%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW285+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 : n010.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 00:49:42 EDT 2023 % Result : Theorem 71.58s 10.45s % Output : Proof 193.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWW285+1 : TPTP v8.1.2. Released v5.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n010.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Sun Aug 27 20:26:34 EDT 2023 % 0.15/0.36 % CPUTime : % 0.22/0.62 ________ _____ % 0.22/0.62 ___ __ \_________(_)________________________________ % 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.62 % 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.62 (2023-06-19) % 0.22/0.62 % 0.22/0.62 (c) Philipp Rümmer, 2009-2023 % 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.62 Amanda Stjerna. % 0.22/0.62 Free software under BSD-3-Clause. % 0.22/0.62 % 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.62 % 0.22/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.63 Running up to 7 provers in parallel. % 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 20.69/3.64 Prover 1: Preprocessing ... % 20.83/3.68 Prover 4: Preprocessing ... % 20.83/3.69 Prover 3: Preprocessing ... % 20.83/3.69 Prover 2: Preprocessing ... % 20.83/3.69 Prover 0: Preprocessing ... % 20.83/3.69 Prover 5: Preprocessing ... % 21.43/3.77 Prover 6: Preprocessing ... % 59.04/8.90 Prover 3: Warning: ignoring some quantifiers % 60.24/8.92 Prover 1: Warning: ignoring some quantifiers % 61.52/9.16 Prover 3: Constructing countermodel ... % 62.56/9.22 Prover 6: Proving ... % 63.79/9.39 Prover 1: Constructing countermodel ... % 68.13/9.99 Prover 4: Warning: ignoring some quantifiers % 71.03/10.36 Prover 4: Constructing countermodel ... % 71.58/10.45 Prover 3: proved (9810ms) % 71.58/10.45 % 71.58/10.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 71.58/10.45 % 71.58/10.46 Prover 6: stopped % 71.58/10.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 71.88/10.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 78.59/11.40 Prover 0: Proving ... % 78.59/11.41 Prover 0: stopped % 78.59/11.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 79.31/11.57 Prover 5: Proving ... % 79.31/11.58 Prover 5: stopped % 79.31/11.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 79.31/11.64 Prover 8: Preprocessing ... % 82.85/11.93 Prover 7: Preprocessing ... % 89.46/12.85 Prover 10: Preprocessing ... % 89.46/12.87 Prover 2: Proving ... % 89.46/12.87 Prover 2: stopped % 89.46/12.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 90.77/13.06 Prover 11: Preprocessing ... % 96.90/13.85 Prover 8: Warning: ignoring some quantifiers % 97.37/13.90 Prover 13: Preprocessing ... % 98.91/14.09 Prover 8: Constructing countermodel ... % 101.00/14.39 Prover 10: Warning: ignoring some quantifiers % 101.63/14.45 Prover 7: Warning: ignoring some quantifiers % 103.09/14.64 Prover 10: Constructing countermodel ... % 104.50/14.87 Prover 7: Constructing countermodel ... % 111.61/15.80 Prover 11: Warning: ignoring some quantifiers % 112.49/15.99 Prover 1: stopped % 113.15/16.01 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 113.94/16.15 Prover 11: Constructing countermodel ... % 119.56/17.01 Prover 13: Warning: ignoring some quantifiers % 122.86/17.33 Prover 16: Preprocessing ... % 122.86/17.37 Prover 13: Constructing countermodel ... % 134.14/18.86 Prover 16: Warning: ignoring some quantifiers % 134.83/18.97 Prover 16: Constructing countermodel ... % 149.65/20.88 Prover 16: stopped % 150.20/20.90 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 155.53/21.68 Prover 19: Preprocessing ... % 162.19/22.50 Prover 13: stopped % 167.73/23.22 Prover 19: Warning: ignoring some quantifiers % 169.07/23.41 Prover 19: Constructing countermodel ... % 173.24/23.97 Prover 19: stopped % 188.86/26.02 Prover 10: Found proof (size 1011) % 188.86/26.02 Prover 10: proved (14614ms) % 188.86/26.02 Prover 11: stopped % 188.86/26.02 Prover 7: stopped % 188.86/26.03 Prover 8: stopped % 188.86/26.03 Prover 4: stopped % 188.86/26.03 % 188.86/26.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 188.86/26.03 % 190.35/26.63 % SZS output start Proof for theBenchmark % 190.35/26.65 Assumptions after simplification: % 190.35/26.65 --------------------------------- % 190.35/26.66 % 190.35/26.66 (arity_Complex__Ocomplex__Groups_Ozero) % 190.35/26.66 $i(tc_Complex_Ocomplex) & class_Groups_Ozero(tc_Complex_Ocomplex) % 190.35/26.66 % 190.35/26.66 (arity_Complex__Ocomplex__Int_Oring__char__0) % 190.35/26.66 $i(tc_Complex_Ocomplex) & class_Int_Oring__char__0(tc_Complex_Ocomplex) % 190.35/26.66 % 190.35/26.66 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) % 190.35/26.66 $i(tc_Complex_Ocomplex) & class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) % 190.35/26.66 % 190.35/26.66 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) % 190.35/26.66 $i(tc_Complex_Ocomplex) & class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) % 190.35/26.66 % 190.35/26.66 (arity_Complex__Ocomplex__Rings_Odvd) % 190.35/26.66 $i(tc_Complex_Ocomplex) & class_Rings_Odvd(tc_Complex_Ocomplex) % 190.35/26.66 % 190.35/26.66 (arity_Complex__Ocomplex__Rings_Oidom) % 190.35/26.66 $i(tc_Complex_Ocomplex) & class_Rings_Oidom(tc_Complex_Ocomplex) % 190.35/26.66 % 190.35/26.66 (arity_Nat__Onat__Rings_Odvd) % 190.35/26.66 $i(tc_Nat_Onat) & class_Rings_Odvd(tc_Nat_Onat) % 190.35/26.66 % 190.35/26.66 (arity_Nat__Onat__Rings_Olinordered__semidom) % 190.35/26.66 $i(tc_Nat_Onat) & class_Rings_Olinordered__semidom(tc_Nat_Onat) % 190.35/26.66 % 190.35/26.66 (arity_Nat__Onat__Rings_Ozero__neq__one) % 190.35/26.66 $i(tc_Nat_Onat) & class_Rings_Ozero__neq__one(tc_Nat_Onat) % 190.35/26.66 % 190.35/26.66 (arity_Polynomial__Opoly__Power_Opower) % 190.58/26.68 ! [v0: $i] : ! [v1: $i] : ( ~ (tc_Polynomial_Opoly(v0) = v1) | ~ $i(v0) | % 190.58/26.68 ~ class_Rings_Ocomm__semiring__1(v0) | class_Power_Opower(v1)) % 190.58/26.68 % 190.58/26.68 (arity_Polynomial__Opoly__Rings_Omult__zero) % 190.58/26.68 ! [v0: $i] : ! [v1: $i] : ( ~ (tc_Polynomial_Opoly(v0) = v1) | ~ $i(v0) | % 190.58/26.69 ~ class_Rings_Ocomm__semiring__0(v0) | class_Rings_Omult__zero(v1)) % 190.58/26.69 % 190.58/26.69 (arity_Polynomial__Opoly__Rings_Ono__zero__divisors) % 190.58/26.69 ! [v0: $i] : ! [v1: $i] : ( ~ (tc_Polynomial_Opoly(v0) = v1) | ~ $i(v0) | % 190.58/26.69 ~ class_Rings_Oidom(v0) | class_Rings_Ono__zero__divisors(v1)) % 190.58/26.69 % 190.58/26.69 (arity_Polynomial__Opoly__Rings_Ozero__neq__one) % 190.58/26.69 ! [v0: $i] : ! [v1: $i] : ( ~ (tc_Polynomial_Opoly(v0) = v1) | ~ $i(v0) | % 190.58/26.69 ~ class_Rings_Ocomm__semiring__1(v0) | class_Rings_Ozero__neq__one(v1)) % 190.58/26.69 % 190.58/26.69 (fact_Nat_Oadd__0__right) % 190.58/26.69 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.69 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 190.58/26.69 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 190.58/26.69 % 190.58/26.69 (fact_One__nat__def) % 190.58/26.69 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & % 190.58/26.69 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.69 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)) % 190.58/26.69 % 190.58/26.69 (fact_Suc__diff__1) % 190.58/26.69 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 190.58/26.69 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 190.58/26.69 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.69 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 190.58/26.69 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 190.58/26.69 v0, v2) | c_Nat_OSuc(v3) = v2)) % 190.58/26.69 % 190.58/26.69 (fact_Suc__eq__plus1) % 190.58/26.69 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.69 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 190.58/26.69 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) | % 190.58/26.69 (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 190.58/26.69 % 190.58/26.69 (fact_Suc__eq__plus1__left) % 190.58/26.69 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.69 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 190.58/26.69 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) | % 190.58/26.69 (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 190.58/26.69 % 190.58/26.69 (fact_Suc__neq__Zero) % 190.58/26.70 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.70 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 190.58/26.70 % 190.58/26.70 (fact_Suc__not__Zero) % 190.58/26.70 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.70 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 190.58/26.70 % 190.58/26.70 (fact_Suc__pred) % 190.58/26.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 190.58/26.70 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.70 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 190.58/26.70 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 190.58/26.70 v0, v2) | c_Nat_OSuc(v3) = v2)) % 190.58/26.70 % 190.58/26.70 (fact_Suc__pred_H) % 190.58/26.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 190.58/26.70 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 190.58/26.70 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.70 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 190.58/26.70 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 190.58/26.70 v0, v2) | c_Nat_OSuc(v3) = v2)) % 190.58/26.70 % 190.58/26.70 (fact_Suc__times__mod__eq) % 190.58/26.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 190.58/26.70 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.70 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.70 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 190.58/26.70 : (v7 = v0 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v6, v3) = v7) | ~ % 190.58/26.70 (c_Nat_OSuc(v5) = v6) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | % 190.58/26.70 ~ $i(v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 190.58/26.70 v3))) % 190.58/26.70 % 190.58/26.70 (fact_Zero__neq__Suc) % 190.58/26.70 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.70 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 190.58/26.70 % 190.58/26.70 (fact_Zero__not__Suc) % 190.58/26.71 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.71 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 190.58/26.71 % 190.58/26.71 (fact__096_B_Bthesis_O_A_I_B_Br_O_Aq_A_094_Adegree_Ap_A_061_Ap_A_K_Ar_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) % 190.58/26.71 $i(v_q) & $i(v_p) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? % 190.58/26.71 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 190.58/26.71 : (c_Power_Opower__class_Opower(v0) = v1 & c_Groups_Otimes__class_Otimes(v0) = % 190.58/26.71 v5 & c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v3 & % 190.58/26.71 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & hAPP(v6, v7) = v4 & hAPP(v5, % 190.58/26.71 v_p) = v6 & hAPP(v2, v3) = v4 & hAPP(v1, v_q) = v2 & $i(v7) & $i(v6) & % 190.58/26.71 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 190.58/26.71 % 190.58/26.71 (fact__096p_Advd_Aq_A_094_Adegree_Ap_096) % 190.58/26.71 $i(v_q) & $i(v_p) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? % 190.58/26.71 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (c_Power_Opower__class_Opower(v0) = v1 % 190.58/26.71 & c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v3 & % 190.58/26.71 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & hAPP(v2, v3) = v4 & hAPP(v1, % 190.58/26.71 v_q) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 190.58/26.71 c_Rings_Odvd__class_Odvd(v0, v_p, v4)) % 190.58/26.71 % 190.58/26.71 (fact_add__eq__if) % 190.58/26.71 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 190.58/26.71 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 190.58/26.71 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.71 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | ~ % 190.58/26.71 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 190.58/26.71 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = v5) | ~ $i(v3) | ~ % 190.58/26.71 $i(v2) | ? [v6: $i] : (c_Nat_OSuc(v5) = v6 & % 190.58/26.71 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v6 & $i(v6))) & ! % 190.58/26.71 [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 190.58/26.71 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = v3) | ~ $i(v2))) % 190.58/26.71 % 190.58/26.71 (fact_add__eq__self__zero) % 190.58/26.71 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.71 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 190.58/26.71 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ $i(v2) | ~ % 190.58/26.71 $i(v1))) % 190.58/26.71 % 190.58/26.71 (fact_add__gr__0) % 190.58/26.72 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.72 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 190.58/26.72 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 190.58/26.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 190.58/26.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i] : ! % 190.58/26.72 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, % 190.58/26.72 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 190.58/26.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 190.58/26.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : ! % 190.58/26.72 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, % 190.58/26.72 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 190.58/26.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 190.58/26.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 190.58/26.72 % 190.58/26.72 (fact_add__is__0) % 190.58/26.72 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.72 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~ % 190.58/26.72 $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~ % 190.58/26.72 $i(v1)) & ! [v1: $i] : (v1 = v0 | ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1))) % 190.58/26.72 % 190.58/26.72 (fact_add__is__1) % 190.58/26.72 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 190.58/26.72 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.72 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 190.58/26.72 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 190.58/26.72 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 190.58/26.72 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 190.58/26.72 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~ % 190.58/26.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] : % 190.58/26.72 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2))) % 190.58/26.72 % 190.58/26.72 (fact_bool_Osize_I1_J) % 190.58/26.73 $i(c_fTrue) & $i(tc_Nat_Onat) & ? [v0: $i] : % 190.58/26.73 (c_HOL_Obool_Obool__size(c_fTrue) = v0 & % 190.58/26.73 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 190.58/26.73 % 190.58/26.73 (fact_bool_Osize_I2_J) % 190.58/26.73 $i(c_fFalse) & $i(tc_Nat_Onat) & ? [v0: $i] : % 190.58/26.73 (c_HOL_Obool_Obool__size(c_fFalse) = v0 & % 190.58/26.73 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 190.58/26.73 % 190.58/26.73 (fact_coeff__1) % 190.58/26.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.73 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 190.58/26.73 $i] : ! [v6: $i] : ( ~ (c_Groups_Oone__class_Oone(v3) = v4) | ~ % 190.58/26.73 (c_Polynomial_Ocoeff(v2, v4) = v5) | ~ (tc_Polynomial_Opoly(v2) = v3) | % 190.58/26.73 ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ~ % 190.58/26.73 class_Rings_Ocomm__semiring__1(v2) | ? [v7: $i] : ? [v8: $i] : (( ~ (v1 % 190.58/26.73 = v0) | (v7 = v6 & c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))) & % 190.58/26.73 (v1 = v0 | (v8 = v6 & c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6)))))) % 190.58/26.73 % 190.58/26.73 (fact_coeff__pCons__0) % 190.58/26.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.73 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 190.58/26.73 $i] : ( ~ (c_Polynomial_OpCons(v3, v2, v1) = v4) | ~ % 190.58/26.73 (c_Polynomial_Ocoeff(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 190.58/26.73 ~ class_Groups_Ozero(v3) | hAPP(v5, v0) = v2)) % 190.58/26.73 % 190.58/26.73 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) % 190.58/26.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.73 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 190.58/26.73 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 190.58/26.73 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | ? [v5: $i] : % 190.58/26.73 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5)))) % 190.58/26.73 % 190.58/26.73 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) % 190.58/26.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.73 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 190.58/26.73 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 190.58/26.73 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | hAPP(v4, v0) % 190.58/26.73 = v1)) % 190.58/26.73 % 190.58/26.73 (fact_degree__0) % 190.58/26.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.73 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 190.58/26.73 | ~ (c_Polynomial_Odegree(v1, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = % 190.58/26.73 v2) | ~ (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ % 190.58/26.73 class_Groups_Ozero(v1))) % 190.58/26.73 % 190.58/26.73 (fact_degree__1) % 190.58/26.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.73 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 190.58/26.73 | ~ (c_Groups_Oone__class_Oone(v2) = v3) | ~ (c_Polynomial_Odegree(v1, % 190.58/26.73 v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = v2) | ~ $i(v1) | ~ % 190.58/26.73 class_Rings_Ocomm__semiring__1(v1))) % 190.58/26.73 % 190.58/26.73 (fact_degree__pCons__0) % 190.58/26.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.74 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 190.58/26.74 $i] : ! [v6: $i] : (v6 = v0 | ~ (c_Polynomial_Odegree(v2, v5) = v6) | ~ % 190.58/26.74 (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ (tc_Polynomial_Opoly(v2) = v3) % 190.58/26.74 | ~ (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 190.58/26.74 class_Groups_Ozero(v2))) % 190.58/26.74 % 190.58/26.74 (fact_degree__pCons__eq__if) % 190.58/26.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.74 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 190.58/26.74 $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~ % 190.58/26.74 (c_Polynomial_OpCons(v3, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 190.58/26.74 | ~ class_Groups_Ozero(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 190.58/26.74 [v9: $i] : ((v5 = v0 | ( ~ (v7 = v2) & tc_Polynomial_Opoly(v3) = v6 & % 190.58/26.74 c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6))) & ((v9 = v5 % 190.58/26.74 & c_Nat_OSuc(v8) = v5 & c_Polynomial_Odegree(v3, v2) = v8 & $i(v8) & % 190.58/26.74 $i(v5)) | (v7 = v2 & tc_Polynomial_Opoly(v3) = v6 & % 190.58/26.74 c_Groups_Ozero__class_Ozero(v6) = v2 & $i(v6)))))) % 190.58/26.74 % 190.58/26.74 (fact_degree__smult__eq) % 190.58/26.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.74 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 190.58/26.74 $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~ % 190.58/26.74 (c_Polynomial_Osmult(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 190.58/26.74 | ~ class_Rings_Oidom(v3) | ? [v6: $i] : ? [v7: $i] : ((v5 = v0 | ( ~ % 190.58/26.74 (v6 = v2) & c_Groups_Ozero__class_Ozero(v3) = v6 & $i(v6))) & ((v7 = % 190.58/26.74 v5 & c_Polynomial_Odegree(v3, v1) = v5 & $i(v5)) | (v6 = v2 & % 190.58/26.74 c_Groups_Ozero__class_Ozero(v3) = v2))))) % 190.58/26.74 % 190.58/26.74 (fact_degree__synthetic__div) % 190.58/26.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.74 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 190.58/26.74 : ( ~ (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ % 190.58/26.74 (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 190.58/26.74 ~ class_Rings_Ocomm__semiring__0(v3) | ? [v6: $i] : % 190.58/26.74 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v0) = v5 & % 190.58/26.74 c_Polynomial_Odegree(v3, v2) = v6 & $i(v6) & $i(v5)))) % 190.58/26.74 % 190.58/26.74 (fact_diff__0__eq__0) % 190.58/26.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.74 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 190.58/26.74 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 190.58/26.74 % 190.58/26.74 (fact_diff__Suc__1) % 190.58/26.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.74 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 190.58/26.74 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v1)) % 190.58/26.74 % 190.58/26.74 (fact_diff__Suc__eq__diff__pred) % 190.58/26.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.74 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 190.58/26.74 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 190.58/26.74 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ $i(v2) | ~ % 190.58/26.74 $i(v1) | ? [v5: $i] : (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) % 190.58/26.74 = v4 & c_Nat_OSuc(v1) = v5 & $i(v5) & $i(v4)))) % 190.58/26.74 % 190.58/26.74 (fact_diff__Suc__less) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 190.58/26.75 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 190.58/26.75 (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 190.58/26.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 190.58/26.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 190.58/26.75 % 190.58/26.75 (fact_diff__add__0) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 190.58/26.75 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 190.58/26.75 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 190.58/26.75 $i(v1))) % 190.58/26.75 % 190.58/26.75 (fact_diff__less) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 190.58/26.75 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~ % 190.58/26.75 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 190.58/26.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 190.58/26.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1))) % 190.58/26.75 % 190.58/26.75 (fact_diff__self__eq__0) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 190.58/26.75 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ $i(v1))) % 190.58/26.75 % 190.58/26.75 (fact_diffs0__imp__equal) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 190.58/26.75 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ $i(v2) | ~ % 190.58/26.75 $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) & % 190.58/26.75 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & $i(v3)))) % 190.58/26.75 % 190.58/26.75 (fact_div__1) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 190.58/26.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.75 $i] : ! [v3: $i] : (v3 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, % 190.58/26.75 v2, v1) = v3) | ~ $i(v2))) % 190.58/26.75 % 190.58/26.75 (fact_div__less) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 190.58/26.75 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 190.58/26.75 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1))) % 190.58/26.75 % 190.58/26.75 (fact_div__less__dividend) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 190.58/26.75 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.75 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 190.58/26.75 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v3) | ~ % 190.58/26.75 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~ % 190.58/26.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 190.58/26.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 190.58/26.75 % 190.58/26.75 (fact_div__mult__self1__is__m) % 190.58/26.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 190.58/26.75 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 190.58/26.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.75 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | % 190.58/26.75 ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = v6) | ~ (hAPP(v4, % 190.58/26.75 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 190.58/26.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 190.58/26.75 % 190.58/26.75 (fact_div__mult__self__is__m) % 190.58/26.76 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 190.58/26.76 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 190.58/26.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.76 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | % 190.58/26.76 ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = v6) | ~ (hAPP(v4, % 190.58/26.76 v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 190.58/26.76 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 190.58/26.76 % 190.58/26.76 (fact_dvd__1__iff__1) % 190.58/26.76 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 190.58/26.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 190.58/26.76 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v1) & ! [v2: $i] : (v2 = v1 | ~ % 190.58/26.76 $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1))) % 190.58/26.76 % 190.58/26.76 (fact_dvd__1__left) % 190.58/26.76 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 190.58/26.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ? [v2: % 190.58/26.76 $i] : ( ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2))) % 190.58/26.76 % 190.58/26.76 (fact_dvd__mult__cancel) % 190.58/26.76 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 190.58/26.76 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 190.58/26.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 190.58/26.76 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 190.58/26.76 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) % 190.58/26.76 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 190.58/26.76 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 190.58/26.76 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 190.58/26.76 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2))) % 190.58/26.76 % 190.58/26.76 (fact_dvd__mult__cancel1) % 190.58/26.76 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 190.58/26.76 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 190.58/26.76 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 190.58/26.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 190.58/26.76 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ % 190.58/26.76 (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 190.58/26.76 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 190.58/26.76 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : ! [v4: $i] % 190.58/26.76 : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) % 190.58/26.76 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 190.58/26.76 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 190.58/26.76 % 190.58/26.76 (fact_dvd__mult__cancel2) % 190.58/26.76 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 190.58/26.76 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 190.58/26.76 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 190.58/26.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 190.58/26.76 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ % 190.58/26.76 (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 190.58/26.76 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 190.58/26.76 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : ! [v4: $i] % 190.58/26.76 : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ $i(v3) % 190.58/26.76 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 190.58/26.76 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 190.58/26.76 % 190.58/26.76 (fact_dvd__pos__nat) % 190.58/26.76 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.76 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 190.58/26.76 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 190.58/26.76 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) | % 190.58/26.76 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 190.58/26.76 % 190.58/26.76 (fact_dvd__power) % 190.58/26.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 190.58/26.77 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 190.58/26.77 (hAPP(v5, v2) = v6) | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 190.58/26.77 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 190.58/26.77 class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3, v1, v6)) % 190.58/26.77 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 190.58/26.77 [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v2) = % 190.58/26.77 v6) | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 190.58/26.77 class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3, v1, v6) % 190.58/26.77 | ? [v7: $i] : ( ~ (v7 = v1) & c_Groups_Oone__class_Oone(v3) = v7 & % 190.58/26.77 $i(v7)))) % 190.58/26.77 % 190.58/26.77 (fact_eq) % 190.58/26.77 $i(v_q) & $i(v_p) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? % 190.58/26.77 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 190.58/26.77 : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q) = v2 & % 190.58/26.77 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p) = v0 & % 190.58/26.77 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v3 & % 190.58/26.77 c_Groups_Ozero__class_Ozero(v3) = v4 & % 190.58/26.77 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v5) & $i(v4) & % 190.58/26.77 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = v1 & ~ (v7 = v1) & ~ (v4 = v_q) % 190.58/26.77 & hAPP(v2, v5) = v7 & hAPP(v0, v5) = v1 & $i(v7)) | (v4 = v_q & ! [v8: % 190.58/26.77 $i] : ! [v9: $i] : (v9 = v1 | ~ (hAPP(v2, v8) = v9) | ~ $i(v8) | ? % 190.58/26.77 [v10: $i] : ( ~ (v10 = v1) & hAPP(v0, v8) = v10 & $i(v10)))))) % 190.58/26.77 % 190.58/26.77 (fact_gcd__lcm__complete__lattice__nat_Obot__least) % 190.58/26.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 190.58/26.77 $i(v0) & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 190.58/26.77 v0, v1))) % 190.58/26.77 % 190.58/26.77 (fact_gcd__lcm__complete__lattice__nat_Otop__greatest) % 190.58/26.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.77 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 190.58/26.77 v1, v0))) % 190.58/26.77 % 190.58/26.77 (fact_gr0I) % 190.58/26.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 190.58/26.77 & $i(v0) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | % 190.58/26.77 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 190.58/26.77 % 190.58/26.77 (fact_gr0__conv__Suc) % 191.03/26.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.03/26.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2) % 191.03/26.77 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! % 191.03/26.77 [v1: $i] : ( ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 191.03/26.77 v1) | ? [v2: $i] : (c_Nat_OSuc(v2) = v1 & $i(v2)))) % 191.03/26.77 % 191.03/26.77 (fact_gr__implies__not0) % 191.03/26.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.03/26.77 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 191.03/26.77 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 191.03/26.77 % 191.03/26.77 (fact_int__power__div__base) % 191.03/26.77 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.03/26.77 ? [v3: $i] : (c_Nat_OSuc(v0) = v3 & c_Power_Opower__class_Opower(tc_Int_Oint) % 191.03/26.77 = v2 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & % 191.03/26.77 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) & % 191.03/26.77 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 191.03/26.77 : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v3) = v7) | ~ % 191.03/26.77 (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 191.03/26.77 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~ % 191.03/26.77 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v9: $i] : % 191.03/26.77 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v9, v4) = v8 & hAPP(v6, v5) = v9 % 191.03/26.77 & $i(v9) & $i(v8)))) % 191.03/26.77 % 191.03/26.77 (fact_less__Suc0) % 191.03/26.77 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.03/26.77 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.03/26.77 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] : (v2 = v0 % 191.03/26.77 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1))) % 191.03/26.78 % 191.03/26.78 (fact_less__Suc__eq__0__disj) % 191.03/26.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.03/26.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.03/26.78 (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~ $i(v2) | % 191.03/26.78 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) | % 191.03/26.78 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v1: $i] : ! % 191.03/26.78 [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | % 191.03/26.78 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4: % 191.03/26.78 $i] : (c_Nat_OSuc(v4) = v2 & $i(v4) & % 191.03/26.78 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1: $i] : ! % 191.03/26.78 [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 191.03/26.78 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 191.03/26.78 % 191.03/26.78 (fact_less__nat__zero__code) % 191.03/26.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.03/26.78 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 191.03/26.78 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 191.03/26.78 % 191.03/26.78 (fact_less__zeroE) % 191.03/26.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.03/26.78 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 191.03/26.78 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 191.03/26.78 % 191.03/26.78 (fact_minus__nat_Odiff__0) % 191.03/26.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.03/26.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 191.03/26.78 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 191.03/26.78 % 191.03/26.78 (fact_mod__1) % 191.03/26.78 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.03/26.78 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.03/26.78 $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, % 191.03/26.78 v2, v1) = v3) | ~ $i(v2))) % 191.03/26.78 % 191.03/26.78 (fact_mod__Suc) % 191.03/26.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.03/26.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 191.03/26.78 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~ % 191.03/26.78 (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? [v6: $i] % 191.03/26.78 : ( ~ (v6 = v1) & c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v5 & % 191.03/26.78 c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5))) & ! [v1: $i] : ! [v2: $i] : ! % 191.03/26.78 [v3: $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, % 191.03/26.78 v1) = v4) | ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: % 191.03/26.78 $i] : ? [v6: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = % 191.03/26.78 v5 & c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5) & (v6 = v4 | v6 = v1)))) % 191.03/26.78 % 191.03/26.78 (fact_mod__eq__0__iff) % 191.03/26.78 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.03/26.78 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.03/26.78 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.03/26.78 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 191.03/26.78 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v4) | ~ $i(v3) | ~ % 191.03/26.78 $i(v2) | ? [v5: $i] : (hAPP(v1, v2) = v5 & $i(v5) & ! [v6: $i] : ( ~ % 191.03/26.78 (hAPP(v5, v6) = v3) | ~ $i(v6)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 191.03/26.78 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v0) | ~ $i(v3) | ~ % 191.03/26.78 $i(v2) | ? [v4: $i] : ? [v5: $i] : (hAPP(v4, v5) = v3 & hAPP(v1, v2) = % 191.03/26.78 v4 & $i(v5) & $i(v4)))) % 191.03/26.78 % 191.03/26.78 (fact_mod__lemma) % 191.03/26.78 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.03/26.78 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.03/26.78 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.03/26.78 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.03/26.78 : ! [v8: $i] : ! [v9: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, % 191.03/26.78 v2, v5) = v7) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v8, v4) = % 191.03/26.78 v9) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v1, v3) = v6) | ~ $i(v5) | ~ % 191.03/26.78 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.03/26.78 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 191.03/26.78 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v10: $i] : % 191.03/26.78 (hAPP(v6, v5) = v10 & $i(v10) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.03/26.78 v9, v10)))) % 191.03/26.78 % 191.03/26.78 (fact_mod__less__divisor) % 191.03/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.03/26.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.03/26.79 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~ % 191.03/26.79 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.03/26.79 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 191.03/26.79 % 191.03/26.79 (fact_monom__0) % 191.10/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.10/26.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.10/26.79 $i] : ( ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ % 191.10/26.79 (tc_Polynomial_Opoly(v2) = v3) | ~ (c_Groups_Ozero__class_Ozero(v3) = v4) % 191.10/26.79 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | % 191.10/26.79 (c_Polynomial_Omonom(v2, v1, v0) = v5 & $i(v5)))) % 191.10/26.79 % 191.10/26.79 (fact_mult__0) % 191.10/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.10/26.79 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) & % 191.10/26.79 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v2, v3) = % 191.10/26.79 v4) | ~ $i(v3))) % 191.10/26.79 % 191.10/26.79 (fact_mult__0__right) % 191.10/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.79 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.79 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = % 191.10/26.79 v1)) % 191.10/26.79 % 191.10/26.79 (fact_mult__cancel1) % 191.10/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.79 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | % 191.10/26.79 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | % 191.10/26.79 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.10/26.79 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ % 191.10/26.79 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 191.10/26.79 $i(v2))) % 191.10/26.79 % 191.10/26.79 (fact_mult__cancel2) % 191.10/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.79 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.10/26.79 : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, % 191.10/26.79 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 191.10/26.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.10/26.79 : (v4 = v2 | v3 = v1 | ~ (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ % 191.10/26.79 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 191.10/26.79 $i(v2))) % 191.10/26.79 % 191.10/26.79 (fact_mult__eq__1__iff) % 191.10/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 191.10/26.79 v2 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & % 191.10/26.79 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v3) = v2) | % 191.10/26.79 ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: % 191.10/26.79 $i] : ! [v5: $i] : (v3 = v2 | ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = % 191.10/26.79 v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 191.10/26.79 (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v2) = v3))) % 191.10/26.79 % 191.10/26.79 (fact_mult__eq__if) % 191.10/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.10/26.79 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 191.10/26.79 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.10/26.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 191.10/26.79 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 191.10/26.79 $i] : (v4 = v0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = % 191.10/26.79 v5) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~ % 191.10/26.79 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ? % 191.10/26.79 [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & $i(v9) & $i(v8))) & ! % 191.10/26.79 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v0 | ~ (hAPP(v4, v3) = v5) | % 191.10/26.79 ~ (hAPP(v1, v0) = v4) | ~ $i(v3))) % 191.10/26.79 % 191.10/26.79 (fact_mult__eq__self__implies__10) % 191.10/26.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.10/26.79 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.10/26.79 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & % 191.10/26.79 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, % 191.10/26.79 v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 191.10/26.79 % 191.10/26.79 (fact_mult__is__0) % 191.10/26.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.80 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.80 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) = v4) | ~ % 191.10/26.80 (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 191.10/26.80 : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v0, v2) = v3) | ~ $i(v2)) & % 191.10/26.80 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, % 191.10/26.80 v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2))) % 191.10/26.80 % 191.10/26.80 (fact_mult__less__cancel1) % 191.10/26.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.80 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.80 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.10/26.80 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) % 191.10/26.80 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 191.10/26.80 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 191.10/26.80 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 191.10/26.80 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i] : ! % 191.10/26.80 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 191.10/26.80 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 191.10/26.80 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 191.10/26.80 % 191.10/26.80 (fact_mult__less__cancel2) % 191.10/26.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.80 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.10/26.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.80 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.10/26.80 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ % 191.10/26.80 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 191.10/26.80 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : ! % 191.10/26.80 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 191.10/26.80 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 191.10/26.80 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] : ! % 191.10/26.80 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 191.10/26.80 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 191.10/26.80 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 191.10/26.80 % 191.10/26.80 (fact_mult__less__mono1) % 191.10/26.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.80 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.10/26.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.80 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.10/26.80 : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5, v2) = v6) | ~ % 191.10/26.80 (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 191.10/26.80 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 191.10/26.80 % 191.10/26.80 (fact_mult__less__mono2) % 191.10/26.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.80 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.10/26.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.80 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.10/26.80 : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ (hAPP(v1, v2) = v5) % 191.10/26.80 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.10/26.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 191.10/26.80 % 191.10/26.80 (fact_mult__poly__0__left) % 191.10/26.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.10/26.80 $i] : ! [v6: $i] : (v6 = v4 | ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | % 191.10/26.80 ~ (tc_Polynomial_Opoly(v1) = v2) | ~ (c_Groups_Ozero__class_Ozero(v2) = % 191.10/26.80 v4) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v4) = v5) | ~ $i(v1) | ~ % 191.10/26.80 $i(v0) | ~ class_Rings_Ocomm__semiring__0(v1)) % 191.10/26.80 % 191.10/26.80 (fact_n__less__m__mult__n) % 191.10/26.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 191.10/26.80 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 191.10/26.81 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 191.10/26.81 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) = % 191.10/26.81 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 191.10/26.81 % 191.10/26.81 (fact_n__less__n__mult__m) % 191.10/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 191.10/26.81 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 191.10/26.81 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 191.10/26.81 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = % 191.10/26.81 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 191.10/26.81 % 191.10/26.81 (fact_nat_Osimps_I2_J) % 191.10/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.10/26.81 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 191.10/26.81 % 191.10/26.81 (fact_nat_Osimps_I3_J) % 191.10/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.10/26.81 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 191.10/26.81 % 191.10/26.81 (fact_nat_Osize_I1_J) % 191.10/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Nat_Onat_Onat__size(v0) = v0 & % 191.10/26.81 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 191.10/26.81 % 191.10/26.81 (fact_nat_Osize_I2_J) % 191.10/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.10/26.81 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.81 $i] : ! [v3: $i] : ( ~ (c_Nat_Onat_Onat__size(v2) = v3) | ~ $i(v2) | ? % 191.10/26.81 [v4: $i] : ? [v5: $i] : (c_Nat_Onat_Onat__size(v4) = v5 & c_Nat_OSuc(v2) % 191.10/26.81 = v4 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5 & $i(v5) & % 191.10/26.81 $i(v4)))) % 191.10/26.81 % 191.10/26.81 (fact_nat_Osize_I3_J) % 191.10/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Nat_Osize__class_Osize(tc_Nat_Onat, v0) = % 191.10/26.81 v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 191.10/26.81 % 191.10/26.81 (fact_nat_Osize_I4_J) % 191.10/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.10/26.81 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.81 $i] : ! [v3: $i] : ( ~ (c_Nat_Osize__class_Osize(tc_Nat_Onat, v2) = v3) | % 191.10/26.81 ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 191.10/26.81 (c_Nat_Osize__class_Osize(tc_Nat_Onat, v4) = v5 & c_Nat_OSuc(v2) = v4 & % 191.10/26.81 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5 & $i(v5) & % 191.10/26.81 $i(v4)))) % 191.10/26.81 % 191.10/26.81 (fact_nat__0__less__mult__iff) % 191.10/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.10/26.81 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.10/26.81 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.10/26.81 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | % 191.10/26.81 ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 191.10/26.81 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 191.10/26.81 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i] : ! % 191.10/26.81 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 191.10/26.81 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.10/26.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5))) % 191.10/26.81 % 191.10/26.81 (fact_nat__1__eq__mult__iff) % 191.22/26.81 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.22/26.81 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 191.22/26.81 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.22/26.81 $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = v0) | ~ % 191.22/26.81 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : % 191.22/26.81 ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | % 191.22/26.81 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 191.22/26.81 (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2))) % 191.22/26.81 % 191.22/26.81 (fact_nat__diff__split) % 191.22/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.22/26.82 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.22/26.82 $i] : ! [v6: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 191.22/26.82 v1) = v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2) % 191.22/26.82 | ~ (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 191.22/26.82 ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) & hBOOL(v7))) & % 191.22/26.82 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.22/26.82 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 191.22/26.82 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.22/26.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ hBOOL(v5) | ? % 191.22/26.82 [v6: $i] : (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! [v1: $i] : ! % 191.22/26.82 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.22/26.82 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 191.22/26.82 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 191.22/26.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | hBOOL(v5) | ? [v6: % 191.22/26.82 $i] : ? [v7: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = % 191.22/26.82 v2 & hAPP(v3, v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] % 191.22/26.82 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.22/26.82 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 191.22/26.82 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | ? [v6: % 191.22/26.82 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ((v8 = v2 & % 191.22/26.82 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v7) = v2 & hAPP(v3, v7) % 191.22/26.82 = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, v0) = v6 & $i(v6) & ~ % 191.22/26.82 hBOOL(v6)))))) % 191.22/26.82 % 191.22/26.82 (fact_nat__diff__split__asm) % 191.22/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.22/26.82 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.22/26.82 $i] : ! [v6: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 191.22/26.82 v1) = v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2) % 191.22/26.82 | ~ (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 191.22/26.82 ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) & hBOOL(v7))) & % 191.22/26.82 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.22/26.82 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 191.22/26.82 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.22/26.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ hBOOL(v5) | ? % 191.22/26.82 [v6: $i] : (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! [v1: $i] : ! % 191.22/26.82 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.22/26.82 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 191.22/26.82 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 191.22/26.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | hBOOL(v5) | ? [v6: % 191.22/26.82 $i] : ? [v7: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = % 191.22/26.82 v2 & hAPP(v3, v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] % 191.22/26.82 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.22/26.82 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 191.22/26.82 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | ? [v6: % 191.22/26.82 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ((v8 = v2 & % 191.22/26.82 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v7) = v2 & hAPP(v3, v7) % 191.22/26.82 = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, v0) = v6 & $i(v6) & ~ % 191.22/26.82 hBOOL(v6)))))) % 191.22/26.82 % 191.22/26.82 (fact_nat__dvd__1__iff__1) % 191.22/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 191.22/26.82 $i(v0) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 = % 191.22/26.82 v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0))) % 191.22/26.82 % 191.22/26.82 (fact_nat__dvd__not__less) % 191.22/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.22/26.82 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 191.22/26.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ % 191.22/26.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 191.22/26.82 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2))) % 191.22/26.82 % 191.22/26.82 (fact_nat__lt__two__imp__zero__or__one) % 191.22/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 191.22/26.82 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 191.22/26.82 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ $i(v3) | ~ % 191.22/26.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 191.22/26.82 % 191.22/26.82 (fact_nat__mult__1) % 191.22/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.22/26.82 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.22/26.82 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 & $i(v2) % 191.22/26.82 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3) % 191.22/26.82 = v4) | ~ $i(v3))) % 191.22/26.82 % 191.22/26.82 (fact_nat__mult__1__right) % 191.22/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.22/26.82 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.22/26.82 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.22/26.82 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = % 191.22/26.82 v2)) % 191.22/26.82 % 191.22/26.82 (fact_nat__mult__div__cancel1) % 191.26/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.82 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.26/26.82 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.82 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.82 : ! [v8: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) | % 191.26/26.82 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | % 191.26/26.82 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 191.26/26.82 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8)))) % 191.26/26.82 % 191.26/26.82 (fact_nat__mult__div__cancel__disj) % 191.26/26.82 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.82 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.26/26.82 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.82 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.82 : ! [v8: $i] : (v4 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, % 191.26/26.82 v7) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 191.26/26.82 (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 191.26/26.82 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8))) & ! [v2: % 191.26/26.82 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.82 : (v7 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v6) = v7) | ~ % 191.26/26.82 (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v1, v0) = v4) | ~ % 191.26/26.82 $i(v3) | ~ $i(v2))) % 191.26/26.82 % 191.26/26.82 (fact_nat__mult__dvd__cancel1) % 191.26/26.83 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.83 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.26/26.83 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.83 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.83 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 191.26/26.83 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 191.26/26.83 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 191.26/26.83 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i] % 191.26/26.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) % 191.26/26.83 = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ % 191.26/26.83 $i(v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) % 191.26/26.83 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 191.26/26.83 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7))) % 191.26/26.83 % 191.26/26.83 (fact_nat__mult__dvd__cancel__disj) % 191.26/26.83 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.83 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.26/26.83 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.83 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.83 : (v4 = v1 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, % 191.26/26.83 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.83 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 191.26/26.83 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i] % 191.26/26.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) % 191.26/26.83 = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 191.26/26.83 $i(v3) | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 191.26/26.83 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : ! [v3: $i] % 191.26/26.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ % 191.26/26.83 (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 191.26/26.83 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v6))) % 191.26/26.83 % 191.26/26.83 (fact_nat__mult__eq__1__iff) % 191.26/26.83 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.83 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.26/26.83 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.83 $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = v1) | ~ % 191.26/26.83 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : % 191.26/26.83 ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | % 191.26/26.83 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 191.26/26.83 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2))) % 191.26/26.83 % 191.26/26.83 (fact_nat__mult__eq__cancel1) % 191.26/26.83 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.83 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.26/26.83 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.83 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | % 191.26/26.83 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | % 191.26/26.83 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 191.26/26.83 % 191.26/26.83 (fact_nat__mult__eq__cancel__disj) % 191.26/26.83 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.83 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.26/26.83 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.83 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | % 191.26/26.83 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | % 191.26/26.83 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.83 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ % 191.26/26.83 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 191.26/26.83 $i(v2))) % 191.26/26.83 % 191.26/26.83 (fact_nat__mult__less__cancel1) % 191.26/26.83 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.83 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.26/26.83 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.83 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.83 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 191.26/26.83 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 191.26/26.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 191.26/26.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 191.26/26.83 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 191.26/26.83 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ % 191.26/26.83 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 191.26/26.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 191.26/26.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 191.26/26.83 % 191.26/26.83 (fact_nat__power__eq__Suc__0__iff) % 191.26/26.83 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 191.26/26.83 v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 191.26/26.83 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & % 191.26/26.83 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v3) = v5) | % 191.26/26.83 ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.83 $i] : (v5 = v2 | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, v3) = v4) | ~ % 191.26/26.83 $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | % 191.26/26.83 ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 191.26/26.83 % 191.26/26.83 (fact_nat__power__less__imp__less) % 191.26/26.84 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.84 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 191.26/26.84 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.84 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.84 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 191.26/26.84 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 191.26/26.84 % 191.26/26.84 (fact_nat__zero__less__power__iff) % 191.26/26.84 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.84 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 191.26/26.84 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.84 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4, % 191.26/26.84 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 191.26/26.84 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 191.26/26.84 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : ! % 191.26/26.84 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) | % 191.26/26.84 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 191.26/26.84 % 191.26/26.84 (fact_neq0__conv) % 191.26/26.84 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.84 & $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1: % 191.26/26.84 $i] : (v1 = v0 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.26/26.84 v0, v1))) % 191.26/26.84 % 191.26/26.84 (fact_not__less0) % 191.26/26.84 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.84 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 191.26/26.84 % 191.26/26.84 (fact_not__one__le__zero) % 191.26/26.84 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 191.26/26.84 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 191.26/26.84 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~ % 191.26/26.84 c_Orderings_Oord__class_Oless__eq(v0, v1, v2))) % 191.26/26.84 % 191.26/26.84 (fact_not__one__less__zero) % 191.26/26.84 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 191.26/26.84 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 191.26/26.84 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(v0, v1, v2))) % 191.26/26.84 % 191.26/26.84 (fact_nullstellensatz__lemma) % 191.26/26.84 $i(tc_Nat_Onat) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? [v1: $i] : ? % 191.26/26.84 [v2: $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(v2) = v3 & % 191.26/26.84 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v2 & % 191.26/26.84 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 191.26/26.84 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v3) & $i(v2) & % 191.26/26.84 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 191.26/26.84 [v8: $i] : ! [v9: $i] : (v4 = v1 | ~ % 191.26/26.84 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v6) = v7) | ~ (hAPP(v8, v4) = % 191.26/26.84 v9) | ~ (hAPP(v3, v5) = v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 191.26/26.84 c_Rings_Odvd__class_Odvd(v2, v6, v9) | ? [v10: $i] : ? [v11: $i] : ? % 191.26/26.84 [v12: $i] : ? [v13: $i] : ? [v14: $i] : ($i(v12) & ((v13 = v0 & ~ (v14 % 191.26/26.84 = v0) & c_Polynomial_Opoly(tc_Complex_Ocomplex, v5) = v10 & % 191.26/26.84 hAPP(v10, v12) = v14 & hAPP(v7, v12) = v0 & $i(v14) & $i(v10)) | ( ~ % 191.26/26.84 (v11 = v4) & c_Polynomial_Odegree(tc_Complex_Ocomplex, v6) = v11 & % 191.26/26.84 $i(v11)))))) % 191.26/26.84 % 191.26/26.84 (fact_one__is__add) % 191.26/26.84 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.26/26.84 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.84 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 191.26/26.84 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 191.26/26.84 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~ % 191.26/26.84 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 191.26/26.84 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~ % 191.26/26.84 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 191.26/26.84 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~ % 191.26/26.84 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 191.26/26.84 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~ % 191.26/26.84 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] : % 191.26/26.84 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2))) % 191.26/26.84 % 191.26/26.84 (fact_one__less__mult) % 191.26/26.84 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 191.26/26.84 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 191.26/26.84 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 191.26/26.84 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) = % 191.26/26.84 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6))) % 191.26/26.84 % 191.26/26.84 (fact_one__less__power) % 191.26/26.84 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.84 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.84 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 191.26/26.84 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.84 $i(v1) | ~ class_Rings_Olinordered__semidom(v3) | ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v7: $i] : % 191.26/26.84 (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~ % 191.26/26.84 c_Orderings_Oord__class_Oless(v3, v7, v2) | % 191.26/26.84 c_Orderings_Oord__class_Oless(v3, v7, v6))))) % 191.26/26.84 % 191.26/26.84 (fact_one__neq__zero) % 191.26/26.84 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 191.26/26.84 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) & % 191.26/26.84 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2))) % 191.26/26.84 % 191.26/26.84 (fact_order__root) % 191.26/26.85 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.85 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.85 $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~ % 191.26/26.85 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: $i] : % 191.26/26.85 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) & % 191.26/26.85 c_Polynomial_Oorder(v3, v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7 % 191.26/26.85 & c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | (v6 = v5 % 191.26/26.85 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & ((v8 = v2 & % 191.26/26.85 tc_Polynomial_Opoly(v3) = v7 & c_Groups_Ozero__class_Ozero(v7) = v2 % 191.26/26.85 & $i(v7)) | ( ~ (v9 = v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & % 191.26/26.85 $i(v9)) | ( ~ (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 & % 191.26/26.85 $i(v6)))))) % 191.26/26.85 % 191.26/26.85 (fact_pe) % 191.26/26.85 $i(v_p) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : % 191.26/26.85 (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & % 191.26/26.85 c_Groups_Ozero__class_Ozero(v0) = v_p & $i(v0)) % 191.26/26.85 % 191.26/26.85 (fact_plus__nat_Oadd__0) % 191.26/26.85 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.85 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 191.26/26.85 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 191.26/26.85 % 191.26/26.85 (fact_poly__decompose) % 191.26/26.85 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.85 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.26/26.85 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.85 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.26/26.85 (c_Polynomial_Opoly(v3, v2) = v4) | ~ (c_Groups_Ozero__class_Ozero(v3) = % 191.26/26.85 v5) | ~ (hAPP(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.85 class_Rings_Oidom(v3) | % 191.26/26.85 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(v3, v3, v4) | ? [v7: % 191.26/26.85 $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 191.26/26.85 $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ( ~ % 191.26/26.85 (v11 = v5) & ~ (v10 = v0) & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 191.26/26.85 v14, v1) = v7 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v13, v10) = % 191.26/26.85 v14 & c_Power_Opower__class_Opower(v3) = v9 & % 191.26/26.85 c_Groups_Otimes__class_Otimes(v3) = v8 & % 191.26/26.85 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v12) = v13 & % 191.26/26.85 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v7 & % 191.26/26.85 c_Polynomial_OpCons(v3, v11, v12) = v15 & c_Polynomial_Opoly(v3, v15) = % 191.26/26.85 v16 & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 191.26/26.85 $i(v10) & $i(v9) & $i(v8) & $i(v7) & ! [v17: $i] : ! [v18: $i] : ! % 191.26/26.85 [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : % 191.26/26.85 ( ~ (c_Groups_Oplus__class_Oplus(v3, v6, v22) = v23) | ~ (hAPP(v20, % 191.26/26.85 v21) = v22) | ~ (hAPP(v18, v10) = v19) | ~ (hAPP(v16, v17) = % 191.26/26.85 v21) | ~ (hAPP(v9, v17) = v18) | ~ (hAPP(v8, v19) = v20) | ~ % 191.26/26.85 $i(v17) | (hAPP(v4, v17) = v23 & $i(v23)))))) % 191.26/26.85 % 191.26/26.85 (fact_poly__zero) % 191.26/26.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Polynomial_Opoly(v1, v0) = % 191.26/26.85 v2) | ~ $i(v1) | ~ $i(v0) | ~ class_Int_Oring__char__0(v1) | ~ % 191.26/26.85 class_Rings_Oidom(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 191.26/26.85 (tc_Polynomial_Opoly(v1) = v3 & c_Groups_Ozero__class_Ozero(v3) = v4 & % 191.26/26.85 $i(v4) & $i(v3) & ( ~ (v4 = v0) | v5 = v2) & (v4 = v0 | ( ~ (v5 = v2) & % 191.26/26.85 c_Polynomial_Opoly(v1, v4) = v5 & $i(v5))))) % 191.26/26.85 % 191.26/26.85 (fact_pow__divides__eq__int) % 191.26/26.85 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.85 (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 & % 191.26/26.85 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.85 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.85 : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | % 191.26/26.85 ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 191.26/26.85 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) | % 191.26/26.85 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)) & ! [v2: $i] : ! [v3: $i] % 191.26/26.85 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 % 191.26/26.85 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) % 191.26/26.85 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.85 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2) | % 191.26/26.85 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8))) % 191.26/26.85 % 191.26/26.85 (fact_pow__divides__eq__nat) % 191.26/26.85 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.85 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 191.26/26.85 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.85 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.85 : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | % 191.26/26.85 ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 191.26/26.85 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) | % 191.26/26.85 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i] % 191.26/26.85 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 % 191.26/26.85 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) % 191.26/26.85 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.85 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 191.26/26.85 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8))) % 191.26/26.85 % 191.26/26.85 (fact_pow__divides__pow__int) % 191.26/26.85 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.85 (c_Power_Opower__class_Opower(tc_Int_Oint) = v0 & % 191.26/26.85 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.85 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.85 : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | % 191.26/26.85 ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 191.26/26.85 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) | % 191.26/26.85 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v2))) % 191.26/26.85 % 191.26/26.85 (fact_pow__divides__pow__nat) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.86 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 191.26/26.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.86 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.86 : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | % 191.26/26.86 ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 191.26/26.86 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) | % 191.26/26.86 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v2))) % 191.26/26.86 % 191.26/26.86 (fact_power_Opower_Opower__0) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.86 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.86 $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | ~ % 191.26/26.86 (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 191.26/26.86 hAPP(v6, v0) = v3)) % 191.26/26.86 % 191.26/26.86 (fact_power__0) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.86 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.26/26.86 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 191.26/26.86 $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] : % 191.26/26.86 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5)))) % 191.26/26.86 % 191.26/26.86 (fact_power__0__left) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.86 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.86 $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~ % 191.26/26.86 (c_Power_Opower__class_Opower(v2) = v3) | ~ % 191.26/26.86 (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | ~ % 191.26/26.86 (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | % 191.26/26.86 ~ class_Rings_Osemiring__0(v2)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 191.26/26.86 : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | % 191.26/26.86 ~ (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | ~ % 191.26/26.86 (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ class_Power_Opower(v1) | ~ % 191.26/26.86 class_Rings_Osemiring__0(v1) | (c_Groups_Oone__class_Oone(v1) = v5 & % 191.26/26.86 $i(v5)))) % 191.26/26.86 % 191.26/26.86 (fact_power__Suc__0) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 191.26/26.86 (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 191.26/26.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 & $i(v3) & % 191.26/26.86 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ % 191.26/26.86 (hAPP(v3, v4) = v5) | ~ $i(v4))) % 191.26/26.86 % 191.26/26.86 (fact_power__eq__0__iff) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.86 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.86 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 191.26/26.86 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.86 $i(v1) | ~ class_Rings_Ozero__neq__one(v3) | ~ % 191.26/26.86 class_Rings_Ono__zero__divisors(v3) | ~ class_Rings_Omult__zero(v3) | ~ % 191.26/26.86 class_Power_Opower(v3) | ? [v7: $i] : (c_Groups_Ozero__class_Ozero(v3) = % 191.26/26.86 v7 & $i(v7) & ( ~ (v7 = v6) | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2) % 191.26/26.86 | v6 = v2 | v1 = v0)))) % 191.26/26.86 % 191.26/26.86 (fact_power__eq__if) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 191.26/26.86 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 191.26/26.86 c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 191.26/26.86 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 & % 191.26/26.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) & % 191.26/26.86 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 191.26/26.86 : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~ % 191.26/26.86 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ (hAPP(v7, % 191.26/26.86 v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = v7) | ~ % 191.26/26.86 (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, v5) = v10 & % 191.26/26.86 $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | ~ % 191.26/26.86 (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4))) % 191.26/26.86 % 191.26/26.86 (fact_power__one__right) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 191.26/26.86 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.26/26.86 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 191.26/26.86 $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | hAPP(v4, v0) = % 191.26/26.86 v1)) % 191.26/26.86 % 191.26/26.86 (fact_psize__def) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.86 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.26/26.86 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | ~ % 191.26/26.86 $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i] : ? [v5: $i] % 191.26/26.86 : ? [v6: $i] : ? [v7: $i] : ((v3 = v0 | ( ~ (v5 = v1) & % 191.26/26.86 tc_Polynomial_Opoly(v2) = v4 & c_Groups_Ozero__class_Ozero(v4) = v5 % 191.26/26.86 & $i(v5) & $i(v4))) & ((v7 = v3 & c_Nat_OSuc(v6) = v3 & % 191.26/26.86 c_Polynomial_Odegree(v2, v1) = v6 & $i(v6) & $i(v3)) | (v5 = v1 & % 191.26/26.86 tc_Polynomial_Opoly(v2) = v4 & c_Groups_Ozero__class_Ozero(v4) = v1 % 191.26/26.86 & $i(v4)))))) % 191.26/26.86 % 191.26/26.86 (fact_psize__eq__0__iff) % 191.26/26.86 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.86 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.26/26.86 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | ~ % 191.26/26.86 $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i] : ? [v5: $i] % 191.26/26.86 : (( ~ (v3 = v0) | (v5 = v1 & tc_Polynomial_Opoly(v2) = v4 & % 191.26/26.86 c_Groups_Ozero__class_Ozero(v4) = v1 & $i(v4))) & (v3 = v0 | ( ~ (v5 % 191.26/26.86 = v1) & tc_Polynomial_Opoly(v2) = v4 & % 191.26/26.86 c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4)))))) % 191.26/26.86 % 191.26/26.86 (fact_r) % 191.26/26.87 $i(v_r____) & $i(v_q) & $i(v_p) & $i(tc_Complex_Ocomplex) & ? [v0: $i] : ? % 191.26/26.87 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 191.26/26.87 : (c_Power_Opower__class_Opower(v0) = v1 & c_Groups_Otimes__class_Otimes(v0) = % 191.26/26.87 v5 & c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v3 & % 191.26/26.87 tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & hAPP(v6, v_r____) = v4 & % 191.26/26.87 hAPP(v5, v_p) = v6 & hAPP(v2, v3) = v4 & hAPP(v1, v_q) = v2 & $i(v6) & % 191.26/26.87 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 191.26/26.87 % 191.26/26.87 (fact_realpow__minus__mult) % 191.26/26.87 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.87 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.26/26.87 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.87 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.87 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 191.26/26.87 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~ % 191.26/26.87 (c_Power_Opower__class_Opower(v4) = v6) | ~ % 191.26/26.87 (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = v11) | ~ % 191.26/26.87 (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v9) = v10) | % 191.26/26.87 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.87 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 191.26/26.87 class_Groups_Omonoid__mult(v4) | (hAPP(v7, v3) = v11 & $i(v11)))) % 191.26/26.87 % 191.26/26.87 (fact_realpow__num__eq__if) % 191.26/26.87 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.87 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.26/26.87 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.87 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 191.26/26.87 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 191.26/26.87 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~ % 191.26/26.87 (c_Power_Opower__class_Opower(v4) = v5) | ~ % 191.26/26.87 (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ (hAPP(v8, v10) = v11) | ~ % 191.26/26.87 (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ (hAPP(v5, v2) = v6) | % 191.26/26.87 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ class_Power_Opower(v4) | ? [v12: % 191.26/26.87 $i] : ? [v13: $i] : (( ~ (v3 = v0) | (v13 = v12 & % 191.26/26.87 c_Groups_Oone__class_Oone(v4) = v12 & hAPP(v6, v0) = v12 & $i(v12))) % 191.26/26.87 & (v3 = v0 | (v12 = v11 & hAPP(v6, v3) = v11 & $i(v11)))))) % 191.26/26.87 % 191.26/26.87 (fact_realpow__two__diff) % 191.26/26.87 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 191.26/26.87 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 191.26/26.87 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 191.26/26.87 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: % 191.26/26.87 $i] : ( ~ (c_Groups_Ominus__class_Ominus(v5, v8, v10) = v11) | ~ % 191.26/26.87 (c_Power_Opower__class_Opower(v5) = v6) | ~ (hAPP(v9, v2) = v10) | ~ % 191.26/26.87 (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, v3) = v9) | ~ % 191.26/26.87 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ class_Rings_Ocomm__ring__1(v5) | ? % 191.26/26.87 [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : % 191.26/26.87 (c_Groups_Ominus__class_Ominus(v5, v4, v3) = v13 & % 191.26/26.87 c_Groups_Oplus__class_Oplus(v5, v4, v3) = v15 & % 191.26/26.87 c_Groups_Otimes__class_Otimes(v5) = v12 & hAPP(v14, v15) = v11 & % 191.26/26.87 hAPP(v12, v13) = v14 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 191.26/26.87 $i(v11)))) % 191.26/26.87 % 191.26/26.87 (fact_realpow__two__disj) % 191.26/26.87 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 191.26/26.87 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 191.26/26.87 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 191.26/26.87 $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v5) = % 191.26/26.87 v6) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ % 191.26/26.87 $i(v4) | ~ $i(v3) | ~ class_Rings_Oidom(v5) | ? [v9: $i] : ? [v10: $i] % 191.26/26.87 : ? [v11: $i] : ((v4 = v3 | (v11 = v4 & % 191.26/26.87 c_Groups_Ouminus__class_Ouminus(v5, v3) = v4) | ( ~ (v10 = v9) & % 191.26/26.87 hAPP(v8, v2) = v10 & hAPP(v7, v2) = v9 & $i(v10) & $i(v9))) & ((v10 % 191.26/26.87 = v9 & hAPP(v8, v2) = v9 & hAPP(v7, v2) = v9 & $i(v9)) | ( ~ (v11 = % 191.26/26.87 v4) & ~ (v4 = v3) & c_Groups_Ouminus__class_Ouminus(v5, v3) = v11 % 191.26/26.87 & $i(v11)))))) % 191.26/26.87 % 191.26/26.87 (fact_split__mod) % 191.26/26.87 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.87 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.26/26.87 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.87 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.26/26.87 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5) % 191.26/26.87 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ? [v7: $i] : % 191.26/26.87 ? [v8: $i] : (( ~ (v2 = v0) | (hAPP(v4, v3) = v7 & $i(v7) & hBOOL(v7))) & % 191.26/26.87 (v2 = v0 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : ! % 191.26/26.87 [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) % 191.26/26.87 = v3) | ~ (hAPP(v8, v9) = v11) | ~ $i(v10) | ~ $i(v9) | ~ % 191.26/26.87 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) | ? [v12: $i] % 191.26/26.87 : (hAPP(v4, v10) = v12 & $i(v12) & hBOOL(v12))))))) & ! [v2: $i] % 191.26/26.87 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.26/26.87 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5) % 191.26/26.87 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | hBOOL(v6) | ? [v7: $i] : ? % 191.26/26.87 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 191.26/26.87 [v13: $i] : ($i(v10) & $i(v9) & ((v12 = v3 & ~ (v2 = v0) & % 191.26/26.87 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) = v3 & hAPP(v8, % 191.26/26.87 v9) = v11 & hAPP(v4, v10) = v13 & hAPP(v1, v2) = v8 & $i(v13) & % 191.26/26.87 $i(v11) & $i(v8) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, % 191.26/26.87 v2) & ~ hBOOL(v13)) | (v2 = v0 & hAPP(v4, v3) = v7 & $i(v7) & ~ % 191.26/26.87 hBOOL(v7)))))) % 191.26/26.87 % 191.26/26.87 (fact_synthetic__div__eq__0__iff) % 191.26/26.88 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.88 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.26/26.88 (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 191.26/26.88 ~ $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? [v5: $i] : ? [v6: % 191.26/26.88 $i] : ? [v7: $i] : (((v7 = v0 & c_Polynomial_Odegree(v3, v2) = v0) | ( % 191.26/26.88 ~ (v6 = v4) & tc_Polynomial_Opoly(v3) = v5 & % 191.26/26.88 c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) & ((v6 = v4 % 191.26/26.88 & tc_Polynomial_Opoly(v3) = v5 & c_Groups_Ozero__class_Ozero(v5) = % 191.26/26.88 v4 & $i(v5) & $i(v4)) | ( ~ (v7 = v0) & c_Polynomial_Odegree(v3, v2) % 191.26/26.88 = v7 & $i(v7)))))) % 191.26/26.88 % 191.26/26.88 (fact_zero__le__one) % 191.26/26.88 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 191.26/26.88 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 191.26/26.88 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & % 191.26/26.88 c_Orderings_Oord__class_Oless__eq(v0, v2, v1))) % 191.26/26.88 % 191.26/26.88 (fact_zero__less__Suc) % 191.26/26.88 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.88 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) % 191.26/26.88 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 191.26/26.88 % 191.26/26.88 (fact_zero__less__diff) % 191.26/26.88 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.26/26.88 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.26/26.88 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 191.26/26.88 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | % 191.26/26.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : ! % 191.26/26.88 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 191.26/26.88 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.26/26.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 191.26/26.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2))) % 191.26/26.88 % 191.26/26.88 (fact_zero__less__power__nat__eq) % 191.26/26.88 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 191.26/26.88 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 191.26/26.88 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 191.26/26.88 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4, % 191.26/26.88 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 191.26/26.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 191.26/26.88 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 191.26/26.88 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 191.26/26.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : ! % 191.26/26.88 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) | % 191.26/26.88 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 191.26/26.88 % 191.26/26.88 (fact_zero__neq__one) % 191.26/26.88 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 191.26/26.88 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) & % 191.26/26.88 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2))) % 191.26/26.88 % 191.26/26.88 (function-axioms) % 191.26/26.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.89 $i] : ! [v6: $i] : (v1 = v0 | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, % 191.26/26.89 v2) = v1) | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, v2) = v0)) & ! % 191.26/26.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 191.26/26.89 : (v1 = v0 | ~ (c_If(v5, v4, v3, v2) = v1) | ~ (c_If(v5, v4, v3, v2) = v0)) % 191.26/26.89 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 191.26/26.89 v0 | ~ (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 191.26/26.89 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 191.26/26.89 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 191.26/26.89 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 191.26/26.89 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Polynomial_Opoly__gcd(v4, v3, v2) = v1) | ~ (c_Polynomial_Opoly__gcd(v4, % 191.26/26.89 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 191.26/26.89 ! [v4: $i] : (v1 = v0 | ~ (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Power_Opower_Opower(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 191.26/26.89 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 191.26/26.89 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 191.26/26.89 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Polynomial_Opcompose(v4, v3, v2) = v1) | ~ (c_Polynomial_Opcompose(v4, % 191.26/26.89 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 191.26/26.89 ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_OpCons(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Polynomial_OpCons(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 191.26/26.89 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Oorder(v4, % 191.26/26.89 v3, v2) = v1) | ~ (c_Polynomial_Oorder(v4, v3, v2) = v0)) & ! [v0: $i] % 191.26/26.89 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Polynomial_Osmult(v4, v3, v2) = v1) | ~ (c_Polynomial_Osmult(v4, v3, v2) % 191.26/26.89 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 191.26/26.89 $i] : (v1 = v0 | ~ (c_Polynomial_Omonom(v4, v3, v2) = v1) | ~ % 191.26/26.89 (c_Polynomial_Omonom(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 191.26/26.89 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v4, v3, v2) = v1) % 191.26/26.89 | ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v4, v3, v2) = % 191.26/26.89 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 191.26/26.89 ~ (c_Groups_Osgn__class_Osgn(v3, v2) = v1) | ~ % 191.26/26.89 (c_Groups_Osgn__class_Osgn(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 191.26/26.89 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Rings_Oinverse__class_Oinverse(v3, % 191.26/26.89 v2) = v1) | ~ (c_Rings_Oinverse__class_Oinverse(v3, v2) = v0)) & ! % 191.26/26.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Nat_Osize__class_Osize(v3, v2) = v1) | ~ (c_Nat_Osize__class_Osize(v3, % 191.26/26.89 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 191.26/26.89 = v0 | ~ (c_Groups_Ouminus__class_Ouminus(v3, v2) = v1) | ~ % 191.26/26.89 (c_Groups_Ouminus__class_Ouminus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 191.26/26.89 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_fequal(v3, v2) = v1) | ~ % 191.26/26.89 (c_fequal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.26/26.89 $i] : (v1 = v0 | ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, % 191.26/26.89 v2) = v1) | ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, % 191.26/26.89 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 191.26/26.89 = v0 | ~ (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, % 191.26/26.89 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 191.26/26.89 = v0 | ~ (c_Polynomial_Ocoeff(v3, v2) = v1) | ~ (c_Polynomial_Ocoeff(v3, % 191.26/26.89 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 191.26/26.89 = v0 | ~ (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) % 191.26/26.89 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 191.26/26.89 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 191.26/26.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_HOL_Obool_Obool__size(v2) = v1) | ~ % 191.26/26.89 (c_HOL_Obool_Obool__size(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.26/26.89 $i] : (v1 = v0 | ~ (c_Nat_Onat_Onat__size(v2) = v1) | ~ % 191.26/26.89 (c_Nat_Onat_Onat__size(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 191.26/26.89 : (v1 = v0 | ~ (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0)) & ! [v0: % 191.26/26.89 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Groups_Oone__class_Oone(v2) = v1) | ~ (c_Groups_Oone__class_Oone(v2) = % 191.26/26.89 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.26/26.89 (c_Power_Opower__class_Opower(v2) = v1) | ~ % 191.26/26.89 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 191.26/26.89 [v2: $i] : (v1 = v0 | ~ (c_Groups_Otimes__class_Otimes(v2) = v1) | ~ % 191.26/26.89 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 191.26/26.89 [v2: $i] : (v1 = v0 | ~ (tc_Polynomial_Opoly(v2) = v1) | ~ % 191.26/26.89 (tc_Polynomial_Opoly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 191.26/26.89 (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 191.26/26.89 (c_Groups_Ozero__class_Ozero(v2) = v0)) % 191.26/26.89 % 191.26/26.89 Further assumptions not needed in the proof: % 191.26/26.89 -------------------------------------------- % 191.26/26.89 arity_Complex__Ocomplex__Fields_Ofield, % 191.26/26.89 arity_Complex__Ocomplex__Fields_Ofield__inverse__zero, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Oab__group__add, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Oab__semigroup__add, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Ogroup__add, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Omonoid__add, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Omonoid__mult, % 191.26/26.89 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Power_Opower, % 191.26/26.89 arity_Complex__Ocomplex__RealVector_Oreal__field, % 191.26/26.89 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, % 191.26/26.89 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, % 191.26/26.89 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, % 191.26/26.89 arity_Complex__Ocomplex__RealVector_Oreal__normed__field, % 191.26/26.89 arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Ocomm__ring, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Ocomm__ring__1, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Ocomm__semiring, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Odivision__ring, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Omult__zero, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Ono__zero__divisors, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Osemiring, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Osemiring__0, % 191.26/26.89 arity_Complex__Ocomplex__Rings_Ozero__neq__one, % 191.26/26.89 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 191.26/26.89 arity_Int__Oint__Divides_Oring__div, arity_Int__Oint__Divides_Osemiring__div, % 191.26/26.89 arity_Int__Oint__Groups_Oab__group__add, % 191.26/26.89 arity_Int__Oint__Groups_Oab__semigroup__add, % 191.26/26.89 arity_Int__Oint__Groups_Oab__semigroup__mult, % 191.26/26.89 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, % 191.26/26.89 arity_Int__Oint__Groups_Ocancel__comm__monoid__add, % 191.26/26.89 arity_Int__Oint__Groups_Ocancel__semigroup__add, % 191.26/26.89 arity_Int__Oint__Groups_Ocomm__monoid__add, % 191.26/26.89 arity_Int__Oint__Groups_Ocomm__monoid__mult, % 191.26/26.89 arity_Int__Oint__Groups_Ogroup__add, % 191.26/26.89 arity_Int__Oint__Groups_Olinordered__ab__group__add, % 191.26/26.89 arity_Int__Oint__Groups_Omonoid__add, arity_Int__Oint__Groups_Omonoid__mult, % 191.26/26.89 arity_Int__Oint__Groups_Oone, arity_Int__Oint__Groups_Oordered__ab__group__add, % 191.26/26.89 arity_Int__Oint__Groups_Oordered__ab__semigroup__add, % 191.26/26.89 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, % 191.26/26.89 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, % 191.26/26.89 arity_Int__Oint__Groups_Oordered__comm__monoid__add, % 191.26/26.89 arity_Int__Oint__Groups_Osgn__if, arity_Int__Oint__Groups_Ozero, % 191.26/26.89 arity_Int__Oint__Int_Oring__char__0, arity_Int__Oint__Power_Opower, % 191.26/26.89 arity_Int__Oint__Rings_Ocomm__ring, arity_Int__Oint__Rings_Ocomm__ring__1, % 191.26/26.89 arity_Int__Oint__Rings_Ocomm__semiring, % 191.26/26.89 arity_Int__Oint__Rings_Ocomm__semiring__0, % 191.26/26.89 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Odvd, % 191.26/26.89 arity_Int__Oint__Rings_Oidom, % 191.26/26.89 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, % 191.26/26.89 arity_Int__Oint__Rings_Olinordered__idom, % 191.26/26.89 arity_Int__Oint__Rings_Olinordered__ring, % 191.26/26.89 arity_Int__Oint__Rings_Olinordered__ring__strict, % 191.26/26.89 arity_Int__Oint__Rings_Olinordered__semidom, % 191.26/26.89 arity_Int__Oint__Rings_Olinordered__semiring, % 191.26/26.89 arity_Int__Oint__Rings_Olinordered__semiring__strict, % 191.26/26.89 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors, % 191.26/26.89 arity_Int__Oint__Rings_Oordered__cancel__semiring, % 191.26/26.89 arity_Int__Oint__Rings_Oordered__comm__semiring, % 191.26/26.89 arity_Int__Oint__Rings_Oordered__ring, % 191.26/26.89 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring, % 191.26/26.89 arity_Int__Oint__Rings_Oring__1, % 191.26/26.89 arity_Int__Oint__Rings_Oring__1__no__zero__divisors, % 191.26/26.89 arity_Int__Oint__Rings_Oring__no__zero__divisors, % 191.26/26.89 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0, % 191.26/26.89 arity_Int__Oint__Rings_Ozero__neq__one, % 191.26/26.89 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 191.26/26.89 arity_Nat__Onat__Divides_Osemiring__div, % 191.26/26.89 arity_Nat__Onat__Groups_Oab__semigroup__add, % 191.26/26.89 arity_Nat__Onat__Groups_Oab__semigroup__mult, % 191.26/26.89 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, % 191.26/26.89 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, % 191.26/26.89 arity_Nat__Onat__Groups_Ocancel__semigroup__add, % 191.26/26.89 arity_Nat__Onat__Groups_Ocomm__monoid__add, % 191.26/26.89 arity_Nat__Onat__Groups_Ocomm__monoid__mult, % 191.26/26.89 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult, % 191.26/26.89 arity_Nat__Onat__Groups_Oone, % 191.26/26.89 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, % 191.26/26.89 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, % 191.26/26.89 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, % 191.26/26.89 arity_Nat__Onat__Groups_Oordered__comm__monoid__add, % 191.26/26.89 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Power_Opower, % 191.26/26.89 arity_Nat__Onat__Rings_Ocomm__semiring, % 191.26/26.89 arity_Nat__Onat__Rings_Ocomm__semiring__0, % 191.26/26.89 arity_Nat__Onat__Rings_Ocomm__semiring__1, % 191.26/26.89 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, % 191.26/26.89 arity_Nat__Onat__Rings_Olinordered__semiring, % 191.26/26.89 arity_Nat__Onat__Rings_Olinordered__semiring__strict, % 191.26/26.89 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors, % 191.26/26.89 arity_Nat__Onat__Rings_Oordered__cancel__semiring, % 191.26/26.89 arity_Nat__Onat__Rings_Oordered__comm__semiring, % 191.26/26.89 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring, % 191.26/26.89 arity_Nat__Onat__Rings_Osemiring__0, % 191.26/26.89 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 191.26/26.89 arity_Polynomial__Opoly__Divides_Oring__div, % 191.26/26.89 arity_Polynomial__Opoly__Divides_Osemiring__div, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oab__group__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oab__semigroup__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Ogroup__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Omonoid__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Omonoid__mult, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oone, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, % 191.26/26.89 arity_Polynomial__Opoly__Groups_Osgn__if, arity_Polynomial__Opoly__Groups_Ozero, % 191.26/26.89 arity_Polynomial__Opoly__Int_Oring__char__0, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Ocomm__ring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Ocomm__ring__1, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Ocomm__semiring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Oidom, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Olinordered__idom, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Olinordered__ring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Olinordered__semidom, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Olinordered__semiring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Oordered__ring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Oordered__semiring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Osemiring, % 191.26/26.89 arity_Polynomial__Opoly__Rings_Osemiring__0, % 191.26/26.89 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 191.26/26.89 conj_0, fact_DERIV__inverse__lemma, fact_DERIV__mult__lemma, % 191.26/26.89 fact_DIVISION__BY__ZERO, fact_Deriv_Oadd__diff__add, % 191.26/26.89 fact_Deriv_Oinverse__diff__inverse, % 191.26/26.89 fact_Divides_Otransfer__nat__int__function__closures_I1_J, % 191.26/26.89 fact_Divides_Otransfer__nat__int__function__closures_I2_J, % 191.26/26.89 fact_Limits_Ominus__diff__minus, fact_Suc__diff__diff, fact_Suc__inject, % 191.26/26.89 fact_Suc__lessD, fact_Suc__lessI, fact_Suc__less__SucD, fact_Suc__less__eq, % 191.26/26.89 fact_Suc__mono, fact_Suc__mult__cancel1, fact_Suc__mult__less__cancel1, % 191.26/26.89 fact_Suc__n__not__n, fact_ab__diff__minus, fact_ab__left__minus, % 191.26/26.89 fact_ab__semigroup__add__class_Oadd__ac_I1_J, % 191.26/26.89 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_add_Ocomm__neutral, % 191.26/26.89 fact_add__0, fact_add__0__iff, fact_add__0__left, fact_add__0__right, % 191.26/26.89 fact_add__Suc, fact_add__Suc__right, fact_add__Suc__shift, % 191.26/26.89 fact_add__diff__cancel, fact_add__diff__inverse, fact_add__divide__distrib, % 191.26/26.89 fact_add__divide__eq__iff, fact_add__eq__0__iff, fact_add__frac__eq, % 191.26/26.89 fact_add__frac__num, fact_add__imp__eq, fact_add__increasing, % 191.26/26.89 fact_add__increasing2, fact_add__le__cancel__left, fact_add__le__cancel__right, % 191.26/26.89 fact_add__le__imp__le__left, fact_add__le__imp__le__right, % 191.26/26.89 fact_add__le__less__mono, fact_add__left__cancel, fact_add__left__imp__eq, % 191.26/26.89 fact_add__left__mono, fact_add__lessD1, fact_add__less__cancel__left, % 191.26/26.89 fact_add__less__cancel__right, fact_add__less__imp__less__left, % 191.26/26.89 fact_add__less__imp__less__right, fact_add__less__le__mono, % 191.26/26.89 fact_add__less__mono, fact_add__less__mono1, fact_add__minus__cancel, % 191.26/26.89 fact_add__mono, fact_add__monom, fact_add__mult__distrib, % 191.26/26.89 fact_add__mult__distrib2, fact_add__neg__neg, fact_add__nonneg__eq__0__iff, % 191.26/26.89 fact_add__nonneg__nonneg, fact_add__nonneg__pos, fact_add__nonpos__nonpos, % 191.26/26.89 fact_add__num__frac, fact_add__pCons, fact_add__poly__code_I1_J, % 191.26/26.89 fact_add__poly__code_I2_J, fact_add__pos__nonneg, fact_add__pos__pos, % 191.26/26.89 fact_add__right__cancel, fact_add__right__imp__eq, fact_add__right__mono, % 191.26/26.89 fact_add__scale__eq__noteq, fact_add__strict__increasing, % 191.26/26.89 fact_add__strict__left__mono, fact_add__strict__mono, % 191.26/26.89 fact_add__strict__right__mono, fact_coeff__0, fact_coeff__add, fact_coeff__diff, % 191.26/26.89 fact_coeff__eq__0, fact_coeff__inject, fact_coeff__linear__power, % 191.26/26.89 fact_coeff__minus, fact_coeff__monom, fact_coeff__mult__degree__sum, % 191.26/26.89 fact_coeff__pCons__Suc, fact_coeff__smult, fact_combine__common__factor, % 191.26/26.89 fact_comm__mult__left__mono, fact_comm__mult__strict__left__mono, % 191.26/26.89 fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, % 191.26/26.89 fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, % 191.26/26.89 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, % 191.26/26.89 fact_comm__semiring__class_Odistrib, fact_constant__def, fact_crossproduct__eq, % 191.26/26.89 fact_crossproduct__noteq, fact_degree__add__eq__left, % 191.26/26.89 fact_degree__add__eq__right, fact_degree__add__less, fact_degree__diff__less, % 191.26/26.89 fact_degree__linear__power, fact_degree__minus, fact_degree__mod__less, % 191.26/26.89 fact_degree__monom__eq, fact_degree__mult__eq, fact_degree__offset__poly, % 191.26/26.89 fact_degree__pCons__eq, fact_diff__0, fact_diff__0__right, fact_diff__Suc__Suc, % 191.26/26.89 fact_diff__add__cancel, fact_diff__add__inverse, fact_diff__add__inverse2, % 191.26/26.89 fact_diff__cancel, fact_diff__cancel2, fact_diff__commute, fact_diff__def, % 191.26/26.89 fact_diff__diff__left, fact_diff__divide__distrib, fact_diff__divide__eq__iff, % 191.26/26.89 fact_diff__eq__diff__eq, fact_diff__eq__diff__less, % 191.26/26.89 fact_diff__eq__diff__less__eq, fact_diff__frac__eq, fact_diff__int__def, % 191.26/26.89 fact_diff__int__def__symmetric, fact_diff__less__Suc, fact_diff__less__mono2, % 191.26/26.89 fact_diff__minus__eq__add, fact_diff__monom, fact_diff__mult__distrib, % 191.26/26.89 fact_diff__mult__distrib2, fact_diff__pCons, fact_diff__poly__code_I1_J, % 191.26/26.89 fact_diff__poly__code_I2_J, fact_diff__self, fact_div__0, fact_div__add, % 191.26/26.89 fact_div__add1__eq, fact_div__add__self1, fact_div__add__self2, fact_div__by__0, % 191.26/26.89 fact_div__by__1, fact_div__dvd__div, fact_div__mod__equality, % 191.26/26.89 fact_div__mod__equality2, fact_div__mult1__eq, fact_div__mult2__eq, % 191.26/26.89 fact_div__mult__div__if__dvd, fact_div__mult__mult1, fact_div__mult__mult1__if, % 191.26/26.89 fact_div__mult__mult2, fact_div__mult__self1, fact_div__mult__self1__is__id, % 191.26/26.89 fact_div__mult__self2, fact_div__mult__self2__is__id, fact_div__mult__swap, % 191.26/26.89 fact_div__neg__pos__less0, fact_div__poly__eq, fact_div__power, fact_div__self, % 191.26/26.89 fact_div__smult__left, fact_divide_Oadd, fact_divide_Odiff, fact_divide_Ominus, % 191.26/26.89 fact_divide_Ozero, fact_divide__1, fact_divide__add__eq__iff, % 191.26/26.89 fact_divide__diff__eq__iff, fact_divide__eq__eq, fact_divide__eq__imp, % 191.26/26.89 fact_divide__inverse, fact_divide__le__0__iff, fact_divide__less__0__iff, % 191.26/26.89 fact_divide__less__eq, fact_divide__neg__neg, fact_divide__neg__pos, % 191.26/26.89 fact_divide__pos__neg, fact_divide__pos__pos, fact_divide__right__mono, % 191.26/26.89 fact_divide__right__mono__neg, fact_divide__self, fact_divide__self__if, % 191.26/26.89 fact_divide__strict__left__mono, fact_divide__strict__left__mono__neg, % 191.26/26.89 fact_divide__strict__right__mono, fact_divide__strict__right__mono__neg, % 191.26/26.89 fact_divide__zero, fact_divide__zero__left, fact_division__ring__inverse__add, % 191.26/26.89 fact_division__ring__inverse__diff, fact_divisors__zero, % 191.26/26.89 fact_double__add__le__zero__iff__single__add__le__zero, % 191.26/26.89 fact_double__add__less__zero__iff__single__add__less__zero, % 191.26/26.89 fact_double__eq__0__iff, fact_double__zero__sym, fact_dvdI, fact_dvd_Oantisym, % 191.26/26.89 fact_dvd_Oantisym__conv, fact_dvd_Oeq__iff, fact_dvd_Oeq__refl, % 191.26/26.89 fact_dvd_Ole__imp__less__or__eq, fact_dvd_Ole__less, fact_dvd_Ole__less__trans, % 191.26/26.89 fact_dvd_Ole__neq__trans, fact_dvd_Oless__asym, fact_dvd_Oless__asym_H, % 191.26/26.89 fact_dvd_Oless__imp__le, fact_dvd_Oless__imp__neq, fact_dvd_Oless__imp__not__eq, % 191.26/26.89 fact_dvd_Oless__imp__not__eq2, fact_dvd_Oless__imp__not__less, % 191.26/26.89 fact_dvd_Oless__le, fact_dvd_Oless__le__trans, fact_dvd_Oless__not__sym, % 191.26/26.89 fact_dvd_Oless__trans, fact_dvd_Oneq__le__trans, fact_dvd_Oord__eq__le__trans, % 191.26/26.89 fact_dvd_Oord__eq__less__trans, fact_dvd_Oord__le__eq__trans, % 191.26/26.89 fact_dvd_Oord__less__eq__trans, fact_dvd_Oorder__refl, fact_dvd_Oorder__trans, % 191.26/26.89 fact_dvd__0__left, fact_dvd__0__right, fact_dvd__add, fact_dvd__antisym, % 191.26/26.89 fact_dvd__diff, fact_dvd__diff__nat, fact_dvd__div__div__eq__mult, % 191.26/26.89 fact_dvd__div__eq__mult, fact_dvd__div__mult, fact_dvd__div__mult__self, % 191.26/26.89 fact_dvd__div__neg, fact_dvd__eq__mod__eq__0, fact_dvd__iff__poly__eq__0, % 191.26/26.89 fact_dvd__imp__mod__0, fact_dvd__minus__iff, fact_dvd__mod, fact_dvd__mod__iff, % 191.26/26.89 fact_dvd__mod__imp__dvd, fact_dvd__mult, fact_dvd__mult2, % 191.26/26.89 fact_dvd__mult__cancel__left, fact_dvd__mult__cancel__right, % 191.26/26.89 fact_dvd__mult__div__cancel, fact_dvd__mult__left, fact_dvd__mult__right, % 191.26/26.89 fact_dvd__neg__div, fact_dvd__poly__gcd__iff, fact_dvd__power__same, % 191.26/26.89 fact_dvd__reduce, fact_dvd__refl, fact_dvd__smult, fact_dvd__smult__cancel, % 191.26/26.89 fact_dvd__smult__iff, fact_dvd__trans, fact_dvd__triv__left, % 191.26/26.89 fact_dvd__triv__right, fact_eq__add__iff1, fact_eq__add__iff2, % 191.26/26.89 fact_eq__divide__eq, fact_eq__divide__imp, fact_eq__iff__diff__eq__0, % 191.26/26.89 fact_eq__neg__iff__add__eq__0, fact_equal__neg__zero, fact_equation__minus__iff, % 191.26/26.89 fact_even__less__0__iff, fact_expand__poly__eq, fact_ext, % 191.26/26.89 fact_field__class_Onormalizing__field__rules_I2_J, fact_field__divide__inverse, % 191.26/26.89 fact_field__inverse, fact_field__inverse__zero, fact_field__power__not__zero, % 191.26/26.89 fact_frac__eq__eq, fact_fundamental__theorem__of__algebra, fact_gt__half__sum, % 191.26/26.89 fact_inf__period_I3_J, fact_inf__period_I4_J, fact_int__0__less__1, % 191.26/26.89 fact_int__0__neq__1, fact_int__div__less__self, fact_inverse__1, % 191.26/26.89 fact_inverse__add, fact_inverse__divide, fact_inverse__eq__1__iff, % 191.26/26.89 fact_inverse__eq__divide, fact_inverse__eq__iff__eq, fact_inverse__eq__imp__eq, % 191.26/26.89 fact_inverse__inverse__eq, fact_inverse__less__imp__less, % 191.26/26.89 fact_inverse__less__imp__less__neg, fact_inverse__minus__eq, % 191.26/26.89 fact_inverse__mult__distrib, fact_inverse__negative__iff__negative, % 191.26/26.89 fact_inverse__negative__imp__negative, % 191.26/26.89 fact_inverse__nonnegative__iff__nonnegative, % 191.26/26.89 fact_inverse__nonpositive__iff__nonpositive, % 191.26/26.89 fact_inverse__nonzero__iff__nonzero, fact_inverse__positive__iff__positive, % 191.26/26.89 fact_inverse__positive__imp__positive, fact_inverse__unique, fact_inverse__zero, % 191.26/26.89 fact_inverse__zero__imp__zero, fact_le__iff__diff__le__0, fact_le__imp__neg__le, % 191.26/26.89 fact_le__minus__iff, fact_le__minus__self__iff, fact_leading__coeff__0__iff, % 191.26/26.89 fact_leading__coeff__neq__0, fact_left__add__mult__distrib, fact_left__inverse, % 191.26/26.89 fact_left__minus, fact_lessI, fact_less__1__mult, fact_less__SucE, % 191.26/26.89 fact_less__SucI, fact_less__Suc__eq, fact_less__add__Suc1, fact_less__add__Suc2, % 191.26/26.89 fact_less__add__eq__less, fact_less__add__iff1, fact_less__add__iff2, % 191.26/26.89 fact_less__add__one, fact_less__antisym, fact_less__bin__lemma, % 191.26/26.89 fact_less__diff__conv, fact_less__divide__eq, fact_less__half__sum, % 191.26/26.89 fact_less__iff__Suc__add, fact_less__iff__diff__less__0, % 191.26/26.89 fact_less__imp__diff__less, fact_less__imp__inverse__less, % 191.26/26.89 fact_less__imp__inverse__less__neg, fact_less__irrefl__nat, % 191.26/26.89 fact_less__minus__iff, fact_less__minus__self__iff, fact_less__not__refl, % 191.26/26.89 fact_less__not__refl2, fact_less__not__refl3, fact_less__poly__def, % 191.26/26.89 fact_less__trans__Suc, fact_linorder__neqE__linordered__idom, % 191.26/26.89 fact_linorder__neqE__nat, fact_minus__add, fact_minus__add__cancel, % 191.26/26.89 fact_minus__add__distrib, fact_minus__diff__eq, fact_minus__divide__divide, % 191.26/26.89 fact_minus__divide__left, fact_minus__divide__right, fact_minus__dvd__iff, % 191.26/26.89 fact_minus__equation__iff, fact_minus__le__iff, fact_minus__le__self__iff, % 191.26/26.89 fact_minus__less__iff, fact_minus__minus, fact_minus__monom, % 191.26/26.89 fact_minus__mult__commute, fact_minus__mult__left, fact_minus__mult__minus, % 191.26/26.89 fact_minus__mult__right, fact_minus__pCons, fact_minus__poly__code_I1_J, % 191.26/26.89 fact_minus__poly__code_I2_J, fact_minus__unique, fact_minus__zero, fact_mod__0, % 191.26/26.89 fact_mod__Suc__eq__Suc__mod, fact_mod__add__cong, fact_mod__add__eq, % 191.26/26.89 fact_mod__add__left__eq, fact_mod__add__right__eq, fact_mod__add__self1, % 191.26/26.89 fact_mod__add__self2, fact_mod__by__0, fact_mod__by__1, fact_mod__diff__cong, % 191.26/26.89 fact_mod__diff__eq, fact_mod__diff__left__eq, fact_mod__diff__right__eq, % 191.26/26.89 fact_mod__div__equality, fact_mod__div__equality2, fact_mod__div__trivial, % 191.26/26.89 fact_mod__geq, fact_mod__if, fact_mod__less, fact_mod__minus__cong, % 191.26/26.89 fact_mod__minus__eq, fact_mod__mod__cancel, fact_mod__mod__trivial, % 191.26/26.89 fact_mod__mult2__eq, fact_mod__mult__cong, fact_mod__mult__distrib, % 191.26/26.89 fact_mod__mult__distrib2, fact_mod__mult__eq, fact_mod__mult__left__eq, % 191.26/26.89 fact_mod__mult__mult1, fact_mod__mult__mult2, fact_mod__mult__right__eq, % 191.26/26.89 fact_mod__mult__self1, fact_mod__mult__self1__is__0, fact_mod__mult__self2, % 191.26/26.89 fact_mod__mult__self2__is__0, fact_mod__mult__self3, fact_mod__mult__self4, % 191.26/26.89 fact_mod__pCons, fact_mod__poly__eq, fact_mod__poly__less, fact_mod__self, % 191.26/26.89 fact_mod__smult__left, fact_mod__smult__right, fact_monom__Suc, % 191.26/26.89 fact_monom__eq__0, fact_monom__eq__0__iff, fact_monom__eq__iff, % 191.26/26.89 fact_mult_Oadd__left, fact_mult_Oadd__right, fact_mult_Ocomm__neutral, % 191.26/26.89 fact_mult_Odiff__left, fact_mult_Odiff__right, fact_mult_Ominus__left, % 191.26/26.89 fact_mult_Ominus__right, fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, % 191.26/26.89 fact_mult_Ozero__right, fact_mult__1, fact_mult__1__left, fact_mult__1__right, % 191.26/26.89 fact_mult__Suc, fact_mult__Suc__right, fact_mult__diff__mult, % 191.26/26.89 fact_mult__divide__mult__cancel__left, fact_mult__divide__mult__cancel__right, % 191.26/26.89 fact_mult__dvd__mono, fact_mult__eq__0__iff, fact_mult__imp__div__pos__less, % 191.26/26.89 fact_mult__imp__less__div__pos, fact_mult__le__0__iff, % 191.26/26.89 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos, % 191.26/26.89 fact_mult__le__less__imp__less, fact_mult__left_Oadd, fact_mult__left_Odiff, % 191.26/26.89 fact_mult__left_Ominus, fact_mult__left_Ozero, fact_mult__left__le__imp__le, % 191.26/26.89 fact_mult__left__less__imp__less, fact_mult__left__mono, % 191.26/26.89 fact_mult__left__mono__neg, fact_mult__less__cancel__left__disj, % 191.26/26.89 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos, % 191.26/26.89 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left, % 191.26/26.89 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less, % 191.26/26.89 fact_mult__mono, fact_mult__mono_H, fact_mult__monom, fact_mult__neg__neg, % 191.26/26.89 fact_mult__neg__pos, fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos, % 191.26/26.89 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg, % 191.26/26.89 fact_mult__nonpos__nonpos, fact_mult__pCons__left, fact_mult__pCons__right, % 191.26/26.89 fact_mult__poly__0__right, fact_mult__poly__add__left, fact_mult__pos__neg, % 191.26/26.89 fact_mult__pos__neg2, fact_mult__pos__pos, fact_mult__right_Oadd, % 191.26/26.89 fact_mult__right_Odiff, fact_mult__right_Ominus, fact_mult__right_Ozero, % 191.26/26.89 fact_mult__right__le__imp__le, fact_mult__right__less__imp__less, % 191.26/26.89 fact_mult__right__mono, fact_mult__right__mono__neg, fact_mult__smult__left, % 191.26/26.89 fact_mult__smult__right, fact_mult__strict__left__mono, % 191.26/26.89 fact_mult__strict__left__mono__neg, fact_mult__strict__mono, % 191.26/26.89 fact_mult__strict__mono_H, fact_mult__strict__right__mono, % 191.26/26.89 fact_mult__strict__right__mono__neg, fact_mult__zero__left, % 191.26/26.89 fact_mult__zero__right, fact_n__not__Suc__n, fact_nat_Oinject, % 191.26/26.89 fact_nat__add__assoc, fact_nat__add__commute, fact_nat__add__left__cancel, % 191.26/26.89 fact_nat__add__left__cancel__less, fact_nat__add__left__commute, % 191.26/26.89 fact_nat__add__right__cancel, fact_nat__less__cases, fact_nat__mult__assoc, % 191.26/26.89 fact_nat__mult__commute, fact_nat__neq__iff, fact_nat__size, % 191.26/26.89 fact_neg__0__equal__iff__equal, fact_neg__0__le__iff__le, % 191.26/26.89 fact_neg__0__less__iff__less, fact_neg__divide__less__eq, % 191.26/26.89 fact_neg__equal__0__iff__equal, fact_neg__equal__iff__equal, % 191.26/26.89 fact_neg__equal__zero, fact_neg__imp__zdiv__neg__iff, fact_neg__le__0__iff__le, % 191.26/26.89 fact_neg__le__iff__le, fact_neg__less__0__iff__less, fact_neg__less__divide__eq, % 191.26/26.89 fact_neg__less__iff__less, fact_neg__less__nonneg, fact_neg__mod__bound, % 191.26/26.89 fact_negative__imp__inverse__negative, fact_no__zero__divisors, % 191.26/26.89 fact_nonzero__divide__eq__eq, fact_nonzero__eq__divide__eq, % 191.26/26.89 fact_nonzero__imp__inverse__nonzero, fact_nonzero__inverse__eq__divide, % 191.26/26.89 fact_nonzero__inverse__eq__imp__eq, fact_nonzero__inverse__inverse__eq, % 191.26/26.89 fact_nonzero__inverse__minus__eq, fact_nonzero__inverse__mult__distrib, % 191.26/26.89 fact_nonzero__minus__divide__divide, fact_nonzero__minus__divide__right, % 191.26/26.89 fact_nonzero__power__divide, fact_nonzero__power__inverse, fact_not__add__less1, % 191.26/26.89 fact_not__add__less2, fact_not__less__eq, fact_not__less__less__Suc__eq, % 191.26/26.89 fact_not__pos__poly__0, fact_not__square__less__zero, % 191.26/26.89 fact_not__sum__squares__lt__zero, fact_odd__less__0, fact_odd__nonzero, % 191.26/26.89 fact_offset__poly__0, fact_offset__poly__eq__0__iff, % 191.26/26.89 fact_offset__poly__eq__0__lemma, fact_offset__poly__pCons, % 191.26/26.89 fact_offset__poly__single, fact_one__dvd, fact_one__le__power, % 191.26/26.89 fact_one__less__inverse, fact_one__less__inverse__iff, fact_one__poly__def, % 191.26/26.89 fact_one__reorient, fact_order, fact_order__1, fact_order__2, fact_pCons__0__0, % 191.26/26.89 fact_pCons__eq__0__iff, fact_pCons__eq__iff, fact_pcompose__0, % 191.26/26.89 fact_pcompose__pCons, fact_pdivmod__rel, fact_pdivmod__rel__0, % 191.26/26.89 fact_pdivmod__rel__0__iff, fact_pdivmod__rel__by__0, % 191.26/26.89 fact_pdivmod__rel__by__0__iff, fact_pdivmod__rel__def, fact_pdivmod__rel__mult, % 191.26/26.89 fact_pdivmod__rel__pCons, fact_pdivmod__rel__smult__left, % 191.26/26.89 fact_pdivmod__rel__smult__right, fact_pdivmod__rel__unique, % 191.26/26.89 fact_pdivmod__rel__unique__div, fact_pdivmod__rel__unique__mod, fact_poly__0, % 191.26/26.89 fact_poly__1, fact_poly__add, fact_poly__diff, fact_poly__div__minus__left, % 191.26/26.89 fact_poly__div__minus__right, fact_poly__div__mult__right, % 191.26/26.89 fact_poly__dvd__antisym, fact_poly__eq__0__iff__dvd, fact_poly__eq__iff, % 191.26/26.89 fact_poly__gcd_Oassoc, fact_poly__gcd_Ocommute, fact_poly__gcd_Oleft__commute, % 191.26/26.89 fact_poly__gcd_Osimps_I1_J, fact_poly__gcd_Osimps_I2_J, fact_poly__gcd__0__0, % 191.26/26.89 fact_poly__gcd__1__left, fact_poly__gcd__1__right, fact_poly__gcd__code, % 191.26/26.89 fact_poly__gcd__dvd1, fact_poly__gcd__dvd2, fact_poly__gcd__greatest, % 191.26/26.89 fact_poly__gcd__minus__left, fact_poly__gcd__minus__right, % 191.26/26.89 fact_poly__gcd__monic, fact_poly__gcd__unique, fact_poly__gcd__zero__iff, % 191.26/26.89 fact_poly__minus, fact_poly__mod__minus__left, fact_poly__mod__minus__right, % 191.26/26.89 fact_poly__monom, fact_poly__mult, fact_poly__offset__poly, fact_poly__pCons, % 191.26/26.89 fact_poly__pcompose, fact_poly__power, fact_poly__rec_Osimps, fact_poly__rec__0, % 191.26/26.89 fact_poly__rec__pCons, fact_poly__replicate__append, fact_poly__smult, % 191.26/26.89 fact_pos__add__strict, fact_pos__divide__less__eq, % 191.26/26.89 fact_pos__imp__zdiv__neg__iff, fact_pos__less__divide__eq, fact_pos__mod__bound, % 191.26/26.89 fact_pos__poly__add, fact_pos__poly__def, fact_pos__poly__mult, % 191.26/26.89 fact_pos__poly__pCons, fact_pos__poly__total, fact_pos__zmult__eq__1__iff, % 191.26/26.89 fact_positive__imp__inverse__positive, fact_power_Opower_Opower__Suc, % 191.26/26.89 fact_power__0__Suc, fact_power__Suc, fact_power__Suc2, fact_power__Suc__less, % 191.26/26.89 fact_power__Suc__less__one, fact_power__add, fact_power__commutes, % 191.26/26.89 fact_power__decreasing, fact_power__divide, fact_power__gt1, % 191.26/26.89 fact_power__gt1__lemma, fact_power__increasing, fact_power__increasing__iff, % 191.26/26.89 fact_power__inject__exp, fact_power__inverse, fact_power__le__imp__le__exp, % 191.26/26.89 fact_power__less__imp__less__exp, fact_power__less__power__Suc, % 191.26/26.89 fact_power__minus, fact_power__mono, fact_power__mult, % 191.26/26.89 fact_power__mult__distrib, fact_power__one, fact_power__one__over, % 191.26/26.89 fact_power__power__power, fact_power__strict__decreasing, % 191.26/26.89 fact_power__strict__increasing, fact_power__strict__increasing__iff, % 191.26/26.89 fact_real__squared__diff__one__factored, fact_right__inverse, % 191.26/26.89 fact_right__inverse__eq, fact_right__minus, fact_right__minus__eq, % 191.26/26.89 fact_semiring__div__class_Omod__div__equality_H, fact_sgn0, fact_sgn__0__0, % 191.26/26.89 fact_sgn__1__neg, fact_sgn__1__pos, fact_sgn__greater, fact_sgn__if, % 191.26/26.89 fact_sgn__less, fact_sgn__minus, fact_sgn__mult, fact_sgn__neg, fact_sgn__one, % 191.26/26.89 fact_sgn__poly__def, fact_sgn__pos, fact_sgn__sgn, fact_sgn__times, % 191.26/26.89 fact_sgn__zero, fact_sgn__zero__iff, fact_smult__0__left, fact_smult__0__right, % 191.26/26.89 fact_smult__1__left, fact_smult__add__left, fact_smult__add__right, % 191.26/26.89 fact_smult__diff__left, fact_smult__diff__right, fact_smult__dvd, % 191.26/26.89 fact_smult__dvd__cancel, fact_smult__dvd__iff, fact_smult__eq__0__iff, % 191.26/26.89 fact_smult__minus__left, fact_smult__minus__right, fact_smult__monom, % 191.26/26.89 fact_smult__pCons, fact_smult__smult, fact_split__mult__neg__le, % 191.26/26.89 fact_split__mult__pos__le, fact_split__neg__lemma, fact_split__pos__lemma, % 191.26/26.89 fact_square__eq__1__iff, fact_square__eq__iff, fact_sum__squares__eq__zero__iff, % 191.26/26.89 fact_sum__squares__gt__zero__iff, fact_synthetic__div__0, % 191.26/26.89 fact_synthetic__div__correct, fact_synthetic__div__correct_H, % 191.26/26.89 fact_synthetic__div__pCons, fact_synthetic__div__unique, % 191.26/26.89 fact_synthetic__div__unique__lemma, fact_termination__basic__simps_I1_J, % 191.26/26.89 fact_termination__basic__simps_I2_J, fact_times__divide__eq__right, % 191.26/26.89 fact_times__divide__times__eq, fact_trans__less__add1, fact_trans__less__add2, % 191.26/26.89 fact_uminus__dvd__conv_I1_J, fact_uminus__dvd__conv_I2_J, fact_unity__coeff__ex, % 191.26/26.89 fact_zadd__0, fact_zadd__0__right, fact_zadd__assoc, fact_zadd__commute, % 191.26/26.89 fact_zadd__left__commute, fact_zadd__left__mono, fact_zadd__strict__right__mono, % 191.26/26.89 fact_zadd__zless__mono, fact_zadd__zminus__inverse2, fact_zadd__zmult__distrib, % 191.26/26.89 fact_zadd__zmult__distrib2, fact_zdiff__zmod__left, fact_zdiff__zmod__right, % 191.26/26.89 fact_zdiff__zmult__distrib, fact_zdiff__zmult__distrib2, fact_zdiv__self, % 191.26/26.89 fact_zdiv__zadd1__eq, fact_zdiv__zero, fact_zdiv__zminus1__eq__if, % 191.26/26.89 fact_zdiv__zminus2, fact_zdiv__zminus2__eq__if, fact_zdiv__zminus__zminus, % 191.26/26.89 fact_zdiv__zmod__equality, fact_zdiv__zmod__equality2, fact_zdiv__zmult1__eq, % 191.26/26.89 fact_zdiv__zmult2__eq, fact_zdvd__antisym__nonneg, fact_zdvd__mono, % 191.26/26.89 fact_zdvd__mult__cancel, fact_zdvd__mult__div__cancel, fact_zdvd__not__zless, % 191.26/26.89 fact_zdvd__period, fact_zdvd__reduce, fact_zdvd__zdiffD, fact_zdvd__zmod, % 191.26/26.89 fact_zdvd__zmod__imp__zdvd, fact_zero__le__divide__iff, % 191.26/26.89 fact_zero__le__double__add__iff__zero__le__single__add, % 191.26/26.89 fact_zero__le__mult__iff, fact_zero__le__power, fact_zero__le__square, % 191.26/26.89 fact_zero__less__divide__iff, % 191.26/26.89 fact_zero__less__double__add__iff__zero__less__single__add, % 191.26/26.89 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, fact_zero__less__one, % 191.26/26.89 fact_zero__less__power, fact_zero__less__two, fact_zero__reorient, % 191.26/26.89 fact_zle__antisym, fact_zle__linear, fact_zle__refl, fact_zle__trans, % 191.26/26.89 fact_zless__add1__eq, fact_zless__le, fact_zless__linear, fact_zminus__0, % 191.26/26.89 fact_zminus__zadd__distrib, fact_zminus__zminus, fact_zminus__zmod, % 191.26/26.89 fact_zmod__eq__0__iff, fact_zmod__eq__dvd__iff, fact_zmod__le__nonneg__dividend, % 191.26/26.89 fact_zmod__self, fact_zmod__simps_I1_J, fact_zmod__simps_I2_J, % 191.26/26.89 fact_zmod__simps_I3_J, fact_zmod__simps_I4_J, fact_zmod__zdiv__equality, % 191.26/26.89 fact_zmod__zdiv__equality_H, fact_zmod__zdiv__trivial, fact_zmod__zero, % 191.26/26.89 fact_zmod__zminus1__eq__if, fact_zmod__zminus1__not__zero, fact_zmod__zminus2, % 191.26/26.89 fact_zmod__zminus2__eq__if, fact_zmod__zminus2__not__zero, % 191.26/26.89 fact_zmod__zminus__zminus, fact_zmod__zmult1__eq, fact_zmod__zmult2__eq, % 191.26/26.89 fact_zmult__1, fact_zmult__1__right, fact_zmult__assoc, fact_zmult__commute, % 191.26/26.89 fact_zmult__div__cancel, fact_zmult__zless__mono2, fact_zmult__zminus, % 191.26/26.89 fact_zpower__zadd__distrib, fact_zpower__zmod, fact_zpower__zpower, % 191.26/26.89 help_c__fFalse__1, help_c__fTrue__1, help_c__fequal__1, help_c__fequal__2 % 191.26/26.89 % 191.26/26.89 Those formulas are unsatisfiable: % 191.26/26.89 --------------------------------- % 191.26/26.89 % 191.26/26.89 Begin of proof % 191.26/26.90 | % 191.26/26.90 | ALPHA: (fact_pe) implies: % 191.26/26.90 | (1) ? [v0: $i] : (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & % 191.26/26.90 | c_Groups_Ozero__class_Ozero(v0) = v_p & $i(v0)) % 191.26/26.90 | % 191.26/26.90 | ALPHA: (fact_eq) implies: % 191.26/26.90 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 191.26/26.90 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 191.26/26.90 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q) = v2 & % 191.26/26.90 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p) = v0 & % 191.26/26.90 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v3 & % 191.26/26.90 | c_Groups_Ozero__class_Ozero(v3) = v4 & % 191.26/26.90 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 & $i(v5) & % 191.26/26.90 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = v1 & ~ (v7 = v1) % 191.26/26.90 | & ~ (v4 = v_q) & hAPP(v2, v5) = v7 & hAPP(v0, v5) = v1 & $i(v7)) % 191.26/26.90 | | (v4 = v_q & ! [v8: $i] : ! [v9: $i] : (v9 = v1 | ~ (hAPP(v2, % 191.26/26.90 | v8) = v9) | ~ $i(v8) | ? [v10: $i] : ( ~ (v10 = v1) & % 191.26/26.90 | hAPP(v0, v8) = v10 & $i(v10)))))) % 191.26/26.90 | % 191.26/26.90 | ALPHA: (fact_order__root) implies: % 191.26/26.90 | (3) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 191.26/26.90 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.26/26.90 | ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~ % 191.26/26.90 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: % 191.26/26.90 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (((v9 = v0 & ~ % 191.26/26.90 | (v8 = v2) & c_Polynomial_Oorder(v3, v1, v2) = v0 & % 191.26/26.90 | tc_Polynomial_Opoly(v3) = v7 & % 191.26/26.90 | c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | (v6 % 191.26/26.90 | = v5 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & ((v8 % 191.26/26.90 | = v2 & tc_Polynomial_Opoly(v3) = v7 & % 191.26/26.90 | c_Groups_Ozero__class_Ozero(v7) = v2 & $i(v7)) | ( ~ (v9 = % 191.26/26.90 | v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & $i(v9)) | ( ~ % 191.26/26.90 | (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 & % 191.26/26.90 | $i(v6)))))) % 191.26/26.90 | % 191.26/26.90 | ALPHA: (fact_psize__eq__0__iff) implies: % 191.26/26.90 | (4) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 191.26/26.90 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.26/26.90 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | % 191.26/26.90 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i] : ? % 191.26/26.90 | [v5: $i] : (( ~ (v3 = v0) | (v5 = v1 & tc_Polynomial_Opoly(v2) = v4 % 191.26/26.90 | & c_Groups_Ozero__class_Ozero(v4) = v1 & $i(v4))) & (v3 = v0 % 191.26/26.90 | | ( ~ (v5 = v1) & tc_Polynomial_Opoly(v2) = v4 & % 191.26/26.90 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4)))))) % 191.26/26.90 | % 191.26/26.90 | ALPHA: (fact_r) implies: % 191.26/26.90 | (5) $i(v_r____) % 191.26/26.90 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 191.26/26.90 | ? [v5: $i] : ? [v6: $i] : (c_Power_Opower__class_Opower(v0) = v1 & % 191.26/26.90 | c_Groups_Otimes__class_Otimes(v0) = v5 & % 191.26/26.90 | c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v3 & % 191.26/26.90 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & hAPP(v6, v_r____) = % 191.26/26.90 | v4 & hAPP(v5, v_p) = v6 & hAPP(v2, v3) = v4 & hAPP(v1, v_q) = v2 & % 191.26/26.90 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 191.26/26.90 | % 191.26/26.90 | ALPHA: (fact__096p_Advd_Aq_A_094_Adegree_Ap_096) implies: % 191.26/26.90 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 191.26/26.90 | (c_Power_Opower__class_Opower(v0) = v1 & % 191.26/26.90 | c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v3 & % 191.26/26.90 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & hAPP(v2, v3) = v4 & % 191.26/26.90 | hAPP(v1, v_q) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 191.26/26.90 | c_Rings_Odvd__class_Odvd(v0, v_p, v4)) % 191.26/26.90 | % 191.26/26.90 | ALPHA: (fact_degree__pCons__0) implies: % 191.26/26.91 | (8) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 191.26/26.91 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.26/26.91 | ! [v6: $i] : (v6 = v0 | ~ (c_Polynomial_Odegree(v2, v5) = v6) | ~ % 191.26/26.91 | (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ % 191.26/26.91 | (tc_Polynomial_Opoly(v2) = v3) | ~ % 191.26/26.91 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 191.26/26.91 | class_Groups_Ozero(v2))) % 191.26/26.91 | % 191.26/26.91 | ALPHA: (fact_degree__0) implies: % 191.26/26.91 | (9) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 191.26/26.91 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 191.26/26.91 | (c_Polynomial_Odegree(v1, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = % 191.26/26.91 | v2) | ~ (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ % 191.26/26.91 | class_Groups_Ozero(v1))) % 191.26/26.91 | % 191.26/26.91 | ALPHA: (fact_coeff__pCons__0) implies: % 191.26/26.91 | (10) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.26/26.91 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.26/26.91 | $i] : ( ~ (c_Polynomial_OpCons(v3, v2, v1) = v4) | ~ % 191.26/26.91 | (c_Polynomial_Ocoeff(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 191.26/26.91 | $i(v1) | ~ class_Groups_Ozero(v3) | hAPP(v5, v0) = v2)) % 191.26/26.91 | % 191.26/26.91 | ALPHA: (fact_degree__smult__eq) implies: % 191.62/26.91 | (11) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.91 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.62/26.91 | $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~ % 191.62/26.91 | (c_Polynomial_Osmult(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 191.62/26.91 | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: $i] : ? [v7: $i] : % 191.62/26.91 | ((v5 = v0 | ( ~ (v6 = v2) & c_Groups_Ozero__class_Ozero(v3) = v6 & % 191.62/26.91 | $i(v6))) & ((v7 = v5 & c_Polynomial_Odegree(v3, v1) = v5 & % 191.62/26.91 | $i(v5)) | (v6 = v2 & c_Groups_Ozero__class_Ozero(v3) = % 191.62/26.91 | v2))))) % 191.62/26.91 | % 191.62/26.91 | ALPHA: (fact_monom__0) implies: % 191.62/26.91 | (12) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.91 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.62/26.91 | $i] : ( ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ % 191.62/26.91 | (tc_Polynomial_Opoly(v2) = v3) | ~ % 191.62/26.91 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | % 191.62/26.91 | ~ class_Groups_Ozero(v2) | (c_Polynomial_Omonom(v2, v1, v0) = v5 & % 191.62/26.91 | $i(v5)))) % 191.62/26.91 | % 191.62/26.91 | ALPHA: (fact__096_B_Bthesis_O_A_I_B_Br_O_Aq_A_094_Adegree_Ap_A_061_Ap_A_K_Ar_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) % 191.62/26.91 | implies: % 191.62/26.91 | (13) $i(v_q) % 191.62/26.91 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 191.62/26.91 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 191.62/26.91 | (c_Power_Opower__class_Opower(v0) = v1 & % 191.62/26.91 | c_Groups_Otimes__class_Otimes(v0) = v5 & % 191.62/26.91 | c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v3 & % 191.62/26.91 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & hAPP(v6, v7) = v4 & % 191.62/26.91 | hAPP(v5, v_p) = v6 & hAPP(v2, v3) = v4 & hAPP(v1, v_q) = v2 & $i(v7) % 191.62/26.91 | & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 191.62/26.91 | % 191.62/26.91 | ALPHA: (fact_power__eq__0__iff) implies: % 191.62/26.91 | (15) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.91 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.62/26.91 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 191.62/26.91 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ % 191.62/26.91 | $i(v2) | ~ $i(v1) | ~ class_Rings_Ozero__neq__one(v3) | ~ % 191.62/26.91 | class_Rings_Ono__zero__divisors(v3) | ~ % 191.62/26.91 | class_Rings_Omult__zero(v3) | ~ class_Power_Opower(v3) | ? [v7: % 191.62/26.91 | $i] : (c_Groups_Ozero__class_Ozero(v3) = v7 & $i(v7) & ( ~ (v7 = % 191.62/26.91 | v6) | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2) | v6 = v2 | % 191.62/26.91 | v1 = v0)))) % 191.62/26.91 | % 191.62/26.91 | ALPHA: (fact_nullstellensatz__lemma) implies: % 191.62/26.91 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 191.62/26.91 | (c_Power_Opower__class_Opower(v2) = v3 & % 191.62/26.91 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v2 & % 191.62/26.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 191.62/26.91 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & $i(v3) & % 191.62/26.91 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.62/26.91 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v4 = v1 | ~ % 191.62/26.91 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v6) = v7) | ~ (hAPP(v8, % 191.62/26.91 | v4) = v9) | ~ (hAPP(v3, v5) = v8) | ~ $i(v6) | ~ $i(v5) | % 191.62/26.91 | ~ $i(v4) | c_Rings_Odvd__class_Odvd(v2, v6, v9) | ? [v10: $i] : % 191.62/26.91 | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 191.62/26.91 | ($i(v12) & ((v13 = v0 & ~ (v14 = v0) & % 191.62/26.91 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v5) = v10 & % 191.62/26.91 | hAPP(v10, v12) = v14 & hAPP(v7, v12) = v0 & $i(v14) & % 191.62/26.91 | $i(v10)) | ( ~ (v11 = v4) & % 191.62/26.91 | c_Polynomial_Odegree(tc_Complex_Ocomplex, v6) = v11 & % 191.62/26.91 | $i(v11)))))) % 191.62/26.91 | % 191.62/26.91 | ALPHA: (fact_add__eq__self__zero) implies: % 191.62/26.91 | (17) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.91 | & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.62/26.91 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ % 191.62/26.91 | $i(v2) | ~ $i(v1))) % 191.62/26.91 | % 191.62/26.91 | ALPHA: (fact_add__is__0) implies: % 191.62/26.91 | (18) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.91 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 191.62/26.91 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ % 191.62/26.91 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.62/26.91 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ % 191.62/26.91 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : (v1 = v0 | ~ % 191.62/26.91 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1))) % 191.62/26.91 | % 191.62/26.91 | ALPHA: (fact_Nat_Oadd__0__right) implies: % 191.62/26.91 | (19) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.91 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 191.62/26.91 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ % 191.62/26.91 | $i(v1))) % 191.62/26.91 | % 191.62/26.92 | ALPHA: (fact_plus__nat_Oadd__0) implies: % 191.62/26.92 | (20) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.92 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 191.62/26.92 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ % 191.62/26.92 | $i(v1))) % 191.62/26.92 | % 191.62/26.92 | ALPHA: (fact_mult__0) implies: % 191.62/26.92 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.62/26.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.62/26.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & % 191.62/26.92 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ % 191.62/26.92 | (hAPP(v2, v3) = v4) | ~ $i(v3))) % 191.62/26.92 | % 191.62/26.92 | ALPHA: (fact_mult__0__right) implies: % 191.62/26.92 | (22) ? [v0: $i] : ? [v1: $i] : % 191.62/26.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.62/26.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 191.62/26.92 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | % 191.62/26.92 | hAPP(v3, v1) = v1)) % 191.62/26.92 | % 191.62/26.92 | ALPHA: (fact_mult__is__0) implies: % 191.62/26.92 | (23) ? [v0: $i] : ? [v1: $i] : % 191.62/26.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.62/26.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 191.62/26.92 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) = % 191.62/26.92 | v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ! % 191.62/26.92 | [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~ % 191.62/26.92 | (hAPP(v0, v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! % 191.62/26.92 | [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ % 191.62/26.92 | (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2))) % 191.62/26.92 | % 191.62/26.92 | ALPHA: (fact_mult__cancel2) implies: % 191.62/26.92 | (24) ? [v0: $i] : ? [v1: $i] : % 191.62/26.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.62/26.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 191.62/26.92 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.62/26.92 | ! [v7: $i] : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = % 191.62/26.92 | v5) | ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ % 191.62/26.92 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 191.62/26.92 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v2 | v3 = v1 | ~ % 191.62/26.92 | (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 191.62/26.92 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 191.62/26.92 | $i(v2))) % 191.62/26.92 | % 191.62/26.92 | ALPHA: (fact_synthetic__div__eq__0__iff) implies: % 191.62/26.92 | (25) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.92 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.62/26.92 | (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ $i(v3) | ~ % 191.62/26.92 | $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? % 191.62/26.92 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (((v7 = v0 & % 191.62/26.92 | c_Polynomial_Odegree(v3, v2) = v0) | ( ~ (v6 = v4) & % 191.62/26.92 | tc_Polynomial_Opoly(v3) = v5 & % 191.62/26.92 | c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) & % 191.62/26.92 | ((v6 = v4 & tc_Polynomial_Opoly(v3) = v5 & % 191.62/26.92 | c_Groups_Ozero__class_Ozero(v5) = v4 & $i(v5) & $i(v4)) | ( % 191.62/26.92 | ~ (v7 = v0) & c_Polynomial_Odegree(v3, v2) = v7 & % 191.62/26.92 | $i(v7)))))) % 191.62/26.92 | % 191.62/26.92 | ALPHA: (fact_nat__mult__eq__cancel__disj) implies: % 191.62/26.92 | (26) ? [v0: $i] : ? [v1: $i] : % 191.62/26.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.62/26.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 191.62/26.92 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.62/26.92 | (v6 = v5 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ % 191.62/26.92 | (hAPP(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! % 191.62/26.92 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | v3 = % 191.62/26.92 | v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ % 191.62/26.92 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 191.62/26.92 | % 191.62/26.92 | ALPHA: (fact_nat__mult__dvd__cancel__disj) implies: % 191.62/26.92 | (27) ? [v0: $i] : ? [v1: $i] : % 191.62/26.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.62/26.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 191.62/26.92 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.62/26.92 | ! [v7: $i] : (v4 = v1 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 191.62/26.92 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 191.62/26.92 | | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 191.62/26.92 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 191.62/26.92 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 191.62/26.92 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) % 191.62/26.92 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.92 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 191.62/26.92 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : ! % 191.62/26.92 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, % 191.62/26.92 | v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | % 191.62/26.92 | ~ $i(v3) | ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, % 191.62/26.92 | v6))) % 191.62/26.92 | % 191.62/26.92 | ALPHA: (fact_psize__def) implies: % 191.62/26.93 | (28) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.93 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.62/26.93 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | % 191.62/26.93 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | ? [v4: $i] : % 191.62/26.93 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v3 = v0 | ( ~ (v5 = v1) % 191.62/26.93 | & tc_Polynomial_Opoly(v2) = v4 & % 191.62/26.93 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))) & % 191.62/26.93 | ((v7 = v3 & c_Nat_OSuc(v6) = v3 & c_Polynomial_Odegree(v2, v1) = % 191.62/26.93 | v6 & $i(v6) & $i(v3)) | (v5 = v1 & tc_Polynomial_Opoly(v2) = % 191.62/26.93 | v4 & c_Groups_Ozero__class_Ozero(v4) = v1 & $i(v4)))))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_dvd__1__left) implies: % 191.62/26.93 | (29) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.62/26.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ? % 191.62/26.93 | [v2: $i] : ( ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, % 191.62/26.93 | v2))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_nat__dvd__1__iff__1) implies: % 191.62/26.93 | (30) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.93 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 = % 191.62/26.93 | v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, % 191.62/26.93 | v0))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_One__nat__def) implies: % 191.62/26.93 | (31) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & % 191.62/26.93 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 191.62/26.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_Suc__eq__plus1) implies: % 191.62/26.93 | (32) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.93 | ! [v1: $i] : ! [v2: $i] : ( ~ % 191.62/26.93 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ % 191.62/26.93 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_Suc__eq__plus1__left) implies: % 191.62/26.93 | (33) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.93 | ! [v1: $i] : ! [v2: $i] : ( ~ % 191.62/26.93 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ % 191.62/26.93 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_power__Suc__0) implies: % 191.62/26.93 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 191.62/26.93 | (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 % 191.62/26.93 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 % 191.62/26.93 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : % 191.62/26.93 | (v5 = v2 | ~ (hAPP(v3, v4) = v5) | ~ $i(v4))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_nat__power__eq__Suc__0__iff) implies: % 191.62/26.93 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 191.62/26.93 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 191.62/26.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 191.62/26.93 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ % 191.62/26.93 | (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & ! % 191.62/26.93 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v1) = % 191.62/26.93 | v5) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3)) & ! [v3: $i] : ! % 191.62/26.93 | [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3) = v2) % 191.62/26.93 | | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_dvd__1__iff__1) implies: % 191.62/26.93 | (36) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.62/26.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.62/26.93 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v1) & ! [v2: $i] : (v2 = % 191.62/26.93 | v1 | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, % 191.62/26.93 | v1))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_nat_Osimps_I3_J) implies: % 191.62/26.93 | (37) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.93 | & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) % 191.62/26.93 | implies: % 191.62/26.93 | (38) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.93 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.62/26.93 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 191.62/26.93 | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | % 191.62/26.93 | hAPP(v4, v0) = v1)) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_power__one__right) implies: % 191.62/26.93 | (39) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.93 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.62/26.93 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 191.62/26.93 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | % 191.62/26.93 | hAPP(v4, v0) = v1)) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_nat__mult__eq__1__iff) implies: % 191.62/26.93 | (40) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.62/26.93 | v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & % 191.62/26.93 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ % 191.62/26.93 | (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ % 191.62/26.93 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ % 191.62/26.93 | (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ % 191.62/26.93 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (hAPP(v2, v1) % 191.62/26.93 | = v3) | ~ (hAPP(v0, v1) = v2))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_nat__mult__1__right) implies: % 191.62/26.93 | (41) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.62/26.93 | v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & % 191.62/26.93 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ % 191.62/26.93 | $i(v2) | hAPP(v3, v1) = v2)) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_nat__1__eq__mult__iff) implies: % 191.62/26.93 | (42) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.62/26.93 | v0 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & % 191.62/26.93 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ % 191.62/26.93 | (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 191.62/26.93 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ % 191.62/26.93 | (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 191.62/26.93 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (hAPP(v2, v0) % 191.62/26.93 | = v3) | ~ (hAPP(v1, v0) = v2))) % 191.62/26.93 | % 191.62/26.93 | ALPHA: (fact_nat__mult__1) implies: % 191.62/26.94 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.62/26.94 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.62/26.94 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 % 191.62/26.94 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | % 191.62/26.94 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_coeff__1) implies: % 191.62/26.94 | (44) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.94 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.62/26.94 | $i] : ! [v6: $i] : ( ~ (c_Groups_Oone__class_Oone(v3) = v4) | ~ % 191.62/26.94 | (c_Polynomial_Ocoeff(v2, v4) = v5) | ~ (tc_Polynomial_Opoly(v2) = % 191.62/26.94 | v3) | ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ~ % 191.62/26.94 | class_Rings_Ocomm__semiring__1(v2) | ? [v7: $i] : ? [v8: $i] : % 191.62/26.94 | (( ~ (v1 = v0) | (v7 = v6 & c_Groups_Oone__class_Oone(v2) = v6 & % 191.62/26.94 | $i(v6))) & (v1 = v0 | (v8 = v6 & % 191.62/26.94 | c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6)))))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_one__is__add) implies: % 191.62/26.94 | (45) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.62/26.94 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 191.62/26.94 | [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 191.62/26.94 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ % 191.62/26.94 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = % 191.62/26.94 | v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | % 191.62/26.94 | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 % 191.62/26.94 | = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) % 191.62/26.94 | | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | % 191.62/26.94 | v2 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = % 191.62/26.94 | v1) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : (v2 = v1 | ~ % 191.62/26.94 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: % 191.62/26.94 | $i] : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, % 191.62/26.94 | v1) = v2))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_mult__eq__1__iff) implies: % 191.62/26.94 | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 191.62/26.94 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.62/26.94 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 191.62/26.94 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ % 191.62/26.94 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 191.62/26.94 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v2 | ~ % 191.62/26.94 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 191.62/26.94 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (hAPP(v3, v2) % 191.62/26.94 | = v4) | ~ (hAPP(v0, v2) = v3))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) % 191.62/26.94 | implies: % 191.62/26.94 | (47) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.94 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.62/26.94 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 191.62/26.94 | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | ? % 191.62/26.94 | [v5: $i] : (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 % 191.62/26.94 | & $i(v5)))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_power__0) implies: % 191.62/26.94 | (48) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.94 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.62/26.94 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 191.62/26.94 | ~ $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] : % 191.62/26.94 | (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & % 191.62/26.94 | $i(v5)))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_mult__eq__self__implies__10) implies: % 191.62/26.94 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.62/26.94 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 191.62/26.94 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.62/26.94 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 191.62/26.94 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = % 191.62/26.94 | v1 | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | % 191.62/26.94 | ~ $i(v3))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_degree__1) implies: % 191.62/26.94 | (50) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.94 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | % 191.62/26.94 | ~ (c_Groups_Oone__class_Oone(v2) = v3) | ~ % 191.62/26.94 | (c_Polynomial_Odegree(v1, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) % 191.62/26.94 | = v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v1))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_power__0__left) implies: % 191.62/26.94 | (51) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.94 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.62/26.94 | $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~ % 191.62/26.94 | (c_Power_Opower__class_Opower(v2) = v3) | ~ % 191.62/26.94 | (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | % 191.62/26.94 | ~ (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 191.62/26.94 | class_Power_Opower(v2) | ~ class_Rings_Osemiring__0(v2)) & ! % 191.62/26.94 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 191.62/26.94 | ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ % 191.62/26.94 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | % 191.62/26.94 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ class_Power_Opower(v1) | ~ % 191.62/26.94 | class_Rings_Osemiring__0(v1) | (c_Groups_Oone__class_Oone(v1) = v5 % 191.62/26.94 | & $i(v5)))) % 191.62/26.94 | % 191.62/26.94 | ALPHA: (fact_degree__pCons__eq__if) implies: % 191.62/26.95 | (52) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.95 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.62/26.95 | $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~ % 191.62/26.95 | (c_Polynomial_OpCons(v3, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | % 191.62/26.95 | ~ $i(v1) | ~ class_Groups_Ozero(v3) | ? [v6: $i] : ? [v7: $i] : % 191.62/26.95 | ? [v8: $i] : ? [v9: $i] : ((v5 = v0 | ( ~ (v7 = v2) & % 191.62/26.95 | tc_Polynomial_Opoly(v3) = v6 & % 191.62/26.95 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6))) & % 191.62/26.95 | ((v9 = v5 & c_Nat_OSuc(v8) = v5 & c_Polynomial_Odegree(v3, v2) = % 191.62/26.95 | v8 & $i(v8) & $i(v5)) | (v7 = v2 & tc_Polynomial_Opoly(v3) = % 191.62/26.95 | v6 & c_Groups_Ozero__class_Ozero(v6) = v2 & $i(v6)))))) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_pow__divides__eq__nat) implies: % 191.62/26.95 | (53) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 191.62/26.95 | = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 191.62/26.95 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 191.62/26.95 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = % 191.62/26.95 | v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ % 191.62/26.95 | (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) | % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 191.62/26.95 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 191.62/26.95 | ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = % 191.62/26.95 | v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ % 191.62/26.95 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8))) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_pow__divides__pow__nat) implies: % 191.62/26.95 | (54) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 191.62/26.95 | = v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & % 191.62/26.95 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 191.62/26.95 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = % 191.62/26.95 | v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 191.62/26.95 | (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) | % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v2))) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Otop__greatest) implies: % 191.62/26.95 | (55) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.95 | & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 191.62/26.95 | v1, v0))) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_power_Opower_Opower__0) implies: % 191.62/26.95 | (56) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.95 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.62/26.95 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | % 191.62/26.95 | ~ (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.95 | $i(v1) | hAPP(v6, v0) = v3)) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_pow__divides__pow__int) implies: % 191.62/26.95 | (57) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Int_Oint) % 191.62/26.95 | = v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & % 191.62/26.95 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 191.62/26.95 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = % 191.62/26.95 | v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 191.62/26.95 | (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) | % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v2))) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_pow__divides__eq__int) implies: % 191.62/26.95 | (58) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Int_Oint) % 191.62/26.95 | = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 191.62/26.95 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 191.62/26.95 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = % 191.62/26.95 | v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ % 191.62/26.95 | (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) | % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)) & ! [v2: $i] : ! % 191.62/26.95 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 191.62/26.95 | ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = % 191.62/26.95 | v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ % 191.62/26.95 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2) | % 191.62/26.95 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8))) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Obot__least) implies: % 191.62/26.95 | (59) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.95 | ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, % 191.62/26.95 | v1))) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_realpow__two__disj) implies: % 191.62/26.95 | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 191.62/26.95 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.62/26.95 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 191.62/26.95 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 191.62/26.95 | (c_Power_Opower__class_Opower(v5) = v6) | ~ (hAPP(v6, v4) = v7) | % 191.62/26.95 | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 191.62/26.95 | class_Rings_Oidom(v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] % 191.62/26.95 | : ((v4 = v3 | (v11 = v4 & c_Groups_Ouminus__class_Ouminus(v5, v3) % 191.62/26.95 | = v4) | ( ~ (v10 = v9) & hAPP(v8, v2) = v10 & hAPP(v7, v2) = % 191.62/26.95 | v9 & $i(v10) & $i(v9))) & ((v10 = v9 & hAPP(v8, v2) = v9 & % 191.62/26.95 | hAPP(v7, v2) = v9 & $i(v9)) | ( ~ (v11 = v4) & ~ (v4 = v3) % 191.62/26.95 | & c_Groups_Ouminus__class_Ouminus(v5, v3) = v11 & % 191.62/26.95 | $i(v11)))))) % 191.62/26.95 | % 191.62/26.95 | ALPHA: (fact_poly__decompose) implies: % 191.62/26.96 | (61) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.62/26.96 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 191.62/26.96 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 191.62/26.96 | $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ % 191.62/26.96 | (c_Groups_Ozero__class_Ozero(v3) = v5) | ~ (hAPP(v4, v5) = v6) | % 191.62/26.96 | ~ $i(v3) | ~ $i(v2) | ~ class_Rings_Oidom(v3) | % 191.62/26.96 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(v3, v3, v4) | % 191.62/26.96 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 191.62/26.96 | $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] % 191.62/26.96 | : ? [v16: $i] : ( ~ (v11 = v5) & ~ (v10 = v0) & % 191.62/26.96 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v14, v1) = v7 & % 191.62/26.96 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v13, v10) = v14 & % 191.62/26.96 | c_Power_Opower__class_Opower(v3) = v9 & % 191.62/26.96 | c_Groups_Otimes__class_Otimes(v3) = v8 & % 191.62/26.96 | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v12) = v13 % 191.62/26.96 | & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v7 % 191.62/26.96 | & c_Polynomial_OpCons(v3, v11, v12) = v15 & % 191.62/26.96 | c_Polynomial_Opoly(v3, v15) = v16 & $i(v16) & $i(v15) & $i(v14) % 191.62/26.96 | & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 191.62/26.96 | $i(v7) & ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: % 191.62/26.96 | $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ % 191.62/26.96 | (c_Groups_Oplus__class_Oplus(v3, v6, v22) = v23) | ~ % 191.62/26.96 | (hAPP(v20, v21) = v22) | ~ (hAPP(v18, v10) = v19) | ~ % 191.62/26.96 | (hAPP(v16, v17) = v21) | ~ (hAPP(v9, v17) = v18) | ~ % 191.62/26.96 | (hAPP(v8, v19) = v20) | ~ $i(v17) | (hAPP(v4, v17) = v23 & % 191.62/26.96 | $i(v23)))))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_nat_Osize_I2_J) implies: % 191.62/26.96 | (62) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.62/26.96 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 191.62/26.96 | [v2: $i] : ! [v3: $i] : ( ~ (c_Nat_Onat_Onat__size(v2) = v3) | ~ % 191.62/26.96 | $i(v2) | ? [v4: $i] : ? [v5: $i] : (c_Nat_Onat_Onat__size(v4) = % 191.62/26.96 | v5 & c_Nat_OSuc(v2) = v4 & % 191.62/26.96 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5 & $i(v5) & % 191.62/26.96 | $i(v4)))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_power__eq__if) implies: % 191.62/26.96 | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 191.62/26.96 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 191.62/26.96 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 191.62/26.96 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 & % 191.62/26.96 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & % 191.62/26.96 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 191.62/26.96 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~ % 191.62/26.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ % 191.62/26.96 | (hAPP(v7, v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = % 191.62/26.96 | v7) | ~ (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, % 191.62/26.96 | v5) = v10 & $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 191.62/26.96 | $i] : (v6 = v2 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | % 191.62/26.96 | ~ $i(v4))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_diffs0__imp__equal) implies: % 191.62/26.96 | (64) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.96 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 191.62/26.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ % 191.62/26.96 | $i(v2) | ~ $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) & % 191.62/26.96 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & % 191.62/26.96 | $i(v3)))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_diff__self__eq__0) implies: % 191.62/26.96 | (65) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.96 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 191.62/26.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ % 191.62/26.96 | $i(v1))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_minus__nat_Odiff__0) implies: % 191.62/26.96 | (66) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.96 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 191.62/26.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 191.62/26.96 | $i(v1))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_diff__0__eq__0) implies: % 191.62/26.96 | (67) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.96 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 191.62/26.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 191.62/26.96 | $i(v1))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_nat_Osize_I1_J) implies: % 191.62/26.96 | (68) ? [v0: $i] : (c_Nat_Onat_Onat__size(v0) = v0 & % 191.62/26.96 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_diff__add__0) implies: % 191.62/26.96 | (69) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.96 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | % 191.62/26.96 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 191.62/26.96 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.62/26.96 | $i(v2) | ~ $i(v1))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_diff__Suc__1) implies: % 191.62/26.96 | (70) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.96 | ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 191.62/26.96 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v1)) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_diff__Suc__eq__diff__pred) implies: % 191.62/26.96 | (71) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.96 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.62/26.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 191.62/26.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ % 191.62/26.96 | $i(v2) | ~ $i(v1) | ? [v5: $i] : % 191.62/26.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) = v4 & % 191.62/26.96 | c_Nat_OSuc(v1) = v5 & $i(v5) & $i(v4)))) % 191.62/26.96 | % 191.62/26.96 | ALPHA: (fact_realpow__two__diff) implies: % 191.62/26.97 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 191.62/26.97 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.62/26.97 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 191.62/26.97 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 191.62/26.97 | $i] : ! [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(v5, v8, % 191.62/26.97 | v10) = v11) | ~ (c_Power_Opower__class_Opower(v5) = v6) | ~ % 191.62/26.97 | (hAPP(v9, v2) = v10) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = % 191.62/26.97 | v7) | ~ (hAPP(v6, v3) = v9) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 191.62/26.97 | | ~ class_Rings_Ocomm__ring__1(v5) | ? [v12: $i] : ? [v13: $i] % 191.62/26.97 | : ? [v14: $i] : ? [v15: $i] : (c_Groups_Ominus__class_Ominus(v5, % 191.62/26.97 | v4, v3) = v13 & c_Groups_Oplus__class_Oplus(v5, v4, v3) = v15 % 191.62/26.97 | & c_Groups_Otimes__class_Otimes(v5) = v12 & hAPP(v14, v15) = v11 % 191.62/26.97 | & hAPP(v12, v13) = v14 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 191.62/26.97 | $i(v11)))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_degree__synthetic__div) implies: % 191.62/26.97 | (73) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 191.62/26.97 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.62/26.97 | ( ~ (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ % 191.62/26.97 | (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.97 | $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? [v6: $i] : % 191.62/26.97 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v0) = v5 & % 191.62/26.97 | c_Polynomial_Odegree(v3, v2) = v6 & $i(v6) & $i(v5)))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_add__eq__if) implies: % 191.62/26.97 | (74) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.62/26.97 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 191.62/26.97 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | % 191.62/26.97 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 191.62/26.97 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = v5) | ~ % 191.62/26.97 | $i(v3) | ~ $i(v2) | ? [v6: $i] : (c_Nat_OSuc(v5) = v6 & % 191.62/26.97 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v6 & $i(v6))) % 191.62/26.97 | & ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 191.62/26.97 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = v3) | ~ % 191.62/26.97 | $i(v2))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_mult__eq__if) implies: % 191.62/26.97 | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.62/26.97 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 191.62/26.97 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.62/26.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 191.62/26.97 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 191.62/26.97 | [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ % 191.62/26.97 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~ % 191.62/26.97 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~ % 191.62/26.97 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ % 191.62/26.97 | $i(v3) | ? [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & % 191.62/26.97 | $i(v9) & $i(v8))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.62/26.97 | (v5 = v0 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v0) = v4) | ~ % 191.62/26.97 | $i(v3))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_realpow__num__eq__if) implies: % 191.62/26.97 | (76) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.62/26.97 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 191.62/26.97 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 191.62/26.97 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 191.62/26.97 | [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) % 191.62/26.97 | = v9) | ~ (c_Power_Opower__class_Opower(v4) = v5) | ~ % 191.62/26.97 | (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ (hAPP(v8, v10) = % 191.62/26.97 | v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ % 191.62/26.97 | (hAPP(v5, v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.97 | class_Power_Opower(v4) | ? [v12: $i] : ? [v13: $i] : (( ~ (v3 = % 191.62/26.97 | v0) | (v13 = v12 & c_Groups_Oone__class_Oone(v4) = v12 & % 191.62/26.97 | hAPP(v6, v0) = v12 & $i(v12))) & (v3 = v0 | (v12 = v11 & % 191.62/26.97 | hAPP(v6, v3) = v11 & $i(v11)))))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_nat_Osize_I4_J) implies: % 191.62/26.97 | (77) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.62/26.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 191.62/26.97 | [v2: $i] : ! [v3: $i] : ( ~ (c_Nat_Osize__class_Osize(tc_Nat_Onat, % 191.62/26.97 | v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 191.62/26.97 | (c_Nat_Osize__class_Osize(tc_Nat_Onat, v4) = v5 & c_Nat_OSuc(v2) = % 191.62/26.97 | v4 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5 & % 191.62/26.97 | $i(v5) & $i(v4)))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_nat_Osize_I3_J) implies: % 191.62/26.97 | (78) ? [v0: $i] : (c_Nat_Osize__class_Osize(tc_Nat_Onat, v0) = v0 & % 191.62/26.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_realpow__minus__mult) implies: % 191.62/26.97 | (79) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.62/26.97 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 191.62/26.97 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 191.62/26.97 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 191.62/26.97 | [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) % 191.62/26.97 | = v8) | ~ (c_Power_Opower__class_Opower(v4) = v6) | ~ % 191.62/26.97 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = % 191.62/26.97 | v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ % 191.62/26.97 | (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.62/26.97 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 191.62/26.97 | class_Groups_Omonoid__mult(v4) | (hAPP(v7, v3) = v11 & $i(v11)))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_bool_Osize_I1_J) implies: % 191.62/26.97 | (80) ? [v0: $i] : (c_HOL_Obool_Obool__size(c_fTrue) = v0 & % 191.62/26.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_bool_Osize_I2_J) implies: % 191.62/26.97 | (81) ? [v0: $i] : (c_HOL_Obool_Obool__size(c_fFalse) = v0 & % 191.62/26.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_zero__less__Suc) implies: % 191.62/26.97 | (82) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.97 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) % 191.62/26.97 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_neq0__conv) implies: % 191.62/26.97 | (83) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.97 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1: % 191.62/26.97 | $i] : (v1 = v0 | ~ $i(v1) | % 191.62/26.97 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_not__less0) implies: % 191.62/26.97 | (84) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.97 | & ! [v1: $i] : ( ~ $i(v1) | ~ % 191.62/26.97 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 191.62/26.97 | % 191.62/26.97 | ALPHA: (fact_gr0I) implies: % 191.62/26.97 | (85) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.97 | & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | % 191.62/26.97 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 191.62/26.98 | % 191.62/26.98 | ALPHA: (fact_one__less__power) implies: % 191.62/26.98 | (86) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.98 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.62/26.98 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 191.62/26.98 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ % 191.62/26.98 | $i(v2) | ~ $i(v1) | ~ class_Rings_Olinordered__semidom(v3) | ~ % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v7: $i] : % 191.62/26.98 | (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~ % 191.62/26.98 | c_Orderings_Oord__class_Oless(v3, v7, v2) | % 191.62/26.98 | c_Orderings_Oord__class_Oless(v3, v7, v6))))) % 191.62/26.98 | % 191.62/26.98 | ALPHA: (fact_less__Suc__eq__0__disj) implies: % 191.62/26.98 | (87) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.98 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.62/26.98 | (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~ % 191.62/26.98 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.62/26.98 | v4, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & % 191.62/26.98 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ % 191.62/26.98 | (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4: $i] : % 191.62/26.98 | (c_Nat_OSuc(v4) = v2 & $i(v4) & % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1: % 191.62/26.98 | $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 191.62/26.98 | % 191.62/26.98 | ALPHA: (fact_less__Suc0) implies: % 191.62/26.98 | (88) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.62/26.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] : % 191.62/26.98 | (v2 = v0 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.62/26.98 | v2, v1))) % 191.62/26.98 | % 191.62/26.98 | ALPHA: (fact_gr0__conv__Suc) implies: % 191.62/26.98 | (89) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.98 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2) % 191.62/26.98 | | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) % 191.62/26.98 | & ! [v1: $i] : ( ~ $i(v1) | ~ % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v2: $i] : % 191.62/26.98 | (c_Nat_OSuc(v2) = v1 & $i(v2)))) % 191.62/26.98 | % 191.62/26.98 | ALPHA: (fact_nat__dvd__not__less) implies: % 191.62/26.98 | (90) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.98 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 191.62/26.98 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2))) % 191.62/26.98 | % 191.62/26.98 | ALPHA: (fact_dvd__pos__nat) implies: % 191.62/26.98 | (91) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.98 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 191.62/26.98 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) | % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 191.62/26.98 | % 191.62/26.98 | ALPHA: (fact_add__gr__0) implies: % 191.62/26.98 | (92) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.62/26.98 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.62/26.98 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.62/26.98 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.62/26.98 | v0, v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.62/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i] % 191.62/26.98 | : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.62/26.98 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.62/26.98 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.62/26.98 | v0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & % 191.62/26.98 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.62/26.98 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.62/26.98 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.62/26.98 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 191.62/26.98 | % 191.62/26.98 | ALPHA: (fact_nat__mult__less__cancel1) implies: % 191.62/26.98 | (93) ? [v0: $i] : ? [v1: $i] : % 191.62/26.98 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.62/26.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 191.62/26.98 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.62/26.98 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 191.93/26.98 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] % 191.93/26.98 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 191.93/26.98 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 191.93/26.98 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 191.93/26.98 | % 191.93/26.98 | ALPHA: (fact_nat__mult__eq__cancel1) implies: % 191.93/26.98 | (94) ? [v0: $i] : ? [v1: $i] : % 191.93/26.98 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/26.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 191.93/26.98 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/26.98 | (v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ % 191.93/26.98 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 191.93/26.98 | % 191.93/26.98 | ALPHA: (fact_mult__less__mono2) implies: % 191.93/26.98 | (95) ? [v0: $i] : ? [v1: $i] : % 191.93/26.98 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/26.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 191.93/26.98 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/26.98 | ! [v7: $i] : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ % 191.93/26.98 | (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.93/26.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 191.93/26.98 | % 191.93/26.98 | ALPHA: (fact_mult__less__mono1) implies: % 191.93/26.99 | (96) ? [v0: $i] : ? [v1: $i] : % 191.93/26.99 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/26.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 191.93/26.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/26.99 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5, % 191.93/26.99 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) | % 191.93/26.99 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 191.93/26.99 | % 191.93/26.99 | ALPHA: (fact_mult__less__cancel2) implies: % 191.93/26.99 | (97) ? [v0: $i] : ? [v1: $i] : % 191.93/26.99 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.93/26.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 191.93/26.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/26.99 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, % 191.93/26.99 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | % 191.93/26.99 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] % 191.93/26.99 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 191.93/26.99 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = % 191.93/26.99 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 191.93/26.99 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] % 191.93/26.99 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 191.93/26.99 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = % 191.93/26.99 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 191.93/26.99 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 191.93/26.99 | % 191.93/26.99 | ALPHA: (fact_mult__less__cancel1) implies: % 191.93/26.99 | (98) ? [v0: $i] : ? [v1: $i] : % 191.93/26.99 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.93/26.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 191.93/26.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/26.99 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 191.93/26.99 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] % 191.93/26.99 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 191.93/26.99 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 191.93/26.99 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i] % 191.93/26.99 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 191.93/26.99 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 191.93/26.99 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 191.93/26.99 | % 191.93/26.99 | ALPHA: (fact_nat__0__less__mult__iff) implies: % 191.93/26.99 | (99) ? [v0: $i] : ? [v1: $i] : % 191.93/26.99 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/26.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 191.93/26.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, % 191.93/26.99 | v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 191.93/26.99 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] % 191.93/26.99 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 191.93/26.99 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i] % 191.93/26.99 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 191.93/26.99 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5))) % 191.93/26.99 | % 191.93/26.99 | ALPHA: (fact_diff__less) implies: % 191.93/26.99 | (100) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.93/26.99 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/26.99 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 191.93/26.99 | $i(v2) | ~ $i(v1) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1))) % 191.93/26.99 | % 191.93/26.99 | ALPHA: (fact_zero__less__diff) implies: % 191.93/26.99 | (101) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.93/26.99 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/26.99 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.93/26.99 | $i(v2) | ~ $i(v1) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] % 191.93/26.99 | : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/26.99 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.93/26.99 | $i(v2) | ~ $i(v1) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2))) % 191.93/26.99 | % 191.93/26.99 | ALPHA: (fact_nat__power__less__imp__less) implies: % 191.93/26.99 | (102) ? [v0: $i] : ? [v1: $i] : % 191.93/26.99 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 191.93/26.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/26.99 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/26.99 | : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | % 191.93/26.99 | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 191.93/26.99 | % 191.93/26.99 | ALPHA: (fact_one__less__mult) implies: % 191.93/26.99 | (103) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 191.93/26.99 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 191.93/26.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 191.93/26.99 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 191.93/26.99 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ % 191.93/26.99 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 191.93/26.99 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 191.93/26.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6))) % 191.93/26.99 | % 191.93/26.99 | ALPHA: (fact_n__less__n__mult__m) implies: % 191.93/27.00 | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 191.93/27.00 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 191.93/27.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 191.93/27.00 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 191.93/27.00 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 191.93/27.00 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 191.93/27.00 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 191.93/27.00 | % 191.93/27.00 | ALPHA: (fact_n__less__m__mult__n) implies: % 191.93/27.00 | (105) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 191.93/27.00 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 191.93/27.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 191.93/27.00 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 191.93/27.00 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ % 191.93/27.00 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 191.93/27.00 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 191.93/27.00 | % 191.93/27.00 | ALPHA: (fact_diff__Suc__less) implies: % 191.93/27.00 | (106) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.93/27.00 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.93/27.00 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 191.93/27.00 | (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 191.93/27.00 | % 191.93/27.00 | ALPHA: (fact_Suc__pred) implies: % 191.93/27.00 | (107) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.93/27.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.00 | ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.00 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.93/27.00 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.93/27.00 | c_Nat_OSuc(v3) = v2)) % 191.93/27.00 | % 191.93/27.00 | ALPHA: (fact_nat__mult__dvd__cancel1) implies: % 191.93/27.00 | (108) ? [v0: $i] : ? [v1: $i] : % 191.93/27.00 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.00 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/27.00 | : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | % 191.93/27.00 | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 191.93/27.00 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 191.93/27.00 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 191.93/27.00 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 191.93/27.00 | ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) % 191.93/27.00 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 191.93/27.00 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 191.93/27.00 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7))) % 191.93/27.00 | % 191.93/27.00 | ALPHA: (fact_dvd__mult__cancel) implies: % 191.93/27.00 | (109) ? [v0: $i] : ? [v1: $i] : % 191.93/27.00 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 191.93/27.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & % 191.93/27.00 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/27.00 | : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | % 191.93/27.00 | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 191.93/27.00 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 191.93/27.00 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2))) % 191.93/27.00 | % 191.93/27.00 | ALPHA: (fact_nat__diff__split__asm) implies: % 191.93/27.00 | (110) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.93/27.00 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.93/27.00 | $i] : ! [v6: $i] : ( ~ % 191.93/27.00 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 191.93/27.00 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2) | ~ % 191.93/27.00 | (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.00 | $i(v1) | ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) % 191.93/27.00 | & hBOOL(v7))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 191.93/27.00 | [v4: $i] : ! [v5: $i] : ( ~ % 191.93/27.00 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 191.93/27.00 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ hBOOL(v5) % 191.93/27.00 | | ? [v6: $i] : (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! % 191.93/27.00 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.93/27.00 | ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 191.93/27.00 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 191.93/27.00 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | hBOOL(v5) | % 191.93/27.00 | ? [v6: $i] : ? [v7: $i] : % 191.93/27.00 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3, % 191.93/27.00 | v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : % 191.93/27.00 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.93/27.00 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 191.93/27.00 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 191.93/27.00 | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 191.93/27.00 | : ($i(v7) & ((v8 = v2 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 191.93/27.01 | v1, v7) = v2 & hAPP(v3, v7) = v9 & $i(v9) & ~ hBOOL(v9)) % 191.93/27.01 | | (hAPP(v3, v0) = v6 & $i(v6) & ~ hBOOL(v6)))))) % 191.93/27.01 | % 191.93/27.01 | ALPHA: (fact_dvd__power) implies: % 191.93/27.01 | (111) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.93/27.01 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.93/27.01 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 191.93/27.01 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ % 191.93/27.01 | $i(v2) | ~ $i(v1) | ~ % 191.93/27.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 191.93/27.01 | class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3, % 191.93/27.01 | v1, v6)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 191.93/27.01 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.93/27.01 | (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v2) = v6) % 191.93/27.01 | | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.93/27.01 | class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3, % 191.93/27.01 | v1, v6) | ? [v7: $i] : ( ~ (v7 = v1) & % 191.93/27.01 | c_Groups_Oone__class_Oone(v3) = v7 & $i(v7)))) % 191.93/27.01 | % 191.93/27.01 | ALPHA: (fact_Suc__pred_H) implies: % 191.93/27.01 | (112) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.93/27.01 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 191.93/27.01 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.01 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.93/27.01 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.93/27.01 | c_Nat_OSuc(v3) = v2)) % 191.93/27.01 | % 191.93/27.01 | ALPHA: (fact_dvd__mult__cancel2) implies: % 191.93/27.01 | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.93/27.01 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 191.93/27.01 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 191.93/27.01 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/27.01 | (v3 = v2 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ % 191.93/27.01 | $i(v4) | ~ $i(v3) | ~ % 191.93/27.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 191.93/27.01 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : ! % 191.93/27.01 | [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) % 191.93/27.01 | = v4) | ~ $i(v3) | ~ % 191.93/27.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 191.93/27.01 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 191.93/27.01 | % 191.93/27.01 | ALPHA: (fact_dvd__mult__cancel1) implies: % 191.93/27.01 | (114) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 191.93/27.01 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 191.93/27.01 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 191.93/27.01 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/27.01 | (v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ % 191.93/27.01 | $i(v4) | ~ $i(v3) | ~ % 191.93/27.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 191.93/27.01 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : ! % 191.93/27.01 | [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) % 191.93/27.01 | = v4) | ~ $i(v3) | ~ % 191.93/27.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 191.93/27.01 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 191.93/27.01 | % 191.93/27.01 | ALPHA: (fact_zero__less__power__nat__eq) implies: % 191.93/27.02 | (115) ? [v0: $i] : ? [v1: $i] : % 191.93/27.02 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 191.93/27.02 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.02 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | % 191.93/27.02 | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 191.93/27.02 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 191.93/27.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] % 191.93/27.02 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 191.93/27.02 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 191.93/27.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] % 191.93/27.02 | : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ % 191.93/27.02 | (hAPP(v1, v2) = v3) | ~ $i(v2) | % 191.93/27.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 191.93/27.02 | % 191.93/27.02 | ALPHA: (fact_nat__lt__two__imp__zero__or__one) implies: % 191.93/27.02 | (116) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 191.93/27.02 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 191.93/27.02 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 191.93/27.02 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 191.93/27.02 | % 191.93/27.02 | ALPHA: (fact_mod__Suc) implies: % 191.93/27.02 | (117) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.93/27.02 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 191.93/27.02 | | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~ % 191.93/27.02 | (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? % 191.93/27.02 | [v6: $i] : ( ~ (v6 = v1) & % 191.93/27.02 | c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v5 & % 191.93/27.02 | c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5))) & ! [v1: $i] : ! [v2: % 191.93/27.02 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.93/27.02 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~ % 191.93/27.02 | (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? % 191.93/27.02 | [v6: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v5 % 191.93/27.02 | & c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5) & (v6 = v4 | v6 = % 191.93/27.02 | v1)))) % 191.93/27.02 | % 191.93/27.02 | ALPHA: (fact_mod__1) implies: % 191.93/27.02 | (118) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.93/27.02 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.02 | ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 191.93/27.02 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.93/27.02 | $i(v2))) % 191.93/27.02 | % 191.93/27.02 | ALPHA: (fact_mod__eq__0__iff) implies: % 191.93/27.02 | (119) ? [v0: $i] : ? [v1: $i] : % 191.93/27.02 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.02 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.02 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 191.93/27.02 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v4) | ~ % 191.93/27.02 | $i(v3) | ~ $i(v2) | ? [v5: $i] : (hAPP(v1, v2) = v5 & $i(v5) & % 191.93/27.02 | ! [v6: $i] : ( ~ (hAPP(v5, v6) = v3) | ~ $i(v6)))) & ! [v2: % 191.93/27.02 | $i] : ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, % 191.93/27.02 | v3, v2) = v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: % 191.93/27.02 | $i] : (hAPP(v4, v5) = v3 & hAPP(v1, v2) = v4 & $i(v5) & % 191.93/27.02 | $i(v4)))) % 191.93/27.02 | % 191.93/27.02 | ALPHA: (fact_mod__less__divisor) implies: % 191.93/27.02 | (120) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.93/27.02 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.02 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~ % 191.93/27.02 | $i(v2) | ~ $i(v1) | ~ % 191.93/27.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 191.93/27.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 191.93/27.02 | % 191.93/27.02 | ALPHA: (fact_split__mod) implies: % 191.93/27.03 | (121) ? [v0: $i] : ? [v1: $i] : % 191.93/27.03 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.03 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.03 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/27.03 | : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v5) | ~ % 191.93/27.03 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.03 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : (( ~ (v2 = v0) | % 191.93/27.03 | (hAPP(v4, v3) = v7 & $i(v7) & hBOOL(v7))) & (v2 = v0 | % 191.93/27.03 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : ! % 191.93/27.03 | [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 191.93/27.03 | v11, v10) = v3) | ~ (hAPP(v8, v9) = v11) | ~ % 191.93/27.03 | $i(v10) | ~ $i(v9) | ~ % 191.93/27.03 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) | ? % 191.93/27.03 | [v12: $i] : (hAPP(v4, v10) = v12 & $i(v12) & % 191.93/27.03 | hBOOL(v12))))))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 191.93/27.03 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.93/27.03 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v5) | ~ % 191.93/27.03 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 191.93/27.03 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 191.93/27.03 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v10) & % 191.93/27.03 | $i(v9) & ((v12 = v3 & ~ (v2 = v0) & % 191.93/27.03 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) = v3 & % 191.93/27.03 | hAPP(v8, v9) = v11 & hAPP(v4, v10) = v13 & hAPP(v1, v2) = % 191.93/27.03 | v8 & $i(v13) & $i(v11) & $i(v8) & % 191.93/27.03 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) & ~ % 191.93/27.03 | hBOOL(v13)) | (v2 = v0 & hAPP(v4, v3) = v7 & $i(v7) & ~ % 191.93/27.03 | hBOOL(v7)))))) % 191.93/27.03 | % 191.93/27.03 | ALPHA: (fact_mod__lemma) implies: % 191.93/27.03 | (122) ? [v0: $i] : ? [v1: $i] : % 191.93/27.03 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.03 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.03 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/27.03 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 191.93/27.03 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v5) = v7) | ~ % 191.93/27.03 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v8, v4) = v9) | ~ % 191.93/27.03 | (hAPP(v6, v7) = v8) | ~ (hAPP(v1, v3) = v6) | ~ $i(v5) | ~ % 191.93/27.03 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.03 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 191.93/27.03 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v10: $i] % 191.93/27.03 | : (hAPP(v6, v5) = v10 & $i(v10) & % 191.93/27.03 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v9, v10)))) % 191.93/27.03 | % 191.93/27.03 | ALPHA: (fact_Suc__times__mod__eq) implies: % 191.93/27.03 | (123) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.93/27.03 | v0 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & % 191.93/27.03 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 191.93/27.03 | [v6: $i] : ! [v7: $i] : (v7 = v0 | ~ % 191.93/27.03 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v6, v3) = v7) | ~ % 191.93/27.03 | (c_Nat_OSuc(v5) = v6) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) % 191.93/27.03 | = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.03 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 191.93/27.03 | % 191.93/27.03 | ALPHA: (fact_int__power__div__base) implies: % 191.93/27.04 | (124) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 191.93/27.04 | (c_Nat_OSuc(v0) = v3 & c_Power_Opower__class_Opower(tc_Int_Oint) = v2 % 191.93/27.04 | & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & % 191.93/27.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & % 191.93/27.04 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 191.93/27.04 | $i] : ! [v8: $i] : ( ~ % 191.93/27.04 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v3) = v7) | ~ % 191.93/27.04 | (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v4) = v6) | ~ $i(v5) | ~ % 191.93/27.04 | $i(v4) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | % 191.93/27.04 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v9: % 191.93/27.04 | $i] : (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v9, v4) = v8 & % 191.93/27.04 | hAPP(v6, v5) = v9 & $i(v9) & $i(v8)))) % 191.93/27.04 | % 191.93/27.04 | ALPHA: (fact_div__less) implies: % 191.93/27.04 | (125) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 191.93/27.04 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 191.93/27.04 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.93/27.04 | $i(v2) | ~ $i(v1) | ~ % 191.93/27.04 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1))) % 191.93/27.04 | % 191.93/27.04 | ALPHA: (fact_div__1) implies: % 191.93/27.04 | (126) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 191.93/27.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.04 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 191.93/27.04 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~ % 191.93/27.04 | $i(v2))) % 191.93/27.04 | % 191.93/27.04 | ALPHA: (fact_nat__mult__div__cancel__disj) implies: % 191.93/27.04 | (127) ? [v0: $i] : ? [v1: $i] : % 191.93/27.04 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.04 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/27.04 | : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ % 191.93/27.04 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) | ~ % 191.93/27.04 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = % 191.93/27.04 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 191.93/27.04 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8))) % 191.93/27.04 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 191.93/27.04 | $i] : ! [v7: $i] : (v7 = v0 | ~ % 191.93/27.04 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v6) = v7) | ~ % 191.93/27.04 | (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v1, v0) = % 191.93/27.04 | v4) | ~ $i(v3) | ~ $i(v2))) % 191.93/27.04 | % 191.93/27.04 | ALPHA: (fact_div__mult__self__is__m) implies: % 191.93/27.04 | (128) ? [v0: $i] : ? [v1: $i] : % 191.93/27.04 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.04 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/27.04 | : (v6 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = % 191.93/27.04 | v6) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ % 191.93/27.04 | $i(v3) | ~ $i(v2) | ~ % 191.93/27.04 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 191.93/27.04 | % 191.93/27.04 | ALPHA: (fact_div__mult__self1__is__m) implies: % 191.93/27.04 | (129) ? [v0: $i] : ? [v1: $i] : % 191.93/27.04 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.04 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/27.04 | : (v6 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = % 191.93/27.04 | v6) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ % 191.93/27.04 | $i(v3) | ~ $i(v2) | ~ % 191.93/27.04 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 191.93/27.04 | % 191.93/27.04 | ALPHA: (fact_nat__mult__div__cancel1) implies: % 191.93/27.04 | (130) ? [v0: $i] : ? [v1: $i] : % 191.93/27.04 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 191.93/27.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 191.93/27.04 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 191.93/27.04 | : ! [v7: $i] : ! [v8: $i] : ( ~ % 191.93/27.04 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) | ~ % 191.93/27.04 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = % 191.93/27.04 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 191.93/27.04 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 191.93/27.04 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8)))) % 191.93/27.04 | % 191.93/27.04 | ALPHA: (fact_div__less__dividend) implies: % 191.93/27.05 | (131) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 191.93/27.05 | v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & % 191.93/27.05 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.93/27.05 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ % 191.93/27.05 | $i(v3) | ~ $i(v2) | ~ % 191.93/27.05 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~ % 191.93/27.05 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 191.93/27.05 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Nat__Onat__Rings_Olinordered__semidom) implies: % 191.93/27.05 | (132) class_Rings_Olinordered__semidom(tc_Nat_Onat) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Nat__Onat__Rings_Ozero__neq__one) implies: % 191.93/27.05 | (133) class_Rings_Ozero__neq__one(tc_Nat_Onat) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Nat__Onat__Rings_Odvd) implies: % 191.93/27.05 | (134) $i(tc_Nat_Onat) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) implies: % 191.93/27.05 | (135) class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) implies: % 191.93/27.05 | (136) class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Complex__Ocomplex__Int_Oring__char__0) implies: % 191.93/27.05 | (137) class_Int_Oring__char__0(tc_Complex_Ocomplex) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Complex__Ocomplex__Groups_Ozero) implies: % 191.93/27.05 | (138) class_Groups_Ozero(tc_Complex_Ocomplex) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Complex__Ocomplex__Rings_Oidom) implies: % 191.93/27.05 | (139) class_Rings_Oidom(tc_Complex_Ocomplex) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (arity_Complex__Ocomplex__Rings_Odvd) implies: % 191.93/27.05 | (140) $i(tc_Complex_Ocomplex) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (function-axioms) implies: % 191.93/27.05 | (141) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.93/27.05 | (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 191.93/27.05 | (c_Groups_Ozero__class_Ozero(v2) = v0)) % 191.93/27.05 | (142) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.93/27.05 | (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0)) % 191.93/27.05 | (143) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.93/27.05 | (c_Groups_Otimes__class_Otimes(v2) = v1) | ~ % 191.93/27.05 | (c_Groups_Otimes__class_Otimes(v2) = v0)) % 191.93/27.05 | (144) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.93/27.05 | (c_Power_Opower__class_Opower(v2) = v1) | ~ % 191.93/27.05 | (c_Power_Opower__class_Opower(v2) = v0)) % 191.93/27.05 | (145) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 191.93/27.05 | (c_Groups_Oone__class_Oone(v2) = v1) | ~ % 191.93/27.05 | (c_Groups_Oone__class_Oone(v2) = v0)) % 191.93/27.05 | (146) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 191.93/27.05 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) % 191.93/27.05 | (147) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 191.93/27.05 | (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, % 191.93/27.05 | v2) = v0)) % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (78) with fresh symbol all_789_0 gives: % 191.93/27.05 | (148) c_Nat_Osize__class_Osize(tc_Nat_Onat, all_789_0) = all_789_0 & % 191.93/27.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_789_0 & $i(all_789_0) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (148) implies: % 191.93/27.05 | (149) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_789_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (80) with fresh symbol all_791_0 gives: % 191.93/27.05 | (150) c_HOL_Obool_Obool__size(c_fTrue) = all_791_0 & % 191.93/27.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_791_0 & $i(all_791_0) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (150) implies: % 191.93/27.05 | (151) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_791_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (81) with fresh symbol all_793_0 gives: % 191.93/27.05 | (152) c_HOL_Obool_Obool__size(c_fFalse) = all_793_0 & % 191.93/27.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_793_0 & $i(all_793_0) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (152) implies: % 191.93/27.05 | (153) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_793_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (1) with fresh symbol all_797_0 gives: % 191.93/27.05 | (154) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_797_0 & % 191.93/27.05 | c_Groups_Ozero__class_Ozero(all_797_0) = v_p & $i(all_797_0) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (154) implies: % 191.93/27.05 | (155) c_Groups_Ozero__class_Ozero(all_797_0) = v_p % 191.93/27.05 | (156) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_797_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (68) with fresh symbol all_799_0 gives: % 191.93/27.05 | (157) c_Nat_Onat_Onat__size(all_799_0) = all_799_0 & % 191.93/27.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_799_0 & $i(all_799_0) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (157) implies: % 191.93/27.05 | (158) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_799_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (37) with fresh symbol all_801_0 gives: % 191.93/27.05 | (159) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_801_0 & $i(all_801_0) % 191.93/27.05 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_801_0) | ~ $i(v0)) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (159) implies: % 191.93/27.05 | (160) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_801_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (84) with fresh symbol all_807_0 gives: % 191.93/27.05 | (161) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_807_0 & $i(all_807_0) % 191.93/27.05 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 191.93/27.05 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_807_0)) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (161) implies: % 191.93/27.05 | (162) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_807_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (37) with fresh symbol all_810_0 gives: % 191.93/27.05 | (163) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_810_0 & $i(all_810_0) % 191.93/27.05 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_810_0) | ~ $i(v0)) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (163) implies: % 191.93/27.05 | (164) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_810_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (37) with fresh symbol all_813_0 gives: % 191.93/27.05 | (165) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_813_0 & $i(all_813_0) % 191.93/27.05 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_813_0) | ~ $i(v0)) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (165) implies: % 191.93/27.05 | (166) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_813_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (37) with fresh symbol all_816_0 gives: % 191.93/27.05 | (167) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_816_0 & $i(all_816_0) % 191.93/27.05 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_816_0) | ~ $i(v0)) % 191.93/27.05 | % 191.93/27.05 | ALPHA: (167) implies: % 191.93/27.05 | (168) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_816_0 % 191.93/27.05 | % 191.93/27.05 | DELTA: instantiating (37) with fresh symbol all_819_0 gives: % 191.93/27.06 | (169) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_819_0 & $i(all_819_0) % 191.93/27.06 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_819_0) | ~ $i(v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (169) implies: % 191.93/27.06 | (170) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_819_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (59) with fresh symbol all_822_0 gives: % 191.93/27.06 | (171) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_822_0 & $i(all_822_0) & % 191.93/27.06 | ? [v0: $i] : ( ~ $i(v0) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 191.93/27.06 | all_822_0, v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (171) implies: % 191.93/27.06 | (172) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_822_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (37) with fresh symbol all_824_0 gives: % 191.93/27.06 | (173) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_824_0 & $i(all_824_0) % 191.93/27.06 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_824_0) | ~ $i(v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (173) implies: % 191.93/27.06 | (174) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_824_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (84) with fresh symbol all_827_0 gives: % 191.93/27.06 | (175) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_827_0 & $i(all_827_0) % 191.93/27.06 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 191.93/27.06 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_827_0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (175) implies: % 191.93/27.06 | (176) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_827_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (84) with fresh symbol all_830_0 gives: % 191.93/27.06 | (177) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_830_0 & $i(all_830_0) % 191.93/27.06 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 191.93/27.06 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_830_0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (177) implies: % 191.93/27.06 | (178) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_830_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (55) with fresh symbol all_833_0 gives: % 191.93/27.06 | (179) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_833_0 & $i(all_833_0) % 191.93/27.06 | & ? [v0: $i] : ( ~ $i(v0) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 191.93/27.06 | v0, all_833_0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (179) implies: % 191.93/27.06 | (180) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_833_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (84) with fresh symbol all_835_0 gives: % 191.93/27.06 | (181) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_835_0 & $i(all_835_0) % 191.93/27.06 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 191.93/27.06 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_835_0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (181) implies: % 191.93/27.06 | (182) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_835_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (20) with fresh symbol all_847_0 gives: % 191.93/27.06 | (183) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_847_0 & $i(all_847_0) % 191.93/27.06 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 191.93/27.06 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_847_0, v0) = v1) | ~ % 191.93/27.06 | $i(v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (183) implies: % 191.93/27.06 | (184) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_847_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (65) with fresh symbol all_850_0 gives: % 191.93/27.06 | (185) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_850_0 & $i(all_850_0) % 191.93/27.06 | & ! [v0: $i] : ! [v1: int] : (v1 = all_850_0 | ~ % 191.93/27.06 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v0) = v1) | ~ % 191.93/27.06 | $i(v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (185) implies: % 191.93/27.06 | (186) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_850_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (70) with fresh symbol all_859_0 gives: % 191.93/27.06 | (187) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_859_0 & $i(all_859_0) & % 191.93/27.06 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 191.93/27.06 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_859_0) = v0) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (187) implies: % 191.93/27.06 | (188) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_859_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (67) with fresh symbol all_865_0 gives: % 191.93/27.06 | (189) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_865_0 & $i(all_865_0) % 191.93/27.06 | & ! [v0: $i] : ! [v1: int] : (v1 = all_865_0 | ~ % 191.93/27.06 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, all_865_0, v0) = v1) | % 191.93/27.06 | ~ $i(v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (189) implies: % 191.93/27.06 | (190) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_865_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (19) with fresh symbol all_870_0 gives: % 191.93/27.06 | (191) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_870_0 & $i(all_870_0) % 191.93/27.06 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 191.93/27.06 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_870_0) = v1) | ~ % 191.93/27.06 | $i(v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (191) implies: % 191.93/27.06 | (192) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_870_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (66) with fresh symbol all_876_0 gives: % 191.93/27.06 | (193) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_876_0 & $i(all_876_0) % 191.93/27.06 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 191.93/27.06 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_876_0) = v1) | % 191.93/27.06 | ~ $i(v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (193) implies: % 191.93/27.06 | (194) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_876_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (82) with fresh symbol all_882_0 gives: % 191.93/27.06 | (195) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_882_0 & $i(all_882_0) % 191.93/27.06 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 191.93/27.06 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_882_0, v1)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (195) implies: % 191.93/27.06 | (196) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_882_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (85) with fresh symbol all_885_0 gives: % 191.93/27.06 | (197) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_885_0 & $i(all_885_0) % 191.93/27.06 | & ? [v0: any] : (v0 = all_885_0 | ~ $i(v0) | % 191.93/27.06 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_885_0, v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (197) implies: % 191.93/27.06 | (198) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_885_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (31) with fresh symbols all_887_0, all_887_1 gives: % 191.93/27.06 | (199) c_Nat_OSuc(all_887_0) = all_887_1 & % 191.93/27.06 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_887_1 & % 191.93/27.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_887_0 & $i(all_887_0) % 191.93/27.06 | & $i(all_887_1) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (199) implies: % 191.93/27.06 | (200) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_887_0 % 191.93/27.06 | (201) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_887_1 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (29) with fresh symbols all_891_0, all_891_1 gives: % 191.93/27.06 | (202) c_Nat_OSuc(all_891_1) = all_891_0 & % 191.93/27.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_891_1 & $i(all_891_0) % 191.93/27.06 | & $i(all_891_1) & ? [v0: $i] : ( ~ $i(v0) | % 191.93/27.06 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_891_0, v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (202) implies: % 191.93/27.06 | (203) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_891_1 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (17) with fresh symbol all_893_0 gives: % 191.93/27.06 | (204) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_893_0 & $i(all_893_0) % 191.93/27.06 | & ! [v0: any] : ! [v1: $i] : (v0 = all_893_0 | ~ % 191.93/27.06 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v1) | ~ $i(v1) % 191.93/27.06 | | ~ $i(v0)) % 191.93/27.06 | % 191.93/27.06 | ALPHA: (204) implies: % 191.93/27.06 | (205) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_893_0 % 191.93/27.06 | % 191.93/27.06 | DELTA: instantiating (30) with fresh symbol all_896_0 gives: % 191.93/27.06 | (206) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_896_0 & $i(all_896_0) & % 191.93/27.06 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_896_0, all_896_0) & ! [v0: % 191.93/27.06 | any] : (v0 = all_896_0 | ~ $i(v0) | ~ % 191.93/27.06 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_896_0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (206) implies: % 191.93/27.07 | (207) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_896_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (32) with fresh symbol all_902_0 gives: % 191.93/27.07 | (208) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_902_0 & $i(all_902_0) & % 191.93/27.07 | ! [v0: $i] : ! [v1: $i] : ( ~ % 191.93/27.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_902_0) = v1) | ~ % 191.93/27.07 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1))) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (208) implies: % 191.93/27.07 | (209) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_902_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (33) with fresh symbol all_905_0 gives: % 191.93/27.07 | (210) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_905_0 & $i(all_905_0) & % 191.93/27.07 | ! [v0: $i] : ! [v1: $i] : ( ~ % 191.93/27.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_905_0, v0) = v1) | ~ % 191.93/27.07 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1))) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (210) implies: % 191.93/27.07 | (211) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_905_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (83) with fresh symbol all_908_0 gives: % 191.93/27.07 | (212) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_908_0 & $i(all_908_0) % 191.93/27.07 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_908_0, all_908_0) % 191.93/27.07 | & ? [v0: any] : (v0 = all_908_0 | ~ $i(v0) | % 191.93/27.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_908_0, v0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (212) implies: % 191.93/27.07 | (213) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_908_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (22) with fresh symbols all_913_0, all_913_1 gives: % 191.93/27.07 | (214) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_913_1 & % 191.93/27.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_913_0 & $i(all_913_0) % 191.93/27.07 | & $i(all_913_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_913_1, % 191.93/27.07 | v0) = v1) | ~ $i(v0) | hAPP(v1, all_913_0) = all_913_0) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (214) implies: % 191.93/27.07 | (215) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_913_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (90) with fresh symbol all_925_0 gives: % 191.93/27.07 | (216) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_925_0 & $i(all_925_0) % 191.93/27.07 | & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~ % 191.93/27.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_925_0, v1) | ~ % 191.93/27.07 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v1)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (216) implies: % 191.93/27.07 | (217) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_925_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (69) with fresh symbol all_928_0 gives: % 191.93/27.07 | (218) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_928_0 & $i(all_928_0) % 191.93/27.07 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 191.93/27.07 | all_928_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) % 191.93/27.07 | = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = % 191.93/27.07 | v2) | ~ $i(v1) | ~ $i(v0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (218) implies: % 191.93/27.07 | (219) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_928_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (125) with fresh symbol all_931_0 gives: % 191.93/27.07 | (220) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_931_0 & $i(all_931_0) % 191.93/27.07 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_931_0 | ~ % 191.93/27.07 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 191.93/27.07 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 191.93/27.07 | v0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (220) implies: % 191.93/27.07 | (221) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_931_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (118) with fresh symbols all_937_0, all_937_1 gives: % 191.93/27.07 | (222) c_Nat_OSuc(all_937_1) = all_937_0 & % 191.93/27.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_937_1 & $i(all_937_0) % 191.93/27.07 | & $i(all_937_1) & ! [v0: $i] : ! [v1: int] : (v1 = all_937_1 | ~ % 191.93/27.07 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, all_937_0) = v1) | ~ % 191.93/27.07 | $i(v0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (222) implies: % 191.93/27.07 | (223) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_937_1 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (41) with fresh symbols all_945_0, all_945_1 gives: % 191.93/27.07 | (224) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_945_0 & % 191.93/27.07 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_945_1 & % 191.93/27.07 | $i(all_945_0) & $i(all_945_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 191.93/27.07 | (hAPP(all_945_1, v0) = v1) | ~ $i(v0) | hAPP(v1, all_945_0) = v0) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (224) implies: % 191.93/27.07 | (225) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_945_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (91) with fresh symbol all_954_0 gives: % 191.93/27.07 | (226) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_954_0 & $i(all_954_0) % 191.93/27.07 | & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_954_0, v1) | ~ % 191.93/27.07 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v1) | % 191.93/27.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_954_0, v0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (226) implies: % 191.93/27.07 | (227) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_954_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (120) with fresh symbol all_957_0 gives: % 191.93/27.07 | (228) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_957_0 & $i(all_957_0) % 191.93/27.07 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.07 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) % 191.93/27.07 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.07 | all_957_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, % 191.93/27.07 | v1)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (228) implies: % 191.93/27.07 | (229) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_957_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (126) with fresh symbols all_962_0, all_962_1 gives: % 191.93/27.07 | (230) c_Nat_OSuc(all_962_1) = all_962_0 & % 191.93/27.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_962_1 & $i(all_962_0) % 191.93/27.07 | & $i(all_962_1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 191.93/27.07 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, all_962_0) = v1) | ~ % 191.93/27.07 | $i(v0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (230) implies: % 191.93/27.07 | (231) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_962_1 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (100) with fresh symbol all_969_0 gives: % 191.93/27.07 | (232) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_969_0 & $i(all_969_0) % 191.93/27.07 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.07 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 191.93/27.07 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.07 | all_969_0, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.07 | all_969_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, % 191.93/27.07 | v0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (232) implies: % 191.93/27.07 | (233) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_969_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (39) with fresh symbol all_972_0 gives: % 191.93/27.07 | (234) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_972_0 & $i(all_972_0) & % 191.93/27.07 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.07 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 191.93/27.07 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Omonoid__mult(v1) | hAPP(v3, % 191.93/27.07 | all_972_0) = v0) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (234) implies: % 191.93/27.07 | (235) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_972_0 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (88) with fresh symbols all_975_0, all_975_1 gives: % 191.93/27.07 | (236) c_Nat_OSuc(all_975_1) = all_975_0 & % 191.93/27.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_975_1 & $i(all_975_0) % 191.93/27.07 | & $i(all_975_1) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.07 | all_975_1, all_975_0) & ! [v0: any] : (v0 = all_975_1 | ~ $i(v0) % 191.93/27.07 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_975_0)) % 191.93/27.07 | % 191.93/27.07 | ALPHA: (236) implies: % 191.93/27.07 | (237) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_975_1 % 191.93/27.07 | % 191.93/27.07 | DELTA: instantiating (50) with fresh symbol all_978_0 gives: % 191.93/27.08 | (238) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_978_0 & $i(all_978_0) % 191.93/27.08 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 191.93/27.08 | all_978_0 | ~ (c_Groups_Oone__class_Oone(v1) = v2) | ~ % 191.93/27.08 | (c_Polynomial_Odegree(v0, v2) = v3) | ~ (tc_Polynomial_Opoly(v0) = % 191.93/27.08 | v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v0)) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (238) implies: % 191.93/27.08 | (239) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_978_0 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (112) with fresh symbols all_984_0, all_984_1 gives: % 191.93/27.08 | (240) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_984_0 & % 191.93/27.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_984_1 & $i(all_984_0) % 191.93/27.08 | & $i(all_984_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 191.93/27.08 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_984_0) = v1) | % 191.93/27.08 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_984_1, % 191.93/27.08 | v0) | c_Nat_OSuc(v1) = v0) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (240) implies: % 191.93/27.08 | (241) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_984_1 % 191.93/27.08 | (242) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_984_0 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (36) with fresh symbols all_987_0, all_987_1 gives: % 191.93/27.08 | (243) c_Nat_OSuc(all_987_1) = all_987_0 & % 191.93/27.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_987_1 & $i(all_987_0) % 191.93/27.08 | & $i(all_987_1) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_987_0, % 191.93/27.08 | all_987_0) & ! [v0: any] : (v0 = all_987_0 | ~ $i(v0) | ~ % 191.93/27.08 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_987_0)) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (243) implies: % 191.93/27.08 | (244) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_987_1 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (106) with fresh symbol all_990_0 gives: % 191.93/27.08 | (245) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_990_0 & $i(all_990_0) % 191.93/27.08 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.08 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 191.93/27.08 | (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_990_0, v1) | % 191.93/27.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1)) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (245) implies: % 191.93/27.08 | (246) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_990_0 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (38) with fresh symbol all_996_0 gives: % 191.93/27.08 | (247) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_996_0 & $i(all_996_0) & % 191.93/27.08 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.08 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 191.93/27.08 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | % 191.93/27.08 | hAPP(v3, all_996_0) = v0) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (247) implies: % 191.93/27.08 | (248) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_996_0 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (9) with fresh symbol all_1005_0 gives: % 191.93/27.08 | (249) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1005_0 & % 191.93/27.08 | $i(all_1005_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.08 | int] : (v3 = all_1005_0 | ~ (c_Polynomial_Odegree(v0, v2) = v3) | % 191.93/27.08 | ~ (tc_Polynomial_Opoly(v0) = v1) | ~ % 191.93/27.08 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v0) | ~ % 191.93/27.08 | class_Groups_Ozero(v0)) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (249) implies: % 191.93/27.08 | (250) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1005_0 % 191.93/27.08 | (251) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 191.93/27.08 | all_1005_0 | ~ (c_Polynomial_Odegree(v0, v2) = v3) | ~ % 191.93/27.08 | (tc_Polynomial_Opoly(v0) = v1) | ~ % 191.93/27.08 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v0) | ~ % 191.93/27.08 | class_Groups_Ozero(v0)) % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (107) with fresh symbols all_1008_0, all_1008_1 gives: % 191.93/27.08 | (252) c_Nat_OSuc(all_1008_1) = all_1008_0 & % 191.93/27.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1008_1 & % 191.93/27.08 | $i(all_1008_0) & $i(all_1008_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 191.93/27.08 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_1008_0) = v1) | % 191.93/27.08 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.08 | all_1008_1, v0) | c_Nat_OSuc(v1) = v0) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (252) implies: % 191.93/27.08 | (253) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1008_1 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (112) with fresh symbols all_1014_0, all_1014_1 gives: % 191.93/27.08 | (254) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1014_0 & % 191.93/27.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1014_1 & % 191.93/27.08 | $i(all_1014_0) & $i(all_1014_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 191.93/27.08 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_1014_0) = v1) | % 191.93/27.08 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.08 | all_1014_1, v0) | c_Nat_OSuc(v1) = v0) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (254) implies: % 191.93/27.08 | (255) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1014_1 % 191.93/27.08 | (256) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1014_0 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (43) with fresh symbols all_1017_0, all_1017_1, % 191.93/27.08 | all_1017_2 gives: % 191.93/27.08 | (257) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1017_1 & % 191.93/27.08 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1017_2 & % 191.93/27.08 | hAPP(all_1017_2, all_1017_1) = all_1017_0 & $i(all_1017_0) & % 191.93/27.08 | $i(all_1017_1) & $i(all_1017_2) & ! [v0: $i] : ! [v1: $i] : (v1 = % 191.93/27.08 | v0 | ~ (hAPP(all_1017_0, v0) = v1) | ~ $i(v0)) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (257) implies: % 191.93/27.08 | (258) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1017_1 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (21) with fresh symbols all_1020_0, all_1020_1, % 191.93/27.08 | all_1020_2 gives: % 191.93/27.08 | (259) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1020_2 & % 191.93/27.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1020_1 & % 191.93/27.08 | hAPP(all_1020_2, all_1020_1) = all_1020_0 & $i(all_1020_0) & % 191.93/27.08 | $i(all_1020_1) & $i(all_1020_2) & ! [v0: $i] : ! [v1: int] : (v1 = % 191.93/27.08 | all_1020_1 | ~ (hAPP(all_1020_0, v0) = v1) | ~ $i(v0)) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (259) implies: % 191.93/27.08 | (260) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1020_1 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (64) with fresh symbol all_1027_0 gives: % 191.93/27.08 | (261) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1027_0 & % 191.93/27.08 | $i(all_1027_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 191.93/27.08 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = all_1027_0) | % 191.93/27.08 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = all_1027_0) & % 191.93/27.08 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2 & % 191.93/27.08 | $i(v2))) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (261) implies: % 191.93/27.08 | (262) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1027_0 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (56) with fresh symbol all_1030_0 gives: % 191.93/27.08 | (263) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1030_0 & % 191.93/27.08 | $i(all_1030_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.08 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower_Opower(v3, % 191.93/27.08 | v2, v1) = v4) | ~ (hAPP(v4, v0) = v5) | ~ $i(v3) | ~ $i(v2) % 191.93/27.08 | | ~ $i(v1) | ~ $i(v0) | hAPP(v5, all_1030_0) = v2) % 191.93/27.08 | % 191.93/27.08 | ALPHA: (263) implies: % 191.93/27.08 | (264) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1030_0 % 191.93/27.08 | % 191.93/27.08 | DELTA: instantiating (10) with fresh symbol all_1039_0 gives: % 191.93/27.09 | (265) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1039_0 & % 191.93/27.09 | $i(all_1039_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.09 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_OpCons(v2, v1, v0) = v3) | ~ % 191.93/27.09 | (c_Polynomial_Ocoeff(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 191.93/27.09 | $i(v0) | ~ class_Groups_Ozero(v2) | hAPP(v4, all_1039_0) = v1) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (265) implies: % 191.93/27.09 | (266) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1039_0 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (131) with fresh symbols all_1042_0, all_1042_1 gives: % 191.93/27.09 | (267) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1042_1 & % 191.93/27.09 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1042_0 & % 191.93/27.09 | $i(all_1042_0) & $i(all_1042_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.09 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v2) | % 191.93/27.09 | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1042_0, v0) | ~ % 191.93/27.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1042_1, v1) | % 191.93/27.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0)) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (267) implies: % 191.93/27.09 | (268) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1042_0 % 191.93/27.09 | (269) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1042_1 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (116) with fresh symbols all_1045_0, all_1045_1, % 191.93/27.09 | all_1045_2 gives: % 191.93/27.09 | (270) c_Nat_OSuc(all_1045_1) = all_1045_0 & c_Nat_OSuc(all_1045_2) = % 191.93/27.09 | all_1045_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1045_2 & % 191.93/27.09 | $i(all_1045_0) & $i(all_1045_1) & $i(all_1045_2) & ! [v0: any] : (v0 % 191.93/27.09 | = all_1045_1 | v0 = all_1045_2 | ~ $i(v0) | ~ % 191.93/27.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1045_0)) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (270) implies: % 191.93/27.09 | (271) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1045_2 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (48) with fresh symbol all_1048_0 gives: % 191.93/27.09 | (272) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1048_0 & % 191.93/27.09 | $i(all_1048_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.09 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, % 191.93/27.09 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ class_Power_Opower(v1) | % 191.93/27.09 | ? [v4: $i] : (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, % 191.93/27.09 | all_1048_0) = v4 & $i(v4))) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (272) implies: % 191.93/27.09 | (273) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1048_0 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (12) with fresh symbol all_1057_0 gives: % 191.93/27.09 | (274) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1057_0 & % 191.93/27.09 | $i(all_1057_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.09 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_OpCons(v1, v0, v3) = v4) | ~ % 191.93/27.09 | (tc_Polynomial_Opoly(v1) = v2) | ~ % 191.93/27.09 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.09 | class_Groups_Ozero(v1) | (c_Polynomial_Omonom(v1, v0, all_1057_0) = % 191.93/27.09 | v4 & $i(v4))) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (274) implies: % 191.93/27.09 | (275) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1057_0 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (71) with fresh symbol all_1065_0 gives: % 191.93/27.09 | (276) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1065_0 & $i(all_1065_0) % 191.93/27.09 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.09 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ % 191.93/27.09 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1065_0) = v2) | % 191.93/27.09 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 191.93/27.09 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v4) = v3 & % 191.93/27.09 | c_Nat_OSuc(v0) = v4 & $i(v4) & $i(v3))) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (276) implies: % 191.93/27.09 | (277) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1065_0 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (8) with fresh symbol all_1068_0 gives: % 191.93/27.09 | (278) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1068_0 & % 191.93/27.09 | $i(all_1068_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.09 | $i] : ! [v4: $i] : ! [v5: int] : (v5 = all_1068_0 | ~ % 191.93/27.09 | (c_Polynomial_Odegree(v1, v4) = v5) | ~ (c_Polynomial_OpCons(v1, % 191.93/27.09 | v0, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = v2) | ~ % 191.93/27.09 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.09 | class_Groups_Ozero(v1)) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (278) implies: % 191.93/27.09 | (279) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1068_0 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (47) with fresh symbol all_1077_0 gives: % 191.93/27.09 | (280) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1077_0 & % 191.93/27.09 | $i(all_1077_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.09 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, % 191.93/27.09 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.09 | class_Rings_Ocomm__semiring__1(v1) | ? [v4: $i] : % 191.93/27.09 | (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, all_1077_0) = v4 & % 191.93/27.09 | $i(v4))) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (280) implies: % 191.93/27.09 | (281) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1077_0 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (89) with fresh symbol all_1091_0 gives: % 191.93/27.09 | (282) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1091_0 & % 191.93/27.09 | $i(all_1091_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = % 191.93/27.09 | v0) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1091_0, v0)) & ! % 191.93/27.09 | [v0: $i] : ( ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.09 | all_1091_0, v0) | ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & $i(v1))) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (282) implies: % 191.93/27.09 | (283) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1091_0 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (128) with fresh symbols all_1097_0, all_1097_1 gives: % 191.93/27.09 | (284) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1097_0 & % 191.93/27.09 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1097_1 & % 191.93/27.09 | $i(all_1097_0) & $i(all_1097_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.09 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 191.93/27.09 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v1) = v4) | ~ % 191.93/27.09 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1097_0, v0) = v2) | ~ $i(v1) | % 191.93/27.09 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.09 | all_1097_1, v1)) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (284) implies: % 191.93/27.09 | (285) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1097_1 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (129) with fresh symbols all_1103_0, all_1103_1 gives: % 191.93/27.09 | (286) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1103_0 & % 191.93/27.09 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1103_1 & % 191.93/27.09 | $i(all_1103_0) & $i(all_1103_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.09 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 191.93/27.09 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v1) = v4) | ~ % 191.93/27.09 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1103_0, v1) = v2) | ~ $i(v1) | % 191.93/27.09 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.09 | all_1103_1, v1)) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (286) implies: % 191.93/27.09 | (287) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1103_1 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (34) with fresh symbols all_1106_0, all_1106_1, % 191.93/27.09 | all_1106_2, all_1106_3 gives: % 191.93/27.09 | (288) c_Nat_OSuc(all_1106_2) = all_1106_1 & % 191.93/27.09 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1106_3 & % 191.93/27.09 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1106_2 & % 191.93/27.09 | hAPP(all_1106_3, all_1106_1) = all_1106_0 & $i(all_1106_0) & % 191.93/27.09 | $i(all_1106_1) & $i(all_1106_2) & $i(all_1106_3) & ! [v0: $i] : ! % 191.93/27.09 | [v1: int] : (v1 = all_1106_1 | ~ (hAPP(all_1106_0, v0) = v1) | ~ % 191.93/27.09 | $i(v0)) % 191.93/27.09 | % 191.93/27.09 | ALPHA: (288) implies: % 191.93/27.09 | (289) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1106_2 % 191.93/27.09 | % 191.93/27.09 | DELTA: instantiating (62) with fresh symbols all_1110_0, all_1110_1 gives: % 191.93/27.10 | (290) c_Nat_OSuc(all_1110_1) = all_1110_0 & % 191.93/27.10 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1110_1 & % 191.93/27.10 | $i(all_1110_0) & $i(all_1110_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 191.93/27.10 | (c_Nat_Onat_Onat__size(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 191.93/27.10 | [v3: $i] : (c_Nat_Onat_Onat__size(v2) = v3 & c_Nat_OSuc(v0) = v2 & % 191.93/27.10 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, all_1110_0) = v3 & % 191.93/27.10 | $i(v3) & $i(v2))) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (290) implies: % 191.93/27.10 | (291) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1110_1 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (77) with fresh symbols all_1113_0, all_1113_1 gives: % 191.93/27.10 | (292) c_Nat_OSuc(all_1113_1) = all_1113_0 & % 191.93/27.10 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1113_1 & % 191.93/27.10 | $i(all_1113_0) & $i(all_1113_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 191.93/27.10 | (c_Nat_Osize__class_Osize(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ? % 191.93/27.10 | [v2: $i] : ? [v3: $i] : (c_Nat_Osize__class_Osize(tc_Nat_Onat, v2) % 191.93/27.10 | = v3 & c_Nat_OSuc(v0) = v2 & % 191.93/27.10 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, all_1113_0) = v3 & % 191.93/27.10 | $i(v3) & $i(v2))) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (292) implies: % 191.93/27.10 | (293) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1113_1 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (7) with fresh symbols all_1116_0, all_1116_1, % 191.93/27.10 | all_1116_2, all_1116_3, all_1116_4 gives: % 191.93/27.10 | (294) c_Power_Opower__class_Opower(all_1116_4) = all_1116_3 & % 191.93/27.10 | c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = all_1116_1 & % 191.93/27.10 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1116_4 & % 191.93/27.10 | hAPP(all_1116_2, all_1116_1) = all_1116_0 & hAPP(all_1116_3, v_q) = % 191.93/27.10 | all_1116_2 & $i(all_1116_0) & $i(all_1116_1) & $i(all_1116_2) & % 191.93/27.10 | $i(all_1116_3) & $i(all_1116_4) & % 191.93/27.10 | c_Rings_Odvd__class_Odvd(all_1116_4, v_p, all_1116_0) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (294) implies: % 191.93/27.10 | (295) hAPP(all_1116_3, v_q) = all_1116_2 % 191.93/27.10 | (296) hAPP(all_1116_2, all_1116_1) = all_1116_0 % 191.93/27.10 | (297) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1116_4 % 191.93/27.10 | (298) c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = all_1116_1 % 191.93/27.10 | (299) c_Power_Opower__class_Opower(all_1116_4) = all_1116_3 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (123) with fresh symbols all_1126_0, all_1126_1 gives: % 191.93/27.10 | (300) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1126_1 & % 191.93/27.10 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1126_0 & % 191.93/27.10 | $i(all_1126_0) & $i(all_1126_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.10 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = all_1126_1 | % 191.93/27.10 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v4, v1) = v5) | ~ % 191.93/27.10 | (c_Nat_OSuc(v3) = v4) | ~ (hAPP(v2, v0) = v3) | ~ % 191.93/27.10 | (hAPP(all_1126_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.10 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1126_1, v1)) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (300) implies: % 191.93/27.10 | (301) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1126_1 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (73) with fresh symbol all_1132_0 gives: % 191.93/27.10 | (302) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1132_0 & $i(all_1132_0) % 191.93/27.10 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 191.93/27.10 | : ( ~ (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3) | ~ % 191.93/27.10 | (c_Polynomial_Odegree(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 191.93/27.10 | $i(v0) | ~ class_Rings_Ocomm__semiring__0(v2) | ? [v5: $i] : % 191.93/27.10 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, all_1132_0) = v4 & % 191.93/27.10 | c_Polynomial_Odegree(v2, v1) = v5 & $i(v5) & $i(v4))) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (302) implies: % 191.93/27.10 | (303) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1132_0 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (18) with fresh symbol all_1135_0 gives: % 191.93/27.10 | (304) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1135_0 & % 191.93/27.10 | $i(all_1135_0) & ! [v0: $i] : ! [v1: any] : (v1 = all_1135_0 | ~ % 191.93/27.10 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1135_0) | % 191.93/27.10 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 191.93/27.10 | all_1135_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = % 191.93/27.10 | all_1135_0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = % 191.93/27.10 | all_1135_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 191.93/27.10 | all_1135_0, all_1135_0) = v0)) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (304) implies: % 191.93/27.10 | (305) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1135_0 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (101) with fresh symbol all_1138_0 gives: % 191.93/27.10 | (306) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1138_0 & % 191.93/27.10 | $i(all_1138_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.10 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 191.93/27.10 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.10 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1138_0, % 191.93/27.10 | v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.10 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 191.93/27.10 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.10 | all_1138_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 191.93/27.10 | v1)) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (306) implies: % 191.93/27.10 | (307) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1138_0 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (49) with fresh symbols all_1141_0, all_1141_1, % 191.93/27.10 | all_1141_2 gives: % 191.93/27.10 | (308) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1141_1 & % 191.93/27.10 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1141_2 & % 191.93/27.10 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1141_0 & % 191.93/27.10 | $i(all_1141_0) & $i(all_1141_1) & $i(all_1141_2) & ! [v0: any] : ! % 191.93/27.10 | [v1: any] : ! [v2: $i] : (v1 = all_1141_0 | v0 = all_1141_1 | ~ % 191.93/27.10 | (hAPP(v2, v0) = v1) | ~ (hAPP(all_1141_2, v1) = v2) | ~ $i(v1) | % 191.93/27.10 | ~ $i(v0)) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (308) implies: % 191.93/27.10 | (309) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1141_0 % 191.93/27.10 | (310) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1141_1 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (94) with fresh symbols all_1144_0, all_1144_1 gives: % 191.93/27.10 | (311) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1144_0 & % 191.93/27.10 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1144_1 & % 191.93/27.10 | $i(all_1144_0) & $i(all_1144_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.10 | $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (hAPP(v3, v1) = v4) % 191.93/27.10 | | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1144_0, v2) = v3) | ~ % 191.93/27.10 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.10 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1144_1, v2)) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (311) implies: % 191.93/27.10 | (312) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1144_1 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (105) with fresh symbols all_1156_0, all_1156_1, % 191.93/27.10 | all_1156_2 gives: % 191.93/27.10 | (313) c_Nat_OSuc(all_1156_2) = all_1156_1 & % 191.93/27.10 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1156_0 & % 191.93/27.10 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1156_2 & % 191.93/27.10 | $i(all_1156_0) & $i(all_1156_1) & $i(all_1156_2) & ! [v0: $i] : ! % 191.93/27.10 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~ % 191.93/27.10 | (hAPP(all_1156_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.10 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1156_1, v1) | ~ % 191.93/27.10 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1156_1, v0) | % 191.93/27.10 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) % 191.93/27.10 | % 191.93/27.10 | ALPHA: (313) implies: % 191.93/27.10 | (314) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1156_2 % 191.93/27.10 | % 191.93/27.10 | DELTA: instantiating (104) with fresh symbols all_1177_0, all_1177_1, % 191.93/27.10 | all_1177_2 gives: % 191.93/27.11 | (315) c_Nat_OSuc(all_1177_2) = all_1177_1 & % 191.93/27.11 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1177_0 & % 191.93/27.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1177_2 & % 191.93/27.11 | $i(all_1177_0) & $i(all_1177_1) & $i(all_1177_2) & ! [v0: $i] : ! % 191.93/27.11 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ % 191.93/27.11 | (hAPP(all_1177_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1177_1, v1) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1177_1, v0) | % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (315) implies: % 191.93/27.11 | (316) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1177_2 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (109) with fresh symbols all_1186_0, all_1186_1 gives: % 191.93/27.11 | (317) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1186_1 & % 191.93/27.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_0 & % 191.93/27.11 | $i(all_1186_0) & $i(all_1186_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.11 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 191.93/27.11 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1186_1, v2) = v3) | % 191.93/27.11 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1186_0, v2) | ~ % 191.93/27.11 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) | % 191.93/27.11 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (317) implies: % 191.93/27.11 | (318) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_0 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (95) with fresh symbols all_1192_0, all_1192_1 gives: % 191.93/27.11 | (319) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1192_0 & % 191.93/27.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1192_1 & % 191.93/27.11 | $i(all_1192_0) & $i(all_1192_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.11 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v2) = % 191.93/27.11 | v4) | ~ (hAPP(v3, v1) = v5) | ~ (hAPP(all_1192_0, v0) = v3) | % 191.93/27.11 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1192_1, v0) | % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (319) implies: % 191.93/27.11 | (320) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1192_1 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (102) with fresh symbols all_1195_0, all_1195_1 gives: % 191.93/27.11 | (321) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1195_0 & % 191.93/27.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1195_1 & % 191.93/27.11 | $i(all_1195_0) & $i(all_1195_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.11 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 191.93/27.11 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1195_0, v2) = v3) | % 191.93/27.11 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1195_1, v2) | % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (321) implies: % 191.93/27.11 | (322) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1195_1 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (103) with fresh symbols all_1198_0, all_1198_1, % 191.93/27.11 | all_1198_2 gives: % 191.93/27.11 | (323) c_Nat_OSuc(all_1198_2) = all_1198_1 & % 191.93/27.11 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1198_0 & % 191.93/27.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1198_2 & % 191.93/27.11 | $i(all_1198_0) & $i(all_1198_1) & $i(all_1198_2) & ! [v0: $i] : ! % 191.93/27.11 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~ % 191.93/27.11 | (hAPP(all_1198_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1198_1, v1) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1198_1, v0) | % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1198_1, v3)) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (323) implies: % 191.93/27.11 | (324) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1198_2 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (130) with fresh symbols all_1208_0, all_1208_1 gives: % 191.93/27.11 | (325) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1208_0 & % 191.93/27.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1208_1 & % 191.93/27.11 | $i(all_1208_0) & $i(all_1208_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.11 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.93/27.11 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v4, v5) = v6) | ~ % 191.93/27.11 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1208_0, % 191.93/27.11 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1208_1, v2) | % 191.93/27.11 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v6 & $i(v6))) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (325) implies: % 191.93/27.11 | (326) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1208_1 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (86) with fresh symbol all_1214_0 gives: % 191.93/27.11 | (327) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1214_0 & % 191.93/27.11 | $i(all_1214_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.11 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.93/27.11 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) | % 191.93/27.11 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.11 | class_Rings_Olinordered__semidom(v2) | ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1214_0, v0) | ? % 191.93/27.11 | [v6: $i] : (c_Groups_Oone__class_Oone(v2) = v6 & $i(v6) & ( ~ % 191.93/27.11 | c_Orderings_Oord__class_Oless(v2, v6, v1) | % 191.93/27.11 | c_Orderings_Oord__class_Oless(v2, v6, v5)))) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (327) implies: % 191.93/27.11 | (328) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1214_0 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (54) with fresh symbols all_1220_0, all_1220_1 gives: % 191.93/27.11 | (329) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1220_1 & % 191.93/27.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1220_0 & % 191.93/27.11 | $i(all_1220_0) & $i(all_1220_1) & ! [v0: $i] : ! [v1: any] : ! % 191.93/27.11 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/27.11 | (v1 = all_1220_0 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | % 191.93/27.11 | ~ (hAPP(all_1220_1, v2) = v3) | ~ (hAPP(all_1220_1, v0) = v5) | ~ % 191.93/27.11 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.11 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6) | % 191.93/27.11 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0)) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (329) implies: % 191.93/27.11 | (330) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1220_0 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (96) with fresh symbols all_1226_0, all_1226_1 gives: % 191.93/27.11 | (331) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1226_0 & % 191.93/27.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1226_1 & % 191.93/27.11 | $i(all_1226_0) & $i(all_1226_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.11 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.93/27.11 | (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1226_0, % 191.93/27.11 | v2) = v3) | ~ (hAPP(all_1226_0, v1) = v5) | ~ $i(v2) | ~ % 191.93/27.11 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.11 | v2, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.11 | all_1226_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, % 191.93/27.11 | v6)) % 191.93/27.11 | % 191.93/27.11 | ALPHA: (331) implies: % 191.93/27.11 | (332) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1226_1 % 191.93/27.11 | % 191.93/27.11 | DELTA: instantiating (57) with fresh symbols all_1238_0, all_1238_1 gives: % 191.93/27.12 | (333) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1238_1 & % 191.93/27.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1238_0 & % 191.93/27.12 | $i(all_1238_0) & $i(all_1238_1) & ! [v0: $i] : ! [v1: any] : ! % 191.93/27.12 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 191.93/27.12 | (v1 = all_1238_0 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | % 191.93/27.12 | ~ (hAPP(all_1238_1, v2) = v3) | ~ (hAPP(all_1238_1, v0) = v5) | ~ % 191.93/27.12 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.12 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6) | % 191.93/27.12 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v2, v0)) % 191.93/27.12 | % 191.93/27.12 | ALPHA: (333) implies: % 191.93/27.12 | (334) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1238_0 % 191.93/27.12 | % 191.93/27.12 | DELTA: instantiating (6) with fresh symbols all_1247_0, all_1247_1, % 191.93/27.12 | all_1247_2, all_1247_3, all_1247_4, all_1247_5, all_1247_6 gives: % 191.93/27.12 | (335) c_Power_Opower__class_Opower(all_1247_6) = all_1247_5 & % 191.93/27.12 | c_Groups_Otimes__class_Otimes(all_1247_6) = all_1247_1 & % 191.93/27.12 | c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = all_1247_3 & % 191.93/27.12 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1247_6 & % 191.93/27.12 | hAPP(all_1247_0, v_r____) = all_1247_2 & hAPP(all_1247_1, v_p) = % 191.93/27.12 | all_1247_0 & hAPP(all_1247_4, all_1247_3) = all_1247_2 & % 191.93/27.12 | hAPP(all_1247_5, v_q) = all_1247_4 & $i(all_1247_0) & $i(all_1247_1) % 191.93/27.12 | & $i(all_1247_2) & $i(all_1247_3) & $i(all_1247_4) & $i(all_1247_5) & % 191.93/27.12 | $i(all_1247_6) % 191.93/27.12 | % 191.93/27.12 | ALPHA: (335) implies: % 191.93/27.12 | (336) hAPP(all_1247_5, v_q) = all_1247_4 % 191.93/27.12 | (337) hAPP(all_1247_4, all_1247_3) = all_1247_2 % 191.93/27.12 | (338) hAPP(all_1247_1, v_p) = all_1247_0 % 191.93/27.12 | (339) hAPP(all_1247_0, v_r____) = all_1247_2 % 191.93/27.12 | (340) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1247_6 % 191.93/27.12 | (341) c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = all_1247_3 % 191.93/27.12 | (342) c_Groups_Otimes__class_Otimes(all_1247_6) = all_1247_1 % 191.93/27.12 | (343) c_Power_Opower__class_Opower(all_1247_6) = all_1247_5 % 191.93/27.12 | % 191.93/27.12 | DELTA: instantiating (74) with fresh symbols all_1264_0, all_1264_1 gives: % 191.93/27.12 | (344) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1264_0 & % 191.93/27.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1264_1 & % 191.93/27.12 | $i(all_1264_0) & $i(all_1264_1) & ! [v0: $i] : ! [v1: any] : ! % 191.93/27.12 | [v2: $i] : ! [v3: $i] : (v1 = all_1264_1 | ~ % 191.93/27.12 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1264_0) = v2) | % 191.93/27.12 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v0) = v3) | ~ % 191.93/27.12 | $i(v1) | ~ $i(v0) | ? [v4: $i] : (c_Nat_OSuc(v3) = v4 & % 191.93/27.12 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v4 & $i(v4))) % 191.93/27.12 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 191.93/27.12 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1264_1, v0) = v1) | % 191.93/27.12 | ~ $i(v0)) % 191.93/27.12 | % 191.93/27.12 | ALPHA: (344) implies: % 191.93/27.12 | (345) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1264_1 % 191.93/27.12 | (346) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1264_0 % 191.93/27.12 | % 191.93/27.12 | DELTA: instantiating (14) with fresh symbols all_1276_0, all_1276_1, % 191.93/27.12 | all_1276_2, all_1276_3, all_1276_4, all_1276_5, all_1276_6, all_1276_7 % 191.93/27.12 | gives: % 191.93/27.12 | (347) c_Power_Opower__class_Opower(all_1276_7) = all_1276_6 & % 191.93/27.12 | c_Groups_Otimes__class_Otimes(all_1276_7) = all_1276_2 & % 191.93/27.12 | c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = all_1276_4 & % 191.93/27.12 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1276_7 & % 191.93/27.12 | hAPP(all_1276_1, all_1276_0) = all_1276_3 & hAPP(all_1276_2, v_p) = % 191.93/27.12 | all_1276_1 & hAPP(all_1276_5, all_1276_4) = all_1276_3 & % 191.93/27.12 | hAPP(all_1276_6, v_q) = all_1276_5 & $i(all_1276_0) & $i(all_1276_1) % 191.93/27.12 | & $i(all_1276_2) & $i(all_1276_3) & $i(all_1276_4) & $i(all_1276_5) & % 191.93/27.12 | $i(all_1276_6) & $i(all_1276_7) % 191.93/27.12 | % 191.93/27.12 | ALPHA: (347) implies: % 191.93/27.12 | (348) hAPP(all_1276_6, v_q) = all_1276_5 % 191.93/27.12 | (349) hAPP(all_1276_5, all_1276_4) = all_1276_3 % 191.93/27.12 | (350) hAPP(all_1276_2, v_p) = all_1276_1 % 191.93/27.12 | (351) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1276_7 % 191.93/27.12 | (352) c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = all_1276_4 % 191.93/27.12 | (353) c_Groups_Otimes__class_Otimes(all_1276_7) = all_1276_2 % 191.93/27.12 | (354) c_Power_Opower__class_Opower(all_1276_7) = all_1276_6 % 191.93/27.12 | % 191.93/27.12 | DELTA: instantiating (4) with fresh symbol all_1296_0 gives: % 191.93/27.12 | (355) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1296_0 & % 191.93/27.12 | $i(all_1296_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.12 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v2) | % 191.93/27.12 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Ozero(v1) | ? [v3: $i] : ? % 191.93/27.12 | [v4: $i] : (( ~ (v2 = all_1296_0) | (v4 = v0 & % 191.93/27.12 | tc_Polynomial_Opoly(v1) = v3 & % 191.93/27.12 | c_Groups_Ozero__class_Ozero(v3) = v0 & $i(v3))) & (v2 = % 191.93/27.12 | all_1296_0 | ( ~ (v4 = v0) & tc_Polynomial_Opoly(v1) = v3 & % 191.93/27.12 | c_Groups_Ozero__class_Ozero(v3) = v4 & $i(v4) & $i(v3))))) % 191.93/27.12 | % 191.93/27.12 | ALPHA: (355) implies: % 191.93/27.12 | (356) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1296_0 % 191.93/27.12 | % 191.93/27.12 | DELTA: instantiating (122) with fresh symbols all_1302_0, all_1302_1 gives: % 191.93/27.12 | (357) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1302_0 & % 191.93/27.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1302_1 & % 191.93/27.12 | $i(all_1302_0) & $i(all_1302_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.12 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 191.93/27.12 | [v7: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, v3) = v5) % 191.93/27.12 | | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v7) | ~ % 191.93/27.12 | (hAPP(v4, v5) = v6) | ~ (hAPP(all_1302_0, v1) = v4) | ~ $i(v3) | % 191.93/27.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ % 191.93/27.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1302_1, v3) | ? % 191.93/27.12 | [v8: $i] : (hAPP(v4, v3) = v8 & $i(v8) & % 191.93/27.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v7, v8))) % 191.93/27.12 | % 191.93/27.12 | ALPHA: (357) implies: % 191.93/27.12 | (358) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1302_1 % 191.93/27.12 | % 191.93/27.12 | DELTA: instantiating (44) with fresh symbol all_1305_0 gives: % 191.93/27.12 | (359) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1305_0 & % 191.93/27.12 | $i(all_1305_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.12 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.93/27.12 | (c_Groups_Oone__class_Oone(v2) = v3) | ~ (c_Polynomial_Ocoeff(v1, % 191.93/27.12 | v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = v2) | ~ (hAPP(v4, % 191.93/27.12 | v0) = v5) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.12 | class_Rings_Ocomm__semiring__1(v1) | ? [v6: $i] : ? [v7: $i] : (( % 191.93/27.12 | ~ (v0 = all_1305_0) | (v6 = v5 & c_Groups_Oone__class_Oone(v1) % 191.93/27.12 | = v5 & $i(v5))) & (v0 = all_1305_0 | (v7 = v5 & % 191.93/27.12 | c_Groups_Ozero__class_Ozero(v1) = v5 & $i(v5))))) % 191.93/27.12 | % 191.93/27.12 | ALPHA: (359) implies: % 191.93/27.12 | (360) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1305_0 % 191.93/27.12 | % 191.93/27.12 | DELTA: instantiating (11) with fresh symbol all_1308_0 gives: % 191.93/27.12 | (361) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1308_0 & % 191.93/27.12 | $i(all_1308_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.12 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Odegree(v2, v3) = v4) | ~ % 191.93/27.12 | (c_Polynomial_Osmult(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.93/27.12 | $i(v0) | ~ class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] : % 191.93/27.12 | ((v4 = all_1308_0 | ( ~ (v5 = v1) & c_Groups_Ozero__class_Ozero(v2) % 191.93/27.12 | = v5 & $i(v5))) & ((v6 = v4 & c_Polynomial_Odegree(v2, v0) = % 191.93/27.12 | v4 & $i(v4)) | (v5 = v1 & c_Groups_Ozero__class_Ozero(v2) = % 191.93/27.12 | v1)))) % 191.93/27.12 | % 191.93/27.12 | ALPHA: (361) implies: % 191.93/27.12 | (362) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1308_0 % 191.93/27.12 | % 191.93/27.12 | DELTA: instantiating (40) with fresh symbols all_1311_0, all_1311_1 gives: % 191.93/27.13 | (363) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1311_0 & % 191.93/27.13 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1311_1 & % 191.93/27.13 | $i(all_1311_0) & $i(all_1311_1) & ! [v0: $i] : ! [v1: any] : ! % 191.93/27.13 | [v2: $i] : (v1 = all_1311_0 | ~ (hAPP(v2, v0) = all_1311_0) | ~ % 191.93/27.13 | (hAPP(all_1311_1, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] % 191.93/27.13 | : ! [v1: $i] : ! [v2: $i] : (v0 = all_1311_0 | ~ (hAPP(v2, v0) = % 191.93/27.13 | all_1311_0) | ~ (hAPP(all_1311_1, v1) = v2) | ~ $i(v1) | ~ % 191.93/27.13 | $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1311_0 | ~ % 191.93/27.13 | (hAPP(v0, all_1311_0) = v1) | ~ (hAPP(all_1311_1, all_1311_0) = % 191.93/27.13 | v0)) % 191.93/27.13 | % 191.93/27.13 | ALPHA: (363) implies: % 191.93/27.13 | (364) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1311_0 % 191.93/27.13 | % 191.93/27.13 | DELTA: instantiating (42) with fresh symbols all_1314_0, all_1314_1 gives: % 191.93/27.13 | (365) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1314_1 & % 191.93/27.13 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1314_0 & % 191.93/27.13 | $i(all_1314_0) & $i(all_1314_1) & ! [v0: $i] : ! [v1: any] : ! % 191.93/27.13 | [v2: $i] : (v1 = all_1314_1 | ~ (hAPP(v2, v0) = all_1314_1) | ~ % 191.93/27.13 | (hAPP(all_1314_0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] % 191.93/27.13 | : ! [v1: $i] : ! [v2: $i] : (v0 = all_1314_1 | ~ (hAPP(v2, v0) = % 191.93/27.13 | all_1314_1) | ~ (hAPP(all_1314_0, v1) = v2) | ~ $i(v1) | ~ % 191.93/27.13 | $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1314_1 | ~ % 191.93/27.13 | (hAPP(v0, all_1314_1) = v1) | ~ (hAPP(all_1314_0, all_1314_1) = % 191.93/27.13 | v0)) % 191.93/27.13 | % 191.93/27.13 | ALPHA: (365) implies: % 191.93/27.13 | (366) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1314_1 % 191.93/27.13 | % 191.93/27.13 | DELTA: instantiating (92) with fresh symbol all_1317_0 gives: % 191.93/27.13 | (367) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1317_0 & % 191.93/27.13 | $i(all_1317_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.13 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 191.93/27.13 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.13 | all_1317_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.13 | all_1317_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.13 | all_1317_0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.13 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 191.93/27.13 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.13 | all_1317_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.13 | all_1317_0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.13 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 191.93/27.13 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.13 | all_1317_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.13 | all_1317_0, v2)) % 191.93/27.13 | % 191.93/27.13 | ALPHA: (367) implies: % 191.93/27.13 | (368) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1317_0 % 191.93/27.13 | % 191.93/27.13 | DELTA: instantiating (79) with fresh symbols all_1320_0, all_1320_1 gives: % 191.93/27.13 | (369) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1320_0 & % 191.93/27.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1320_1 & % 191.93/27.13 | $i(all_1320_0) & $i(all_1320_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.13 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 191.93/27.13 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 191.93/27.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1320_0) = v6) | % 191.93/27.13 | ~ (c_Power_Opower__class_Opower(v2) = v4) | ~ % 191.93/27.13 | (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v8, v0) = v9) | % 191.93/27.13 | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v3, v7) % 191.93/27.13 | = v8) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1320_1, v1) | ~ % 191.93/27.13 | class_Groups_Omonoid__mult(v2) | (hAPP(v5, v1) = v9 & $i(v9))) % 191.93/27.13 | % 191.93/27.13 | ALPHA: (369) implies: % 191.93/27.13 | (370) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1320_1 % 191.93/27.13 | (371) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1320_0 % 191.93/27.13 | % 191.93/27.13 | DELTA: instantiating (114) with fresh symbols all_1326_0, all_1326_1, % 191.93/27.13 | all_1326_2 gives: % 191.93/27.13 | (372) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1326_0 & % 191.93/27.13 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1326_1 & % 191.93/27.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1326_2 & % 191.93/27.13 | $i(all_1326_0) & $i(all_1326_1) & $i(all_1326_2) & ! [v0: any] : ! % 191.93/27.13 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = all_1326_0 | ~ % 191.93/27.13 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1326_1, v1) = v2) | ~ $i(v1) | % 191.93/27.13 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.13 | all_1326_2, v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, % 191.93/27.13 | v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, % 191.93/27.13 | all_1326_0) = v2) | ~ (hAPP(all_1326_1, v0) = v1) | ~ $i(v0) % 191.93/27.13 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1326_2, v0) | % 191.93/27.13 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0)) % 191.93/27.13 | % 191.93/27.13 | ALPHA: (372) implies: % 191.93/27.13 | (373) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1326_2 % 191.93/27.13 | (374) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1326_0 % 191.93/27.13 | % 191.93/27.13 | DELTA: instantiating (26) with fresh symbols all_1335_0, all_1335_1 gives: % 191.93/27.13 | (375) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1335_1 & % 191.93/27.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1335_0 & % 191.93/27.13 | $i(all_1335_0) & $i(all_1335_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.13 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3) % 191.93/27.13 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1335_1, all_1335_0) = v2) | % 191.93/27.13 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 191.93/27.13 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1335_0 | v1 = v0 | ~ (hAPP(v3, % 191.93/27.13 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1335_1, v2) = % 191.93/27.13 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 191.93/27.13 | % 191.93/27.13 | ALPHA: (375) implies: % 191.93/27.13 | (376) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1335_0 % 191.93/27.13 | % 191.93/27.13 | DELTA: instantiating (26) with fresh symbols all_1338_0, all_1338_1 gives: % 191.93/27.13 | (377) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1338_1 & % 191.93/27.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1338_0 & % 191.93/27.13 | $i(all_1338_0) & $i(all_1338_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.13 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3) % 191.93/27.13 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1338_1, all_1338_0) = v2) | % 191.93/27.13 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 191.93/27.13 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1338_0 | v1 = v0 | ~ (hAPP(v3, % 191.93/27.13 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1338_1, v2) = % 191.93/27.13 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 191.93/27.13 | % 191.93/27.13 | ALPHA: (377) implies: % 191.93/27.13 | (378) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1338_0 % 191.93/27.13 | % 191.93/27.13 | DELTA: instantiating (23) with fresh symbols all_1344_0, all_1344_1 gives: % 191.93/27.13 | (379) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1344_1 & % 191.93/27.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1344_0 & % 191.93/27.13 | $i(all_1344_0) & $i(all_1344_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.13 | int] : (v2 = all_1344_0 | ~ (hAPP(v1, v0) = v2) | ~ % 191.93/27.13 | (hAPP(all_1344_1, all_1344_0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! % 191.93/27.13 | [v1: $i] : ! [v2: int] : (v2 = all_1344_0 | ~ (hAPP(v1, all_1344_0) % 191.93/27.13 | = v2) | ~ (hAPP(all_1344_1, v0) = v1) | ~ $i(v0)) & ! [v0: % 191.93/27.13 | any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1344_0 | v0 = % 191.93/27.13 | all_1344_0 | ~ (hAPP(v2, v0) = all_1344_0) | ~ (hAPP(all_1344_1, % 191.93/27.13 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 191.93/27.13 | % 191.93/27.13 | ALPHA: (379) implies: % 191.93/27.13 | (380) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1344_0 % 191.93/27.13 | % 191.93/27.13 | DELTA: instantiating (113) with fresh symbols all_1347_0, all_1347_1, % 191.93/27.13 | all_1347_2 gives: % 191.93/27.14 | (381) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1347_0 & % 191.93/27.14 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1347_1 & % 191.93/27.14 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1347_2 & % 191.93/27.14 | $i(all_1347_0) & $i(all_1347_1) & $i(all_1347_2) & ! [v0: any] : ! % 191.93/27.14 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = all_1347_0 | ~ % 191.93/27.14 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1347_1, v0) = v2) | ~ $i(v1) | % 191.93/27.14 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.14 | all_1347_2, v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, % 191.93/27.14 | v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, % 191.93/27.14 | v0) = v2) | ~ (hAPP(all_1347_1, all_1347_0) = v1) | ~ $i(v0) % 191.93/27.14 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1347_2, v0) | % 191.93/27.14 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0)) % 191.93/27.14 | % 191.93/27.14 | ALPHA: (381) implies: % 191.93/27.14 | (382) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1347_2 % 191.93/27.14 | (383) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1347_0 % 191.93/27.14 | % 191.93/27.14 | DELTA: instantiating (124) with fresh symbols all_1350_0, all_1350_1, % 191.93/27.14 | all_1350_2, all_1350_3 gives: % 191.93/27.14 | (384) c_Nat_OSuc(all_1350_3) = all_1350_0 & % 191.93/27.14 | c_Power_Opower__class_Opower(tc_Int_Oint) = all_1350_1 & % 191.93/27.14 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1350_2 & % 191.93/27.14 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1350_3 & % 191.93/27.14 | $i(all_1350_0) & $i(all_1350_1) & $i(all_1350_2) & $i(all_1350_3) & % 191.93/27.14 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 191.93/27.14 | ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1350_0) = v3) % 191.93/27.14 | | ~ (hAPP(v2, v3) = v4) | ~ (hAPP(all_1350_1, v0) = v2) | ~ % 191.93/27.14 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, % 191.93/27.14 | all_1350_2, v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.14 | all_1350_3, v1) | ? [v5: $i] : % 191.93/27.14 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5, v0) = v4 & hAPP(v2, % 191.93/27.14 | v1) = v5 & $i(v5) & $i(v4))) % 191.93/27.14 | % 191.93/27.14 | ALPHA: (384) implies: % 191.93/27.14 | (385) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1350_3 % 191.93/27.14 | % 191.93/27.14 | DELTA: instantiating (46) with fresh symbols all_1353_0, all_1353_1, % 191.93/27.14 | all_1353_2 gives: % 191.93/27.14 | (386) c_Nat_OSuc(all_1353_1) = all_1353_0 & % 191.93/27.14 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1353_2 & % 191.93/27.14 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1353_1 & % 191.93/27.14 | $i(all_1353_0) & $i(all_1353_1) & $i(all_1353_2) & ! [v0: $i] : ! % 191.93/27.14 | [v1: any] : ! [v2: $i] : (v1 = all_1353_0 | ~ (hAPP(v2, v0) = % 191.93/27.14 | all_1353_0) | ~ (hAPP(all_1353_2, v1) = v2) | ~ $i(v1) | ~ % 191.93/27.14 | $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 = % 191.93/27.14 | all_1353_0 | ~ (hAPP(v2, v0) = all_1353_0) | ~ (hAPP(all_1353_2, % 191.93/27.14 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int] % 191.93/27.14 | : (v1 = all_1353_0 | ~ (hAPP(v0, all_1353_0) = v1) | ~ % 191.93/27.14 | (hAPP(all_1353_2, all_1353_0) = v0)) % 191.93/27.14 | % 191.93/27.14 | ALPHA: (386) implies: % 191.93/27.14 | (387) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1353_1 % 191.93/27.14 | % 191.93/27.14 | DELTA: instantiating (119) with fresh symbols all_1359_0, all_1359_1 gives: % 191.93/27.14 | (388) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1359_0 & % 191.93/27.14 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1359_1 & % 191.93/27.14 | $i(all_1359_0) & $i(all_1359_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.14 | int] : (v2 = all_1359_1 | ~ % 191.93/27.14 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 191.93/27.14 | | ~ $i(v0) | ? [v3: $i] : (hAPP(all_1359_0, v0) = v3 & $i(v3) & % 191.93/27.14 | ! [v4: $i] : ( ~ (hAPP(v3, v4) = v1) | ~ $i(v4)))) & ! [v0: $i] % 191.93/27.14 | : ! [v1: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) % 191.93/27.14 | = all_1359_1) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 191.93/27.14 | : (hAPP(v2, v3) = v1 & hAPP(all_1359_0, v0) = v2 & $i(v3) & % 191.93/27.14 | $i(v2))) % 191.93/27.14 | % 191.93/27.14 | ALPHA: (388) implies: % 191.93/27.14 | (389) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1359_1 % 191.93/27.14 | % 191.93/27.14 | DELTA: instantiating (24) with fresh symbols all_1368_0, all_1368_1 gives: % 191.93/27.14 | (390) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1368_1 & % 191.93/27.14 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1368_0 & % 191.93/27.14 | $i(all_1368_0) & $i(all_1368_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.14 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 191.93/27.14 | (hAPP(v4, all_1368_0) = v5) | ~ (hAPP(v2, all_1368_0) = v3) | ~ % 191.93/27.14 | (hAPP(all_1368_1, v1) = v2) | ~ (hAPP(all_1368_1, v0) = v4) | ~ % 191.93/27.14 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! % 191.93/27.14 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | v1 = all_1368_0 | % 191.93/27.14 | ~ (hAPP(v5, v1) = v4) | ~ (hAPP(v3, v1) = v4) | ~ % 191.93/27.14 | (hAPP(all_1368_1, v2) = v3) | ~ (hAPP(all_1368_1, v0) = v5) | ~ % 191.93/27.14 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 191.93/27.14 | % 191.93/27.14 | ALPHA: (390) implies: % 191.93/27.14 | (391) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1368_0 % 191.93/27.14 | % 191.93/27.14 | DELTA: instantiating (87) with fresh symbol all_1374_0 gives: % 191.93/27.14 | (392) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1374_0 & % 191.93/27.14 | $i(all_1374_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.14 | $i] : ( ~ (c_Nat_OSuc(v3) = v1) | ~ (c_Nat_OSuc(v0) = v2) | ~ % 191.93/27.14 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0) | % 191.93/27.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)) & ! [v0: $i] : % 191.93/27.14 | ! [v1: any] : ! [v2: $i] : (v1 = all_1374_0 | ~ (c_Nat_OSuc(v0) = % 191.93/27.14 | v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v3: $i] : % 191.93/27.14 | (c_Nat_OSuc(v3) = v1 & $i(v3) & % 191.93/27.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))) & ! [v0: % 191.93/27.14 | $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 191.93/27.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1374_0, v1)) % 191.93/27.14 | % 191.93/27.14 | ALPHA: (392) implies: % 191.93/27.14 | (393) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1374_0 % 191.93/27.14 | % 191.93/27.14 | DELTA: instantiating (15) with fresh symbol all_1380_0 gives: % 191.93/27.14 | (394) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1380_0 & % 191.93/27.14 | $i(all_1380_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.14 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.93/27.14 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) | % 191.93/27.14 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.14 | class_Rings_Ozero__neq__one(v2) | ~ % 191.93/27.14 | class_Rings_Ono__zero__divisors(v2) | ~ % 191.93/27.14 | class_Rings_Omult__zero(v2) | ~ class_Power_Opower(v2) | ? [v6: % 191.93/27.14 | $i] : (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = % 191.93/27.14 | v5) | (v5 = v1 & ~ (v0 = all_1380_0))) & ( ~ (v6 = v1) | v5 % 191.93/27.14 | = v1 | v0 = all_1380_0))) % 191.93/27.14 | % 191.93/27.14 | ALPHA: (394) implies: % 191.93/27.14 | (395) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1380_0 % 191.93/27.15 | (396) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 191.93/27.15 | ! [v5: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ % 191.93/27.15 | (hAPP(v4, v0) = v5) | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ % 191.93/27.15 | $i(v1) | ~ $i(v0) | ~ class_Rings_Ozero__neq__one(v2) | ~ % 191.93/27.15 | class_Rings_Ono__zero__divisors(v2) | ~ % 191.93/27.15 | class_Rings_Omult__zero(v2) | ~ class_Power_Opower(v2) | ? [v6: % 191.93/27.15 | $i] : (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = % 191.93/27.15 | v5) | (v5 = v1 & ~ (v0 = all_1380_0))) & ( ~ (v6 = v1) | v5 % 191.93/27.15 | = v1 | v0 = all_1380_0))) % 191.93/27.15 | % 191.93/27.15 | DELTA: instantiating (35) with fresh symbols all_1383_0, all_1383_1, % 191.93/27.15 | all_1383_2 gives: % 191.93/27.15 | (397) c_Nat_OSuc(all_1383_1) = all_1383_0 & % 191.93/27.15 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1383_2 & % 191.93/27.15 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1383_1 & % 191.93/27.15 | $i(all_1383_0) & $i(all_1383_1) & $i(all_1383_2) & ! [v0: $i] : ! % 191.93/27.15 | [v1: $i] : ! [v2: int] : (v2 = all_1383_0 | ~ (hAPP(v1, v0) = v2) | % 191.93/27.15 | ~ (hAPP(all_1383_2, all_1383_0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 191.93/27.15 | ! [v1: $i] : ! [v2: int] : (v2 = all_1383_0 | ~ (hAPP(v1, % 191.93/27.15 | all_1383_1) = v2) | ~ (hAPP(all_1383_2, v0) = v1) | ~ $i(v0)) % 191.93/27.15 | & ! [v0: any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1383_0 | v0 = % 191.93/27.15 | all_1383_1 | ~ (hAPP(v2, v0) = all_1383_0) | ~ (hAPP(all_1383_2, % 191.93/27.15 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 191.93/27.15 | % 191.93/27.15 | ALPHA: (397) implies: % 191.93/27.15 | (398) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1383_1 % 191.93/27.15 | % 191.93/27.15 | DELTA: instantiating (75) with fresh symbols all_1389_0, all_1389_1, % 191.93/27.15 | all_1389_2 gives: % 191.93/27.15 | (399) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1389_0 & % 191.93/27.15 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1389_1 & % 191.93/27.15 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1389_2 & % 191.93/27.15 | $i(all_1389_0) & $i(all_1389_1) & $i(all_1389_2) & ! [v0: $i] : ! % 191.93/27.15 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.93/27.15 | (v1 = all_1389_2 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, % 191.93/27.15 | all_1389_0) = v2) | ~ % 191.93/27.15 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v4) = v5) | ~ % 191.93/27.15 | (hAPP(v3, v0) = v4) | ~ (hAPP(all_1389_1, v2) = v3) | ~ $i(v1) | % 191.93/27.15 | ~ $i(v0) | ? [v6: $i] : (hAPP(v6, v0) = v5 & hAPP(all_1389_1, v1) % 191.93/27.15 | = v6 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.15 | int] : (v2 = all_1389_2 | ~ (hAPP(v1, v0) = v2) | ~ % 191.93/27.15 | (hAPP(all_1389_1, all_1389_2) = v1) | ~ $i(v0)) % 191.93/27.15 | % 191.93/27.15 | ALPHA: (399) implies: % 191.93/27.15 | (400) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1389_2 % 191.93/27.15 | (401) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1389_0 % 191.93/27.15 | % 191.93/27.15 | DELTA: instantiating (115) with fresh symbols all_1392_0, all_1392_1 gives: % 191.93/27.15 | (402) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1392_0 & % 191.93/27.15 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1392_1 & % 191.93/27.15 | $i(all_1392_0) & $i(all_1392_1) & ! [v0: any] : ! [v1: $i] : ! % 191.93/27.15 | [v2: $i] : ! [v3: $i] : (v0 = all_1392_1 | ~ (hAPP(v2, v0) = v3) | % 191.93/27.15 | ~ (hAPP(all_1392_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1392_1, v3) | % 191.93/27.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1392_1, v1)) & ! % 191.93/27.15 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 191.93/27.15 | v0) = v3) | ~ (hAPP(all_1392_0, v1) = v2) | ~ $i(v1) | ~ % 191.93/27.15 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1392_1, % 191.93/27.15 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1392_1, v3)) % 191.93/27.15 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1392_1) % 191.93/27.15 | = v2) | ~ (hAPP(all_1392_0, v0) = v1) | ~ $i(v0) | % 191.93/27.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1392_1, v2)) % 191.93/27.15 | % 191.93/27.15 | ALPHA: (402) implies: % 191.93/27.15 | (403) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1392_1 % 191.93/27.15 | % 191.93/27.15 | DELTA: instantiating (115) with fresh symbols all_1395_0, all_1395_1 gives: % 191.93/27.15 | (404) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1395_0 & % 191.93/27.15 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1395_1 & % 191.93/27.15 | $i(all_1395_0) & $i(all_1395_1) & ! [v0: any] : ! [v1: $i] : ! % 191.93/27.15 | [v2: $i] : ! [v3: $i] : (v0 = all_1395_1 | ~ (hAPP(v2, v0) = v3) | % 191.93/27.15 | ~ (hAPP(all_1395_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1395_1, v3) | % 191.93/27.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1395_1, v1)) & ! % 191.93/27.15 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 191.93/27.15 | v0) = v3) | ~ (hAPP(all_1395_0, v1) = v2) | ~ $i(v1) | ~ % 191.93/27.15 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1395_1, % 191.93/27.15 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1395_1, v3)) % 191.93/27.15 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1395_1) % 191.93/27.15 | = v2) | ~ (hAPP(all_1395_0, v0) = v1) | ~ $i(v0) | % 191.93/27.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1395_1, v2)) % 191.93/27.15 | % 191.93/27.15 | ALPHA: (404) implies: % 191.93/27.15 | (405) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1395_1 % 191.93/27.15 | % 191.93/27.15 | DELTA: instantiating (28) with fresh symbol all_1398_0 gives: % 191.93/27.15 | (406) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1398_0 & % 191.93/27.15 | $i(all_1398_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 191.93/27.15 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v2) | % 191.93/27.15 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Ozero(v1) | ? [v3: $i] : ? % 191.93/27.15 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v2 = all_1398_0 | ( ~ (v4 % 191.93/27.15 | = v0) & tc_Polynomial_Opoly(v1) = v3 & % 191.93/27.15 | c_Groups_Ozero__class_Ozero(v3) = v4 & $i(v4) & $i(v3))) & % 191.93/27.15 | ((v6 = v2 & c_Nat_OSuc(v5) = v2 & c_Polynomial_Odegree(v1, v0) = % 191.93/27.15 | v5 & $i(v5) & $i(v2)) | (v4 = v0 & tc_Polynomial_Opoly(v1) = % 191.93/27.15 | v3 & c_Groups_Ozero__class_Ozero(v3) = v0 & $i(v3))))) % 191.93/27.15 | % 191.93/27.15 | ALPHA: (406) implies: % 191.93/27.15 | (407) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1398_0 % 191.93/27.15 | % 191.93/27.15 | DELTA: instantiating (51) with fresh symbol all_1401_0 gives: % 191.93/27.15 | (408) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1401_0 & % 191.93/27.15 | $i(all_1401_0) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.15 | $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | v0 = all_1401_0 | ~ % 191.93/27.15 | (c_Power_Opower__class_Opower(v1) = v2) | ~ % 191.93/27.15 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | % 191.93/27.15 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.15 | class_Power_Opower(v1) | ~ class_Rings_Osemiring__0(v1)) & ! [v0: % 191.93/27.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.93/27.15 | (c_Power_Opower__class_Opower(v0) = v1) | ~ % 191.93/27.15 | (c_Groups_Ozero__class_Ozero(v0) = v2) | ~ (hAPP(v3, all_1401_0) = % 191.93/27.15 | v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v0) | ~ % 191.93/27.15 | class_Power_Opower(v0) | ~ class_Rings_Osemiring__0(v0) | % 191.93/27.15 | (c_Groups_Oone__class_Oone(v0) = v4 & $i(v4))) % 191.93/27.15 | % 191.93/27.15 | ALPHA: (408) implies: % 191.93/27.15 | (409) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1401_0 % 191.93/27.15 | % 191.93/27.15 | DELTA: instantiating (127) with fresh symbols all_1404_0, all_1404_1 gives: % 191.93/27.16 | (410) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1404_0 & % 191.93/27.16 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1404_1 & % 191.93/27.16 | $i(all_1404_0) & $i(all_1404_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.16 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2 % 191.93/27.16 | = all_1404_1 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v4, v5) % 191.93/27.16 | = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 191.93/27.16 | (hAPP(all_1404_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.16 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v6 & $i(v6))) & % 191.93/27.16 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 191.93/27.16 | ! [v5: int] : (v5 = all_1404_1 | ~ % 191.93/27.16 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v4) = v5) | ~ % 191.93/27.16 | (hAPP(v2, v1) = v3) | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1404_0, % 191.93/27.16 | all_1404_1) = v2) | ~ $i(v1) | ~ $i(v0)) % 191.93/27.16 | % 191.93/27.16 | ALPHA: (410) implies: % 191.93/27.16 | (411) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1404_1 % 191.93/27.16 | % 191.93/27.16 | DELTA: instantiating (111) with fresh symbol all_1407_0 gives: % 191.93/27.16 | (412) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1407_0 & % 191.93/27.16 | $i(all_1407_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.16 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.93/27.16 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v1) = v5) | % 191.93/27.16 | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.16 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1407_0, v1) | ~ % 191.93/27.16 | class_Rings_Ocomm__semiring__1(v2) | c_Rings_Odvd__class_Odvd(v2, % 191.93/27.16 | v0, v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 191.93/27.16 | : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = % 191.93/27.16 | v3) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) % 191.93/27.16 | | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v2) | % 191.93/27.16 | c_Rings_Odvd__class_Odvd(v2, v0, v5) | ? [v6: $i] : ( ~ (v6 = v0) % 191.93/27.16 | & c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))) % 191.93/27.16 | % 191.93/27.16 | ALPHA: (412) implies: % 191.93/27.16 | (413) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1407_0 % 191.93/27.16 | % 191.93/27.16 | DELTA: instantiating (63) with fresh symbols all_1410_0, all_1410_1, % 191.93/27.16 | all_1410_2, all_1410_3 gives: % 191.93/27.16 | (414) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1410_1 & % 191.93/27.16 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1410_2 & % 191.93/27.16 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1410_0 & % 191.93/27.16 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1410_3 & % 191.93/27.16 | $i(all_1410_0) & $i(all_1410_1) & $i(all_1410_2) & $i(all_1410_3) & % 191.93/27.16 | ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 191.93/27.16 | ! [v5: $i] : ! [v6: $i] : (v1 = all_1410_3 | ~ % 191.93/27.16 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1410_1) = v4) | % 191.93/27.16 | ~ (hAPP(v3, v5) = v6) | ~ (hAPP(v2, v4) = v5) | ~ % 191.93/27.16 | (hAPP(all_1410_0, v0) = v3) | ~ (hAPP(all_1410_2, v0) = v2) | ~ % 191.93/27.16 | $i(v1) | ~ $i(v0) | (hAPP(v2, v1) = v6 & $i(v6))) & ! [v0: $i] : % 191.93/27.16 | ! [v1: $i] : ! [v2: int] : (v2 = all_1410_1 | ~ (hAPP(v1, % 191.93/27.16 | all_1410_3) = v2) | ~ (hAPP(all_1410_2, v0) = v1) | ~ $i(v0)) % 191.93/27.16 | % 191.93/27.16 | ALPHA: (414) implies: % 191.93/27.16 | (415) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1410_3 % 191.93/27.16 | (416) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1410_1 % 191.93/27.16 | % 191.93/27.16 | DELTA: instantiating (117) with fresh symbol all_1413_0 gives: % 191.93/27.16 | (417) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1413_0 & % 191.93/27.16 | $i(all_1413_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.16 | int] : (v3 = all_1413_0 | ~ % 191.93/27.16 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v0) = v3) | ~ % 191.93/27.16 | (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 191.93/27.16 | [v5: $i] : ( ~ (v5 = v0) & c_Divides_Odiv__class_Omod(tc_Nat_Onat, % 191.93/27.16 | v1, v0) = v4 & c_Nat_OSuc(v4) = v5 & $i(v5) & $i(v4))) & ! % 191.93/27.16 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.16 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v0) = v3) | ~ % 191.93/27.16 | (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 191.93/27.16 | [v5: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v4 & % 191.93/27.16 | c_Nat_OSuc(v4) = v5 & $i(v5) & $i(v4) & (v5 = v3 | v5 = v0))) % 191.93/27.16 | % 191.93/27.16 | ALPHA: (417) implies: % 191.93/27.16 | (418) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1413_0 % 191.93/27.16 | % 191.93/27.16 | DELTA: instantiating (25) with fresh symbol all_1422_0 gives: % 191.93/27.16 | (419) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1422_0 & % 191.93/27.16 | $i(all_1422_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.16 | $i] : ( ~ (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3) | ~ % 191.93/27.16 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.16 | class_Rings_Ocomm__semiring__0(v2) | ? [v4: $i] : ? [v5: $i] : ? % 191.93/27.16 | [v6: any] : (((v6 = all_1422_0 & c_Polynomial_Odegree(v2, v1) = % 191.93/27.16 | all_1422_0) | ( ~ (v5 = v3) & tc_Polynomial_Opoly(v2) = v4 & % 191.93/27.16 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))) & % 191.93/27.16 | ((v5 = v3 & tc_Polynomial_Opoly(v2) = v4 & % 191.93/27.16 | c_Groups_Ozero__class_Ozero(v4) = v3 & $i(v4) & $i(v3)) | ( ~ % 191.93/27.16 | (v6 = all_1422_0) & c_Polynomial_Odegree(v2, v1) = v6 & % 191.93/27.16 | $i(v6))))) % 191.93/27.16 | % 191.93/27.16 | ALPHA: (419) implies: % 191.93/27.16 | (420) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1422_0 % 191.93/27.16 | % 191.93/27.16 | DELTA: instantiating (93) with fresh symbols all_1425_0, all_1425_1 gives: % 191.93/27.16 | (421) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1425_0 & % 191.93/27.16 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1425_1 & % 191.93/27.16 | $i(all_1425_0) & $i(all_1425_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.16 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 191.93/27.16 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1425_0, v2) = v3) | % 191.93/27.16 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.16 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~ % 191.93/27.16 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1425_1, v2) | % 191.93/27.16 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : % 191.93/27.16 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.93/27.16 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 191.93/27.16 | (hAPP(all_1425_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.16 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~ % 191.93/27.16 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1425_1, v2) | % 191.93/27.16 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 191.93/27.16 | % 191.93/27.16 | ALPHA: (421) implies: % 191.93/27.16 | (422) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1425_1 % 191.93/27.16 | % 191.93/27.16 | DELTA: instantiating (108) with fresh symbols all_1428_0, all_1428_1 gives: % 191.93/27.17 | (423) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1428_0 & % 191.93/27.17 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1428_1 & % 191.93/27.17 | $i(all_1428_0) & $i(all_1428_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.17 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 191.93/27.17 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1428_0, v2) = v3) | % 191.93/27.17 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.17 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1428_1, v2) | ~ % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) | % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! % 191.93/27.17 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 191.93/27.17 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 191.93/27.17 | (hAPP(all_1428_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.17 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1428_1, v2) | ~ % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) | % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5)) % 191.93/27.17 | % 191.93/27.17 | ALPHA: (423) implies: % 191.93/27.17 | (424) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1428_1 % 191.93/27.17 | % 191.93/27.17 | DELTA: instantiating (99) with fresh symbols all_1431_0, all_1431_1 gives: % 191.93/27.17 | (425) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1431_0 & % 191.93/27.17 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1431_1 & % 191.93/27.17 | $i(all_1431_0) & $i(all_1431_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.17 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1431_0, % 191.93/27.17 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.17 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1431_1, v3) | % 191.93/27.17 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1431_1, v1)) & ! % 191.93/27.17 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 191.93/27.17 | v0) = v3) | ~ (hAPP(all_1431_0, v1) = v2) | ~ $i(v1) | ~ % 191.93/27.17 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1431_1, % 191.93/27.17 | v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1431_1, v0)) % 191.93/27.17 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.93/27.17 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1431_0, v1) = v2) | ~ $i(v1) | % 191.93/27.17 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.17 | all_1431_1, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.17 | all_1431_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.17 | all_1431_1, v3)) % 191.93/27.17 | % 191.93/27.17 | ALPHA: (425) implies: % 191.93/27.17 | (426) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1431_1 % 191.93/27.17 | % 191.93/27.17 | DELTA: instantiating (52) with fresh symbol all_1434_0 gives: % 191.93/27.17 | (427) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1434_0 & % 191.93/27.17 | $i(all_1434_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.17 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Odegree(v2, v3) = v4) | ~ % 191.93/27.17 | (c_Polynomial_OpCons(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 191.93/27.17 | $i(v0) | ~ class_Groups_Ozero(v2) | ? [v5: $i] : ? [v6: $i] : ? % 191.93/27.17 | [v7: $i] : ? [v8: $i] : ((v4 = all_1434_0 | ( ~ (v6 = v1) & % 191.93/27.17 | tc_Polynomial_Opoly(v2) = v5 & % 191.93/27.17 | c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) & % 191.93/27.17 | ((v8 = v4 & c_Nat_OSuc(v7) = v4 & c_Polynomial_Odegree(v2, v1) = % 191.93/27.17 | v7 & $i(v7) & $i(v4)) | (v6 = v1 & tc_Polynomial_Opoly(v2) = % 191.93/27.17 | v5 & c_Groups_Ozero__class_Ozero(v5) = v1 & $i(v5))))) % 191.93/27.17 | % 191.93/27.17 | ALPHA: (427) implies: % 191.93/27.17 | (428) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1434_0 % 191.93/27.17 | % 191.93/27.17 | DELTA: instantiating (53) with fresh symbols all_1437_0, all_1437_1 gives: % 191.93/27.17 | (429) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1437_0 & % 191.93/27.17 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1437_1 & % 191.93/27.17 | $i(all_1437_0) & $i(all_1437_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.17 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2 % 191.93/27.17 | = all_1437_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ % 191.93/27.17 | (hAPP(all_1437_0, v1) = v3) | ~ (hAPP(all_1437_0, v0) = v5) | ~ % 191.93/27.17 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6) | % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! % 191.93/27.17 | [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.93/27.17 | ! [v6: $i] : (v2 = all_1437_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, % 191.93/27.17 | v2) = v4) | ~ (hAPP(all_1437_0, v1) = v3) | ~ % 191.93/27.17 | (hAPP(all_1437_0, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.17 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) | % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6)) % 191.93/27.17 | % 191.93/27.17 | ALPHA: (429) implies: % 191.93/27.17 | (430) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1437_1 % 191.93/27.17 | % 191.93/27.17 | DELTA: instantiating (58) with fresh symbols all_1440_0, all_1440_1 gives: % 191.93/27.17 | (431) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1440_0 & % 191.93/27.17 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1440_1 & % 191.93/27.17 | $i(all_1440_0) & $i(all_1440_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.17 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2 % 191.93/27.17 | = all_1440_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ % 191.93/27.17 | (hAPP(all_1440_0, v1) = v3) | ~ (hAPP(all_1440_0, v0) = v5) | ~ % 191.93/27.17 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6) | % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0)) & ! [v0: $i] : ! % 191.93/27.17 | [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.93/27.17 | ! [v6: $i] : (v2 = all_1440_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, % 191.93/27.17 | v2) = v4) | ~ (hAPP(all_1440_0, v1) = v3) | ~ % 191.93/27.17 | (hAPP(all_1440_0, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.17 | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0) | % 191.93/27.17 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6)) % 191.93/27.17 | % 191.93/27.17 | ALPHA: (431) implies: % 191.93/27.17 | (432) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1440_1 % 191.93/27.17 | % 191.93/27.17 | DELTA: instantiating (76) with fresh symbols all_1443_0, all_1443_1 gives: % 191.93/27.17 | (433) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1443_0 & % 191.93/27.17 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1443_1 & % 191.93/27.17 | $i(all_1443_0) & $i(all_1443_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.17 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 191.93/27.17 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 191.93/27.17 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1443_0) = v7) | % 191.93/27.17 | ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ % 191.93/27.17 | (c_Groups_Otimes__class_Otimes(v2) = v5) | ~ (hAPP(v6, v8) = v9) | % 191.93/27.17 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v7) = v8) | ~ (hAPP(v3, v0) % 191.93/27.17 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.17 | class_Power_Opower(v2) | ? [v10: $i] : ? [v11: $i] : (( ~ (v1 = % 191.93/27.17 | all_1443_1) | (v11 = v10 & c_Groups_Oone__class_Oone(v2) = % 191.93/27.17 | v10 & hAPP(v4, all_1443_1) = v10 & $i(v10))) & (v1 = % 191.93/27.17 | all_1443_1 | (v10 = v9 & hAPP(v4, v1) = v9 & $i(v9))))) % 191.93/27.17 | % 191.93/27.17 | ALPHA: (433) implies: % 191.93/27.17 | (434) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1443_1 % 191.93/27.17 | (435) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1443_0 % 191.93/27.17 | % 191.93/27.17 | DELTA: instantiating (2) with fresh symbols all_1446_0, all_1446_1, % 191.93/27.17 | all_1446_2, all_1446_3, all_1446_4, all_1446_5, all_1446_6, all_1446_7 % 191.93/27.17 | gives: % 191.93/27.18 | (436) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q) = all_1446_5 & % 191.93/27.18 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p) = all_1446_7 & % 191.93/27.18 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1446_4 & % 191.93/27.18 | c_Groups_Ozero__class_Ozero(all_1446_4) = all_1446_3 & % 191.93/27.18 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1446_6 & % 191.93/27.18 | $i(all_1446_2) & $i(all_1446_3) & $i(all_1446_4) & $i(all_1446_5) & % 191.93/27.18 | $i(all_1446_6) & $i(all_1446_7) & ((all_1446_1 = all_1446_6 & ~ % 191.93/27.18 | (all_1446_0 = all_1446_6) & ~ (all_1446_3 = v_q) & % 191.93/27.18 | hAPP(all_1446_5, all_1446_2) = all_1446_0 & hAPP(all_1446_7, % 191.93/27.18 | all_1446_2) = all_1446_6 & $i(all_1446_0)) | (all_1446_3 = v_q % 191.93/27.18 | & ! [v0: $i] : ! [v1: int] : (v1 = all_1446_6 | ~ % 191.93/27.18 | (hAPP(all_1446_5, v0) = v1) | ~ $i(v0) | ? [v2: any] : ( ~ % 191.93/27.18 | (v2 = all_1446_6) & hAPP(all_1446_7, v0) = v2 & $i(v2))))) % 191.93/27.18 | % 191.93/27.18 | ALPHA: (436) implies: % 191.93/27.18 | (437) c_Groups_Ozero__class_Ozero(all_1446_4) = all_1446_3 % 191.93/27.18 | (438) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1446_4 % 191.93/27.18 | (439) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q) = all_1446_5 % 191.93/27.18 | % 191.93/27.18 | DELTA: instantiating (72) with fresh symbols all_1448_0, all_1448_1, % 191.93/27.18 | all_1448_2 gives: % 191.93/27.18 | (440) c_Nat_OSuc(all_1448_1) = all_1448_0 & c_Nat_OSuc(all_1448_2) = % 191.93/27.18 | all_1448_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1448_2 & % 191.93/27.18 | $i(all_1448_0) & $i(all_1448_1) & $i(all_1448_2) & ! [v0: $i] : ! % 191.93/27.18 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 191.93/27.18 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 191.93/27.18 | (c_Groups_Ominus__class_Ominus(v2, v5, v7) = v8) | ~ % 191.93/27.18 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v6, all_1448_0) % 191.93/27.18 | = v7) | ~ (hAPP(v4, all_1448_0) = v5) | ~ (hAPP(v3, v1) = v4) | % 191.93/27.18 | ~ (hAPP(v3, v0) = v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.18 | class_Rings_Ocomm__ring__1(v2) | ? [v9: $i] : ? [v10: $i] : ? % 191.93/27.18 | [v11: $i] : ? [v12: $i] : (c_Groups_Ominus__class_Ominus(v2, v1, % 191.93/27.18 | v0) = v10 & c_Groups_Oplus__class_Oplus(v2, v1, v0) = v12 & % 191.93/27.18 | c_Groups_Otimes__class_Otimes(v2) = v9 & hAPP(v11, v12) = v8 & % 191.93/27.18 | hAPP(v9, v10) = v11 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & % 191.93/27.18 | $i(v8))) % 191.93/27.18 | % 191.93/27.18 | ALPHA: (440) implies: % 191.93/27.18 | (441) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1448_2 % 191.93/27.18 | % 191.93/27.18 | DELTA: instantiating (27) with fresh symbols all_1459_0, all_1459_1 gives: % 191.93/27.18 | (442) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1459_1 & % 191.93/27.18 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1459_0 & % 191.93/27.18 | $i(all_1459_0) & $i(all_1459_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.18 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1459_0 | % 191.93/27.18 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 191.93/27.18 | (hAPP(all_1459_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.18 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) | % 191.93/27.18 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! % 191.93/27.18 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 191.93/27.18 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 191.93/27.18 | (hAPP(all_1459_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.18 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) | % 191.93/27.18 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5)) & ! [v0: $i] : ! % 191.93/27.18 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v2, % 191.93/27.18 | v1) = v3) | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1459_1, % 191.93/27.18 | all_1459_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.18 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v4)) % 191.93/27.18 | % 191.93/27.18 | ALPHA: (442) implies: % 191.93/27.18 | (443) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1459_0 % 191.93/27.18 | % 191.93/27.18 | DELTA: instantiating (16) with fresh symbols all_1462_0, all_1462_1, % 191.93/27.18 | all_1462_2, all_1462_3 gives: % 191.93/27.18 | (444) c_Power_Opower__class_Opower(all_1462_1) = all_1462_0 & % 191.93/27.18 | tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1462_1 & % 191.93/27.18 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1462_2 & % 191.93/27.18 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1462_3 & % 191.93/27.18 | $i(all_1462_0) & $i(all_1462_1) & $i(all_1462_2) & $i(all_1462_3) & % 191.93/27.18 | ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 191.93/27.18 | ! [v5: $i] : (v0 = all_1462_2 | ~ % 191.93/27.18 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v2) = v3) | ~ (hAPP(v4, % 191.93/27.18 | v0) = v5) | ~ (hAPP(all_1462_0, v1) = v4) | ~ $i(v2) | ~ % 191.93/27.18 | $i(v1) | ~ $i(v0) | c_Rings_Odvd__class_Odvd(all_1462_1, v2, v5) | % 191.93/27.18 | ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : ? [v10: % 191.93/27.18 | any] : ($i(v8) & ((v9 = all_1462_3 & ~ (v10 = all_1462_3) & % 191.93/27.18 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v6 & hAPP(v6, % 191.93/27.18 | v8) = v10 & hAPP(v3, v8) = all_1462_3 & $i(v10) & $i(v6)) | % 191.93/27.18 | ( ~ (v7 = v0) & c_Polynomial_Odegree(tc_Complex_Ocomplex, v2) = % 191.93/27.18 | v7 & $i(v7))))) % 191.93/27.18 | % 191.93/27.18 | ALPHA: (444) implies: % 191.93/27.18 | (445) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1462_2 % 191.93/27.18 | (446) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1462_1 % 191.93/27.18 | (447) c_Power_Opower__class_Opower(all_1462_1) = all_1462_0 % 191.93/27.18 | % 191.93/27.18 | DELTA: instantiating (3) with fresh symbol all_1465_0 gives: % 191.93/27.18 | (448) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1465_0 & % 191.93/27.18 | $i(all_1465_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.18 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(v2, v1) = v3) | ~ % 191.93/27.18 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.18 | class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 191.93/27.18 | ? [v8: any] : (((v8 = all_1465_0 & ~ (v7 = v1) & % 191.93/27.18 | c_Polynomial_Oorder(v2, v0, v1) = all_1465_0 & % 191.93/27.18 | tc_Polynomial_Opoly(v2) = v6 & % 191.93/27.18 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6)) | (v5 % 191.93/27.18 | = v4 & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) & ((v7 % 191.93/27.18 | = v1 & tc_Polynomial_Opoly(v2) = v6 & % 191.93/27.18 | c_Groups_Ozero__class_Ozero(v6) = v1 & $i(v6)) | ( ~ (v8 = % 191.93/27.18 | all_1465_0) & c_Polynomial_Oorder(v2, v0, v1) = v8 & % 191.93/27.18 | $i(v8)) | ( ~ (v5 = v4) & c_Groups_Ozero__class_Ozero(v2) = % 191.93/27.18 | v5 & $i(v5))))) % 191.93/27.18 | % 191.93/27.18 | ALPHA: (448) implies: % 191.93/27.18 | (449) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1465_0 % 191.93/27.18 | % 191.93/27.18 | DELTA: instantiating (45) with fresh symbols all_1468_0, all_1468_1 gives: % 191.93/27.18 | (450) c_Nat_OSuc(all_1468_1) = all_1468_0 & % 191.93/27.18 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1468_1 & % 191.93/27.18 | $i(all_1468_0) & $i(all_1468_1) & ! [v0: $i] : ! [v1: any] : (v1 = % 191.93/27.18 | all_1468_0 | v1 = all_1468_1 | ~ % 191.93/27.18 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1468_0) | % 191.93/27.18 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 191.93/27.18 | all_1468_0 | v0 = all_1468_0 | ~ % 191.93/27.18 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1468_0) | % 191.93/27.18 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 191.93/27.18 | all_1468_1 | v0 = all_1468_1 | ~ % 191.93/27.18 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1468_0) | % 191.93/27.18 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 191.93/27.18 | all_1468_0 | v0 = all_1468_1 | ~ % 191.93/27.18 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1468_0) | % 191.93/27.18 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1468_0 | ~ % 191.93/27.18 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1468_0, all_1468_1) = % 191.93/27.18 | v0)) & ! [v0: int] : (v0 = all_1468_0 | ~ % 191.93/27.18 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1468_1, all_1468_0) = % 191.93/27.18 | v0)) % 191.93/27.18 | % 191.93/27.18 | ALPHA: (450) implies: % 191.93/27.19 | (451) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1468_1 % 191.93/27.19 | % 191.93/27.19 | DELTA: instantiating (45) with fresh symbols all_1471_0, all_1471_1 gives: % 191.93/27.19 | (452) c_Nat_OSuc(all_1471_1) = all_1471_0 & % 191.93/27.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1471_1 & % 191.93/27.19 | $i(all_1471_0) & $i(all_1471_1) & ! [v0: $i] : ! [v1: any] : (v1 = % 191.93/27.19 | all_1471_0 | v1 = all_1471_1 | ~ % 191.93/27.19 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1471_0) | % 191.93/27.19 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 191.93/27.19 | all_1471_0 | v0 = all_1471_0 | ~ % 191.93/27.19 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1471_0) | % 191.93/27.19 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 191.93/27.19 | all_1471_1 | v0 = all_1471_1 | ~ % 191.93/27.19 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1471_0) | % 191.93/27.19 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 191.93/27.19 | all_1471_0 | v0 = all_1471_1 | ~ % 191.93/27.19 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1471_0) | % 191.93/27.19 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1471_0 | ~ % 191.93/27.19 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1471_0, all_1471_1) = % 191.93/27.19 | v0)) & ! [v0: int] : (v0 = all_1471_0 | ~ % 191.93/27.19 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1471_1, all_1471_0) = % 191.93/27.19 | v0)) % 191.93/27.19 | % 191.93/27.19 | ALPHA: (452) implies: % 191.93/27.19 | (453) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1471_1 % 191.93/27.19 | % 191.93/27.19 | DELTA: instantiating (98) with fresh symbols all_1474_0, all_1474_1 gives: % 191.93/27.19 | (454) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1474_1 & % 191.93/27.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1474_0 & % 191.93/27.19 | $i(all_1474_0) & $i(all_1474_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.19 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 191.93/27.19 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1474_1, v2) = v3) | % 191.93/27.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : % 191.93/27.19 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 191.93/27.19 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 191.93/27.19 | (hAPP(all_1474_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.19 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1474_0, v2)) & ! % 191.93/27.19 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 191.93/27.19 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 191.93/27.19 | (hAPP(all_1474_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 191.93/27.19 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~ % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1474_0, v2) | % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 191.93/27.19 | % 191.93/27.19 | ALPHA: (454) implies: % 191.93/27.19 | (455) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1474_0 % 191.93/27.19 | % 191.93/27.19 | DELTA: instantiating (60) with fresh symbols all_1477_0, all_1477_1, % 191.93/27.19 | all_1477_2 gives: % 191.93/27.19 | (456) c_Nat_OSuc(all_1477_1) = all_1477_0 & c_Nat_OSuc(all_1477_2) = % 191.93/27.19 | all_1477_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1477_2 & % 191.93/27.19 | $i(all_1477_0) & $i(all_1477_1) & $i(all_1477_2) & ! [v0: $i] : ! % 191.93/27.19 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 191.93/27.19 | ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) % 191.93/27.19 | | ~ (hAPP(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.19 | class_Rings_Oidom(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 191.93/27.19 | ((v1 = v0 | (v8 = v1 & c_Groups_Ouminus__class_Ouminus(v2, v0) = % 191.93/27.19 | v1) | ( ~ (v7 = v6) & hAPP(v5, all_1477_0) = v7 & hAPP(v4, % 191.93/27.19 | all_1477_0) = v6 & $i(v7) & $i(v6))) & ((v7 = v6 & hAPP(v5, % 191.93/27.19 | all_1477_0) = v6 & hAPP(v4, all_1477_0) = v6 & $i(v6)) | ( % 191.93/27.19 | ~ (v8 = v1) & ~ (v1 = v0) & % 191.93/27.19 | c_Groups_Ouminus__class_Ouminus(v2, v0) = v8 & $i(v8))))) % 191.93/27.19 | % 191.93/27.19 | ALPHA: (456) implies: % 191.93/27.19 | (457) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1477_2 % 191.93/27.19 | % 191.93/27.19 | DELTA: instantiating (97) with fresh symbols all_1480_0, all_1480_1 gives: % 191.93/27.19 | (458) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1480_1 & % 191.93/27.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1480_0 & % 191.93/27.19 | $i(all_1480_0) & $i(all_1480_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.19 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.93/27.19 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1480_1, % 191.93/27.19 | v2) = v3) | ~ (hAPP(all_1480_1, v0) = v5) | ~ $i(v2) | ~ % 191.93/27.19 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 191.93/27.19 | v4, v6) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0)) & % 191.93/27.19 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 191.93/27.19 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) % 191.93/27.19 | = v4) | ~ (hAPP(all_1480_1, v2) = v3) | ~ (hAPP(all_1480_1, v0) % 191.93/27.19 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) | % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1480_0, v1)) & ! % 191.93/27.19 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 191.93/27.19 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = % 191.93/27.19 | v4) | ~ (hAPP(all_1480_1, v2) = v3) | ~ (hAPP(all_1480_1, v0) = % 191.93/27.19 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0) | ~ % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1480_0, v1) | % 191.93/27.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)) % 191.93/27.19 | % 191.93/27.19 | ALPHA: (458) implies: % 191.93/27.19 | (459) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1480_0 % 191.93/27.19 | % 191.93/27.19 | DELTA: instantiating (61) with fresh symbols all_1487_0, all_1487_1 gives: % 191.93/27.19 | (460) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1487_0 & % 191.93/27.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1487_1 & % 191.93/27.19 | $i(all_1487_0) & $i(all_1487_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.19 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(v1, v0) = % 191.93/27.19 | v2) | ~ (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v2, % 191.93/27.19 | v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Oidom(v1) | % 191.93/27.19 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(v1, v1, v2) | % 191.93/27.19 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] % 191.93/27.19 | : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 191.93/27.19 | [v14: $i] : ( ~ (v9 = v3) & ~ (v8 = all_1487_1) & % 191.93/27.19 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v12, all_1487_0) = v5 & % 191.93/27.19 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v8) = v12 & % 191.93/27.19 | c_Power_Opower__class_Opower(v1) = v7 & % 191.93/27.19 | c_Groups_Otimes__class_Otimes(v1) = v6 & % 191.93/27.19 | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v10) = v11 % 191.93/27.19 | & c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v5 % 191.93/27.19 | & c_Polynomial_OpCons(v1, v9, v10) = v13 & c_Polynomial_Opoly(v1, % 191.93/27.19 | v13) = v14 & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 191.93/27.19 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ! [v15: $i] : ! % 191.93/27.20 | [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: % 191.93/27.20 | $i] : ! [v21: $i] : ( ~ (c_Groups_Oplus__class_Oplus(v1, v4, % 191.93/27.20 | v20) = v21) | ~ (hAPP(v18, v19) = v20) | ~ (hAPP(v16, v8) % 191.93/27.20 | = v17) | ~ (hAPP(v14, v15) = v19) | ~ (hAPP(v7, v15) = v16) % 191.93/27.20 | | ~ (hAPP(v6, v17) = v18) | ~ $i(v15) | (hAPP(v2, v15) = v21 % 191.93/27.20 | & $i(v21))))) % 191.93/27.20 | % 191.93/27.20 | ALPHA: (460) implies: % 191.93/27.20 | (461) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1487_1 % 191.93/27.20 | (462) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1487_0 % 191.93/27.20 | % 191.93/27.20 | DELTA: instantiating (121) with fresh symbols all_1496_0, all_1496_1 gives: % 191.93/27.20 | (463) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1496_0 & % 191.93/27.20 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1496_1 & % 191.93/27.20 | $i(all_1496_0) & $i(all_1496_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.20 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.93/27.20 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v3) | ~ % 191.93/27.20 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 191.93/27.20 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : (( ~ (v0 = all_1496_1) | % 191.93/27.20 | (hAPP(v2, v1) = v5 & $i(v5) & hBOOL(v5))) & (v0 = all_1496_1 | % 191.93/27.20 | (hAPP(all_1496_0, v0) = v6 & $i(v6) & ! [v7: $i] : ! [v8: $i] % 191.93/27.20 | : ! [v9: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 191.93/27.20 | v9, v8) = v1) | ~ (hAPP(v6, v7) = v9) | ~ $i(v8) | ~ % 191.93/27.20 | $i(v7) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v8, % 191.93/27.20 | v0) | ? [v10: $i] : (hAPP(v2, v8) = v10 & $i(v10) & % 191.93/27.20 | hBOOL(v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 191.93/27.20 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.93/27.20 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v3) | ~ % 191.93/27.20 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4) % 191.93/27.20 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 191.93/27.20 | $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & $i(v7) & ((v10 = v1 % 191.93/27.20 | & ~ (v0 = all_1496_1) & % 191.93/27.20 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v9, v8) = v1 & % 191.93/27.20 | hAPP(v6, v7) = v9 & hAPP(v2, v8) = v11 & hAPP(all_1496_0, v0) % 191.93/27.20 | = v6 & $i(v11) & $i(v9) & $i(v6) & % 191.93/27.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v8, v0) & ~ % 191.93/27.20 | hBOOL(v11)) | (v0 = all_1496_1 & hAPP(v2, v1) = v5 & $i(v5) & % 191.93/27.20 | ~ hBOOL(v5))))) % 191.93/27.20 | % 191.93/27.20 | ALPHA: (463) implies: % 191.93/27.20 | (464) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1496_1 % 191.93/27.20 | % 191.93/27.20 | DELTA: instantiating (110) with fresh symbol all_1499_0 gives: % 191.93/27.20 | (465) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1499_0 & % 191.93/27.20 | $i(all_1499_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.20 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.93/27.20 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 191.93/27.20 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1) | ~ % 191.93/27.20 | (hAPP(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 191.93/27.20 | | ~ hBOOL(v4) | ? [v6: $i] : (hAPP(v2, v5) = v6 & $i(v6) & % 191.93/27.20 | hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.20 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 191.93/27.20 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 191.93/27.20 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) % 191.93/27.20 | | ~ hBOOL(v4) | ? [v5: $i] : (hAPP(v2, all_1499_0) = v5 & $i(v5) % 191.93/27.20 | & hBOOL(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 191.93/27.20 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 191.93/27.20 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 191.93/27.20 | | ~ $i(v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | % 191.93/27.20 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : % 191.93/27.20 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1 & hAPP(v2, % 191.93/27.20 | v5) = v6 & $i(v6) & $i(v5) & ~ hBOOL(v6))) & ! [v0: $i] : ! % 191.93/27.20 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 191.93/27.20 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 191.93/27.20 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4) % 191.93/27.20 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 191.93/27.20 | ((v7 = v1 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v6) = v1 % 191.93/27.20 | & hAPP(v2, v6) = v8 & $i(v8) & ~ hBOOL(v8)) | (hAPP(v2, % 191.93/27.20 | all_1499_0) = v5 & $i(v5) & ~ hBOOL(v5))))) % 191.93/27.20 | % 191.93/27.20 | ALPHA: (465) implies: % 191.93/27.20 | (466) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1499_0 % 191.93/27.20 | % 191.93/27.20 | DELTA: instantiating (110) with fresh symbol all_1502_0 gives: % 192.49/27.20 | (467) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1502_0 & % 192.49/27.20 | $i(all_1502_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 192.49/27.20 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 192.49/27.20 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 192.49/27.20 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1) | ~ % 192.49/27.20 | (hAPP(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 192.49/27.20 | | ~ hBOOL(v4) | ? [v6: $i] : (hAPP(v2, v5) = v6 & $i(v6) & % 192.49/27.20 | hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 192.49/27.20 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 192.49/27.20 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 192.49/27.20 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) % 192.49/27.20 | | ~ hBOOL(v4) | ? [v5: $i] : (hAPP(v2, all_1502_0) = v5 & $i(v5) % 192.49/27.20 | & hBOOL(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 192.49/27.20 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 192.49/27.20 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 192.49/27.20 | | ~ $i(v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | % 192.49/27.20 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : % 192.49/27.20 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1 & hAPP(v2, % 192.49/27.20 | v5) = v6 & $i(v6) & $i(v5) & ~ hBOOL(v6))) & ! [v0: $i] : ! % 192.49/27.20 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 192.49/27.20 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 192.49/27.20 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4) % 192.49/27.20 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 192.49/27.20 | ((v7 = v1 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v6) = v1 % 192.49/27.20 | & hAPP(v2, v6) = v8 & $i(v8) & ~ hBOOL(v8)) | (hAPP(v2, % 192.49/27.20 | all_1502_0) = v5 & $i(v5) & ~ hBOOL(v5))))) % 192.49/27.20 | % 192.49/27.20 | ALPHA: (467) implies: % 192.49/27.20 | (468) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1502_0 % 192.49/27.20 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_827_0, all_830_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (176), (178) gives: % 192.49/27.21 | (469) all_830_0 = all_827_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_830_0, all_833_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (178), (180) gives: % 192.49/27.21 | (470) all_833_0 = all_830_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_833_0, all_835_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (180), (182) gives: % 192.49/27.21 | (471) all_835_0 = all_833_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_835_0, all_847_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (182), (184) gives: % 192.49/27.21 | (472) all_847_0 = all_835_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_847_0, all_850_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (184), (186) gives: % 192.49/27.21 | (473) all_850_0 = all_847_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_850_0, all_865_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (186), (190) gives: % 192.49/27.21 | (474) all_865_0 = all_850_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_865_0, all_870_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (190), (192) gives: % 192.49/27.21 | (475) all_870_0 = all_865_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_870_0, all_876_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (192), (194) gives: % 192.49/27.21 | (476) all_876_0 = all_870_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_876_0, all_882_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (194), (196) gives: % 192.49/27.21 | (477) all_882_0 = all_876_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_882_0, all_885_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (196), (198) gives: % 192.49/27.21 | (478) all_885_0 = all_882_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_887_0, all_891_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (200), (203) gives: % 192.49/27.21 | (479) all_891_1 = all_887_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_885_0, all_891_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (198), (203) gives: % 192.49/27.21 | (480) all_891_1 = all_885_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_891_1, all_908_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (203), (213) gives: % 192.49/27.21 | (481) all_908_0 = all_891_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_908_0, all_913_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (213), (215) gives: % 192.49/27.21 | (482) all_913_0 = all_908_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_827_0, all_925_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (176), (217) gives: % 192.49/27.21 | (483) all_925_0 = all_827_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_819_0, all_928_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (170), (219) gives: % 192.49/27.21 | (484) all_928_0 = all_819_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_913_0, all_931_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (215), (221) gives: % 192.49/27.21 | (485) all_931_0 = all_913_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_931_0, all_937_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (221), (223) gives: % 192.49/27.21 | (486) all_937_1 = all_931_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_937_1, all_954_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (223), (227) gives: % 192.49/27.21 | (487) all_954_0 = all_937_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_954_0, all_957_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (227), (229) gives: % 192.49/27.21 | (488) all_957_0 = all_954_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_957_0, all_962_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (229), (231) gives: % 192.49/27.21 | (489) all_962_1 = all_957_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_962_1, all_975_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (231), (237) gives: % 192.49/27.21 | (490) all_975_1 = all_962_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1014_1, all_1020_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (255), (260) gives: % 192.49/27.21 | (491) all_1020_1 = all_1014_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1020_1, all_1027_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (260), (262) gives: % 192.49/27.21 | (492) all_1027_0 = all_1020_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1027_0, all_1030_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (262), (264) gives: % 192.49/27.21 | (493) all_1030_0 = all_1027_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1039_0, all_1045_2, tc_Nat_Onat, % 192.49/27.21 | simplifying with (266), (271) gives: % 192.49/27.21 | (494) all_1045_2 = all_1039_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1057_0, all_1077_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (275), (281) gives: % 192.49/27.21 | (495) all_1077_0 = all_1057_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1103_1, all_1106_2, tc_Nat_Onat, % 192.49/27.21 | simplifying with (287), (289) gives: % 192.49/27.21 | (496) all_1106_2 = all_1103_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1106_2, all_1110_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (289), (291) gives: % 192.49/27.21 | (497) all_1110_1 = all_1106_2 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1048_0, all_1113_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (273), (293) gives: % 192.49/27.21 | (498) all_1113_1 = all_1048_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1030_0, all_1113_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (264), (293) gives: % 192.49/27.21 | (499) all_1113_1 = all_1030_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1045_2, all_1135_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (271), (305) gives: % 192.49/27.21 | (500) all_1135_0 = all_1045_2 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1097_1, all_1138_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (285), (307) gives: % 192.49/27.21 | (501) all_1138_0 = all_1097_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1135_0, all_1144_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (305), (312) gives: % 192.49/27.21 | (502) all_1144_1 = all_1135_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1113_1, all_1156_2, tc_Nat_Onat, % 192.49/27.21 | simplifying with (293), (314) gives: % 192.49/27.21 | (503) all_1156_2 = all_1113_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1110_1, all_1177_2, tc_Nat_Onat, % 192.49/27.21 | simplifying with (291), (316) gives: % 192.49/27.21 | (504) all_1177_2 = all_1110_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1156_2, all_1186_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (314), (318) gives: % 192.49/27.21 | (505) all_1186_0 = all_1156_2 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_925_0, all_1192_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (217), (320) gives: % 192.49/27.21 | (506) all_1192_1 = all_925_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_824_0, all_1192_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (174), (320) gives: % 192.49/27.21 | (507) all_1192_1 = all_824_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1177_2, all_1198_2, tc_Nat_Onat, % 192.49/27.21 | simplifying with (316), (324) gives: % 192.49/27.21 | (508) all_1198_2 = all_1177_2 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1198_2, all_1208_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (324), (326) gives: % 192.49/27.21 | (509) all_1208_1 = all_1198_2 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1186_0, all_1214_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (318), (328) gives: % 192.49/27.21 | (510) all_1214_0 = all_1186_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_925_0, all_1220_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (217), (330) gives: % 192.49/27.21 | (511) all_1220_0 = all_925_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_816_0, all_1220_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (168), (330) gives: % 192.49/27.21 | (512) all_1220_0 = all_816_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_810_0, all_1220_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (164), (330) gives: % 192.49/27.21 | (513) all_1220_0 = all_810_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_801_0, all_1220_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (160), (330) gives: % 192.49/27.21 | (514) all_1220_0 = all_801_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_799_0, all_1220_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (158), (330) gives: % 192.49/27.21 | (515) all_1220_0 = all_799_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1097_1, all_1226_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (285), (332) gives: % 192.49/27.21 | (516) all_1226_1 = all_1097_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_984_1, all_1226_1, tc_Nat_Onat, % 192.49/27.21 | simplifying with (241), (332) gives: % 192.49/27.21 | (517) all_1226_1 = all_984_1 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_1214_0, all_1238_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (328), (334) gives: % 192.49/27.21 | (518) all_1238_0 = all_1214_0 % 192.49/27.21 | % 192.49/27.21 | GROUND_INST: instantiating (141) with all_975_1, all_1296_0, tc_Nat_Onat, % 192.49/27.21 | simplifying with (237), (356) gives: % 192.49/27.21 | (519) all_1296_0 = all_975_1 % 192.49/27.21 | % 192.49/27.22 | GROUND_INST: instantiating (141) with all_908_0, all_1302_1, tc_Nat_Onat, % 192.49/27.22 | simplifying with (213), (358) gives: % 192.49/27.22 | (520) all_1302_1 = all_908_0 % 192.49/27.22 | % 192.49/27.22 | GROUND_INST: instantiating (141) with all_1238_0, all_1308_0, tc_Nat_Onat, % 192.49/27.22 | simplifying with (334), (362) gives: % 192.49/27.22 | (521) all_1308_0 = all_1238_0 % 192.49/27.22 | % 192.49/27.22 | GROUND_INST: instantiating (141) with all_1305_0, all_1326_2, tc_Nat_Onat, % 192.49/27.22 | simplifying with (360), (373) gives: % 192.49/27.22 | (522) all_1326_2 = all_1305_0 % 192.49/27.22 | % 192.49/27.22 | GROUND_INST: instantiating (141) with all_969_0, all_1326_2, tc_Nat_Onat, % 192.49/27.22 | simplifying with (233), (373) gives: % 192.49/27.22 | (523) all_1326_2 = all_969_0 % 192.49/27.22 | % 192.49/27.22 | GROUND_INST: instantiating (141) with all_1308_0, all_1335_0, tc_Nat_Onat, % 192.49/27.22 | simplifying with (362), (376) gives: % 192.49/27.22 | (524) all_1335_0 = all_1308_0 % 192.49/27.22 | % 192.49/27.22 | GROUND_INST: instantiating (141) with all_1335_0, all_1344_0, tc_Nat_Onat, % 192.49/27.22 | simplifying with (376), (380) gives: % 192.49/27.22 | (525) all_1344_0 = all_1335_0 % 192.49/27.22 | % 192.49/27.22 | GROUND_INST: instantiating (141) with all_1302_1, all_1347_2, tc_Nat_Onat, % 192.49/27.22 | simplifying with (358), (382) gives: % 192.49/27.22 | (526) all_1347_2 = all_1302_1 % 192.49/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1226_1, all_1353_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (332), (387) gives: % 192.92/27.22 | (527) all_1353_1 = all_1226_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1103_1, all_1359_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (287), (389) gives: % 192.92/27.22 | (528) all_1359_1 = all_1103_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1077_0, all_1359_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (281), (389) gives: % 192.92/27.22 | (529) all_1359_1 = all_1077_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1344_0, all_1368_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (380), (391) gives: % 192.92/27.22 | (530) all_1368_0 = all_1344_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1368_0, all_1374_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (391), (393) gives: % 192.92/27.22 | (531) all_1374_0 = all_1368_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1374_0, all_1380_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (393), (395) gives: % 192.92/27.22 | (532) all_1380_0 = all_1374_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1144_1, all_1389_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (312), (400) gives: % 192.92/27.22 | (533) all_1389_2 = all_1144_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_978_0, all_1389_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (239), (400) gives: % 192.92/27.22 | (534) all_1389_2 = all_978_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1305_0, all_1392_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (360), (403) gives: % 192.92/27.22 | (535) all_1392_1 = all_1305_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1141_0, all_1392_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (309), (403) gives: % 192.92/27.22 | (536) all_1392_1 = all_1141_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1138_0, all_1392_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (307), (403) gives: % 192.92/27.22 | (537) all_1392_1 = all_1138_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_928_0, all_1395_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (219), (405) gives: % 192.92/27.22 | (538) all_1395_1 = all_928_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_807_0, all_1395_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (162), (405) gives: % 192.92/27.22 | (539) all_1395_1 = all_807_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_801_0, all_1395_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (160), (405) gives: % 192.92/27.22 | (540) all_1395_1 = all_801_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1057_0, all_1401_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (275), (409) gives: % 192.92/27.22 | (541) all_1401_0 = all_1057_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1014_1, all_1401_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (255), (409) gives: % 192.92/27.22 | (542) all_1401_0 = all_1014_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1008_1, all_1401_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (253), (409) gives: % 192.92/27.22 | (543) all_1401_0 = all_1008_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1353_1, all_1404_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (387), (411) gives: % 192.92/27.22 | (544) all_1404_1 = all_1353_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1048_0, all_1407_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (273), (413) gives: % 192.92/27.22 | (545) all_1407_0 = all_1048_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_987_1, all_1407_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (244), (413) gives: % 192.92/27.22 | (546) all_1407_0 = all_987_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1317_0, all_1422_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (368), (420) gives: % 192.92/27.22 | (547) all_1422_0 = all_1317_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_928_0, all_1425_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (219), (422) gives: % 192.92/27.22 | (548) all_1425_1 = all_928_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1347_2, all_1428_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (382), (424) gives: % 192.92/27.22 | (549) all_1428_1 = all_1347_2 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_813_0, all_1428_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (166), (424) gives: % 192.92/27.22 | (550) all_1428_1 = all_813_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1398_0, all_1431_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (407), (426) gives: % 192.92/27.22 | (551) all_1431_1 = all_1398_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1296_0, all_1431_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (356), (426) gives: % 192.92/27.22 | (552) all_1431_1 = all_1296_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1195_1, all_1431_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (322), (426) gives: % 192.92/27.22 | (553) all_1431_1 = all_1195_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1317_0, all_1434_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (368), (428) gives: % 192.92/27.22 | (554) all_1434_0 = all_1317_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1264_1, all_1434_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (345), (428) gives: % 192.92/27.22 | (555) all_1434_0 = all_1264_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1208_1, all_1434_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (326), (428) gives: % 192.92/27.22 | (556) all_1434_0 = all_1208_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1410_3, all_1437_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (415), (430) gives: % 192.92/27.22 | (557) all_1437_1 = all_1410_3 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1437_1, all_1440_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (430), (432) gives: % 192.92/27.22 | (558) all_1440_1 = all_1437_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1440_1, all_1443_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (432), (434) gives: % 192.92/27.22 | (559) all_1443_1 = all_1440_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1057_0, all_1448_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (275), (441) gives: % 192.92/27.22 | (560) all_1448_2 = all_1057_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1039_0, all_1448_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (266), (441) gives: % 192.92/27.22 | (561) all_1448_2 = all_1039_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_990_0, all_1448_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (246), (441) gives: % 192.92/27.22 | (562) all_1448_2 = all_990_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_984_1, all_1448_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (241), (441) gives: % 192.92/27.22 | (563) all_1448_2 = all_984_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_975_1, all_1448_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (237), (441) gives: % 192.92/27.22 | (564) all_1448_2 = all_975_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1389_2, all_1459_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (400), (443) gives: % 192.92/27.22 | (565) all_1459_0 = all_1389_2 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1338_0, all_1459_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (378), (443) gives: % 192.92/27.22 | (566) all_1459_0 = all_1338_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1422_0, all_1462_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (420), (445) gives: % 192.92/27.22 | (567) all_1462_2 = all_1422_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1005_0, all_1462_2, tc_Nat_Onat, % 192.92/27.22 | simplifying with (250), (445) gives: % 192.92/27.22 | (568) all_1462_2 = all_1005_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1407_0, all_1465_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (413), (449) gives: % 192.92/27.22 | (569) all_1465_0 = all_1407_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1350_3, all_1465_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (385), (449) gives: % 192.92/27.22 | (570) all_1465_0 = all_1350_3 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1413_0, all_1471_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (418), (453) gives: % 192.92/27.22 | (571) all_1471_1 = all_1413_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1410_3, all_1471_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (415), (453) gives: % 192.92/27.22 | (572) all_1471_1 = all_1410_3 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1383_1, all_1471_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (398), (453) gives: % 192.92/27.22 | (573) all_1471_1 = all_1383_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1380_0, all_1471_1, tc_Nat_Onat, % 192.92/27.22 | simplifying with (395), (453) gives: % 192.92/27.22 | (574) all_1471_1 = all_1380_0 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1468_1, all_1474_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (451), (455) gives: % 192.92/27.22 | (575) all_1474_0 = all_1468_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1404_1, all_1474_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (411), (455) gives: % 192.92/27.22 | (576) all_1474_0 = all_1404_1 % 192.92/27.22 | % 192.92/27.22 | GROUND_INST: instantiating (141) with all_1068_0, all_1474_0, tc_Nat_Onat, % 192.92/27.22 | simplifying with (279), (455) gives: % 192.92/27.23 | (577) all_1474_0 = all_1068_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_1359_1, all_1477_2, tc_Nat_Onat, % 192.92/27.23 | simplifying with (389), (457) gives: % 192.92/27.23 | (578) all_1477_2 = all_1359_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_1091_0, all_1477_2, tc_Nat_Onat, % 192.92/27.23 | simplifying with (283), (457) gives: % 192.92/27.23 | (579) all_1477_2 = all_1091_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_1389_2, all_1480_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (400), (459) gives: % 192.92/27.23 | (580) all_1480_0 = all_1389_2 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_1320_1, all_1480_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (370), (459) gives: % 192.92/27.23 | (581) all_1480_0 = all_1320_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_1443_1, all_1487_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (434), (461) gives: % 192.92/27.23 | (582) all_1487_1 = all_1443_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_1042_0, all_1487_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (268), (461) gives: % 192.92/27.23 | (583) all_1487_1 = all_1042_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_1425_1, all_1496_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (422), (464) gives: % 192.92/27.23 | (584) all_1496_1 = all_1425_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_789_0, all_1496_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (149), (464) gives: % 192.92/27.23 | (585) all_1496_1 = all_789_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_1296_0, all_1499_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (356), (466) gives: % 192.92/27.23 | (586) all_1499_0 = all_1296_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_893_0, all_1499_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (205), (466) gives: % 192.92/27.23 | (587) all_1499_0 = all_893_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_801_0, all_1502_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (160), (468) gives: % 192.92/27.23 | (588) all_1502_0 = all_801_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_793_0, all_1502_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (153), (468) gives: % 192.92/27.23 | (589) all_1502_0 = all_793_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (141) with all_791_0, all_1502_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (151), (468) gives: % 192.92/27.23 | (590) all_1502_0 = all_791_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (142) with all_1116_4, all_1276_7, % 192.92/27.23 | tc_Complex_Ocomplex, simplifying with (297), (351) gives: % 192.92/27.23 | (591) all_1276_7 = all_1116_4 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (142) with all_797_0, all_1276_7, % 192.92/27.23 | tc_Complex_Ocomplex, simplifying with (156), (351) gives: % 192.92/27.23 | (592) all_1276_7 = all_797_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (142) with all_1276_7, all_1446_4, % 192.92/27.23 | tc_Complex_Ocomplex, simplifying with (351), (438) gives: % 192.92/27.23 | (593) all_1446_4 = all_1276_7 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (142) with all_1446_4, all_1462_1, % 192.92/27.23 | tc_Complex_Ocomplex, simplifying with (438), (446) gives: % 192.92/27.23 | (594) all_1462_1 = all_1446_4 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (142) with all_1247_6, all_1462_1, % 192.92/27.23 | tc_Complex_Ocomplex, simplifying with (340), (446) gives: % 192.92/27.23 | (595) all_1462_1 = all_1247_6 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (147) with all_1247_3, all_1276_4, v_p, % 192.92/27.23 | tc_Complex_Ocomplex, simplifying with (341), (352) gives: % 192.92/27.23 | (596) all_1276_4 = all_1247_3 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (147) with all_1116_1, all_1276_4, v_p, % 192.92/27.23 | tc_Complex_Ocomplex, simplifying with (298), (352) gives: % 192.92/27.23 | (597) all_1276_4 = all_1116_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_887_1, all_896_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (201), (207) gives: % 192.92/27.23 | (598) all_896_0 = all_887_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_902_0, all_905_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (209), (211) gives: % 192.92/27.23 | (599) all_905_0 = all_902_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_896_0, all_905_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (207), (211) gives: % 192.92/27.23 | (600) all_905_0 = all_896_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_822_0, all_905_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (172), (211) gives: % 192.92/27.23 | (601) all_905_0 = all_822_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_972_0, all_984_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (235), (242) gives: % 192.92/27.23 | (602) all_984_0 = all_972_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_984_0, all_996_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (242), (248) gives: % 192.92/27.23 | (603) all_996_0 = all_984_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_996_0, all_1014_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (248), (256) gives: % 192.92/27.23 | (604) all_1014_0 = all_996_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1014_0, all_1017_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (256), (258) gives: % 192.92/27.23 | (605) all_1017_1 = all_1014_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1017_1, all_1042_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (258), (269) gives: % 192.92/27.23 | (606) all_1042_1 = all_1017_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_972_0, all_1065_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (235), (277) gives: % 192.92/27.23 | (607) all_1065_0 = all_972_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_887_1, all_1065_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (201), (277) gives: % 192.92/27.23 | (608) all_1065_0 = all_887_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1042_1, all_1126_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (269), (301) gives: % 192.92/27.23 | (609) all_1126_1 = all_1042_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1065_0, all_1132_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (277), (303) gives: % 192.92/27.23 | (610) all_1132_0 = all_1065_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1132_0, all_1141_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (303), (310) gives: % 192.92/27.23 | (611) all_1141_1 = all_1132_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1126_1, all_1264_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (301), (346) gives: % 192.92/27.23 | (612) all_1264_0 = all_1126_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1141_1, all_1311_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (310), (364) gives: % 192.92/27.23 | (613) all_1311_0 = all_1141_1 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_859_0, all_1347_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (188), (383) gives: % 192.92/27.23 | (614) all_1347_0 = all_859_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1347_0, all_1389_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (383), (401) gives: % 192.92/27.23 | (615) all_1389_0 = all_1347_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1326_0, all_1389_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (374), (401) gives: % 192.92/27.23 | (616) all_1389_0 = all_1326_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1264_0, all_1389_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (346), (401) gives: % 192.92/27.23 | (617) all_1389_0 = all_1264_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1320_0, all_1410_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (371), (416) gives: % 192.92/27.23 | (618) all_1410_1 = all_1320_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1311_0, all_1410_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (364), (416) gives: % 192.92/27.23 | (619) all_1410_1 = all_1311_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_945_0, all_1410_1, tc_Nat_Onat, % 192.92/27.23 | simplifying with (225), (416) gives: % 192.92/27.23 | (620) all_1410_1 = all_945_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1443_0, all_1487_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (435), (462) gives: % 192.92/27.23 | (621) all_1487_0 = all_1443_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1389_0, all_1487_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (401), (462) gives: % 192.92/27.23 | (622) all_1487_0 = all_1389_0 % 192.92/27.23 | % 192.92/27.23 | GROUND_INST: instantiating (145) with all_1314_1, all_1487_0, tc_Nat_Onat, % 192.92/27.23 | simplifying with (366), (462) gives: % 192.92/27.23 | (623) all_1487_0 = all_1314_1 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (589), (590) imply: % 192.92/27.23 | (624) all_793_0 = all_791_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (588), (589) imply: % 192.92/27.23 | (625) all_801_0 = all_793_0 % 192.92/27.23 | % 192.92/27.23 | SIMP: (625) implies: % 192.92/27.23 | (626) all_801_0 = all_793_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (586), (587) imply: % 192.92/27.23 | (627) all_1296_0 = all_893_0 % 192.92/27.23 | % 192.92/27.23 | SIMP: (627) implies: % 192.92/27.23 | (628) all_1296_0 = all_893_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (584), (585) imply: % 192.92/27.23 | (629) all_1425_1 = all_789_0 % 192.92/27.23 | % 192.92/27.23 | SIMP: (629) implies: % 192.92/27.23 | (630) all_1425_1 = all_789_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (621), (623) imply: % 192.92/27.23 | (631) all_1443_0 = all_1314_1 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (621), (622) imply: % 192.92/27.23 | (632) all_1443_0 = all_1389_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (582), (583) imply: % 192.92/27.23 | (633) all_1443_1 = all_1042_0 % 192.92/27.23 | % 192.92/27.23 | SIMP: (633) implies: % 192.92/27.23 | (634) all_1443_1 = all_1042_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (580), (581) imply: % 192.92/27.23 | (635) all_1389_2 = all_1320_1 % 192.92/27.23 | % 192.92/27.23 | SIMP: (635) implies: % 192.92/27.23 | (636) all_1389_2 = all_1320_1 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (578), (579) imply: % 192.92/27.23 | (637) all_1359_1 = all_1091_0 % 192.92/27.23 | % 192.92/27.23 | SIMP: (637) implies: % 192.92/27.23 | (638) all_1359_1 = all_1091_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (575), (576) imply: % 192.92/27.23 | (639) all_1468_1 = all_1404_1 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (575), (577) imply: % 192.92/27.23 | (640) all_1468_1 = all_1068_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (571), (572) imply: % 192.92/27.23 | (641) all_1413_0 = all_1410_3 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (571), (574) imply: % 192.92/27.23 | (642) all_1413_0 = all_1380_0 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (571), (573) imply: % 192.92/27.23 | (643) all_1413_0 = all_1383_1 % 192.92/27.23 | % 192.92/27.23 | COMBINE_EQS: (639), (640) imply: % 192.92/27.23 | (644) all_1404_1 = all_1068_0 % 192.92/27.23 | % 192.92/27.23 | SIMP: (644) implies: % 192.92/27.23 | (645) all_1404_1 = all_1068_0 % 192.92/27.23 | % 192.92/27.24 | COMBINE_EQS: (569), (570) imply: % 192.92/27.24 | (646) all_1407_0 = all_1350_3 % 192.92/27.24 | % 192.92/27.24 | SIMP: (646) implies: % 192.92/27.24 | (647) all_1407_0 = all_1350_3 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (594), (595) imply: % 192.92/27.24 | (648) all_1446_4 = all_1247_6 % 192.92/27.24 | % 192.92/27.24 | SIMP: (648) implies: % 192.92/27.24 | (649) all_1446_4 = all_1247_6 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (567), (568) imply: % 192.92/27.24 | (650) all_1422_0 = all_1005_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (650) implies: % 192.92/27.24 | (651) all_1422_0 = all_1005_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (565), (566) imply: % 192.92/27.24 | (652) all_1389_2 = all_1338_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (652) implies: % 192.92/27.24 | (653) all_1389_2 = all_1338_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (560), (562) imply: % 192.92/27.24 | (654) all_1057_0 = all_990_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (654) implies: % 192.92/27.24 | (655) all_1057_0 = all_990_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (561), (562) imply: % 192.92/27.24 | (656) all_1039_0 = all_990_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (656) implies: % 192.92/27.24 | (657) all_1039_0 = all_990_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (562), (563) imply: % 192.92/27.24 | (658) all_990_0 = all_984_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (562), (564) imply: % 192.92/27.24 | (659) all_990_0 = all_975_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (593), (649) imply: % 192.92/27.24 | (660) all_1276_7 = all_1247_6 % 192.92/27.24 | % 192.92/27.24 | SIMP: (660) implies: % 192.92/27.24 | (661) all_1276_7 = all_1247_6 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (631), (632) imply: % 192.92/27.24 | (662) all_1389_0 = all_1314_1 % 192.92/27.24 | % 192.92/27.24 | SIMP: (662) implies: % 192.92/27.24 | (663) all_1389_0 = all_1314_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (559), (634) imply: % 192.92/27.24 | (664) all_1440_1 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (664) implies: % 192.92/27.24 | (665) all_1440_1 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (558), (665) imply: % 192.92/27.24 | (666) all_1437_1 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (666) implies: % 192.92/27.24 | (667) all_1437_1 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (557), (667) imply: % 192.92/27.24 | (668) all_1410_3 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (668) implies: % 192.92/27.24 | (669) all_1410_3 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (554), (555) imply: % 192.92/27.24 | (670) all_1317_0 = all_1264_1 % 192.92/27.24 | % 192.92/27.24 | SIMP: (670) implies: % 192.92/27.24 | (671) all_1317_0 = all_1264_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (555), (556) imply: % 192.92/27.24 | (672) all_1264_1 = all_1208_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (551), (553) imply: % 192.92/27.24 | (673) all_1398_0 = all_1195_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (551), (552) imply: % 192.92/27.24 | (674) all_1398_0 = all_1296_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (549), (550) imply: % 192.92/27.24 | (675) all_1347_2 = all_813_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (675) implies: % 192.92/27.24 | (676) all_1347_2 = all_813_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (548), (630) imply: % 192.92/27.24 | (677) all_928_0 = all_789_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (677) implies: % 192.92/27.24 | (678) all_928_0 = all_789_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (547), (651) imply: % 192.92/27.24 | (679) all_1317_0 = all_1005_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (679) implies: % 192.92/27.24 | (680) all_1317_0 = all_1005_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (642), (643) imply: % 192.92/27.24 | (681) all_1383_1 = all_1380_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (641), (643) imply: % 192.92/27.24 | (682) all_1410_3 = all_1383_1 % 192.92/27.24 | % 192.92/27.24 | SIMP: (682) implies: % 192.92/27.24 | (683) all_1410_3 = all_1383_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (618), (619) imply: % 192.92/27.24 | (684) all_1320_0 = all_1311_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (618), (620) imply: % 192.92/27.24 | (685) all_1320_0 = all_945_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (669), (683) imply: % 192.92/27.24 | (686) all_1383_1 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (686) implies: % 192.92/27.24 | (687) all_1383_1 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (546), (647) imply: % 192.92/27.24 | (688) all_1350_3 = all_987_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (545), (647) imply: % 192.92/27.24 | (689) all_1350_3 = all_1048_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (544), (645) imply: % 192.92/27.24 | (690) all_1353_1 = all_1068_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (690) implies: % 192.92/27.24 | (691) all_1353_1 = all_1068_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (542), (543) imply: % 192.92/27.24 | (692) all_1014_1 = all_1008_1 % 192.92/27.24 | % 192.92/27.24 | SIMP: (692) implies: % 192.92/27.24 | (693) all_1014_1 = all_1008_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (541), (543) imply: % 192.92/27.24 | (694) all_1057_0 = all_1008_1 % 192.92/27.24 | % 192.92/27.24 | SIMP: (694) implies: % 192.92/27.24 | (695) all_1057_0 = all_1008_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (673), (674) imply: % 192.92/27.24 | (696) all_1296_0 = all_1195_1 % 192.92/27.24 | % 192.92/27.24 | SIMP: (696) implies: % 192.92/27.24 | (697) all_1296_0 = all_1195_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (539), (540) imply: % 192.92/27.24 | (698) all_807_0 = all_801_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (538), (539) imply: % 192.92/27.24 | (699) all_928_0 = all_807_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (699) implies: % 192.92/27.24 | (700) all_928_0 = all_807_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (536), (537) imply: % 192.92/27.24 | (701) all_1141_0 = all_1138_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (535), (536) imply: % 192.92/27.24 | (702) all_1305_0 = all_1141_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (702) implies: % 192.92/27.24 | (703) all_1305_0 = all_1141_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (616), (663) imply: % 192.92/27.24 | (704) all_1326_0 = all_1314_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (616), (617) imply: % 192.92/27.24 | (705) all_1326_0 = all_1264_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (615), (616) imply: % 192.92/27.24 | (706) all_1347_0 = all_1326_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (706) implies: % 192.92/27.24 | (707) all_1347_0 = all_1326_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (533), (653) imply: % 192.92/27.24 | (708) all_1338_0 = all_1144_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (534), (653) imply: % 192.92/27.24 | (709) all_1338_0 = all_978_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (636), (653) imply: % 192.92/27.24 | (710) all_1338_0 = all_1320_1 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (681), (687) imply: % 192.92/27.24 | (711) all_1380_0 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (711) implies: % 192.92/27.24 | (712) all_1380_0 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (532), (712) imply: % 192.92/27.24 | (713) all_1374_0 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (713) implies: % 192.92/27.24 | (714) all_1374_0 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | COMBINE_EQS: (531), (714) imply: % 192.92/27.24 | (715) all_1368_0 = all_1042_0 % 192.92/27.24 | % 192.92/27.24 | SIMP: (715) implies: % 193.03/27.24 | (716) all_1368_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (530), (716) imply: % 193.03/27.24 | (717) all_1344_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (717) implies: % 193.03/27.24 | (718) all_1344_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (528), (638) imply: % 193.03/27.24 | (719) all_1103_1 = all_1091_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (719) implies: % 193.03/27.24 | (720) all_1103_1 = all_1091_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (529), (638) imply: % 193.03/27.24 | (721) all_1091_0 = all_1077_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (527), (691) imply: % 193.03/27.24 | (722) all_1226_1 = all_1068_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (722) implies: % 193.03/27.24 | (723) all_1226_1 = all_1068_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (688), (689) imply: % 193.03/27.24 | (724) all_1048_0 = all_987_1 % 193.03/27.24 | % 193.03/27.24 | SIMP: (724) implies: % 193.03/27.24 | (725) all_1048_0 = all_987_1 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (614), (707) imply: % 193.03/27.24 | (726) all_1326_0 = all_859_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (726) implies: % 193.03/27.24 | (727) all_1326_0 = all_859_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (526), (676) imply: % 193.03/27.24 | (728) all_1302_1 = all_813_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (728) implies: % 193.03/27.24 | (729) all_1302_1 = all_813_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (525), (718) imply: % 193.03/27.24 | (730) all_1335_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (730) implies: % 193.03/27.24 | (731) all_1335_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (708), (710) imply: % 193.03/27.24 | (732) all_1320_1 = all_1144_1 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (709), (710) imply: % 193.03/27.24 | (733) all_1320_1 = all_978_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (524), (731) imply: % 193.03/27.24 | (734) all_1308_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (734) implies: % 193.03/27.24 | (735) all_1308_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (704), (727) imply: % 193.03/27.24 | (736) all_1314_1 = all_859_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (704), (705) imply: % 193.03/27.24 | (737) all_1314_1 = all_1264_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (522), (523) imply: % 193.03/27.24 | (738) all_1305_0 = all_969_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (738) implies: % 193.03/27.24 | (739) all_1305_0 = all_969_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (684), (685) imply: % 193.03/27.24 | (740) all_1311_0 = all_945_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (740) implies: % 193.03/27.24 | (741) all_1311_0 = all_945_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (732), (733) imply: % 193.03/27.24 | (742) all_1144_1 = all_978_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (742) implies: % 193.03/27.24 | (743) all_1144_1 = all_978_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (671), (680) imply: % 193.03/27.24 | (744) all_1264_1 = all_1005_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (744) implies: % 193.03/27.24 | (745) all_1264_1 = all_1005_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (736), (737) imply: % 193.03/27.24 | (746) all_1264_0 = all_859_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (746) implies: % 193.03/27.24 | (747) all_1264_0 = all_859_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (613), (741) imply: % 193.03/27.24 | (748) all_1141_1 = all_945_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (748) implies: % 193.03/27.24 | (749) all_1141_1 = all_945_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (521), (735) imply: % 193.03/27.24 | (750) all_1238_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (750) implies: % 193.03/27.24 | (751) all_1238_0 = all_1042_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (703), (739) imply: % 193.03/27.24 | (752) all_1141_0 = all_969_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (752) implies: % 193.03/27.24 | (753) all_1141_0 = all_969_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (520), (729) imply: % 193.03/27.24 | (754) all_908_0 = all_813_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (754) implies: % 193.03/27.24 | (755) all_908_0 = all_813_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (519), (697) imply: % 193.03/27.24 | (756) all_1195_1 = all_975_1 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (628), (697) imply: % 193.03/27.24 | (757) all_1195_1 = all_893_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (596), (597) imply: % 193.03/27.24 | (758) all_1247_3 = all_1116_1 % 193.03/27.24 | % 193.03/27.24 | SIMP: (758) implies: % 193.03/27.24 | (759) all_1247_3 = all_1116_1 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (591), (661) imply: % 193.03/27.24 | (760) all_1247_6 = all_1116_4 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (592), (661) imply: % 193.03/27.24 | (761) all_1247_6 = all_797_0 % 193.03/27.24 | % 193.03/27.24 | COMBINE_EQS: (612), (747) imply: % 193.03/27.24 | (762) all_1126_1 = all_859_0 % 193.03/27.24 | % 193.03/27.24 | SIMP: (762) implies: % 193.03/27.25 | (763) all_1126_1 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (672), (745) imply: % 193.03/27.25 | (764) all_1208_1 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (764) implies: % 193.03/27.25 | (765) all_1208_1 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (760), (761) imply: % 193.03/27.25 | (766) all_1116_4 = all_797_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (766) implies: % 193.03/27.25 | (767) all_1116_4 = all_797_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (518), (751) imply: % 193.03/27.25 | (768) all_1214_0 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (768) implies: % 193.03/27.25 | (769) all_1214_0 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (517), (723) imply: % 193.03/27.25 | (770) all_1068_0 = all_984_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (516), (723) imply: % 193.03/27.25 | (771) all_1097_1 = all_1068_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (771) implies: % 193.03/27.25 | (772) all_1097_1 = all_1068_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (512), (513) imply: % 193.03/27.25 | (773) all_816_0 = all_810_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (511), (512) imply: % 193.03/27.25 | (774) all_925_0 = all_816_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (774) implies: % 193.03/27.25 | (775) all_925_0 = all_816_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (512), (514) imply: % 193.03/27.25 | (776) all_816_0 = all_801_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (512), (515) imply: % 193.03/27.25 | (777) all_816_0 = all_799_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (510), (769) imply: % 193.03/27.25 | (778) all_1186_0 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (778) implies: % 193.03/27.25 | (779) all_1186_0 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (509), (765) imply: % 193.03/27.25 | (780) all_1198_2 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (780) implies: % 193.03/27.25 | (781) all_1198_2 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (508), (781) imply: % 193.03/27.25 | (782) all_1177_2 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (782) implies: % 193.03/27.25 | (783) all_1177_2 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (756), (757) imply: % 193.03/27.25 | (784) all_975_1 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (784) implies: % 193.03/27.25 | (785) all_975_1 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (506), (507) imply: % 193.03/27.25 | (786) all_925_0 = all_824_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (786) implies: % 193.03/27.25 | (787) all_925_0 = all_824_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (505), (779) imply: % 193.03/27.25 | (788) all_1156_2 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (788) implies: % 193.03/27.25 | (789) all_1156_2 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (504), (783) imply: % 193.03/27.25 | (790) all_1110_1 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (790) implies: % 193.03/27.25 | (791) all_1110_1 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (503), (789) imply: % 193.03/27.25 | (792) all_1113_1 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (792) implies: % 193.03/27.25 | (793) all_1113_1 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (502), (743) imply: % 193.03/27.25 | (794) all_1135_0 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (794) implies: % 193.03/27.25 | (795) all_1135_0 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (701), (753) imply: % 193.03/27.25 | (796) all_1138_0 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (796) implies: % 193.03/27.25 | (797) all_1138_0 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (611), (749) imply: % 193.03/27.25 | (798) all_1132_0 = all_945_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (798) implies: % 193.03/27.25 | (799) all_1132_0 = all_945_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (501), (797) imply: % 193.03/27.25 | (800) all_1097_1 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (800) implies: % 193.03/27.25 | (801) all_1097_1 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (500), (795) imply: % 193.03/27.25 | (802) all_1045_2 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (802) implies: % 193.03/27.25 | (803) all_1045_2 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (610), (799) imply: % 193.03/27.25 | (804) all_1065_0 = all_945_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (804) implies: % 193.03/27.25 | (805) all_1065_0 = all_945_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (609), (763) imply: % 193.03/27.25 | (806) all_1042_1 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (806) implies: % 193.03/27.25 | (807) all_1042_1 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (498), (793) imply: % 193.03/27.25 | (808) all_1048_0 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (808) implies: % 193.03/27.25 | (809) all_1048_0 = all_1042_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (499), (793) imply: % 193.03/27.25 | (810) all_1042_0 = all_1030_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (497), (791) imply: % 193.03/27.25 | (811) all_1106_2 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (811) implies: % 193.03/27.25 | (812) all_1106_2 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (496), (812) imply: % 193.03/27.25 | (813) all_1103_1 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (813) implies: % 193.03/27.25 | (814) all_1103_1 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (720), (814) imply: % 193.03/27.25 | (815) all_1091_0 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (815) implies: % 193.03/27.25 | (816) all_1091_0 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (772), (801) imply: % 193.03/27.25 | (817) all_1068_0 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (817) implies: % 193.03/27.25 | (818) all_1068_0 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (721), (816) imply: % 193.03/27.25 | (819) all_1077_0 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (819) implies: % 193.03/27.25 | (820) all_1077_0 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (495), (820) imply: % 193.03/27.25 | (821) all_1057_0 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (821) implies: % 193.03/27.25 | (822) all_1057_0 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (770), (818) imply: % 193.03/27.25 | (823) all_984_1 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (823) implies: % 193.03/27.25 | (824) all_984_1 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (608), (805) imply: % 193.03/27.25 | (825) all_945_0 = all_887_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (607), (805) imply: % 193.03/27.25 | (826) all_972_0 = all_945_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (826) implies: % 193.03/27.25 | (827) all_972_0 = all_945_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (695), (822) imply: % 193.03/27.25 | (828) all_1008_1 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (828) implies: % 193.03/27.25 | (829) all_1008_1 = all_1005_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (655), (822) imply: % 193.03/27.25 | (830) all_1005_0 = all_990_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (725), (809) imply: % 193.03/27.25 | (831) all_1042_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | SIMP: (831) implies: % 193.03/27.25 | (832) all_1042_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (494), (803) imply: % 193.03/27.25 | (833) all_1039_0 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (833) implies: % 193.03/27.25 | (834) all_1039_0 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (810), (832) imply: % 193.03/27.25 | (835) all_1030_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | SIMP: (835) implies: % 193.03/27.25 | (836) all_1030_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (606), (807) imply: % 193.03/27.25 | (837) all_1017_1 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (837) implies: % 193.03/27.25 | (838) all_1017_1 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (657), (834) imply: % 193.03/27.25 | (839) all_990_0 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (839) implies: % 193.03/27.25 | (840) all_990_0 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (493), (836) imply: % 193.03/27.25 | (841) all_1027_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | SIMP: (841) implies: % 193.03/27.25 | (842) all_1027_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (492), (842) imply: % 193.03/27.25 | (843) all_1020_1 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | SIMP: (843) implies: % 193.03/27.25 | (844) all_1020_1 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (491), (844) imply: % 193.03/27.25 | (845) all_1014_1 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | SIMP: (845) implies: % 193.03/27.25 | (846) all_1014_1 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (605), (838) imply: % 193.03/27.25 | (847) all_1014_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (847) implies: % 193.03/27.25 | (848) all_1014_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (604), (848) imply: % 193.03/27.25 | (849) all_996_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (849) implies: % 193.03/27.25 | (850) all_996_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (693), (846) imply: % 193.03/27.25 | (851) all_1008_1 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | SIMP: (851) implies: % 193.03/27.25 | (852) all_1008_1 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (829), (852) imply: % 193.03/27.25 | (853) all_1005_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | SIMP: (853) implies: % 193.03/27.25 | (854) all_1005_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (830), (854) imply: % 193.03/27.25 | (855) all_990_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | SIMP: (855) implies: % 193.03/27.25 | (856) all_990_0 = all_987_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (603), (850) imply: % 193.03/27.25 | (857) all_984_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (857) implies: % 193.03/27.25 | (858) all_984_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (658), (856) imply: % 193.03/27.25 | (859) all_987_1 = all_984_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (659), (856) imply: % 193.03/27.25 | (860) all_987_1 = all_975_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (840), (856) imply: % 193.03/27.25 | (861) all_987_1 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (860), (861) imply: % 193.03/27.25 | (862) all_978_0 = all_975_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (859), (861) imply: % 193.03/27.25 | (863) all_984_1 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (863) implies: % 193.03/27.25 | (864) all_984_1 = all_978_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (602), (858) imply: % 193.03/27.25 | (865) all_972_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (865) implies: % 193.03/27.25 | (866) all_972_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (824), (864) imply: % 193.03/27.25 | (867) all_978_0 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (867) implies: % 193.03/27.25 | (868) all_978_0 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (862), (868) imply: % 193.03/27.25 | (869) all_975_1 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (869) implies: % 193.03/27.25 | (870) all_975_1 = all_969_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (785), (870) imply: % 193.03/27.25 | (871) all_969_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (490), (870) imply: % 193.03/27.25 | (872) all_969_0 = all_962_1 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (827), (866) imply: % 193.03/27.25 | (873) all_945_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (873) implies: % 193.03/27.25 | (874) all_945_0 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (871), (872) imply: % 193.03/27.25 | (875) all_962_1 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (875) implies: % 193.03/27.25 | (876) all_962_1 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (489), (876) imply: % 193.03/27.25 | (877) all_957_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (877) implies: % 193.03/27.25 | (878) all_957_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (488), (878) imply: % 193.03/27.25 | (879) all_954_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (879) implies: % 193.03/27.25 | (880) all_954_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (487), (880) imply: % 193.03/27.25 | (881) all_937_1 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (881) implies: % 193.03/27.25 | (882) all_937_1 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (825), (874) imply: % 193.03/27.25 | (883) all_887_1 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (883) implies: % 193.03/27.25 | (884) all_887_1 = all_859_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (486), (882) imply: % 193.03/27.25 | (885) all_931_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (885) implies: % 193.03/27.25 | (886) all_931_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (485), (886) imply: % 193.03/27.25 | (887) all_913_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (887) implies: % 193.03/27.25 | (888) all_913_0 = all_893_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (484), (700) imply: % 193.03/27.25 | (889) all_819_0 = all_807_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (484), (678) imply: % 193.03/27.25 | (890) all_819_0 = all_789_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (775), (787) imply: % 193.03/27.25 | (891) all_824_0 = all_816_0 % 193.03/27.25 | % 193.03/27.25 | COMBINE_EQS: (483), (787) imply: % 193.03/27.25 | (892) all_827_0 = all_824_0 % 193.03/27.25 | % 193.03/27.25 | SIMP: (892) implies: % 193.03/27.26 | (893) all_827_0 = all_824_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (482), (888) imply: % 193.03/27.26 | (894) all_908_0 = all_893_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (894) implies: % 193.03/27.26 | (895) all_908_0 = all_893_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (481), (895) imply: % 193.03/27.26 | (896) all_893_0 = all_891_1 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (755), (895) imply: % 193.03/27.26 | (897) all_893_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (599), (601) imply: % 193.03/27.26 | (898) all_902_0 = all_822_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (599), (600) imply: % 193.03/27.26 | (899) all_902_0 = all_896_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (898), (899) imply: % 193.03/27.26 | (900) all_896_0 = all_822_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (900) implies: % 193.03/27.26 | (901) all_896_0 = all_822_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (598), (901) imply: % 193.03/27.26 | (902) all_887_1 = all_822_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (902) implies: % 193.03/27.26 | (903) all_887_1 = all_822_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (896), (897) imply: % 193.03/27.26 | (904) all_891_1 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (904) implies: % 193.03/27.26 | (905) all_891_1 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (479), (480) imply: % 193.03/27.26 | (906) all_887_0 = all_885_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (479), (905) imply: % 193.03/27.26 | (907) all_887_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (906), (907) imply: % 193.03/27.26 | (908) all_885_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (908) implies: % 193.03/27.26 | (909) all_885_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (884), (903) imply: % 193.03/27.26 | (910) all_859_0 = all_822_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (910) implies: % 193.03/27.26 | (911) all_859_0 = all_822_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (478), (909) imply: % 193.03/27.26 | (912) all_882_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (912) implies: % 193.03/27.26 | (913) all_882_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (477), (913) imply: % 193.03/27.26 | (914) all_876_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (914) implies: % 193.03/27.26 | (915) all_876_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (476), (915) imply: % 193.03/27.26 | (916) all_870_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (916) implies: % 193.03/27.26 | (917) all_870_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (475), (917) imply: % 193.03/27.26 | (918) all_865_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (918) implies: % 193.03/27.26 | (919) all_865_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (474), (919) imply: % 193.03/27.26 | (920) all_850_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (920) implies: % 193.03/27.26 | (921) all_850_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (473), (921) imply: % 193.03/27.26 | (922) all_847_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (922) implies: % 193.03/27.26 | (923) all_847_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (472), (923) imply: % 193.03/27.26 | (924) all_835_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (924) implies: % 193.03/27.26 | (925) all_835_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (471), (925) imply: % 193.03/27.26 | (926) all_833_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (926) implies: % 193.03/27.26 | (927) all_833_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (470), (927) imply: % 193.03/27.26 | (928) all_830_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (928) implies: % 193.03/27.26 | (929) all_830_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (469), (929) imply: % 193.03/27.26 | (930) all_827_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (930) implies: % 193.03/27.26 | (931) all_827_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (893), (931) imply: % 193.03/27.26 | (932) all_824_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (932) implies: % 193.03/27.26 | (933) all_824_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (891), (933) imply: % 193.03/27.26 | (934) all_816_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (934) implies: % 193.03/27.26 | (935) all_816_0 = all_813_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (889), (890) imply: % 193.03/27.26 | (936) all_807_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (936) implies: % 193.03/27.26 | (937) all_807_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (777), (935) imply: % 193.03/27.26 | (938) all_813_0 = all_799_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (776), (935) imply: % 193.03/27.26 | (939) all_813_0 = all_801_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (773), (935) imply: % 193.03/27.26 | (940) all_813_0 = all_810_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (938), (940) imply: % 193.03/27.26 | (941) all_810_0 = all_799_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (939), (940) imply: % 193.03/27.26 | (942) all_810_0 = all_801_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (941), (942) imply: % 193.03/27.26 | (943) all_801_0 = all_799_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (943) implies: % 193.03/27.26 | (944) all_801_0 = all_799_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (698), (937) imply: % 193.03/27.26 | (945) all_801_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (945) implies: % 193.03/27.26 | (946) all_801_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (626), (944) imply: % 193.03/27.26 | (947) all_799_0 = all_793_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (944), (946) imply: % 193.03/27.26 | (948) all_799_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (947), (948) imply: % 193.03/27.26 | (949) all_793_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (949) implies: % 193.03/27.26 | (950) all_793_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (624), (950) imply: % 193.03/27.26 | (951) all_791_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | SIMP: (951) implies: % 193.03/27.26 | (952) all_791_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (941), (948) imply: % 193.03/27.26 | (953) all_810_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (940), (953) imply: % 193.03/27.26 | (954) all_813_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (897), (954) imply: % 193.03/27.26 | (955) all_893_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (871), (955) imply: % 193.03/27.26 | (956) all_969_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (868), (956) imply: % 193.03/27.26 | (957) all_978_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (861), (957) imply: % 193.03/27.26 | (958) all_987_1 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (854), (958) imply: % 193.03/27.26 | (959) all_1005_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (832), (958) imply: % 193.03/27.26 | (960) all_1042_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (712), (960) imply: % 193.03/27.26 | (961) all_1380_0 = all_789_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (649), (761) imply: % 193.03/27.26 | (962) all_1446_4 = all_797_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (595), (761) imply: % 193.03/27.26 | (963) all_1462_1 = all_797_0 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (447), (963) imply: % 193.03/27.26 | (964) c_Power_Opower__class_Opower(all_797_0) = all_1462_0 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (354), (592) imply: % 193.03/27.26 | (965) c_Power_Opower__class_Opower(all_797_0) = all_1276_6 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (343), (761) imply: % 193.03/27.26 | (966) c_Power_Opower__class_Opower(all_797_0) = all_1247_5 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (299), (767) imply: % 193.03/27.26 | (967) c_Power_Opower__class_Opower(all_797_0) = all_1116_3 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (353), (592) imply: % 193.03/27.26 | (968) c_Groups_Otimes__class_Otimes(all_797_0) = all_1276_2 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (342), (761) imply: % 193.03/27.26 | (969) c_Groups_Otimes__class_Otimes(all_797_0) = all_1247_1 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (437), (962) imply: % 193.03/27.26 | (970) c_Groups_Ozero__class_Ozero(all_797_0) = all_1446_3 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (349), (597) imply: % 193.03/27.26 | (971) hAPP(all_1276_5, all_1116_1) = all_1276_3 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (337), (759) imply: % 193.03/27.26 | (972) hAPP(all_1247_4, all_1116_1) = all_1247_2 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (141) with v_p, all_1446_3, all_797_0, simplifying % 193.03/27.26 | with (155), (970) gives: % 193.03/27.26 | (973) all_1446_3 = v_p % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (143) with all_1247_1, all_1276_2, all_797_0, % 193.03/27.26 | simplifying with (968), (969) gives: % 193.03/27.26 | (974) all_1276_2 = all_1247_1 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (144) with all_1276_6, all_1462_0, all_797_0, % 193.03/27.26 | simplifying with (964), (965) gives: % 193.03/27.26 | (975) all_1462_0 = all_1276_6 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (144) with all_1247_5, all_1462_0, all_797_0, % 193.03/27.26 | simplifying with (964), (966) gives: % 193.03/27.26 | (976) all_1462_0 = all_1247_5 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (144) with all_1116_3, all_1462_0, all_797_0, % 193.03/27.26 | simplifying with (964), (967) gives: % 193.03/27.26 | (977) all_1462_0 = all_1116_3 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (975), (977) imply: % 193.03/27.26 | (978) all_1276_6 = all_1116_3 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (975), (976) imply: % 193.03/27.26 | (979) all_1276_6 = all_1247_5 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (978), (979) imply: % 193.03/27.26 | (980) all_1247_5 = all_1116_3 % 193.03/27.26 | % 193.03/27.26 | SIMP: (980) implies: % 193.03/27.26 | (981) all_1247_5 = all_1116_3 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (350), (974) imply: % 193.03/27.26 | (982) hAPP(all_1247_1, v_p) = all_1276_1 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (348), (978) imply: % 193.03/27.26 | (983) hAPP(all_1116_3, v_q) = all_1276_5 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (336), (981) imply: % 193.03/27.26 | (984) hAPP(all_1116_3, v_q) = all_1247_4 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (146) with all_1116_2, all_1276_5, v_q, all_1116_3, % 193.03/27.26 | simplifying with (295), (983) gives: % 193.03/27.26 | (985) all_1276_5 = all_1116_2 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (146) with all_1247_4, all_1276_5, v_q, all_1116_3, % 193.03/27.26 | simplifying with (983), (984) gives: % 193.03/27.26 | (986) all_1276_5 = all_1247_4 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (146) with all_1247_0, all_1276_1, v_p, all_1247_1, % 193.03/27.26 | simplifying with (338), (982) gives: % 193.03/27.26 | (987) all_1276_1 = all_1247_0 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (985), (986) imply: % 193.03/27.26 | (988) all_1247_4 = all_1116_2 % 193.03/27.26 | % 193.03/27.26 | SIMP: (988) implies: % 193.03/27.26 | (989) all_1247_4 = all_1116_2 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (971), (985) imply: % 193.03/27.26 | (990) hAPP(all_1116_2, all_1116_1) = all_1276_3 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (972), (989) imply: % 193.03/27.26 | (991) hAPP(all_1116_2, all_1116_1) = all_1247_2 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (146) with all_1116_0, all_1276_3, all_1116_1, % 193.03/27.26 | all_1116_2, simplifying with (296), (990) gives: % 193.03/27.26 | (992) all_1276_3 = all_1116_0 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (146) with all_1247_2, all_1276_3, all_1116_1, % 193.03/27.26 | all_1116_2, simplifying with (990), (991) gives: % 193.03/27.26 | (993) all_1276_3 = all_1247_2 % 193.03/27.26 | % 193.03/27.26 | COMBINE_EQS: (992), (993) imply: % 193.03/27.26 | (994) all_1247_2 = all_1116_0 % 193.03/27.26 | % 193.03/27.26 | REDUCE: (339), (994) imply: % 193.03/27.26 | (995) hAPP(all_1247_0, v_r____) = all_1116_0 % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (arity_Polynomial__Opoly__Rings_Ozero__neq__one) % 193.03/27.26 | with tc_Complex_Ocomplex, all_797_0, simplifying with (135), % 193.03/27.26 | (140), (156) gives: % 193.03/27.26 | (996) class_Rings_Ozero__neq__one(all_797_0) % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (arity_Polynomial__Opoly__Power_Opower) with % 193.03/27.26 | tc_Complex_Ocomplex, all_797_0, simplifying with (135), (140), % 193.03/27.26 | (156) gives: % 193.03/27.26 | (997) class_Power_Opower(all_797_0) % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating % 193.03/27.26 | (arity_Polynomial__Opoly__Rings_Ono__zero__divisors) with % 193.03/27.26 | tc_Complex_Ocomplex, all_797_0, simplifying with (139), (140), % 193.03/27.26 | (156) gives: % 193.03/27.26 | (998) class_Rings_Ono__zero__divisors(all_797_0) % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (arity_Polynomial__Opoly__Rings_Omult__zero) with % 193.03/27.26 | tc_Complex_Ocomplex, all_797_0, simplifying with (136), (140), % 193.03/27.26 | (156) gives: % 193.03/27.26 | (999) class_Rings_Omult__zero(all_797_0) % 193.03/27.26 | % 193.03/27.26 | GROUND_INST: instantiating (fact_poly__zero) with v_q, tc_Complex_Ocomplex, % 193.03/27.26 | all_1446_5, simplifying with (13), (137), (139), (140), (439) % 193.03/27.26 | gives: % 193.03/27.26 | (1000) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : % 193.03/27.26 | (tc_Polynomial_Opoly(tc_Complex_Ocomplex) = v0 & % 193.03/27.26 | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ (v1 = % 193.03/27.26 | v_q) | v2 = all_1446_5) & (v1 = v_q | ( ~ (v2 = all_1446_5) & % 193.03/27.26 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v1) = v2 & $i(v2)))) % 193.03/27.26 | % 193.03/27.27 | GROUND_INST: instantiating (251) with tc_Complex_Ocomplex, all_797_0, v_p, % 193.03/27.27 | all_1116_1, simplifying with (138), (140), (155), (156), (298) % 193.03/27.27 | gives: % 193.03/27.27 | (1001) all_1116_1 = all_1005_0 % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (fact_mult__poly__0__left) with v_r____, % 193.03/27.27 | tc_Complex_Ocomplex, all_797_0, all_1247_1, v_p, all_1247_0, % 193.03/27.27 | all_1116_0, simplifying with (5), (136), (140), (155), (156), % 193.03/27.27 | (338), (969), (995) gives: % 193.03/27.27 | (1002) all_1116_0 = v_p % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (fact_zero__le__one) with tc_Nat_Onat, all_822_0, % 193.03/27.27 | simplifying with (132), (134), (172) gives: % 193.03/27.27 | (1003) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 193.03/27.27 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, % 193.03/27.27 | all_822_0)) % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (fact_not__one__le__zero) with tc_Nat_Onat, % 193.03/27.27 | all_822_0, simplifying with (132), (134), (172) gives: % 193.03/27.27 | (1004) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 193.03/27.27 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 193.03/27.27 | all_822_0, v0)) % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_Nat_Onat, % 193.03/27.27 | all_822_0, simplifying with (132), (134), (172) gives: % 193.03/27.27 | (1005) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 193.03/27.27 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_822_0, % 193.03/27.27 | v0)) % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (fact_zero__neq__one) with tc_Nat_Onat, all_822_0, % 193.03/27.27 | simplifying with (133), (134), (172) gives: % 193.03/27.27 | (1006) ? [v0: any] : ( ~ (v0 = all_822_0) & % 193.03/27.27 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 193.03/27.27 | % 193.03/27.27 | COMBINE_EQS: (959), (1001) imply: % 193.03/27.27 | (1007) all_1116_1 = all_789_0 % 193.03/27.27 | % 193.03/27.27 | DELTA: instantiating (1005) with fresh symbol all_1540_0 gives: % 193.03/27.27 | (1008) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1540_0 & % 193.03/27.27 | $i(all_1540_0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 193.03/27.27 | all_822_0, all_1540_0) % 193.03/27.27 | % 193.03/27.27 | ALPHA: (1008) implies: % 193.03/27.27 | (1009) $i(all_1540_0) % 193.03/27.27 | (1010) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1540_0 % 193.03/27.27 | % 193.03/27.27 | DELTA: instantiating (1004) with fresh symbol all_1542_0 gives: % 193.03/27.27 | (1011) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1542_0 & % 193.03/27.27 | $i(all_1542_0) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 193.03/27.27 | all_822_0, all_1542_0) % 193.03/27.27 | % 193.03/27.27 | ALPHA: (1011) implies: % 193.03/27.27 | (1012) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1542_0 % 193.03/27.27 | % 193.03/27.27 | DELTA: instantiating (1003) with fresh symbol all_1544_0 gives: % 193.03/27.27 | (1013) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1544_0 & % 193.03/27.27 | $i(all_1544_0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 193.03/27.27 | all_1544_0, all_822_0) % 193.03/27.27 | % 193.03/27.27 | ALPHA: (1013) implies: % 193.03/27.27 | (1014) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1544_0 % 193.03/27.27 | % 193.03/27.27 | DELTA: instantiating (1006) with fresh symbol all_1546_0 gives: % 193.03/27.27 | (1015) ~ (all_1546_0 = all_822_0) & % 193.03/27.27 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1546_0 & % 193.03/27.27 | $i(all_1546_0) % 193.03/27.27 | % 193.03/27.27 | ALPHA: (1015) implies: % 193.03/27.27 | (1016) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1546_0 % 193.03/27.27 | % 193.03/27.27 | DELTA: instantiating (1000) with fresh symbols all_1560_0, all_1560_1, % 193.03/27.27 | all_1560_2 gives: % 193.03/27.27 | (1017) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1560_2 & % 193.03/27.27 | c_Groups_Ozero__class_Ozero(all_1560_2) = all_1560_1 & % 193.03/27.27 | $i(all_1560_1) & $i(all_1560_2) & ( ~ (all_1560_1 = v_q) | % 193.03/27.27 | all_1560_0 = all_1446_5) & (all_1560_1 = v_q | ( ~ (all_1560_0 = % 193.03/27.27 | all_1446_5) & c_Polynomial_Opoly(tc_Complex_Ocomplex, % 193.03/27.27 | all_1560_1) = all_1560_0 & $i(all_1560_0))) % 193.03/27.27 | % 193.03/27.27 | ALPHA: (1017) implies: % 193.03/27.27 | (1018) $i(all_1560_2) % 193.03/27.27 | (1019) c_Groups_Ozero__class_Ozero(all_1560_2) = all_1560_1 % 193.03/27.27 | (1020) tc_Polynomial_Opoly(tc_Complex_Ocomplex) = all_1560_2 % 193.03/27.27 | % 193.03/27.27 | REDUCE: (296), (1002), (1007) imply: % 193.03/27.27 | (1021) hAPP(all_1116_2, all_789_0) = v_p % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (141) with all_1542_0, all_1544_0, tc_Nat_Onat, % 193.03/27.27 | simplifying with (1012), (1014) gives: % 193.03/27.27 | (1022) all_1544_0 = all_1542_0 % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (141) with all_1540_0, all_1544_0, tc_Nat_Onat, % 193.03/27.27 | simplifying with (1010), (1014) gives: % 193.03/27.27 | (1023) all_1544_0 = all_1540_0 % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (141) with all_789_0, all_1546_0, tc_Nat_Onat, % 193.03/27.27 | simplifying with (149), (1016) gives: % 193.03/27.27 | (1024) all_1546_0 = all_789_0 % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (141) with all_1542_0, all_1546_0, tc_Nat_Onat, % 193.03/27.27 | simplifying with (1012), (1016) gives: % 193.03/27.27 | (1025) all_1546_0 = all_1542_0 % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (142) with all_797_0, all_1560_2, % 193.03/27.27 | tc_Complex_Ocomplex, simplifying with (156), (1020) gives: % 193.03/27.27 | (1026) all_1560_2 = all_797_0 % 193.03/27.27 | % 193.03/27.27 | COMBINE_EQS: (1024), (1025) imply: % 193.03/27.27 | (1027) all_1542_0 = all_789_0 % 193.03/27.27 | % 193.03/27.27 | SIMP: (1027) implies: % 193.03/27.27 | (1028) all_1542_0 = all_789_0 % 193.03/27.27 | % 193.03/27.27 | COMBINE_EQS: (1022), (1023) imply: % 193.03/27.27 | (1029) all_1542_0 = all_1540_0 % 193.03/27.27 | % 193.03/27.27 | SIMP: (1029) implies: % 193.03/27.27 | (1030) all_1542_0 = all_1540_0 % 193.03/27.27 | % 193.03/27.27 | COMBINE_EQS: (1028), (1030) imply: % 193.03/27.27 | (1031) all_1540_0 = all_789_0 % 193.03/27.27 | % 193.03/27.27 | REDUCE: (1019), (1026) imply: % 193.03/27.27 | (1032) c_Groups_Ozero__class_Ozero(all_797_0) = all_1560_1 % 193.03/27.27 | % 193.03/27.27 | REDUCE: (1018), (1026) imply: % 193.03/27.27 | (1033) $i(all_797_0) % 193.03/27.27 | % 193.03/27.27 | REDUCE: (1009), (1031) imply: % 193.03/27.27 | (1034) $i(all_789_0) % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (141) with v_p, all_1560_1, all_797_0, simplifying % 193.03/27.27 | with (155), (1032) gives: % 193.03/27.27 | (1035) all_1560_1 = v_p % 193.03/27.27 | % 193.03/27.27 | GROUND_INST: instantiating (396) with all_789_0, v_q, all_797_0, all_1116_3, % 193.03/27.27 | all_1116_2, v_p, simplifying with (13), (295), (967), (996), % 193.03/27.27 | (997), (998), (999), (1021), (1033), (1034) gives: % 193.03/27.27 | (1036) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(all_797_0) = v0 & $i(v0) % 193.03/27.27 | & ( ~ (v0 = v_q) | all_1380_0 = all_789_0 | v_q = v_p) & ( ~ (v0 = % 193.03/27.27 | v_p) | (v_q = v_p & ~ (all_1380_0 = all_789_0)))) % 193.03/27.27 | % 193.03/27.27 | DELTA: instantiating (1036) with fresh symbol all_1704_0 gives: % 193.03/27.27 | (1037) c_Groups_Ozero__class_Ozero(all_797_0) = all_1704_0 & $i(all_1704_0) % 193.03/27.27 | & ( ~ (all_1704_0 = v_q) | all_1380_0 = all_789_0 | v_q = v_p) & ( ~ % 193.03/27.27 | (all_1704_0 = v_p) | (v_q = v_p & ~ (all_1380_0 = all_789_0))) % 193.03/27.27 | % 193.03/27.27 | ALPHA: (1037) implies: % 193.03/27.27 | (1038) c_Groups_Ozero__class_Ozero(all_797_0) = all_1704_0 % 193.03/27.27 | (1039) ~ (all_1704_0 = v_p) | (v_q = v_p & ~ (all_1380_0 = all_789_0)) % 193.03/27.27 | % 193.03/27.27 | BETA: splitting (1039) gives: % 193.03/27.27 | % 193.03/27.27 | Case 1: % 193.03/27.27 | | % 193.03/27.27 | | (1040) ~ (all_1704_0 = v_p) % 193.03/27.27 | | % 193.03/27.27 | | GROUND_INST: instantiating (141) with v_p, all_1704_0, all_797_0, % 193.03/27.27 | | simplifying with (155), (1038) gives: % 193.03/27.27 | | (1041) all_1704_0 = v_p % 193.03/27.27 | | % 193.03/27.27 | | REDUCE: (1040), (1041) imply: % 193.03/27.27 | | (1042) $false % 193.03/27.27 | | % 193.03/27.27 | | CLOSE: (1042) is inconsistent. % 193.03/27.27 | | % 193.03/27.27 | Case 2: % 193.03/27.27 | | % 193.03/27.27 | | (1043) v_q = v_p & ~ (all_1380_0 = all_789_0) % 193.03/27.27 | | % 193.03/27.27 | | ALPHA: (1043) implies: % 193.03/27.27 | | (1044) ~ (all_1380_0 = all_789_0) % 193.03/27.27 | | % 193.03/27.27 | | REDUCE: (961), (1044) imply: % 193.03/27.27 | | (1045) $false % 193.03/27.27 | | % 193.03/27.27 | | CLOSE: (1045) is inconsistent. % 193.03/27.27 | | % 193.03/27.27 | End of split % 193.03/27.27 | % 193.03/27.27 End of proof % 193.03/27.27 % SZS output end Proof for theBenchmark % 193.03/27.27 % 193.03/27.27 26655ms %------------------------------------------------------------------------------