%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW288+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 : n013.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 00:49:43 EDT 2023 % Result : Theorem 62.46s 9.95s % Output : Proof 183.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWW288+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 : n013.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 17:54:32 EDT 2023 % 0.15/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 18.04/3.49 Prover 1: Preprocessing ... % 18.04/3.60 Prover 5: Preprocessing ... % 18.04/3.62 Prover 2: Preprocessing ... % 18.04/3.62 Prover 3: Preprocessing ... % 21.21/3.92 Prover 4: Preprocessing ... % 21.21/3.96 Prover 0: Preprocessing ... % 21.21/3.98 Prover 6: Preprocessing ... % 49.51/8.06 Prover 1: Warning: ignoring some quantifiers % 50.81/8.30 Prover 3: Warning: ignoring some quantifiers % 51.73/8.43 Prover 1: Constructing countermodel ... % 51.73/8.44 Prover 3: Constructing countermodel ... % 55.70/8.96 Prover 6: Proving ... % 58.51/9.39 Prover 4: Warning: ignoring some quantifiers % 62.46/9.94 Prover 3: proved (9292ms) % 62.46/9.95 % 62.46/9.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 62.46/9.95 % 62.58/9.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 62.58/9.97 Prover 4: Constructing countermodel ... % 63.98/10.22 Prover 6: stopped % 63.98/10.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 65.24/10.34 Prover 5: Proving ... % 65.24/10.34 Prover 5: stopped % 65.24/10.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 70.53/11.11 Prover 0: Proving ... % 70.53/11.11 Prover 0: stopped % 70.53/11.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 71.04/11.19 Prover 7: Preprocessing ... % 73.11/11.51 Prover 2: Proving ... % 73.11/11.52 Prover 2: stopped % 73.11/11.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 74.00/11.68 Prover 8: Preprocessing ... % 76.70/12.03 Prover 10: Preprocessing ... % 79.90/12.54 Prover 11: Preprocessing ... % 82.89/12.98 Prover 13: Preprocessing ... % 86.68/13.48 Prover 7: Warning: ignoring some quantifiers % 88.22/13.75 Prover 7: Constructing countermodel ... % 89.04/13.87 Prover 8: Warning: ignoring some quantifiers % 89.04/13.91 Prover 10: Warning: ignoring some quantifiers % 90.90/14.10 Prover 8: Constructing countermodel ... % 91.49/14.29 Prover 10: Constructing countermodel ... % 101.36/15.65 Prover 13: Warning: ignoring some quantifiers % 102.52/15.79 Prover 11: Warning: ignoring some quantifiers % 104.05/15.99 Prover 1: stopped % 104.05/16.01 Prover 13: Constructing countermodel ... % 104.05/16.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 104.70/16.09 Prover 11: Constructing countermodel ... % 113.47/17.42 Prover 16: Preprocessing ... % 124.10/18.94 Prover 16: Warning: ignoring some quantifiers % 124.32/19.02 Prover 16: Constructing countermodel ... % 137.33/20.91 Prover 16: stopped % 137.33/20.92 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 137.33/21.00 Prover 13: stopped % 144.57/21.89 Prover 19: Preprocessing ... % 155.51/23.49 Prover 19: Warning: ignoring some quantifiers % 157.05/23.71 Prover 19: Constructing countermodel ... % 159.19/24.01 Prover 19: stopped % 178.21/26.78 Prover 8: Found proof (size 917) % 178.21/26.78 Prover 8: proved (16375ms) % 178.21/26.79 Prover 4: stopped % 178.21/26.79 Prover 11: stopped % 178.21/26.79 Prover 10: stopped % 178.21/26.79 Prover 7: stopped % 178.21/26.79 % 178.21/26.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 178.21/26.79 % 180.38/27.51 % SZS output start Proof for theBenchmark % 180.46/27.55 Assumptions after simplification: % 180.46/27.55 --------------------------------- % 180.46/27.55 % 180.46/27.55 (clrel_Int_Oring__char__0__Groups_Ozero) % 180.46/27.58 ! [v0: $i] : ( ~ (class_Int_Oring__char__0(v0) = 0) | ~ $i(v0) | % 180.46/27.58 class_Groups_Ozero(v0) = 0) % 180.46/27.58 % 180.46/27.58 (conj_0) % 180.46/27.58 $i(tc_Nat_Onat) & $i(v_p) & $i(t_a) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 180.46/27.58 v0) & c_Polynomial_Odegree(t_a, v_p) = v0 & % 180.46/27.58 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)) % 180.46/27.58 % 180.46/27.58 (fact_Nat_Oadd__0__right) % 180.46/27.58 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.58 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 180.46/27.58 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 180.46/27.58 % 180.46/27.58 (fact_One__nat__def) % 180.46/27.58 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.46/27.58 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v0 & % 180.46/27.58 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)) % 180.46/27.58 % 180.46/27.58 (fact_Suc__diff__1) % 180.46/27.59 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.46/27.59 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 180.46/27.59 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.46/27.59 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 180.46/27.59 v1) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : % 180.46/27.59 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v4 & c_Nat_OSuc(v3) % 180.46/27.59 = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v2)))) % 180.46/27.59 % 180.46/27.59 (fact_Suc__neq__Zero) % 180.46/27.59 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.59 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 180.46/27.59 % 180.46/27.59 (fact_Suc__not__Zero) % 180.46/27.59 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.59 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 180.46/27.59 % 180.46/27.59 (fact_Suc__pred) % 180.46/27.59 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 180.46/27.59 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.46/27.59 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 180.46/27.59 v1) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : % 180.46/27.59 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v4 & c_Nat_OSuc(v3) % 180.46/27.59 = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v2)))) % 180.46/27.59 % 180.46/27.59 (fact_Suc__pred_H) % 180.46/27.60 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.46/27.60 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 180.46/27.60 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.46/27.60 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 180.46/27.60 v1) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : % 180.46/27.60 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v4 & c_Nat_OSuc(v3) % 180.46/27.60 = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v2)))) % 180.46/27.60 % 180.46/27.60 (fact_Zero__neq__Suc) % 180.46/27.60 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.60 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 180.46/27.60 % 180.46/27.60 (fact_Zero__not__Suc) % 180.46/27.60 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.60 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 180.46/27.60 % 180.46/27.60 (fact__096_B_Bx_O_Apoly_Ap_Ax_A_061_Apoly_Ap_A_I0_058_058_Ha_J_096) % 180.46/27.60 $i(v_p) & $i(t_a) & ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 180.46/27.60 ? [v4: $i] : (c_Groups_Ozero__class_Ozero(t_a) = v3 & % 180.46/27.60 class_Int_Oring__char__0(t_a) = v0 & class_Rings_Oidom(t_a) = v1 & % 180.46/27.60 c_Polynomial_Opoly(t_a, v_p) = v2 & hAPP(v2, v3) = v4 & $i(v4) & $i(v3) & % 180.46/27.60 $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~ (v1 = 0) | ~ (v0 = 0) | v6 = v4 | % 180.46/27.60 ~ (hAPP(v2, v5) = v6) | ~ $i(v5))) % 180.46/27.60 % 180.46/27.60 (fact__096degree_Ap_A_061_Adegree_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096) % 180.46/27.61 $i(v_p) & $i(t_a) & ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 180.46/27.61 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 180.46/27.61 $i] : (tc_Polynomial_Opoly(t_a) = v6 & c_Polynomial_OpCons(t_a, v5, v7) = v8 % 180.46/27.61 & c_Polynomial_Odegree(t_a, v8) = v9 & c_Polynomial_Odegree(t_a, v_p) = v2 & % 180.46/27.61 c_Groups_Ozero__class_Ozero(v6) = v7 & c_Groups_Ozero__class_Ozero(t_a) = v4 % 180.46/27.61 & class_Int_Oring__char__0(t_a) = v0 & class_Rings_Oidom(t_a) = v1 & % 180.46/27.61 c_Polynomial_Opoly(t_a, v_p) = v3 & hAPP(v3, v4) = v5 & $i(v9) & $i(v8) & % 180.46/27.61 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 % 180.46/27.61 = 0) | v9 = v2)) % 180.46/27.61 % 180.46/27.61 (fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096) % 180.46/27.61 $i(v_p) & $i(t_a) & ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 180.46/27.61 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 180.46/27.61 (tc_Polynomial_Opoly(t_a) = v5 & c_Polynomial_OpCons(t_a, v4, v6) = v7 & % 180.46/27.61 c_Groups_Ozero__class_Ozero(v5) = v6 & c_Groups_Ozero__class_Ozero(t_a) = v3 % 180.46/27.61 & class_Int_Oring__char__0(t_a) = v0 & class_Rings_Oidom(t_a) = v1 & % 180.46/27.61 c_Polynomial_Opoly(t_a, v_p) = v2 & hAPP(v2, v3) = v4 & $i(v7) & $i(v6) & % 180.46/27.61 $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v7 = v_p)) % 180.46/27.61 % 180.46/27.61 (fact_add__eq__if) % 180.46/27.61 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.46/27.61 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 180.46/27.61 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.46/27.61 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | ~ % 180.46/27.61 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 180.46/27.61 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = v5) | ~ $i(v3) | ~ % 180.46/27.61 $i(v2) | ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = % 180.46/27.61 v6 & c_Nat_OSuc(v5) = v6 & $i(v6))) & ! [v2: $i] : ! [v3: $i] : (v3 = % 180.46/27.61 v2 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = v3) | ~ % 180.46/27.61 $i(v2))) % 180.46/27.61 % 180.46/27.61 (fact_add__eq__self__zero) % 180.46/27.61 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.61 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 180.46/27.61 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ $i(v2) | ~ % 180.46/27.61 $i(v1))) % 180.46/27.61 % 180.46/27.61 (fact_add__gr__0) % 180.46/27.62 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.62 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 % 180.46/27.62 | v3 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v3) | % 180.46/27.62 ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v4) | ~ $i(v2) | % 180.46/27.62 ~ $i(v1) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 180.46/27.62 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = v6 & % 180.46/27.62 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v5 & $i(v5))) & ! % 180.46/27.62 [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 180.46/27.62 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v3) | ~ % 180.46/27.62 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v4) | ~ $i(v2) | ~ % 180.46/27.62 $i(v1) | ? [v5: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) % 180.46/27.62 = 0 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v5 & $i(v5)) | % 180.46/27.62 ( ~ (v4 = 0) & ~ (v3 = 0)))) % 180.46/27.62 % 180.46/27.62 (fact_add__is__0) % 180.46/27.62 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.62 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 180.46/27.62 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~ % 180.46/27.62 $i(v1) | (v2 = v0 & v1 = v0)) & ! [v1: $i] : (v1 = v0 | ~ % 180.46/27.62 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1))) % 180.46/27.62 % 180.46/27.62 (fact_add__is__1) % 180.46/27.62 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 180.46/27.62 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.46/27.62 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ % 180.46/27.62 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v4) | ~ $i(v3) | ~ % 180.46/27.62 $i(v2) | (( ~ (v3 = v1) | ~ (v2 = v0)) & ( ~ (v3 = v0) | ~ (v2 = v1)))) % 180.46/27.62 & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 180.46/27.62 v3, v2) = v1) | ~ $i(v3) | ~ $i(v2) | (v3 = v1 & v2 = v0) | (v3 = v0 % 180.46/27.62 & v2 = v1))) % 180.46/27.62 % 180.46/27.62 (fact_bool_Osize_I1_J) % 180.46/27.63 $i(c_fTrue) & $i(tc_Nat_Onat) & ? [v0: $i] : % 180.46/27.63 (c_HOL_Obool_Obool__size(c_fTrue) = v0 & % 180.46/27.63 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 180.46/27.63 % 180.46/27.63 (fact_bool_Osize_I2_J) % 180.46/27.63 $i(c_fFalse) & $i(tc_Nat_Onat) & ? [v0: $i] : % 180.46/27.63 (c_HOL_Obool_Obool__size(c_fFalse) = v0 & % 180.46/27.63 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 180.46/27.63 % 180.46/27.63 (fact_bool_Osize_I3_J) % 180.46/27.63 $i(tc_HOL_Obool) & $i(c_fTrue) & $i(tc_Nat_Onat) & ? [v0: $i] : % 180.46/27.63 (c_Nat_Osize__class_Osize(tc_HOL_Obool, c_fTrue) = v0 & % 180.46/27.63 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 180.46/27.63 % 180.46/27.63 (fact_bool_Osize_I4_J) % 180.46/27.63 $i(tc_HOL_Obool) & $i(c_fFalse) & $i(tc_Nat_Onat) & ? [v0: $i] : % 180.46/27.63 (c_Nat_Osize__class_Osize(tc_HOL_Obool, c_fFalse) = v0 & % 180.46/27.63 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 180.46/27.63 % 180.46/27.63 (fact_char__size) % 180.46/27.63 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.63 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 180.46/27.63 (c_String_Ochar_Ochar__size(v1) = v2) | ~ $i(v1))) % 180.46/27.63 % 180.46/27.63 (fact_coeff__1) % 180.46/27.63 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.63 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.46/27.63 $i] : ! [v6: $i] : ( ~ (c_Groups_Oone__class_Oone(v3) = v4) | ~ % 180.46/27.63 (c_Polynomial_Ocoeff(v2, v4) = v5) | ~ (tc_Polynomial_Opoly(v2) = v3) | % 180.46/27.63 ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ? [v7: any] : ? [v8: $i] % 180.46/27.63 : ? [v9: $i] : (c_Groups_Oone__class_Oone(v2) = v8 & % 180.46/27.63 class_Rings_Ocomm__semiring__1(v2) = v7 & % 180.46/27.63 c_Groups_Ozero__class_Ozero(v2) = v9 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | % 180.46/27.63 (( ~ (v1 = v0) | v8 = v6) & (v9 = v6 | v1 = v0)))))) % 180.46/27.63 % 180.46/27.63 (fact_coeff__pCons__0) % 180.46/27.63 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.63 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.46/27.63 $i] : ( ~ (c_Polynomial_Ocoeff(v3, v4) = v5) | ~ (c_Polynomial_OpCons(v3, % 180.46/27.63 v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: any] : ? % 180.46/27.63 [v7: $i] : (class_Groups_Ozero(v3) = v6 & hAPP(v5, v0) = v7 & $i(v7) & ( ~ % 180.46/27.63 (v6 = 0) | v7 = v2)))) % 180.46/27.63 % 180.46/27.63 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) % 180.46/27.64 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.64 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 180.46/27.64 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 180.46/27.64 $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 180.46/27.64 (c_Groups_Oone__class_Oone(v2) = v7 & class_Rings_Ocomm__semiring__1(v2) = % 180.46/27.64 v5 & hAPP(v4, v0) = v6 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v7 = v6)))) % 180.46/27.64 % 180.46/27.64 (fact_degree__0) % 180.46/27.64 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.64 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 180.46/27.64 | ~ (tc_Polynomial_Opoly(v1) = v2) | ~ (c_Polynomial_Odegree(v1, v3) = % 180.46/27.64 v4) | ~ (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ? [v5: % 180.46/27.64 int] : ( ~ (v5 = 0) & class_Groups_Ozero(v1) = v5))) % 180.46/27.64 % 180.46/27.64 (fact_degree__1) % 180.46/27.64 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.64 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 180.46/27.64 | ~ (c_Groups_Oone__class_Oone(v2) = v3) | ~ (tc_Polynomial_Opoly(v1) = % 180.46/27.64 v2) | ~ (c_Polynomial_Odegree(v1, v3) = v4) | ~ $i(v1) | ? [v5: int] % 180.46/27.64 : ( ~ (v5 = 0) & class_Rings_Ocomm__semiring__1(v1) = v5))) % 180.46/27.64 % 180.46/27.64 (fact_degree__pCons__0) % 180.46/27.64 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.64 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.46/27.64 $i] : ! [v6: $i] : (v6 = v0 | ~ (tc_Polynomial_Opoly(v2) = v3) | ~ % 180.46/27.64 (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ (c_Polynomial_Odegree(v2, v5) % 180.46/27.64 = v6) | ~ (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ % 180.46/27.64 $i(v1) | ? [v7: int] : ( ~ (v7 = 0) & class_Groups_Ozero(v2) = v7))) % 180.46/27.64 % 180.46/27.64 (fact_degree__pCons__eq__if) % 180.46/27.64 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.64 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.46/27.64 $i] : ( ~ (c_Polynomial_OpCons(v3, v1, v2) = v4) | ~ % 180.46/27.64 (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 180.46/27.64 ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 180.46/27.64 (c_Nat_OSuc(v9) = v10 & tc_Polynomial_Opoly(v3) = v7 & % 180.46/27.64 c_Polynomial_Odegree(v3, v2) = v9 & class_Groups_Ozero(v3) = v6 & % 180.46/27.64 c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v10) & $i(v9) & $i(v8) & % 180.46/27.64 $i(v7) & ( ~ (v6 = 0) | (( ~ (v8 = v2) | v5 = v0) & (v10 = v5 | v8 = % 180.46/27.64 v2)))))) % 180.46/27.64 % 180.46/27.64 (fact_degree__smult__eq) % 180.46/27.65 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.65 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.46/27.65 $i] : ( ~ (c_Polynomial_Osmult(v3, v2, v1) = v4) | ~ % 180.46/27.65 (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 180.46/27.65 ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (c_Polynomial_Odegree(v3, v1) = % 180.46/27.65 v8 & c_Groups_Ozero__class_Ozero(v3) = v7 & class_Rings_Oidom(v3) = v6 & % 180.46/27.65 $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = v2) | v5 = v0) & (v8 = v5 | % 180.46/27.65 v7 = v2)))))) % 180.46/27.65 % 180.46/27.65 (fact_diff__0__eq__0) % 180.46/27.65 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.65 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 180.46/27.65 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 180.46/27.65 % 180.46/27.65 (fact_diff__Suc__less) % 180.46/27.65 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.65 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.46/27.65 int] : (v5 = 0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = % 180.46/27.65 v4) | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) = v5) | ~ % 180.46/27.65 (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: int] : ( ~ (v6 = % 180.46/27.65 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v6))) % 180.46/27.65 % 180.46/27.65 (fact_diff__add__0) % 180.46/27.65 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.65 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 180.46/27.65 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 180.46/27.65 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 180.46/27.65 $i(v1))) % 180.46/27.65 % 180.46/27.65 (fact_diff__is__0__eq) % 180.46/27.65 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.65 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 180.46/27.65 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 180.46/27.65 $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 180.46/27.65 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) = v4)) & ! [v1: % 180.46/27.65 $i] : ! [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 180.46/27.65 v1) = v0) | ~ $i(v2) | ~ $i(v1) | % 180.46/27.65 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) = 0)) % 180.46/27.65 % 180.46/27.65 (fact_diff__is__0__eq_H) % 180.46/27.65 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.65 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 180.46/27.65 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 180.46/27.65 $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 180.46/27.65 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) = v4))) % 180.46/27.65 % 180.46/27.65 (fact_diff__less) % 180.46/27.66 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.66 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 180.46/27.66 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 180.46/27.66 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1) = v4) | ~ $i(v2) | ~ % 180.46/27.66 $i(v1) | ? [v5: any] : ? [v6: any] : % 180.46/27.66 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v5 & % 180.46/27.66 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v6 & ( ~ (v6 = 0) | % 180.46/27.66 ~ (v5 = 0))))) % 180.46/27.66 % 180.46/27.66 (fact_diff__self__eq__0) % 180.46/27.66 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.66 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 180.46/27.66 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ $i(v1))) % 180.46/27.66 % 180.46/27.66 (fact_diffs0__imp__equal) % 180.46/27.66 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.66 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 180.46/27.66 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ $i(v2) | ~ % 180.46/27.66 $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) & % 180.46/27.66 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & $i(v3)))) % 180.46/27.66 % 180.46/27.66 (fact_dvd__1__iff__1) % 180.46/27.66 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 180.46/27.66 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.46/27.66 $i] : (v2 = v1 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1) = 0) | % 180.46/27.66 ~ $i(v2)) & ! [v2: int] : (v2 = 0 | ~ % 180.46/27.66 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v1) = v2))) % 180.46/27.66 % 180.46/27.66 (fact_dvd__1__left) % 180.46/27.66 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 180.46/27.66 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.46/27.66 $i] : ! [v3: int] : (v3 = 0 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 180.46/27.66 v1, v2) = v3) | ~ $i(v2))) % 180.46/27.66 % 180.46/27.66 (fact_dvd__imp__le) % 180.46/27.66 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.46/27.66 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 180.46/27.66 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1) = 0) | ~ $i(v2) | ~ % 180.46/27.66 $i(v1) | ? [v3: any] : ? [v4: any] : % 180.46/27.66 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v3 & % 180.46/27.66 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) = v4 & ( ~ (v3 = % 180.46/27.66 0) | v4 = 0)))) % 180.46/27.66 % 180.46/27.66 (fact_dvd__mult__cancel) % 180.46/27.66 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.46/27.66 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.46/27.66 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.46/27.66 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.46/27.66 : ( ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) = 0) | ~ (hAPP(v5, v3) % 180.46/27.67 = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 180.46/27.67 $i(v3) | ~ $i(v2) | ? [v8: any] : ? [v9: any] : % 180.46/27.67 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = v8 & % 180.46/27.67 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) = v9 & ( ~ (v8 = 0) | v9 = % 180.46/27.67 0)))) % 180.46/27.67 % 180.46/27.67 (fact_dvd__mult__cancel1) % 180.46/27.67 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 180.46/27.67 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 180.46/27.67 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 180.46/27.67 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 180.46/27.67 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~ % 180.46/27.67 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) = v7) | ~ (hAPP(v5, v3) = % 180.46/27.67 v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: int] : ( % 180.46/27.67 ~ (v8 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v8) | % 180.46/27.67 (( ~ (v7 = 0) | v3 = v2) & ( ~ (v3 = v2) | v7 = 0)))) % 180.46/27.67 % 180.46/27.67 (fact_dvd__mult__cancel2) % 180.46/27.67 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 180.46/27.67 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 180.46/27.67 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 180.46/27.67 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 180.46/27.67 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~ % 180.46/27.67 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) = v7) | ~ (hAPP(v5, v4) = % 180.46/27.67 v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: int] : ( % 180.46/27.67 ~ (v8 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v8) | % 180.46/27.67 (( ~ (v7 = 0) | v3 = v2) & ( ~ (v3 = v2) | v7 = 0)))) % 180.46/27.67 % 180.46/27.67 (fact_dvd__pos__nat) % 180.86/27.67 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.67 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 180.86/27.67 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = 0) | ~ % 180.86/27.67 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v3) | ~ $i(v2) | ~ % 180.86/27.67 $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 180.86/27.67 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) = v4))) % 180.86/27.67 % 180.86/27.67 (fact_dvd__power) % 180.86/27.67 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.67 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.86/27.67 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ % 180.86/27.67 (c_Rings_Odvd__class_Odvd(v3, v1, v6) = v7) | ~ % 180.86/27.67 (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v2) = v6) | ~ % 180.86/27.67 (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v8: any] : % 180.86/27.67 ? [v9: any] : ? [v10: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 180.86/27.67 v0, v2) = v9 & c_Groups_Oone__class_Oone(v3) = v10 & % 180.86/27.67 class_Rings_Ocomm__semiring__1(v3) = v8 & $i(v10) & ( ~ (v8 = 0) | ( ~ % 180.86/27.67 (v10 = v1) & ~ (v9 = 0)))))) % 180.86/27.67 % 180.86/27.67 (fact_gcd__lcm__complete__lattice__nat_Otop__greatest) % 180.86/27.67 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.67 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 180.86/27.67 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 180.86/27.67 % 180.86/27.67 (fact_gr0I) % 180.86/27.68 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.68 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 180.86/27.68 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 180.86/27.68 % 180.86/27.68 (fact_gr0__conv__Suc) % 180.86/27.68 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.68 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 180.86/27.68 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) | ! % 180.86/27.68 [v3: $i] : ( ~ (c_Nat_OSuc(v3) = v1) | ~ $i(v3))) & ! [v1: $i] : ( ~ % 180.86/27.68 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = 0) | ~ $i(v1) | ? % 180.86/27.68 [v2: $i] : (c_Nat_OSuc(v2) = v1 & $i(v2)))) % 180.86/27.68 % 180.86/27.68 (fact_gr__implies__not0) % 180.86/27.68 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.68 & $i(v0) & ! [v1: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 180.86/27.68 v0) = 0) | ~ $i(v1))) % 180.86/27.68 % 180.86/27.68 (fact_l) % 180.86/27.68 $i(v_p) & $i(t_a) & ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 180.86/27.68 (class_Int_Oring__char__0(t_a) = v0 & class_Rings_Oidom(t_a) = v1 & % 180.86/27.68 c_Polynomial_Opoly(t_a, v_p) = v2 & % 180.86/27.68 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a, t_a, v2) = v3 & % 180.86/27.68 $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 180.86/27.68 % 180.86/27.68 (fact_le0) % 180.86/27.68 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.68 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 180.86/27.68 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1) = v2) | ~ % 180.86/27.68 $i(v1))) % 180.86/27.68 % 180.86/27.68 (fact_le__0__eq) % 180.86/27.68 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.68 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~ % 180.86/27.68 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = 0) | ~ $i(v1)) % 180.86/27.68 & ! [v1: int] : (v1 = 0 | ~ % 180.86/27.68 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) = v1))) % 180.86/27.68 % 180.86/27.68 (fact_less__Suc0) % 180.86/27.68 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 180.86/27.68 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.68 $i] : (v2 = v0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = % 180.86/27.68 0) | ~ $i(v2)) & ! [v2: int] : (v2 = 0 | ~ % 180.86/27.68 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v2))) % 180.86/27.68 % 180.86/27.68 (fact_less__Suc__eq__0__disj) % 180.86/27.68 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.68 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 180.86/27.68 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) = v4) | ~ % 180.86/27.68 (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v2 = v0) & ! [v5: % 180.86/27.68 $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v5, v1) = 0) | % 180.86/27.68 ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v2) & c_Nat_OSuc(v5) = v6 & % 180.86/27.68 $i(v6))))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ % 180.86/27.68 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) = 0) | ~ % 180.86/27.68 (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : % 180.86/27.68 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) = 0 & c_Nat_OSuc(v4) = % 180.86/27.68 v2 & $i(v4)))) % 180.86/27.68 % 180.86/27.68 (fact_less__eq__nat_Osimps_I1_J) % 180.86/27.69 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.69 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 180.86/27.69 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1) = v2) | ~ % 180.86/27.69 $i(v1))) % 180.86/27.69 % 180.86/27.69 (fact_less__nat__zero__code) % 180.86/27.69 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.69 & $i(v0) & ! [v1: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 180.86/27.69 v0) = 0) | ~ $i(v1))) % 180.86/27.69 % 180.86/27.69 (fact_less__zeroE) % 180.86/27.69 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.69 & $i(v0) & ! [v1: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 180.86/27.69 v0) = 0) | ~ $i(v1))) % 180.86/27.69 % 180.86/27.69 (fact_minus__nat_Odiff__0) % 180.86/27.69 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.69 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 180.86/27.69 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 180.86/27.69 % 180.86/27.69 (fact_monom__0) % 180.86/27.69 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.69 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.86/27.69 $i] : ( ~ (tc_Polynomial_Opoly(v2) = v3) | ~ (c_Polynomial_OpCons(v2, v1, % 180.86/27.69 v4) = v5) | ~ (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ % 180.86/27.69 $i(v1) | ? [v6: any] : ? [v7: $i] : (c_Polynomial_Omonom(v2, v1, v0) = % 180.86/27.69 v7 & class_Groups_Ozero(v2) = v6 & $i(v7) & ( ~ (v6 = 0) | v7 = v5)))) % 180.86/27.69 % 180.86/27.69 (fact_mult__0) % 180.86/27.69 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 180.86/27.69 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.69 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) & % 180.86/27.69 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v2, v3) = % 180.86/27.69 v4) | ~ $i(v3))) % 180.86/27.69 % 180.86/27.69 (fact_mult__0__right) % 180.86/27.69 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.69 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.69 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.69 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = % 180.86/27.69 v1)) % 180.86/27.69 % 180.86/27.69 (fact_mult__cancel1) % 180.86/27.69 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.69 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.69 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.69 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.69 : (v7 = v6 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, % 180.86/27.69 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ( ~ (v4 = v1) & ~ (v3 % 180.86/27.69 = v2))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 180.86/27.69 [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 180.86/27.69 v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 180.86/27.69 % 180.86/27.69 (fact_mult__cancel2) % 180.86/27.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.70 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.70 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.70 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.70 : ! [v8: $i] : (v8 = v6 | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | % 180.86/27.70 ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 180.86/27.70 ~ $i(v2) | ( ~ (v4 = v2) & ~ (v3 = v1))) & ! [v2: $i] : ! [v3: $i] : ! % 180.86/27.70 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v2 | v3 = v1 | ~ % 180.86/27.70 (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 180.86/27.70 (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 180.86/27.70 % 180.86/27.70 (fact_mult__eq__1__iff) % 180.86/27.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 180.86/27.70 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v2 & % 180.86/27.70 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & % 180.86/27.70 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v5, v3) = v2) | ~ % 180.86/27.70 (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | (v4 = v2 & v3 = v2)) & ! % 180.86/27.70 [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(v0, % 180.86/27.70 v2) = v3))) % 180.86/27.70 % 180.86/27.70 (fact_mult__eq__if) % 180.86/27.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 180.86/27.70 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 180.86/27.70 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 180.86/27.70 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 180.86/27.70 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 180.86/27.70 $i] : (v4 = v0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = % 180.86/27.70 v5) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~ % 180.86/27.70 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ? % 180.86/27.70 [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & $i(v9) & $i(v8))) & ! % 180.86/27.70 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v0 | ~ (hAPP(v4, v3) = v5) | % 180.86/27.70 ~ (hAPP(v1, v0) = v4) | ~ $i(v3))) % 180.86/27.70 % 180.86/27.70 (fact_mult__eq__self__implies__10) % 180.86/27.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 180.86/27.70 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 180.86/27.70 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.70 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & % 180.86/27.70 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, % 180.86/27.70 v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 180.86/27.70 % 180.86/27.70 (fact_mult__is__0) % 180.86/27.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.70 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.70 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.70 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~ (hAPP(v4, % 180.86/27.70 v2) = v5) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ( ~ (v3 = % 180.86/27.70 v1) & ~ (v2 = v1))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = % 180.86/27.70 v1 | v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) % 180.86/27.70 | ~ $i(v2))) % 180.86/27.70 % 180.86/27.70 (fact_mult__le__cancel1) % 180.86/27.71 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.71 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.71 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.71 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.71 : ! [v8: int] : (v8 = 0 | ~ % 180.86/27.71 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) = v8) | ~ % 180.86/27.71 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 180.86/27.71 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: int] : ( ~ (v9 = 0) & % 180.86/27.71 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = 0 & % 180.86/27.71 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) = v9)) & ! [v2: % 180.86/27.71 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.71 : ( ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) = 0) | ~ % 180.86/27.71 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 180.86/27.71 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: any] : ? [v9: any] : % 180.86/27.71 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = v8 & % 180.86/27.71 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) = v9 & ( ~ (v8 = % 180.86/27.71 0) | v9 = 0)))) % 180.86/27.71 % 180.86/27.71 (fact_mult__le__cancel2) % 180.86/27.71 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.71 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.71 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.71 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.71 : ! [v8: $i] : ! [v9: int] : (v9 = 0 | ~ % 180.86/27.71 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) = v9) | ~ % 180.86/27.71 (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 180.86/27.71 (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v10: int] : % 180.86/27.71 ( ~ (v10 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = 0 & % 180.86/27.71 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) = v10)) & ! [v2: % 180.86/27.71 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.71 : ! [v8: $i] : ( ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) % 180.86/27.71 = 0) | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, % 180.86/27.71 v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 180.86/27.71 | ? [v9: any] : ? [v10: any] : % 180.86/27.71 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v9 & % 180.86/27.71 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) = v10 & ( ~ (v9 = % 180.86/27.71 0) | v10 = 0)))) % 180.86/27.71 % 180.86/27.71 (fact_mult__less__cancel1) % 180.86/27.71 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.71 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.71 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.71 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.71 : ! [v8: int] : (v8 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 180.86/27.71 v6, v7) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 180.86/27.71 (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : % 180.86/27.71 ? [v10: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = v10 & % 180.86/27.71 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = v9 & ( ~ (v10 = 0) % 180.86/27.71 | ~ (v9 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.86/27.71 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 180.86/27.71 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) = 0) | ~ (hAPP(v5, % 180.86/27.71 v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 180.86/27.71 $i(v4) | ~ $i(v3) | ~ $i(v2) | % 180.86/27.71 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = 0 & % 180.86/27.71 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = 0))) % 180.86/27.71 % 180.86/27.71 (fact_mult__less__cancel2) % 180.86/27.72 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.72 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.72 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.72 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.72 : ! [v8: $i] : ! [v9: int] : (v9 = 0 | ~ % 180.86/27.72 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) = v9) | ~ (hAPP(v7, % 180.86/27.72 v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 180.86/27.72 (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v10: any] : % 180.86/27.72 ? [v11: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) = v11 & % 180.86/27.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v10 & ( ~ (v11 = 0) % 180.86/27.72 | ~ (v10 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.86/27.72 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 180.86/27.72 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) = 0) | ~ (hAPP(v7, % 180.86/27.72 v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 180.86/27.72 (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 180.86/27.72 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) = 0 & % 180.86/27.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = 0))) % 180.86/27.72 % 180.86/27.72 (fact_mult__less__mono1) % 180.86/27.72 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.72 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 180.86/27.72 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.72 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.72 : ! [v8: $i] : ! [v9: int] : (v9 = 0 | ~ % 180.86/27.72 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) = v9) | ~ (hAPP(v7, % 180.86/27.72 v2) = v8) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ % 180.86/27.72 (hAPP(v1, v3) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v10: any] : % 180.86/27.72 ? [v11: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) = v10 & % 180.86/27.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v11 & ( ~ (v11 = 0) % 180.86/27.72 | ~ (v10 = 0))))) % 180.86/27.72 % 180.86/27.72 (fact_mult__less__mono2) % 180.86/27.72 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.72 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 180.86/27.72 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.72 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.72 : ! [v8: int] : (v8 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 180.86/27.72 v6, v7) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ % 180.86/27.72 (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : % 180.86/27.72 ? [v10: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) = v9 & % 180.86/27.72 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v10 & ( ~ (v10 = 0) % 180.86/27.72 | ~ (v9 = 0))))) % 180.86/27.72 % 180.86/27.72 (fact_n__less__m__mult__n) % 180.86/27.72 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 180.86/27.72 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 & % 180.86/27.72 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 180.86/27.72 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = % 180.86/27.72 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) = v7) | ~ % 180.86/27.72 (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ? % 180.86/27.72 [v8: any] : ? [v9: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 180.86/27.72 v4) = v8 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v9 & ( % 180.86/27.72 ~ (v9 = 0) | ~ (v8 = 0))))) % 180.86/27.72 % 180.86/27.72 (fact_n__less__n__mult__m) % 180.86/27.72 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 180.86/27.72 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 & % 180.86/27.72 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 180.86/27.72 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = % 180.86/27.72 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) = v7) | ~ % 180.86/27.72 (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? % 180.86/27.72 [v8: any] : ? [v9: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 180.86/27.72 v4) = v8 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v9 & ( % 180.86/27.72 ~ (v9 = 0) | ~ (v8 = 0))))) % 180.86/27.72 % 180.86/27.72 (fact_nat_Osimps_I2_J) % 180.86/27.72 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.72 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 180.86/27.72 % 180.86/27.72 (fact_nat_Osimps_I3_J) % 180.86/27.72 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.72 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 180.86/27.72 % 180.86/27.72 (fact_nat_Osize_I1_J) % 180.86/27.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Nat_Onat_Onat__size(v0) = v0 & % 180.86/27.73 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 180.86/27.73 % 180.86/27.73 (fact_nat_Osize_I2_J) % 180.86/27.73 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 180.86/27.73 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.73 $i] : ! [v3: $i] : ( ~ (c_Nat_Onat_Onat__size(v2) = v3) | ~ $i(v2) | ? % 180.86/27.73 [v4: $i] : ? [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) % 180.86/27.73 = v5 & c_Nat_Onat_Onat__size(v4) = v5 & c_Nat_OSuc(v2) = v4 & $i(v5) & % 180.86/27.73 $i(v4)))) % 180.86/27.73 % 180.86/27.73 (fact_nat_Osize_I3_J) % 180.86/27.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Nat_Osize__class_Osize(tc_Nat_Onat, v0) = % 180.86/27.73 v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 180.86/27.73 % 180.86/27.73 (fact_nat_Osize_I4_J) % 180.86/27.73 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 180.86/27.73 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.73 $i] : ! [v3: $i] : ( ~ (c_Nat_Osize__class_Osize(tc_Nat_Onat, v2) = v3) | % 180.86/27.73 ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 180.86/27.73 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5 & c_Nat_OSuc(v2) = % 180.86/27.73 v4 & c_Nat_Osize__class_Osize(tc_Nat_Onat, v4) = v5 & $i(v5) & $i(v4)))) % 180.86/27.73 % 180.86/27.73 (fact_nat__0__less__mult__iff) % 180.86/27.73 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.73 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 180.86/27.73 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.73 $i] : ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~ % 180.86/27.73 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v4) | ~ % 180.86/27.73 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v5) | ~ $i(v3) | ~ % 180.86/27.73 $i(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 180.86/27.73 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v7) = v8 & hAPP(v6, v2) = % 180.86/27.73 v7 & hAPP(v1, v3) = v6 & $i(v7) & $i(v6)) | (v5 = 0 & v4 = 0)) & ! [v2: % 180.86/27.73 $i] : ! [v3: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 180.86/27.73 v3) = 0) | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = 0) % 180.86/27.73 | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 180.86/27.73 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = 0 & hAPP(v4, v2) = % 180.86/27.73 v5 & hAPP(v1, v3) = v4 & $i(v5) & $i(v4)))) % 180.86/27.73 % 180.86/27.73 (fact_nat__diff__split) % 180.86/27.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.73 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.86/27.73 $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 180.86/27.73 (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: any] : % 180.86/27.73 ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 180.86/27.73 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v7 & hBOOL(v8) = v9 % 180.86/27.73 & hBOOL(v5) = v6 & hAPP(v3, v0) = v8 & $i(v8) & ( ~ (v6 = 0) | ( ! [v10: % 180.86/27.73 $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v10) = v2) % 180.86/27.73 | ~ $i(v10) | ? [v11: $i] : (hBOOL(v11) = 0 & hAPP(v3, v10) = % 180.86/27.73 v11 & $i(v11))) & ( ~ (v7 = 0) | v9 = 0))))) & ! [v1: $i] : ! % 180.86/27.73 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 180.86/27.73 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 180.86/27.73 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: any] : ? [v7: % 180.86/27.73 $i] : ? [v8: any] : ? [v9: any] : % 180.86/27.73 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v6 & hBOOL(v7) = v8 % 180.86/27.73 & hBOOL(v5) = v9 & hAPP(v3, v0) = v7 & $i(v7) & (v9 = 0 | (v6 = 0 & ~ % 180.86/27.73 (v8 = 0)))) | ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = % 180.86/27.73 0) & hBOOL(v7) = v8 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) % 180.86/27.73 = v2 & hAPP(v3, v6) = v7 & $i(v7) & $i(v6)))) % 180.86/27.73 % 180.86/27.73 (fact_nat__diff__split__asm) % 180.86/27.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.74 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 180.86/27.74 $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 180.86/27.74 (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: any] : % 180.86/27.74 ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 180.86/27.74 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v7 & hBOOL(v8) = v9 % 180.86/27.74 & hBOOL(v5) = v6 & hAPP(v3, v0) = v8 & $i(v8) & ( ~ (v6 = 0) | ( ! [v10: % 180.86/27.74 $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v10) = v2) % 180.86/27.74 | ~ $i(v10) | ? [v11: $i] : (hBOOL(v11) = 0 & hAPP(v3, v10) = % 180.86/27.74 v11 & $i(v11))) & ( ~ (v7 = 0) | v9 = 0))))) & ! [v1: $i] : ! % 180.86/27.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 180.86/27.74 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 180.86/27.74 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: any] : ? [v7: % 180.86/27.74 $i] : ? [v8: any] : ? [v9: any] : % 180.86/27.74 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v6 & hBOOL(v7) = v8 % 180.86/27.74 & hBOOL(v5) = v9 & hAPP(v3, v0) = v7 & $i(v7) & (v9 = 0 | (v6 = 0 & ~ % 180.86/27.74 (v8 = 0)))) | ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = % 180.86/27.74 0) & hBOOL(v7) = v8 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) % 180.86/27.74 = v2 & hAPP(v3, v6) = v7 & $i(v7) & $i(v6)))) % 180.86/27.74 % 180.86/27.74 (fact_nat__dvd__not__less) % 180.86/27.74 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 180.86/27.74 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 180.86/27.74 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) = 0) | ~ $i(v2) | ~ % 180.86/27.74 $i(v1) | ? [v3: any] : ? [v4: any] : % 180.86/27.74 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v4 & % 180.86/27.74 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v3 & ( ~ (v4 = 0) | % 180.86/27.74 ~ (v3 = 0))))) % 180.86/27.74 % 180.86/27.74 (fact_nat__lt__two__imp__zero__or__one) % 180.86/27.74 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 180.86/27.74 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 180.86/27.74 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 180.86/27.74 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = 0) | ~ $i(v3))) % 180.86/27.74 % 180.86/27.74 (fact_nat__mult__dvd__cancel1) % 180.86/27.74 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.74 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 180.86/27.74 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.74 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.74 : ! [v8: any] : ( ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) = v8) | % 180.86/27.74 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | % 180.86/27.74 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : ? [v10: any] : % 180.86/27.74 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v9 & % 180.86/27.74 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) = v10 & ( ~ (v9 = 0) | (( % 180.86/27.74 ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = 0)))))) % 180.86/27.74 % 180.86/27.74 (fact_nat__mult__dvd__cancel__disj) % 180.86/27.74 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.74 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 180.86/27.74 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.74 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.74 : ! [v8: int] : (v8 = 0 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) % 180.86/27.74 = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, % 180.86/27.74 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ( ~ (v4 = v1) & ? % 180.86/27.74 [v9: int] : ( ~ (v9 = 0) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) % 180.86/27.74 = v9))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 180.86/27.74 [v6: $i] : ! [v7: $i] : (v4 = v1 | ~ % 180.86/27.74 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) = 0) | ~ (hAPP(v5, v3) = % 180.86/27.74 v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 180.86/27.74 $i(v3) | ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) = 0)) % 180.86/27.74 % 180.86/27.74 (fact_nat__mult__eq__cancel1) % 180.86/27.74 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 180.86/27.74 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 180.86/27.74 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 180.86/27.74 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 180.86/27.74 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 180.86/27.74 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: int] : ( ~ (v8 = 0) & % 180.86/27.74 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v8) | (( ~ (v7 = % 180.86/27.74 v6) | v3 = v2) & ( ~ (v3 = v2) | v7 = v6)))) % 180.86/27.74 % 180.86/27.74 (fact_nat__mult__eq__cancel__disj) % 181.48/27.74 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.74 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 181.48/27.74 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.74 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.74 : (v7 = v6 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, % 181.48/27.74 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ( ~ (v4 = v1) & ~ (v3 % 181.48/27.74 = v2))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 181.48/27.74 [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 181.48/27.74 v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 181.48/27.74 % 181.48/27.74 (fact_nat__mult__le__cancel1) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.75 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 181.48/27.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.75 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.75 : ! [v8: any] : ( ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) % 181.48/27.75 = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, % 181.48/27.75 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : ? % 181.48/27.75 [v10: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v9 & % 181.48/27.75 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) = v10 & ( ~ (v9 = % 181.48/27.75 0) | (( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = 0)))))) % 181.48/27.75 % 181.48/27.75 (fact_nat__mult__less__cancel1) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.75 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 181.48/27.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.75 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.75 : ! [v8: any] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) = % 181.48/27.75 v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) % 181.48/27.75 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : ? [v10: any] % 181.48/27.75 : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = v10 & % 181.48/27.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v9 & ( ~ (v9 = 0) | % 181.48/27.75 (( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = 0)))))) % 181.48/27.75 % 181.48/27.75 (fact_nat__one__le__power) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.48/27.75 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 & % 181.48/27.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 181.48/27.75 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = % 181.48/27.75 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? % 181.48/27.75 [v8: any] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) = v8 & % 181.48/27.75 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) = v7 & ( ~ (v7 = % 181.48/27.75 0) | v8 = 0)))) % 181.48/27.75 % 181.48/27.75 (fact_nat__power__eq__Suc__0__iff) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.48/27.75 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v2 & % 181.48/27.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & % 181.48/27.75 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | ~ % 181.48/27.75 (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ( ~ % 181.48/27.75 (v4 = v2) & ~ (v3 = v1))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 181.48/27.75 (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ % 181.48/27.75 $i(v4) | ~ $i(v3))) % 181.48/27.75 % 181.48/27.75 (fact_nat__power__less__imp__less) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.75 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 181.48/27.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.75 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.75 : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) = 0) | ~ % 181.48/27.75 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ % 181.48/27.75 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: any] : ? [v9: any] : % 181.48/27.75 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = v9 & % 181.48/27.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v8 & ( ~ (v8 = 0) | % 181.48/27.75 v9 = 0)))) % 181.48/27.75 % 181.48/27.75 (fact_nat__zero__less__power__iff) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.75 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 181.48/27.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.75 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4, % 181.48/27.75 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: % 181.48/27.75 any] : ? [v7: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 181.48/27.75 v5) = v6 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v7 & ( % 181.48/27.75 ~ (v6 = 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 181.48/27.75 [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 181.48/27.75 $i(v2) | ? [v6: any] : ? [v7: any] : % 181.48/27.75 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = v7 & % 181.48/27.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v6 & (v7 = 0 | ( ~ % 181.48/27.75 (v6 = 0) & ~ (v2 = v0)))))) % 181.48/27.75 % 181.48/27.75 (fact_neq0__conv) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.75 & $i(v0) & ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) = 0) & ! % 181.48/27.75 [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 181.48/27.75 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 181.48/27.75 % 181.48/27.75 (fact_not__less0) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.75 & $i(v0) & ! [v1: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 181.48/27.75 v0) = 0) | ~ $i(v1))) % 181.48/27.75 % 181.48/27.75 (fact_one__is__add) % 181.48/27.75 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 181.48/27.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.75 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ % 181.48/27.75 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v4) | ~ $i(v3) | ~ % 181.48/27.75 $i(v2) | (( ~ (v3 = v1) | ~ (v2 = v0)) & ( ~ (v3 = v0) | ~ (v2 = v1)))) % 181.48/27.75 & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 181.48/27.75 v3, v2) = v1) | ~ $i(v3) | ~ $i(v2) | (v3 = v1 & v2 = v0) | (v3 = v0 % 181.48/27.75 & v2 = v1))) % 181.48/27.75 % 181.48/27.75 (fact_one__le__mult__iff) % 181.48/27.76 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.48/27.76 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 & % 181.48/27.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 181.48/27.76 ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ! [v6: any] : ( ~ % 181.48/27.76 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) = v5) | ~ % 181.48/27.76 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) = v6) | ~ $i(v4) % 181.48/27.76 | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & % 181.48/27.76 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v8) = v9 & hAPP(v7, % 181.48/27.76 v3) = v8 & hAPP(v2, v4) = v7 & $i(v8) & $i(v7)) | (v6 = 0 & v5 = 0)) & % 181.48/27.76 ! [v3: $i] : ! [v4: $i] : ( ~ % 181.48/27.76 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) = 0) | ~ % 181.48/27.76 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) = 0) | ~ $i(v4) | % 181.48/27.76 ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : % 181.48/27.76 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) = 0 & hAPP(v5, v3) % 181.48/27.76 = v6 & hAPP(v2, v4) = v5 & $i(v6) & $i(v5)))) % 181.48/27.76 % 181.48/27.76 (fact_one__less__mult) % 181.48/27.76 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.48/27.76 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 & % 181.48/27.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 181.48/27.76 ! [v3: $i] : ! [v4: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 181.48/27.76 v1, v4) = 0) | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) % 181.48/27.76 = 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : % 181.48/27.76 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6) = 0 & hAPP(v5, v4) = % 181.48/27.76 v6 & hAPP(v2, v3) = v5 & $i(v6) & $i(v5)))) % 181.48/27.76 % 181.48/27.76 (fact_one__less__power) % 181.48/27.76 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.76 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.48/27.76 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ % 181.48/27.76 (c_Orderings_Oord__class_Oless(v3, v4, v7) = v8) | ~ % 181.48/27.76 (c_Power_Opower__class_Opower(v3) = v5) | ~ % 181.48/27.76 (c_Groups_Oone__class_Oone(v3) = v4) | ~ (hAPP(v6, v1) = v7) | ~ % 181.48/27.76 (hAPP(v5, v2) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v9: any] : % 181.48/27.76 ? [v10: any] : ? [v11: any] : (c_Orderings_Oord__class_Oless(v3, v4, v2) % 181.48/27.76 = v10 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v11 & % 181.48/27.76 class_Rings_Olinordered__semidom(v3) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) % 181.48/27.76 | ~ (v9 = 0))))) % 181.48/27.76 % 181.48/27.76 (fact_order__root) % 181.48/27.76 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.76 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.48/27.76 $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~ % 181.48/27.76 $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] % 181.48/27.76 : ? [v9: $i] : ? [v10: $i] : (c_Polynomial_Oorder(v3, v1, v2) = v10 & % 181.48/27.76 tc_Polynomial_Opoly(v3) = v8 & c_Groups_Ozero__class_Ozero(v8) = v9 & % 181.48/27.76 c_Groups_Ozero__class_Ozero(v3) = v7 & class_Rings_Oidom(v3) = v6 & % 181.48/27.76 $i(v10) & $i(v9) & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ (v10 = v0) | ~ % 181.48/27.76 (v7 = v5) | v9 = v2) & (v7 = v5 | (v10 = v0 & ~ (v9 = v2)))))))) % 181.48/27.76 % 181.48/27.76 (fact_pCons__eq__0__iff) % 181.48/27.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 181.48/27.76 (c_Polynomial_OpCons(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 181.48/27.76 ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 181.48/27.76 (tc_Polynomial_Opoly(v2) = v5 & class_Groups_Ozero(v2) = v4 & % 181.48/27.76 c_Groups_Ozero__class_Ozero(v5) = v6 & c_Groups_Ozero__class_Ozero(v2) = % 181.48/27.76 v7 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | (( ~ (v7 = v1) | ~ (v6 = % 181.48/27.76 v0) | v3 = v0) & ( ~ (v6 = v3) | (v7 = v1 & v3 = v0)))))) % 181.48/27.76 % 181.48/27.76 (fact_plus__nat_Oadd__0) % 181.48/27.76 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.76 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 181.48/27.76 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 181.48/27.76 % 181.48/27.76 (fact_pow__divides__eq__int) % 181.48/27.76 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.76 (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 & % 181.48/27.76 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.76 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.76 : ! [v8: $i] : ! [v9: any] : (v4 = v0 | ~ % 181.48/27.76 (c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) = v9) | ~ (hAPP(v7, v4) = % 181.48/27.76 v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) % 181.48/27.76 = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v10: any] : % 181.48/27.76 (c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2) = v10 & ( ~ (v10 = 0) | v9 % 181.48/27.76 = 0) & ( ~ (v9 = 0) | v10 = 0)))) % 181.48/27.76 % 181.48/27.76 (fact_pow__divides__eq__nat) % 181.48/27.77 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.77 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 181.48/27.77 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.77 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.77 : ! [v8: $i] : ! [v9: any] : (v4 = v0 | ~ % 181.48/27.77 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) = v9) | ~ (hAPP(v7, v4) = % 181.48/27.77 v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) % 181.48/27.77 = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v10: any] : % 181.48/27.77 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) = v10 & ( ~ (v10 = 0) | v9 % 181.48/27.77 = 0) & ( ~ (v9 = 0) | v10 = 0)))) % 181.48/27.77 % 181.48/27.77 (fact_pow__divides__pow__int) % 181.48/27.77 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.77 (c_Power_Opower__class_Opower(tc_Int_Oint) = v0 & % 181.48/27.77 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.77 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.77 : ! [v8: $i] : (v3 = v1 | ~ (c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) % 181.48/27.77 = 0) | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, % 181.48/27.77 v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 181.48/27.77 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v2) = 0)) % 181.48/27.77 % 181.48/27.77 (fact_pow__divides__pow__nat) % 181.48/27.77 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.77 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 181.48/27.77 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.77 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.77 : ! [v8: $i] : (v3 = v1 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) % 181.48/27.77 = 0) | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, % 181.48/27.77 v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 181.48/27.77 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v2) = 0)) % 181.48/27.77 % 181.48/27.77 (fact_power_Opower_Opower__0) % 181.48/27.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.48/27.77 $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | ~ % 181.48/27.77 (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 181.48/27.77 hAPP(v6, v0) = v3)) % 181.48/27.77 % 181.48/27.77 (fact_power__0) % 181.48/27.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 181.48/27.77 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 181.48/27.77 $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 181.48/27.77 (class_Power_Opower(v2) = v5 & c_Groups_Oone__class_Oone(v2) = v7 & % 181.48/27.77 hAPP(v4, v0) = v6 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v7 = v6)))) % 181.48/27.77 % 181.48/27.77 (fact_power__0__left) % 181.48/27.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.48/27.77 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ % 181.48/27.77 (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | ~ % 181.48/27.77 (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ? [v7: any] : ? [v8: any] % 181.48/27.77 : ? [v9: $i] : (class_Power_Opower(v2) = v7 & % 181.48/27.77 class_Rings_Osemiring__0(v2) = v8 & c_Groups_Oone__class_Oone(v2) = v9 & % 181.48/27.77 $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v1 = v0) | v9 = v6) & (v6 = % 181.48/27.77 v4 | v1 = v0)))))) % 181.48/27.77 % 181.48/27.77 (fact_power__Suc__0) % 181.48/27.77 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 181.48/27.77 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v2 & % 181.48/27.77 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 & $i(v3) & % 181.48/27.77 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ % 181.48/27.77 (hAPP(v3, v4) = v5) | ~ $i(v4))) % 181.48/27.77 % 181.48/27.77 (fact_power__eq__0__iff) % 181.48/27.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.48/27.77 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 181.48/27.77 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 181.48/27.77 $i(v1) | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? % 181.48/27.77 [v11: $i] : (class_Power_Opower(v3) = v7 & class_Rings_Ozero__neq__one(v3) % 181.48/27.77 = v10 & class_Rings_Omult__zero(v3) = v8 & % 181.48/27.77 class_Rings_Ono__zero__divisors(v3) = v9 & % 181.48/27.77 c_Groups_Ozero__class_Ozero(v3) = v11 & $i(v11) & ( ~ (v10 = 0) | ~ (v9 % 181.48/27.77 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v11 = v6) | (v6 = v2 & ~ % 181.48/27.77 (v1 = v0))) & ( ~ (v11 = v2) | v6 = v2 | v1 = v0)))))) % 181.48/27.77 % 181.48/27.77 (fact_power__eq__if) % 181.48/27.77 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 181.48/27.77 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 181.48/27.77 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 181.48/27.77 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 & % 181.48/27.77 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) & % 181.48/27.77 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 181.48/27.77 : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~ % 181.48/27.77 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ (hAPP(v7, % 181.48/27.77 v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = v7) | ~ % 181.48/27.77 (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, v5) = v10 & % 181.48/27.77 $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | ~ % 181.48/27.77 (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4))) % 181.48/27.77 % 181.48/27.77 (fact_power__eq__imp__eq__base) % 181.48/27.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.48/27.78 $i] : (v3 = v1 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = % 181.48/27.78 0) | ~ (c_Orderings_Oord__class_Oless__eq(v4, v5, v3) = 0) | ~ % 181.48/27.78 (c_Orderings_Oord__class_Oless__eq(v4, v5, v1) = 0) | ~ % 181.48/27.78 (c_Groups_Ozero__class_Ozero(v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 181.48/27.78 | ~ $i(v1) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 181.48/27.78 [v10: $i] : ? [v11: $i] : (class_Rings_Olinordered__semidom(v4) = v6 & % 181.48/27.78 c_Power_Opower__class_Opower(v4) = v7 & hAPP(v10, v2) = v11 & hAPP(v8, % 181.48/27.78 v2) = v9 & hAPP(v7, v3) = v8 & hAPP(v7, v1) = v10 & $i(v11) & $i(v10) % 181.48/27.78 & $i(v9) & $i(v8) & $i(v7) & ( ~ (v11 = v9) | ~ (v6 = 0))))) % 181.48/27.78 % 181.48/27.78 (fact_power__strict__mono) % 181.48/27.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.48/27.78 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 181.48/27.78 int] : (v10 = 0 | ~ (c_Orderings_Oord__class_Oless(v4, v7, v9) = v10) | % 181.48/27.78 ~ (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9) | ~ % 181.48/27.78 (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v8) | ~ % 181.48/27.78 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v11: any] : ? [v12: any] % 181.48/27.78 : ? [v13: $i] : ? [v14: any] : ? [v15: any] : % 181.48/27.78 (c_Orderings_Oord__class_Oless(v4, v3, v2) = v12 & % 181.48/27.78 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v15 & % 181.48/27.78 class_Rings_Olinordered__semidom(v4) = v11 & % 181.48/27.78 c_Orderings_Oord__class_Oless__eq(v4, v13, v3) = v14 & % 181.48/27.78 c_Groups_Ozero__class_Ozero(v4) = v13 & $i(v13) & ( ~ (v15 = 0) | ~ % 181.48/27.78 (v14 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) % 181.48/27.78 % 181.48/27.78 (fact_psize__def) % 181.48/27.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 181.48/27.78 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | ~ % 181.48/27.78 $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 181.48/27.78 $i] : ? [v8: $i] : (c_Nat_OSuc(v7) = v8 & tc_Polynomial_Opoly(v2) = v5 % 181.48/27.78 & c_Polynomial_Odegree(v2, v1) = v7 & class_Groups_Ozero(v2) = v4 & % 181.48/27.78 c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) % 181.48/27.78 & ( ~ (v4 = 0) | (( ~ (v6 = v1) | v3 = v0) & (v8 = v3 | v6 = v1)))))) % 181.48/27.78 % 181.48/27.78 (fact_psize__eq__0__iff) % 181.48/27.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 181.48/27.78 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | ~ % 181.48/27.78 $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 181.48/27.78 (tc_Polynomial_Opoly(v2) = v5 & class_Groups_Ozero(v2) = v4 & % 181.48/27.78 c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | % 181.48/27.78 (( ~ (v6 = v1) | v3 = v0) & ( ~ (v3 = v0) | v6 = v1)))))) % 181.48/27.78 % 181.48/27.78 (fact_realpow__minus__mult) % 181.48/27.78 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.78 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 181.48/27.78 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.78 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.78 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 181.48/27.78 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~ % 181.48/27.78 (c_Power_Opower__class_Opower(v4) = v6) | ~ % 181.48/27.78 (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = v11) | ~ % 181.48/27.78 (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v9) = v10) | % 181.48/27.78 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v12: any] : ? [v13: any] : ? % 181.48/27.78 [v14: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v13 & % 181.48/27.78 class_Groups_Omonoid__mult(v4) = v12 & hAPP(v7, v3) = v14 & $i(v14) & ( % 181.48/27.78 ~ (v13 = 0) | ~ (v12 = 0) | v14 = v11)))) % 181.48/27.78 % 181.48/27.78 (fact_realpow__num__eq__if) % 181.48/27.78 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.78 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 181.48/27.78 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.78 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 181.48/27.78 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 181.48/27.78 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~ % 181.48/27.78 (c_Power_Opower__class_Opower(v4) = v5) | ~ % 181.48/27.78 (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ (hAPP(v8, v10) = v11) | ~ % 181.48/27.78 (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ (hAPP(v5, v2) = v6) | % 181.48/27.78 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v12: any] : ? [v13: $i] : ? [v14: % 181.48/27.78 $i] : (class_Power_Opower(v4) = v12 & c_Groups_Oone__class_Oone(v4) = % 181.48/27.78 v14 & hAPP(v6, v3) = v13 & $i(v14) & $i(v13) & ( ~ (v12 = 0) | (( ~ (v3 % 181.48/27.78 = v0) | v14 = v13) & (v13 = v11 | v3 = v0)))))) % 181.48/27.78 % 181.48/27.78 (fact_realpow__two__diff) % 181.48/27.78 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 181.48/27.78 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 181.48/27.78 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 181.48/27.78 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: % 181.48/27.78 $i] : ( ~ (c_Groups_Ominus__class_Ominus(v5, v8, v10) = v11) | ~ % 181.48/27.78 (c_Power_Opower__class_Opower(v5) = v6) | ~ (hAPP(v9, v2) = v10) | ~ % 181.48/27.78 (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, v3) = v9) | ~ % 181.48/27.78 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: any] : ? [v13: $i] : ? [v14: % 181.48/27.78 $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : % 181.48/27.78 (c_Groups_Ominus__class_Ominus(v5, v4, v3) = v14 & % 181.48/27.78 class_Rings_Ocomm__ring__1(v5) = v12 & c_Groups_Otimes__class_Otimes(v5) % 181.48/27.78 = v13 & c_Groups_Oplus__class_Oplus(v5, v4, v3) = v16 & hAPP(v15, v16) = % 181.48/27.78 v17 & hAPP(v13, v14) = v15 & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 181.48/27.78 $i(v13) & ( ~ (v12 = 0) | v17 = v11)))) % 181.48/27.78 % 181.48/27.78 (fact_realpow__two__disj) % 181.48/27.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 181.48/27.79 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 181.48/27.79 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 181.48/27.79 $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v5) = % 181.48/27.79 v6) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ % 181.48/27.79 $i(v4) | ~ $i(v3) | ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 181.48/27.79 $i] : (c_Groups_Ouminus__class_Ouminus(v5, v3) = v12 & % 181.48/27.79 class_Rings_Oidom(v5) = v9 & hAPP(v8, v2) = v11 & hAPP(v7, v2) = v10 & % 181.48/27.79 $i(v12) & $i(v11) & $i(v10) & ( ~ (v9 = 0) | (( ~ (v11 = v10) | v12 = v4 % 181.48/27.79 | v4 = v3) & (v11 = v10 | ( ~ (v12 = v4) & ~ (v4 = v3)))))))) % 181.48/27.79 % 181.48/27.79 (fact_size__char) % 181.48/27.79 $i(tc_String_Ochar) & $i(tc_Nat_Onat) & ? [v0: $i] : % 181.48/27.79 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! % 181.48/27.79 [v2: $i] : (v2 = v0 | ~ (c_Nat_Osize__class_Osize(tc_String_Ochar, v1) = % 181.48/27.79 v2) | ~ $i(v1))) % 181.48/27.79 % 181.48/27.79 (fact_size__literal__def) % 181.48/27.79 $i(tc_String_Oliteral) & $i(tc_Nat_Onat) & ? [v0: $i] : % 181.48/27.79 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! % 181.48/27.79 [v2: $i] : (v2 = v0 | ~ (c_Nat_Osize__class_Osize(tc_String_Oliteral, v1) = % 181.48/27.79 v2) | ~ $i(v1))) % 181.48/27.79 % 181.48/27.79 (fact_synthetic__div__eq__0__iff) % 181.48/27.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 181.48/27.79 (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 181.48/27.79 ~ $i(v1) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 181.48/27.79 (tc_Polynomial_Opoly(v3) = v6 & class_Rings_Ocomm__semiring__0(v3) = v5 & % 181.48/27.79 c_Polynomial_Odegree(v3, v2) = v8 & c_Groups_Ozero__class_Ozero(v6) = v7 % 181.48/27.79 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v8 = v0) | v7 = v4) & % 181.48/27.79 ( ~ (v7 = v4) | v8 = v0)))))) % 181.48/27.79 % 181.48/27.79 (fact_th) % 181.48/27.79 $i(v_p) & $i(t_a) & ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 181.48/27.79 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 181.48/27.79 (tc_Polynomial_Opoly(t_a) = v5 & c_Polynomial_OpCons(t_a, v4, v6) = v7 & % 181.48/27.79 c_Groups_Ozero__class_Ozero(v5) = v6 & c_Groups_Ozero__class_Ozero(t_a) = v3 % 181.48/27.79 & class_Int_Oring__char__0(t_a) = v0 & class_Rings_Oidom(t_a) = v1 & % 181.48/27.79 c_Polynomial_Opoly(t_a, v7) = v8 & c_Polynomial_Opoly(t_a, v_p) = v2 & % 181.48/27.79 hAPP(v2, v3) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 181.48/27.79 $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v8 = v2)) % 181.48/27.79 % 181.48/27.79 (fact_zero__less__Suc) % 181.48/27.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) % 181.48/27.79 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = 0)) % 181.48/27.79 % 181.48/27.79 (fact_zero__less__diff) % 181.48/27.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 181.48/27.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 181.48/27.79 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 181.48/27.79 $i(v1) | ? [v4: any] : ? [v5: any] : % 181.48/27.79 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) = v5 & % 181.48/27.79 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v4 & ( ~ (v4 = 0) | % 181.48/27.79 v5 = 0))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 181.48/27.79 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 181.48/27.79 $i(v1) | ? [v4: any] : ? [v5: any] : % 181.48/27.79 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) = v4 & % 181.48/27.79 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v5 & ( ~ (v4 = 0) | % 181.48/27.79 v5 = 0)))) % 181.48/27.79 % 181.48/27.79 (fact_zero__less__power__nat__eq) % 181.48/27.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 181.48/27.79 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 181.48/27.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 181.48/27.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4, % 181.48/27.79 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: % 181.48/27.79 any] : ? [v7: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 181.48/27.79 v5) = v6 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v7 & ( % 181.48/27.79 ~ (v6 = 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 181.48/27.79 [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 181.48/27.79 $i(v2) | ? [v6: any] : ? [v7: any] : % 181.48/27.79 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = v7 & % 181.48/27.79 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v6 & (v7 = 0 | ( ~ % 181.48/27.79 (v6 = 0) & ~ (v2 = v0)))))) % 181.48/27.79 % 181.48/27.79 (tfree_0) % 181.48/27.79 class_Int_Oring__char__0(t_a) = 0 & $i(t_a) % 181.48/27.79 % 181.48/27.79 (tfree_1) % 181.48/27.79 class_Rings_Oidom(t_a) = 0 & $i(t_a) % 181.48/27.79 % 181.48/27.79 (function-axioms) % 181.77/27.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 181.77/27.82 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Polynomial_Opdivmod__rel(v6, v5, v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Polynomial_Opdivmod__rel(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! % 181.77/27.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 181.77/27.82 : (v1 = v0 | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Polynomial_Opoly__rec(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 181.77/27.82 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_If(v5, v4, v3, v2) = v1) | ~ (c_If(v5, v4, v3, v2) = v0)) & ! [v0: $i] % 181.77/27.82 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 181.77/27.82 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 181.77/27.82 : ! [v4: $i] : (v1 = v0 | ~ (c_Orderings_Oord__class_Oless(v4, v3, v2) = v1) % 181.77/27.82 | ~ (c_Orderings_Oord__class_Oless(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 181.77/27.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Polynomial_Opoly__gcd(v4, v3, v2) = v1) | ~ (c_Polynomial_Opoly__gcd(v4, % 181.77/27.82 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 181.77/27.82 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Rings_Odvd__class_Odvd(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Rings_Odvd__class_Odvd(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 181.77/27.82 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ (c_Power_Opower_Opower(v4, v3, % 181.77/27.82 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 181.77/27.82 [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Opcompose(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Polynomial_Opcompose(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 181.77/27.82 ~ (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 181.77/27.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 181.77/27.82 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 181.77/27.82 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~ (c_Polynomial_Oorder(v4, v3, v2) % 181.77/27.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 181.77/27.82 $i] : (v1 = v0 | ~ (c_Polynomial_Omonom(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Polynomial_Omonom(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 181.77/27.82 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_OpCons(v4, % 181.77/27.82 v3, v2) = v1) | ~ (c_Polynomial_OpCons(v4, v3, v2) = v0)) & ! [v0: $i] % 181.77/27.82 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Polynomial_Osmult(v4, v3, v2) = v1) | ~ (c_Polynomial_Osmult(v4, v3, v2) % 181.77/27.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 181.77/27.82 $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v4, v3, v2) = v1) % 181.77/27.82 | ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v4, v3, v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(v4, v3, v2) = v1) | ~ % 181.77/27.82 (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(v4, v3, v2) = v0)) & % 181.77/27.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Nat__Transfer_Otsub(v3, v2) = v1) | ~ (c_Nat__Transfer_Otsub(v3, v2) = % 181.77/27.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 181.77/27.82 ~ (c_Groups_Ouminus__class_Ouminus(v3, v2) = v1) | ~ % 181.77/27.82 (c_Groups_Ouminus__class_Ouminus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 181.77/27.82 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Polynomial_Ocoeff(v3, v2) = v1) % 181.77/27.82 | ~ (c_Polynomial_Ocoeff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 181.77/27.82 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, % 181.77/27.82 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 181.77/27.82 = v0 | ~ (c_fequal(v3, v2) = v1) | ~ (c_fequal(v3, v2) = v0)) & ! [v0: % 181.77/27.82 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v1) | ~ % 181.77/27.82 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v0)) & ! [v0: % 181.77/27.82 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_Nat_Osize__class_Osize(v3, v2) = v1) | ~ (c_Nat_Osize__class_Osize(v3, % 181.77/27.82 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 181.77/27.82 = v0 | ~ (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, % 181.77/27.82 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 181.77/27.82 = v0 | ~ (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) % 181.77/27.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 181.77/27.82 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Ocancel__comm__monoid__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Ocancel__comm__monoid__add(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Fields_Olinordered__field(v2) = v1) | ~ % 181.77/27.82 (class_Fields_Olinordered__field(v2) = v0)) & ! [v0: MultipleValueBool] : % 181.77/27.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Fields_Olinordered__field__inverse__zero(v2) = v1) | ~ % 181.77/27.82 (class_Fields_Olinordered__field__inverse__zero(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Fields_Ofield__inverse__zero(v2) = v1) | ~ % 181.77/27.82 (class_Fields_Ofield__inverse__zero(v2) = v0)) & ! [v0: MultipleValueBool] % 181.77/27.82 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Odivision__ring__inverse__zero(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Odivision__ring__inverse__zero(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_RealVector_Oreal__normed__field(v2) = v1) | ~ % 181.77/27.82 (class_RealVector_Oreal__normed__field(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Rings_Odivision__ring(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Odivision__ring(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Olinordered__semiring(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__semiring(v2) = v0)) & ! [v0: MultipleValueBool] : % 181.77/27.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Olinordered__semiring__strict(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__semiring__strict(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Rings_Olinordered__comm__semiring__strict(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__comm__semiring__strict(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Ominus(v2) = v1) | ~ (class_Groups_Ominus(v2) = v0)) & ! % 181.77/27.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 181.77/27.82 | ~ (class_Groups_Oordered__cancel__ab__semigroup__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Oordered__cancel__ab__semigroup__add(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Rings_Olinordered__semiring__1__strict(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__semiring__1__strict(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Groups_Ouminus(v2) = v1) | ~ (class_Groups_Ouminus(v2) = v0)) & ! % 181.77/27.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 181.77/27.82 | ~ (class_Lattices_Oab__semigroup__idem__mult(v2) = v1) | ~ % 181.77/27.82 (class_Lattices_Oab__semigroup__idem__mult(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Fields_Ofield(v2) = v1) | ~ (class_Fields_Ofield(v2) = v0)) & ! % 181.77/27.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 181.77/27.82 | ~ (class_Rings_Odvd(v2) = v1) | ~ (class_Rings_Odvd(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Lattices_Oboolean__algebra(v2) = v1) | ~ % 181.77/27.82 (class_Lattices_Oboolean__algebra(v2) = v0)) & ! [v0: MultipleValueBool] : % 181.77/27.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Power_Opower(v2) = v1) | ~ (class_Power_Opower(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Rings_Osemiring__0(v2) = v1) | ~ (class_Rings_Osemiring__0(v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Rings_Oring__1(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Oring__1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 181.77/27.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Olinordered__idom(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__idom(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Olinordered__semidom(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__semidom(v2) = v0)) & ! [v0: MultipleValueBool] : % 181.77/27.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Groups_Omonoid__mult(v2) = v1) | ~ (class_Groups_Omonoid__mult(v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Groups_Ocomm__monoid__mult(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Ocomm__monoid__mult(v2) = v0)) & ! [v0: MultipleValueBool] : % 181.77/27.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Ozero__neq__one(v2) = v1) | ~ (class_Rings_Ozero__neq__one(v2) % 181.77/27.82 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Rings_Oring(v2) = v1) | ~ (class_Rings_Oring(v2) % 181.77/27.82 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Groups_Oordered__ab__group__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Oordered__ab__group__add(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Oone(v2) = v1) | ~ (class_Groups_Oone(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Ogroup__add(v2) = v1) | ~ (class_Groups_Ogroup__add(v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Rings_Ocomm__ring(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Ocomm__ring(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 181.77/27.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Groups_Oab__group__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Oab__group__add(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Oring__1__no__zero__divisors(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Oring__1__no__zero__divisors(v2) = v0)) & ! [v0: $i] : ! [v1: % 181.77/27.82 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Power_Opower__class_Opower(v2) = v1) | % 181.77/27.82 ~ (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Ocomm__ring__1(v2) = v1) | ~ (class_Rings_Ocomm__ring__1(v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Rings_Olinordered__semiring__1(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__semiring__1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 181.77/27.82 : ! [v2: $i] : (v1 = v0 | ~ (c_Groups_Oone__class_Oone(v2) = v1) | ~ % 181.77/27.82 (c_Groups_Oone__class_Oone(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 181.77/27.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_RealVector_Oreal__normed__algebra(v2) = v1) | ~ % 181.77/27.82 (class_RealVector_Oreal__normed__algebra(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Rings_Osemiring(v2) = v1) | ~ (class_Rings_Osemiring(v2) = v0)) & % 181.77/27.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 181.77/27.82 v0 | ~ (class_Rings_Ocomm__semiring(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Ocomm__semiring(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Omult__zero(v2) = v1) | ~ (class_Rings_Omult__zero(v2) = v0)) % 181.77/27.82 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 181.77/27.82 = v0 | ~ (class_Rings_Oring__no__zero__divisors(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Oring__no__zero__divisors(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Rings_Ono__zero__divisors(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Ono__zero__divisors(v2) = v0)) & ! [v0: MultipleValueBool] : % 181.77/27.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Oordered__comm__semiring(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Oordered__comm__semiring(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Rings_Oordered__semiring(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Oordered__semiring(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Oordered__ring(v2) = v1) | ~ (class_Rings_Oordered__ring(v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Rings_Oordered__cancel__semiring(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Oordered__cancel__semiring(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Orderings_Oorder(v2) = v1) | ~ (class_Orderings_Oorder(v2) = v0)) % 181.77/27.82 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 181.77/27.82 = v0 | ~ (class_Orderings_Oord(v2) = v1) | ~ (class_Orderings_Oord(v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Orderings_Olinorder(v2) = v1) | ~ % 181.77/27.82 (class_Orderings_Olinorder(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 181.77/27.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Olinordered__ring(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__ring(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Olinordered__ring__strict(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Olinordered__ring__strict(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Oab__semigroup__mult(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Oab__semigroup__mult(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 181.77/27.82 ! [v2: $i] : (v1 = v0 | ~ (c_Groups_Otimes__class_Otimes(v2) = v1) | ~ % 181.77/27.82 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Rings_Ocomm__semiring__1(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Ocomm__semiring__1(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(v2) % 181.77/27.82 = v1) | ~ % 181.77/27.82 (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(v2) % 181.77/27.82 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Orderings_Opreorder(v2) = v1) | ~ % 181.77/27.82 (class_Orderings_Opreorder(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 181.77/27.82 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Groups_Omonoid__add(v2) = v1) | ~ (class_Groups_Omonoid__add(v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Groups_Ocomm__monoid__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Ocomm__monoid__add(v2) = v0)) & ! [v0: MultipleValueBool] : % 181.77/27.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Groups_Oordered__comm__monoid__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Oordered__comm__monoid__add(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Olinordered__ab__group__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Olinordered__ab__group__add(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Oab__semigroup__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Oab__semigroup__add(v2) = v0)) & ! [v0: MultipleValueBool] : % 181.77/27.82 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Groups_Oordered__ab__semigroup__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Oordered__ab__semigroup__add(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Ocancel__ab__semigroup__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Ocancel__ab__semigroup__add(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Ocancel__semigroup__add(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Ocancel__semigroup__add(v2) = v0)) & ! [v0: % 181.77/27.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 181.77/27.82 ~ (class_Groups_Oordered__ab__semigroup__add__imp__le(v2) = v1) | ~ % 181.77/27.82 (class_Groups_Oordered__ab__semigroup__add__imp__le(v2) = v0)) & ! [v0: $i] % 181.77/27.82 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Nat_Onat_Onat__size(v2) = v1) | % 181.77/27.82 ~ (c_Nat_Onat_Onat__size(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0)) & ! % 181.77/27.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_String_Ochar_Ochar__size(v2) = v1) | ~ (c_String_Ochar_Ochar__size(v2) = % 181.77/27.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (c_HOL_Obool_Obool__size(v2) = v1) | ~ (c_HOL_Obool_Obool__size(v2) = v0)) % 181.77/27.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0)) & ! % 181.77/27.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 181.77/27.82 | ~ (class_Rings_Ocomm__semiring__0(v2) = v1) | ~ % 181.77/27.82 (class_Rings_Ocomm__semiring__0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (class_Groups_Ozero(v2) % 181.77/27.82 = v1) | ~ (class_Groups_Ozero(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 181.77/27.82 [v2: $i] : (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 181.77/27.82 (c_Groups_Ozero__class_Ozero(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 181.77/27.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.82 (class_Int_Oring__char__0(v2) = v1) | ~ (class_Int_Oring__char__0(v2) = % 181.77/27.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 181.77/27.82 $i] : (v1 = v0 | ~ (class_Rings_Oidom(v2) = v1) | ~ (class_Rings_Oidom(v2) % 181.77/27.82 = v0)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 181.77/27.82 $i] : ? [v5: MultipleValueBool] : (c_Polynomial_Opdivmod__rel(v4, v3, v2, % 181.77/27.82 v1, v0) = v5) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 181.77/27.82 [v4: $i] : ? [v5: $i] : (c_Polynomial_Opoly__rec(v4, v3, v2, v1, v0) = v5 & % 181.77/27.82 $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 181.77/27.82 $i] : (c_If(v3, v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : ? [v1: $i] : ? % 181.77/27.82 [v2: $i] : ? [v3: MultipleValueBool] : (c_Orderings_Oord__class_Oless(v2, v1, % 181.77/27.82 v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 181.77/27.82 MultipleValueBool] : (c_Rings_Odvd__class_Odvd(v2, v1, v0) = v3) & ? [v0: % 181.77/27.82 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 181.77/27.82 (c_Orderings_Oord__class_Oless__eq(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: % 181.77/27.82 $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 181.77/27.82 (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(v2, v1, v0) = v3) & ? % 181.77/27.82 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 181.77/27.82 (c_Rings_Oinverse__class_Odivide(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? % 181.77/27.82 [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_Groups_Ominus__class_Ominus(v2, v1, % 181.77/27.82 v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 181.77/27.82 : (c_Polynomial_Opoly__gcd(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: % 181.77/27.82 $i] : ? [v2: $i] : ? [v3: $i] : (c_Power_Opower_Opower(v2, v1, v0) = v3 & % 181.77/27.82 $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 181.77/27.82 (c_Polynomial_Opcompose(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] % 181.77/27.82 : ? [v2: $i] : ? [v3: $i] : (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3 & % 181.77/27.82 $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 181.77/27.82 (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? % 181.77/27.82 [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_Polynomial_Oorder(v2, v1, v0) = v3 & % 181.77/27.82 $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 181.77/27.82 (c_Polynomial_Omonom(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : % 181.77/27.82 ? [v2: $i] : ? [v3: $i] : (c_Polynomial_OpCons(v2, v1, v0) = v3 & $i(v3)) & % 181.77/27.82 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 181.77/27.82 (c_Polynomial_Osmult(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : % 181.77/27.82 ? [v2: $i] : ? [v3: $i] : % 181.77/27.82 (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v2, v1, v0) = v3 & % 181.77/27.82 $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.77/27.82 (c_Nat__Transfer_Otsub(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? % 181.77/27.82 [v2: $i] : (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2 & $i(v2)) & ? [v0: % 181.77/27.82 $i] : ? [v1: $i] : ? [v2: $i] : (c_Polynomial_Ocoeff(v1, v0) = v2 & % 181.77/27.82 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (tc_fun(v1, v0) = v2 & % 181.77/27.82 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_fequal(v1, v0) = v2 & % 181.77/27.82 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.77/27.82 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v2 & $i(v2)) & ? % 181.77/27.82 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_Osize__class_Osize(v1, v0) = v2 % 181.77/27.82 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.77/27.82 (c_Polynomial_Odegree(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? % 181.77/27.82 [v2: $i] : (c_Polynomial_Opoly(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: % 181.77/27.82 $i] : ? [v2: $i] : (hAPP(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Groups_Ocancel__comm__monoid__add(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : (class_Fields_Olinordered__field(v0) = % 181.77/27.82 v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Fields_Olinordered__field__inverse__zero(v0) = v1) & ? [v0: $i] : ? % 181.77/27.82 [v1: MultipleValueBool] : (class_Fields_Ofield__inverse__zero(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Odivision__ring__inverse__zero(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_RealVector_Oreal__normed__field(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : (class_Rings_Odivision__ring(v0) = v1) % 181.77/27.82 & ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Olinordered__semiring(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Rings_Olinordered__semiring__strict(v0) = v1) & % 181.77/27.82 ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Olinordered__comm__semiring__strict(v0) = v1) & ? [v0: $i] : ? % 181.77/27.82 [v1: MultipleValueBool] : (class_Groups_Ominus(v0) = v1) & ? [v0: $i] : ? % 181.77/27.82 [v1: MultipleValueBool] : % 181.77/27.82 (class_Groups_Oordered__cancel__ab__semigroup__add(v0) = v1) & ? [v0: $i] : % 181.77/27.82 ? [v1: MultipleValueBool] : (class_Rings_Olinordered__semiring__1__strict(v0) % 181.77/27.82 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (hBOOL(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : (class_Groups_Ouminus(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Lattices_Oab__semigroup__idem__mult(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Fields_Ofield(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Rings_Odvd(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Lattices_Oboolean__algebra(v0) = v1) & ? [v0: % 181.77/27.82 $i] : ? [v1: MultipleValueBool] : (class_Power_Opower(v0) = v1) & ? [v0: % 181.77/27.82 $i] : ? [v1: MultipleValueBool] : (class_Rings_Osemiring__0(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : (class_Rings_Oring__1(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : (class_Rings_Olinordered__idom(v0) = % 181.77/27.82 v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Olinordered__semidom(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Groups_Omonoid__mult(v0) = v1) & ? [v0: $i] : % 181.77/27.82 ? [v1: MultipleValueBool] : (class_Groups_Ocomm__monoid__mult(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : (class_Rings_Ozero__neq__one(v0) = v1) % 181.77/27.82 & ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Rings_Oring(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Groups_Oordered__ab__group__add(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Groups_Oone(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Groups_Ogroup__add(v0) = v1) & ? [v0: $i] : ? % 181.77/27.82 [v1: MultipleValueBool] : (class_Rings_Ocomm__ring(v0) = v1) & ? [v0: $i] : % 181.77/27.82 ? [v1: MultipleValueBool] : (class_Groups_Oab__group__add(v0) = v1) & ? [v0: % 181.77/27.82 $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Oring__1__no__zero__divisors(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Rings_Ocomm__ring__1(v0) = v1) & ? [v0: $i] : % 181.77/27.82 ? [v1: MultipleValueBool] : (class_Rings_Olinordered__semiring__1(v0) = v1) & % 181.77/27.82 ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_RealVector_Oreal__normed__algebra(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Rings_Osemiring(v0) = v1) & ? [v0: $i] : ? % 181.77/27.82 [v1: MultipleValueBool] : (class_Rings_Ocomm__semiring(v0) = v1) & ? [v0: $i] % 181.77/27.82 : ? [v1: MultipleValueBool] : (class_Rings_Omult__zero(v0) = v1) & ? [v0: % 181.77/27.82 $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Oring__no__zero__divisors(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Rings_Ono__zero__divisors(v0) = v1) & ? [v0: % 181.77/27.82 $i] : ? [v1: MultipleValueBool] : (class_Rings_Oordered__comm__semiring(v0) % 181.77/27.82 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Oordered__semiring(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Rings_Oordered__ring(v0) = v1) & ? [v0: $i] : % 181.77/27.82 ? [v1: MultipleValueBool] : (class_Rings_Oordered__cancel__semiring(v0) = v1) % 181.77/27.82 & ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Orderings_Oorder(v0) = v1) % 181.77/27.82 & ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Orderings_Oord(v0) = v1) & % 181.77/27.82 ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Orderings_Olinorder(v0) = % 181.77/27.82 v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Olinordered__ring(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Rings_Olinordered__ring__strict(v0) = v1) & ? % 181.77/27.82 [v0: $i] : ? [v1: MultipleValueBool] : (class_Groups_Oab__semigroup__mult(v0) % 181.77/27.82 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Rings_Ocomm__semiring__1(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : % 181.77/27.82 (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(v0) = % 181.77/27.82 v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Orderings_Opreorder(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Groups_Omonoid__add(v0) = v1) & ? [v0: $i] : ? % 181.77/27.82 [v1: MultipleValueBool] : (class_Groups_Ocomm__monoid__add(v0) = v1) & ? [v0: % 181.77/27.82 $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Groups_Oordered__comm__monoid__add(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Groups_Olinordered__ab__group__add(v0) = v1) & % 181.77/27.82 ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.82 (class_Groups_Oab__semigroup__add(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.82 MultipleValueBool] : (class_Groups_Oordered__ab__semigroup__add(v0) = v1) & % 181.77/27.82 ? [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.83 (class_Groups_Ocancel__ab__semigroup__add(v0) = v1) & ? [v0: $i] : ? [v1: % 181.77/27.83 MultipleValueBool] : (class_Groups_Ocancel__semigroup__add(v0) = v1) & ? % 181.77/27.83 [v0: $i] : ? [v1: MultipleValueBool] : % 181.77/27.83 (class_Groups_Oordered__ab__semigroup__add__imp__le(v0) = v1) & ? [v0: $i] : % 181.77/27.83 ? [v1: MultipleValueBool] : (class_Rings_Ocomm__semiring__0(v0) = v1) & ? % 181.77/27.83 [v0: $i] : ? [v1: MultipleValueBool] : (class_Groups_Ozero(v0) = v1) & ? % 181.77/27.83 [v0: $i] : ? [v1: MultipleValueBool] : (class_Int_Oring__char__0(v0) = v1) & % 181.77/27.83 ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Rings_Oidom(v0) = v1) & ? % 181.77/27.83 [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(v0) = v1 & $i(v1)) & ? % 181.77/27.83 [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(v0) = v1 & $i(v1)) & ? % 181.77/27.83 [v0: $i] : ? [v1: $i] : (c_Groups_Otimes__class_Otimes(v0) = v1 & $i(v1)) & % 181.77/27.83 ? [v0: $i] : ? [v1: $i] : (c_Nat_Onat_Onat__size(v0) = v1 & $i(v1)) & ? [v0: % 181.77/27.83 $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: % 181.77/27.83 $i] : (c_String_Ochar_Ochar__size(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: % 181.77/27.83 $i] : (c_HOL_Obool_Obool__size(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: % 181.77/27.83 $i] : (tc_Polynomial_Opoly(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 181.77/27.83 (c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1)) % 181.77/27.83 % 181.77/27.83 Further assumptions not needed in the proof: % 181.77/27.83 -------------------------------------------- % 181.77/27.83 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Groups_Ouminus, % 181.77/27.83 arity_HOL__Obool__Lattices_Oboolean__algebra, arity_HOL__Obool__Orderings_Oord, % 181.77/27.83 arity_HOL__Obool__Orderings_Oorder, arity_HOL__Obool__Orderings_Opreorder, % 181.77/27.83 arity_Int__Oint__Groups_Oab__group__add, % 181.77/27.83 arity_Int__Oint__Groups_Oab__semigroup__add, % 181.77/27.83 arity_Int__Oint__Groups_Oab__semigroup__mult, % 181.77/27.83 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, % 181.77/27.83 arity_Int__Oint__Groups_Ocancel__comm__monoid__add, % 181.77/27.83 arity_Int__Oint__Groups_Ocancel__semigroup__add, % 181.77/27.83 arity_Int__Oint__Groups_Ocomm__monoid__add, % 181.77/27.83 arity_Int__Oint__Groups_Ocomm__monoid__mult, % 181.77/27.83 arity_Int__Oint__Groups_Ogroup__add, % 181.77/27.83 arity_Int__Oint__Groups_Olinordered__ab__group__add, % 181.77/27.83 arity_Int__Oint__Groups_Ominus, arity_Int__Oint__Groups_Omonoid__add, % 181.77/27.83 arity_Int__Oint__Groups_Omonoid__mult, arity_Int__Oint__Groups_Oone, % 181.77/27.83 arity_Int__Oint__Groups_Oordered__ab__group__add, % 181.77/27.83 arity_Int__Oint__Groups_Oordered__ab__semigroup__add, % 181.77/27.83 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, % 181.77/27.83 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, % 181.77/27.83 arity_Int__Oint__Groups_Oordered__comm__monoid__add, % 181.77/27.83 arity_Int__Oint__Groups_Ouminus, arity_Int__Oint__Groups_Ozero, % 181.77/27.83 arity_Int__Oint__Int_Oring__char__0, arity_Int__Oint__Orderings_Olinorder, % 181.77/27.83 arity_Int__Oint__Orderings_Oord, arity_Int__Oint__Orderings_Oorder, % 181.77/27.83 arity_Int__Oint__Orderings_Opreorder, arity_Int__Oint__Power_Opower, % 181.77/27.83 arity_Int__Oint__Rings_Ocomm__ring, arity_Int__Oint__Rings_Ocomm__ring__1, % 181.77/27.83 arity_Int__Oint__Rings_Ocomm__semiring, % 181.77/27.83 arity_Int__Oint__Rings_Ocomm__semiring__0, % 181.77/27.83 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Odvd, % 181.77/27.83 arity_Int__Oint__Rings_Oidom, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__idom, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__ring, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__ring__strict, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__semidom, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__semiring, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__semiring__1, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__semiring__1__strict, % 181.77/27.83 arity_Int__Oint__Rings_Olinordered__semiring__strict, % 181.77/27.83 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors, % 181.77/27.83 arity_Int__Oint__Rings_Oordered__cancel__semiring, % 181.77/27.83 arity_Int__Oint__Rings_Oordered__comm__semiring, % 181.77/27.83 arity_Int__Oint__Rings_Oordered__ring, % 181.77/27.83 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring, % 181.77/27.83 arity_Int__Oint__Rings_Oring__1, % 181.77/27.83 arity_Int__Oint__Rings_Oring__1__no__zero__divisors, % 181.77/27.83 arity_Int__Oint__Rings_Oring__no__zero__divisors, % 181.77/27.83 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0, % 181.77/27.83 arity_Int__Oint__Rings_Ozero__neq__one, % 181.77/27.83 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 181.77/27.83 arity_Nat__Onat__Groups_Oab__semigroup__add, % 181.77/27.83 arity_Nat__Onat__Groups_Oab__semigroup__mult, % 181.77/27.83 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, % 181.77/27.83 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, % 181.77/27.83 arity_Nat__Onat__Groups_Ocancel__semigroup__add, % 181.77/27.83 arity_Nat__Onat__Groups_Ocomm__monoid__add, % 181.77/27.83 arity_Nat__Onat__Groups_Ocomm__monoid__mult, arity_Nat__Onat__Groups_Ominus, % 181.77/27.83 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult, % 181.77/27.83 arity_Nat__Onat__Groups_Oone, % 181.77/27.83 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, % 181.77/27.83 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, % 181.77/27.83 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, % 181.77/27.83 arity_Nat__Onat__Groups_Oordered__comm__monoid__add, % 181.77/27.83 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Orderings_Olinorder, % 181.77/27.83 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder, % 181.77/27.83 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Power_Opower, % 181.77/27.83 arity_Nat__Onat__Rings_Ocomm__semiring, % 181.77/27.83 arity_Nat__Onat__Rings_Ocomm__semiring__0, % 181.77/27.83 arity_Nat__Onat__Rings_Ocomm__semiring__1, arity_Nat__Onat__Rings_Odvd, % 181.77/27.83 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, % 181.77/27.83 arity_Nat__Onat__Rings_Olinordered__semidom, % 181.77/27.83 arity_Nat__Onat__Rings_Olinordered__semiring, % 181.77/27.83 arity_Nat__Onat__Rings_Olinordered__semiring__strict, % 181.77/27.83 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors, % 181.77/27.83 arity_Nat__Onat__Rings_Oordered__cancel__semiring, % 181.77/27.83 arity_Nat__Onat__Rings_Oordered__comm__semiring, % 181.77/27.83 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring, % 181.77/27.83 arity_Nat__Onat__Rings_Osemiring__0, arity_Nat__Onat__Rings_Ozero__neq__one, % 181.77/27.83 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oab__group__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oab__semigroup__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Ogroup__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Ominus, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Omonoid__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Omonoid__mult, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oone, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, % 181.77/27.83 arity_Polynomial__Opoly__Groups_Ouminus, arity_Polynomial__Opoly__Groups_Ozero, % 181.77/27.83 arity_Polynomial__Opoly__Int_Oring__char__0, % 181.77/27.83 arity_Polynomial__Opoly__Orderings_Olinorder, % 181.77/27.83 arity_Polynomial__Opoly__Orderings_Oord, % 181.77/27.83 arity_Polynomial__Opoly__Orderings_Oorder, % 181.77/27.83 arity_Polynomial__Opoly__Orderings_Opreorder, % 181.77/27.83 arity_Polynomial__Opoly__Power_Opower, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Ocomm__ring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Ocomm__ring__1, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Ocomm__semiring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Oidom, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__idom, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__ring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__semidom, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__semiring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Omult__zero, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Ono__zero__divisors, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Oordered__ring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Oordered__semiring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Osemiring, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Osemiring__0, % 181.77/27.83 arity_Polynomial__Opoly__Rings_Ozero__neq__one, % 181.77/27.83 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 181.77/27.83 arity_fun__Groups_Ominus, arity_fun__Groups_Ouminus, % 181.77/27.83 arity_fun__Lattices_Oboolean__algebra, arity_fun__Orderings_Oord, % 181.77/27.83 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Oab__group__add, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Oab__semigroup__add, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Ocancel__ab__semigroup__add, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Ocancel__comm__monoid__add, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Ocancel__semigroup__add, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Ocomm__monoid__add, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Ogroup__add, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Ominus, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Omonoid__add, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Omonoid__mult, % 181.77/27.83 clrel_Int_Oring__char__0__Groups_Oone, clrel_Int_Oring__char__0__Groups_Ouminus, % 181.77/27.83 clrel_Int_Oring__char__0__Power_Opower, % 181.77/27.83 clrel_Int_Oring__char__0__Rings_Omult__zero, % 181.77/27.83 clrel_Int_Oring__char__0__Rings_Oring, clrel_Int_Oring__char__0__Rings_Oring__1, % 181.77/27.83 clrel_Int_Oring__char__0__Rings_Osemiring, % 181.77/27.83 clrel_Int_Oring__char__0__Rings_Osemiring__0, % 181.77/27.83 clrel_Int_Oring__char__0__Rings_Ozero__neq__one, % 181.77/27.83 clrel_Rings_Oidom__Groups_Oab__group__add, % 181.77/27.83 clrel_Rings_Oidom__Groups_Oab__semigroup__add, % 181.77/27.83 clrel_Rings_Oidom__Groups_Oab__semigroup__mult, % 181.77/27.83 clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add, % 181.77/27.83 clrel_Rings_Oidom__Groups_Ocancel__comm__monoid__add, % 181.77/27.83 clrel_Rings_Oidom__Groups_Ocancel__semigroup__add, % 181.77/27.83 clrel_Rings_Oidom__Groups_Ocomm__monoid__add, % 181.77/27.83 clrel_Rings_Oidom__Groups_Ocomm__monoid__mult, % 181.77/27.83 clrel_Rings_Oidom__Groups_Ogroup__add, clrel_Rings_Oidom__Groups_Ominus, % 181.77/27.83 clrel_Rings_Oidom__Groups_Omonoid__add, clrel_Rings_Oidom__Groups_Omonoid__mult, % 181.77/27.83 clrel_Rings_Oidom__Groups_Oone, clrel_Rings_Oidom__Groups_Ouminus, % 181.77/27.83 clrel_Rings_Oidom__Groups_Ozero, clrel_Rings_Oidom__Power_Opower, % 181.77/27.83 clrel_Rings_Oidom__Rings_Ocomm__ring, clrel_Rings_Oidom__Rings_Ocomm__ring__1, % 181.77/27.83 clrel_Rings_Oidom__Rings_Ocomm__semiring, % 181.77/27.83 clrel_Rings_Oidom__Rings_Ocomm__semiring__0, % 181.77/27.83 clrel_Rings_Oidom__Rings_Ocomm__semiring__1, clrel_Rings_Oidom__Rings_Odvd, % 181.77/27.83 clrel_Rings_Oidom__Rings_Omult__zero, % 181.77/27.83 clrel_Rings_Oidom__Rings_Ono__zero__divisors, clrel_Rings_Oidom__Rings_Oring, % 181.77/27.83 clrel_Rings_Oidom__Rings_Oring__1, % 181.77/27.83 clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors, % 181.77/27.83 clrel_Rings_Oidom__Rings_Oring__no__zero__divisors, % 181.77/27.83 clrel_Rings_Oidom__Rings_Osemiring, clrel_Rings_Oidom__Rings_Osemiring__0, % 181.77/27.83 clrel_Rings_Oidom__Rings_Ozero__neq__one, % 181.77/27.83 clrel_Rings_Oidom__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 181.77/27.83 fact_Nat_Odiff__diff__eq, % 181.77/27.83 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, % 181.77/27.83 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, % 181.77/27.83 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, % 181.77/27.83 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, % 181.77/27.83 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, % 181.77/27.83 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, % 181.77/27.83 fact_Suc__diff__diff, fact_Suc__diff__le, fact_Suc__eq__plus1, % 181.77/27.83 fact_Suc__eq__plus1__left, fact_Suc__inject, fact_Suc__leD, fact_Suc__leI, % 181.77/27.83 fact_Suc__le__eq, fact_Suc__le__lessD, fact_Suc__le__mono, fact_Suc__lessD, % 181.77/27.83 fact_Suc__lessI, fact_Suc__less__SucD, fact_Suc__less__eq, fact_Suc__mono, % 181.77/27.83 fact_Suc__mult__cancel1, fact_Suc__mult__le__cancel1, % 181.77/27.83 fact_Suc__mult__less__cancel1, fact_Suc__n__not__le__n, fact_Suc__n__not__n, % 181.77/27.83 fact_ab__diff__minus, fact_ab__left__minus, % 181.77/27.83 fact_ab__semigroup__add__class_Oadd__ac_I1_J, % 181.77/27.83 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_add1__zle__eq, % 181.77/27.83 fact_add_Ocomm__neutral, fact_add__0, fact_add__0__iff, fact_add__0__left, % 181.77/27.83 fact_add__0__right, fact_add__Suc, fact_add__Suc__right, fact_add__Suc__shift, % 181.77/27.83 fact_add__diff__assoc, fact_add__diff__assoc2, fact_add__diff__cancel, % 181.77/27.83 fact_add__diff__inverse, fact_add__divide__distrib, fact_add__divide__eq__iff, % 181.77/27.83 fact_add__eq__0__iff, fact_add__frac__eq, fact_add__frac__num, % 181.77/27.83 fact_add__imp__eq, fact_add__increasing, fact_add__increasing2, fact_add__leD1, % 181.77/27.83 fact_add__leD2, fact_add__leE, fact_add__le__cancel__left, % 181.77/27.83 fact_add__le__cancel__right, fact_add__le__imp__le__left, % 181.77/27.83 fact_add__le__imp__le__right, fact_add__le__less__mono, fact_add__le__mono, % 181.77/27.83 fact_add__le__mono1, fact_add__left__cancel, fact_add__left__imp__eq, % 181.77/27.83 fact_add__left__mono, fact_add__lessD1, fact_add__less__cancel__left, % 181.77/27.83 fact_add__less__cancel__right, fact_add__less__imp__less__left, % 181.77/27.83 fact_add__less__imp__less__right, fact_add__less__le__mono, % 181.77/27.83 fact_add__less__mono, fact_add__less__mono1, fact_add__minus__cancel, % 181.77/27.83 fact_add__mono, fact_add__monom, fact_add__mult__distrib, % 181.77/27.83 fact_add__mult__distrib2, fact_add__neg__neg, fact_add__neg__nonpos, % 181.77/27.83 fact_add__nonneg__eq__0__iff, fact_add__nonneg__nonneg, fact_add__nonneg__pos, % 181.77/27.83 fact_add__nonpos__neg, fact_add__nonpos__nonpos, fact_add__num__frac, % 181.77/27.83 fact_add__pCons, fact_add__poly__code_I1_J, fact_add__poly__code_I2_J, % 181.77/27.83 fact_add__pos__nonneg, fact_add__pos__pos, fact_add__right__cancel, % 181.77/27.83 fact_add__right__imp__eq, fact_add__right__mono, fact_add__scale__eq__noteq, % 181.77/27.83 fact_add__strict__increasing, fact_add__strict__increasing2, % 181.77/27.83 fact_add__strict__left__mono, fact_add__strict__mono, % 181.77/27.83 fact_add__strict__right__mono, fact_coeff__0, fact_coeff__add, fact_coeff__diff, % 181.77/27.83 fact_coeff__eq__0, fact_coeff__inject, fact_coeff__linear__power, % 181.77/27.83 fact_coeff__minus, fact_coeff__monom, fact_coeff__mult__degree__sum, % 181.77/27.83 fact_coeff__pCons__Suc, fact_coeff__smult, fact_combine__common__factor, % 181.77/27.83 fact_comm__mult__left__mono, fact_comm__mult__strict__left__mono, % 181.77/27.83 fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, % 181.77/27.83 fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, % 181.77/27.83 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, % 181.77/27.83 fact_comm__semiring__class_Odistrib, fact_compl__eq__compl__iff, % 181.77/27.83 fact_compl__le__compl__iff, fact_compl__mono, fact_constant__def, % 181.77/27.83 fact_convex__bound__le, fact_convex__bound__lt, fact_crossproduct__eq, % 181.77/27.83 fact_crossproduct__noteq, fact_degree__add__eq__left, % 181.77/27.83 fact_degree__add__eq__right, fact_degree__add__le, fact_degree__add__less, % 181.77/27.83 fact_degree__diff__le, fact_degree__diff__less, fact_degree__linear__power, % 181.77/27.83 fact_degree__minus, fact_degree__monom__eq, fact_degree__monom__le, % 181.77/27.83 fact_degree__mult__eq, fact_degree__mult__le, fact_degree__offset__poly, % 181.77/27.83 fact_degree__pCons__eq, fact_degree__pCons__le, fact_degree__pcompose__le, % 181.77/27.83 fact_degree__power__le, fact_degree__smult__le, fact_degree__synthetic__div, % 181.77/27.83 fact_diff__0, fact_diff__0__right, fact_diff__Suc__1, fact_diff__Suc__Suc, % 181.77/27.83 fact_diff__Suc__diff__eq1, fact_diff__Suc__diff__eq2, % 181.77/27.83 fact_diff__Suc__eq__diff__pred, fact_diff__add__assoc, fact_diff__add__assoc2, % 181.77/27.83 fact_diff__add__cancel, fact_diff__add__inverse, fact_diff__add__inverse2, % 181.77/27.83 fact_diff__cancel, fact_diff__cancel2, fact_diff__commute, fact_diff__def, % 181.77/27.83 fact_diff__diff__cancel, fact_diff__diff__left, fact_diff__diff__right, % 181.77/27.83 fact_diff__divide__distrib, fact_diff__divide__eq__iff, fact_diff__eq__diff__eq, % 181.77/27.83 fact_diff__eq__diff__less, fact_diff__eq__diff__less__eq, fact_diff__frac__eq, % 181.77/27.83 fact_diff__int__def, fact_diff__int__def__symmetric, fact_diff__le__mono, % 181.77/27.83 fact_diff__le__mono2, fact_diff__le__self, fact_diff__less__Suc, % 181.77/27.83 fact_diff__less__mono, fact_diff__less__mono2, fact_diff__minus__eq__add, % 181.77/27.83 fact_diff__monom, fact_diff__mult__distrib, fact_diff__mult__distrib2, % 181.77/27.83 fact_diff__pCons, fact_diff__poly__code_I1_J, fact_diff__poly__code_I2_J, % 181.77/27.83 fact_diff__self, fact_divide_Oadd, fact_divide_Odiff, fact_divide_Ominus, % 181.77/27.83 fact_divide_Ozero, fact_divide__1, fact_divide__add__eq__iff, % 181.77/27.83 fact_divide__diff__eq__iff, fact_divide__eq__eq, fact_divide__eq__imp, % 181.77/27.83 fact_divide__le__0__iff, fact_divide__le__eq, fact_divide__left__mono, % 181.77/27.83 fact_divide__left__mono__neg, fact_divide__less__0__iff, fact_divide__less__eq, % 181.77/27.83 fact_divide__neg__neg, fact_divide__neg__pos, fact_divide__nonneg__neg, % 181.77/27.83 fact_divide__nonneg__pos, fact_divide__nonpos__neg, fact_divide__nonpos__pos, % 181.77/27.83 fact_divide__pos__neg, fact_divide__pos__pos, fact_divide__right__mono, % 181.77/27.83 fact_divide__right__mono__neg, fact_divide__self, fact_divide__self__if, % 181.77/27.83 fact_divide__strict__left__mono, fact_divide__strict__left__mono__neg, % 181.77/27.83 fact_divide__strict__right__mono, fact_divide__strict__right__mono__neg, % 181.77/27.83 fact_divide__zero, fact_divide__zero__left, fact_divisors__zero, % 181.77/27.83 fact_double__add__le__zero__iff__single__add__le__zero, % 181.77/27.83 fact_double__add__less__zero__iff__single__add__less__zero, fact_double__compl, % 181.77/27.83 fact_double__eq__0__iff, fact_double__zero__sym, fact_dvdI, fact_dvd_Oantisym, % 181.77/27.83 fact_dvd_Oantisym__conv, fact_dvd_Oeq__iff, fact_dvd_Oeq__refl, % 181.77/27.83 fact_dvd_Ole__imp__less__or__eq, fact_dvd_Ole__less, fact_dvd_Ole__less__trans, % 181.77/27.83 fact_dvd_Ole__neq__trans, fact_dvd_Oless__asym, fact_dvd_Oless__asym_H, % 181.77/27.83 fact_dvd_Oless__imp__le, fact_dvd_Oless__imp__neq, fact_dvd_Oless__imp__not__eq, % 181.77/27.83 fact_dvd_Oless__imp__not__eq2, fact_dvd_Oless__imp__not__less, % 181.77/27.83 fact_dvd_Oless__le, fact_dvd_Oless__le__trans, fact_dvd_Oless__not__sym, % 181.77/27.83 fact_dvd_Oless__trans, fact_dvd_Oneq__le__trans, fact_dvd_Oord__eq__le__trans, % 181.77/27.83 fact_dvd_Oord__eq__less__trans, fact_dvd_Oord__le__eq__trans, % 181.77/27.83 fact_dvd_Oord__less__eq__trans, fact_dvd_Oorder__refl, fact_dvd_Oorder__trans, % 181.77/27.83 fact_dvd__0__left, fact_dvd__0__right, fact_dvd__add, fact_dvd__antisym, % 181.77/27.83 fact_dvd__diff, fact_dvd__diffD, fact_dvd__diffD1, fact_dvd__diff__nat, % 181.77/27.83 fact_dvd__iff__poly__eq__0, fact_dvd__imp__degree__le, fact_dvd__minus__iff, % 181.77/27.83 fact_dvd__mult, fact_dvd__mult2, fact_dvd__mult__cancel__left, % 181.77/27.83 fact_dvd__mult__cancel__right, fact_dvd__mult__left, fact_dvd__mult__right, % 181.77/27.83 fact_dvd__poly__gcd__iff, fact_dvd__power__le, fact_dvd__power__same, % 181.77/27.83 fact_dvd__reduce, fact_dvd__refl, fact_dvd__smult, fact_dvd__smult__cancel, % 181.77/27.83 fact_dvd__smult__iff, fact_dvd__trans, fact_dvd__triv__left, % 181.77/27.83 fact_dvd__triv__right, fact_eq__add__iff1, fact_eq__add__iff2, % 181.77/27.83 fact_eq__diff__iff, fact_eq__divide__eq, fact_eq__divide__imp, % 181.77/27.83 fact_eq__iff__diff__eq__0, fact_eq__imp__le, fact_eq__neg__iff__add__eq__0, % 181.77/27.83 fact_eq__zero__or__degree__less, fact_equal__neg__zero, % 181.77/27.83 fact_equation__minus__iff, fact_even__less__0__iff, fact_expand__poly__eq, % 181.77/27.83 fact_ext, fact_field__power__not__zero, fact_frac__eq__eq, fact_frac__le, % 181.77/27.83 fact_frac__less, fact_frac__less2, % 181.77/27.83 fact_gcd__lcm__complete__lattice__nat_Obot__least, fact_gt__half__sum, % 181.77/27.83 fact_inf__period_I3_J, fact_inf__period_I4_J, fact_int__0__less__1, % 181.77/27.83 fact_int__0__neq__1, fact_int__one__le__iff__zero__less, fact_leD, fact_leI, % 181.77/27.83 fact_le__SucE, fact_le__SucI, fact_le__Suc__eq, fact_le__Suc__ex__iff, % 181.77/27.83 fact_le__add1, fact_le__add2, fact_le__add__diff, fact_le__add__diff__inverse, % 181.77/27.83 fact_le__add__diff__inverse2, fact_le__add__iff1, fact_le__add__iff2, % 181.77/27.83 fact_le__antisym, fact_le__cube, fact_le__degree, fact_le__diff__conv, % 181.77/27.83 fact_le__diff__conv2, fact_le__diff__iff, fact_le__divide__eq, % 181.77/27.83 fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE, fact_le__fun__def, % 181.77/27.83 fact_le__iff__add, fact_le__iff__diff__le__0, fact_le__imp__0__less, % 181.77/27.83 fact_le__imp__diff__is__add, fact_le__imp__less__Suc, fact_le__imp__neg__le, % 181.77/27.83 fact_le__imp__power__dvd, fact_le__less__Suc__eq, fact_le__minus__iff, % 181.77/27.83 fact_le__minus__self__iff, fact_le__neq__implies__less, fact_le__refl, % 181.77/27.83 fact_le__square, fact_le__trans, fact_leading__coeff__0__iff, % 181.77/27.83 fact_leading__coeff__neq__0, fact_left__add__mult__distrib, fact_left__minus, % 181.77/27.83 fact_lemma__realpow__diff, fact_lessI, fact_less__1__mult, fact_less__SucE, % 181.77/27.83 fact_less__SucI, fact_less__Suc__eq, fact_less__Suc__eq__le, % 181.77/27.83 fact_less__add__Suc1, fact_less__add__Suc2, fact_less__add__eq__less, % 181.77/27.83 fact_less__add__iff1, fact_less__add__iff2, fact_less__add__one, % 181.77/27.83 fact_less__antisym, fact_less__bin__lemma, fact_less__diff__conv, % 181.77/27.83 fact_less__diff__iff, fact_less__divide__eq, fact_less__eq__Suc__le, % 181.77/27.83 fact_less__fun__def, fact_less__half__sum, fact_less__iff__Suc__add, % 181.77/27.83 fact_less__iff__diff__less__0, fact_less__imp__diff__less, % 181.77/27.83 fact_less__imp__le__nat, fact_less__imp__neq, fact_less__irrefl__nat, % 181.77/27.83 fact_less__le__not__le, fact_less__minus__iff, fact_less__minus__self__iff, % 181.77/27.83 fact_less__not__refl, fact_less__not__refl2, fact_less__not__refl3, % 181.77/27.83 fact_less__or__eq__imp__le, fact_less__trans__Suc, fact_lift__Suc__mono__le, % 181.77/27.83 fact_linorder__antisym__conv1, fact_linorder__antisym__conv2, % 181.77/27.83 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases, % 181.77/27.83 fact_linorder__le__less__linear, fact_linorder__less__linear, % 181.77/27.83 fact_linorder__linear, fact_linorder__neqE, % 181.77/27.83 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat, % 181.77/27.83 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less, % 181.77/27.83 fact_minus__add, fact_minus__add__cancel, fact_minus__add__distrib, % 181.77/27.83 fact_minus__apply, fact_minus__diff__eq, fact_minus__divide__divide, % 181.77/27.83 fact_minus__divide__left, fact_minus__divide__right, fact_minus__dvd__iff, % 181.77/27.83 fact_minus__equation__iff, fact_minus__le__iff, fact_minus__le__self__iff, % 181.77/27.83 fact_minus__less__iff, fact_minus__minus, fact_minus__monom, % 181.77/27.83 fact_minus__mult__commute, fact_minus__mult__left, fact_minus__mult__minus, % 181.77/27.83 fact_minus__mult__right, fact_minus__pCons, fact_minus__poly__code_I1_J, % 181.77/27.83 fact_minus__poly__code_I2_J, fact_minus__unique, fact_minus__zero, % 181.77/27.83 fact_monom__Suc, fact_monom__eq__0, fact_monom__eq__0__iff, fact_monom__eq__iff, % 181.77/27.83 fact_mult_Oadd__left, fact_mult_Oadd__right, fact_mult_Ocomm__neutral, % 181.77/27.83 fact_mult_Odiff__left, fact_mult_Odiff__right, fact_mult_Ominus__left, % 181.77/27.83 fact_mult_Ominus__right, fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, % 181.77/27.83 fact_mult_Ozero__right, fact_mult__1, fact_mult__1__left, fact_mult__1__right, % 181.77/27.83 fact_mult__Suc, fact_mult__Suc__right, fact_mult__diff__mult, % 181.77/27.83 fact_mult__divide__mult__cancel__left, fact_mult__divide__mult__cancel__right, % 181.77/27.83 fact_mult__dvd__mono, fact_mult__eq__0__iff, fact_mult__idem, % 181.77/27.83 fact_mult__imp__div__pos__le, fact_mult__imp__div__pos__less, % 181.77/27.83 fact_mult__imp__less__div__pos, fact_mult__le__0__iff, % 181.77/27.83 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos, % 181.77/27.83 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1, % 181.77/27.83 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Odiff, % 181.77/27.83 fact_mult__left_Ominus, fact_mult__left_Ozero, fact_mult__left__idem, % 181.77/27.83 fact_mult__left__le__imp__le, fact_mult__left__le__one__le, % 181.77/27.83 fact_mult__left__less__imp__less, fact_mult__left__mono, % 181.77/27.83 fact_mult__left__mono__neg, fact_mult__less__cancel__left__disj, % 181.77/27.83 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos, % 181.77/27.83 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left, % 181.77/27.83 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less, % 181.77/27.83 fact_mult__mono, fact_mult__mono_H, fact_mult__monom, fact_mult__neg__neg, % 181.77/27.83 fact_mult__neg__pos, fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos, % 181.77/27.83 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg, % 181.77/27.83 fact_mult__nonpos__nonpos, fact_mult__pCons__left, fact_mult__pCons__right, % 181.77/27.83 fact_mult__poly__0__left, fact_mult__poly__0__right, fact_mult__poly__add__left, % 181.77/27.83 fact_mult__pos__neg, fact_mult__pos__neg2, fact_mult__pos__pos, % 181.77/27.83 fact_mult__right_Oadd, fact_mult__right_Odiff, fact_mult__right_Ominus, % 181.77/27.83 fact_mult__right_Ozero, fact_mult__right__le__imp__le, % 181.77/27.83 fact_mult__right__le__one__le, fact_mult__right__less__imp__less, % 181.77/27.83 fact_mult__right__mono, fact_mult__right__mono__neg, fact_mult__smult__left, % 181.77/27.83 fact_mult__smult__right, fact_mult__strict__left__mono, % 181.77/27.83 fact_mult__strict__left__mono__neg, fact_mult__strict__mono, % 181.77/27.83 fact_mult__strict__mono_H, fact_mult__strict__right__mono, % 181.77/27.83 fact_mult__strict__right__mono__neg, fact_mult__zero__left, % 181.77/27.83 fact_mult__zero__right, fact_n__not__Suc__n, fact_nat_Oinject, % 181.77/27.83 fact_nat__1__eq__mult__iff, fact_nat__add__assoc, fact_nat__add__commute, % 181.77/27.83 fact_nat__add__left__cancel, fact_nat__add__left__cancel__le, % 181.77/27.83 fact_nat__add__left__cancel__less, fact_nat__add__left__commute, % 181.77/27.83 fact_nat__add__right__cancel, fact_nat__diff__add__eq1, % 181.77/27.83 fact_nat__diff__add__eq2, fact_nat__dvd__1__iff__1, fact_nat__eq__add__iff1, % 181.77/27.83 fact_nat__eq__add__iff2, fact_nat__le__add__iff1, fact_nat__le__add__iff2, % 181.77/27.83 fact_nat__le__linear, fact_nat__less__add__iff1, fact_nat__less__add__iff2, % 181.77/27.83 fact_nat__less__cases, fact_nat__less__le, fact_nat__mult__1, % 181.77/27.83 fact_nat__mult__1__right, fact_nat__mult__assoc, fact_nat__mult__commute, % 181.77/27.83 fact_nat__mult__eq__1__iff, fact_nat__neq__iff, fact_nat__size, % 181.77/27.83 fact_neg__0__equal__iff__equal, fact_neg__0__le__iff__le, % 181.77/27.83 fact_neg__0__less__iff__less, fact_neg__divide__less__eq, % 181.77/27.83 fact_neg__equal__0__iff__equal, fact_neg__equal__iff__equal, % 181.77/27.83 fact_neg__equal__zero, fact_neg__le__0__iff__le, fact_neg__le__iff__le, % 181.77/27.83 fact_neg__less__0__iff__less, fact_neg__less__divide__eq, % 181.77/27.83 fact_neg__less__iff__less, fact_neg__less__nonneg, fact_no__zero__divisors, % 181.77/27.83 fact_nonzero__divide__eq__eq, fact_nonzero__eq__divide__eq, % 181.77/27.83 fact_nonzero__minus__divide__divide, fact_nonzero__minus__divide__right, % 181.77/27.83 fact_nonzero__power__divide, fact_not__add__less1, fact_not__add__less2, % 181.77/27.83 fact_not__leE, fact_not__less__eq, fact_not__less__eq__eq, % 181.77/27.83 fact_not__less__iff__gr__or__eq, fact_not__less__less__Suc__eq, % 181.77/27.83 fact_not__one__le__zero, fact_not__one__less__zero, % 181.77/27.83 fact_not__square__less__zero, fact_not__sum__squares__lt__zero, % 181.77/27.83 fact_odd__less__0, fact_odd__nonzero, fact_offset__poly__0, % 181.77/27.83 fact_offset__poly__eq__0__iff, fact_offset__poly__eq__0__lemma, % 181.77/27.83 fact_offset__poly__pCons, fact_offset__poly__single, fact_one__dvd, % 181.77/27.83 fact_one__le__power, fact_one__neq__zero, fact_one__poly__def, % 181.77/27.83 fact_one__reorient, fact_ord__eq__le__trans, fact_ord__eq__less__trans, % 181.77/27.83 fact_ord__le__eq__trans, fact_ord__less__eq__trans, fact_order, fact_order__1, % 181.77/27.83 fact_order__2, fact_order__antisym, fact_order__antisym__conv, % 181.77/27.83 fact_order__degree, fact_order__eq__iff, fact_order__eq__refl, % 181.77/27.83 fact_order__le__imp__less__or__eq, fact_order__le__less, % 181.77/27.83 fact_order__le__less__trans, fact_order__le__neq__trans, fact_order__less__asym, % 181.77/27.83 fact_order__less__asym_H, fact_order__less__imp__le, % 181.77/27.83 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2, % 181.77/27.83 fact_order__less__imp__not__less, fact_order__less__irrefl, % 181.77/27.83 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym, % 181.77/27.83 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl, % 181.77/27.83 fact_order__trans, fact_pCons__0__0, fact_pCons__eq__iff, fact_pcompose__0, % 181.77/27.83 fact_pcompose__pCons, fact_pdivmod__rel__0, fact_pdivmod__rel__0__iff, % 181.77/27.83 fact_pdivmod__rel__by__0, fact_pdivmod__rel__by__0__iff, fact_pdivmod__rel__def, % 181.77/27.83 fact_pdivmod__rel__mult, fact_pdivmod__rel__pCons, % 181.77/27.83 fact_pdivmod__rel__smult__left, fact_pdivmod__rel__unique, % 181.77/27.83 fact_pdivmod__rel__unique__div, fact_pdivmod__rel__unique__mod, fact_poly__0, % 181.77/27.83 fact_poly__1, fact_poly__add, fact_poly__diff, fact_poly__dvd__antisym, % 181.77/27.83 fact_poly__eq__0__iff__dvd, fact_poly__eq__iff, fact_poly__gcd_Oassoc, % 181.77/27.83 fact_poly__gcd_Ocommute, fact_poly__gcd_Oleft__commute, fact_poly__gcd__0__0, % 181.77/27.83 fact_poly__gcd__1__left, fact_poly__gcd__1__right, fact_poly__gcd__dvd1, % 181.77/27.83 fact_poly__gcd__dvd2, fact_poly__gcd__greatest, fact_poly__gcd__minus__left, % 181.77/27.83 fact_poly__gcd__minus__right, fact_poly__gcd__monic, fact_poly__gcd__unique, % 181.77/27.83 fact_poly__gcd__zero__iff, fact_poly__minus, fact_poly__monom, fact_poly__mult, % 181.77/27.83 fact_poly__offset__poly, fact_poly__pCons, fact_poly__pcompose, % 181.77/27.83 fact_poly__power, fact_poly__rec_Osimps, fact_poly__rec__0, % 181.77/27.83 fact_poly__rec__pCons, fact_poly__replicate__append, fact_poly__smult, % 181.77/27.83 fact_poly__zero, fact_pos__add__strict, fact_pos__divide__le__eq, % 181.77/27.83 fact_pos__divide__less__eq, fact_pos__le__divide__eq, % 181.77/27.83 fact_pos__less__divide__eq, fact_pos__zmult__eq__1__iff, % 181.77/27.83 fact_power_Opower_Opower__Suc, fact_power__0__Suc, fact_power__Suc, % 181.77/27.83 fact_power__Suc2, fact_power__Suc__less, fact_power__Suc__less__one, % 181.77/27.83 fact_power__add, fact_power__commutes, fact_power__decreasing, fact_power__diff, % 181.77/27.83 fact_power__divide, fact_power__dvd__imp__le, fact_power__gt1, % 181.77/27.83 fact_power__gt1__lemma, fact_power__increasing, fact_power__increasing__iff, % 181.77/27.83 fact_power__inject__base, fact_power__inject__exp, fact_power__le__dvd, % 181.77/27.83 fact_power__le__imp__le__base, fact_power__le__imp__le__exp, % 181.77/27.83 fact_power__less__imp__less__base, fact_power__less__imp__less__exp, % 181.77/27.83 fact_power__less__power__Suc, fact_power__minus, fact_power__mono, % 181.77/27.83 fact_power__mult, fact_power__mult__distrib, fact_power__one, % 181.77/27.83 fact_power__one__over, fact_power__one__right, fact_power__power__power, % 181.77/27.83 fact_power__strict__decreasing, fact_power__strict__increasing, % 181.77/27.83 fact_power__strict__increasing__iff, fact_q__neg__lemma, fact_q__pos__lemma, % 181.77/27.83 fact_real__squared__diff__one__factored, fact_realpow__Suc__le__self, % 181.77/27.83 fact_right__inverse__eq, fact_right__minus, fact_right__minus__eq, % 181.77/27.83 fact_self__quotient__aux1, fact_self__quotient__aux2, fact_smult__0__left, % 181.77/27.83 fact_smult__0__right, fact_smult__1__left, fact_smult__add__left, % 181.77/27.83 fact_smult__add__right, fact_smult__diff__left, fact_smult__diff__right, % 181.77/27.83 fact_smult__dvd, fact_smult__dvd__cancel, fact_smult__dvd__iff, % 181.77/27.83 fact_smult__eq__0__iff, fact_smult__minus__left, fact_smult__minus__right, % 181.77/27.83 fact_smult__monom, fact_smult__pCons, fact_smult__smult, % 181.77/27.83 fact_split__mult__neg__le, fact_split__mult__pos__le, fact_square__eq__1__iff, % 181.77/27.83 fact_square__eq__iff, fact_sum__squares__eq__zero__iff, % 181.77/27.83 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff, % 181.77/27.83 fact_sum__squares__le__zero__iff, fact_synthetic__div__0, % 181.77/27.83 fact_synthetic__div__correct, fact_synthetic__div__correct_H, % 181.77/27.83 fact_synthetic__div__pCons, fact_synthetic__div__unique, % 181.77/27.83 fact_synthetic__div__unique__lemma, fact_termination__basic__simps_I1_J, % 181.77/27.83 fact_termination__basic__simps_I2_J, fact_termination__basic__simps_I3_J, % 181.77/27.83 fact_termination__basic__simps_I4_J, fact_termination__basic__simps_I5_J, % 181.77/27.83 fact_times_Oidem, fact_times__divide__eq__right, fact_times__divide__times__eq, % 181.77/27.83 fact_trans__le__add1, fact_trans__le__add2, fact_trans__less__add1, % 181.77/27.83 fact_trans__less__add2, fact_tsub__def, fact_tsub__eq, fact_uminus__apply, % 181.77/27.83 fact_uminus__dvd__conv_I1_J, fact_uminus__dvd__conv_I2_J, % 181.77/27.83 fact_unique__quotient__lemma, fact_unique__quotient__lemma__neg, % 181.77/27.83 fact_unity__coeff__ex, fact_xt1_I10_J, fact_xt1_I11_J, fact_xt1_I12_J, % 181.77/27.83 fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J, fact_xt1_I5_J, % 181.77/27.83 fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J, fact_zadd__0, % 181.77/27.83 fact_zadd__0__right, fact_zadd__assoc, fact_zadd__commute, % 181.77/27.83 fact_zadd__left__commute, fact_zadd__left__mono, fact_zadd__strict__right__mono, % 181.77/27.83 fact_zadd__zless__mono, fact_zadd__zminus__inverse2, fact_zadd__zmult__distrib, % 181.77/27.83 fact_zadd__zmult__distrib2, fact_zdiff__zmult__distrib, % 181.77/27.83 fact_zdiff__zmult__distrib2, fact_zdiv__mono2__lemma, % 181.77/27.83 fact_zdiv__mono2__neg__lemma, fact_zdvd__antisym__nonneg, fact_zdvd__imp__le, % 181.77/27.83 fact_zdvd__mono, fact_zdvd__mult__cancel, fact_zdvd__not__zless, % 181.77/27.83 fact_zdvd__period, fact_zdvd__reduce, fact_zdvd__zdiffD, % 181.77/27.83 fact_zero__le__divide__iff, % 181.77/27.83 fact_zero__le__double__add__iff__zero__le__single__add, % 181.77/27.83 fact_zero__le__mult__iff, fact_zero__le__one, fact_zero__le__power, % 181.77/27.83 fact_zero__le__square, fact_zero__less__divide__iff, % 181.77/27.83 fact_zero__less__double__add__iff__zero__less__single__add, % 181.77/27.83 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, fact_zero__less__one, % 181.77/27.83 fact_zero__less__power, fact_zero__less__two, fact_zero__neq__one, % 181.77/27.83 fact_zero__reorient, fact_zle__add1__eq__le, fact_zle__antisym, % 181.77/27.83 fact_zle__diff1__eq, fact_zle__linear, fact_zle__refl, fact_zle__trans, % 181.77/27.83 fact_zless__add1__eq, fact_zless__imp__add1__zle, fact_zless__le, % 181.77/27.83 fact_zless__linear, fact_zminus__0, fact_zminus__zadd__distrib, % 181.77/27.83 fact_zminus__zminus, fact_zmult__1, fact_zmult__1__right, fact_zmult__assoc, % 181.77/27.83 fact_zmult__commute, fact_zmult__zless__mono2, fact_zmult__zminus, % 181.77/27.83 fact_zpower__zadd__distrib, fact_zpower__zpower, help_c__fFalse__1, % 181.77/27.83 help_c__fTrue__1, help_c__fequal__1, help_c__fequal__2 % 181.77/27.83 % 181.77/27.83 Those formulas are unsatisfiable: % 181.77/27.83 --------------------------------- % 181.77/27.83 % 181.77/27.83 Begin of proof % 181.77/27.83 | % 181.77/27.83 | ALPHA: (fact_l) implies: % 181.77/27.84 | (1) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 181.77/27.84 | (class_Int_Oring__char__0(t_a) = v0 & class_Rings_Oidom(t_a) = v1 & % 181.77/27.84 | c_Polynomial_Opoly(t_a, v_p) = v2 & % 181.77/27.84 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a, t_a, v2) = % 181.77/27.84 | v3 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_degree__smult__eq) implies: % 181.77/27.84 | (2) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 181.77/27.84 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 181.77/27.84 | ( ~ (c_Polynomial_Osmult(v3, v2, v1) = v4) | ~ % 181.77/27.84 | (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 181.77/27.84 | $i(v1) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 181.77/27.84 | (c_Polynomial_Odegree(v3, v1) = v8 & % 181.77/27.84 | c_Groups_Ozero__class_Ozero(v3) = v7 & class_Rings_Oidom(v3) = v6 % 181.77/27.84 | & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = v2) | v5 = v0) & % 181.77/27.84 | (v8 = v5 | v7 = v2)))))) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact__096degree_Ap_A_061_Adegree_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096) % 181.77/27.84 | implies: % 181.77/27.84 | (3) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 181.77/27.84 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 181.77/27.84 | (tc_Polynomial_Opoly(t_a) = v6 & c_Polynomial_OpCons(t_a, v5, v7) = v8 % 181.77/27.84 | & c_Polynomial_Odegree(t_a, v8) = v9 & c_Polynomial_Odegree(t_a, v_p) % 181.77/27.84 | = v2 & c_Groups_Ozero__class_Ozero(v6) = v7 & % 181.77/27.84 | c_Groups_Ozero__class_Ozero(t_a) = v4 & class_Int_Oring__char__0(t_a) % 181.77/27.84 | = v0 & class_Rings_Oidom(t_a) = v1 & c_Polynomial_Opoly(t_a, v_p) = % 181.77/27.84 | v3 & hAPP(v3, v4) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 181.77/27.84 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = v2)) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact__096_B_Bx_O_Apoly_Ap_Ax_A_061_Apoly_Ap_A_I0_058_058_Ha_J_096) % 181.77/27.84 | implies: % 181.77/27.84 | (4) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 181.77/27.84 | (c_Groups_Ozero__class_Ozero(t_a) = v3 & class_Int_Oring__char__0(t_a) % 181.77/27.84 | = v0 & class_Rings_Oidom(t_a) = v1 & c_Polynomial_Opoly(t_a, v_p) = % 181.77/27.84 | v2 & hAPP(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] : ! % 181.77/27.84 | [v6: $i] : ( ~ (v1 = 0) | ~ (v0 = 0) | v6 = v4 | ~ (hAPP(v2, v5) = % 181.77/27.84 | v6) | ~ $i(v5))) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_bool_Osize_I1_J) implies: % 181.77/27.84 | (5) ? [v0: $i] : (c_HOL_Obool_Obool__size(c_fTrue) = v0 & % 181.77/27.84 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_bool_Osize_I2_J) implies: % 181.77/27.84 | (6) ? [v0: $i] : (c_HOL_Obool_Obool__size(c_fFalse) = v0 & % 181.77/27.84 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_size__literal__def) implies: % 181.77/27.84 | (7) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 181.77/27.84 | ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 181.77/27.84 | (c_Nat_Osize__class_Osize(tc_String_Oliteral, v1) = v2) | ~ % 181.77/27.84 | $i(v1))) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_char__size) implies: % 181.77/27.84 | (8) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 181.77/27.84 | ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 181.77/27.84 | (c_String_Ochar_Ochar__size(v1) = v2) | ~ $i(v1))) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_th) implies: % 181.77/27.84 | (9) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 181.77/27.84 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 181.77/27.84 | (tc_Polynomial_Opoly(t_a) = v5 & c_Polynomial_OpCons(t_a, v4, v6) = v7 % 181.77/27.84 | & c_Groups_Ozero__class_Ozero(v5) = v6 & % 181.77/27.84 | c_Groups_Ozero__class_Ozero(t_a) = v3 & class_Int_Oring__char__0(t_a) % 181.77/27.84 | = v0 & class_Rings_Oidom(t_a) = v1 & c_Polynomial_Opoly(t_a, v7) = v8 % 181.77/27.84 | & c_Polynomial_Opoly(t_a, v_p) = v2 & hAPP(v2, v3) = v4 & $i(v8) & % 181.77/27.84 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | % 181.77/27.84 | ~ (v0 = 0) | v8 = v2)) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096) % 181.77/27.84 | implies: % 181.77/27.84 | (10) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 181.77/27.84 | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (tc_Polynomial_Opoly(t_a) % 181.77/27.84 | = v5 & c_Polynomial_OpCons(t_a, v4, v6) = v7 & % 181.77/27.84 | c_Groups_Ozero__class_Ozero(v5) = v6 & % 181.77/27.84 | c_Groups_Ozero__class_Ozero(t_a) = v3 & % 181.77/27.84 | class_Int_Oring__char__0(t_a) = v0 & class_Rings_Oidom(t_a) = v1 & % 181.77/27.84 | c_Polynomial_Opoly(t_a, v_p) = v2 & hAPP(v2, v3) = v4 & $i(v7) & % 181.77/27.84 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = % 181.77/27.84 | 0) | v7 = v_p)) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_monom__0) implies: % 181.77/27.84 | (11) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.84 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.77/27.84 | $i] : ( ~ (tc_Polynomial_Opoly(v2) = v3) | ~ % 181.77/27.84 | (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ % 181.77/27.84 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | % 181.77/27.84 | ? [v6: any] : ? [v7: $i] : (c_Polynomial_Omonom(v2, v1, v0) = v7 % 181.77/27.84 | & class_Groups_Ozero(v2) = v6 & $i(v7) & ( ~ (v6 = 0) | v7 = % 181.77/27.84 | v5)))) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_degree__pCons__0) implies: % 181.77/27.84 | (12) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.84 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.77/27.84 | $i] : ! [v6: $i] : (v6 = v0 | ~ (tc_Polynomial_Opoly(v2) = v3) | % 181.77/27.84 | ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ % 181.77/27.84 | (c_Polynomial_Odegree(v2, v5) = v6) | ~ % 181.77/27.84 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | % 181.77/27.84 | ? [v7: int] : ( ~ (v7 = 0) & class_Groups_Ozero(v2) = v7))) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_degree__0) implies: % 181.77/27.84 | (13) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.84 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | % 181.77/27.84 | ~ (tc_Polynomial_Opoly(v1) = v2) | ~ (c_Polynomial_Odegree(v1, % 181.77/27.84 | v3) = v4) | ~ (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ % 181.77/27.84 | $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & class_Groups_Ozero(v1) = % 181.77/27.84 | v5))) % 181.77/27.84 | % 181.77/27.84 | ALPHA: (fact_order__root) implies: % 181.77/27.85 | (14) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.77/27.85 | $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = % 181.77/27.85 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: any] : ? [v7: % 181.77/27.85 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 181.77/27.85 | (c_Polynomial_Oorder(v3, v1, v2) = v10 & tc_Polynomial_Opoly(v3) = % 181.77/27.85 | v8 & c_Groups_Ozero__class_Ozero(v8) = v9 & % 181.77/27.85 | c_Groups_Ozero__class_Ozero(v3) = v7 & class_Rings_Oidom(v3) = % 181.77/27.85 | v6 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ % 181.77/27.85 | (v10 = v0) | ~ (v7 = v5) | v9 = v2) & (v7 = v5 | (v10 = % 181.77/27.85 | v0 & ~ (v9 = v2)))))))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_synthetic__div__eq__0__iff) implies: % 181.77/27.85 | (15) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 181.77/27.85 | (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ $i(v3) | ~ % 181.77/27.85 | $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? % 181.77/27.85 | [v8: $i] : (tc_Polynomial_Opoly(v3) = v6 & % 181.77/27.85 | class_Rings_Ocomm__semiring__0(v3) = v5 & % 181.77/27.85 | c_Polynomial_Odegree(v3, v2) = v8 & % 181.77/27.85 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v8) & $i(v7) & $i(v6) % 181.77/27.85 | & ( ~ (v5 = 0) | (( ~ (v8 = v0) | v7 = v4) & ( ~ (v7 = v4) | v8 % 181.77/27.85 | = v0)))))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_psize__eq__0__iff) implies: % 181.77/27.85 | (16) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 181.77/27.85 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | % 181.77/27.85 | ~ $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 181.77/27.85 | (tc_Polynomial_Opoly(v2) = v5 & class_Groups_Ozero(v2) = v4 & % 181.77/27.85 | c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 % 181.77/27.85 | = 0) | (( ~ (v6 = v1) | v3 = v0) & ( ~ (v3 = v0) | v6 = % 181.77/27.85 | v1)))))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_degree__pCons__eq__if) implies: % 181.77/27.85 | (17) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.77/27.85 | $i] : ( ~ (c_Polynomial_OpCons(v3, v1, v2) = v4) | ~ % 181.77/27.85 | (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 181.77/27.85 | $i(v1) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 181.77/27.85 | ? [v10: $i] : (c_Nat_OSuc(v9) = v10 & tc_Polynomial_Opoly(v3) = v7 % 181.77/27.85 | & c_Polynomial_Odegree(v3, v2) = v9 & class_Groups_Ozero(v3) = % 181.77/27.85 | v6 & c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v10) & $i(v9) & % 181.77/27.85 | $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ (v8 = v2) | v5 = v0) & % 181.77/27.85 | (v10 = v5 | v8 = v2)))))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_size__char) implies: % 181.77/27.85 | (18) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 181.77/27.85 | (c_Nat_Osize__class_Osize(tc_String_Ochar, v1) = v2) | ~ $i(v1))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_bool_Osize_I4_J) implies: % 181.77/27.85 | (19) ? [v0: $i] : (c_Nat_Osize__class_Osize(tc_HOL_Obool, c_fFalse) = v0 & % 181.77/27.85 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_bool_Osize_I3_J) implies: % 181.77/27.85 | (20) ? [v0: $i] : (c_Nat_Osize__class_Osize(tc_HOL_Obool, c_fTrue) = v0 & % 181.77/27.85 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_nat_Osize_I1_J) implies: % 181.77/27.85 | (21) ? [v0: $i] : (c_Nat_Onat_Onat__size(v0) = v0 & % 181.77/27.85 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_psize__def) implies: % 181.77/27.85 | (22) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 181.77/27.85 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v2, v1) = v3) | % 181.77/27.85 | ~ $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 181.77/27.85 | ? [v7: $i] : ? [v8: $i] : (c_Nat_OSuc(v7) = v8 & % 181.77/27.85 | tc_Polynomial_Opoly(v2) = v5 & c_Polynomial_Odegree(v2, v1) = v7 % 181.77/27.85 | & class_Groups_Ozero(v2) = v4 & c_Groups_Ozero__class_Ozero(v5) % 181.77/27.85 | = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | (( ~ % 181.77/27.85 | (v6 = v1) | v3 = v0) & (v8 = v3 | v6 = v1)))))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_nat_Osimps_I3_J) implies: % 181.77/27.85 | (23) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_nat_Osize_I2_J) implies: % 181.77/27.85 | (24) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 181.77/27.85 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 181.77/27.85 | [v2: $i] : ! [v3: $i] : ( ~ (c_Nat_Onat_Onat__size(v2) = v3) | ~ % 181.77/27.85 | $i(v2) | ? [v4: $i] : ? [v5: $i] : % 181.77/27.85 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5 & % 181.77/27.85 | c_Nat_Onat_Onat__size(v4) = v5 & c_Nat_OSuc(v2) = v4 & $i(v5) & % 181.77/27.85 | $i(v4)))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_add__eq__self__zero) implies: % 181.77/27.85 | (25) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 181.77/27.85 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ % 181.77/27.85 | $i(v2) | ~ $i(v1))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_add__is__0) implies: % 181.77/27.85 | (26) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : ( ~ % 181.77/27.85 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ % 181.77/27.85 | $i(v2) | ~ $i(v1) | (v2 = v0 & v1 = v0)) & ! [v1: $i] : (v1 = v0 % 181.77/27.85 | | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_Nat_Oadd__0__right) implies: % 181.77/27.85 | (27) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 181.77/27.85 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ % 181.77/27.85 | $i(v1))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_plus__nat_Oadd__0) implies: % 181.77/27.85 | (28) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.85 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 181.77/27.85 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ % 181.77/27.85 | $i(v1))) % 181.77/27.85 | % 181.77/27.85 | ALPHA: (fact_le__0__eq) implies: % 181.77/27.86 | (29) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.86 | & ! [v1: $i] : (v1 = v0 | ~ % 181.77/27.86 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = 0) | ~ % 181.77/27.86 | $i(v1)) & ! [v1: int] : (v1 = 0 | ~ % 181.77/27.86 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) = v1))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_less__eq__nat_Osimps_I1_J) implies: % 181.77/27.86 | (30) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.86 | & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 181.77/27.86 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1) = v2) | ~ % 181.77/27.86 | $i(v1))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_one__is__add) implies: % 181.77/27.86 | (31) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 181.77/27.86 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 181.77/27.86 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ % 181.77/27.86 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v4) | ~ % 181.77/27.86 | $i(v3) | ~ $i(v2) | (( ~ (v3 = v1) | ~ (v2 = v0)) & ( ~ (v3 = % 181.77/27.86 | v0) | ~ (v2 = v1)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 181.77/27.86 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ % 181.77/27.86 | $i(v3) | ~ $i(v2) | (v3 = v1 & v2 = v0) | (v3 = v0 & v2 = v1))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_nat_Osize_I4_J) implies: % 181.77/27.86 | (32) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 181.77/27.86 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 181.77/27.86 | [v2: $i] : ! [v3: $i] : ( ~ (c_Nat_Osize__class_Osize(tc_Nat_Onat, % 181.77/27.86 | v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 181.77/27.86 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5 & % 181.77/27.86 | c_Nat_OSuc(v2) = v4 & c_Nat_Osize__class_Osize(tc_Nat_Onat, v4) % 181.77/27.86 | = v5 & $i(v5) & $i(v4)))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_nat_Osize_I3_J) implies: % 181.77/27.86 | (33) ? [v0: $i] : (c_Nat_Osize__class_Osize(tc_Nat_Onat, v0) = v0 & % 181.77/27.86 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_mult__cancel2) implies: % 181.77/27.86 | (34) ? [v0: $i] : ? [v1: $i] : % 181.77/27.86 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 181.77/27.86 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 181.77/27.86 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 181.77/27.86 | ! [v7: $i] : ! [v8: $i] : (v8 = v6 | ~ (hAPP(v7, v3) = v8) | ~ % 181.77/27.86 | (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = % 181.77/27.86 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ( ~ (v4 = v2) & ~ (v3 % 181.77/27.86 | = v1))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 181.77/27.86 | $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v2 | v3 = v1 | ~ % 181.77/27.86 | (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 181.77/27.86 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 181.77/27.86 | $i(v2))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_mult__is__0) implies: % 181.77/27.86 | (35) ? [v0: $i] : ? [v1: $i] : % 181.77/27.86 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 181.77/27.86 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 181.77/27.86 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~ % 181.77/27.86 | (hAPP(v4, v2) = v5) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ % 181.77/27.86 | $i(v2) | ( ~ (v3 = v1) & ~ (v2 = v1))) & ! [v2: $i] : ! [v3: % 181.77/27.86 | $i] : ! [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, v2) = v1) | % 181.77/27.86 | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_mult__0__right) implies: % 181.77/27.86 | (36) ? [v0: $i] : ? [v1: $i] : % 181.77/27.86 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 181.77/27.86 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 181.77/27.86 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | % 181.77/27.86 | hAPP(v3, v1) = v1)) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_mult__0) implies: % 181.77/27.86 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.77/27.86 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 181.77/27.86 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & % 181.77/27.86 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ % 181.77/27.86 | (hAPP(v2, v3) = v4) | ~ $i(v3))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_mult__eq__1__iff) implies: % 181.77/27.86 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.77/27.86 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v2 % 181.77/27.86 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 181.77/27.86 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v5, v3) % 181.77/27.86 | = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | (v4 = % 181.77/27.86 | v2 & v3 = v2)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 181.77/27.86 | (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v2) = v3))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_one__le__mult__iff) implies: % 181.77/27.86 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 181.77/27.86 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 % 181.77/27.86 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 181.77/27.86 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ! [v6: any] : ( % 181.77/27.86 | ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) = v5) | % 181.77/27.86 | ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) = v6) | % 181.77/27.86 | ~ $i(v4) | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: int] : % 181.77/27.86 | ( ~ (v9 = 0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, % 181.77/27.86 | v8) = v9 & hAPP(v7, v3) = v8 & hAPP(v2, v4) = v7 & $i(v8) & % 181.77/27.86 | $i(v7)) | (v6 = 0 & v5 = 0)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 181.77/27.86 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) = 0) | ~ % 181.77/27.86 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) = 0) | ~ % 181.77/27.86 | $i(v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : % 181.77/27.86 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) = 0 & % 181.77/27.86 | hAPP(v5, v3) = v6 & hAPP(v2, v4) = v5 & $i(v6) & $i(v5)))) % 181.77/27.86 | % 181.77/27.86 | ALPHA: (fact_nat__mult__eq__cancel__disj) implies: % 181.77/27.87 | (40) ? [v0: $i] : ? [v1: $i] : % 181.77/27.87 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 181.77/27.87 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 181.77/27.87 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 181.77/27.87 | ! [v7: $i] : (v7 = v6 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 181.77/27.87 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 181.77/27.87 | | ( ~ (v4 = v1) & ~ (v3 = v2))) & ! [v2: $i] : ! [v3: $i] : ! % 181.77/27.87 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ % 181.77/27.87 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = % 181.77/27.87 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 181.77/27.87 | % 181.77/27.87 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) % 181.77/27.87 | implies: % 181.77/27.87 | (41) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 181.77/27.87 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 181.77/27.87 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 181.77/27.87 | ~ $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 181.77/27.87 | (c_Groups_Oone__class_Oone(v2) = v7 & % 181.77/27.87 | class_Rings_Ocomm__semiring__1(v2) = v5 & hAPP(v4, v0) = v6 & % 181.77/27.87 | $i(v7) & $i(v6) & ( ~ (v5 = 0) | v7 = v6)))) % 181.77/27.87 | % 181.77/27.87 | ALPHA: (fact_coeff__1) implies: % 182.00/27.87 | (42) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.87 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.87 | $i] : ! [v6: $i] : ( ~ (c_Groups_Oone__class_Oone(v3) = v4) | ~ % 182.00/27.87 | (c_Polynomial_Ocoeff(v2, v4) = v5) | ~ (tc_Polynomial_Opoly(v2) = % 182.00/27.87 | v3) | ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ? [v7: % 182.00/27.87 | any] : ? [v8: $i] : ? [v9: $i] : % 182.00/27.87 | (c_Groups_Oone__class_Oone(v2) = v8 & % 182.00/27.87 | class_Rings_Ocomm__semiring__1(v2) = v7 & % 182.00/27.87 | c_Groups_Ozero__class_Ozero(v2) = v9 & $i(v9) & $i(v8) & ( ~ (v7 % 182.00/27.87 | = 0) | (( ~ (v1 = v0) | v8 = v6) & (v9 = v6 | v1 = v0)))))) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_coeff__pCons__0) implies: % 182.00/27.87 | (43) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.87 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.87 | $i] : ( ~ (c_Polynomial_Ocoeff(v3, v4) = v5) | ~ % 182.00/27.87 | (c_Polynomial_OpCons(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 182.00/27.87 | ~ $i(v1) | ? [v6: any] : ? [v7: $i] : (class_Groups_Ozero(v3) = % 182.00/27.87 | v6 & hAPP(v5, v0) = v7 & $i(v7) & ( ~ (v6 = 0) | v7 = v2)))) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_One__nat__def) implies: % 182.00/27.87 | (44) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 182.00/27.87 | v0 & c_Nat_OSuc(v1) = v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 182.00/27.87 | = v1 & $i(v1) & $i(v0)) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_mult__eq__self__implies__10) implies: % 182.00/27.87 | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.87 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 182.00/27.87 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 182.00/27.87 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 182.00/27.87 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = % 182.00/27.87 | v1 | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | % 182.00/27.87 | ~ $i(v3))) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_degree__1) implies: % 182.00/27.87 | (46) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.87 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | % 182.00/27.87 | ~ (c_Groups_Oone__class_Oone(v2) = v3) | ~ % 182.00/27.87 | (tc_Polynomial_Opoly(v1) = v2) | ~ (c_Polynomial_Odegree(v1, v3) % 182.00/27.87 | = v4) | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & % 182.00/27.87 | class_Rings_Ocomm__semiring__1(v1) = v5))) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_realpow__two__disj) implies: % 182.00/27.87 | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 182.00/27.87 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 182.00/27.87 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 182.00/27.87 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 182.00/27.87 | (c_Power_Opower__class_Opower(v5) = v6) | ~ (hAPP(v6, v4) = v7) | % 182.00/27.87 | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 182.00/27.87 | [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : % 182.00/27.87 | (c_Groups_Ouminus__class_Ouminus(v5, v3) = v12 & % 182.00/27.87 | class_Rings_Oidom(v5) = v9 & hAPP(v8, v2) = v11 & hAPP(v7, v2) = % 182.00/27.87 | v10 & $i(v12) & $i(v11) & $i(v10) & ( ~ (v9 = 0) | (( ~ (v11 = % 182.00/27.87 | v10) | v12 = v4 | v4 = v3) & (v11 = v10 | ( ~ (v12 = v4) % 182.00/27.87 | & ~ (v4 = v3)))))))) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_power__0__left) implies: % 182.00/27.87 | (48) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.87 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.87 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = v3) | % 182.00/27.87 | ~ (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) % 182.00/27.87 | | ~ (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ? [v7: any] : % 182.00/27.87 | ? [v8: any] : ? [v9: $i] : (class_Power_Opower(v2) = v7 & % 182.00/27.87 | class_Rings_Osemiring__0(v2) = v8 & % 182.00/27.87 | c_Groups_Oone__class_Oone(v2) = v9 & $i(v9) & ( ~ (v8 = 0) | ~ % 182.00/27.87 | (v7 = 0) | (( ~ (v1 = v0) | v9 = v6) & (v6 = v4 | v1 = % 182.00/27.87 | v0)))))) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_power__Suc__0) implies: % 182.00/27.87 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 182.00/27.87 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v2 % 182.00/27.87 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 % 182.00/27.87 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : % 182.00/27.87 | (v5 = v2 | ~ (hAPP(v3, v4) = v5) | ~ $i(v4))) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_nat__power__eq__Suc__0__iff) implies: % 182.00/27.87 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.87 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v2 % 182.00/27.87 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 182.00/27.87 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 % 182.00/27.87 | = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) % 182.00/27.87 | | ~ $i(v3) | ( ~ (v4 = v2) & ~ (v3 = v1))) & ! [v3: $i] : ! % 182.00/27.87 | [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3) = v2) % 182.00/27.87 | | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 182.00/27.87 | % 182.00/27.87 | ALPHA: (fact_power__eq__0__iff) implies: % 182.00/27.88 | (51) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.88 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.88 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 182.00/27.88 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ % 182.00/27.88 | $i(v2) | ~ $i(v1) | ? [v7: any] : ? [v8: any] : ? [v9: any] : % 182.00/27.88 | ? [v10: any] : ? [v11: $i] : (class_Power_Opower(v3) = v7 & % 182.00/27.88 | class_Rings_Ozero__neq__one(v3) = v10 & % 182.00/27.88 | class_Rings_Omult__zero(v3) = v8 & % 182.00/27.88 | class_Rings_Ono__zero__divisors(v3) = v9 & % 182.00/27.88 | c_Groups_Ozero__class_Ozero(v3) = v11 & $i(v11) & ( ~ (v10 = 0) % 182.00/27.88 | | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v11 = v6) | % 182.00/27.88 | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v11 = v2) | v6 = v2 | v1 % 182.00/27.88 | = v0)))))) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_power__0) implies: % 182.00/27.88 | (52) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.88 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 182.00/27.88 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 182.00/27.88 | ~ $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 182.00/27.88 | (class_Power_Opower(v2) = v5 & c_Groups_Oone__class_Oone(v2) = v7 % 182.00/27.88 | & hAPP(v4, v0) = v6 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v7 = % 182.00/27.88 | v6)))) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_nat__one__le__power) implies: % 182.00/27.88 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.88 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 % 182.00/27.88 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 182.00/27.88 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 182.00/27.88 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 182.00/27.88 | $i(v3) | ? [v7: any] : ? [v8: any] : % 182.00/27.88 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) = v8 & % 182.00/27.88 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) = v7 & ( % 182.00/27.88 | ~ (v7 = 0) | v8 = 0)))) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_power_Opower_Opower__0) implies: % 182.00/27.88 | (54) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.88 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.88 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | % 182.00/27.88 | ~ (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 182.00/27.88 | $i(v1) | hAPP(v6, v0) = v3)) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_realpow__two__diff) implies: % 182.00/27.88 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 182.00/27.88 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 182.00/27.88 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 182.00/27.88 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 182.00/27.88 | $i] : ! [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(v5, v8, % 182.00/27.88 | v10) = v11) | ~ (c_Power_Opower__class_Opower(v5) = v6) | ~ % 182.00/27.88 | (hAPP(v9, v2) = v10) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = % 182.00/27.88 | v7) | ~ (hAPP(v6, v3) = v9) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 182.00/27.88 | | ? [v12: any] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? % 182.00/27.88 | [v16: $i] : ? [v17: $i] : (c_Groups_Ominus__class_Ominus(v5, v4, % 182.00/27.88 | v3) = v14 & class_Rings_Ocomm__ring__1(v5) = v12 & % 182.00/27.88 | c_Groups_Otimes__class_Otimes(v5) = v13 & % 182.00/27.88 | c_Groups_Oplus__class_Oplus(v5, v4, v3) = v16 & hAPP(v15, v16) = % 182.00/27.88 | v17 & hAPP(v13, v14) = v15 & $i(v17) & $i(v16) & $i(v15) & % 182.00/27.88 | $i(v14) & $i(v13) & ( ~ (v12 = 0) | v17 = v11)))) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_dvd__1__left) implies: % 182.00/27.88 | (56) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 182.00/27.88 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.88 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 182.00/27.88 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2))) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_zero__less__Suc) implies: % 182.00/27.88 | (57) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.88 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) % 182.00/27.88 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = 0)) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_nat__diff__split__asm) implies: % 182.00/27.88 | (58) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.88 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.88 | $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = % 182.00/27.88 | v4) | ~ (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 182.00/27.88 | | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 182.00/27.88 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v7 & % 182.00/27.88 | hBOOL(v8) = v9 & hBOOL(v5) = v6 & hAPP(v3, v0) = v8 & $i(v8) & ( % 182.00/27.88 | ~ (v6 = 0) | ( ! [v10: $i] : ( ~ % 182.00/27.88 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v10) = v2) | % 182.00/27.88 | ~ $i(v10) | ? [v11: $i] : (hBOOL(v11) = 0 & hAPP(v3, % 182.00/27.88 | v10) = v11 & $i(v11))) & ( ~ (v7 = 0) | v9 = 0))))) & % 182.00/27.88 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 182.00/27.88 | ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 182.00/27.88 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: % 182.00/27.88 | any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : % 182.00/27.88 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v6 & % 182.00/27.88 | hBOOL(v7) = v8 & hBOOL(v5) = v9 & hAPP(v3, v0) = v7 & $i(v7) & % 182.00/27.88 | (v9 = 0 | (v6 = 0 & ~ (v8 = 0)))) | ? [v6: $i] : ? [v7: $i] : % 182.00/27.88 | ? [v8: int] : ( ~ (v8 = 0) & hBOOL(v7) = v8 & % 182.00/27.88 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3, % 182.00/27.88 | v6) = v7 & $i(v7) & $i(v6)))) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_dvd__imp__le) implies: % 182.00/27.88 | (59) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.88 | & ! [v1: $i] : ! [v2: $i] : ( ~ % 182.00/27.88 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1) = 0) | ~ $i(v2) | % 182.00/27.88 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 182.00/27.88 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v3 & % 182.00/27.88 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) = v4 & ( % 182.00/27.88 | ~ (v3 = 0) | v4 = 0)))) % 182.00/27.88 | % 182.00/27.88 | ALPHA: (fact_dvd__mult__cancel) implies: % 182.00/27.89 | (60) ? [v0: $i] : ? [v1: $i] : % 182.00/27.89 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 182.00/27.89 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 182.00/27.89 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.89 | ! [v7: $i] : ( ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) = 0) % 182.00/27.89 | | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, % 182.00/27.89 | v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: any] : % 182.00/27.89 | ? [v9: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) % 182.00/27.89 | = v8 & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) = v9 & ( ~ % 182.00/27.89 | (v8 = 0) | v9 = 0)))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_nat__mult__dvd__cancel1) implies: % 182.00/27.89 | (61) ? [v0: $i] : ? [v1: $i] : % 182.00/27.89 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.89 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.89 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.89 | ! [v7: $i] : ! [v8: any] : ( ~ % 182.00/27.89 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) = v8) | ~ % 182.00/27.89 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = % 182.00/27.89 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : ? % 182.00/27.89 | [v10: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = % 182.00/27.89 | v9 & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) = v10 & ( ~ % 182.00/27.89 | (v9 = 0) | (( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = % 182.00/27.89 | 0)))))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_nat__dvd__not__less) implies: % 182.00/27.89 | (62) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.89 | & ! [v1: $i] : ! [v2: $i] : ( ~ % 182.00/27.89 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) = 0) | ~ $i(v2) | % 182.00/27.89 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 182.00/27.89 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v4 & % 182.00/27.89 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v3 & ( ~ % 182.00/27.89 | (v4 = 0) | ~ (v3 = 0))))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_gr0I) implies: % 182.00/27.89 | (63) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.89 | & ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 182.00/27.89 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v2) | ~ % 182.00/27.89 | $i(v1))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_neq0__conv) implies: % 182.00/27.89 | (64) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.89 | & ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) = 0) & ! % 182.00/27.89 | [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 182.00/27.89 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v2) | ~ % 182.00/27.89 | $i(v1))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_not__less0) implies: % 182.00/27.89 | (65) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.89 | & ! [v1: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 182.00/27.89 | v0) = 0) | ~ $i(v1))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_zero__less__diff) implies: % 182.00/27.89 | (66) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.89 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 182.00/27.89 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 182.00/27.89 | $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: any] : % 182.00/27.89 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) = v5 & % 182.00/27.89 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v4 & ( ~ % 182.00/27.89 | (v4 = 0) | v5 = 0))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 182.00/27.89 | : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 182.00/27.89 | $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: any] : % 182.00/27.89 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) = v4 & % 182.00/27.89 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v5 & ( ~ % 182.00/27.89 | (v4 = 0) | v5 = 0)))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_diff__less) implies: % 182.00/27.89 | (67) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.89 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | % 182.00/27.89 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 182.00/27.89 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1) = v4) | ~ % 182.00/27.89 | $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: any] : % 182.00/27.89 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v5 & % 182.00/27.89 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v6 & ( ~ % 182.00/27.89 | (v6 = 0) | ~ (v5 = 0))))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_diffs0__imp__equal) implies: % 182.00/27.89 | (68) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.89 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 182.00/27.89 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ % 182.00/27.89 | $i(v2) | ~ $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) & % 182.00/27.89 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & % 182.00/27.89 | $i(v3)))) % 182.00/27.89 | % 182.00/27.89 | ALPHA: (fact_diff__self__eq__0) implies: % 182.00/27.90 | (69) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 182.00/27.90 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ % 182.00/27.90 | $i(v1))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_minus__nat_Odiff__0) implies: % 182.00/27.90 | (70) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 182.00/27.90 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 182.00/27.90 | $i(v1))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_diff__0__eq__0) implies: % 182.00/27.90 | (71) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 182.00/27.90 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 182.00/27.90 | $i(v1))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_diff__Suc__less) implies: % 182.00/27.90 | (72) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.90 | int] : (v5 = 0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 182.00/27.90 | v2, v3) = v4) | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.00/27.90 | v4, v2) = v5) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ % 182.00/27.90 | $i(v1) | ? [v6: int] : ( ~ (v6 = 0) & % 182.00/27.90 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v6))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_Suc__pred) implies: % 182.00/27.90 | (73) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 182.00/27.90 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.90 | [v2: $i] : ! [v3: $i] : ( ~ % 182.00/27.90 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 182.00/27.90 | $i(v2) | ? [v4: any] : ? [v5: $i] : % 182.00/27.90 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v4 & % 182.00/27.90 | c_Nat_OSuc(v3) = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v2)))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_one__less__power) implies: % 182.00/27.90 | (74) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.90 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ % 182.00/27.90 | (c_Orderings_Oord__class_Oless(v3, v4, v7) = v8) | ~ % 182.00/27.90 | (c_Power_Opower__class_Opower(v3) = v5) | ~ % 182.00/27.90 | (c_Groups_Oone__class_Oone(v3) = v4) | ~ (hAPP(v6, v1) = v7) | ~ % 182.00/27.90 | (hAPP(v5, v2) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v9: % 182.00/27.90 | any] : ? [v10: any] : ? [v11: any] : % 182.00/27.90 | (c_Orderings_Oord__class_Oless(v3, v4, v2) = v10 & % 182.00/27.90 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v11 & % 182.00/27.90 | class_Rings_Olinordered__semidom(v3) = v9 & ( ~ (v11 = 0) | ~ % 182.00/27.90 | (v10 = 0) | ~ (v9 = 0))))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_Suc__pred_H) implies: % 182.00/27.90 | (75) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 182.00/27.90 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 182.00/27.90 | & ! [v2: $i] : ! [v3: $i] : ( ~ % 182.00/27.90 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 182.00/27.90 | $i(v2) | ? [v4: any] : ? [v5: $i] : % 182.00/27.90 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v4 & % 182.00/27.90 | c_Nat_OSuc(v3) = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v2)))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_dvd__mult__cancel2) implies: % 182.00/27.90 | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.90 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 182.00/27.90 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.90 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 182.00/27.90 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.00/27.90 | [v7: any] : ( ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) = v7) % 182.00/27.90 | | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) | ~ % 182.00/27.90 | $i(v3) | ? [v8: int] : ( ~ (v8 = 0) & % 182.00/27.90 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v8) | (( ~ % 182.00/27.90 | (v7 = 0) | v3 = v2) & ( ~ (v3 = v2) | v7 = 0)))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_dvd__mult__cancel1) implies: % 182.00/27.90 | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.90 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 182.00/27.90 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.90 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 182.00/27.90 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.00/27.90 | [v7: any] : ( ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) = v7) % 182.00/27.90 | | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ % 182.00/27.90 | $i(v3) | ? [v8: int] : ( ~ (v8 = 0) & % 182.00/27.90 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v8) | (( ~ % 182.00/27.90 | (v7 = 0) | v3 = v2) & ( ~ (v3 = v2) | v7 = 0)))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_power__strict__mono) implies: % 182.00/27.90 | (78) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.90 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 182.00/27.90 | [v10: int] : (v10 = 0 | ~ (c_Orderings_Oord__class_Oless(v4, v7, % 182.00/27.90 | v9) = v10) | ~ (c_Power_Opower__class_Opower(v4) = v5) | ~ % 182.00/27.90 | (hAPP(v8, v1) = v9) | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = % 182.00/27.90 | v6) | ~ (hAPP(v5, v2) = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 182.00/27.90 | | ~ $i(v1) | ? [v11: any] : ? [v12: any] : ? [v13: $i] : ? % 182.00/27.90 | [v14: any] : ? [v15: any] : (c_Orderings_Oord__class_Oless(v4, % 182.00/27.90 | v3, v2) = v12 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 182.00/27.90 | v1) = v15 & class_Rings_Olinordered__semidom(v4) = v11 & % 182.00/27.90 | c_Orderings_Oord__class_Oless__eq(v4, v13, v3) = v14 & % 182.00/27.90 | c_Groups_Ozero__class_Ozero(v4) = v13 & $i(v13) & ( ~ (v15 = 0) % 182.00/27.90 | | ~ (v14 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_realpow__minus__mult) implies: % 182.00/27.90 | (79) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 182.00/27.90 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 182.00/27.90 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 182.00/27.90 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 182.00/27.90 | [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) % 182.00/27.90 | = v8) | ~ (c_Power_Opower__class_Opower(v4) = v6) | ~ % 182.00/27.90 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = % 182.00/27.90 | v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ % 182.00/27.90 | (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? % 182.00/27.90 | [v12: any] : ? [v13: any] : ? [v14: $i] : % 182.00/27.90 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v13 & % 182.00/27.90 | class_Groups_Omonoid__mult(v4) = v12 & hAPP(v7, v3) = v14 & % 182.00/27.90 | $i(v14) & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = v11)))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_dvd__1__iff__1) implies: % 182.00/27.90 | (80) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 182.00/27.90 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.90 | [v2: $i] : (v2 = v1 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, % 182.00/27.90 | v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 = 0 | ~ % 182.00/27.90 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v1) = v2))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_diff__add__0) implies: % 182.00/27.90 | (81) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | % 182.00/27.90 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 182.00/27.90 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 182.00/27.90 | $i(v2) | ~ $i(v1))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_diff__is__0__eq_H) implies: % 182.00/27.90 | (82) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 182.00/27.90 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 182.00/27.90 | $i(v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 182.00/27.90 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) = v4))) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_diff__is__0__eq) implies: % 182.00/27.90 | (83) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.90 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 182.00/27.90 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 182.00/27.90 | $i(v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 182.00/27.90 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) = v4)) & % 182.00/27.90 | ! [v1: $i] : ! [v2: $i] : ( ~ % 182.00/27.90 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v0) | ~ % 182.00/27.90 | $i(v2) | ~ $i(v1) | % 182.00/27.90 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) = 0)) % 182.00/27.90 | % 182.00/27.90 | ALPHA: (fact_nat__mult__dvd__cancel__disj) implies: % 182.00/27.91 | (84) ? [v0: $i] : ? [v1: $i] : % 182.00/27.91 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 182.00/27.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 182.00/27.91 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.91 | ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ % 182.00/27.91 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) = v8) | ~ % 182.00/27.91 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = % 182.00/27.91 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ( ~ (v4 = v1) & ? % 182.00/27.91 | [v9: int] : ( ~ (v9 = 0) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 182.00/27.91 | v3, v2) = v9))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 182.00/27.91 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v1 | ~ % 182.00/27.91 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) = 0) | ~ (hAPP(v5, % 182.00/27.91 | v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | % 182.00/27.91 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 182.00/27.91 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) = 0)) % 182.00/27.91 | % 182.00/27.91 | ALPHA: (fact_gr0__conv__Suc) implies: % 182.00/27.91 | (85) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.91 | & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v2) | ~ % 182.00/27.91 | $i(v1) | ! [v3: $i] : ( ~ (c_Nat_OSuc(v3) = v1) | ~ $i(v3))) & % 182.00/27.91 | ! [v1: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) % 182.00/27.91 | = 0) | ~ $i(v1) | ? [v2: $i] : (c_Nat_OSuc(v2) = v1 & % 182.00/27.91 | $i(v2)))) % 182.00/27.91 | % 182.00/27.91 | ALPHA: (fact_less__Suc0) implies: % 182.00/27.91 | (86) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 182.00/27.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.91 | [v2: $i] : (v2 = v0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.00/27.91 | v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 = 0 | ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v2))) % 182.00/27.91 | % 182.00/27.91 | ALPHA: (fact_less__Suc__eq__0__disj) implies: % 182.00/27.91 | (87) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.91 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | % 182.00/27.91 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) = v4) | ~ % 182.00/27.91 | (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v2 = v0) & ! % 182.00/27.91 | [v5: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v5, % 182.00/27.91 | v1) = 0) | ~ $i(v5) | ? [v6: $i] : ( ~ (v6 = v2) & % 182.00/27.91 | c_Nat_OSuc(v5) = v6 & $i(v6))))) & ! [v1: $i] : ! [v2: $i] % 182.00/27.91 | : ! [v3: $i] : (v2 = v0 | ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) = 0) | ~ % 182.00/27.91 | (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) = 0 & % 182.00/27.91 | c_Nat_OSuc(v4) = v2 & $i(v4)))) % 182.00/27.91 | % 182.00/27.91 | ALPHA: (fact_add__gr__0) implies: % 182.00/27.91 | (88) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.91 | & ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 % 182.00/27.91 | | v3 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) % 182.00/27.91 | = v3) | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = % 182.00/27.91 | v4) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? [v6: int] : ( ~ % 182.00/27.91 | (v6 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = % 182.00/27.91 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v5 & % 182.00/27.91 | $i(v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: % 182.00/27.91 | any] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = % 182.00/27.91 | v3) | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = % 182.00/27.91 | v4) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = 0 & % 182.00/27.91 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v5 & $i(v5)) % 182.00/27.91 | | ( ~ (v4 = 0) & ~ (v3 = 0)))) % 182.00/27.91 | % 182.00/27.91 | ALPHA: (fact_nat__0__less__mult__iff) implies: % 182.00/27.91 | (89) ? [v0: $i] : ? [v1: $i] : % 182.00/27.91 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.91 | [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v4) | ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v5) | ~ % 182.00/27.91 | $i(v3) | ~ $i(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( % 182.00/27.91 | ~ (v8 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v7) % 182.00/27.91 | = v8 & hAPP(v6, v2) = v7 & hAPP(v1, v3) = v6 & $i(v7) & $i(v6)) % 182.00/27.91 | | (v5 = 0 & v4 = 0)) & ! [v2: $i] : ! [v3: $i] : ( ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = 0) | ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = 0) | ~ % 182.00/27.91 | $i(v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = 0 & hAPP(v4, % 182.00/27.91 | v2) = v5 & hAPP(v1, v3) = v4 & $i(v5) & $i(v4)))) % 182.00/27.91 | % 182.00/27.91 | ALPHA: (fact_mult__less__cancel1) implies: % 182.00/27.91 | (90) ? [v0: $i] : ? [v1: $i] : % 182.00/27.91 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 182.00/27.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 182.00/27.91 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.91 | ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) = v8) | ~ % 182.00/27.91 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = % 182.00/27.91 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : ? % 182.00/27.91 | [v10: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = % 182.00/27.91 | v10 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = v9 & % 182.00/27.91 | ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! % 182.00/27.91 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) = 0) | ~ % 182.00/27.91 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = % 182.00/27.91 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = 0 & % 182.00/27.91 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = 0))) % 182.00/27.91 | % 182.00/27.91 | ALPHA: (fact_mult__less__cancel2) implies: % 182.00/27.91 | (91) ? [v0: $i] : ? [v1: $i] : % 182.00/27.91 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 182.00/27.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 182.00/27.91 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.91 | ! [v7: $i] : ! [v8: $i] : ! [v9: int] : (v9 = 0 | ~ % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) = v9) | ~ % 182.00/27.91 | (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 182.00/27.91 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 182.00/27.91 | | ? [v10: any] : ? [v11: any] : % 182.00/27.91 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) = v11 & % 182.00/27.91 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v10 & ( ~ % 182.00/27.91 | (v11 = 0) | ~ (v10 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! % 182.00/27.91 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( % 182.00/27.91 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) = 0) | ~ % 182.00/27.91 | (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 182.00/27.91 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 182.00/27.91 | | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) = 0 & % 182.00/27.91 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = 0))) % 182.00/27.91 | % 182.00/27.91 | ALPHA: (fact_mult__less__mono1) implies: % 182.00/27.92 | (92) ? [v0: $i] : ? [v1: $i] : % 182.00/27.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.92 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.92 | ! [v7: $i] : ! [v8: $i] : ! [v9: int] : (v9 = 0 | ~ % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) = v9) | ~ % 182.00/27.92 | (hAPP(v7, v2) = v8) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = % 182.00/27.92 | v5) | ~ (hAPP(v1, v3) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 182.00/27.92 | | ? [v10: any] : ? [v11: any] : % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) = v10 & % 182.00/27.92 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v11 & ( ~ % 182.00/27.92 | (v11 = 0) | ~ (v10 = 0))))) % 182.00/27.92 | % 182.00/27.92 | ALPHA: (fact_mult__less__mono2) implies: % 182.00/27.92 | (93) ? [v0: $i] : ? [v1: $i] : % 182.00/27.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.92 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.92 | ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) = v8) | ~ % 182.00/27.92 | (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ (hAPP(v1, v2) = % 182.00/27.92 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : ? % 182.00/27.92 | [v10: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) = % 182.00/27.92 | v9 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v10 & % 182.00/27.92 | ( ~ (v10 = 0) | ~ (v9 = 0))))) % 182.00/27.92 | % 182.00/27.92 | ALPHA: (fact_nat__mult__less__cancel1) implies: % 182.00/27.92 | (94) ? [v0: $i] : ? [v1: $i] : % 182.00/27.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.92 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.92 | ! [v7: $i] : ! [v8: any] : ( ~ % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) = v8) | ~ % 182.00/27.92 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = % 182.00/27.92 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : ? % 182.00/27.92 | [v10: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = % 182.00/27.92 | v10 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v9 & % 182.00/27.92 | ( ~ (v9 = 0) | (( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = % 182.00/27.92 | 0)))))) % 182.00/27.92 | % 182.00/27.92 | ALPHA: (fact_nat__mult__eq__cancel1) implies: % 182.00/27.92 | (95) ? [v0: $i] : ? [v1: $i] : % 182.00/27.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.92 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 182.00/27.92 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.00/27.92 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 182.00/27.92 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: % 182.00/27.92 | int] : ( ~ (v8 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.00/27.92 | v0, v4) = v8) | (( ~ (v7 = v6) | v3 = v2) & ( ~ (v3 = v2) | v7 % 182.00/27.92 | = v6)))) % 182.00/27.92 | % 182.00/27.92 | ALPHA: (fact_nat__power__less__imp__less) implies: % 182.00/27.92 | (96) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 182.00/27.92 | = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 182.00/27.92 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 182.00/27.92 | [v6: $i] : ! [v7: $i] : ( ~ % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) = 0) | ~ % 182.00/27.92 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = % 182.00/27.92 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: any] : ? [v9: % 182.00/27.92 | any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = v9 % 182.00/27.92 | & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) = v8 & ( ~ % 182.00/27.92 | (v8 = 0) | v9 = 0)))) % 182.00/27.92 | % 182.00/27.92 | ALPHA: (fact_n__less__m__mult__n) implies: % 182.00/27.92 | (97) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 % 182.00/27.92 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 182.00/27.92 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.00/27.92 | [v7: int] : (v7 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.00/27.92 | v4, v6) = v7) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = % 182.00/27.92 | v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : ? [v9: any] : % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = v8 & % 182.00/27.92 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v9 & ( ~ % 182.00/27.92 | (v9 = 0) | ~ (v8 = 0))))) % 182.00/27.92 | % 182.00/27.92 | ALPHA: (fact_n__less__n__mult__m) implies: % 182.00/27.92 | (98) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 % 182.00/27.92 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 182.00/27.92 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.00/27.92 | [v7: int] : (v7 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.00/27.92 | v4, v6) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = % 182.00/27.92 | v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : ? [v9: any] : % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = v8 & % 182.00/27.92 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v9 & ( ~ % 182.00/27.92 | (v9 = 0) | ~ (v8 = 0))))) % 182.00/27.92 | % 182.00/27.92 | ALPHA: (fact_one__less__mult) implies: % 182.00/27.92 | (99) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.92 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & c_Nat_OSuc(v0) = v1 % 182.00/27.92 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 182.00/27.92 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = 0) | ~ % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = 0) | ~ % 182.00/27.92 | $i(v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : % 182.00/27.92 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6) = 0 & hAPP(v5, % 182.00/27.92 | v4) = v6 & hAPP(v2, v3) = v5 & $i(v6) & $i(v5)))) % 182.00/27.92 | % 182.00/27.92 | ALPHA: (fact_mult__le__cancel2) implies: % 182.00/27.93 | (100) ? [v0: $i] : ? [v1: $i] : % 182.00/27.93 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 182.00/27.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & % 182.00/27.93 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 182.00/27.93 | : ! [v7: $i] : ! [v8: $i] : ! [v9: int] : (v9 = 0 | ~ % 182.00/27.93 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) = v9) | % 182.00/27.93 | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 182.00/27.93 | = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 182.00/27.93 | $i(v2) | ? [v10: int] : ( ~ (v10 = 0) & % 182.00/27.93 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = 0 & % 182.00/27.93 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) = v10)) % 182.00/27.93 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 182.00/27.93 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 182.00/27.93 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) = 0) | ~ % 182.00/27.93 | (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 182.00/27.93 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 182.00/27.93 | $i(v2) | ? [v9: any] : ? [v10: any] : % 182.00/27.93 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v9 & % 182.00/27.93 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) = v10 & % 182.00/27.93 | ( ~ (v9 = 0) | v10 = 0)))) % 182.00/27.93 | % 182.00/27.93 | ALPHA: (fact_mult__le__cancel1) implies: % 182.00/27.93 | (101) ? [v0: $i] : ? [v1: $i] : % 182.00/27.93 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 182.00/27.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & % 182.00/27.93 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 182.00/27.93 | : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ % 182.00/27.93 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) = v8) | % 182.00/27.93 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) % 182.00/27.93 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: int] : ( ~ % 182.00/27.93 | (v9 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = % 182.00/27.93 | 0 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) = % 182.00/27.93 | v9)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 182.00/27.93 | ! [v6: $i] : ! [v7: $i] : ( ~ % 182.00/27.93 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) = 0) | ~ % 182.00/27.93 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = % 182.00/27.93 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: any] : ? % 182.00/27.93 | [v9: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) = % 182.00/27.93 | v8 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) = % 182.00/27.93 | v9 & ( ~ (v8 = 0) | v9 = 0)))) % 182.00/27.93 | % 182.00/27.93 | ALPHA: (fact_nat__mult__le__cancel1) implies: % 182.00/27.93 | (102) ? [v0: $i] : ? [v1: $i] : % 182.00/27.93 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 182.00/27.93 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 182.00/27.93 | : ! [v7: $i] : ! [v8: any] : ( ~ % 182.00/27.93 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) = v8) | % 182.00/27.93 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) % 182.00/27.93 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: any] : ? % 182.00/27.93 | [v10: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) % 182.00/27.93 | = v9 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) = % 182.00/27.93 | v10 & ( ~ (v9 = 0) | (( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | % 182.00/27.93 | v10 = 0)))))) % 182.00/27.93 | % 182.00/27.93 | ALPHA: (fact_power__eq__imp__eq__base) implies: % 182.00/27.93 | (103) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.93 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.93 | $i] : (v3 = v1 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.00/27.93 | v0, v2) = 0) | ~ (c_Orderings_Oord__class_Oless__eq(v4, v5, % 182.00/27.93 | v3) = 0) | ~ (c_Orderings_Oord__class_Oless__eq(v4, v5, v1) % 182.00/27.93 | = 0) | ~ (c_Groups_Ozero__class_Ozero(v4) = v5) | ~ $i(v4) | % 182.00/27.93 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v6: any] : ? [v7: $i] : % 182.00/27.93 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 182.00/27.93 | (class_Rings_Olinordered__semidom(v4) = v6 & % 182.00/27.93 | c_Power_Opower__class_Opower(v4) = v7 & hAPP(v10, v2) = v11 & % 182.00/27.93 | hAPP(v8, v2) = v9 & hAPP(v7, v3) = v8 & hAPP(v7, v1) = v10 & % 182.00/27.93 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & ( ~ (v11 = v9) | % 182.00/27.93 | ~ (v6 = 0))))) % 182.00/27.93 | % 182.00/27.93 | ALPHA: (fact_add__eq__if) implies: % 182.00/27.93 | (104) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 182.00/27.93 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 182.00/27.93 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 182.00/27.93 | (v3 = v0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = % 182.00/27.93 | v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = % 182.00/27.93 | v5) | ~ $i(v3) | ~ $i(v2) | ? [v6: $i] : % 182.00/27.93 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v6 & % 182.00/27.93 | c_Nat_OSuc(v5) = v6 & $i(v6))) & ! [v2: $i] : ! [v3: $i] : % 182.00/27.93 | (v3 = v2 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = % 182.00/27.93 | v3) | ~ $i(v2))) % 182.00/27.93 | % 182.00/27.93 | ALPHA: (fact_mult__eq__if) implies: % 182.00/27.93 | (105) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 182.00/27.93 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 182.00/27.93 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 182.00/27.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 182.00/27.93 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.00/27.93 | [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ % 182.00/27.93 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~ % 182.00/27.93 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~ % 182.00/27.93 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ % 182.00/27.93 | $i(v3) | ? [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & % 182.00/27.93 | $i(v9) & $i(v8))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 182.00/27.93 | (v5 = v0 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v0) = v4) | ~ % 182.00/27.93 | $i(v3))) % 182.00/27.93 | % 182.00/27.93 | ALPHA: (fact_dvd__power) implies: % 182.00/27.93 | (106) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.93 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 182.00/27.93 | $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ % 182.00/27.93 | (c_Rings_Odvd__class_Odvd(v3, v1, v6) = v7) | ~ % 182.00/27.93 | (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v2) = v6) % 182.00/27.93 | | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? % 182.00/27.93 | [v8: any] : ? [v9: any] : ? [v10: $i] : % 182.00/27.93 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = v9 & % 182.00/27.93 | c_Groups_Oone__class_Oone(v3) = v10 & % 182.00/27.93 | class_Rings_Ocomm__semiring__1(v3) = v8 & $i(v10) & ( ~ (v8 = % 182.00/27.93 | 0) | ( ~ (v10 = v1) & ~ (v9 = 0)))))) % 182.00/27.93 | % 182.00/27.93 | ALPHA: (fact_power__eq__if) implies: % 182.00/27.93 | (107) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 182.00/27.93 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 182.00/27.93 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 182.00/27.93 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 & % 182.00/27.93 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & % 182.00/27.93 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 182.00/27.93 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~ % 182.00/27.93 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ % 182.00/27.93 | (hAPP(v7, v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) % 182.00/27.93 | = v7) | ~ (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | % 182.00/27.93 | (hAPP(v6, v5) = v10 & $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! % 182.00/27.93 | [v6: $i] : (v6 = v2 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = % 182.00/27.93 | v5) | ~ $i(v4))) % 182.00/27.93 | % 182.00/27.93 | ALPHA: (fact_realpow__num__eq__if) implies: % 182.00/27.94 | (108) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 182.00/27.94 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 182.00/27.94 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 182.00/27.94 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 182.00/27.94 | ! [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, % 182.00/27.94 | v1) = v9) | ~ (c_Power_Opower__class_Opower(v4) = v5) | ~ % 182.00/27.94 | (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ (hAPP(v8, v10) = % 182.00/27.94 | v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ % 182.00/27.94 | (hAPP(v5, v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? % 182.00/27.94 | [v12: any] : ? [v13: $i] : ? [v14: $i] : % 182.00/27.94 | (class_Power_Opower(v4) = v12 & c_Groups_Oone__class_Oone(v4) = % 182.00/27.94 | v14 & hAPP(v6, v3) = v13 & $i(v14) & $i(v13) & ( ~ (v12 = 0) | % 182.00/27.94 | (( ~ (v3 = v0) | v14 = v13) & (v13 = v11 | v3 = v0)))))) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (fact_pow__divides__pow__int) implies: % 182.00/27.94 | (109) ? [v0: $i] : ? [v1: $i] : % 182.00/27.94 | (c_Power_Opower__class_Opower(tc_Int_Oint) = v0 & % 182.00/27.94 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & % 182.00/27.94 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 182.00/27.94 | : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ % 182.00/27.94 | (c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) = 0) | ~ % 182.00/27.94 | (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 182.00/27.94 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 182.00/27.94 | $i(v2) | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v2) = 0)) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (fact_pow__divides__eq__int) implies: % 182.00/27.94 | (110) ? [v0: $i] : ? [v1: $i] : % 182.00/27.94 | (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 & % 182.00/27.94 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 182.00/27.94 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 182.00/27.94 | : ! [v7: $i] : ! [v8: $i] : ! [v9: any] : (v4 = v0 | ~ % 182.00/27.94 | (c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) = v9) | ~ % 182.00/27.94 | (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = % 182.00/27.94 | v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 182.00/27.94 | $i(v2) | ? [v10: any] : (c_Rings_Odvd__class_Odvd(tc_Int_Oint, % 182.00/27.94 | v3, v2) = v10 & ( ~ (v10 = 0) | v9 = 0) & ( ~ (v9 = 0) | v10 % 182.00/27.94 | = 0)))) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Otop__greatest) implies: % 182.00/27.94 | (111) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.94 | & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 182.00/27.94 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) = v2) | ~ % 182.00/27.94 | $i(v1))) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (fact_dvd__pos__nat) implies: % 182.00/27.94 | (112) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 182.00/27.94 | & ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 182.00/27.94 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) = 0) | ~ % 182.00/27.94 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v3) | ~ % 182.00/27.94 | $i(v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 182.00/27.94 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) = v4))) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (fact_pow__divides__pow__nat) implies: % 182.00/27.94 | (113) ? [v0: $i] : ? [v1: $i] : % 182.00/27.94 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 182.00/27.94 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & % 182.00/27.94 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 182.00/27.94 | : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ % 182.00/27.94 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) = 0) | ~ % 182.00/27.94 | (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 182.00/27.94 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 182.00/27.94 | $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v2) = 0)) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (fact_pow__divides__eq__nat) implies: % 182.00/27.94 | (114) ? [v0: $i] : ? [v1: $i] : % 182.00/27.94 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 182.00/27.94 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 182.00/27.94 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 182.00/27.94 | : ! [v7: $i] : ! [v8: $i] : ! [v9: any] : (v4 = v0 | ~ % 182.00/27.94 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) = v9) | ~ % 182.00/27.94 | (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = % 182.00/27.94 | v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 182.00/27.94 | $i(v2) | ? [v10: any] : (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 182.00/27.94 | v3, v2) = v10 & ( ~ (v10 = 0) | v9 = 0) & ( ~ (v9 = 0) | v10 % 182.00/27.94 | = 0)))) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (fact_zero__less__power__nat__eq) implies: % 182.00/27.94 | (115) ? [v0: $i] : ? [v1: $i] : % 182.00/27.94 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 182.00/27.94 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 182.00/27.94 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | % 182.00/27.94 | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 182.00/27.94 | $i(v2) | ? [v6: any] : ? [v7: any] : % 182.00/27.94 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = v6 & % 182.00/27.94 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v7 & ( ~ % 182.00/27.94 | (v6 = 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 182.00/27.94 | $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = % 182.00/27.94 | v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : % 182.00/27.94 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) = v7 & % 182.00/27.94 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) = v6 & (v7 = % 182.00/27.94 | 0 | ( ~ (v6 = 0) & ~ (v2 = v0)))))) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (fact_nat__lt__two__imp__zero__or__one) implies: % 182.00/27.94 | (116) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 182.00/27.94 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 182.00/27.94 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 182.00/27.94 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) = 0) | ~ % 182.00/27.94 | $i(v3))) % 182.00/27.94 | % 182.00/27.94 | ALPHA: (tfree_0) implies: % 182.00/27.94 | (117) class_Int_Oring__char__0(t_a) = 0 % 182.00/27.94 | % 182.00/27.94 | ALPHA: (tfree_1) implies: % 182.00/27.94 | (118) class_Rings_Oidom(t_a) = 0 % 182.00/27.94 | % 182.00/27.94 | ALPHA: (conj_0) implies: % 182.00/27.95 | (119) $i(t_a) % 182.00/27.95 | (120) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & c_Polynomial_Odegree(t_a, % 182.00/27.95 | v_p) = v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 182.00/27.95 | $i(v1) & $i(v0)) % 182.00/27.95 | % 182.00/27.95 | ALPHA: (function-axioms) implies: % 182.00/27.95 | (121) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 182.00/27.95 | : (v1 = v0 | ~ (class_Rings_Oidom(v2) = v1) | ~ % 182.00/27.95 | (class_Rings_Oidom(v2) = v0)) % 182.00/27.95 | (122) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 182.00/27.95 | : (v1 = v0 | ~ (class_Int_Oring__char__0(v2) = v1) | ~ % 182.00/27.95 | (class_Int_Oring__char__0(v2) = v0)) % 182.00/27.95 | (123) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 182.00/27.95 | (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 182.00/27.95 | (c_Groups_Ozero__class_Ozero(v2) = v0)) % 182.00/27.95 | (124) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 182.00/27.95 | : (v1 = v0 | ~ (class_Groups_Ozero(v2) = v1) | ~ % 182.00/27.95 | (class_Groups_Ozero(v2) = v0)) % 182.00/27.95 | (125) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 182.00/27.95 | (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0)) % 182.00/27.95 | (126) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 182.00/27.95 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) % 182.00/27.95 | (127) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 182.00/27.95 | (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) % 182.00/27.95 | = v0)) % 182.00/27.95 | (128) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 182.00/27.95 | (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, % 182.00/27.95 | v2) = v0)) % 182.00/27.95 | (129) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 182.00/27.95 | (v1 = v0 | ~ (c_Polynomial_OpCons(v4, v3, v2) = v1) | ~ % 182.00/27.95 | (c_Polynomial_OpCons(v4, v3, v2) = v0)) % 182.00/27.95 | % 182.00/27.95 | DELTA: instantiating (5) with fresh symbol all_1083_0 gives: % 182.00/27.95 | (130) c_HOL_Obool_Obool__size(c_fTrue) = all_1083_0 & % 182.00/27.95 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1083_0 & % 182.00/27.95 | $i(all_1083_0) % 182.00/27.95 | % 182.00/27.95 | ALPHA: (130) implies: % 182.00/27.95 | (131) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1083_0 % 182.00/27.95 | % 182.00/27.95 | DELTA: instantiating (6) with fresh symbol all_1085_0 gives: % 182.00/27.95 | (132) c_HOL_Obool_Obool__size(c_fFalse) = all_1085_0 & % 182.00/27.95 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1085_0 & % 182.00/27.95 | $i(all_1085_0) % 182.00/27.95 | % 182.00/27.95 | ALPHA: (132) implies: % 182.00/27.95 | (133) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1085_0 % 182.00/27.95 | % 182.00/27.95 | DELTA: instantiating (33) with fresh symbol all_1087_0 gives: % 182.00/27.95 | (134) c_Nat_Osize__class_Osize(tc_Nat_Onat, all_1087_0) = all_1087_0 & % 182.00/27.95 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1087_0 & % 182.00/27.95 | $i(all_1087_0) % 182.00/27.95 | % 182.00/27.95 | ALPHA: (134) implies: % 182.00/27.95 | (135) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1087_0 % 182.00/27.95 | % 182.00/27.95 | DELTA: instantiating (19) with fresh symbol all_1089_0 gives: % 182.00/27.95 | (136) c_Nat_Osize__class_Osize(tc_HOL_Obool, c_fFalse) = all_1089_0 & % 182.00/27.95 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1089_0 & % 182.00/27.95 | $i(all_1089_0) % 182.00/27.95 | % 182.00/27.95 | ALPHA: (136) implies: % 182.00/27.95 | (137) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1089_0 % 182.00/27.95 | % 182.00/27.95 | DELTA: instantiating (20) with fresh symbol all_1091_0 gives: % 182.00/27.95 | (138) c_Nat_Osize__class_Osize(tc_HOL_Obool, c_fTrue) = all_1091_0 & % 182.00/27.95 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1091_0 & % 182.00/27.95 | $i(all_1091_0) % 182.00/27.95 | % 182.00/27.95 | ALPHA: (138) implies: % 182.00/27.95 | (139) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1091_0 % 182.00/27.95 | % 182.00/27.95 | DELTA: instantiating (21) with fresh symbol all_1097_0 gives: % 182.00/27.95 | (140) c_Nat_Onat_Onat__size(all_1097_0) = all_1097_0 & % 182.00/27.95 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1097_0 & % 182.00/27.95 | $i(all_1097_0) % 182.00/27.95 | % 182.00/27.95 | ALPHA: (140) implies: % 182.00/27.95 | (141) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1097_0 % 182.00/27.95 | % 182.00/27.95 | DELTA: instantiating (65) with fresh symbol all_1099_0 gives: % 182.00/27.95 | (142) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1099_0 & % 182.00/27.95 | $i(all_1099_0) & ! [v0: $i] : ( ~ % 182.00/27.95 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1099_0) = 0) | % 182.00/27.95 | ~ $i(v0)) % 182.00/27.95 | % 182.00/27.95 | ALPHA: (142) implies: % 182.00/27.95 | (143) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1099_0 % 182.00/27.95 | % 182.37/27.95 | DELTA: instantiating (65) with fresh symbol all_1102_0 gives: % 182.37/27.95 | (144) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1102_0 & % 182.37/27.95 | $i(all_1102_0) & ! [v0: $i] : ( ~ % 182.37/27.95 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1102_0) = 0) | % 182.37/27.95 | ~ $i(v0)) % 182.37/27.95 | % 182.37/27.95 | ALPHA: (144) implies: % 182.37/27.95 | (145) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1102_0 % 182.37/27.95 | % 182.37/27.95 | DELTA: instantiating (23) with fresh symbol all_1105_0 gives: % 182.37/27.95 | (146) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1105_0 & % 182.37/27.95 | $i(all_1105_0) & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_1105_0) | ~ % 182.37/27.95 | $i(v0)) % 182.37/27.95 | % 182.37/27.95 | ALPHA: (146) implies: % 182.37/27.95 | (147) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1105_0 % 182.37/27.95 | % 182.37/27.95 | DELTA: instantiating (23) with fresh symbol all_1108_0 gives: % 182.37/27.95 | (148) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1108_0 & % 182.37/27.95 | $i(all_1108_0) & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_1108_0) | ~ % 182.37/27.95 | $i(v0)) % 182.37/27.95 | % 182.37/27.95 | ALPHA: (148) implies: % 182.37/27.95 | (149) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1108_0 % 182.37/27.95 | % 182.37/27.95 | DELTA: instantiating (23) with fresh symbol all_1111_0 gives: % 182.37/27.95 | (150) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1111_0 & % 182.37/27.95 | $i(all_1111_0) & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_1111_0) | ~ % 182.37/27.95 | $i(v0)) % 182.37/27.95 | % 182.37/27.95 | ALPHA: (150) implies: % 182.37/27.95 | (151) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1111_0 % 182.37/27.95 | % 182.37/27.95 | DELTA: instantiating (65) with fresh symbol all_1114_0 gives: % 182.37/27.95 | (152) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1114_0 & % 182.37/27.95 | $i(all_1114_0) & ! [v0: $i] : ( ~ % 182.37/27.95 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1114_0) = 0) | % 182.37/27.95 | ~ $i(v0)) % 182.37/27.95 | % 182.37/27.95 | ALPHA: (152) implies: % 182.37/27.95 | (153) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1114_0 % 182.37/27.95 | % 182.37/27.95 | DELTA: instantiating (23) with fresh symbol all_1117_0 gives: % 182.37/27.95 | (154) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1117_0 & % 182.37/27.95 | $i(all_1117_0) & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_1117_0) | ~ % 182.37/27.95 | $i(v0)) % 182.37/27.95 | % 182.37/27.95 | ALPHA: (154) implies: % 182.37/27.95 | (155) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1117_0 % 182.37/27.95 | % 182.37/27.95 | DELTA: instantiating (65) with fresh symbol all_1120_0 gives: % 182.37/27.95 | (156) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1120_0 & % 182.37/27.95 | $i(all_1120_0) & ! [v0: $i] : ( ~ % 182.37/27.95 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1120_0) = 0) | % 182.37/27.95 | ~ $i(v0)) % 182.37/27.95 | % 182.37/27.95 | ALPHA: (156) implies: % 182.37/27.95 | (157) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1120_0 % 182.37/27.95 | % 182.37/27.95 | DELTA: instantiating (23) with fresh symbol all_1123_0 gives: % 182.37/27.96 | (158) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1123_0 & % 182.37/27.96 | $i(all_1123_0) & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_1123_0) | ~ % 182.37/27.96 | $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (158) implies: % 182.37/27.96 | (159) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1123_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (23) with fresh symbol all_1126_0 gives: % 182.37/27.96 | (160) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1126_0 & % 182.37/27.96 | $i(all_1126_0) & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_1126_0) | ~ % 182.37/27.96 | $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (160) implies: % 182.37/27.96 | (161) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1126_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (30) with fresh symbol all_1129_0 gives: % 182.37/27.96 | (162) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1129_0 & % 182.37/27.96 | $i(all_1129_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 182.37/27.96 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1129_0, v0) = % 182.37/27.96 | v1) | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (162) implies: % 182.37/27.96 | (163) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1129_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (28) with fresh symbol all_1134_0 gives: % 182.37/27.96 | (164) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1134_0 & % 182.37/27.96 | $i(all_1134_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 182.37/27.96 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1134_0, v0) = v1) | % 182.37/27.96 | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (164) implies: % 182.37/27.96 | (165) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1134_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (44) with fresh symbols all_1137_0, all_1137_1 gives: % 182.37/27.96 | (166) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1137_1 & % 182.37/27.96 | c_Nat_OSuc(all_1137_0) = all_1137_1 & % 182.37/27.96 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1137_0 & % 182.37/27.96 | $i(all_1137_0) & $i(all_1137_1) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (166) implies: % 182.37/27.96 | (167) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1137_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (57) with fresh symbol all_1139_0 gives: % 182.37/27.96 | (168) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1139_0 & % 182.37/27.96 | $i(all_1139_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = % 182.37/27.96 | v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.37/27.96 | all_1139_0, v1) = 0) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (168) implies: % 182.37/27.96 | (169) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1139_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (7) with fresh symbol all_1144_0 gives: % 182.37/27.96 | (170) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1144_0 & % 182.37/27.96 | $i(all_1144_0) & ! [v0: $i] : ! [v1: int] : (v1 = all_1144_0 | ~ % 182.37/27.96 | (c_Nat_Osize__class_Osize(tc_String_Oliteral, v0) = v1) | ~ % 182.37/27.96 | $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (170) implies: % 182.37/27.96 | (171) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1144_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (8) with fresh symbol all_1149_0 gives: % 182.37/27.96 | (172) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1149_0 & % 182.37/27.96 | $i(all_1149_0) & ! [v0: $i] : ! [v1: int] : (v1 = all_1149_0 | ~ % 182.37/27.96 | (c_String_Ochar_Ochar__size(v0) = v1) | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (172) implies: % 182.37/27.96 | (173) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1149_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (70) with fresh symbol all_1155_0 gives: % 182.37/27.96 | (174) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1155_0 & % 182.37/27.96 | $i(all_1155_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 182.37/27.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_1155_0) = v1) | % 182.37/27.96 | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (174) implies: % 182.37/27.96 | (175) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1155_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (71) with fresh symbol all_1158_0 gives: % 182.37/27.96 | (176) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1158_0 & % 182.37/27.96 | $i(all_1158_0) & ! [v0: $i] : ! [v1: int] : (v1 = all_1158_0 | ~ % 182.37/27.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, all_1158_0, v0) = v1) | % 182.37/27.96 | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (176) implies: % 182.37/27.96 | (177) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1158_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (27) with fresh symbol all_1167_0 gives: % 182.37/27.96 | (178) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1167_0 & % 182.37/27.96 | $i(all_1167_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 182.37/27.96 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_1167_0) = v1) | % 182.37/27.96 | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (178) implies: % 182.37/27.96 | (179) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1167_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (69) with fresh symbol all_1170_0 gives: % 182.37/27.96 | (180) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1170_0 & % 182.37/27.96 | $i(all_1170_0) & ! [v0: $i] : ! [v1: int] : (v1 = all_1170_0 | ~ % 182.37/27.96 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v0) = v1) | ~ % 182.37/27.96 | $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (180) implies: % 182.37/27.96 | (181) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1170_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (18) with fresh symbol all_1173_0 gives: % 182.37/27.96 | (182) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1173_0 & % 182.37/27.96 | $i(all_1173_0) & ! [v0: $i] : ! [v1: int] : (v1 = all_1173_0 | ~ % 182.37/27.96 | (c_Nat_Osize__class_Osize(tc_String_Ochar, v0) = v1) | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (182) implies: % 182.37/27.96 | (183) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1173_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (111) with fresh symbol all_1183_0 gives: % 182.37/27.96 | (184) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1183_0 & % 182.37/27.96 | $i(all_1183_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 182.37/27.96 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_1183_0) = v1) | ~ % 182.37/27.96 | $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (184) implies: % 182.37/27.96 | (185) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1183_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (30) with fresh symbol all_1186_0 gives: % 182.37/27.96 | (186) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_0 & % 182.37/27.96 | $i(all_1186_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 182.37/27.96 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1186_0, v0) = % 182.37/27.96 | v1) | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (186) implies: % 182.37/27.96 | (187) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (120) with fresh symbols all_1189_0, all_1189_1 gives: % 182.37/27.96 | (188) ~ (all_1189_0 = all_1189_1) & c_Polynomial_Odegree(t_a, v_p) = % 182.37/27.96 | all_1189_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1189_0 & % 182.37/27.96 | $i(all_1189_0) & $i(all_1189_1) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (188) implies: % 182.37/27.96 | (189) ~ (all_1189_0 = all_1189_1) % 182.37/27.96 | (190) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1189_0 % 182.37/27.96 | (191) c_Polynomial_Odegree(t_a, v_p) = all_1189_1 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (63) with fresh symbol all_1191_0 gives: % 182.37/27.96 | (192) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1191_0 & % 182.37/27.96 | $i(all_1191_0) & ! [v0: any] : ! [v1: int] : (v1 = 0 | v0 = % 182.37/27.96 | all_1191_0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.37/27.96 | all_1191_0, v0) = v1) | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (192) implies: % 182.37/27.96 | (193) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1191_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (25) with fresh symbol all_1203_0 gives: % 182.37/27.96 | (194) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1203_0 & % 182.37/27.96 | $i(all_1203_0) & ! [v0: any] : ! [v1: $i] : (v0 = all_1203_0 | ~ % 182.37/27.96 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v1) | ~ $i(v1) % 182.37/27.96 | | ~ $i(v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (194) implies: % 182.37/27.96 | (195) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1203_0 % 182.37/27.96 | % 182.37/27.96 | DELTA: instantiating (29) with fresh symbol all_1206_0 gives: % 182.37/27.96 | (196) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1206_0 & % 182.37/27.96 | $i(all_1206_0) & ! [v0: any] : (v0 = all_1206_0 | ~ % 182.37/27.96 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, all_1206_0) = % 182.37/27.96 | 0) | ~ $i(v0)) & ! [v0: int] : (v0 = 0 | ~ % 182.37/27.96 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1206_0, % 182.37/27.96 | all_1206_0) = v0)) % 182.37/27.96 | % 182.37/27.96 | ALPHA: (196) implies: % 182.37/27.96 | (197) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1206_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (64) with fresh symbol all_1218_0 gives: % 182.37/27.97 | (198) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1218_0 & % 182.37/27.97 | $i(all_1218_0) & ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.37/27.97 | all_1218_0, all_1218_0) = 0) & ! [v0: any] : ! [v1: int] : (v1 % 182.37/27.97 | = 0 | v0 = all_1218_0 | ~ % 182.37/27.97 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1218_0, v0) = v1) | % 182.37/27.97 | ~ $i(v0)) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (198) implies: % 182.37/27.97 | (199) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1218_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (36) with fresh symbols all_1221_0, all_1221_1 gives: % 182.37/27.97 | (200) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1221_1 & % 182.37/27.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1221_0 & % 182.37/27.97 | $i(all_1221_0) & $i(all_1221_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.37/27.97 | (hAPP(all_1221_1, v0) = v1) | ~ $i(v0) | hAPP(v1, all_1221_0) = % 182.37/27.97 | all_1221_0) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (200) implies: % 182.37/27.97 | (201) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1221_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (56) with fresh symbols all_1224_0, all_1224_1 gives: % 182.37/27.97 | (202) c_Nat_OSuc(all_1224_1) = all_1224_0 & % 182.37/27.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1224_1 & % 182.37/27.97 | $i(all_1224_0) & $i(all_1224_1) & ! [v0: $i] : ! [v1: int] : (v1 = % 182.37/27.97 | 0 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_1224_0, v0) = v1) % 182.37/27.97 | | ~ $i(v0)) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (202) implies: % 182.37/27.97 | (203) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1224_1 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (81) with fresh symbol all_1227_0 gives: % 182.37/27.97 | (204) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1227_0 & % 182.37/27.97 | $i(all_1227_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.37/27.97 | int] : (v3 = all_1227_0 | ~ % 182.37/27.97 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 182.37/27.97 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 182.37/27.97 | | ~ $i(v0)) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (204) implies: % 182.37/27.97 | (205) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1227_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (1) with fresh symbols all_1236_0, all_1236_1, % 182.37/27.97 | all_1236_2, all_1236_3 gives: % 182.37/27.97 | (206) class_Int_Oring__char__0(t_a) = all_1236_3 & class_Rings_Oidom(t_a) = % 182.37/27.97 | all_1236_2 & c_Polynomial_Opoly(t_a, v_p) = all_1236_1 & % 182.37/27.97 | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a, t_a, % 182.37/27.97 | all_1236_1) = all_1236_0 & $i(all_1236_1) & ( ~ (all_1236_2 = 0) | % 182.37/27.97 | ~ (all_1236_3 = 0) | all_1236_0 = 0) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (206) implies: % 182.37/27.97 | (207) c_Polynomial_Opoly(t_a, v_p) = all_1236_1 % 182.37/27.97 | (208) class_Rings_Oidom(t_a) = all_1236_2 % 182.37/27.97 | (209) class_Int_Oring__char__0(t_a) = all_1236_3 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (82) with fresh symbol all_1238_0 gives: % 182.37/27.97 | (210) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1238_0 & % 182.37/27.97 | $i(all_1238_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 182.37/27.97 | all_1238_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) % 182.37/27.97 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 182.37/27.97 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = v3)) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (210) implies: % 182.37/27.97 | (211) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1238_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (112) with fresh symbol all_1244_0 gives: % 182.37/27.97 | (212) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1244_0 & % 182.37/27.97 | $i(all_1244_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 182.37/27.97 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1244_0, v1) = 0) % 182.37/27.97 | | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1244_0, v0) = % 182.37/27.97 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 182.37/27.97 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v1) = v3)) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (212) implies: % 182.37/27.97 | (213) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1244_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (62) with fresh symbol all_1247_0 gives: % 182.37/27.97 | (214) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1247_0 & % 182.37/27.97 | $i(all_1247_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.37/27.97 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v1) = 0) | ~ $i(v1) | % 182.37/27.97 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 182.37/27.97 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = v3 & % 182.37/27.97 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1247_0, v1) = v2 & % 182.37/27.97 | ( ~ (v3 = 0) | ~ (v2 = 0)))) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (214) implies: % 182.37/27.97 | (215) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1247_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (68) with fresh symbol all_1253_0 gives: % 182.37/27.97 | (216) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1253_0 & % 182.37/27.97 | $i(all_1253_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 182.37/27.97 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = all_1253_0) | % 182.37/27.97 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = all_1253_0) & % 182.37/27.97 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2 & % 182.37/27.97 | $i(v2))) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (216) implies: % 182.37/27.97 | (217) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1253_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (80) with fresh symbols all_1256_0, all_1256_1 gives: % 182.37/27.97 | (218) c_Nat_OSuc(all_1256_1) = all_1256_0 & % 182.37/27.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1256_1 & % 182.37/27.97 | $i(all_1256_0) & $i(all_1256_1) & ! [v0: any] : (v0 = all_1256_0 | % 182.37/27.97 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_1256_0) = 0) | ~ % 182.37/27.97 | $i(v0)) & ! [v0: int] : (v0 = 0 | ~ % 182.37/27.97 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_1256_0, all_1256_0) = % 182.37/27.97 | v0)) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (218) implies: % 182.37/27.97 | (219) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1256_1 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (13) with fresh symbol all_1259_0 gives: % 182.37/27.97 | (220) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1259_0 & % 182.37/27.97 | $i(all_1259_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.37/27.97 | int] : (v3 = all_1259_0 | ~ (tc_Polynomial_Opoly(v0) = v1) | ~ % 182.37/27.97 | (c_Polynomial_Odegree(v0, v2) = v3) | ~ % 182.37/27.97 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v0) | ? [v4: int] : % 182.37/27.97 | ( ~ (v4 = 0) & class_Groups_Ozero(v0) = v4)) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (220) implies: % 182.37/27.97 | (221) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1259_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (37) with fresh symbols all_1263_0, all_1263_1, % 182.37/27.97 | all_1263_2 gives: % 182.37/27.97 | (222) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1263_2 & % 182.37/27.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1263_1 & % 182.37/27.97 | hAPP(all_1263_2, all_1263_1) = all_1263_0 & $i(all_1263_0) & % 182.37/27.97 | $i(all_1263_1) & $i(all_1263_2) & ! [v0: $i] : ! [v1: int] : (v1 = % 182.37/27.97 | all_1263_1 | ~ (hAPP(all_1263_0, v0) = v1) | ~ $i(v0)) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (222) implies: % 182.37/27.97 | (223) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1263_1 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (59) with fresh symbol all_1269_0 gives: % 182.37/27.97 | (224) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1269_0 & % 182.37/27.97 | $i(all_1269_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.37/27.97 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) = 0) | ~ $i(v1) | % 182.37/27.97 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 182.37/27.97 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1269_0, v0) = v2 & % 182.37/27.97 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = v3 & ( ~ % 182.37/27.97 | (v2 = 0) | v3 = 0))) % 182.37/27.97 | % 182.37/27.97 | ALPHA: (224) implies: % 182.37/27.97 | (225) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1269_0 % 182.37/27.97 | % 182.37/27.97 | DELTA: instantiating (54) with fresh symbol all_1275_0 gives: % 182.37/27.98 | (226) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1275_0 & % 182.37/27.98 | $i(all_1275_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.37/27.98 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower_Opower(v3, % 182.37/27.98 | v2, v1) = v4) | ~ (hAPP(v4, v0) = v5) | ~ $i(v3) | ~ $i(v2) % 182.37/27.98 | | ~ $i(v1) | ~ $i(v0) | hAPP(v5, all_1275_0) = v2) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (226) implies: % 182.37/27.98 | (227) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1275_0 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (86) with fresh symbols all_1281_0, all_1281_1 gives: % 182.37/27.98 | (228) c_Nat_OSuc(all_1281_1) = all_1281_0 & % 182.37/27.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1281_1 & % 182.37/27.98 | $i(all_1281_0) & $i(all_1281_1) & ! [v0: any] : (v0 = all_1281_1 | % 182.37/27.98 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1281_0) = 0) % 182.37/27.98 | | ~ $i(v0)) & ! [v0: int] : (v0 = 0 | ~ % 182.37/27.98 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1281_1, all_1281_0) % 182.37/27.98 | = v0)) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (228) implies: % 182.37/27.98 | (229) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1281_1 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (26) with fresh symbol all_1287_0 gives: % 182.37/27.98 | (230) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1287_0 & % 182.37/27.98 | $i(all_1287_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.37/27.98 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1287_0) | % 182.37/27.98 | ~ $i(v1) | ~ $i(v0) | (v1 = all_1287_0 & v0 = all_1287_0)) & ! % 182.37/27.98 | [v0: int] : (v0 = all_1287_0 | ~ % 182.37/27.98 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1287_0, all_1287_0) = % 182.37/27.98 | v0)) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (230) implies: % 182.37/27.98 | (231) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1287_0 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (46) with fresh symbol all_1296_0 gives: % 182.37/27.98 | (232) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1296_0 & % 182.37/27.98 | $i(all_1296_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.37/27.98 | int] : (v3 = all_1296_0 | ~ (c_Groups_Oone__class_Oone(v1) = v2) | % 182.37/27.98 | ~ (tc_Polynomial_Opoly(v0) = v1) | ~ (c_Polynomial_Odegree(v0, % 182.37/27.98 | v2) = v3) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 182.37/27.98 | class_Rings_Ocomm__semiring__1(v0) = v4)) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (232) implies: % 182.37/27.98 | (233) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1296_0 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (116) with fresh symbols all_1302_0, all_1302_1, % 182.37/27.98 | all_1302_2 gives: % 182.37/27.98 | (234) c_Nat_OSuc(all_1302_1) = all_1302_0 & c_Nat_OSuc(all_1302_2) = % 182.37/27.98 | all_1302_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1302_2 & % 182.37/27.98 | $i(all_1302_0) & $i(all_1302_1) & $i(all_1302_2) & ! [v0: any] : (v0 % 182.37/27.98 | = all_1302_1 | v0 = all_1302_2 | ~ % 182.37/27.98 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1302_0) = 0) | % 182.37/27.98 | ~ $i(v0)) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (234) implies: % 182.37/27.98 | (235) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1302_2 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (72) with fresh symbol all_1305_0 gives: % 182.37/27.98 | (236) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1305_0 & % 182.37/27.98 | $i(all_1305_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.37/27.98 | $i] : ! [v4: int] : (v4 = 0 | ~ % 182.37/27.98 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 182.37/27.98 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1) = v4) | ~ % 182.37/27.98 | (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ % 182.37/27.98 | (v5 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1305_0, % 182.37/27.98 | v1) = v5)) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (236) implies: % 182.37/27.98 | (237) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1305_0 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (85) with fresh symbol all_1323_0 gives: % 182.37/27.98 | (238) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1323_0 & % 182.37/27.98 | $i(all_1323_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 182.37/27.98 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1323_0, v0) = v1) | % 182.37/27.98 | ~ $i(v0) | ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v0) | ~ $i(v2))) & % 182.37/27.98 | ! [v0: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.37/27.98 | all_1323_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 182.37/27.98 | (c_Nat_OSuc(v1) = v0 & $i(v1))) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (238) implies: % 182.37/27.98 | (239) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1323_0 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (73) with fresh symbols all_1329_0, all_1329_1 gives: % 182.37/27.98 | (240) c_Nat_OSuc(all_1329_1) = all_1329_0 & % 182.37/27.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1329_1 & % 182.37/27.98 | $i(all_1329_0) & $i(all_1329_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.37/27.98 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_1329_0) = v1) | % 182.37/27.98 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 182.37/27.98 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1329_1, v0) = v2 & % 182.37/27.98 | c_Nat_OSuc(v1) = v3 & $i(v3) & ( ~ (v2 = 0) | v3 = v0))) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (240) implies: % 182.37/27.98 | (241) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1329_1 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (24) with fresh symbols all_1332_0, all_1332_1 gives: % 182.37/27.98 | (242) c_Nat_OSuc(all_1332_1) = all_1332_0 & % 182.37/27.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1332_1 & % 182.37/27.98 | $i(all_1332_0) & $i(all_1332_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.37/27.98 | (c_Nat_Onat_Onat__size(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 182.37/27.98 | [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, % 182.37/27.98 | all_1332_0) = v3 & c_Nat_Onat_Onat__size(v2) = v3 & % 182.37/27.98 | c_Nat_OSuc(v0) = v2 & $i(v3) & $i(v2))) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (242) implies: % 182.37/27.98 | (243) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1332_1 % 182.37/27.98 | % 182.37/27.98 | DELTA: instantiating (49) with fresh symbols all_1335_0, all_1335_1, % 182.37/27.98 | all_1335_2, all_1335_3 gives: % 182.37/27.98 | (244) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1335_3 & % 182.37/27.98 | c_Nat_OSuc(all_1335_2) = all_1335_1 & % 182.37/27.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1335_2 & % 182.37/27.98 | hAPP(all_1335_3, all_1335_1) = all_1335_0 & $i(all_1335_0) & % 182.37/27.98 | $i(all_1335_1) & $i(all_1335_2) & $i(all_1335_3) & ! [v0: $i] : ! % 182.37/27.98 | [v1: int] : (v1 = all_1335_1 | ~ (hAPP(all_1335_0, v0) = v1) | ~ % 182.37/27.98 | $i(v0)) % 182.37/27.98 | % 182.37/27.98 | ALPHA: (244) implies: % 182.37/27.98 | (245) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1335_2 % 182.49/27.98 | % 182.49/27.98 | DELTA: instantiating (32) with fresh symbols all_1338_0, all_1338_1 gives: % 182.49/27.98 | (246) c_Nat_OSuc(all_1338_1) = all_1338_0 & % 182.49/27.98 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1338_1 & % 182.49/27.98 | $i(all_1338_0) & $i(all_1338_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.49/27.98 | (c_Nat_Osize__class_Osize(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ? % 182.49/27.98 | [v2: $i] : ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 182.49/27.98 | v1, all_1338_0) = v3 & c_Nat_OSuc(v0) = v2 & % 182.49/27.98 | c_Nat_Osize__class_Osize(tc_Nat_Onat, v2) = v3 & $i(v3) & % 182.49/27.98 | $i(v2))) % 182.49/27.98 | % 182.49/27.98 | ALPHA: (246) implies: % 182.49/27.98 | (247) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1338_1 % 182.49/27.98 | % 182.49/27.98 | DELTA: instantiating (12) with fresh symbol all_1341_0 gives: % 182.49/27.98 | (248) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1341_0 & % 182.49/27.98 | $i(all_1341_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/27.98 | $i] : ! [v4: $i] : ! [v5: int] : (v5 = all_1341_0 | ~ % 182.49/27.98 | (tc_Polynomial_Opoly(v1) = v2) | ~ (c_Polynomial_OpCons(v1, v0, % 182.49/27.98 | v3) = v4) | ~ (c_Polynomial_Odegree(v1, v4) = v5) | ~ % 182.49/27.98 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 182.49/27.98 | [v6: int] : ( ~ (v6 = 0) & class_Groups_Ozero(v1) = v6)) % 182.49/27.98 | % 182.49/27.98 | ALPHA: (248) implies: % 182.49/27.98 | (249) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1341_0 % 182.49/27.99 | (250) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 182.49/27.99 | ! [v5: int] : (v5 = all_1341_0 | ~ (tc_Polynomial_Opoly(v1) = v2) | % 182.49/27.99 | ~ (c_Polynomial_OpCons(v1, v0, v3) = v4) | ~ % 182.49/27.99 | (c_Polynomial_Odegree(v1, v4) = v5) | ~ % 182.49/27.99 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 182.49/27.99 | [v6: int] : ( ~ (v6 = 0) & class_Groups_Ozero(v1) = v6)) % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (67) with fresh symbol all_1344_0 gives: % 182.49/27.99 | (251) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1344_0 & % 182.49/27.99 | $i(all_1344_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/27.99 | int] : (v3 = 0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, % 182.49/27.99 | v1) = v2) | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, % 182.49/27.99 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] % 182.49/27.99 | : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1344_0, v1) = v4 % 182.49/27.99 | & c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1344_0, v0) = v5 % 182.49/27.99 | & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (251) implies: % 182.49/27.99 | (252) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1344_0 % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (75) with fresh symbols all_1347_0, all_1347_1 gives: % 182.49/27.99 | (253) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1347_0 & % 182.49/27.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1347_1 & % 182.49/27.99 | $i(all_1347_0) & $i(all_1347_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.49/27.99 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_1347_0) = v1) | % 182.49/27.99 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 182.49/27.99 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1347_1, v0) = v2 & % 182.49/27.99 | c_Nat_OSuc(v1) = v3 & $i(v3) & ( ~ (v2 = 0) | v3 = v0))) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (253) implies: % 182.49/27.99 | (254) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1347_1 % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (75) with fresh symbols all_1356_0, all_1356_1 gives: % 182.49/27.99 | (255) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1356_0 & % 182.49/27.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1356_1 & % 182.49/27.99 | $i(all_1356_0) & $i(all_1356_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.49/27.99 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_1356_0) = v1) | % 182.49/27.99 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 182.49/27.99 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1356_1, v0) = v2 & % 182.49/27.99 | c_Nat_OSuc(v1) = v3 & $i(v3) & ( ~ (v2 = 0) | v3 = v0))) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (255) implies: % 182.49/27.99 | (256) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1356_1 % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (43) with fresh symbol all_1359_0 gives: % 182.49/27.99 | (257) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1359_0 & % 182.49/27.99 | $i(all_1359_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/27.99 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v3) = v4) | ~ % 182.49/27.99 | (c_Polynomial_OpCons(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 182.49/27.99 | $i(v0) | ? [v5: any] : ? [v6: $i] : (class_Groups_Ozero(v2) = v5 % 182.49/27.99 | & hAPP(v4, all_1359_0) = v6 & $i(v6) & ( ~ (v5 = 0) | v6 = v1))) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (257) implies: % 182.49/27.99 | (258) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1359_0 % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (11) with fresh symbol all_1362_0 gives: % 182.49/27.99 | (259) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1362_0 & % 182.49/27.99 | $i(all_1362_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/27.99 | $i] : ! [v4: $i] : ( ~ (tc_Polynomial_Opoly(v1) = v2) | ~ % 182.49/27.99 | (c_Polynomial_OpCons(v1, v0, v3) = v4) | ~ % 182.49/27.99 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 182.49/27.99 | [v5: any] : ? [v6: $i] : (c_Polynomial_Omonom(v1, v0, all_1362_0) % 182.49/27.99 | = v6 & class_Groups_Ozero(v1) = v5 & $i(v6) & ( ~ (v5 = 0) | v6 = % 182.49/27.99 | v4))) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (259) implies: % 182.49/27.99 | (260) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1362_0 % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (83) with fresh symbol all_1365_0 gives: % 182.49/27.99 | (261) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1365_0 & % 182.49/27.99 | $i(all_1365_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 182.49/27.99 | all_1365_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) % 182.49/27.99 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 182.49/27.99 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = v3)) & % 182.49/27.99 | ! [v0: $i] : ! [v1: $i] : ( ~ % 182.49/27.99 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = all_1365_0) | % 182.49/27.99 | ~ $i(v1) | ~ $i(v0) | % 182.49/27.99 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = 0) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (261) implies: % 182.49/27.99 | (262) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1365_0 % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (45) with fresh symbols all_1368_0, all_1368_1, % 182.49/27.99 | all_1368_2 gives: % 182.49/27.99 | (263) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1368_1 & % 182.49/27.99 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1368_2 & % 182.49/27.99 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1368_0 & % 182.49/27.99 | $i(all_1368_0) & $i(all_1368_1) & $i(all_1368_2) & ! [v0: any] : ! % 182.49/27.99 | [v1: any] : ! [v2: $i] : (v1 = all_1368_0 | v0 = all_1368_1 | ~ % 182.49/27.99 | (hAPP(v2, v0) = v1) | ~ (hAPP(all_1368_2, v1) = v2) | ~ $i(v1) | % 182.49/27.99 | ~ $i(v0)) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (263) implies: % 182.49/27.99 | (264) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1368_0 % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (4) with fresh symbols all_1392_0, all_1392_1, % 182.49/27.99 | all_1392_2, all_1392_3, all_1392_4 gives: % 182.49/27.99 | (265) c_Groups_Ozero__class_Ozero(t_a) = all_1392_1 & % 182.49/27.99 | class_Int_Oring__char__0(t_a) = all_1392_4 & class_Rings_Oidom(t_a) = % 182.49/27.99 | all_1392_3 & c_Polynomial_Opoly(t_a, v_p) = all_1392_2 & % 182.49/27.99 | hAPP(all_1392_2, all_1392_1) = all_1392_0 & $i(all_1392_0) & % 182.49/27.99 | $i(all_1392_1) & $i(all_1392_2) & ! [v0: $i] : ! [v1: int] : ( ~ % 182.49/27.99 | (all_1392_3 = 0) | ~ (all_1392_4 = 0) | v1 = all_1392_0 | ~ % 182.49/27.99 | (hAPP(all_1392_2, v0) = v1) | ~ $i(v0)) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (265) implies: % 182.49/27.99 | (266) hAPP(all_1392_2, all_1392_1) = all_1392_0 % 182.49/27.99 | (267) c_Polynomial_Opoly(t_a, v_p) = all_1392_2 % 182.49/27.99 | (268) class_Rings_Oidom(t_a) = all_1392_3 % 182.49/27.99 | (269) class_Int_Oring__char__0(t_a) = all_1392_4 % 182.49/27.99 | (270) c_Groups_Ozero__class_Ozero(t_a) = all_1392_1 % 182.49/27.99 | % 182.49/27.99 | DELTA: instantiating (52) with fresh symbol all_1395_0 gives: % 182.49/27.99 | (271) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1395_0 & % 182.49/27.99 | $i(all_1395_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/27.99 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, % 182.49/27.99 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] % 182.49/27.99 | : ? [v6: $i] : (class_Power_Opower(v1) = v4 & % 182.49/27.99 | c_Groups_Oone__class_Oone(v1) = v6 & hAPP(v3, all_1395_0) = v5 & % 182.49/27.99 | $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = v5))) % 182.49/27.99 | % 182.49/27.99 | ALPHA: (271) implies: % 182.49/28.00 | (272) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1395_0 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (41) with fresh symbol all_1410_0 gives: % 182.49/28.00 | (273) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1410_0 & % 182.49/28.00 | $i(all_1410_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/28.00 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, % 182.49/28.00 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] % 182.49/28.00 | : ? [v6: $i] : (c_Groups_Oone__class_Oone(v1) = v6 & % 182.49/28.00 | class_Rings_Ocomm__semiring__1(v1) = v4 & hAPP(v3, all_1410_0) = % 182.49/28.00 | v5 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = v5))) % 182.49/28.00 | % 182.49/28.00 | ALPHA: (273) implies: % 182.49/28.00 | (274) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1410_0 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (113) with fresh symbols all_1431_0, all_1431_1 gives: % 182.49/28.00 | (275) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1431_1 & % 182.49/28.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1431_0 & % 182.49/28.00 | $i(all_1431_0) & $i(all_1431_1) & ! [v0: $i] : ! [v1: any] : ! % 182.49/28.00 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.49/28.00 | (v1 = all_1431_0 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6) % 182.49/28.00 | = 0) | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ % 182.49/28.00 | (hAPP(all_1431_1, v2) = v3) | ~ (hAPP(all_1431_1, v0) = v5) | ~ % 182.49/28.00 | $i(v2) | ~ $i(v1) | ~ $i(v0) | % 182.49/28.00 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0) = 0) % 182.49/28.00 | % 182.49/28.00 | ALPHA: (275) implies: % 182.49/28.00 | (276) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1431_0 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (53) with fresh symbols all_1434_0, all_1434_1, % 182.49/28.00 | all_1434_2 gives: % 182.49/28.00 | (277) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1434_0 & % 182.49/28.00 | c_Nat_OSuc(all_1434_2) = all_1434_1 & % 182.49/28.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1434_2 & % 182.49/28.00 | $i(all_1434_0) & $i(all_1434_1) & $i(all_1434_2) & ! [v0: $i] : ! % 182.49/28.00 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ % 182.49/28.00 | (hAPP(all_1434_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 182.49/28.00 | : ? [v5: any] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 182.49/28.00 | all_1434_1, v3) = v5 & % 182.49/28.00 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1434_1, v1) = % 182.49/28.00 | v4 & ( ~ (v4 = 0) | v5 = 0))) % 182.49/28.00 | % 182.49/28.00 | ALPHA: (277) implies: % 182.49/28.00 | (278) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1434_2 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (109) with fresh symbols all_1437_0, all_1437_1 gives: % 182.49/28.00 | (279) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1437_1 & % 182.49/28.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1437_0 & % 182.49/28.00 | $i(all_1437_0) & $i(all_1437_1) & ! [v0: $i] : ! [v1: any] : ! % 182.49/28.00 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 182.49/28.00 | (v1 = all_1437_0 | ~ (c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6) % 182.49/28.00 | = 0) | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ % 182.49/28.00 | (hAPP(all_1437_1, v2) = v3) | ~ (hAPP(all_1437_1, v0) = v5) | ~ % 182.49/28.00 | $i(v2) | ~ $i(v1) | ~ $i(v0) | % 182.49/28.00 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v2, v0) = 0) % 182.49/28.00 | % 182.49/28.00 | ALPHA: (279) implies: % 182.49/28.00 | (280) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1437_0 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (104) with fresh symbols all_1449_0, all_1449_1 gives: % 182.49/28.00 | (281) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1449_0 & % 182.49/28.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1449_1 & % 182.49/28.00 | $i(all_1449_0) & $i(all_1449_1) & ! [v0: $i] : ! [v1: any] : ! % 182.49/28.00 | [v2: $i] : ! [v3: $i] : (v1 = all_1449_1 | ~ % 182.49/28.00 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1449_0) = v2) | % 182.49/28.00 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v0) = v3) | ~ % 182.49/28.00 | $i(v1) | ~ $i(v0) | ? [v4: $i] : % 182.49/28.00 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v4 & % 182.49/28.00 | c_Nat_OSuc(v3) = v4 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : (v1 % 182.49/28.00 | = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1449_1, v0) % 182.49/28.00 | = v1) | ~ $i(v0)) % 182.49/28.00 | % 182.49/28.00 | ALPHA: (281) implies: % 182.49/28.00 | (282) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1449_1 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (60) with fresh symbols all_1452_0, all_1452_1 gives: % 182.49/28.00 | (283) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1452_1 & % 182.49/28.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1452_0 & % 182.49/28.00 | $i(all_1452_0) & $i(all_1452_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.00 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 182.49/28.00 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) = 0) | ~ (hAPP(v3, % 182.49/28.00 | v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1452_1, v2) = % 182.49/28.00 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 182.49/28.00 | any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1452_0, % 182.49/28.00 | v2) = v6 & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) = v7 & % 182.49/28.00 | ( ~ (v6 = 0) | v7 = 0))) % 182.49/28.00 | % 182.49/28.00 | ALPHA: (283) implies: % 182.49/28.00 | (284) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1452_0 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (38) with fresh symbols all_1461_0, all_1461_1, % 182.49/28.00 | all_1461_2 gives: % 182.49/28.00 | (285) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1461_2 & % 182.49/28.00 | c_Nat_OSuc(all_1461_1) = all_1461_0 & % 182.49/28.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1461_1 & % 182.49/28.00 | $i(all_1461_0) & $i(all_1461_1) & $i(all_1461_2) & ! [v0: $i] : ! % 182.49/28.00 | [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v2, v0) = all_1461_0) | ~ % 182.49/28.00 | (hAPP(all_1461_2, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (v1 = % 182.49/28.00 | all_1461_0 & v0 = all_1461_0)) & ! [v0: $i] : ! [v1: int] : (v1 % 182.49/28.00 | = all_1461_0 | ~ (hAPP(v0, all_1461_0) = v1) | ~ % 182.49/28.00 | (hAPP(all_1461_2, all_1461_0) = v0)) % 182.49/28.00 | % 182.49/28.00 | ALPHA: (285) implies: % 182.49/28.00 | (286) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1461_1 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (96) with fresh symbols all_1464_0, all_1464_1 gives: % 182.49/28.00 | (287) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1464_0 & % 182.49/28.00 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1464_1 & % 182.49/28.00 | $i(all_1464_0) & $i(all_1464_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.00 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 182.49/28.00 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) = 0) | ~ % 182.49/28.00 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1464_0, % 182.49/28.00 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 182.49/28.00 | ? [v7: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = % 182.49/28.00 | v7 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1464_1, v2) = % 182.49/28.00 | v6 & ( ~ (v6 = 0) | v7 = 0))) % 182.49/28.00 | % 182.49/28.00 | ALPHA: (287) implies: % 182.49/28.00 | (288) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1464_1 % 182.49/28.00 | % 182.49/28.00 | DELTA: instantiating (16) with fresh symbol all_1467_0 gives: % 182.49/28.01 | (289) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1467_0 & % 182.49/28.01 | $i(all_1467_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 182.49/28.01 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v2) | % 182.49/28.01 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 182.49/28.01 | (tc_Polynomial_Opoly(v1) = v4 & class_Groups_Ozero(v1) = v3 & % 182.49/28.01 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4) & ( ~ (v3 % 182.49/28.01 | = 0) | (( ~ (v5 = v0) | v2 = all_1467_0) & ( ~ (v2 = % 182.49/28.01 | all_1467_0) | v5 = v0))))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (289) implies: % 182.49/28.01 | (290) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1467_0 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (99) with fresh symbols all_1470_0, all_1470_1, % 182.49/28.01 | all_1470_2 gives: % 182.49/28.01 | (291) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1470_0 & % 182.49/28.01 | c_Nat_OSuc(all_1470_2) = all_1470_1 & % 182.49/28.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1470_2 & % 182.49/28.01 | $i(all_1470_0) & $i(all_1470_1) & $i(all_1470_2) & ! [v0: $i] : ! % 182.49/28.01 | [v1: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.49/28.01 | all_1470_1, v1) = 0) | ~ % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1470_1, v0) = 0) | % 182.49/28.01 | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1470_1, v3) = 0 & % 182.49/28.01 | hAPP(v2, v1) = v3 & hAPP(all_1470_0, v0) = v2 & $i(v3) & $i(v2))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (291) implies: % 182.49/28.01 | (292) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1470_2 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (98) with fresh symbols all_1476_0, all_1476_1, % 182.49/28.01 | all_1476_2 gives: % 182.49/28.01 | (293) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1476_0 & % 182.49/28.01 | c_Nat_OSuc(all_1476_2) = all_1476_1 & % 182.49/28.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1476_2 & % 182.49/28.01 | $i(all_1476_0) & $i(all_1476_1) & $i(all_1476_2) & ! [v0: $i] : ! % 182.49/28.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v4) | ~ % 182.49/28.01 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1476_0, v1) = v2) | ~ $i(v1) | % 182.49/28.01 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1476_1, v1) = v5 & % 182.49/28.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1476_1, v0) = v6 & % 182.49/28.01 | ( ~ (v6 = 0) | ~ (v5 = 0)))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (293) implies: % 182.49/28.01 | (294) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1476_2 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (93) with fresh symbols all_1479_0, all_1479_1 gives: % 182.49/28.01 | (295) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1479_0 & % 182.49/28.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1479_1 & % 182.49/28.01 | $i(all_1479_0) & $i(all_1479_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.01 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 % 182.49/28.01 | = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) = v6) % 182.49/28.01 | | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(v3, v1) = v5) | ~ % 182.49/28.01 | (hAPP(all_1479_0, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 182.49/28.01 | ? [v7: any] : ? [v8: any] : % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v7 & % 182.49/28.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1479_1, v0) = v8 & % 182.49/28.01 | ( ~ (v8 = 0) | ~ (v7 = 0)))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (295) implies: % 182.49/28.01 | (296) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1479_1 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (95) with fresh symbols all_1482_0, all_1482_1 gives: % 182.49/28.01 | (297) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1482_0 & % 182.49/28.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1482_1 & % 182.49/28.01 | $i(all_1482_0) & $i(all_1482_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.01 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 182.49/28.01 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1482_0, v2) = v3) | % 182.49/28.01 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & % 182.49/28.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1482_1, v2) = v6) % 182.49/28.01 | | (( ~ (v5 = v4) | v1 = v0) & ( ~ (v1 = v0) | v5 = v4))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (297) implies: % 182.49/28.01 | (298) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1482_1 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (97) with fresh symbols all_1485_0, all_1485_1, % 182.49/28.01 | all_1485_2 gives: % 182.49/28.01 | (299) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1485_0 & % 182.49/28.01 | c_Nat_OSuc(all_1485_2) = all_1485_1 & % 182.49/28.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1485_2 & % 182.49/28.01 | $i(all_1485_0) & $i(all_1485_1) & $i(all_1485_2) & ! [v0: $i] : ! % 182.49/28.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) = v4) | ~ % 182.49/28.01 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1485_0, v0) = v2) | ~ $i(v1) | % 182.49/28.01 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1485_1, v1) = v5 & % 182.49/28.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1485_1, v0) = v6 & % 182.49/28.01 | ( ~ (v6 = 0) | ~ (v5 = 0)))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (299) implies: % 182.49/28.01 | (300) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1485_2 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (66) with fresh symbol all_1506_0 gives: % 182.49/28.01 | (301) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1506_0 & % 182.49/28.01 | $i(all_1506_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 182.49/28.01 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 182.49/28.01 | $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v4 & % 182.49/28.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1506_0, v2) = v3 & % 182.49/28.01 | ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.01 | $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) % 182.49/28.01 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 182.49/28.01 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) = v3 & % 182.49/28.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1506_0, v2) = v4 & % 182.49/28.01 | ( ~ (v3 = 0) | v4 = 0))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (301) implies: % 182.49/28.01 | (302) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1506_0 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (76) with fresh symbols all_1518_0, all_1518_1, % 182.49/28.01 | all_1518_2 gives: % 182.49/28.01 | (303) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1518_0 & % 182.49/28.01 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1518_1 & % 182.49/28.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1518_2 & % 182.49/28.01 | $i(all_1518_0) & $i(all_1518_1) & $i(all_1518_2) & ! [v0: $i] : ! % 182.49/28.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 182.49/28.01 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v1) = v4) | ~ (hAPP(v2, % 182.49/28.01 | v1) = v3) | ~ (hAPP(all_1518_1, v0) = v2) | ~ $i(v1) | ~ % 182.49/28.01 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 182.49/28.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1518_2, v1) = v5) % 182.49/28.01 | | (( ~ (v4 = 0) | v0 = all_1518_0) & ( ~ (v0 = all_1518_0) | v4 = % 182.49/28.01 | 0))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (303) implies: % 182.49/28.01 | (304) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1518_2 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (74) with fresh symbol all_1524_0 gives: % 182.49/28.01 | (305) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1524_0 & % 182.49/28.01 | $i(all_1524_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/28.01 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 % 182.49/28.01 | = 0 | ~ (c_Orderings_Oord__class_Oless(v2, v3, v6) = v7) | ~ % 182.49/28.01 | (c_Power_Opower__class_Opower(v2) = v4) | ~ % 182.49/28.01 | (c_Groups_Oone__class_Oone(v2) = v3) | ~ (hAPP(v5, v0) = v6) | ~ % 182.49/28.01 | (hAPP(v4, v1) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: % 182.49/28.01 | any] : ? [v9: any] : ? [v10: any] : % 182.49/28.01 | (c_Orderings_Oord__class_Oless(v2, v3, v1) = v9 & % 182.49/28.01 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1524_0, v0) = v10 % 182.49/28.01 | & class_Rings_Olinordered__semidom(v2) = v8 & ( ~ (v10 = 0) | ~ % 182.49/28.01 | (v9 = 0) | ~ (v8 = 0)))) % 182.49/28.01 | % 182.49/28.01 | ALPHA: (305) implies: % 182.49/28.01 | (306) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1524_0 % 182.49/28.01 | % 182.49/28.01 | DELTA: instantiating (77) with fresh symbols all_1530_0, all_1530_1, % 182.49/28.01 | all_1530_2 gives: % 182.49/28.01 | (307) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1530_0 & % 182.49/28.01 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1530_1 & % 182.49/28.01 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1530_2 & % 182.49/28.01 | $i(all_1530_0) & $i(all_1530_1) & $i(all_1530_2) & ! [v0: $i] : ! % 182.49/28.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 182.49/28.01 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v1) = v4) | ~ (hAPP(v2, % 182.49/28.02 | v0) = v3) | ~ (hAPP(all_1530_1, v1) = v2) | ~ $i(v1) | ~ % 182.49/28.02 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 182.49/28.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1530_2, v1) = v5) % 182.49/28.02 | | (( ~ (v4 = 0) | v0 = all_1530_0) & ( ~ (v0 = all_1530_0) | v4 = % 182.49/28.02 | 0))) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (307) implies: % 182.49/28.02 | (308) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1530_2 % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (10) with fresh symbols all_1533_0, all_1533_1, % 182.49/28.02 | all_1533_2, all_1533_3, all_1533_4, all_1533_5, all_1533_6, all_1533_7 % 182.49/28.02 | gives: % 182.49/28.02 | (309) tc_Polynomial_Opoly(t_a) = all_1533_2 & c_Polynomial_OpCons(t_a, % 182.49/28.02 | all_1533_3, all_1533_1) = all_1533_0 & % 182.49/28.02 | c_Groups_Ozero__class_Ozero(all_1533_2) = all_1533_1 & % 182.49/28.02 | c_Groups_Ozero__class_Ozero(t_a) = all_1533_4 & % 182.49/28.02 | class_Int_Oring__char__0(t_a) = all_1533_7 & class_Rings_Oidom(t_a) = % 182.49/28.02 | all_1533_6 & c_Polynomial_Opoly(t_a, v_p) = all_1533_5 & % 182.49/28.02 | hAPP(all_1533_5, all_1533_4) = all_1533_3 & $i(all_1533_0) & % 182.49/28.02 | $i(all_1533_1) & $i(all_1533_2) & $i(all_1533_3) & $i(all_1533_4) & % 182.49/28.02 | $i(all_1533_5) & ( ~ (all_1533_6 = 0) | ~ (all_1533_7 = 0) | % 182.49/28.02 | all_1533_0 = v_p) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (309) implies: % 182.49/28.02 | (310) $i(all_1533_3) % 182.49/28.02 | (311) hAPP(all_1533_5, all_1533_4) = all_1533_3 % 182.49/28.02 | (312) c_Polynomial_Opoly(t_a, v_p) = all_1533_5 % 182.49/28.02 | (313) class_Rings_Oidom(t_a) = all_1533_6 % 182.49/28.02 | (314) class_Int_Oring__char__0(t_a) = all_1533_7 % 182.49/28.02 | (315) c_Groups_Ozero__class_Ozero(t_a) = all_1533_4 % 182.49/28.02 | (316) c_Groups_Ozero__class_Ozero(all_1533_2) = all_1533_1 % 182.49/28.02 | (317) c_Polynomial_OpCons(t_a, all_1533_3, all_1533_1) = all_1533_0 % 182.49/28.02 | (318) tc_Polynomial_Opoly(t_a) = all_1533_2 % 182.49/28.02 | (319) ~ (all_1533_6 = 0) | ~ (all_1533_7 = 0) | all_1533_0 = v_p % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (2) with fresh symbol all_1535_0 gives: % 182.49/28.02 | (320) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1535_0 & % 182.49/28.02 | $i(all_1535_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/28.02 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Osmult(v2, v1, v0) = v3) | ~ % 182.49/28.02 | (c_Polynomial_Odegree(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 182.49/28.02 | $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 182.49/28.02 | (c_Polynomial_Odegree(v2, v0) = v7 & % 182.49/28.02 | c_Groups_Ozero__class_Ozero(v2) = v6 & class_Rings_Oidom(v2) = v5 % 182.49/28.02 | & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | v4 = % 182.49/28.02 | all_1535_0) & (v7 = v4 | v6 = v1))))) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (320) implies: % 182.49/28.02 | (321) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1535_0 % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (35) with fresh symbols all_1538_0, all_1538_1 gives: % 182.49/28.02 | (322) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1538_1 & % 182.49/28.02 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1538_0 & % 182.49/28.02 | $i(all_1538_0) & $i(all_1538_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.02 | $i] : ! [v3: int] : (v3 = all_1538_0 | ~ (hAPP(v2, v0) = v3) | ~ % 182.49/28.02 | (hAPP(all_1538_1, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = % 182.49/28.02 | all_1538_0) & ~ (v0 = all_1538_0))) & ! [v0: any] : ! [v1: % 182.49/28.02 | any] : ! [v2: $i] : (v1 = all_1538_0 | v0 = all_1538_0 | ~ % 182.49/28.02 | (hAPP(v2, v0) = all_1538_0) | ~ (hAPP(all_1538_1, v1) = v2) | ~ % 182.49/28.02 | $i(v1) | ~ $i(v0)) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (322) implies: % 182.49/28.02 | (323) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1538_0 % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (106) with fresh symbol all_1544_0 gives: % 182.49/28.02 | (324) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1544_0 & % 182.49/28.02 | $i(all_1544_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/28.02 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ % 182.49/28.02 | (c_Rings_Odvd__class_Odvd(v2, v0, v5) = v6) | ~ % 182.49/28.02 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v1) = v5) | % 182.49/28.02 | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: % 182.49/28.02 | any] : ? [v8: any] : ? [v9: $i] : % 182.49/28.02 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1544_0, v1) = v8 & % 182.49/28.02 | c_Groups_Oone__class_Oone(v2) = v9 & % 182.49/28.02 | class_Rings_Ocomm__semiring__1(v2) = v7 & $i(v9) & ( ~ (v7 = 0) | % 182.49/28.02 | ( ~ (v9 = v0) & ~ (v8 = 0))))) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (324) implies: % 182.49/28.02 | (325) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1544_0 % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (92) with fresh symbols all_1547_0, all_1547_1 gives: % 182.49/28.02 | (326) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1547_0 & % 182.49/28.02 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1547_1 & % 182.49/28.02 | $i(all_1547_0) & $i(all_1547_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.02 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.49/28.02 | [v7: int] : (v7 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.49/28.02 | v4, v6) = v7) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v0) = v4) % 182.49/28.02 | | ~ (hAPP(all_1547_0, v2) = v3) | ~ (hAPP(all_1547_0, v1) = v5) | % 182.49/28.02 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] : % 182.49/28.02 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) = v8 & % 182.49/28.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1547_1, v0) = v9 & % 182.49/28.02 | ( ~ (v9 = 0) | ~ (v8 = 0)))) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (326) implies: % 182.49/28.02 | (327) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1547_1 % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (15) with fresh symbol all_1556_0 gives: % 182.49/28.02 | (328) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1556_0 & % 182.49/28.02 | $i(all_1556_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/28.02 | $i] : ( ~ (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3) | ~ % 182.49/28.02 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? % 182.49/28.02 | [v6: $i] : ? [v7: $i] : (tc_Polynomial_Opoly(v2) = v5 & % 182.49/28.02 | class_Rings_Ocomm__semiring__0(v2) = v4 & % 182.49/28.02 | c_Polynomial_Odegree(v2, v1) = v7 & % 182.49/28.02 | c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v7) & $i(v6) & $i(v5) & % 182.49/28.02 | ( ~ (v4 = 0) | (( ~ (v7 = all_1556_0) | v6 = v3) & ( ~ (v6 = v3) % 182.49/28.02 | | v7 = all_1556_0))))) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (328) implies: % 182.49/28.02 | (329) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1556_0 % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (48) with fresh symbol all_1559_0 gives: % 182.49/28.02 | (330) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1559_0 & % 182.49/28.02 | $i(all_1559_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.49/28.02 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 182.49/28.02 | (c_Power_Opower__class_Opower(v1) = v2) | ~ % 182.49/28.02 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | % 182.49/28.02 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 182.49/28.02 | [v7: any] : ? [v8: $i] : (class_Power_Opower(v1) = v6 & % 182.49/28.02 | class_Rings_Osemiring__0(v1) = v7 & c_Groups_Oone__class_Oone(v1) % 182.49/28.02 | = v8 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v0 = % 182.49/28.02 | all_1559_0) | v8 = v5) & (v5 = v3 | v0 = all_1559_0))))) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (330) implies: % 182.49/28.02 | (331) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1559_0 % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (61) with fresh symbols all_1565_0, all_1565_1 gives: % 182.49/28.02 | (332) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1565_0 & % 182.49/28.02 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1565_1 & % 182.49/28.02 | $i(all_1565_0) & $i(all_1565_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.02 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 182.49/28.02 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) = v6) | ~ (hAPP(v3, % 182.49/28.02 | v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1565_0, v2) = % 182.49/28.02 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: % 182.49/28.02 | any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1565_1, % 182.49/28.02 | v2) = v7 & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) = v8 & % 182.49/28.02 | ( ~ (v7 = 0) | (( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = % 182.49/28.02 | 0))))) % 182.49/28.02 | % 182.49/28.02 | ALPHA: (332) implies: % 182.49/28.02 | (333) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1565_1 % 182.49/28.02 | % 182.49/28.02 | DELTA: instantiating (110) with fresh symbols all_1568_0, all_1568_1 gives: % 182.49/28.03 | (334) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1568_0 & % 182.49/28.03 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1568_1 & % 182.49/28.03 | $i(all_1568_0) & $i(all_1568_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.49/28.03 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.49/28.03 | [v7: any] : (v2 = all_1568_1 | ~ % 182.49/28.03 | (c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6) = v7) | ~ (hAPP(v5, % 182.49/28.03 | v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1568_0, v1) = % 182.49/28.03 | v3) | ~ (hAPP(all_1568_0, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 182.49/28.03 | $i(v0) | ? [v8: any] : (c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, % 182.49/28.03 | v0) = v8 & ( ~ (v8 = 0) | v7 = 0) & ( ~ (v7 = 0) | v8 = 0))) % 182.49/28.03 | % 182.49/28.03 | ALPHA: (334) implies: % 182.49/28.03 | (335) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1568_1 % 182.49/28.03 | % 182.49/28.03 | DELTA: instantiating (42) with fresh symbol all_1571_0 gives: % 182.68/28.03 | (336) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1571_0 & % 182.68/28.03 | $i(all_1571_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.68/28.03 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 182.68/28.03 | (c_Groups_Oone__class_Oone(v2) = v3) | ~ (c_Polynomial_Ocoeff(v1, % 182.68/28.03 | v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = v2) | ~ (hAPP(v4, % 182.68/28.03 | v0) = v5) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] % 182.68/28.03 | : ? [v8: $i] : (c_Groups_Oone__class_Oone(v1) = v7 & % 182.68/28.03 | class_Rings_Ocomm__semiring__1(v1) = v6 & % 182.68/28.03 | c_Groups_Ozero__class_Ozero(v1) = v8 & $i(v8) & $i(v7) & ( ~ (v6 % 182.68/28.03 | = 0) | (( ~ (v0 = all_1571_0) | v7 = v5) & (v8 = v5 | v0 = % 182.68/28.03 | all_1571_0))))) % 182.68/28.03 | % 182.68/28.03 | ALPHA: (336) implies: % 182.68/28.03 | (337) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1571_0 % 182.68/28.03 | % 182.68/28.03 | DELTA: instantiating (102) with fresh symbols all_1574_0, all_1574_1 gives: % 182.68/28.03 | (338) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1574_0 & % 182.68/28.03 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1574_1 & % 182.68/28.03 | $i(all_1574_0) & $i(all_1574_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.68/28.03 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 182.68/28.03 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) = v6) | ~ % 182.68/28.03 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1574_0, % 182.68/28.03 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : % 182.68/28.03 | ? [v8: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.68/28.03 | all_1574_1, v2) = v7 & % 182.68/28.03 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = v8 & ( ~ % 182.68/28.03 | (v7 = 0) | (( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))) % 182.68/28.03 | % 182.68/28.03 | ALPHA: (338) implies: % 182.68/28.03 | (339) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1574_1 % 182.68/28.03 | % 182.68/28.03 | DELTA: instantiating (94) with fresh symbols all_1577_0, all_1577_1 gives: % 182.68/28.03 | (340) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1577_0 & % 182.68/28.03 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1577_1 & % 182.68/28.03 | $i(all_1577_0) & $i(all_1577_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.68/28.03 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 182.68/28.03 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) = v6) | ~ % 182.68/28.03 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1577_0, % 182.68/28.03 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : % 182.68/28.03 | ? [v8: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = % 182.68/28.03 | v8 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1577_1, v2) = % 182.68/28.03 | v7 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = % 182.68/28.03 | 0))))) % 182.68/28.03 | % 182.68/28.03 | ALPHA: (340) implies: % 182.68/28.03 | (341) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1577_1 % 182.68/28.03 | % 182.68/28.03 | DELTA: instantiating (114) with fresh symbols all_1583_0, all_1583_1 gives: % 182.68/28.03 | (342) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1583_0 & % 182.68/28.03 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1583_1 & % 182.68/28.03 | $i(all_1583_0) & $i(all_1583_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.68/28.03 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.68/28.03 | [v7: any] : (v2 = all_1583_1 | ~ % 182.68/28.03 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6) = v7) | ~ (hAPP(v5, % 182.68/28.03 | v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1583_0, v1) = % 182.68/28.03 | v3) | ~ (hAPP(all_1583_0, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 182.68/28.03 | $i(v0) | ? [v8: any] : (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, % 182.68/28.03 | v0) = v8 & ( ~ (v8 = 0) | v7 = 0) & ( ~ (v7 = 0) | v8 = 0))) % 182.68/28.03 | % 182.68/28.03 | ALPHA: (342) implies: % 182.68/28.03 | (343) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1583_1 % 182.68/28.03 | % 182.68/28.03 | DELTA: instantiating (22) with fresh symbol all_1592_0 gives: % 182.68/28.03 | (344) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1592_0 & % 182.68/28.03 | $i(all_1592_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 182.68/28.03 | (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v1, v0) = v2) | % 182.68/28.03 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 182.68/28.03 | ? [v6: $i] : ? [v7: $i] : (c_Nat_OSuc(v6) = v7 & % 182.68/28.03 | tc_Polynomial_Opoly(v1) = v4 & c_Polynomial_Odegree(v1, v0) = v6 % 182.68/28.03 | & class_Groups_Ozero(v1) = v3 & c_Groups_Ozero__class_Ozero(v4) = % 182.68/28.03 | v5 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 % 182.68/28.03 | = v0) | v2 = all_1592_0) & (v7 = v2 | v5 = v0))))) % 182.68/28.03 | % 182.68/28.03 | ALPHA: (344) implies: % 182.68/28.03 | (345) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1592_0 % 182.68/28.03 | % 182.68/28.03 | DELTA: instantiating (9) with fresh symbols all_1595_0, all_1595_1, % 182.68/28.03 | all_1595_2, all_1595_3, all_1595_4, all_1595_5, all_1595_6, all_1595_7, % 182.68/28.03 | all_1595_8 gives: % 182.68/28.03 | (346) tc_Polynomial_Opoly(t_a) = all_1595_3 & c_Polynomial_OpCons(t_a, % 182.68/28.03 | all_1595_4, all_1595_2) = all_1595_1 & % 182.68/28.03 | c_Groups_Ozero__class_Ozero(all_1595_3) = all_1595_2 & % 182.68/28.03 | c_Groups_Ozero__class_Ozero(t_a) = all_1595_5 & % 182.68/28.03 | class_Int_Oring__char__0(t_a) = all_1595_8 & class_Rings_Oidom(t_a) = % 182.68/28.03 | all_1595_7 & c_Polynomial_Opoly(t_a, all_1595_1) = all_1595_0 & % 182.68/28.03 | c_Polynomial_Opoly(t_a, v_p) = all_1595_6 & hAPP(all_1595_6, % 182.68/28.03 | all_1595_5) = all_1595_4 & $i(all_1595_0) & $i(all_1595_1) & % 182.68/28.03 | $i(all_1595_2) & $i(all_1595_3) & $i(all_1595_4) & $i(all_1595_5) & % 182.68/28.03 | $i(all_1595_6) & ( ~ (all_1595_7 = 0) | ~ (all_1595_8 = 0) | % 182.68/28.03 | all_1595_0 = all_1595_6) % 182.68/28.03 | % 182.68/28.03 | ALPHA: (346) implies: % 182.68/28.03 | (347) $i(all_1595_2) % 182.68/28.03 | (348) hAPP(all_1595_6, all_1595_5) = all_1595_4 % 182.68/28.03 | (349) c_Polynomial_Opoly(t_a, v_p) = all_1595_6 % 182.68/28.03 | (350) class_Rings_Oidom(t_a) = all_1595_7 % 182.68/28.03 | (351) class_Int_Oring__char__0(t_a) = all_1595_8 % 182.68/28.03 | (352) c_Groups_Ozero__class_Ozero(t_a) = all_1595_5 % 182.68/28.03 | (353) c_Groups_Ozero__class_Ozero(all_1595_3) = all_1595_2 % 182.68/28.03 | (354) c_Polynomial_OpCons(t_a, all_1595_4, all_1595_2) = all_1595_1 % 182.68/28.03 | (355) tc_Polynomial_Opoly(t_a) = all_1595_3 % 182.68/28.03 | % 182.68/28.03 | DELTA: instantiating (31) with fresh symbols all_1597_0, all_1597_1 gives: % 182.68/28.03 | (356) c_Nat_OSuc(all_1597_1) = all_1597_0 & % 182.68/28.03 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1597_1 & % 182.68/28.03 | $i(all_1597_0) & $i(all_1597_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.68/28.03 | int] : (v2 = all_1597_0 | ~ % 182.68/28.03 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 182.68/28.03 | | ~ $i(v0) | (( ~ (v1 = all_1597_0) | ~ (v0 = all_1597_1)) & ( ~ % 182.68/28.03 | (v1 = all_1597_1) | ~ (v0 = all_1597_0)))) & ! [v0: $i] : ! % 182.68/28.03 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = % 182.68/28.03 | all_1597_0) | ~ $i(v1) | ~ $i(v0) | (v1 = all_1597_0 & v0 = % 182.68/28.03 | all_1597_1) | (v1 = all_1597_1 & v0 = all_1597_0)) % 182.68/28.03 | % 182.68/28.03 | ALPHA: (356) implies: % 182.68/28.03 | (357) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1597_1 % 182.68/28.03 | % 182.68/28.03 | DELTA: instantiating (50) with fresh symbols all_1600_0, all_1600_1, % 182.68/28.03 | all_1600_2 gives: % 182.68/28.04 | (358) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1600_2 & % 182.68/28.04 | c_Nat_OSuc(all_1600_1) = all_1600_0 & % 182.68/28.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1600_1 & % 182.68/28.04 | $i(all_1600_0) & $i(all_1600_1) & $i(all_1600_2) & ! [v0: $i] : ! % 182.68/28.04 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = all_1600_0 | ~ % 182.68/28.04 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1600_2, v1) = v2) | ~ $i(v1) | % 182.68/28.04 | ~ $i(v0) | ( ~ (v1 = all_1600_0) & ~ (v0 = all_1600_1))) & ! [v0: % 182.68/28.04 | any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1600_0 | v0 = % 182.68/28.04 | all_1600_1 | ~ (hAPP(v2, v0) = all_1600_0) | ~ (hAPP(all_1600_2, % 182.68/28.04 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 182.68/28.04 | % 182.68/28.04 | ALPHA: (358) implies: % 182.68/28.04 | (359) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1600_1 % 182.68/28.04 | % 182.68/28.04 | DELTA: instantiating (31) with fresh symbols all_1603_0, all_1603_1 gives: % 182.68/28.04 | (360) c_Nat_OSuc(all_1603_1) = all_1603_0 & % 182.68/28.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1603_1 & % 182.68/28.04 | $i(all_1603_0) & $i(all_1603_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.68/28.04 | int] : (v2 = all_1603_0 | ~ % 182.68/28.04 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 182.68/28.04 | | ~ $i(v0) | (( ~ (v1 = all_1603_0) | ~ (v0 = all_1603_1)) & ( ~ % 182.68/28.04 | (v1 = all_1603_1) | ~ (v0 = all_1603_0)))) & ! [v0: $i] : ! % 182.68/28.04 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = % 182.68/28.04 | all_1603_0) | ~ $i(v1) | ~ $i(v0) | (v1 = all_1603_0 & v0 = % 182.68/28.04 | all_1603_1) | (v1 = all_1603_1 & v0 = all_1603_0)) % 182.68/28.04 | % 182.68/28.04 | ALPHA: (360) implies: % 182.68/28.04 | (361) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1603_1 % 182.68/28.04 | % 182.68/28.04 | DELTA: instantiating (3) with fresh symbols all_1618_0, all_1618_1, % 182.68/28.04 | all_1618_2, all_1618_3, all_1618_4, all_1618_5, all_1618_6, all_1618_7, % 182.68/28.04 | all_1618_8, all_1618_9 gives: % 182.68/28.04 | (362) tc_Polynomial_Opoly(t_a) = all_1618_3 & c_Polynomial_OpCons(t_a, % 182.68/28.04 | all_1618_4, all_1618_2) = all_1618_1 & c_Polynomial_Odegree(t_a, % 182.68/28.04 | all_1618_1) = all_1618_0 & c_Polynomial_Odegree(t_a, v_p) = % 182.68/28.04 | all_1618_7 & c_Groups_Ozero__class_Ozero(all_1618_3) = all_1618_2 & % 182.68/28.04 | c_Groups_Ozero__class_Ozero(t_a) = all_1618_5 & % 182.68/28.04 | class_Int_Oring__char__0(t_a) = all_1618_9 & class_Rings_Oidom(t_a) = % 182.68/28.04 | all_1618_8 & c_Polynomial_Opoly(t_a, v_p) = all_1618_6 & % 182.68/28.04 | hAPP(all_1618_6, all_1618_5) = all_1618_4 & $i(all_1618_0) & % 182.68/28.04 | $i(all_1618_1) & $i(all_1618_2) & $i(all_1618_3) & $i(all_1618_4) & % 182.68/28.04 | $i(all_1618_5) & $i(all_1618_6) & $i(all_1618_7) & ( ~ (all_1618_8 = % 182.68/28.04 | 0) | ~ (all_1618_9 = 0) | all_1618_0 = all_1618_7) % 182.68/28.04 | % 182.68/28.04 | ALPHA: (362) implies: % 182.68/28.04 | (363) hAPP(all_1618_6, all_1618_5) = all_1618_4 % 182.68/28.04 | (364) c_Polynomial_Opoly(t_a, v_p) = all_1618_6 % 182.68/28.04 | (365) class_Rings_Oidom(t_a) = all_1618_8 % 182.68/28.04 | (366) class_Int_Oring__char__0(t_a) = all_1618_9 % 182.68/28.04 | (367) c_Groups_Ozero__class_Ozero(t_a) = all_1618_5 % 182.68/28.04 | (368) c_Groups_Ozero__class_Ozero(all_1618_3) = all_1618_2 % 182.68/28.04 | (369) c_Polynomial_Odegree(t_a, v_p) = all_1618_7 % 182.68/28.04 | (370) c_Polynomial_Odegree(t_a, all_1618_1) = all_1618_0 % 182.68/28.04 | (371) c_Polynomial_OpCons(t_a, all_1618_4, all_1618_2) = all_1618_1 % 182.68/28.04 | (372) tc_Polynomial_Opoly(t_a) = all_1618_3 % 182.68/28.04 | (373) ~ (all_1618_8 = 0) | ~ (all_1618_9 = 0) | all_1618_0 = all_1618_7 % 182.68/28.04 | % 182.68/28.04 | DELTA: instantiating (40) with fresh symbols all_1620_0, all_1620_1 gives: % 182.68/28.04 | (374) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1620_1 & % 182.68/28.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1620_0 & % 182.68/28.04 | $i(all_1620_0) & $i(all_1620_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.68/28.04 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 182.68/28.04 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1620_1, % 182.68/28.04 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = % 182.68/28.04 | all_1620_0) & ~ (v1 = v0))) & ! [v0: $i] : ! [v1: $i] : ! % 182.68/28.04 | [v2: any] : ! [v3: $i] : ! [v4: $i] : (v2 = all_1620_0 | v1 = v0 | % 182.68/28.04 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ % 182.68/28.04 | (hAPP(all_1620_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 182.68/28.04 | % 182.68/28.04 | ALPHA: (374) implies: % 182.68/28.04 | (375) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1620_0 % 182.68/28.04 | % 182.68/28.04 | DELTA: instantiating (17) with fresh symbol all_1623_0 gives: % 182.74/28.04 | (376) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1623_0 & % 182.74/28.04 | $i(all_1623_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.74/28.04 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_OpCons(v2, v0, v1) = v3) | ~ % 182.74/28.04 | (c_Polynomial_Odegree(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 182.74/28.04 | $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 182.74/28.04 | ? [v9: $i] : (c_Nat_OSuc(v8) = v9 & tc_Polynomial_Opoly(v2) = v6 & % 182.74/28.04 | c_Polynomial_Odegree(v2, v1) = v8 & class_Groups_Ozero(v2) = v5 & % 182.74/28.04 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v9) & $i(v8) & $i(v7) & % 182.74/28.04 | $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 = v1) | v4 = all_1623_0) & (v9 = % 182.74/28.04 | v4 | v7 = v1))))) % 182.74/28.04 | % 182.74/28.04 | ALPHA: (376) implies: % 182.74/28.04 | (377) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1623_0 % 182.74/28.04 | % 182.74/28.04 | DELTA: instantiating (40) with fresh symbols all_1626_0, all_1626_1 gives: % 182.74/28.04 | (378) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1626_1 & % 182.74/28.04 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1626_0 & % 182.74/28.04 | $i(all_1626_0) & $i(all_1626_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.04 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 182.74/28.04 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1626_1, % 182.74/28.04 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = % 182.74/28.04 | all_1626_0) & ~ (v1 = v0))) & ! [v0: $i] : ! [v1: $i] : ! % 182.74/28.04 | [v2: any] : ! [v3: $i] : ! [v4: $i] : (v2 = all_1626_0 | v1 = v0 | % 182.74/28.04 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ % 182.74/28.04 | (hAPP(all_1626_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 182.74/28.04 | % 182.74/28.04 | ALPHA: (378) implies: % 182.74/28.04 | (379) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1626_0 % 182.74/28.04 | % 182.74/28.04 | DELTA: instantiating (87) with fresh symbol all_1629_0 gives: % 182.74/28.04 | (380) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1629_0 & % 182.74/28.04 | $i(all_1629_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.74/28.04 | int] : (v3 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 182.74/28.04 | v2) = v3) | ~ (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | % 182.74/28.04 | ( ~ (v1 = all_1629_0) & ! [v4: $i] : ( ~ % 182.74/28.04 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v0) = 0) | ~ % 182.74/28.04 | $i(v4) | ? [v5: $i] : ( ~ (v5 = v1) & c_Nat_OSuc(v4) = v5 & % 182.74/28.04 | $i(v5))))) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = % 182.74/28.04 | all_1629_0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) % 182.74/28.04 | = 0) | ~ (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 182.74/28.04 | $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0) = 0 & % 182.74/28.04 | c_Nat_OSuc(v3) = v1 & $i(v3))) % 182.74/28.04 | % 182.74/28.04 | ALPHA: (380) implies: % 182.74/28.04 | (381) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1629_0 % 182.74/28.04 | % 182.74/28.04 | DELTA: instantiating (79) with fresh symbols all_1632_0, all_1632_1 gives: % 182.74/28.05 | (382) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1632_0 & % 182.74/28.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1632_1 & % 182.74/28.05 | $i(all_1632_0) & $i(all_1632_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.05 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.74/28.05 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 182.74/28.05 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1632_0) = v6) | % 182.74/28.05 | ~ (c_Power_Opower__class_Opower(v2) = v4) | ~ % 182.74/28.05 | (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v8, v0) = v9) | % 182.74/28.05 | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v3, v7) % 182.74/28.05 | = v8) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? % 182.74/28.05 | [v11: any] : ? [v12: $i] : % 182.74/28.05 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1632_1, v1) = v11 & % 182.74/28.05 | class_Groups_Omonoid__mult(v2) = v10 & hAPP(v5, v1) = v12 & % 182.74/28.05 | $i(v12) & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = v9))) % 182.74/28.05 | % 182.74/28.05 | ALPHA: (382) implies: % 182.74/28.05 | (383) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1632_1 % 182.74/28.05 | % 182.74/28.05 | DELTA: instantiating (105) with fresh symbols all_1638_0, all_1638_1, % 182.74/28.05 | all_1638_2 gives: % 182.74/28.05 | (384) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1638_0 & % 182.74/28.05 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1638_1 & % 182.74/28.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1638_2 & % 182.74/28.05 | $i(all_1638_0) & $i(all_1638_1) & $i(all_1638_2) & ! [v0: $i] : ! % 182.74/28.05 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 182.74/28.05 | (v1 = all_1638_2 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, % 182.74/28.05 | all_1638_0) = v2) | ~ % 182.74/28.05 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v4) = v5) | ~ % 182.74/28.05 | (hAPP(v3, v0) = v4) | ~ (hAPP(all_1638_1, v2) = v3) | ~ $i(v1) | % 182.74/28.05 | ~ $i(v0) | ? [v6: $i] : (hAPP(v6, v0) = v5 & hAPP(all_1638_1, v1) % 182.74/28.05 | = v6 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.05 | int] : (v2 = all_1638_2 | ~ (hAPP(v1, v0) = v2) | ~ % 182.74/28.05 | (hAPP(all_1638_1, all_1638_2) = v1) | ~ $i(v0)) % 182.74/28.05 | % 182.74/28.05 | ALPHA: (384) implies: % 182.74/28.05 | (385) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1638_2 % 182.74/28.05 | % 182.74/28.05 | DELTA: instantiating (88) with fresh symbol all_1641_0 gives: % 182.74/28.05 | (386) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1641_0 & % 182.74/28.05 | $i(all_1641_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: % 182.74/28.05 | int] : (v3 = 0 | v2 = 0 | ~ % 182.74/28.05 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1641_0, v1) = v2) | % 182.74/28.05 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1641_0, v0) = % 182.74/28.05 | v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ % 182.74/28.05 | (v5 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1641_0, % 182.74/28.05 | v4) = v5 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = % 182.74/28.05 | v4 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ! % 182.74/28.05 | [v3: any] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.74/28.05 | all_1641_0, v1) = v2) | ~ % 182.74/28.05 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1641_0, v0) = v3) | % 182.74/28.05 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 182.74/28.05 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1641_0, v4) = 0 & % 182.74/28.05 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v4 & $i(v4)) | % 182.74/28.05 | ( ~ (v3 = 0) & ~ (v2 = 0))) % 182.74/28.05 | % 182.74/28.05 | ALPHA: (386) implies: % 182.74/28.05 | (387) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1641_0 % 182.74/28.05 | % 182.74/28.05 | DELTA: instantiating (107) with fresh symbols all_1647_0, all_1647_1, % 182.74/28.05 | all_1647_2, all_1647_3 gives: % 182.74/28.05 | (388) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1647_2 & % 182.74/28.05 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1647_1 & % 182.74/28.05 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1647_0 & % 182.74/28.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1647_3 & % 182.74/28.05 | $i(all_1647_0) & $i(all_1647_1) & $i(all_1647_2) & $i(all_1647_3) & % 182.74/28.05 | ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 182.74/28.05 | ! [v5: $i] : ! [v6: $i] : (v1 = all_1647_3 | ~ % 182.74/28.05 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1647_1) = v4) | % 182.74/28.05 | ~ (hAPP(v3, v5) = v6) | ~ (hAPP(v2, v4) = v5) | ~ % 182.74/28.05 | (hAPP(all_1647_0, v0) = v3) | ~ (hAPP(all_1647_2, v0) = v2) | ~ % 182.74/28.05 | $i(v1) | ~ $i(v0) | (hAPP(v2, v1) = v6 & $i(v6))) & ! [v0: $i] : % 182.74/28.05 | ! [v1: $i] : ! [v2: int] : (v2 = all_1647_1 | ~ (hAPP(v1, % 182.74/28.05 | all_1647_3) = v2) | ~ (hAPP(all_1647_2, v0) = v1) | ~ $i(v0)) % 182.74/28.05 | % 182.74/28.05 | ALPHA: (388) implies: % 182.74/28.05 | (389) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1647_3 % 182.74/28.05 | % 182.74/28.05 | DELTA: instantiating (115) with fresh symbols all_1653_0, all_1653_1 gives: % 182.74/28.05 | (390) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1653_0 & % 182.74/28.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1653_1 & % 182.74/28.05 | $i(all_1653_0) & $i(all_1653_1) & ! [v0: any] : ! [v1: $i] : ! % 182.74/28.05 | [v2: $i] : ! [v3: $i] : (v0 = all_1653_1 | ~ (hAPP(v2, v0) = v3) | % 182.74/28.05 | ~ (hAPP(all_1653_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 182.74/28.05 | any] : ? [v5: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.74/28.05 | all_1653_1, v3) = v4 & % 182.74/28.05 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1653_1, v1) = v5 & % 182.74/28.05 | ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.05 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1653_0, % 182.74/28.05 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] % 182.74/28.05 | : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1653_1, v3) = v5 % 182.74/28.05 | & c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1653_1, v1) = v4 % 182.74/28.05 | & (v5 = 0 | ( ~ (v4 = 0) & ~ (v0 = all_1653_1))))) % 182.74/28.05 | % 182.74/28.05 | ALPHA: (390) implies: % 182.74/28.05 | (391) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1653_1 % 182.74/28.05 | % 182.74/28.05 | DELTA: instantiating (115) with fresh symbols all_1656_0, all_1656_1 gives: % 182.74/28.05 | (392) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1656_0 & % 182.74/28.05 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1656_1 & % 182.74/28.05 | $i(all_1656_0) & $i(all_1656_1) & ! [v0: any] : ! [v1: $i] : ! % 182.74/28.05 | [v2: $i] : ! [v3: $i] : (v0 = all_1656_1 | ~ (hAPP(v2, v0) = v3) | % 182.74/28.05 | ~ (hAPP(all_1656_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 182.74/28.05 | any] : ? [v5: any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.74/28.05 | all_1656_1, v3) = v4 & % 182.74/28.05 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1656_1, v1) = v5 & % 182.74/28.05 | ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.05 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1656_0, % 182.74/28.05 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] % 182.74/28.05 | : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1656_1, v3) = v5 % 182.74/28.05 | & c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1656_1, v1) = v4 % 182.74/28.05 | & (v5 = 0 | ( ~ (v4 = 0) & ~ (v0 = all_1656_1))))) % 182.74/28.05 | % 182.74/28.05 | ALPHA: (392) implies: % 182.74/28.05 | (393) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1656_1 % 182.74/28.05 | % 182.74/28.05 | DELTA: instantiating (78) with fresh symbol all_1662_0 gives: % 182.74/28.05 | (394) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1662_0 & % 182.74/28.05 | $i(all_1662_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.74/28.05 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 182.74/28.05 | [v8: $i] : ! [v9: int] : (v9 = 0 | ~ % 182.74/28.05 | (c_Orderings_Oord__class_Oless(v3, v6, v8) = v9) | ~ % 182.74/28.05 | (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7, v0) = v8) | % 182.74/28.05 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v4, v1) = % 182.74/28.05 | v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: % 182.74/28.05 | any] : ? [v11: any] : ? [v12: $i] : ? [v13: any] : ? [v14: % 182.74/28.05 | any] : (c_Orderings_Oord__class_Oless(v3, v2, v1) = v11 & % 182.74/28.05 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1662_0, v0) = v14 % 182.74/28.05 | & class_Rings_Olinordered__semidom(v3) = v10 & % 182.74/28.05 | c_Orderings_Oord__class_Oless__eq(v3, v12, v2) = v13 & % 182.74/28.05 | c_Groups_Ozero__class_Ozero(v3) = v12 & $i(v12) & ( ~ (v14 = 0) | % 182.74/28.05 | ~ (v13 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) % 182.74/28.05 | % 182.74/28.05 | ALPHA: (394) implies: % 182.74/28.05 | (395) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1662_0 % 182.74/28.05 | % 182.74/28.05 | DELTA: instantiating (34) with fresh symbols all_1665_0, all_1665_1 gives: % 182.74/28.06 | (396) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1665_1 & % 182.74/28.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1665_0 & % 182.74/28.06 | $i(all_1665_0) & $i(all_1665_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.06 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = % 182.74/28.06 | v4 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ % 182.74/28.06 | (hAPP(all_1665_1, v2) = v3) | ~ (hAPP(all_1665_1, v0) = v5) | ~ % 182.74/28.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = % 182.74/28.06 | all_1665_0))) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! % 182.74/28.06 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | v1 = all_1665_0 | % 182.74/28.06 | ~ (hAPP(v5, v1) = v4) | ~ (hAPP(v3, v1) = v4) | ~ % 182.74/28.06 | (hAPP(all_1665_1, v2) = v3) | ~ (hAPP(all_1665_1, v0) = v5) | ~ % 182.74/28.06 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 182.74/28.06 | % 182.74/28.06 | ALPHA: (396) implies: % 182.74/28.06 | (397) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1665_0 % 182.74/28.06 | % 182.74/28.06 | DELTA: instantiating (14) with fresh symbol all_1671_0 gives: % 182.74/28.06 | (398) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1671_0 & % 182.74/28.06 | $i(all_1671_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.74/28.06 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(v2, v1) = v3) | ~ % 182.74/28.06 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 182.74/28.06 | any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 182.74/28.06 | (c_Polynomial_Oorder(v2, v0, v1) = v9 & tc_Polynomial_Opoly(v2) = % 182.74/28.06 | v7 & c_Groups_Ozero__class_Ozero(v7) = v8 & % 182.74/28.06 | c_Groups_Ozero__class_Ozero(v2) = v6 & class_Rings_Oidom(v2) = v5 % 182.74/28.06 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v9 = % 182.74/28.06 | all_1671_0) | ~ (v6 = v4) | v8 = v1) & (v6 = v4 | (v9 = % 182.74/28.06 | all_1671_0 & ~ (v8 = v1))))))) % 182.74/28.06 | % 182.74/28.06 | ALPHA: (398) implies: % 182.74/28.06 | (399) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1671_0 % 182.74/28.06 | % 182.74/28.06 | DELTA: instantiating (103) with fresh symbol all_1674_0 gives: % 182.74/28.06 | (400) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1674_0 & % 182.74/28.06 | $i(all_1674_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.74/28.06 | $i] : ! [v4: $i] : (v2 = v0 | ~ % 182.74/28.06 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1674_0, v1) = 0) | % 182.74/28.06 | ~ (c_Orderings_Oord__class_Oless__eq(v3, v4, v2) = 0) | ~ % 182.74/28.06 | (c_Orderings_Oord__class_Oless__eq(v3, v4, v0) = 0) | ~ % 182.74/28.06 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 182.74/28.06 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? % 182.74/28.06 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 182.74/28.06 | (class_Rings_Olinordered__semidom(v3) = v5 & % 182.74/28.06 | c_Power_Opower__class_Opower(v3) = v6 & hAPP(v9, v1) = v10 & % 182.74/28.06 | hAPP(v7, v1) = v8 & hAPP(v6, v2) = v7 & hAPP(v6, v0) = v9 & % 182.74/28.06 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v10 = v8) | ~ % 182.74/28.06 | (v5 = 0)))) % 182.74/28.06 | % 182.74/28.06 | ALPHA: (400) implies: % 182.74/28.06 | (401) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1674_0 % 182.74/28.06 | % 182.74/28.06 | DELTA: instantiating (51) with fresh symbol all_1677_0 gives: % 182.74/28.06 | (402) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1677_0 & % 182.74/28.06 | $i(all_1677_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.74/28.06 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 182.74/28.06 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) | % 182.74/28.06 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 182.74/28.06 | any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: $i] % 182.74/28.06 | : (class_Power_Opower(v2) = v6 & class_Rings_Ozero__neq__one(v2) = % 182.74/28.06 | v9 & class_Rings_Omult__zero(v2) = v7 & % 182.74/28.06 | class_Rings_Ono__zero__divisors(v2) = v8 & % 182.74/28.06 | c_Groups_Ozero__class_Ozero(v2) = v10 & $i(v10) & ( ~ (v9 = 0) | % 182.74/28.06 | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v10 = v5) | (v5 % 182.74/28.06 | = v1 & ~ (v0 = all_1677_0))) & ( ~ (v10 = v1) | v5 = v1 % 182.74/28.06 | | v0 = all_1677_0))))) % 182.74/28.06 | % 182.74/28.06 | ALPHA: (402) implies: % 182.74/28.06 | (403) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1677_0 % 182.74/28.06 | % 182.74/28.06 | DELTA: instantiating (108) with fresh symbols all_1680_0, all_1680_1 gives: % 182.74/28.06 | (404) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1680_0 & % 182.74/28.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1680_1 & % 182.74/28.06 | $i(all_1680_0) & $i(all_1680_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.06 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.74/28.06 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 182.74/28.06 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1680_0) = v7) | % 182.74/28.06 | ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ % 182.74/28.06 | (c_Groups_Otimes__class_Otimes(v2) = v5) | ~ (hAPP(v6, v8) = v9) | % 182.74/28.06 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v7) = v8) | ~ (hAPP(v3, v0) % 182.74/28.06 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? % 182.74/28.06 | [v11: $i] : ? [v12: $i] : (class_Power_Opower(v2) = v10 & % 182.74/28.06 | c_Groups_Oone__class_Oone(v2) = v12 & hAPP(v4, v1) = v11 & % 182.74/28.06 | $i(v12) & $i(v11) & ( ~ (v10 = 0) | (( ~ (v1 = all_1680_1) | v12 % 182.74/28.06 | = v11) & (v11 = v9 | v1 = all_1680_1))))) % 182.74/28.06 | % 182.74/28.06 | ALPHA: (404) implies: % 182.74/28.06 | (405) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1680_1 % 182.74/28.06 | % 182.74/28.06 | DELTA: instantiating (84) with fresh symbols all_1683_0, all_1683_1 gives: % 182.74/28.06 | (406) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1683_1 & % 182.74/28.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1683_0 & % 182.74/28.06 | $i(all_1683_0) & $i(all_1683_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.06 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 % 182.74/28.06 | = 0 | ~ (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) = v6) | ~ % 182.74/28.06 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1683_1, % 182.74/28.06 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = % 182.74/28.06 | all_1683_0) & ? [v7: int] : ( ~ (v7 = 0) & % 182.74/28.06 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) = v7))) & ! [v0: % 182.74/28.06 | $i] : ! [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ! % 182.74/28.06 | [v5: $i] : (v2 = all_1683_0 | ~ % 182.74/28.06 | (c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) = 0) | ~ (hAPP(v3, % 182.74/28.06 | v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1683_1, v2) = % 182.74/28.06 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 182.74/28.06 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) = 0) % 182.74/28.06 | % 182.74/28.06 | ALPHA: (406) implies: % 182.74/28.06 | (407) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1683_0 % 182.74/28.06 | % 182.74/28.06 | DELTA: instantiating (89) with fresh symbols all_1686_0, all_1686_1 gives: % 182.74/28.06 | (408) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1686_0 & % 182.74/28.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1686_1 & % 182.74/28.06 | $i(all_1686_0) & $i(all_1686_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.06 | any] : ! [v3: any] : ( ~ % 182.74/28.06 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1686_1, v1) = v2) | % 182.74/28.06 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1686_1, v0) = % 182.74/28.06 | v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 182.74/28.06 | int] : ( ~ (v6 = 0) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.74/28.06 | all_1686_1, v5) = v6 & hAPP(v4, v0) = v5 & hAPP(all_1686_0, v1) % 182.74/28.06 | = v4 & $i(v5) & $i(v4)) | (v3 = 0 & v2 = 0)) & ! [v0: $i] : ! % 182.74/28.06 | [v1: $i] : ( ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.74/28.06 | all_1686_1, v1) = 0) | ~ % 182.74/28.06 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1686_1, v0) = 0) | % 182.74/28.06 | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 182.74/28.06 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1686_1, v3) = 0 & % 182.74/28.06 | hAPP(v2, v0) = v3 & hAPP(all_1686_0, v1) = v2 & $i(v3) & $i(v2))) % 182.74/28.06 | % 182.74/28.06 | ALPHA: (408) implies: % 182.74/28.06 | (409) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1686_1 % 182.74/28.06 | % 182.74/28.06 | DELTA: instantiating (90) with fresh symbols all_1689_0, all_1689_1 gives: % 182.74/28.07 | (410) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1689_1 & % 182.74/28.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1689_0 & % 182.74/28.07 | $i(all_1689_0) & $i(all_1689_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.07 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 % 182.74/28.07 | = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) = v6) % 182.74/28.07 | | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 182.74/28.07 | (hAPP(all_1689_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 182.74/28.07 | ? [v7: any] : ? [v8: any] : % 182.74/28.07 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = v8 & % 182.74/28.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1689_0, v2) = v7 & % 182.74/28.07 | ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 182.74/28.07 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 182.74/28.07 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) = 0) | ~ % 182.74/28.07 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1689_1, % 182.74/28.07 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 182.74/28.07 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = 0 & % 182.74/28.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1689_0, v2) = 0)) % 182.74/28.07 | % 182.74/28.07 | ALPHA: (410) implies: % 182.74/28.07 | (411) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1689_0 % 182.74/28.07 | % 182.74/28.07 | DELTA: instantiating (101) with fresh symbols all_1695_0, all_1695_1 gives: % 182.74/28.07 | (412) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1695_1 & % 182.74/28.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1695_0 & % 182.74/28.07 | $i(all_1695_0) & $i(all_1695_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.07 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 % 182.74/28.07 | = 0 | ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) = % 182.74/28.07 | v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 182.74/28.07 | (hAPP(all_1695_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 182.74/28.07 | ? [v7: int] : ( ~ (v7 = 0) & % 182.74/28.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1695_0, v2) = 0 & % 182.74/28.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = v7)) & % 182.74/28.07 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 182.74/28.07 | ! [v5: $i] : ( ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, % 182.74/28.07 | v5) = 0) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 182.74/28.07 | (hAPP(all_1695_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 182.74/28.07 | ? [v6: any] : ? [v7: any] : % 182.74/28.07 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1695_0, v2) = v6 & % 182.74/28.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) = v7 & ( ~ % 182.74/28.07 | (v6 = 0) | v7 = 0))) % 182.74/28.07 | % 182.74/28.07 | ALPHA: (412) implies: % 182.74/28.07 | (413) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1695_0 % 182.74/28.07 | % 182.74/28.07 | DELTA: instantiating (47) with fresh symbols all_1701_0, all_1701_1, % 182.74/28.07 | all_1701_2 gives: % 182.74/28.07 | (414) c_Nat_OSuc(all_1701_1) = all_1701_0 & c_Nat_OSuc(all_1701_2) = % 182.74/28.07 | all_1701_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1701_2 & % 182.74/28.07 | $i(all_1701_0) & $i(all_1701_1) & $i(all_1701_2) & ! [v0: $i] : ! % 182.74/28.07 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 182.74/28.07 | ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) % 182.74/28.07 | | ~ (hAPP(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 182.74/28.07 | [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 182.74/28.07 | (c_Groups_Ouminus__class_Ouminus(v2, v0) = v9 & % 182.74/28.07 | class_Rings_Oidom(v2) = v6 & hAPP(v5, all_1701_0) = v8 & hAPP(v4, % 182.74/28.07 | all_1701_0) = v7 & $i(v9) & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( % 182.74/28.07 | ~ (v8 = v7) | v9 = v1 | v1 = v0) & (v8 = v7 | ( ~ (v9 = v1) % 182.74/28.07 | & ~ (v1 = v0))))))) % 182.74/28.07 | % 182.74/28.07 | ALPHA: (414) implies: % 182.74/28.07 | (415) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1701_2 % 182.74/28.07 | % 182.74/28.07 | DELTA: instantiating (39) with fresh symbols all_1704_0, all_1704_1, % 182.74/28.07 | all_1704_2 gives: % 182.74/28.07 | (416) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1704_0 & % 182.74/28.07 | c_Nat_OSuc(all_1704_2) = all_1704_1 & % 182.74/28.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1704_2 & % 182.74/28.07 | $i(all_1704_0) & $i(all_1704_1) & $i(all_1704_2) & ! [v0: $i] : ! % 182.74/28.07 | [v1: $i] : ! [v2: any] : ! [v3: any] : ( ~ % 182.74/28.07 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1704_1, v1) = % 182.74/28.07 | v2) | ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 182.74/28.07 | all_1704_1, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 182.74/28.07 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 182.74/28.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1704_1, v5) = % 182.74/28.07 | v6 & hAPP(v4, v0) = v5 & hAPP(all_1704_0, v1) = v4 & $i(v5) & % 182.74/28.07 | $i(v4)) | (v3 = 0 & v2 = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 182.74/28.07 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1704_1, v1) = % 182.74/28.07 | 0) | ~ (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 182.74/28.07 | all_1704_1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 182.74/28.07 | [v3: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 182.74/28.07 | all_1704_1, v3) = 0 & hAPP(v2, v0) = v3 & hAPP(all_1704_0, v1) % 182.74/28.07 | = v2 & $i(v3) & $i(v2))) % 182.74/28.07 | % 182.74/28.07 | ALPHA: (416) implies: % 182.74/28.07 | (417) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1704_2 % 182.74/28.07 | % 182.74/28.07 | DELTA: instantiating (91) with fresh symbols all_1707_0, all_1707_1 gives: % 182.74/28.07 | (418) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1707_1 & % 182.74/28.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1707_0 & % 182.74/28.07 | $i(all_1707_0) & $i(all_1707_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.07 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.74/28.07 | [v7: int] : (v7 = 0 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.74/28.07 | v4, v6) = v7) | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) % 182.74/28.07 | | ~ (hAPP(all_1707_1, v2) = v3) | ~ (hAPP(all_1707_1, v0) = v5) | % 182.74/28.07 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] : % 182.74/28.07 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0) = v9 & % 182.74/28.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1707_0, v1) = v8 & % 182.74/28.07 | ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 182.74/28.07 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 182.74/28.07 | ~ (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) = 0) | ~ % 182.74/28.07 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1707_1, % 182.74/28.07 | v2) = v3) | ~ (hAPP(all_1707_1, v0) = v5) | ~ $i(v2) | ~ % 182.74/28.07 | $i(v1) | ~ $i(v0) | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.74/28.07 | v2, v0) = 0 & c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 182.74/28.07 | all_1707_0, v1) = 0)) % 182.74/28.07 | % 182.74/28.07 | ALPHA: (418) implies: % 182.74/28.07 | (419) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1707_0 % 182.74/28.07 | % 182.74/28.07 | DELTA: instantiating (100) with fresh symbols all_1716_0, all_1716_1 gives: % 182.74/28.07 | (420) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1716_1 & % 182.74/28.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1716_0 & % 182.74/28.07 | $i(all_1716_0) & $i(all_1716_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 182.74/28.07 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 182.74/28.07 | [v7: int] : (v7 = 0 | ~ % 182.74/28.07 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6) = v7) | ~ % 182.74/28.07 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1716_1, % 182.74/28.07 | v2) = v3) | ~ (hAPP(all_1716_1, v0) = v5) | ~ $i(v2) | ~ % 182.74/28.07 | $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & % 182.74/28.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1716_0, v1) = 0 & % 182.74/28.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) = v8)) & % 182.74/28.07 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 182.74/28.07 | ! [v5: $i] : ! [v6: $i] : ( ~ % 182.74/28.07 | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6) = 0) | ~ % 182.74/28.07 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1716_1, % 182.74/28.07 | v2) = v3) | ~ (hAPP(all_1716_1, v0) = v5) | ~ $i(v2) | ~ % 182.74/28.07 | $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 182.74/28.07 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1716_0, v1) = v7 & % 182.74/28.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) = v8 & ( ~ % 182.74/28.07 | (v7 = 0) | v8 = 0))) % 182.74/28.07 | % 182.74/28.07 | ALPHA: (420) implies: % 182.74/28.07 | (421) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1716_0 % 182.74/28.07 | % 182.74/28.07 | DELTA: instantiating (55) with fresh symbols all_1719_0, all_1719_1, % 182.74/28.07 | all_1719_2 gives: % 182.74/28.08 | (422) c_Nat_OSuc(all_1719_1) = all_1719_0 & c_Nat_OSuc(all_1719_2) = % 182.74/28.08 | all_1719_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1719_2 & % 182.74/28.08 | $i(all_1719_0) & $i(all_1719_1) & $i(all_1719_2) & ! [v0: $i] : ! % 182.74/28.08 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 182.74/28.08 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 182.74/28.08 | (c_Groups_Ominus__class_Ominus(v2, v5, v7) = v8) | ~ % 182.74/28.08 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v6, all_1719_0) % 182.74/28.08 | = v7) | ~ (hAPP(v4, all_1719_0) = v5) | ~ (hAPP(v3, v1) = v4) | % 182.74/28.08 | ~ (hAPP(v3, v0) = v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 182.74/28.08 | [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 182.74/28.08 | $i] : ? [v14: $i] : (c_Groups_Ominus__class_Ominus(v2, v1, v0) = % 182.74/28.08 | v11 & class_Rings_Ocomm__ring__1(v2) = v9 & % 182.74/28.08 | c_Groups_Otimes__class_Otimes(v2) = v10 & % 182.74/28.08 | c_Groups_Oplus__class_Oplus(v2, v1, v0) = v13 & hAPP(v12, v13) = % 182.74/28.08 | v14 & hAPP(v10, v11) = v12 & $i(v14) & $i(v13) & $i(v12) & % 182.74/28.08 | $i(v11) & $i(v10) & ( ~ (v9 = 0) | v14 = v8))) % 182.74/28.08 | % 182.74/28.08 | ALPHA: (422) implies: % 182.74/28.08 | (423) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1719_2 % 182.74/28.08 | % 182.74/28.08 | DELTA: instantiating (58) with fresh symbol all_1746_0 gives: % 182.74/28.08 | (424) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1746_0 & % 182.74/28.08 | $i(all_1746_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.74/28.08 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 182.74/28.08 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 182.74/28.08 | | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: % 182.74/28.08 | any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = v6 & % 182.74/28.08 | hBOOL(v7) = v8 & hBOOL(v4) = v5 & hAPP(v2, all_1746_0) = v7 & % 182.74/28.08 | $i(v7) & ( ~ (v5 = 0) | ( ! [v9: $i] : ( ~ % 182.74/28.08 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v9) = v1) | % 182.74/28.08 | ~ $i(v9) | ? [v10: $i] : (hBOOL(v10) = 0 & hAPP(v2, v9) = % 182.74/28.08 | v10 & $i(v10))) & ( ~ (v6 = 0) | v8 = 0))))) & ! [v0: % 182.74/28.08 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 182.74/28.08 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 182.74/28.08 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 182.74/28.08 | any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : % 182.74/28.08 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = v5 & % 182.74/28.08 | hBOOL(v6) = v7 & hBOOL(v4) = v8 & hAPP(v2, all_1746_0) = v6 & % 182.74/28.08 | $i(v6) & (v8 = 0 | (v5 = 0 & ~ (v7 = 0)))) | ? [v5: $i] : ? % 182.74/28.08 | [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & hBOOL(v6) = v7 & % 182.74/28.08 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1 & hAPP(v2, % 182.74/28.08 | v5) = v6 & $i(v6) & $i(v5))) % 182.74/28.08 | % 182.74/28.08 | ALPHA: (424) implies: % 182.74/28.08 | (425) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1746_0 % 182.74/28.08 | % 182.74/28.08 | DELTA: instantiating (58) with fresh symbol all_1749_0 gives: % 182.74/28.08 | (426) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1749_0 & % 182.74/28.08 | $i(all_1749_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 182.74/28.08 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 182.74/28.08 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 182.74/28.08 | | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: % 182.74/28.08 | any] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = v6 & % 182.74/28.08 | hBOOL(v7) = v8 & hBOOL(v4) = v5 & hAPP(v2, all_1749_0) = v7 & % 182.74/28.08 | $i(v7) & ( ~ (v5 = 0) | ( ! [v9: $i] : ( ~ % 182.74/28.08 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v9) = v1) | % 182.74/28.08 | ~ $i(v9) | ? [v10: $i] : (hBOOL(v10) = 0 & hAPP(v2, v9) = % 182.74/28.08 | v10 & $i(v10))) & ( ~ (v6 = 0) | v8 = 0))))) & ! [v0: % 182.74/28.08 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 182.74/28.08 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 182.74/28.08 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 182.74/28.08 | any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : % 182.74/28.08 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) = v5 & % 182.74/28.08 | hBOOL(v6) = v7 & hBOOL(v4) = v8 & hAPP(v2, all_1749_0) = v6 & % 182.74/28.08 | $i(v6) & (v8 = 0 | (v5 = 0 & ~ (v7 = 0)))) | ? [v5: $i] : ? % 182.74/28.08 | [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & hBOOL(v6) = v7 & % 182.74/28.08 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1 & hAPP(v2, % 182.74/28.08 | v5) = v6 & $i(v6) & $i(v5))) % 182.74/28.08 | % 182.74/28.08 | ALPHA: (426) implies: % 182.74/28.08 | (427) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1749_0 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (127) with all_1236_1, all_1595_6, v_p, t_a, % 182.74/28.08 | simplifying with (207), (349) gives: % 182.74/28.08 | (428) all_1595_6 = all_1236_1 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (127) with all_1595_6, all_1618_6, v_p, t_a, % 182.74/28.08 | simplifying with (349), (364) gives: % 182.74/28.08 | (429) all_1618_6 = all_1595_6 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (127) with all_1533_5, all_1618_6, v_p, t_a, % 182.74/28.08 | simplifying with (312), (364) gives: % 182.74/28.08 | (430) all_1618_6 = all_1533_5 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (127) with all_1392_2, all_1618_6, v_p, t_a, % 182.74/28.08 | simplifying with (267), (364) gives: % 182.74/28.08 | (431) all_1618_6 = all_1392_2 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (121) with all_1392_3, all_1533_6, t_a, simplifying % 182.74/28.08 | with (268), (313) gives: % 182.74/28.08 | (432) all_1533_6 = all_1392_3 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (121) with all_1392_3, all_1595_7, t_a, simplifying % 182.74/28.08 | with (268), (350) gives: % 182.74/28.08 | (433) all_1595_7 = all_1392_3 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (121) with 0, all_1595_7, t_a, simplifying with % 182.74/28.08 | (118), (350) gives: % 182.74/28.08 | (434) all_1595_7 = 0 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (121) with all_1533_6, all_1618_8, t_a, simplifying % 182.74/28.08 | with (313), (365) gives: % 182.74/28.08 | (435) all_1618_8 = all_1533_6 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (121) with all_1236_2, all_1618_8, t_a, simplifying % 182.74/28.08 | with (208), (365) gives: % 182.74/28.08 | (436) all_1618_8 = all_1236_2 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (122) with all_1392_4, all_1533_7, t_a, simplifying % 182.74/28.08 | with (269), (314) gives: % 182.74/28.08 | (437) all_1533_7 = all_1392_4 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (122) with all_1533_7, all_1595_8, t_a, simplifying % 182.74/28.08 | with (314), (351) gives: % 182.74/28.08 | (438) all_1595_8 = all_1533_7 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (122) with 0, all_1595_8, t_a, simplifying with % 182.74/28.08 | (117), (351) gives: % 182.74/28.08 | (439) all_1595_8 = 0 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (122) with all_1392_4, all_1618_9, t_a, simplifying % 182.74/28.08 | with (269), (366) gives: % 182.74/28.08 | (440) all_1618_9 = all_1392_4 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (122) with all_1236_3, all_1618_9, t_a, simplifying % 182.74/28.08 | with (209), (366) gives: % 182.74/28.08 | (441) all_1618_9 = all_1236_3 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (123) with all_1595_5, all_1618_5, t_a, simplifying % 182.74/28.08 | with (352), (367) gives: % 182.74/28.08 | (442) all_1618_5 = all_1595_5 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (123) with all_1533_4, all_1618_5, t_a, simplifying % 182.74/28.08 | with (315), (367) gives: % 182.74/28.08 | (443) all_1618_5 = all_1533_4 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (123) with all_1392_1, all_1618_5, t_a, simplifying % 182.74/28.08 | with (270), (367) gives: % 182.74/28.08 | (444) all_1618_5 = all_1392_1 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (123) with all_1083_0, all_1102_0, tc_Nat_Onat, % 182.74/28.08 | simplifying with (131), (145) gives: % 182.74/28.08 | (445) all_1102_0 = all_1083_0 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (123) with all_1102_0, all_1105_0, tc_Nat_Onat, % 182.74/28.08 | simplifying with (145), (147) gives: % 182.74/28.08 | (446) all_1105_0 = all_1102_0 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (123) with all_1102_0, all_1120_0, tc_Nat_Onat, % 182.74/28.08 | simplifying with (145), (157) gives: % 182.74/28.08 | (447) all_1120_0 = all_1102_0 % 182.74/28.08 | % 182.74/28.08 | GROUND_INST: instantiating (123) with all_1123_0, all_1126_0, tc_Nat_Onat, % 182.74/28.08 | simplifying with (159), (161) gives: % 182.74/28.08 | (448) all_1126_0 = all_1123_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1137_0, all_1144_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (167), (171) gives: % 182.74/28.09 | (449) all_1144_0 = all_1137_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1144_0, all_1149_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (171), (173) gives: % 182.74/28.09 | (450) all_1149_0 = all_1144_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1149_0, all_1155_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (173), (175) gives: % 182.74/28.09 | (451) all_1155_0 = all_1149_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1155_0, all_1158_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (175), (177) gives: % 182.74/28.09 | (452) all_1158_0 = all_1155_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1158_0, all_1167_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (177), (179) gives: % 182.74/28.09 | (453) all_1167_0 = all_1158_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1144_0, all_1170_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (171), (181) gives: % 182.74/28.09 | (454) all_1170_0 = all_1144_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1167_0, all_1173_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (179), (183) gives: % 182.74/28.09 | (455) all_1173_0 = all_1167_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1173_0, all_1183_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (183), (185) gives: % 182.74/28.09 | (456) all_1183_0 = all_1173_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1183_0, all_1186_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (185), (187) gives: % 182.74/28.09 | (457) all_1186_0 = all_1183_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1186_0, all_1189_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (187), (190) gives: % 182.74/28.09 | (458) all_1189_0 = all_1186_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1120_0, all_1191_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (157), (193) gives: % 182.74/28.09 | (459) all_1191_0 = all_1120_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1189_0, all_1203_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (190), (195) gives: % 182.74/28.09 | (460) all_1203_0 = all_1189_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1203_0, all_1206_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (195), (197) gives: % 182.74/28.09 | (461) all_1206_0 = all_1203_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1206_0, all_1218_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (197), (199) gives: % 182.74/28.09 | (462) all_1218_0 = all_1206_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1218_0, all_1221_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (199), (201) gives: % 182.74/28.09 | (463) all_1221_0 = all_1218_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1221_0, all_1224_1, tc_Nat_Onat, % 182.74/28.09 | simplifying with (201), (203) gives: % 182.74/28.09 | (464) all_1224_1 = all_1221_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1114_0, all_1247_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (153), (215) gives: % 182.74/28.09 | (465) all_1247_0 = all_1114_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1256_1, all_1259_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (219), (221) gives: % 182.74/28.09 | (466) all_1259_0 = all_1256_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1259_0, all_1263_1, tc_Nat_Onat, % 182.74/28.09 | simplifying with (221), (223) gives: % 182.74/28.09 | (467) all_1263_1 = all_1259_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1263_1, all_1269_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (223), (225) gives: % 182.74/28.09 | (468) all_1269_0 = all_1263_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1269_0, all_1275_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (225), (227) gives: % 182.74/28.09 | (469) all_1275_0 = all_1269_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1105_0, all_1296_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (147), (233) gives: % 182.74/28.09 | (470) all_1296_0 = all_1105_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1296_0, all_1302_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (233), (235) gives: % 182.74/28.09 | (471) all_1302_2 = all_1296_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1170_0, all_1305_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (181), (237) gives: % 182.74/28.09 | (472) all_1305_0 = all_1170_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1302_2, all_1323_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (235), (239) gives: % 182.74/28.09 | (473) all_1323_0 = all_1302_2 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1305_0, all_1329_1, tc_Nat_Onat, % 182.74/28.09 | simplifying with (237), (241) gives: % 182.74/28.09 | (474) all_1329_1 = all_1305_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1287_0, all_1335_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (231), (245) gives: % 182.74/28.09 | (475) all_1335_2 = all_1287_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1323_0, all_1338_1, tc_Nat_Onat, % 182.74/28.09 | simplifying with (239), (247) gives: % 182.74/28.09 | (476) all_1338_1 = all_1323_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1287_0, all_1341_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (231), (249) gives: % 182.74/28.09 | (477) all_1341_0 = all_1287_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1275_0, all_1341_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (227), (249) gives: % 182.74/28.09 | (478) all_1341_0 = all_1275_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1137_0, all_1356_1, tc_Nat_Onat, % 182.74/28.09 | simplifying with (167), (256) gives: % 182.74/28.09 | (479) all_1356_1 = all_1137_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1126_0, all_1356_1, tc_Nat_Onat, % 182.74/28.09 | simplifying with (161), (256) gives: % 182.74/28.09 | (480) all_1356_1 = all_1126_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1362_0, all_1365_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (260), (262) gives: % 182.74/28.09 | (481) all_1365_0 = all_1362_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1329_1, all_1368_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (241), (264) gives: % 182.74/28.09 | (482) all_1368_0 = all_1329_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1365_0, all_1395_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (262), (272) gives: % 182.74/28.09 | (483) all_1395_0 = all_1365_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1332_1, all_1410_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (243), (274) gives: % 182.74/28.09 | (484) all_1410_0 = all_1332_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1089_0, all_1410_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (137), (274) gives: % 182.74/28.09 | (485) all_1410_0 = all_1089_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1256_1, all_1431_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (219), (276) gives: % 182.74/28.09 | (486) all_1431_0 = all_1256_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1253_0, all_1431_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (217), (276) gives: % 182.74/28.09 | (487) all_1431_0 = all_1253_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1238_0, all_1431_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (211), (276) gives: % 182.74/28.09 | (488) all_1431_0 = all_1238_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1395_0, all_1434_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (272), (278) gives: % 182.74/28.09 | (489) all_1434_2 = all_1395_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1434_2, all_1437_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (278), (280) gives: % 182.74/28.09 | (490) all_1437_0 = all_1434_2 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1344_0, all_1449_1, tc_Nat_Onat, % 182.74/28.09 | simplifying with (252), (282) gives: % 182.74/28.09 | (491) all_1449_1 = all_1344_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1437_0, all_1470_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (280), (292) gives: % 182.74/28.09 | (492) all_1470_2 = all_1437_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1470_2, all_1476_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (292), (294) gives: % 182.74/28.09 | (493) all_1476_2 = all_1470_2 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1476_2, all_1485_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (294), (300) gives: % 182.74/28.09 | (494) all_1485_2 = all_1476_2 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1281_1, all_1485_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (229), (300) gives: % 182.74/28.09 | (495) all_1485_2 = all_1281_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1479_1, all_1506_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (296), (302) gives: % 182.74/28.09 | (496) all_1506_0 = all_1479_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1449_1, all_1506_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (282), (302) gives: % 182.74/28.09 | (497) all_1506_0 = all_1449_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1111_0, all_1506_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (151), (302) gives: % 182.74/28.09 | (498) all_1506_0 = all_1111_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1506_0, all_1518_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (302), (304) gives: % 182.74/28.09 | (499) all_1518_2 = all_1506_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1518_2, all_1524_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (304), (306) gives: % 182.74/28.09 | (500) all_1524_0 = all_1518_2 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1452_0, all_1530_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (284), (308) gives: % 182.74/28.09 | (501) all_1530_2 = all_1452_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1359_0, all_1530_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (258), (308) gives: % 182.74/28.09 | (502) all_1530_2 = all_1359_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1335_2, all_1530_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (245), (308) gives: % 182.74/28.09 | (503) all_1530_2 = all_1335_2 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1139_0, all_1530_2, tc_Nat_Onat, % 182.74/28.09 | simplifying with (169), (308) gives: % 182.74/28.09 | (504) all_1530_2 = all_1139_0 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1356_1, all_1535_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (256), (321) gives: % 182.74/28.09 | (505) all_1535_0 = all_1356_1 % 182.74/28.09 | % 182.74/28.09 | GROUND_INST: instantiating (123) with all_1338_1, all_1544_0, tc_Nat_Onat, % 182.74/28.09 | simplifying with (247), (325) gives: % 182.74/28.09 | (506) all_1544_0 = all_1338_1 % 182.74/28.09 | % 182.74/28.10 | GROUND_INST: instantiating (123) with all_1344_0, all_1547_1, tc_Nat_Onat, % 182.74/28.10 | simplifying with (252), (327) gives: % 182.74/28.10 | (507) all_1547_1 = all_1344_0 % 182.74/28.10 | % 182.74/28.10 | GROUND_INST: instantiating (123) with all_1085_0, all_1547_1, tc_Nat_Onat, % 182.74/28.10 | simplifying with (133), (327) gives: % 182.74/28.10 | (508) all_1547_1 = all_1085_0 % 182.74/28.10 | % 182.74/28.10 | GROUND_INST: instantiating (123) with all_1530_2, all_1559_0, tc_Nat_Onat, % 182.74/28.10 | simplifying with (308), (331) gives: % 182.74/28.10 | (509) all_1559_0 = all_1530_2 % 182.74/28.10 | % 182.74/28.10 | GROUND_INST: instantiating (123) with all_1559_0, all_1568_1, tc_Nat_Onat, % 182.74/28.10 | simplifying with (331), (335) gives: % 182.74/28.10 | (510) all_1568_1 = all_1559_0 % 182.74/28.10 | % 182.74/28.10 | GROUND_INST: instantiating (123) with all_1332_1, all_1571_0, tc_Nat_Onat, % 182.74/28.10 | simplifying with (243), (337) gives: % 182.74/28.10 | (511) all_1571_0 = all_1332_1 % 182.74/28.10 | % 182.74/28.10 | GROUND_INST: instantiating (123) with all_1191_0, all_1571_0, tc_Nat_Onat, % 183.07/28.11 | simplifying with (193), (337) gives: % 183.07/28.11 | (512) all_1571_0 = all_1191_0 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1571_0, all_1574_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (337), (339) gives: % 183.07/28.11 | (513) all_1574_1 = all_1571_0 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1574_1, all_1577_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (339), (341) gives: % 183.07/28.11 | (514) all_1577_1 = all_1574_1 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1238_0, all_1583_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (211), (343) gives: % 183.07/28.11 | (515) all_1583_1 = all_1238_0 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1224_1, all_1583_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (203), (343) gives: % 183.07/28.11 | (516) all_1583_1 = all_1224_1 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1344_0, all_1597_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (252), (357) gives: % 183.07/28.11 | (517) all_1597_1 = all_1344_0 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1102_0, all_1597_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (145), (357) gives: % 183.07/28.11 | (518) all_1597_1 = all_1102_0 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1099_0, all_1597_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (143), (357) gives: % 183.07/28.11 | (519) all_1597_1 = all_1099_0 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1087_0, all_1597_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (135), (357) gives: % 183.07/28.11 | (520) all_1597_1 = all_1087_0 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1544_0, all_1600_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (325), (359) gives: % 183.07/28.11 | (521) all_1600_1 = all_1544_0 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1600_1, all_1603_1, tc_Nat_Onat, % 183.07/28.11 | simplifying with (359), (361) gives: % 183.07/28.11 | (522) all_1603_1 = all_1600_1 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1565_1, all_1620_0, tc_Nat_Onat, % 183.07/28.11 | simplifying with (333), (375) gives: % 183.07/28.11 | (523) all_1620_0 = all_1565_1 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1603_1, all_1623_0, tc_Nat_Onat, % 183.07/28.11 | simplifying with (361), (377) gives: % 183.07/28.11 | (524) all_1623_0 = all_1603_1 % 183.07/28.11 | % 183.07/28.11 | GROUND_INST: instantiating (123) with all_1583_1, all_1626_0, tc_Nat_Onat, % 183.07/28.11 | simplifying with (343), (379) gives: % 183.07/28.11 | (525) all_1626_0 = all_1583_1 % 183.07/28.11 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1227_0, all_1626_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (205), (379) gives: % 183.07/28.12 | (526) all_1626_0 = all_1227_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1623_0, all_1632_1, tc_Nat_Onat, % 183.07/28.12 | simplifying with (377), (383) gives: % 183.07/28.12 | (527) all_1632_1 = all_1623_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1556_0, all_1638_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (329), (385) gives: % 183.07/28.12 | (528) all_1638_2 = all_1556_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1362_0, all_1638_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (260), (385) gives: % 183.07/28.12 | (529) all_1638_2 = all_1362_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1347_1, all_1638_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (254), (385) gives: % 183.07/28.12 | (530) all_1638_2 = all_1347_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1341_0, all_1638_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (249), (385) gives: % 183.07/28.12 | (531) all_1638_2 = all_1341_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1620_0, all_1641_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (375), (387) gives: % 183.07/28.12 | (532) all_1641_0 = all_1620_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1629_0, all_1647_3, tc_Nat_Onat, % 183.07/28.12 | simplifying with (381), (389) gives: % 183.07/28.12 | (533) all_1647_3 = all_1629_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1568_1, all_1647_3, tc_Nat_Onat, % 183.07/28.12 | simplifying with (335), (389) gives: % 183.07/28.12 | (534) all_1647_3 = all_1568_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1647_3, all_1653_1, tc_Nat_Onat, % 183.07/28.12 | simplifying with (389), (391) gives: % 183.07/28.12 | (535) all_1653_1 = all_1647_3 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1464_1, all_1653_1, tc_Nat_Onat, % 183.07/28.12 | simplifying with (288), (391) gives: % 183.07/28.12 | (536) all_1653_1 = all_1464_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1632_1, all_1656_1, tc_Nat_Onat, % 183.07/28.12 | simplifying with (383), (393) gives: % 183.07/28.12 | (537) all_1656_1 = all_1632_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1641_0, all_1665_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (387), (397) gives: % 183.07/28.12 | (538) all_1665_0 = all_1641_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1461_1, all_1665_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (286), (397) gives: % 183.07/28.12 | (539) all_1665_0 = all_1461_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1524_0, all_1671_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (306), (399) gives: % 183.07/28.12 | (540) all_1671_0 = all_1524_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1467_0, all_1674_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (290), (401) gives: % 183.07/28.12 | (541) all_1674_0 = all_1467_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1565_1, all_1677_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (333), (403) gives: % 183.07/28.12 | (542) all_1677_0 = all_1565_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1538_0, all_1677_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (323), (403) gives: % 183.07/28.12 | (543) all_1677_0 = all_1538_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1467_0, all_1677_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (290), (403) gives: % 183.07/28.12 | (544) all_1677_0 = all_1467_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1368_0, all_1677_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (264), (403) gives: % 183.07/28.12 | (545) all_1677_0 = all_1368_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1674_0, all_1680_1, tc_Nat_Onat, % 183.07/28.12 | simplifying with (401), (405) gives: % 183.07/28.12 | (546) all_1680_1 = all_1674_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1680_1, all_1683_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (405), (407) gives: % 183.07/28.12 | (547) all_1683_0 = all_1680_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1683_0, all_1686_1, tc_Nat_Onat, % 183.07/28.12 | simplifying with (407), (409) gives: % 183.07/28.12 | (548) all_1686_1 = all_1683_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1344_0, all_1689_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (252), (411) gives: % 183.07/28.12 | (549) all_1689_0 = all_1344_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1247_0, all_1689_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (215), (411) gives: % 183.07/28.12 | (550) all_1689_0 = all_1247_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1129_0, all_1689_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (163), (411) gives: % 183.07/28.12 | (551) all_1689_0 = all_1129_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1097_0, all_1689_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (141), (411) gives: % 183.07/28.12 | (552) all_1689_0 = all_1097_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1592_0, all_1695_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (345), (413) gives: % 183.07/28.12 | (553) all_1695_0 = all_1592_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1535_0, all_1695_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (321), (413) gives: % 183.07/28.12 | (554) all_1695_0 = all_1535_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1656_1, all_1701_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (393), (415) gives: % 183.07/28.12 | (555) all_1701_2 = all_1656_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1091_0, all_1701_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (139), (415) gives: % 183.07/28.12 | (556) all_1701_2 = all_1091_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1671_0, all_1704_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (399), (417) gives: % 183.07/28.12 | (557) all_1704_2 = all_1671_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1482_1, all_1704_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (298), (417) gives: % 183.07/28.12 | (558) all_1704_2 = all_1482_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1695_0, all_1707_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (413), (419) gives: % 183.07/28.12 | (559) all_1707_0 = all_1695_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1134_0, all_1707_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (165), (419) gives: % 183.07/28.12 | (560) all_1707_0 = all_1134_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1689_0, all_1716_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (411), (421) gives: % 183.07/28.12 | (561) all_1716_0 = all_1689_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1662_0, all_1716_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (395), (421) gives: % 183.07/28.12 | (562) all_1716_0 = all_1662_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1577_1, all_1719_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (341), (423) gives: % 183.07/28.12 | (563) all_1719_2 = all_1577_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1244_0, all_1719_2, tc_Nat_Onat, % 183.07/28.12 | simplifying with (213), (423) gives: % 183.07/28.12 | (564) all_1719_2 = all_1244_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1344_0, all_1746_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (252), (425) gives: % 183.07/28.12 | (565) all_1746_0 = all_1344_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1123_0, all_1746_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (159), (425) gives: % 183.07/28.12 | (566) all_1746_0 = all_1123_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1117_0, all_1746_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (155), (425) gives: % 183.07/28.12 | (567) all_1746_0 = all_1117_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1686_1, all_1749_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (409), (427) gives: % 183.07/28.12 | (568) all_1749_0 = all_1686_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (123) with all_1108_0, all_1749_0, tc_Nat_Onat, % 183.07/28.12 | simplifying with (149), (427) gives: % 183.07/28.12 | (569) all_1749_0 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (128) with all_1189_1, all_1618_7, v_p, t_a, % 183.07/28.12 | simplifying with (191), (369) gives: % 183.07/28.12 | (570) all_1618_7 = all_1189_1 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (125) with all_1595_3, all_1618_3, t_a, simplifying % 183.07/28.12 | with (355), (372) gives: % 183.07/28.12 | (571) all_1618_3 = all_1595_3 % 183.07/28.12 | % 183.07/28.12 | GROUND_INST: instantiating (125) with all_1533_2, all_1618_3, t_a, simplifying % 183.07/28.12 | with (318), (372) gives: % 183.07/28.12 | (572) all_1618_3 = all_1533_2 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (568), (569) imply: % 183.07/28.12 | (573) all_1686_1 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (573) implies: % 183.07/28.12 | (574) all_1686_1 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (566), (567) imply: % 183.07/28.12 | (575) all_1123_0 = all_1117_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (575) implies: % 183.07/28.12 | (576) all_1123_0 = all_1117_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (565), (567) imply: % 183.07/28.12 | (577) all_1344_0 = all_1117_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (577) implies: % 183.07/28.12 | (578) all_1344_0 = all_1117_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (563), (564) imply: % 183.07/28.12 | (579) all_1577_1 = all_1244_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (579) implies: % 183.07/28.12 | (580) all_1577_1 = all_1244_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (561), (562) imply: % 183.07/28.12 | (581) all_1689_0 = all_1662_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (581) implies: % 183.07/28.12 | (582) all_1689_0 = all_1662_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (559), (560) imply: % 183.07/28.12 | (583) all_1695_0 = all_1134_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (583) implies: % 183.07/28.12 | (584) all_1695_0 = all_1134_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (557), (558) imply: % 183.07/28.12 | (585) all_1671_0 = all_1482_1 % 183.07/28.12 | % 183.07/28.12 | SIMP: (585) implies: % 183.07/28.12 | (586) all_1671_0 = all_1482_1 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (555), (556) imply: % 183.07/28.12 | (587) all_1656_1 = all_1091_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (587) implies: % 183.07/28.12 | (588) all_1656_1 = all_1091_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (553), (554) imply: % 183.07/28.12 | (589) all_1592_0 = all_1535_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (553), (584) imply: % 183.07/28.12 | (590) all_1592_0 = all_1134_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (549), (582) imply: % 183.07/28.12 | (591) all_1662_0 = all_1344_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (551), (582) imply: % 183.07/28.12 | (592) all_1662_0 = all_1129_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (550), (582) imply: % 183.07/28.12 | (593) all_1662_0 = all_1247_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (552), (582) imply: % 183.07/28.12 | (594) all_1662_0 = all_1097_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (548), (574) imply: % 183.07/28.12 | (595) all_1683_0 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (595) implies: % 183.07/28.12 | (596) all_1683_0 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (547), (596) imply: % 183.07/28.12 | (597) all_1680_1 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (597) implies: % 183.07/28.12 | (598) all_1680_1 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (546), (598) imply: % 183.07/28.12 | (599) all_1674_0 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (599) implies: % 183.07/28.12 | (600) all_1674_0 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (543), (545) imply: % 183.07/28.12 | (601) all_1538_0 = all_1368_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (543), (544) imply: % 183.07/28.12 | (602) all_1538_0 = all_1467_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (542), (543) imply: % 183.07/28.12 | (603) all_1565_1 = all_1538_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (603) implies: % 183.07/28.12 | (604) all_1565_1 = all_1538_0 % 183.07/28.12 | % 183.07/28.12 | COMBINE_EQS: (541), (600) imply: % 183.07/28.12 | (605) all_1467_0 = all_1108_0 % 183.07/28.12 | % 183.07/28.12 | SIMP: (605) implies: % 183.07/28.12 | (606) all_1467_0 = all_1108_0 % 183.07/28.12 | % 183.07/28.13 | COMBINE_EQS: (540), (586) imply: % 183.07/28.13 | (607) all_1524_0 = all_1482_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (607) implies: % 183.07/28.13 | (608) all_1524_0 = all_1482_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (538), (539) imply: % 183.07/28.13 | (609) all_1641_0 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (609) implies: % 183.07/28.13 | (610) all_1641_0 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (592), (593) imply: % 183.07/28.13 | (611) all_1247_0 = all_1129_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (611) implies: % 183.07/28.13 | (612) all_1247_0 = all_1129_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (591), (592) imply: % 183.07/28.13 | (613) all_1344_0 = all_1129_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (613) implies: % 183.07/28.13 | (614) all_1344_0 = all_1129_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (592), (594) imply: % 183.07/28.13 | (615) all_1129_0 = all_1097_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (537), (588) imply: % 183.07/28.13 | (616) all_1632_1 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (616) implies: % 183.07/28.13 | (617) all_1632_1 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (535), (536) imply: % 183.07/28.13 | (618) all_1647_3 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (618) implies: % 183.07/28.13 | (619) all_1647_3 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (533), (619) imply: % 183.07/28.13 | (620) all_1629_0 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (533), (534) imply: % 183.07/28.13 | (621) all_1629_0 = all_1568_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (532), (610) imply: % 183.07/28.13 | (622) all_1620_0 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (622) implies: % 183.07/28.13 | (623) all_1620_0 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (528), (529) imply: % 183.07/28.13 | (624) all_1556_0 = all_1362_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (528), (530) imply: % 183.07/28.13 | (625) all_1556_0 = all_1347_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (528), (531) imply: % 183.07/28.13 | (626) all_1556_0 = all_1341_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (527), (617) imply: % 183.07/28.13 | (627) all_1623_0 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (627) implies: % 183.07/28.13 | (628) all_1623_0 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (620), (621) imply: % 183.07/28.13 | (629) all_1568_1 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (629) implies: % 183.07/28.13 | (630) all_1568_1 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (525), (526) imply: % 183.07/28.13 | (631) all_1583_1 = all_1227_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (631) implies: % 183.07/28.13 | (632) all_1583_1 = all_1227_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (524), (628) imply: % 183.07/28.13 | (633) all_1603_1 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (633) implies: % 183.07/28.13 | (634) all_1603_1 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (523), (623) imply: % 183.07/28.13 | (635) all_1565_1 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (635) implies: % 183.07/28.13 | (636) all_1565_1 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (571), (572) imply: % 183.07/28.13 | (637) all_1595_3 = all_1533_2 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (442), (444) imply: % 183.07/28.13 | (638) all_1595_5 = all_1392_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (442), (443) imply: % 183.07/28.13 | (639) all_1595_5 = all_1533_4 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (429), (430) imply: % 183.07/28.13 | (640) all_1595_6 = all_1533_5 % 183.07/28.13 | % 183.07/28.13 | SIMP: (640) implies: % 183.07/28.13 | (641) all_1595_6 = all_1533_5 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (430), (431) imply: % 183.07/28.13 | (642) all_1533_5 = all_1392_2 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (435), (436) imply: % 183.07/28.13 | (643) all_1533_6 = all_1236_2 % 183.07/28.13 | % 183.07/28.13 | SIMP: (643) implies: % 183.07/28.13 | (644) all_1533_6 = all_1236_2 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (440), (441) imply: % 183.07/28.13 | (645) all_1392_4 = all_1236_3 % 183.07/28.13 | % 183.07/28.13 | SIMP: (645) implies: % 183.07/28.13 | (646) all_1392_4 = all_1236_3 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (522), (634) imply: % 183.07/28.13 | (647) all_1600_1 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (647) implies: % 183.07/28.13 | (648) all_1600_1 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (521), (648) imply: % 183.07/28.13 | (649) all_1544_0 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (649) implies: % 183.07/28.13 | (650) all_1544_0 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (518), (519) imply: % 183.07/28.13 | (651) all_1102_0 = all_1099_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (651) implies: % 183.07/28.13 | (652) all_1102_0 = all_1099_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (517), (519) imply: % 183.07/28.13 | (653) all_1344_0 = all_1099_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (653) implies: % 183.07/28.13 | (654) all_1344_0 = all_1099_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (519), (520) imply: % 183.07/28.13 | (655) all_1099_0 = all_1087_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (638), (639) imply: % 183.07/28.13 | (656) all_1533_4 = all_1392_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (428), (641) imply: % 183.07/28.13 | (657) all_1533_5 = all_1236_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (657) implies: % 183.07/28.13 | (658) all_1533_5 = all_1236_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (433), (434) imply: % 183.07/28.13 | (659) all_1392_3 = 0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (659) implies: % 183.07/28.13 | (660) all_1392_3 = 0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (438), (439) imply: % 183.07/28.13 | (661) all_1533_7 = 0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (661) implies: % 183.07/28.13 | (662) all_1533_7 = 0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (589), (590) imply: % 183.07/28.13 | (663) all_1535_0 = all_1134_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (663) implies: % 183.07/28.13 | (664) all_1535_0 = all_1134_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (516), (632) imply: % 183.07/28.13 | (665) all_1227_0 = all_1224_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (515), (632) imply: % 183.07/28.13 | (666) all_1238_0 = all_1227_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (666) implies: % 183.07/28.13 | (667) all_1238_0 = all_1227_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (514), (580) imply: % 183.07/28.13 | (668) all_1574_1 = all_1244_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (668) implies: % 183.07/28.13 | (669) all_1574_1 = all_1244_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (513), (669) imply: % 183.07/28.13 | (670) all_1571_0 = all_1244_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (670) implies: % 183.07/28.13 | (671) all_1571_0 = all_1244_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (512), (671) imply: % 183.07/28.13 | (672) all_1244_0 = all_1191_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (511), (671) imply: % 183.07/28.13 | (673) all_1332_1 = all_1244_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (673) implies: % 183.07/28.13 | (674) all_1332_1 = all_1244_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (510), (630) imply: % 183.07/28.13 | (675) all_1559_0 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (675) implies: % 183.07/28.13 | (676) all_1559_0 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (604), (636) imply: % 183.07/28.13 | (677) all_1538_0 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (677) implies: % 183.07/28.13 | (678) all_1538_0 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (509), (676) imply: % 183.07/28.13 | (679) all_1530_2 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (679) implies: % 183.07/28.13 | (680) all_1530_2 = all_1464_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (625), (626) imply: % 183.07/28.13 | (681) all_1347_1 = all_1341_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (624), (625) imply: % 183.07/28.13 | (682) all_1362_0 = all_1347_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (682) implies: % 183.07/28.13 | (683) all_1362_0 = all_1347_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (507), (508) imply: % 183.07/28.13 | (684) all_1344_0 = all_1085_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (684) implies: % 183.07/28.13 | (685) all_1344_0 = all_1085_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (506), (650) imply: % 183.07/28.13 | (686) all_1338_1 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (686) implies: % 183.07/28.13 | (687) all_1338_1 = all_1091_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (602), (678) imply: % 183.07/28.13 | (688) all_1467_0 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (688) implies: % 183.07/28.13 | (689) all_1467_0 = all_1461_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (601), (678) imply: % 183.07/28.13 | (690) all_1461_1 = all_1368_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (505), (664) imply: % 183.07/28.13 | (691) all_1356_1 = all_1134_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (691) implies: % 183.07/28.13 | (692) all_1356_1 = all_1134_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (642), (658) imply: % 183.07/28.13 | (693) all_1392_2 = all_1236_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (432), (644) imply: % 183.07/28.13 | (694) all_1392_3 = all_1236_2 % 183.07/28.13 | % 183.07/28.13 | SIMP: (694) implies: % 183.07/28.13 | (695) all_1392_3 = all_1236_2 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (437), (662) imply: % 183.07/28.13 | (696) all_1392_4 = 0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (696) implies: % 183.07/28.13 | (697) all_1392_4 = 0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (504), (680) imply: % 183.07/28.13 | (698) all_1464_1 = all_1139_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (501), (680) imply: % 183.07/28.13 | (699) all_1464_1 = all_1452_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (503), (680) imply: % 183.07/28.13 | (700) all_1464_1 = all_1335_2 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (502), (680) imply: % 183.07/28.13 | (701) all_1464_1 = all_1359_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (500), (608) imply: % 183.07/28.13 | (702) all_1518_2 = all_1482_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (702) implies: % 183.07/28.13 | (703) all_1518_2 = all_1482_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (499), (703) imply: % 183.07/28.13 | (704) all_1506_0 = all_1482_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (704) implies: % 183.07/28.13 | (705) all_1506_0 = all_1482_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (496), (705) imply: % 183.07/28.13 | (706) all_1482_1 = all_1479_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (498), (705) imply: % 183.07/28.13 | (707) all_1482_1 = all_1111_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (497), (705) imply: % 183.07/28.13 | (708) all_1482_1 = all_1449_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (494), (495) imply: % 183.07/28.13 | (709) all_1476_2 = all_1281_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (709) implies: % 183.07/28.13 | (710) all_1476_2 = all_1281_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (706), (708) imply: % 183.07/28.13 | (711) all_1479_1 = all_1449_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (706), (707) imply: % 183.07/28.13 | (712) all_1479_1 = all_1111_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (711), (712) imply: % 183.07/28.13 | (713) all_1449_1 = all_1111_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (713) implies: % 183.07/28.13 | (714) all_1449_1 = all_1111_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (493), (710) imply: % 183.07/28.13 | (715) all_1470_2 = all_1281_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (715) implies: % 183.07/28.13 | (716) all_1470_2 = all_1281_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (492), (716) imply: % 183.07/28.13 | (717) all_1437_0 = all_1281_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (717) implies: % 183.07/28.13 | (718) all_1437_0 = all_1281_1 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (606), (689) imply: % 183.07/28.13 | (719) all_1461_1 = all_1108_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (719) implies: % 183.07/28.13 | (720) all_1461_1 = all_1108_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (698), (699) imply: % 183.07/28.13 | (721) all_1452_0 = all_1139_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (699), (701) imply: % 183.07/28.13 | (722) all_1452_0 = all_1359_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (699), (700) imply: % 183.07/28.13 | (723) all_1452_0 = all_1335_2 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (690), (720) imply: % 183.07/28.13 | (724) all_1368_0 = all_1108_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (724) implies: % 183.07/28.13 | (725) all_1368_0 = all_1108_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (722), (723) imply: % 183.07/28.13 | (726) all_1359_0 = all_1335_2 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (721), (722) imply: % 183.07/28.13 | (727) all_1359_0 = all_1139_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (491), (714) imply: % 183.07/28.13 | (728) all_1344_0 = all_1111_0 % 183.07/28.13 | % 183.07/28.13 | SIMP: (728) implies: % 183.07/28.13 | (729) all_1344_0 = all_1111_0 % 183.07/28.13 | % 183.07/28.13 | COMBINE_EQS: (490), (718) imply: % 183.07/28.13 | (730) all_1434_2 = all_1281_1 % 183.07/28.13 | % 183.07/28.13 | SIMP: (730) implies: % 183.07/28.13 | (731) all_1434_2 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (489), (731) imply: % 183.07/28.14 | (732) all_1395_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | SIMP: (732) implies: % 183.07/28.14 | (733) all_1395_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (487), (488) imply: % 183.07/28.14 | (734) all_1253_0 = all_1238_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (486), (487) imply: % 183.07/28.14 | (735) all_1256_1 = all_1253_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (735) implies: % 183.07/28.14 | (736) all_1256_1 = all_1253_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (484), (485) imply: % 183.07/28.14 | (737) all_1332_1 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (737) implies: % 183.07/28.14 | (738) all_1332_1 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (483), (733) imply: % 183.07/28.14 | (739) all_1365_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | SIMP: (739) implies: % 183.07/28.14 | (740) all_1365_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (660), (695) imply: % 183.07/28.14 | (741) all_1236_2 = 0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (741) implies: % 183.07/28.14 | (742) all_1236_2 = 0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (646), (697) imply: % 183.07/28.14 | (743) all_1236_3 = 0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (743) implies: % 183.07/28.14 | (744) all_1236_3 = 0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (482), (725) imply: % 183.07/28.14 | (745) all_1329_1 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (745) implies: % 183.07/28.14 | (746) all_1329_1 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (481), (740) imply: % 183.07/28.14 | (747) all_1362_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | SIMP: (747) implies: % 183.07/28.14 | (748) all_1362_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (683), (748) imply: % 183.07/28.14 | (749) all_1347_1 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | SIMP: (749) implies: % 183.07/28.14 | (750) all_1347_1 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (726), (727) imply: % 183.07/28.14 | (751) all_1335_2 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (751) implies: % 183.07/28.14 | (752) all_1335_2 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (480), (692) imply: % 183.07/28.14 | (753) all_1134_0 = all_1126_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (479), (692) imply: % 183.07/28.14 | (754) all_1137_0 = all_1134_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (754) implies: % 183.07/28.14 | (755) all_1137_0 = all_1134_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (681), (750) imply: % 183.07/28.14 | (756) all_1341_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | SIMP: (756) implies: % 183.07/28.14 | (757) all_1341_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (654), (729) imply: % 183.07/28.14 | (758) all_1111_0 = all_1099_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (578), (729) imply: % 183.07/28.14 | (759) all_1117_0 = all_1111_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (759) implies: % 183.07/28.14 | (760) all_1117_0 = all_1111_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (685), (729) imply: % 183.07/28.14 | (761) all_1111_0 = all_1085_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (614), (729) imply: % 183.07/28.14 | (762) all_1129_0 = all_1111_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (762) implies: % 183.07/28.14 | (763) all_1129_0 = all_1111_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (478), (757) imply: % 183.07/28.14 | (764) all_1281_1 = all_1275_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (477), (757) imply: % 183.07/28.14 | (765) all_1287_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | SIMP: (765) implies: % 183.07/28.14 | (766) all_1287_0 = all_1281_1 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (476), (687) imply: % 183.07/28.14 | (767) all_1323_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (767) implies: % 183.07/28.14 | (768) all_1323_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (475), (752) imply: % 183.07/28.14 | (769) all_1287_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (769) implies: % 183.07/28.14 | (770) all_1287_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (674), (738) imply: % 183.07/28.14 | (771) all_1244_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (771) implies: % 183.07/28.14 | (772) all_1244_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (474), (746) imply: % 183.07/28.14 | (773) all_1305_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (773) implies: % 183.07/28.14 | (774) all_1305_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (473), (768) imply: % 183.07/28.14 | (775) all_1302_2 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (775) implies: % 183.07/28.14 | (776) all_1302_2 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (472), (774) imply: % 183.07/28.14 | (777) all_1170_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (777) implies: % 183.07/28.14 | (778) all_1170_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (471), (776) imply: % 183.07/28.14 | (779) all_1296_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (779) implies: % 183.07/28.14 | (780) all_1296_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (470), (780) imply: % 183.07/28.14 | (781) all_1105_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (781) implies: % 183.07/28.14 | (782) all_1105_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (766), (770) imply: % 183.07/28.14 | (783) all_1281_1 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (783) implies: % 183.07/28.14 | (784) all_1281_1 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (764), (784) imply: % 183.07/28.14 | (785) all_1275_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (785) implies: % 183.07/28.14 | (786) all_1275_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (469), (786) imply: % 183.07/28.14 | (787) all_1269_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (787) implies: % 183.07/28.14 | (788) all_1269_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (468), (788) imply: % 183.07/28.14 | (789) all_1263_1 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (789) implies: % 183.07/28.14 | (790) all_1263_1 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (467), (790) imply: % 183.07/28.14 | (791) all_1259_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (791) implies: % 183.07/28.14 | (792) all_1259_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (466), (792) imply: % 183.07/28.14 | (793) all_1256_1 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (793) implies: % 183.07/28.14 | (794) all_1256_1 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (736), (794) imply: % 183.07/28.14 | (795) all_1253_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (795) implies: % 183.07/28.14 | (796) all_1253_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (734), (796) imply: % 183.07/28.14 | (797) all_1238_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (797) implies: % 183.07/28.14 | (798) all_1238_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (465), (612) imply: % 183.07/28.14 | (799) all_1129_0 = all_1114_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (799) implies: % 183.07/28.14 | (800) all_1129_0 = all_1114_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (672), (772) imply: % 183.07/28.14 | (801) all_1191_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (801) implies: % 183.07/28.14 | (802) all_1191_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (667), (798) imply: % 183.07/28.14 | (803) all_1227_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (803) implies: % 183.07/28.14 | (804) all_1227_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (665), (804) imply: % 183.07/28.14 | (805) all_1224_1 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (805) implies: % 183.07/28.14 | (806) all_1224_1 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (464), (806) imply: % 183.07/28.14 | (807) all_1221_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (807) implies: % 183.07/28.14 | (808) all_1221_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (463), (808) imply: % 183.07/28.14 | (809) all_1218_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (809) implies: % 183.07/28.14 | (810) all_1218_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (462), (810) imply: % 183.07/28.14 | (811) all_1206_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (811) implies: % 183.07/28.14 | (812) all_1206_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (461), (812) imply: % 183.07/28.14 | (813) all_1203_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (813) implies: % 183.07/28.14 | (814) all_1203_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (460), (814) imply: % 183.07/28.14 | (815) all_1189_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (815) implies: % 183.07/28.14 | (816) all_1189_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (459), (802) imply: % 183.07/28.14 | (817) all_1120_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (817) implies: % 183.07/28.14 | (818) all_1120_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (458), (816) imply: % 183.07/28.14 | (819) all_1186_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (819) implies: % 183.07/28.14 | (820) all_1186_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (457), (820) imply: % 183.07/28.14 | (821) all_1183_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (821) implies: % 183.07/28.14 | (822) all_1183_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (456), (822) imply: % 183.07/28.14 | (823) all_1173_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (823) implies: % 183.07/28.14 | (824) all_1173_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (455), (824) imply: % 183.07/28.14 | (825) all_1167_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (825) implies: % 183.07/28.14 | (826) all_1167_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (454), (778) imply: % 183.07/28.14 | (827) all_1144_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (827) implies: % 183.07/28.14 | (828) all_1144_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (453), (826) imply: % 183.07/28.14 | (829) all_1158_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (829) implies: % 183.07/28.14 | (830) all_1158_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (452), (830) imply: % 183.07/28.14 | (831) all_1155_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (831) implies: % 183.07/28.14 | (832) all_1155_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (451), (832) imply: % 183.07/28.14 | (833) all_1149_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (833) implies: % 183.07/28.14 | (834) all_1149_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (450), (834) imply: % 183.07/28.14 | (835) all_1144_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (835) implies: % 183.07/28.14 | (836) all_1144_0 = all_1139_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (449), (836) imply: % 183.07/28.14 | (837) all_1139_0 = all_1137_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (828), (836) imply: % 183.07/28.14 | (838) all_1139_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (837), (838) imply: % 183.07/28.14 | (839) all_1137_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (839) implies: % 183.07/28.14 | (840) all_1137_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (755), (840) imply: % 183.07/28.14 | (841) all_1134_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (841) implies: % 183.07/28.14 | (842) all_1134_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (753), (842) imply: % 183.07/28.14 | (843) all_1126_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (843) implies: % 183.07/28.14 | (844) all_1126_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (763), (800) imply: % 183.07/28.14 | (845) all_1114_0 = all_1111_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (615), (800) imply: % 183.07/28.14 | (846) all_1114_0 = all_1097_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (448), (844) imply: % 183.07/28.14 | (847) all_1123_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (847) implies: % 183.07/28.14 | (848) all_1123_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (576), (848) imply: % 183.07/28.14 | (849) all_1117_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (849) implies: % 183.07/28.14 | (850) all_1117_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (447), (818) imply: % 183.07/28.14 | (851) all_1102_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (851) implies: % 183.07/28.14 | (852) all_1102_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (760), (850) imply: % 183.07/28.14 | (853) all_1111_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (853) implies: % 183.07/28.14 | (854) all_1111_0 = all_1108_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (845), (846) imply: % 183.07/28.14 | (855) all_1111_0 = all_1097_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (855) implies: % 183.07/28.14 | (856) all_1111_0 = all_1097_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (758), (854) imply: % 183.07/28.14 | (857) all_1108_0 = all_1099_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (761), (854) imply: % 183.07/28.14 | (858) all_1108_0 = all_1085_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (854), (856) imply: % 183.07/28.14 | (859) all_1108_0 = all_1097_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (857), (859) imply: % 183.07/28.14 | (860) all_1099_0 = all_1097_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (860) implies: % 183.07/28.14 | (861) all_1099_0 = all_1097_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (858), (859) imply: % 183.07/28.14 | (862) all_1097_0 = all_1085_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (446), (782) imply: % 183.07/28.14 | (863) all_1102_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (863) implies: % 183.07/28.14 | (864) all_1102_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (652), (864) imply: % 183.07/28.14 | (865) all_1099_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (865) implies: % 183.07/28.14 | (866) all_1099_0 = all_1091_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (445), (864) imply: % 183.07/28.14 | (867) all_1091_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (852), (864) imply: % 183.07/28.14 | (868) all_1091_0 = all_1089_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (655), (866) imply: % 183.07/28.14 | (869) all_1091_0 = all_1087_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (869) implies: % 183.07/28.14 | (870) all_1091_0 = all_1087_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (655), (861) imply: % 183.07/28.14 | (871) all_1097_0 = all_1087_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (871) implies: % 183.07/28.14 | (872) all_1097_0 = all_1087_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (862), (872) imply: % 183.07/28.14 | (873) all_1087_0 = all_1085_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (873) implies: % 183.07/28.14 | (874) all_1087_0 = all_1085_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (867), (868) imply: % 183.07/28.14 | (875) all_1089_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (868), (870) imply: % 183.07/28.14 | (876) all_1089_0 = all_1087_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (875), (876) imply: % 183.07/28.14 | (877) all_1087_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | SIMP: (877) implies: % 183.07/28.14 | (878) all_1087_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (874), (878) imply: % 183.07/28.14 | (879) all_1085_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (862), (879) imply: % 183.07/28.14 | (880) all_1097_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (859), (880) imply: % 183.07/28.14 | (881) all_1108_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (838), (881) imply: % 183.07/28.14 | (882) all_1139_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (816), (882) imply: % 183.07/28.14 | (883) all_1189_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (784), (882) imply: % 183.07/28.14 | (884) all_1281_1 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (757), (884) imply: % 183.07/28.14 | (885) all_1341_0 = all_1083_0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (644), (742) imply: % 183.07/28.14 | (886) all_1533_6 = 0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (441), (744) imply: % 183.07/28.14 | (887) all_1618_9 = 0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (436), (742) imply: % 183.07/28.14 | (888) all_1618_8 = 0 % 183.07/28.14 | % 183.07/28.14 | COMBINE_EQS: (430), (658) imply: % 183.07/28.15 | (889) all_1618_6 = all_1236_1 % 183.07/28.15 | % 183.07/28.15 | REDUCE: (189), (883) imply: % 183.07/28.15 | (890) ~ (all_1189_1 = all_1083_0) % 183.07/28.15 | % 183.07/28.15 | SIMP: (890) implies: % 183.07/28.15 | (891) ~ (all_1189_1 = all_1083_0) % 183.07/28.15 | % 183.07/28.15 | REDUCE: (368), (572) imply: % 183.07/28.15 | (892) c_Groups_Ozero__class_Ozero(all_1533_2) = all_1618_2 % 183.07/28.15 | % 183.07/28.15 | REDUCE: (353), (637) imply: % 183.07/28.15 | (893) c_Groups_Ozero__class_Ozero(all_1533_2) = all_1595_2 % 183.07/28.15 | % 183.07/28.15 | REDUCE: (363), (444), (889) imply: % 183.07/28.15 | (894) hAPP(all_1236_1, all_1392_1) = all_1618_4 % 183.07/28.15 | % 183.07/28.15 | REDUCE: (348), (428), (638) imply: % 183.07/28.15 | (895) hAPP(all_1236_1, all_1392_1) = all_1595_4 % 183.07/28.15 | % 183.07/28.15 | REDUCE: (311), (656), (658) imply: % 183.07/28.15 | (896) hAPP(all_1236_1, all_1392_1) = all_1533_3 % 183.07/28.15 | % 183.07/28.15 | REDUCE: (266), (693) imply: % 183.07/28.15 | (897) hAPP(all_1236_1, all_1392_1) = all_1392_0 % 183.07/28.15 | % 183.07/28.15 | BETA: splitting (319) gives: % 183.07/28.15 | % 183.07/28.15 | Case 1: % 183.07/28.15 | | % 183.07/28.15 | | (898) ~ (all_1533_6 = 0) % 183.07/28.15 | | % 183.07/28.15 | | REDUCE: (886), (898) imply: % 183.07/28.15 | | (899) $false % 183.07/28.15 | | % 183.07/28.15 | | CLOSE: (899) is inconsistent. % 183.07/28.15 | | % 183.07/28.15 | Case 2: % 183.07/28.15 | | % 183.07/28.15 | | (900) ~ (all_1533_7 = 0) | all_1533_0 = v_p % 183.07/28.15 | | % 183.07/28.15 | | BETA: splitting (373) gives: % 183.07/28.15 | | % 183.07/28.15 | | Case 1: % 183.07/28.15 | | | % 183.07/28.15 | | | (901) ~ (all_1618_8 = 0) % 183.07/28.15 | | | % 183.07/28.15 | | | REDUCE: (888), (901) imply: % 183.07/28.15 | | | (902) $false % 183.07/28.15 | | | % 183.07/28.15 | | | CLOSE: (902) is inconsistent. % 183.07/28.15 | | | % 183.07/28.15 | | Case 2: % 183.07/28.15 | | | % 183.07/28.15 | | | (903) ~ (all_1618_9 = 0) | all_1618_0 = all_1618_7 % 183.07/28.15 | | | % 183.07/28.15 | | | BETA: splitting (900) gives: % 183.07/28.15 | | | % 183.07/28.15 | | | Case 1: % 183.07/28.15 | | | | % 183.07/28.15 | | | | (904) ~ (all_1533_7 = 0) % 183.07/28.15 | | | | % 183.07/28.15 | | | | REDUCE: (662), (904) imply: % 183.07/28.15 | | | | (905) $false % 183.07/28.15 | | | | % 183.07/28.15 | | | | CLOSE: (905) is inconsistent. % 183.07/28.15 | | | | % 183.07/28.15 | | | Case 2: % 183.07/28.15 | | | | % 183.07/28.15 | | | | (906) all_1533_0 = v_p % 183.07/28.15 | | | | % 183.07/28.15 | | | | REDUCE: (317), (906) imply: % 183.07/28.15 | | | | (907) c_Polynomial_OpCons(t_a, all_1533_3, all_1533_1) = v_p % 183.07/28.15 | | | | % 183.07/28.15 | | | | BETA: splitting (903) gives: % 183.07/28.15 | | | | % 183.07/28.15 | | | | Case 1: % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | (908) ~ (all_1618_9 = 0) % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | REDUCE: (887), (908) imply: % 183.07/28.15 | | | | | (909) $false % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | CLOSE: (909) is inconsistent. % 183.07/28.15 | | | | | % 183.07/28.15 | | | | Case 2: % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | (910) all_1618_0 = all_1618_7 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | COMBINE_EQS: (570), (910) imply: % 183.07/28.15 | | | | | (911) all_1618_0 = all_1189_1 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | REDUCE: (370), (911) imply: % 183.07/28.15 | | | | | (912) c_Polynomial_Odegree(t_a, all_1618_1) = all_1189_1 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (126) with all_1392_0, all_1595_4, % 183.07/28.15 | | | | | all_1392_1, all_1236_1, simplifying with (895), (897) % 183.07/28.15 | | | | | gives: % 183.07/28.15 | | | | | (913) all_1595_4 = all_1392_0 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (126) with all_1595_4, all_1618_4, % 183.07/28.15 | | | | | all_1392_1, all_1236_1, simplifying with (894), (895) % 183.07/28.15 | | | | | gives: % 183.07/28.15 | | | | | (914) all_1618_4 = all_1595_4 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (126) with all_1533_3, all_1618_4, % 183.07/28.15 | | | | | all_1392_1, all_1236_1, simplifying with (894), (896) % 183.07/28.15 | | | | | gives: % 183.07/28.15 | | | | | (915) all_1618_4 = all_1533_3 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (123) with all_1533_1, all_1618_2, % 183.07/28.15 | | | | | all_1533_2, simplifying with (316), (892) gives: % 183.07/28.15 | | | | | (916) all_1618_2 = all_1533_1 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (123) with all_1595_2, all_1618_2, % 183.07/28.15 | | | | | all_1533_2, simplifying with (892), (893) gives: % 183.07/28.15 | | | | | (917) all_1618_2 = all_1595_2 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | COMBINE_EQS: (916), (917) imply: % 183.07/28.15 | | | | | (918) all_1595_2 = all_1533_1 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | COMBINE_EQS: (914), (915) imply: % 183.07/28.15 | | | | | (919) all_1595_4 = all_1533_3 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | SIMP: (919) implies: % 183.07/28.15 | | | | | (920) all_1595_4 = all_1533_3 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | COMBINE_EQS: (913), (920) imply: % 183.07/28.15 | | | | | (921) all_1533_3 = all_1392_0 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | COMBINE_EQS: (915), (921) imply: % 183.07/28.15 | | | | | (922) all_1618_4 = all_1392_0 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | REDUCE: (371), (916), (922) imply: % 183.07/28.15 | | | | | (923) c_Polynomial_OpCons(t_a, all_1392_0, all_1533_1) = all_1618_1 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | REDUCE: (354), (913), (918) imply: % 183.07/28.15 | | | | | (924) c_Polynomial_OpCons(t_a, all_1392_0, all_1533_1) = all_1595_1 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | REDUCE: (907), (921) imply: % 183.07/28.15 | | | | | (925) c_Polynomial_OpCons(t_a, all_1392_0, all_1533_1) = v_p % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | REDUCE: (347), (918) imply: % 183.07/28.15 | | | | | (926) $i(all_1533_1) % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | REDUCE: (310), (921) imply: % 183.07/28.15 | | | | | (927) $i(all_1392_0) % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (129) with all_1595_1, all_1618_1, % 183.07/28.15 | | | | | all_1533_1, all_1392_0, t_a, simplifying with (923), % 183.07/28.15 | | | | | (924) gives: % 183.07/28.15 | | | | | (928) all_1618_1 = all_1595_1 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (129) with v_p, all_1618_1, all_1533_1, % 183.07/28.15 | | | | | all_1392_0, t_a, simplifying with (923), (925) gives: % 183.07/28.15 | | | | | (929) all_1618_1 = v_p % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | COMBINE_EQS: (928), (929) imply: % 183.07/28.15 | | | | | (930) all_1595_1 = v_p % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (clrel_Int_Oring__char__0__Groups_Ozero) % 183.07/28.15 | | | | | with t_a, simplifying with (117), (119) gives: % 183.07/28.15 | | | | | (931) class_Groups_Ozero(t_a) = 0 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (fact_pCons__eq__0__iff) with all_1533_1, % 183.07/28.15 | | | | | all_1392_0, t_a, v_p, simplifying with (119), (925), % 183.07/28.15 | | | | | (926), (927) gives: % 183.07/28.15 | | | | | (932) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 183.07/28.15 | | | | | (tc_Polynomial_Opoly(t_a) = v1 & class_Groups_Ozero(t_a) = v0 % 183.07/28.15 | | | | | & c_Groups_Ozero__class_Ozero(v1) = v2 & % 183.07/28.15 | | | | | c_Groups_Ozero__class_Ozero(t_a) = v3 & $i(v3) & $i(v2) & % 183.07/28.15 | | | | | $i(v1) & ( ~ (v0 = 0) | (( ~ (v3 = all_1392_0) | ~ (v2 = % 183.07/28.15 | | | | | all_1533_1) | all_1533_1 = v_p) & ( ~ (v2 = v_p) | % 183.07/28.15 | | | | | (v3 = all_1392_0 & all_1533_1 = v_p))))) % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | GROUND_INST: instantiating (250) with all_1392_0, t_a, all_1533_2, % 183.07/28.15 | | | | | all_1533_1, v_p, all_1189_1, simplifying with (119), % 183.07/28.15 | | | | | (191), (316), (318), (925), (927) gives: % 183.07/28.15 | | | | | (933) all_1341_0 = all_1189_1 | ? [v0: int] : ( ~ (v0 = 0) & % 183.07/28.15 | | | | | class_Groups_Ozero(t_a) = v0) % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | DELTA: instantiating (932) with fresh symbols all_2029_0, all_2029_1, % 183.07/28.15 | | | | | all_2029_2, all_2029_3 gives: % 183.07/28.15 | | | | | (934) tc_Polynomial_Opoly(t_a) = all_2029_2 & % 183.07/28.15 | | | | | class_Groups_Ozero(t_a) = all_2029_3 & % 183.07/28.15 | | | | | c_Groups_Ozero__class_Ozero(all_2029_2) = all_2029_1 & % 183.07/28.15 | | | | | c_Groups_Ozero__class_Ozero(t_a) = all_2029_0 & % 183.07/28.15 | | | | | $i(all_2029_0) & $i(all_2029_1) & $i(all_2029_2) & ( ~ % 183.07/28.15 | | | | | (all_2029_3 = 0) | (( ~ (all_2029_0 = all_1392_0) | ~ % 183.07/28.15 | | | | | (all_2029_1 = all_1533_1) | all_1533_1 = v_p) & ( ~ % 183.07/28.15 | | | | | (all_2029_1 = v_p) | (all_2029_0 = all_1392_0 & % 183.07/28.15 | | | | | all_1533_1 = v_p)))) % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | ALPHA: (934) implies: % 183.07/28.15 | | | | | (935) class_Groups_Ozero(t_a) = all_2029_3 % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | BETA: splitting (933) gives: % 183.07/28.15 | | | | | % 183.07/28.15 | | | | | Case 1: % 183.07/28.15 | | | | | | % 183.07/28.15 | | | | | | (936) all_1341_0 = all_1189_1 % 183.07/28.15 | | | | | | % 183.07/28.15 | | | | | | COMBINE_EQS: (885), (936) imply: % 183.07/28.15 | | | | | | (937) all_1189_1 = all_1083_0 % 183.07/28.15 | | | | | | % 183.07/28.15 | | | | | | REDUCE: (891), (937) imply: % 183.07/28.15 | | | | | | (938) $false % 183.07/28.15 | | | | | | % 183.07/28.15 | | | | | | CLOSE: (938) is inconsistent. % 183.07/28.15 | | | | | | % 183.07/28.15 | | | | | Case 2: % 183.07/28.15 | | | | | | % 183.07/28.16 | | | | | | (939) ? [v0: int] : ( ~ (v0 = 0) & class_Groups_Ozero(t_a) = v0) % 183.07/28.16 | | | | | | % 183.07/28.16 | | | | | | DELTA: instantiating (939) with fresh symbol all_2037_0 gives: % 183.07/28.16 | | | | | | (940) ~ (all_2037_0 = 0) & class_Groups_Ozero(t_a) = all_2037_0 % 183.07/28.16 | | | | | | % 183.07/28.16 | | | | | | ALPHA: (940) implies: % 183.07/28.16 | | | | | | (941) ~ (all_2037_0 = 0) % 183.07/28.16 | | | | | | (942) class_Groups_Ozero(t_a) = all_2037_0 % 183.07/28.16 | | | | | | % 183.07/28.16 | | | | | | GROUND_INST: instantiating (124) with all_2029_3, all_2037_0, t_a, % 183.07/28.16 | | | | | | simplifying with (935), (942) gives: % 183.07/28.16 | | | | | | (943) all_2037_0 = all_2029_3 % 183.07/28.16 | | | | | | % 183.07/28.16 | | | | | | GROUND_INST: instantiating (124) with 0, all_2037_0, t_a, % 183.07/28.16 | | | | | | simplifying with (931), (942) gives: % 183.07/28.16 | | | | | | (944) all_2037_0 = 0 % 183.07/28.16 | | | | | | % 183.07/28.16 | | | | | | COMBINE_EQS: (943), (944) imply: % 183.07/28.16 | | | | | | (945) all_2029_3 = 0 % 183.07/28.16 | | | | | | % 183.07/28.16 | | | | | | REDUCE: (941), (944) imply: % 183.07/28.16 | | | | | | (946) $false % 183.07/28.16 | | | | | | % 183.07/28.16 | | | | | | CLOSE: (946) is inconsistent. % 183.07/28.16 | | | | | | % 183.07/28.16 | | | | | End of split % 183.07/28.16 | | | | | % 183.07/28.16 | | | | End of split % 183.07/28.16 | | | | % 183.07/28.16 | | | End of split % 183.07/28.16 | | | % 183.07/28.16 | | End of split % 183.07/28.16 | | % 183.07/28.16 | End of split % 183.07/28.16 | % 183.07/28.16 End of proof % 183.07/28.16 % SZS output end Proof for theBenchmark % 183.07/28.16 % 183.07/28.16 27528ms %------------------------------------------------------------------------------