1495_5 = all_1242_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2007), (2016) imply:
% 222.41/34.61 | (2022) all_1495_5 = all_1457_4
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2021), (2022) imply:
% 222.41/34.61 | (2023) all_1457_4 = all_1242_1
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2023) implies:
% 222.41/34.61 | (2024) all_1457_4 = all_1242_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2006), (2024) imply:
% 222.41/34.61 | (2025) all_1401_3 = all_1242_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2006), (2020) imply:
% 222.41/34.61 | (2026) all_1401_3 = all_1354_2
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2025), (2026) imply:
% 222.41/34.61 | (2027) all_1354_2 = all_1242_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2010), (2027) imply:
% 222.41/34.61 | (2028) all_1535_6 = all_1242_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2012), (2021) imply:
% 222.41/34.61 | (2029) all_1593_10 = all_1242_1
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1817), (2029) imply:
% 222.41/34.61 | (2030) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1242_1) =
% 222.41/34.61 | all_1593_9
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1819), (2028) imply:
% 222.41/34.61 | (2031) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1242_1) =
% 222.41/34.61 | all_1535_5
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1821), (2008) imply:
% 222.41/34.61 | (2032) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1242_1) =
% 222.41/34.61 | all_1527_4
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1823), (2021) imply:
% 222.41/34.61 | (2033) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1242_1) =
% 222.41/34.61 | all_1495_4
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1825), (2024) imply:
% 222.41/34.61 | (2034) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1242_1) =
% 222.41/34.61 | all_1457_3
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1827), (2025) imply:
% 222.41/34.61 | (2035) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1242_1) =
% 222.41/34.61 | all_1401_2
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1829), (2027) imply:
% 222.41/34.61 | (2036) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4, all_1242_1) =
% 222.41/34.61 | all_1354_1
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (640), (2027) imply:
% 222.41/34.61 | (2037) $i(all_1242_1)
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1401_2, all_1495_4, all_1242_1,
% 222.41/34.61 | all_1242_4, tc_Complex_Ocomplex, simplifying with (2033), (2035)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2038) all_1495_4 = all_1401_2
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1457_3, all_1527_4, all_1242_1,
% 222.41/34.61 | all_1242_4, tc_Complex_Ocomplex, simplifying with (2032), (2034)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2039) all_1527_4 = all_1457_3
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1401_2, all_1527_4, all_1242_1,
% 222.41/34.61 | all_1242_4, tc_Complex_Ocomplex, simplifying with (2032), (2035)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2040) all_1527_4 = all_1401_2
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1242_0, all_1535_5, all_1242_1,
% 222.41/34.61 | all_1242_4, tc_Complex_Ocomplex, simplifying with (588), (2031)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2041) all_1535_5 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1495_4, all_1535_5, all_1242_1,
% 222.41/34.61 | all_1242_4, tc_Complex_Ocomplex, simplifying with (2031), (2033)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2042) all_1535_5 = all_1495_4
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1527_4, all_1593_9, all_1242_1,
% 222.41/34.61 | all_1242_4, tc_Complex_Ocomplex, simplifying with (2030), (2032)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2043) all_1593_9 = all_1527_4
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (251) with all_1354_1, all_1593_9, all_1242_1,
% 222.41/34.61 | all_1242_4, tc_Complex_Ocomplex, simplifying with (2030), (2036)
% 222.41/34.61 | gives:
% 222.41/34.61 | (2044) all_1593_9 = all_1354_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2043), (2044) imply:
% 222.41/34.61 | (2045) all_1527_4 = all_1354_1
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2045) implies:
% 222.41/34.61 | (2046) all_1527_4 = all_1354_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2041), (2042) imply:
% 222.41/34.61 | (2047) all_1495_4 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2047) implies:
% 222.41/34.61 | (2048) all_1495_4 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2039), (2040) imply:
% 222.41/34.61 | (2049) all_1457_3 = all_1401_2
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2039), (2046) imply:
% 222.41/34.61 | (2050) all_1457_3 = all_1354_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2038), (2048) imply:
% 222.41/34.61 | (2051) all_1401_2 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2051) implies:
% 222.41/34.61 | (2052) all_1401_2 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2049), (2050) imply:
% 222.41/34.61 | (2053) all_1401_2 = all_1354_1
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2053) implies:
% 222.41/34.61 | (2054) all_1401_2 = all_1354_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2052), (2054) imply:
% 222.41/34.61 | (2055) all_1354_1 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2050), (2055) imply:
% 222.41/34.61 | (2056) all_1457_3 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2039), (2056) imply:
% 222.41/34.61 | (2057) all_1527_4 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2044), (2055) imply:
% 222.41/34.61 | (2058) all_1593_9 = all_1242_0
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1997), (2058) imply:
% 222.41/34.61 | (2059) hAPP(all_1457_8, all_1242_0) = all_1593_8
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1998), (2041) imply:
% 222.41/34.61 | (2060) hAPP(all_1457_8, all_1242_0) = all_1535_4
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (2000), (2057) imply:
% 222.41/34.61 | (2061) hAPP(all_1457_8, all_1242_0) = all_1527_3
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (2002), (2048) imply:
% 222.41/34.61 | (2062) hAPP(all_1457_8, all_1242_0) = all_1495_3
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (720), (2056) imply:
% 222.41/34.61 | (2063) hAPP(all_1457_8, all_1242_0) = all_1457_2
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1495_3, all_1527_3, all_1242_0,
% 222.41/34.61 | all_1457_8, simplifying with (2061), (2062) gives:
% 222.41/34.61 | (2064) all_1527_3 = all_1495_3
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1527_3, all_1535_4, all_1242_0,
% 222.41/34.61 | all_1457_8, simplifying with (2060), (2061) gives:
% 222.41/34.61 | (2065) all_1535_4 = all_1527_3
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1535_4, all_1593_8, all_1242_0,
% 222.41/34.61 | all_1457_8, simplifying with (2059), (2060) gives:
% 222.41/34.61 | (2066) all_1593_8 = all_1535_4
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1457_2, all_1593_8, all_1242_0,
% 222.41/34.61 | all_1457_8, simplifying with (2059), (2063) gives:
% 222.41/34.61 | (2067) all_1593_8 = all_1457_2
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2066), (2067) imply:
% 222.41/34.61 | (2068) all_1535_4 = all_1457_2
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2068) implies:
% 222.41/34.61 | (2069) all_1535_4 = all_1457_2
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2065), (2069) imply:
% 222.41/34.61 | (2070) all_1527_3 = all_1457_2
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2070) implies:
% 222.41/34.61 | (2071) all_1527_3 = all_1457_2
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2064), (2071) imply:
% 222.41/34.61 | (2072) all_1495_3 = all_1457_2
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2072) implies:
% 222.41/34.61 | (2073) all_1495_3 = all_1457_2
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (855), (2067) imply:
% 222.41/34.61 | (2074) hAPP(all_1457_2, all_1593_2) = all_1593_1
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1843), (2067) imply:
% 222.41/34.61 | (2075) hAPP(all_1457_2, all_744_0) = all_1593_4
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (853), (2067) imply:
% 222.41/34.61 | (2076) hAPP(all_1457_2, v_na____) = all_1593_7
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1844), (2069) imply:
% 222.41/34.61 | (2077) hAPP(all_1457_2, all_744_0) = all_1535_2
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1845), (2071) imply:
% 222.41/34.61 | (2078) hAPP(all_1457_2, all_744_0) = all_1527_1
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1457_0, all_1535_2, all_744_0,
% 222.41/34.61 | all_1457_2, simplifying with (1846), (2077) gives:
% 222.41/34.61 | (2079) all_1535_2 = all_1457_0
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1535_2, all_1593_4, all_744_0,
% 222.41/34.61 | all_1457_2, simplifying with (2075), (2077) gives:
% 222.41/34.61 | (2080) all_1593_4 = all_1535_2
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1527_1, all_1593_4, all_744_0,
% 222.41/34.61 | all_1457_2, simplifying with (2075), (2078) gives:
% 222.41/34.61 | (2081) all_1593_4 = all_1527_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2080), (2081) imply:
% 222.41/34.61 | (2082) all_1535_2 = all_1527_1
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2082) implies:
% 222.41/34.61 | (2083) all_1535_2 = all_1527_1
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2079), (2083) imply:
% 222.41/34.61 | (2084) all_1527_1 = all_1457_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2081), (2084) imply:
% 222.41/34.61 | (2085) all_1593_4 = all_1457_0
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1996), (2085) imply:
% 222.41/34.61 | (2086) hAPP(all_1354_6, all_1457_0) = all_1593_3
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (1999), (2079) imply:
% 222.41/34.61 | (2087) hAPP(all_1354_6, all_1457_0) = all_1535_1
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (2001), (2084) imply:
% 222.41/34.61 | (2088) hAPP(all_1354_6, all_1457_0) = all_1527_0
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1535_1, all_1593_3, all_1457_0,
% 222.41/34.61 | all_1354_6, simplifying with (2086), (2087) gives:
% 222.41/34.61 | (2089) all_1593_3 = all_1535_1
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (247) with all_1527_0, all_1593_3, all_1457_0,
% 222.41/34.61 | all_1354_6, simplifying with (2086), (2088) gives:
% 222.41/34.61 | (2090) all_1593_3 = all_1527_0
% 222.41/34.61 |
% 222.41/34.61 | COMBINE_EQS: (2089), (2090) imply:
% 222.41/34.61 | (2091) all_1535_1 = all_1527_0
% 222.41/34.61 |
% 222.41/34.61 | SIMP: (2091) implies:
% 222.41/34.61 | (2092) all_1535_1 = all_1527_0
% 222.41/34.61 |
% 222.41/34.61 | REDUCE: (857), (2090) imply:
% 222.41/34.61 | (2093) hAPP(all_1527_0, all_1593_1) = all_1593_0
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (189) with v_na____, all_744_0, simplifying with
% 222.41/34.61 | (236), (256), (1850) gives:
% 222.41/34.61 | (2094) ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_744_0,
% 222.41/34.61 | v0) = v_na____ & $i(v0))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (arity_Polynomial__Opoly__Groups_Omonoid__mult)
% 222.41/34.61 | with tc_Complex_Ocomplex, all_806_1, simplifying with (229),
% 222.41/34.61 | (237), (298) gives:
% 222.41/34.61 | (2095) class_Groups_Omonoid__mult(all_806_1)
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_pCons__eq__0__iff) with all_806_0, all_880_0,
% 222.41/34.61 | tc_Complex_Ocomplex, v_s____, simplifying with (233), (237),
% 222.41/34.61 | (360), (1995), (2005) gives:
% 222.41/34.61 | (2096) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 222.41/34.61 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 =
% 222.41/34.61 | all_806_0) | all_806_0 = v_s____ | ( ~ (v2 = all_880_0) &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 &
% 222.41/34.61 | $i(v2))) & ( ~ (v1 = v_s____) | (v2 = all_880_0 & all_806_0 =
% 222.41/34.61 | v_s____ & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 222.41/34.61 | all_880_0)))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_pCons__eq__0__iff) with all_806_0, all_882_0,
% 222.41/34.61 | tc_Complex_Ocomplex, v_s____, simplifying with (233), (237),
% 222.41/34.61 | (365), (1994), (2005) gives:
% 222.41/34.61 | (2097) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 222.41/34.61 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 =
% 222.41/34.61 | all_806_0) | all_806_0 = v_s____ | ( ~ (v2 = all_882_0) &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 &
% 222.41/34.61 | $i(v2))) & ( ~ (v1 = v_s____) | (v2 = all_882_0 & all_806_0 =
% 222.41/34.61 | v_s____ & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 222.41/34.61 | all_882_0)))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_pCons__eq__0__iff) with all_1242_1,
% 222.41/34.61 | all_1242_4, tc_Complex_Ocomplex, all_1242_0, simplifying with
% 222.41/34.61 | (233), (237), (588), (1849), (2037) gives:
% 222.41/34.61 | (2098) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 222.41/34.61 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 =
% 222.41/34.61 | all_1242_0) | (v2 = all_1242_4 & all_1242_0 = all_1242_1 &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 222.41/34.61 | all_1242_4)) & ( ~ (v1 = all_1242_1) | all_1242_0 = all_1242_1
% 222.41/34.61 | | ( ~ (v2 = all_1242_4) &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 &
% 222.41/34.61 | $i(v2))))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_pCons__eq__0__iff) with all_806_0,
% 222.41/34.61 | all_1242_3, tc_Complex_Ocomplex, all_1242_1, simplifying with
% 222.41/34.61 | (233), (237), (1848), (1993), (2005) gives:
% 222.41/34.61 | (2099) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 222.41/34.61 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 =
% 222.41/34.61 | all_1242_1) | (v2 = all_1242_3 & all_1242_1 = all_806_0 &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 222.41/34.61 | all_1242_3)) & ( ~ (v1 = all_806_0) | all_1242_1 = all_806_0 |
% 222.41/34.61 | ( ~ (v2 = all_1242_3) &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v2 &
% 222.41/34.61 | $i(v2))))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_zero__neq__one) with tc_Nat_Onat, all_794_0,
% 222.41/34.61 | simplifying with (227), (235), (289) gives:
% 222.41/34.61 | (2100) ? [v0: any] : ( ~ (v0 = all_794_0) &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_zero__le__one) with tc_Nat_Onat, all_794_0,
% 222.41/34.61 | simplifying with (225), (235), (289) gives:
% 222.41/34.61 | (2101) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 222.41/34.61 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 222.41/34.61 | all_794_0))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_Nat_Onat,
% 222.41/34.61 | all_794_0, simplifying with (225), (235), (289) gives:
% 222.41/34.61 | (2102) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 222.41/34.61 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_794_0,
% 222.41/34.61 | v0))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_zero__neq__one) with tc_Complex_Ocomplex,
% 222.41/34.61 | all_1242_3, simplifying with (230), (237), (590) gives:
% 222.41/34.61 | (2103) ? [v0: any] : ( ~ (v0 = all_1242_3) &
% 222.41/34.61 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v0))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_Int_Oint,
% 222.41/34.61 | all_830_0, simplifying with (222), (224), (317) gives:
% 222.41/34.61 | (2104) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 222.41/34.61 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, all_830_0,
% 222.41/34.61 | v0))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_not__one__le__zero) with tc_Int_Oint,
% 222.41/34.61 | all_830_0, simplifying with (222), (224), (317) gives:
% 222.41/34.61 | (2105) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 222.41/34.61 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.61 | all_830_0, v0))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_neg__equal__0__iff__equal) with v_a____,
% 222.41/34.61 | tc_Complex_Ocomplex, all_1242_4, simplifying with (231), (237),
% 222.41/34.61 | (238), (591) gives:
% 222.41/34.61 | (2106) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0
% 222.41/34.61 | & $i(v0) & ( ~ (v0 = all_1242_4) | all_1242_4 = v_a____) & ( ~ (v0
% 222.41/34.61 | = v_a____) | all_1242_4 = v_a____))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_neg__0__less__iff__less) with all_830_0,
% 222.41/34.61 | tc_Int_Oint, all_1392_0, simplifying with (221), (224), (1815),
% 222.41/34.61 | (1851) gives:
% 222.41/34.61 | (2107) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 222.41/34.61 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 222.41/34.61 | all_1392_0) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.41/34.61 | all_830_0, v0)) & ( ~
% 222.41/34.61 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_830_0, v0) |
% 222.41/34.61 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, all_1392_0)))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_neg__less__0__iff__less) with all_830_0,
% 222.41/34.61 | tc_Int_Oint, all_1392_0, simplifying with (221), (224), (1815),
% 222.41/34.61 | (1851) gives:
% 222.41/34.61 | (2108) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 222.41/34.61 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v0,
% 222.41/34.61 | all_830_0) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.41/34.61 | all_1392_0, v0)) & ( ~
% 222.41/34.61 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1392_0, v0) |
% 222.41/34.61 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, all_830_0)))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_neg__0__le__iff__le) with all_830_0,
% 222.41/34.61 | tc_Int_Oint, all_1392_0, simplifying with (221), (224), (1815),
% 222.41/34.61 | (1851) gives:
% 222.41/34.61 | (2109) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 222.41/34.61 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0,
% 222.41/34.61 | all_1392_0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.61 | all_830_0, v0)) & ( ~
% 222.41/34.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_830_0, v0) |
% 222.41/34.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, all_1392_0)))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_neg__le__0__iff__le) with all_830_0,
% 222.41/34.61 | tc_Int_Oint, all_1392_0, simplifying with (221), (224), (1815),
% 222.41/34.61 | (1851) gives:
% 222.41/34.61 | (2110) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 222.41/34.61 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0,
% 222.41/34.61 | all_830_0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.61 | all_1392_0, v0)) & ( ~
% 222.41/34.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1392_0, v0) |
% 222.41/34.61 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, all_830_0)))
% 222.41/34.61 |
% 222.41/34.61 | GROUND_INST: instantiating (fact_neg__equal__0__iff__equal) with all_830_0,
% 222.41/34.61 | tc_Int_Oint, all_1392_0, simplifying with (223), (224), (1815),
% 222.41/34.61 | (1851) gives:
% 222.41/34.62 | (2111) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 &
% 222.41/34.62 | $i(v0) & ( ~ (v0 = all_1392_0) | all_1392_0 = all_830_0) & ( ~ (v0
% 222.41/34.62 | = all_830_0) | all_1392_0 = all_830_0))
% 222.41/34.62 |
% 222.41/34.62 | GROUND_INST: instantiating (497) with all_794_0, tc_Nat_Onat, all_1130_3,
% 222.41/34.62 | all_1130_0, simplifying with (226), (235), (516), (2003), (2004)
% 222.41/34.62 | gives:
% 222.41/34.62 | (2112) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 222.41/34.62 | hAPP(all_1130_0, all_1103_0) = v0 & $i(v0))
% 222.41/34.62 |
% 222.41/34.62 | GROUND_INST: instantiating (500) with all_794_0, tc_Nat_Onat, all_1130_3,
% 222.41/34.62 | all_1130_0, simplifying with (228), (235), (516), (2003), (2004)
% 222.41/34.62 | gives:
% 222.41/34.62 | (2113) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 222.41/34.62 | hAPP(all_1130_0, all_1106_0) = v0 & $i(v0))
% 222.41/34.62 |
% 222.41/34.62 | GROUND_INST: instantiating (fact_poly__zero) with v_qa____,
% 222.41/34.62 | tc_Complex_Ocomplex, all_1180_0, simplifying with (62), (232),
% 222.41/34.62 | (234), (237), (552) gives:
% 222.41/34.62 | (2114) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 222.41/34.62 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 =
% 222.41/34.62 | v_qa____) | v2 = all_1180_0) & (v1 = v_qa____ | ( ~ (v2 =
% 222.41/34.62 | all_1180_0) & c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) =
% 222.41/34.62 | v2 & $i(v2))))
% 222.41/34.62 |
% 222.41/34.62 | GROUND_INST: instantiating (fact_poly__eq__0__iff__dvd) with v_a____,
% 222.41/34.62 | v_pa____, tc_Complex_Ocomplex, all_854_1, all_752_0, simplifying
% 222.41/34.62 | with (234), (237), (238), (239), (339), (1847) gives:
% 222.41/34.62 | (2115) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 222.41/34.62 | : ? [v5: $i] : ? [v6: $i] : (((v0 = all_752_0 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_752_0 &
% 222.41/34.62 | $i(all_752_0)) |
% 222.41/34.62 | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.41/34.62 | v2 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 222.41/34.62 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 222.41/34.62 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 222.41/34.62 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v1 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v6) & $i(v5) &
% 222.41/34.62 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & ~
% 222.41/34.62 | c_Rings_Odvd__class_Odvd(v1, v6, v_pa____))) & (( ~ (v0 =
% 222.41/34.62 | all_752_0) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 222.41/34.62 | $i(v0)) |
% 222.41/34.62 | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.41/34.62 | v2 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v3 &
% 222.41/34.62 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v3, v4) = v5 &
% 222.41/34.62 | c_Polynomial_OpCons(tc_Complex_Ocomplex, v2, v5) = v6 &
% 222.41/34.62 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v1 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(v1) = v4 & $i(v6) & $i(v5) &
% 222.41/34.62 | $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 222.41/34.62 | c_Rings_Odvd__class_Odvd(v1, v6, v_pa____))))
% 222.41/34.62 |
% 222.41/34.62 | GROUND_INST: instantiating (fact_poly__zero) with v_pa____,
% 222.41/34.62 | tc_Complex_Ocomplex, all_854_1, simplifying with (232), (234),
% 222.41/34.62 | (237), (239), (339) gives:
% 222.41/34.62 | (2116) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 222.41/34.62 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 =
% 222.41/34.62 | v_pa____) | v2 = all_854_1) & (v1 = v_pa____ | ( ~ (v2 =
% 222.41/34.62 | all_854_1) & c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) =
% 222.41/34.62 | v2 & $i(v2))))
% 222.41/34.62 |
% 222.41/34.62 | GROUND_INST: instantiating (fact_poly__zero) with v_p, tc_Complex_Ocomplex,
% 222.41/34.62 | all_1151_2, simplifying with (23), (232), (234), (237), (531)
% 222.41/34.62 | gives:
% 222.41/34.62 | (2117) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 222.41/34.62 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 =
% 222.41/34.62 | v_p) | v2 = all_1151_2) & (v1 = v_p | ( ~ (v2 = all_1151_2) &
% 222.41/34.62 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v2 & $i(v2))))
% 222.41/34.62 |
% 222.41/34.62 | GROUND_INST: instantiating (fact_poly__zero) with v_q, tc_Complex_Ocomplex,
% 222.41/34.62 | all_1151_0, simplifying with (20), (232), (234), (237), (532)
% 222.41/34.62 | gives:
% 222.41/34.62 | (2118) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 222.41/34.62 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 =
% 222.41/34.62 | v_q) | v2 = all_1151_0) & (v1 = v_q | ( ~ (v2 = all_1151_0) &
% 222.41/34.62 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v2 & $i(v2))))
% 222.41/34.62 |
% 222.41/34.62 | GROUND_INST: instantiating (75) with all_794_0, all_1091_0, simplifying with
% 222.41/34.62 | (1985), (2004) gives:
% 222.41/34.62 | (2119) c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_794_0, all_1091_0)
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2094) with fresh symbol all_1653_0 gives:
% 222.41/34.62 | (2120) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_744_0, all_1653_0) =
% 222.41/34.62 | v_na____ & $i(all_1653_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2120) implies:
% 222.41/34.62 | (2121) $i(all_1653_0)
% 222.41/34.62 | (2122) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_744_0, all_1653_0) =
% 222.41/34.62 | v_na____
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2105) with fresh symbol all_1657_0 gives:
% 222.41/34.62 | (2123) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1657_0 &
% 222.41/34.62 | $i(all_1657_0) & ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.62 | all_830_0, all_1657_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2123) implies:
% 222.41/34.62 | (2124) ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_830_0,
% 222.41/34.62 | all_1657_0)
% 222.41/34.62 | (2125) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1657_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2103) with fresh symbol all_1659_0 gives:
% 222.41/34.62 | (2126) ~ (all_1659_0 = all_1242_3) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1659_0 &
% 222.41/34.62 | $i(all_1659_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2126) implies:
% 222.41/34.62 | (2127) ~ (all_1659_0 = all_1242_3)
% 222.41/34.62 | (2128) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1659_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2104) with fresh symbol all_1661_0 gives:
% 222.41/34.62 | (2129) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1661_0 &
% 222.41/34.62 | $i(all_1661_0) & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.41/34.62 | all_830_0, all_1661_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2129) implies:
% 222.41/34.62 | (2130) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1661_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2102) with fresh symbol all_1665_0 gives:
% 222.41/34.62 | (2131) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1665_0 &
% 222.41/34.62 | $i(all_1665_0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 222.41/34.62 | all_794_0, all_1665_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2131) implies:
% 222.41/34.62 | (2132) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1665_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2101) with fresh symbol all_1667_0 gives:
% 222.41/34.62 | (2133) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1667_0 &
% 222.41/34.62 | $i(all_1667_0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 222.41/34.62 | all_1667_0, all_794_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2133) implies:
% 222.41/34.62 | (2134) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1667_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2100) with fresh symbol all_1669_0 gives:
% 222.41/34.62 | (2135) ~ (all_1669_0 = all_794_0) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1669_0 &
% 222.41/34.62 | $i(all_1669_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2135) implies:
% 222.41/34.62 | (2136) ~ (all_1669_0 = all_794_0)
% 222.41/34.62 | (2137) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1669_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2113) with fresh symbol all_1671_0 gives:
% 222.41/34.62 | (2138) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1671_0 &
% 222.41/34.62 | hAPP(all_1130_0, all_1106_0) = all_1671_0 & $i(all_1671_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2138) implies:
% 222.41/34.62 | (2139) $i(all_1671_0)
% 222.41/34.62 | (2140) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1671_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2112) with fresh symbol all_1673_0 gives:
% 222.41/34.62 | (2141) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1673_0 &
% 222.41/34.62 | hAPP(all_1130_0, all_1103_0) = all_1673_0 & $i(all_1673_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2141) implies:
% 222.41/34.62 | (2142) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1673_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2107) with fresh symbol all_1681_0 gives:
% 222.41/34.62 | (2143) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1681_0 &
% 222.41/34.62 | $i(all_1681_0) & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.41/34.62 | all_1681_0, all_1392_0) |
% 222.41/34.62 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_830_0, all_1681_0))
% 222.41/34.62 | & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, all_830_0,
% 222.41/34.62 | all_1681_0) | c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.41/34.62 | all_1681_0, all_1392_0))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2143) implies:
% 222.41/34.62 | (2144) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1681_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2111) with fresh symbol all_1683_0 gives:
% 222.41/34.62 | (2145) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1683_0 &
% 222.41/34.62 | $i(all_1683_0) & ( ~ (all_1683_0 = all_1392_0) | all_1392_0 =
% 222.41/34.62 | all_830_0) & ( ~ (all_1683_0 = all_830_0) | all_1392_0 =
% 222.41/34.62 | all_830_0)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2145) implies:
% 222.41/34.62 | (2146) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1683_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2110) with fresh symbol all_1685_0 gives:
% 222.41/34.62 | (2147) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1685_0 &
% 222.41/34.62 | $i(all_1685_0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.62 | all_1685_0, all_830_0) |
% 222.41/34.62 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1392_0,
% 222.41/34.62 | all_1685_0)) & ( ~
% 222.41/34.62 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1392_0,
% 222.41/34.62 | all_1685_0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.62 | all_1685_0, all_830_0))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2147) implies:
% 222.41/34.62 | (2148) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1685_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2106) with fresh symbol all_1687_0 gives:
% 222.41/34.62 | (2149) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1687_0 &
% 222.41/34.62 | $i(all_1687_0) & ( ~ (all_1687_0 = all_1242_4) | all_1242_4 =
% 222.41/34.62 | v_a____) & ( ~ (all_1687_0 = v_a____) | all_1242_4 = v_a____)
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2149) implies:
% 222.41/34.62 | (2150) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1687_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2109) with fresh symbol all_1689_0 gives:
% 222.41/34.62 | (2151) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1689_0 &
% 222.41/34.62 | $i(all_1689_0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.62 | all_1689_0, all_1392_0) |
% 222.41/34.62 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_830_0,
% 222.41/34.62 | all_1689_0)) & ( ~
% 222.41/34.62 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_830_0,
% 222.41/34.62 | all_1689_0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.62 | all_1689_0, all_1392_0))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2151) implies:
% 222.41/34.62 | (2152) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1689_0
% 222.41/34.62 | (2153) ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_1689_0,
% 222.41/34.62 | all_1392_0) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,
% 222.41/34.62 | all_830_0, all_1689_0)
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2108) with fresh symbol all_1691_0 gives:
% 222.41/34.62 | (2154) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1691_0 &
% 222.41/34.62 | $i(all_1691_0) & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.41/34.62 | all_1691_0, all_830_0) |
% 222.41/34.62 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1392_0,
% 222.41/34.62 | all_1691_0)) & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,
% 222.41/34.62 | all_1392_0, all_1691_0) |
% 222.41/34.62 | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1691_0, all_830_0))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2154) implies:
% 222.41/34.62 | (2155) c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1691_0
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2118) with fresh symbols all_1705_0, all_1705_1,
% 222.41/34.62 | all_1705_2 gives:
% 222.41/34.62 | (2156) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1705_2 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(all_1705_2) = all_1705_1 &
% 222.41/34.62 | $i(all_1705_1) & $i(all_1705_2) & ( ~ (all_1705_1 = v_q) |
% 222.41/34.62 | all_1705_0 = all_1151_0) & (all_1705_1 = v_q | ( ~ (all_1705_0 =
% 222.41/34.62 | all_1151_0) & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 222.41/34.62 | all_1705_1) = all_1705_0 & $i(all_1705_0)))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2156) implies:
% 222.41/34.62 | (2157) c_Groups_Ozero__class_Ozero(all_1705_2) = all_1705_1
% 222.41/34.62 | (2158) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1705_2
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2117) with fresh symbols all_1707_0, all_1707_1,
% 222.41/34.62 | all_1707_2 gives:
% 222.41/34.62 | (2159) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1707_2 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(all_1707_2) = all_1707_1 &
% 222.41/34.62 | $i(all_1707_1) & $i(all_1707_2) & ( ~ (all_1707_1 = v_p) |
% 222.41/34.62 | all_1707_0 = all_1151_2) & (all_1707_1 = v_p | ( ~ (all_1707_0 =
% 222.41/34.62 | all_1151_2) & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 222.41/34.62 | all_1707_1) = all_1707_0 & $i(all_1707_0)))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2159) implies:
% 222.41/34.62 | (2160) c_Groups_Ozero__class_Ozero(all_1707_2) = all_1707_1
% 222.41/34.62 | (2161) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1707_2
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2116) with fresh symbols all_1709_0, all_1709_1,
% 222.41/34.62 | all_1709_2 gives:
% 222.41/34.62 | (2162) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1709_2 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(all_1709_2) = all_1709_1 &
% 222.41/34.62 | $i(all_1709_1) & $i(all_1709_2) & ( ~ (all_1709_1 = v_pa____) |
% 222.41/34.62 | all_1709_0 = all_854_1) & (all_1709_1 = v_pa____ | ( ~ (all_1709_0
% 222.41/34.62 | = all_854_1) & c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 222.41/34.62 | all_1709_1) = all_1709_0 & $i(all_1709_0)))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2162) implies:
% 222.41/34.62 | (2163) c_Groups_Ozero__class_Ozero(all_1709_2) = all_1709_1
% 222.41/34.62 | (2164) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1709_2
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2114) with fresh symbols all_1711_0, all_1711_1,
% 222.41/34.62 | all_1711_2 gives:
% 222.41/34.62 | (2165) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1711_2 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(all_1711_2) = all_1711_1 &
% 222.41/34.62 | $i(all_1711_1) & $i(all_1711_2) & ( ~ (all_1711_1 = v_qa____) |
% 222.41/34.62 | all_1711_0 = all_1180_0) & (all_1711_1 = v_qa____ | ( ~
% 222.41/34.62 | (all_1711_0 = all_1180_0) &
% 222.41/34.62 | c_Polynomial_Opoly(tc_Complex_Ocomplex, all_1711_1) = all_1711_0
% 222.41/34.62 | & $i(all_1711_0)))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2165) implies:
% 222.41/34.62 | (2166) c_Groups_Ozero__class_Ozero(all_1711_2) = all_1711_1
% 222.41/34.62 | (2167) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1711_2
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2098) with fresh symbols all_1715_0, all_1715_1,
% 222.41/34.62 | all_1715_2 gives:
% 222.41/34.62 | (2168) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1715_2 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(all_1715_2) = all_1715_1 &
% 222.41/34.62 | $i(all_1715_1) & $i(all_1715_2) & ( ~ (all_1715_1 = all_1242_0) |
% 222.41/34.62 | (all_1715_0 = all_1242_4 & all_1242_0 = all_1242_1 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1242_4))
% 222.41/34.62 | & ( ~ (all_1715_1 = all_1242_1) | all_1242_0 = all_1242_1 | ( ~
% 222.41/34.62 | (all_1715_0 = all_1242_4) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1715_0 &
% 222.41/34.62 | $i(all_1715_0)))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2168) implies:
% 222.41/34.62 | (2169) c_Groups_Ozero__class_Ozero(all_1715_2) = all_1715_1
% 222.41/34.62 | (2170) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1715_2
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2099) with fresh symbols all_1717_0, all_1717_1,
% 222.41/34.62 | all_1717_2 gives:
% 222.41/34.62 | (2171) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1717_2 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(all_1717_2) = all_1717_1 &
% 222.41/34.62 | $i(all_1717_1) & $i(all_1717_2) & ( ~ (all_1717_1 = all_1242_1) |
% 222.41/34.62 | (all_1717_0 = all_1242_3 & all_1242_1 = all_806_0 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1242_3))
% 222.41/34.62 | & ( ~ (all_1717_1 = all_806_0) | all_1242_1 = all_806_0 | ( ~
% 222.41/34.62 | (all_1717_0 = all_1242_3) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1717_0 &
% 222.41/34.62 | $i(all_1717_0)))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2171) implies:
% 222.41/34.62 | (2172) c_Groups_Ozero__class_Ozero(all_1717_2) = all_1717_1
% 222.41/34.62 | (2173) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1717_2
% 222.41/34.62 | (2174) ~ (all_1717_1 = all_806_0) | all_1242_1 = all_806_0 | ( ~
% 222.41/34.62 | (all_1717_0 = all_1242_3) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1717_0 &
% 222.41/34.62 | $i(all_1717_0))
% 222.41/34.62 | (2175) ~ (all_1717_1 = all_1242_1) | (all_1717_0 = all_1242_3 & all_1242_1
% 222.41/34.62 | = all_806_0 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 222.41/34.62 | all_1242_3)
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2097) with fresh symbols all_1719_0, all_1719_1,
% 222.41/34.62 | all_1719_2 gives:
% 222.41/34.62 | (2176) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1719_2 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(all_1719_2) = all_1719_1 &
% 222.41/34.62 | $i(all_1719_1) & $i(all_1719_2) & ( ~ (all_1719_1 = all_806_0) |
% 222.41/34.62 | all_806_0 = v_s____ | ( ~ (all_1719_0 = all_882_0) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1719_0 &
% 222.41/34.62 | $i(all_1719_0))) & ( ~ (all_1719_1 = v_s____) | (all_1719_0 =
% 222.41/34.62 | all_882_0 & all_806_0 = v_s____ &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_882_0))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2176) implies:
% 222.41/34.62 | (2177) c_Groups_Ozero__class_Ozero(all_1719_2) = all_1719_1
% 222.41/34.62 | (2178) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1719_2
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2096) with fresh symbols all_1721_0, all_1721_1,
% 222.41/34.62 | all_1721_2 gives:
% 222.41/34.62 | (2179) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1721_2 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(all_1721_2) = all_1721_1 &
% 222.41/34.62 | $i(all_1721_1) & $i(all_1721_2) & ( ~ (all_1721_1 = all_806_0) |
% 222.41/34.62 | all_806_0 = v_s____ | ( ~ (all_1721_0 = all_880_0) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1721_0 &
% 222.41/34.62 | $i(all_1721_0))) & ( ~ (all_1721_1 = v_s____) | (all_1721_0 =
% 222.41/34.62 | all_880_0 & all_806_0 = v_s____ &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_880_0))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2179) implies:
% 222.41/34.62 | (2180) c_Groups_Ozero__class_Ozero(all_1721_2) = all_1721_1
% 222.41/34.62 | (2181) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1721_2
% 222.41/34.62 |
% 222.41/34.62 | DELTA: instantiating (2115) with fresh symbols all_1724_0, all_1724_1,
% 222.41/34.62 | all_1724_2, all_1724_3, all_1724_4, all_1724_5, all_1724_6 gives:
% 222.41/34.62 | (2182) ((all_1724_6 = all_752_0 &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_752_0 &
% 222.41/34.62 | $i(all_752_0)) |
% 222.41/34.62 | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.41/34.62 | all_1724_4 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.41/34.62 | all_1724_3 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.41/34.62 | all_1724_3, all_1724_2) = all_1724_1 &
% 222.41/34.62 | c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1724_4, all_1724_1)
% 222.41/34.62 | = all_1724_0 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) =
% 222.41/34.62 | all_1724_5 & c_Groups_Ozero__class_Ozero(all_1724_5) =
% 222.41/34.62 | all_1724_2 & $i(all_1724_0) & $i(all_1724_1) & $i(all_1724_2) &
% 222.41/34.62 | $i(all_1724_3) & $i(all_1724_4) & $i(all_1724_5) & ~
% 222.41/34.62 | c_Rings_Odvd__class_Odvd(all_1724_5, all_1724_0, v_pa____))) &
% 222.41/34.62 | (( ~ (all_1724_6 = all_752_0) &
% 222.41/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1724_6 &
% 222.41/34.62 | $i(all_1724_6)) |
% 222.41/34.62 | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.41/34.62 | all_1724_4 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.41/34.62 | all_1724_3 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.41/34.62 | all_1724_3, all_1724_2) = all_1724_1 &
% 222.41/34.62 | c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1724_4, all_1724_1)
% 222.41/34.62 | = all_1724_0 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) =
% 222.41/34.62 | all_1724_5 & c_Groups_Ozero__class_Ozero(all_1724_5) =
% 222.41/34.62 | all_1724_2 & $i(all_1724_0) & $i(all_1724_1) & $i(all_1724_2) &
% 222.41/34.62 | $i(all_1724_3) & $i(all_1724_4) & $i(all_1724_5) &
% 222.41/34.62 | c_Rings_Odvd__class_Odvd(all_1724_5, all_1724_0, v_pa____)))
% 222.41/34.62 |
% 222.41/34.62 | ALPHA: (2182) implies:
% 222.70/34.62 | (2183) ( ~ (all_1724_6 = all_752_0) &
% 222.70/34.62 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1724_6 &
% 222.70/34.62 | $i(all_1724_6)) |
% 222.70/34.62 | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.70/34.62 | all_1724_4 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.70/34.62 | all_1724_3 & c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1724_3,
% 222.70/34.62 | all_1724_2) = all_1724_1 &
% 222.70/34.62 | c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1724_4, all_1724_1) =
% 222.70/34.62 | all_1724_0 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1724_5
% 222.70/34.62 | & c_Groups_Ozero__class_Ozero(all_1724_5) = all_1724_2 &
% 222.70/34.62 | $i(all_1724_0) & $i(all_1724_1) & $i(all_1724_2) & $i(all_1724_3)
% 222.70/34.62 | & $i(all_1724_4) & $i(all_1724_5) &
% 222.70/34.62 | c_Rings_Odvd__class_Odvd(all_1724_5, all_1724_0, v_pa____))
% 222.70/34.62 |
% 222.70/34.62 | BETA: splitting (2175) gives:
% 222.70/34.62 |
% 222.70/34.62 | Case 1:
% 222.70/34.62 | |
% 222.70/34.62 | | (2184) ~ (all_1717_1 = all_1242_1)
% 222.70/34.62 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_746_0, all_1667_0, tc_Nat_Onat,
% 222.70/34.63 | | simplifying with (259), (2134) gives:
% 222.70/34.63 | | (2185) all_1667_0 = all_746_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1667_0, all_1669_0, tc_Nat_Onat,
% 222.70/34.63 | | simplifying with (2134), (2137) gives:
% 222.70/34.63 | | (2186) all_1669_0 = all_1667_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1665_0, all_1669_0, tc_Nat_Onat,
% 222.70/34.63 | | simplifying with (2132), (2137) gives:
% 222.70/34.63 | | (2187) all_1669_0 = all_1665_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_752_0, all_1687_0,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (265), (2150) gives:
% 222.70/34.63 | | (2188) all_1687_0 = all_752_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1659_0, all_1687_0,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (2128), (2150) gives:
% 222.70/34.63 | | (2189) all_1687_0 = all_1659_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1683_0, all_1685_0, tc_Int_Oint,
% 222.70/34.63 | | simplifying with (2146), (2148) gives:
% 222.70/34.63 | | (2190) all_1685_0 = all_1683_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1661_0, all_1685_0, tc_Int_Oint,
% 222.70/34.63 | | simplifying with (2130), (2148) gives:
% 222.70/34.63 | | (2191) all_1685_0 = all_1661_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_742_0, all_1691_0, tc_Int_Oint,
% 222.70/34.63 | | simplifying with (254), (2155) gives:
% 222.70/34.63 | | (2192) all_1691_0 = all_742_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1689_0, all_1691_0, tc_Int_Oint,
% 222.70/34.63 | | simplifying with (2152), (2155) gives:
% 222.70/34.63 | | (2193) all_1691_0 = all_1689_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1683_0, all_1691_0, tc_Int_Oint,
% 222.70/34.63 | | simplifying with (2146), (2155) gives:
% 222.70/34.63 | | (2194) all_1691_0 = all_1683_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1681_0, all_1691_0, tc_Int_Oint,
% 222.70/34.63 | | simplifying with (2144), (2155) gives:
% 222.70/34.63 | | (2195) all_1691_0 = all_1681_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (241) with all_1657_0, all_1691_0, tc_Int_Oint,
% 222.70/34.63 | | simplifying with (2125), (2155) gives:
% 222.70/34.63 | | (2196) all_1691_0 = all_1657_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (242) with all_1709_2, all_1711_2,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (2164), (2167) gives:
% 222.70/34.63 | | (2197) all_1711_2 = all_1709_2
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (242) with all_1709_2, all_1715_2,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (2164), (2170) gives:
% 222.70/34.63 | | (2198) all_1715_2 = all_1709_2
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (242) with all_1715_2, all_1717_2,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (2170), (2173) gives:
% 222.70/34.63 | | (2199) all_1717_2 = all_1715_2
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (242) with all_1707_2, all_1717_2,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (2161), (2173) gives:
% 222.70/34.63 | | (2200) all_1717_2 = all_1707_2
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (242) with all_806_1, all_1719_2,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (298), (2178) gives:
% 222.70/34.63 | | (2201) all_1719_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (242) with all_1715_2, all_1719_2,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (2170), (2178) gives:
% 222.70/34.63 | | (2202) all_1719_2 = all_1715_2
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (242) with all_1711_2, all_1721_2,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (2167), (2181) gives:
% 222.70/34.63 | | (2203) all_1721_2 = all_1711_2
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (242) with all_1705_2, all_1721_2,
% 222.70/34.63 | | tc_Complex_Ocomplex, simplifying with (2158), (2181) gives:
% 222.70/34.63 | | (2204) all_1721_2 = all_1705_2
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (243) with all_794_0, all_1673_0, tc_Nat_Onat,
% 222.70/34.63 | | simplifying with (289), (2142) gives:
% 222.70/34.63 | | (2205) all_1673_0 = all_794_0
% 222.70/34.63 | |
% 222.70/34.63 | | GROUND_INST: instantiating (243) with all_1671_0, all_1673_0, tc_Nat_Onat,
% 222.70/34.63 | | simplifying with (2140), (2142) gives:
% 222.70/34.63 | | (2206) all_1673_0 = all_1671_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2203), (2204) imply:
% 222.70/34.63 | | (2207) all_1711_2 = all_1705_2
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2207) implies:
% 222.70/34.63 | | (2208) all_1711_2 = all_1705_2
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2201), (2202) imply:
% 222.70/34.63 | | (2209) all_1715_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2209) implies:
% 222.70/34.63 | | (2210) all_1715_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2199), (2200) imply:
% 222.70/34.63 | | (2211) all_1715_2 = all_1707_2
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2211) implies:
% 222.70/34.63 | | (2212) all_1715_2 = all_1707_2
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2198), (2212) imply:
% 222.70/34.63 | | (2213) all_1709_2 = all_1707_2
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2213) implies:
% 222.70/34.63 | | (2214) all_1709_2 = all_1707_2
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2210), (2212) imply:
% 222.70/34.63 | | (2215) all_1707_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2197), (2208) imply:
% 222.70/34.63 | | (2216) all_1709_2 = all_1705_2
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2216) implies:
% 222.70/34.63 | | (2217) all_1709_2 = all_1705_2
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2214), (2217) imply:
% 222.70/34.63 | | (2218) all_1707_2 = all_1705_2
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2218) implies:
% 222.70/34.63 | | (2219) all_1707_2 = all_1705_2
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2215), (2219) imply:
% 222.70/34.63 | | (2220) all_1705_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2220) implies:
% 222.70/34.63 | | (2221) all_1705_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2192), (2193) imply:
% 222.70/34.63 | | (2222) all_1689_0 = all_742_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2193), (2194) imply:
% 222.70/34.63 | | (2223) all_1689_0 = all_1683_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2193), (2196) imply:
% 222.70/34.63 | | (2224) all_1689_0 = all_1657_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2193), (2195) imply:
% 222.70/34.63 | | (2225) all_1689_0 = all_1681_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2222), (2225) imply:
% 222.70/34.63 | | (2226) all_1681_0 = all_742_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2223), (2225) imply:
% 222.70/34.63 | | (2227) all_1683_0 = all_1681_0
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2227) implies:
% 222.70/34.63 | | (2228) all_1683_0 = all_1681_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2224), (2225) imply:
% 222.70/34.63 | | (2229) all_1681_0 = all_1657_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2188), (2189) imply:
% 222.70/34.63 | | (2230) all_1659_0 = all_752_0
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2230) implies:
% 222.70/34.63 | | (2231) all_1659_0 = all_752_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2190), (2191) imply:
% 222.70/34.63 | | (2232) all_1683_0 = all_1661_0
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2232) implies:
% 222.70/34.63 | | (2233) all_1683_0 = all_1661_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2228), (2233) imply:
% 222.70/34.63 | | (2234) all_1681_0 = all_1661_0
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2234) implies:
% 222.70/34.63 | | (2235) all_1681_0 = all_1661_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2226), (2235) imply:
% 222.70/34.63 | | (2236) all_1661_0 = all_742_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2229), (2235) imply:
% 222.70/34.63 | | (2237) all_1661_0 = all_1657_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2205), (2206) imply:
% 222.70/34.63 | | (2238) all_1671_0 = all_794_0
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2238) implies:
% 222.70/34.63 | | (2239) all_1671_0 = all_794_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2186), (2187) imply:
% 222.70/34.63 | | (2240) all_1667_0 = all_1665_0
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2240) implies:
% 222.70/34.63 | | (2241) all_1667_0 = all_1665_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2185), (2241) imply:
% 222.70/34.63 | | (2242) all_1665_0 = all_746_0
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2242) implies:
% 222.70/34.63 | | (2243) all_1665_0 = all_746_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2236), (2237) imply:
% 222.70/34.63 | | (2244) all_1657_0 = all_742_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2187), (2243) imply:
% 222.70/34.63 | | (2245) all_1669_0 = all_746_0
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2217), (2221) imply:
% 222.70/34.63 | | (2246) all_1709_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2208), (2221) imply:
% 222.70/34.63 | | (2247) all_1711_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2200), (2215) imply:
% 222.70/34.63 | | (2248) all_1717_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | COMBINE_EQS: (2204), (2221) imply:
% 222.70/34.63 | | (2249) all_1721_2 = all_806_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2136), (2245) imply:
% 222.70/34.63 | | (2250) ~ (all_794_0 = all_746_0)
% 222.70/34.63 | |
% 222.70/34.63 | | SIMP: (2250) implies:
% 222.70/34.63 | | (2251) ~ (all_794_0 = all_746_0)
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2180), (2249) imply:
% 222.70/34.63 | | (2252) c_Groups_Ozero__class_Ozero(all_806_1) = all_1721_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2177), (2201) imply:
% 222.70/34.63 | | (2253) c_Groups_Ozero__class_Ozero(all_806_1) = all_1719_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2172), (2248) imply:
% 222.70/34.63 | | (2254) c_Groups_Ozero__class_Ozero(all_806_1) = all_1717_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2169), (2210) imply:
% 222.70/34.63 | | (2255) c_Groups_Ozero__class_Ozero(all_806_1) = all_1715_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2166), (2247) imply:
% 222.70/34.63 | | (2256) c_Groups_Ozero__class_Ozero(all_806_1) = all_1711_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2163), (2246) imply:
% 222.70/34.63 | | (2257) c_Groups_Ozero__class_Ozero(all_806_1) = all_1709_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2160), (2215) imply:
% 222.70/34.63 | | (2258) c_Groups_Ozero__class_Ozero(all_806_1) = all_1707_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2157), (2221) imply:
% 222.70/34.63 | | (2259) c_Groups_Ozero__class_Ozero(all_806_1) = all_1705_1
% 222.70/34.63 | |
% 222.70/34.63 | | REDUCE: (2124), (2244) imply:
% 222.70/34.63 | | (2260) ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_830_0,
% 222.70/34.63 | | all_742_0)
% 222.70/34.63 | |
% 222.70/34.63 | | BETA: splitting (2183) gives:
% 222.70/34.63 | |
% 222.70/34.63 | | Case 1:
% 222.70/34.63 | | |
% 222.70/34.63 | | | (2261) ~ (all_1724_6 = all_752_0) &
% 222.70/34.63 | | | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1724_6 &
% 222.70/34.63 | | | $i(all_1724_6)
% 222.70/34.63 | | |
% 222.70/34.63 | | | ALPHA: (2261) implies:
% 222.70/34.63 | | | (2262) ~ (all_1724_6 = all_752_0)
% 222.70/34.63 | | | (2263) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1724_6
% 222.70/34.63 | | |
% 222.70/34.63 | | | GROUND_INST: instantiating (241) with all_752_0, all_1724_6,
% 222.70/34.63 | | | tc_Complex_Ocomplex, simplifying with (265), (2263) gives:
% 222.70/34.63 | | | (2264) all_1724_6 = all_752_0
% 222.70/34.63 | | |
% 222.70/34.63 | | | REDUCE: (2262), (2264) imply:
% 222.70/34.63 | | | (2265) $false
% 222.70/34.63 | | |
% 222.70/34.63 | | | CLOSE: (2265) is inconsistent.
% 222.70/34.63 | | |
% 222.70/34.63 | | Case 2:
% 222.70/34.63 | | |
% 222.70/34.63 | | | (2266) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.70/34.63 | | | all_1724_4 & c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) =
% 222.70/34.63 | | | all_1724_3 & c_Polynomial_OpCons(tc_Complex_Ocomplex,
% 222.70/34.63 | | | all_1724_3, all_1724_2) = all_1724_1 &
% 222.70/34.63 | | | c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1724_4, all_1724_1)
% 222.70/34.63 | | | = all_1724_0 & tc_Polynomial_Opoly(tc_Complex_Ocomplex) =
% 222.70/34.63 | | | all_1724_5 & c_Groups_Ozero__class_Ozero(all_1724_5) =
% 222.70/34.63 | | | all_1724_2 & $i(all_1724_0) & $i(all_1724_1) & $i(all_1724_2) &
% 222.70/34.63 | | | $i(all_1724_3) & $i(all_1724_4) & $i(all_1724_5) &
% 222.70/34.63 | | | c_Rings_Odvd__class_Odvd(all_1724_5, all_1724_0, v_pa____)
% 222.70/34.63 | | |
% 222.70/34.63 | | | ALPHA: (2266) implies:
% 222.70/34.63 | | | (2267) $i(all_1724_5)
% 222.70/34.63 | | | (2268) $i(all_1724_0)
% 222.70/34.63 | | | (2269) c_Groups_Ozero__class_Ozero(all_1724_5) = all_1724_2
% 222.70/34.63 | | | (2270) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1724_5
% 222.70/34.63 | | | (2271) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1724_4, all_1724_1)
% 222.70/34.63 | | | = all_1724_0
% 222.70/34.63 | | | (2272) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1724_3, all_1724_2)
% 222.70/34.63 | | | = all_1724_1
% 222.70/34.63 | | | (2273) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1724_3
% 222.70/34.63 | | | (2274) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____) =
% 222.70/34.63 | | | all_1724_4
% 222.70/34.63 | | |
% 222.70/34.63 | | | BETA: splitting (2153) gives:
% 222.70/34.63 | | |
% 222.70/34.63 | | | Case 1:
% 222.70/34.63 | | | |
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (241) with all_806_0, all_1709_1, all_806_1,
% 222.70/34.63 | | | | simplifying with (297), (2257) gives:
% 222.70/34.63 | | | | (2275) all_1709_1 = all_806_0
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (241) with all_1715_1, all_1717_1, all_806_1,
% 222.70/34.63 | | | | simplifying with (2254), (2255) gives:
% 222.70/34.63 | | | | (2276) all_1717_1 = all_1715_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (241) with all_1717_1, all_1719_1, all_806_1,
% 222.70/34.63 | | | | simplifying with (2253), (2254) gives:
% 222.70/34.63 | | | | (2277) all_1719_1 = all_1717_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (241) with all_1707_1, all_1719_1, all_806_1,
% 222.70/34.63 | | | | simplifying with (2253), (2258) gives:
% 222.70/34.63 | | | | (2278) all_1719_1 = all_1707_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (241) with all_1717_1, all_1721_1, all_806_1,
% 222.70/34.63 | | | | simplifying with (2252), (2254) gives:
% 222.70/34.63 | | | | (2279) all_1721_1 = all_1717_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (241) with all_1711_1, all_1721_1, all_806_1,
% 222.70/34.63 | | | | simplifying with (2252), (2256) gives:
% 222.70/34.63 | | | | (2280) all_1721_1 = all_1711_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (241) with all_1709_1, all_1721_1, all_806_1,
% 222.70/34.63 | | | | simplifying with (2252), (2257) gives:
% 222.70/34.63 | | | | (2281) all_1721_1 = all_1709_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (241) with all_1705_1, all_1721_1, all_806_1,
% 222.70/34.63 | | | | simplifying with (2252), (2259) gives:
% 222.70/34.63 | | | | (2282) all_1721_1 = all_1705_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (242) with all_806_1, all_1724_5,
% 222.70/34.63 | | | | tc_Complex_Ocomplex, simplifying with (298), (2270) gives:
% 222.70/34.63 | | | | (2283) all_1724_5 = all_806_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (243) with all_1242_3, all_1724_3,
% 222.70/34.63 | | | | tc_Complex_Ocomplex, simplifying with (590), (2273) gives:
% 222.70/34.63 | | | | (2284) all_1724_3 = all_1242_3
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | GROUND_INST: instantiating (248) with all_1242_4, all_1724_4, v_a____,
% 222.70/34.63 | | | | tc_Complex_Ocomplex, simplifying with (591), (2274) gives:
% 222.70/34.63 | | | | (2285) all_1724_4 = all_1242_4
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2280), (2281) imply:
% 222.70/34.63 | | | | (2286) all_1711_1 = all_1709_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2280), (2282) imply:
% 222.70/34.63 | | | | (2287) all_1711_1 = all_1705_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2279), (2280) imply:
% 222.70/34.63 | | | | (2288) all_1717_1 = all_1711_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | SIMP: (2288) implies:
% 222.70/34.63 | | | | (2289) all_1717_1 = all_1711_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2277), (2278) imply:
% 222.70/34.63 | | | | (2290) all_1717_1 = all_1707_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | SIMP: (2290) implies:
% 222.70/34.63 | | | | (2291) all_1717_1 = all_1707_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2276), (2289) imply:
% 222.70/34.63 | | | | (2292) all_1715_1 = all_1711_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2276), (2291) imply:
% 222.70/34.63 | | | | (2293) all_1715_1 = all_1707_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2292), (2293) imply:
% 222.70/34.63 | | | | (2294) all_1711_1 = all_1707_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | SIMP: (2294) implies:
% 222.70/34.63 | | | | (2295) all_1711_1 = all_1707_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2286), (2295) imply:
% 222.70/34.63 | | | | (2296) all_1709_1 = all_1707_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | SIMP: (2296) implies:
% 222.70/34.63 | | | | (2297) all_1709_1 = all_1707_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2287), (2295) imply:
% 222.70/34.63 | | | | (2298) all_1707_1 = all_1705_1
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2275), (2297) imply:
% 222.70/34.63 | | | | (2299) all_1707_1 = all_806_0
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | SIMP: (2299) implies:
% 222.70/34.63 | | | | (2300) all_1707_1 = all_806_0
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2298), (2300) imply:
% 222.70/34.63 | | | | (2301) all_1705_1 = all_806_0
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | SIMP: (2301) implies:
% 222.70/34.63 | | | | (2302) all_1705_1 = all_806_0
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2293), (2300) imply:
% 222.70/34.63 | | | | (2303) all_1715_1 = all_806_0
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | COMBINE_EQS: (2276), (2303) imply:
% 222.70/34.63 | | | | (2304) all_1717_1 = all_806_0
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | REDUCE: (2184), (2304) imply:
% 222.70/34.63 | | | | (2305) ~ (all_1242_1 = all_806_0)
% 222.70/34.63 | | | |
% 222.70/34.63 | | | | SIMP: (2305) implies:
% 222.70/34.63 | | | | (2306) ~ (all_1242_1 = all_806_0)
% 222.70/34.64 | | | |
% 222.70/34.64 | | | | REDUCE: (2272), (2284) imply:
% 222.70/34.64 | | | | (2307) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3,
% 222.70/34.64 | | | | all_1724_2) = all_1724_1
% 222.70/34.64 | | | |
% 222.70/34.64 | | | | REDUCE: (2271), (2285) imply:
% 222.70/34.64 | | | | (2308) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4,
% 222.70/34.64 | | | | all_1724_1) = all_1724_0
% 222.70/34.64 | | | |
% 222.70/34.64 | | | | REDUCE: (2269), (2283) imply:
% 222.70/34.64 | | | | (2309) c_Groups_Ozero__class_Ozero(all_806_1) = all_1724_2
% 222.70/34.64 | | | |
% 222.70/34.64 | | | | REDUCE: (2267), (2283) imply:
% 222.70/34.64 | | | | (2310) $i(all_806_1)
% 222.70/34.64 | | | |
% 222.70/34.64 | | | | BETA: splitting (2174) gives:
% 222.70/34.64 | | | |
% 222.70/34.64 | | | | Case 1:
% 222.70/34.64 | | | | |
% 222.70/34.64 | | | | | (2311) ~ (all_1717_1 = all_806_0)
% 222.70/34.64 | | | | |
% 222.70/34.64 | | | | | REDUCE: (2304), (2311) imply:
% 222.70/34.64 | | | | | (2312) $false
% 222.70/34.64 | | | | |
% 222.70/34.64 | | | | | CLOSE: (2312) is inconsistent.
% 222.70/34.64 | | | | |
% 222.70/34.64 | | | | Case 2:
% 222.70/34.64 | | | | |
% 222.70/34.64 | | | | | (2313) all_1242_1 = all_806_0 | ( ~ (all_1717_0 = all_1242_3) &
% 222.70/34.64 | | | | | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 222.70/34.64 | | | | | all_1717_0 & $i(all_1717_0))
% 222.70/34.64 | | | | |
% 222.70/34.64 | | | | | BETA: splitting (2313) gives:
% 222.70/34.64 | | | | |
% 222.70/34.64 | | | | | Case 1:
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | (2314) all_1242_1 = all_806_0
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | REDUCE: (2306), (2314) imply:
% 222.70/34.64 | | | | | | (2315) $false
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | CLOSE: (2315) is inconsistent.
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | Case 2:
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | GROUND_INST: instantiating (241) with all_806_0, all_1724_2,
% 222.70/34.64 | | | | | | all_806_1, simplifying with (297), (2309) gives:
% 222.70/34.64 | | | | | | (2316) all_1724_2 = all_806_0
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | REDUCE: (2307), (2316) imply:
% 222.70/34.64 | | | | | | (2317) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_3,
% 222.70/34.64 | | | | | | all_806_0) = all_1724_1
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | GROUND_INST: instantiating (251) with all_1242_1, all_1724_1,
% 222.70/34.64 | | | | | | all_806_0, all_1242_3, tc_Complex_Ocomplex, simplifying
% 222.70/34.64 | | | | | | with (1993), (2317) gives:
% 222.70/34.64 | | | | | | (2318) all_1724_1 = all_1242_1
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | REDUCE: (2308), (2318) imply:
% 222.70/34.64 | | | | | | (2319) c_Polynomial_OpCons(tc_Complex_Ocomplex, all_1242_4,
% 222.70/34.64 | | | | | | all_1242_1) = all_1724_0
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | GROUND_INST: instantiating (251) with all_1242_0, all_1724_0,
% 222.70/34.64 | | | | | | all_1242_1, all_1242_4, tc_Complex_Ocomplex,
% 222.70/34.64 | | | | | | simplifying with (588), (2319) gives:
% 222.70/34.64 | | | | | | (2320) all_1724_0 = all_1242_0
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | REDUCE: (2268), (2320) imply:
% 222.70/34.64 | | | | | | (2321) $i(all_1242_0)
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | GROUND_INST: instantiating (698) with all_794_0, all_794_0,
% 222.70/34.64 | | | | | | all_1091_0, simplifying with (1985), (2004), (2119)
% 222.70/34.64 | | | | | | gives:
% 222.70/34.64 | | | | | | (2322) all_1421_0 = all_794_0 | ? [v0: $i] : (c_Nat_OSuc(v0) =
% 222.70/34.64 | | | | | | all_794_0 & $i(v0) &
% 222.70/34.64 | | | | | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0,
% 222.70/34.64 | | | | | | all_794_0))
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | GROUND_INST: instantiating (163) with all_1593_2, all_744_0,
% 222.70/34.64 | | | | | | all_1242_0, all_806_1, all_1457_8, all_1457_2,
% 222.70/34.64 | | | | | | all_1354_6, all_1457_0, all_1527_0, all_1593_1,
% 222.70/34.64 | | | | | | all_1593_0, simplifying with (851), (1808), (1814),
% 222.70/34.64 | | | | | | (1846), (1850), (2063), (2074), (2088), (2093), (2095),
% 222.70/34.64 | | | | | | (2310), (2321) gives:
% 222.70/34.64 | | | | | | (2323) ? [v0: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,
% 222.70/34.64 | | | | | | all_744_0, all_1593_2) = v0 & hAPP(all_1457_2, v0) =
% 222.70/34.64 | | | | | | all_1593_0 & $i(v0) & $i(all_1593_0))
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | GROUND_INST: instantiating (162) with all_1653_0, all_744_0,
% 222.70/34.64 | | | | | | v_na____, all_1593_2, simplifying with (1803), (1850),
% 222.70/34.64 | | | | | | (2121), (2122) gives:
% 222.70/34.64 | | | | | | (2324) all_1653_0 = all_1593_2
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | DELTA: instantiating (2323) with fresh symbol all_2048_0 gives:
% 222.70/34.64 | | | | | | (2325) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_744_0,
% 222.70/34.64 | | | | | | all_1593_2) = all_2048_0 & hAPP(all_1457_2, all_2048_0)
% 222.70/34.64 | | | | | | = all_1593_0 & $i(all_2048_0) & $i(all_1593_0)
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | ALPHA: (2325) implies:
% 222.70/34.64 | | | | | | (2326) hAPP(all_1457_2, all_2048_0) = all_1593_0
% 222.70/34.64 | | | | | | (2327) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_744_0,
% 222.70/34.64 | | | | | | all_1593_2) = all_2048_0
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | REDUCE: (2122), (2324) imply:
% 222.70/34.64 | | | | | | (2328) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_744_0,
% 222.70/34.64 | | | | | | all_1593_2) = v_na____
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | BETA: splitting (2322) gives:
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | | Case 1:
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | (2329) all_1421_0 = all_794_0
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | COMBINE_EQS: (1770), (2329) imply:
% 222.70/34.64 | | | | | | | (2330) all_794_0 = all_746_0
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | REDUCE: (2251), (2330) imply:
% 222.70/34.64 | | | | | | | (2331) $false
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | CLOSE: (2331) is inconsistent.
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | Case 2:
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | GROUND_INST: instantiating (252) with v_na____, all_2048_0,
% 222.70/34.64 | | | | | | | all_1593_2, all_744_0, tc_Nat_Onat, simplifying with
% 222.70/34.64 | | | | | | | (2327), (2328) gives:
% 222.70/34.64 | | | | | | | (2332) all_2048_0 = v_na____
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | REDUCE: (2326), (2332) imply:
% 222.70/34.64 | | | | | | | (2333) hAPP(all_1457_2, v_na____) = all_1593_0
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | GROUND_INST: instantiating (247) with all_1593_7, all_1593_0,
% 222.70/34.64 | | | | | | | v_na____, all_1457_2, simplifying with (2076), (2333)
% 222.70/34.64 | | | | | | | gives:
% 222.70/34.64 | | | | | | | (2334) all_1593_0 = all_1593_7
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | REDUCE: (850), (2334) imply:
% 222.70/34.64 | | | | | | | (2335) $false
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | | CLOSE: (2335) is inconsistent.
% 222.70/34.64 | | | | | | |
% 222.70/34.64 | | | | | | End of split
% 222.70/34.64 | | | | | |
% 222.70/34.64 | | | | | End of split
% 222.70/34.64 | | | | |
% 222.70/34.64 | | | | End of split
% 222.70/34.64 | | | |
% 222.70/34.65 | | | Case 2:
% 222.70/34.65 | | | |
% 222.70/34.65 | | | | (2336) c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_830_0,
% 222.70/34.65 | | | | all_1689_0)
% 222.70/34.65 | | | |
% 222.70/34.65 | | | | REDUCE: (2222), (2336) imply:
% 222.70/34.65 | | | | (2337) c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, all_830_0,
% 222.70/34.65 | | | | all_742_0)
% 222.70/34.65 | | | |
% 222.70/34.65 | | | | PRED_UNIFY: (2260), (2337) imply:
% 222.70/34.65 | | | | (2338) $false
% 222.70/34.65 | | | |
% 222.70/34.65 | | | | CLOSE: (2338) is inconsistent.
% 222.70/34.65 | | | |
% 222.70/34.65 | | | End of split
% 222.70/34.65 | | |
% 222.70/34.65 | | End of split
% 222.70/34.65 | |
% 222.70/34.66 | Case 2:
% 222.70/34.66 | |
% 222.70/34.66 | | (2339) all_1717_0 = all_1242_3 & all_1242_1 = all_806_0 &
% 222.70/34.66 | | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1242_3
% 222.70/34.66 | |
% 222.70/34.66 | | ALPHA: (2339) implies:
% 222.70/34.66 | | (2340) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1242_3
% 222.70/34.66 | |
% 222.70/34.66 | | GROUND_INST: instantiating (241) with all_752_0, all_1687_0,
% 222.70/34.66 | | tc_Complex_Ocomplex, simplifying with (265), (2150) gives:
% 222.70/34.66 | | (2341) all_1687_0 = all_752_0
% 222.70/34.66 | |
% 222.70/34.66 | | GROUND_INST: instantiating (241) with all_1659_0, all_1687_0,
% 222.70/34.66 | | tc_Complex_Ocomplex, simplifying with (2128), (2150) gives:
% 222.70/34.66 | | (2342) all_1687_0 = all_1659_0
% 222.70/34.66 | |
% 222.70/34.66 | | GROUND_INST: instantiating (241) with all_1242_3, all_1687_0,
% 222.70/34.66 | | tc_Complex_Ocomplex, simplifying with (2150), (2340) gives:
% 222.70/34.66 | | (2343) all_1687_0 = all_1242_3
% 222.70/34.66 | |
% 222.70/34.66 | | COMBINE_EQS: (2341), (2342) imply:
% 222.70/34.66 | | (2344) all_1659_0 = all_752_0
% 222.70/34.66 | |
% 222.70/34.66 | | COMBINE_EQS: (2342), (2343) imply:
% 222.70/34.66 | | (2345) all_1659_0 = all_1242_3
% 222.70/34.66 | |
% 222.70/34.66 | | COMBINE_EQS: (2344), (2345) imply:
% 222.70/34.66 | | (2346) all_1242_3 = all_752_0
% 222.70/34.66 | |
% 222.70/34.66 | | REDUCE: (2127), (2344), (2346) imply:
% 222.70/34.66 | | (2347) $false
% 222.70/34.66 | |
% 222.70/34.66 | | CLOSE: (2347) is inconsistent.
% 222.70/34.66 | |
% 222.70/34.66 | End of split
% 222.70/34.66 |
% 222.70/34.66 End of proof
% 222.70/34.66 % SZS output end Proof for theBenchmark
% 222.70/34.66
% 222.70/34.66 34145ms
%------------------------------------------------------------------------------