%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW186+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 : n012.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 00:49:22 EDT 2023 % Result : Theorem 122.05s 17.33s % Output : Proof 252.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWW186+1 : TPTP v8.1.2. Released v5.2.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Aug 27 21:01:55 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.66 ________ _____ % 0.20/0.66 ___ __ \_________(_)________________________________ % 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.66 % 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.66 (2023-06-19) % 0.20/0.66 % 0.20/0.66 (c) Philipp Rümmer, 2009-2023 % 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.66 Amanda Stjerna. % 0.20/0.66 Free software under BSD-3-Clause. % 0.20/0.66 % 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.66 % 0.20/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.68 Running up to 7 provers in parallel. % 0.20/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 24.70/4.31 Prover 2: Preprocessing ... % 24.70/4.31 Prover 3: Preprocessing ... % 24.70/4.31 Prover 0: Preprocessing ... % 25.02/4.36 Prover 4: Preprocessing ... % 25.02/4.42 Prover 5: Preprocessing ... % 25.02/4.43 Prover 1: Preprocessing ... % 26.10/4.69 Prover 6: Preprocessing ... % 69.74/10.35 Prover 1: Warning: ignoring some quantifiers % 71.09/10.52 Prover 3: Warning: ignoring some quantifiers % 71.34/10.83 Prover 3: Constructing countermodel ... % 71.34/10.86 Prover 1: Constructing countermodel ... % 75.73/11.22 Prover 6: Proving ... % 81.49/11.91 Prover 4: Warning: ignoring some quantifiers % 83.09/12.31 Prover 4: Constructing countermodel ... % 88.58/12.88 Prover 5: Proving ... % 90.57/13.25 Prover 0: Proving ... % 95.54/14.03 Prover 5: stopped % 95.54/14.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 101.56/14.69 Prover 2: Proving ... % 101.56/14.70 Prover 2: stopped % 101.56/14.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 107.23/15.32 Prover 7: Preprocessing ... % 111.98/15.97 Prover 8: Preprocessing ... % 112.54/16.04 Prover 1: stopped % 112.54/16.04 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 122.05/17.33 Prover 3: proved (16557ms) % 122.05/17.33 % 122.05/17.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 122.05/17.33 % 122.05/17.34 Prover 6: stopped % 122.05/17.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 122.05/17.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 122.05/17.36 Prover 0: stopped % 122.65/17.38 Prover 9: Preprocessing ... % 122.65/17.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 129.88/18.42 Prover 7: Warning: ignoring some quantifiers % 131.75/18.75 Prover 8: Warning: ignoring some quantifiers % 133.88/18.89 Prover 7: Constructing countermodel ... % 135.48/19.17 Prover 8: Constructing countermodel ... % 136.47/19.24 Prover 10: Preprocessing ... % 137.27/19.46 Prover 13: Preprocessing ... % 139.77/19.70 Prover 11: Preprocessing ... % 152.50/21.45 Prover 10: Warning: ignoring some quantifiers % 154.64/21.78 Prover 10: Constructing countermodel ... % 171.07/24.20 Prover 13: Warning: ignoring some quantifiers % 171.07/24.33 Prover 11: Warning: ignoring some quantifiers % 175.39/24.67 Prover 13: Constructing countermodel ... % 175.39/24.71 Prover 9: Warning: ignoring some quantifiers % 176.17/24.79 Prover 11: Constructing countermodel ... % 177.27/24.92 Prover 13: stopped % 177.27/24.94 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 177.27/24.99 Prover 9: Constructing countermodel ... % 177.27/25.00 Prover 9: stopped % 177.27/25.00 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 185.67/26.15 Prover 19: Preprocessing ... % 188.17/26.54 Prover 16: Preprocessing ... % 199.68/28.05 Prover 4: stopped % 202.80/28.58 Prover 16: Warning: ignoring some quantifiers % 202.80/28.73 Prover 16: Constructing countermodel ... % 204.04/28.85 Prover 19: Warning: ignoring some quantifiers % 207.01/29.03 Prover 19: Constructing countermodel ... % 207.42/29.10 Prover 16: stopped % 227.62/32.23 Prover 7: stopped % 233.71/33.07 Prover 19: stopped % 246.63/35.23 Prover 10: Found proof (size 958) % 246.63/35.23 Prover 10: proved (17891ms) % 246.63/35.24 Prover 11: stopped % 246.63/35.24 Prover 8: stopped % 246.63/35.24 % 246.63/35.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 246.63/35.24 % 249.44/36.61 % SZS output start Proof for theBenchmark % 249.57/36.65 Assumptions after simplification: % 249.57/36.65 --------------------------------- % 249.57/36.65 % 249.57/36.65 (arity_Nat__Onat__Power_Opower) % 249.57/36.66 $i(tc_Nat_Onat) & class_Power_Opower(tc_Nat_Onat) % 249.57/36.66 % 249.57/36.66 (arity_Nat__Onat__Rings_Ocomm__semiring__1) % 249.57/36.66 $i(tc_Nat_Onat) & class_Rings_Ocomm__semiring__1(tc_Nat_Onat) % 249.57/36.66 % 249.57/36.66 (arity_Nat__Onat__Rings_Odvd) % 249.57/36.66 $i(tc_Nat_Onat) & class_Rings_Odvd(tc_Nat_Onat) % 249.57/36.66 % 249.57/36.66 (arity_Nat__Onat__Rings_Olinordered__semidom) % 249.57/36.66 $i(tc_Nat_Onat) & class_Rings_Olinordered__semidom(tc_Nat_Onat) % 249.57/36.66 % 249.57/36.66 (arity_Nat__Onat__Rings_Ozero__neq__one) % 249.57/36.66 $i(tc_Nat_Onat) & class_Rings_Ozero__neq__one(tc_Nat_Onat) % 249.57/36.66 % 249.57/36.66 (clrel_Rings_Ocomm__semiring__0__Groups_Ozero) % 249.57/36.66 ! [v0: $i] : ( ~ $i(v0) | ~ class_Rings_Ocomm__semiring__0(v0) | % 249.57/36.66 class_Groups_Ozero(v0)) % 249.57/36.66 % 249.57/36.66 (conj_0) % 249.73/36.69 $i(v_h) & $i(v_p) & $i(t_a) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 249.73/36.69 (tc_Polynomial_Opoly(t_a) = v1 & c_Groups_Ozero__class_Ozero(v1) = v2 & $i(v2) % 249.73/36.69 & $i(v1) & (v2 = v_p | ( ~ (v2 = v0) & % 249.73/36.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, v_p, v_h) % 249.73/36.69 = v0 & $i(v0)))) % 249.73/36.69 % 249.73/36.69 (conj_1) % 249.73/36.70 $i(v_a) & $i(v_h) & $i(v_p) & $i(t_a) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 249.73/36.70 $i] : ? [v3: $i] : ? [v4: $i] : (c_Polynomial_Osmult(t_a, v_h, v1) = v2 & % 249.73/36.70 c_Groups_Oplus__class_Oplus(v0, v2, v3) = v4 & c_Polynomial_OpCons(t_a, v_a, % 249.73/36.70 v1) = v3 & tc_Polynomial_Opoly(t_a) = v0 & c_Groups_Ozero__class_Ozero(v0) % 249.73/36.70 = v4 & c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, v_p, % 249.73/36.70 v_h) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 249.73/36.70 % 249.73/36.70 (conj_2) % 249.73/36.70 $i(v_a) & $i(v_p) & $i(t_a) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (( ~ % 249.73/36.70 (v2 = v_p) & tc_Polynomial_Opoly(t_a) = v1 & % 249.73/36.70 c_Groups_Ozero__class_Ozero(v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v0 = v_a) & % 249.73/36.70 c_Groups_Ozero__class_Ozero(t_a) = v0 & $i(v0))) % 249.73/36.70 % 249.73/36.70 (fact_Nat_Oadd__0__right) % 249.73/36.70 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 249.73/36.70 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 249.73/36.70 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 249.73/36.70 % 249.73/36.70 (fact_One__nat__def) % 249.73/36.70 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & % 249.73/36.71 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 249.73/36.71 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)) % 249.73/36.71 % 249.73/36.71 (fact_Suc__eq__plus1) % 249.73/36.71 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 249.73/36.71 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 249.73/36.71 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) | % 249.73/36.71 (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 249.73/36.71 % 249.73/36.71 (fact_Suc__eq__plus1__left) % 249.73/36.71 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 249.73/36.71 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 249.73/36.71 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) | % 249.73/36.71 (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 249.73/36.71 % 249.73/36.71 (fact_Suc__neq__Zero) % 249.73/36.71 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 249.73/36.71 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 249.73/36.71 % 249.73/36.71 (fact_Suc__not__Zero) % 249.73/36.71 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 249.73/36.71 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 249.73/36.72 % 249.73/36.72 (fact_Zero__neq__Suc) % 249.73/36.72 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 249.73/36.72 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 249.73/36.72 % 249.73/36.72 (fact_Zero__not__Suc) % 249.73/36.72 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 249.73/36.72 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 249.73/36.72 % 249.73/36.72 (fact_add__eq__self__zero) % 249.73/36.72 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 249.73/36.72 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 249.73/36.72 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ $i(v2) | ~ % 249.73/36.72 $i(v1))) % 249.73/36.72 % 249.73/36.72 (fact_add__gr__0) % 249.73/36.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 249.73/36.73 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 249.73/36.73 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 249.73/36.73 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 249.73/36.73 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 249.73/36.73 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i] : ! % 249.73/36.73 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, % 249.73/36.73 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 249.73/36.73 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 249.73/36.73 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : ! % 249.73/36.73 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, % 249.73/36.73 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 249.73/36.73 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 249.73/36.73 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 249.73/36.73 % 249.73/36.73 (fact_add__is__0) % 249.73/36.73 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 249.73/36.73 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 249.73/36.73 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~ % 249.73/36.73 $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 249.73/36.74 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~ % 249.73/36.74 $i(v1)) & ! [v1: $i] : (v1 = v0 | ~ % 249.73/36.74 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1))) % 249.73/36.74 % 249.73/36.74 (fact_add__is__1) % 250.10/36.74 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 250.10/36.74 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.10/36.74 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 250.10/36.74 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 250.10/36.74 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~ % 250.10/36.74 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 250.10/36.74 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~ % 250.10/36.74 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 250.10/36.74 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~ % 250.10/36.74 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 250.10/36.74 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~ % 250.10/36.74 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] : % 250.10/36.74 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2))) % 250.10/36.74 % 250.10/36.74 (fact_coeff__1) % 250.10/36.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.10/36.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.10/36.75 $i] : ! [v6: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v4) = v5) | ~ % 250.10/36.75 (c_Groups_Oone__class_Oone(v3) = v4) | ~ (tc_Polynomial_Opoly(v2) = v3) | % 250.10/36.75 ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ~ % 250.10/36.75 class_Rings_Ocomm__semiring__1(v2) | ? [v7: $i] : ? [v8: $i] : (( ~ (v1 % 250.10/36.75 = v0) | (v7 = v6 & c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))) & % 250.10/36.75 (v1 = v0 | (v8 = v6 & c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6)))))) % 250.10/36.75 % 250.10/36.75 (fact_coeff__pCons__0) % 250.10/36.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.10/36.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.10/36.75 $i] : ( ~ (c_Polynomial_Ocoeff(v3, v4) = v5) | ~ (c_Polynomial_OpCons(v3, % 250.10/36.75 v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 250.10/36.75 class_Groups_Ozero(v3) | hAPP(v5, v0) = v2)) % 250.10/36.75 % 250.10/36.75 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) % 250.10/36.75 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.10/36.75 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 250.10/36.75 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 250.10/36.75 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | ? [v5: $i] : % 250.10/36.75 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5)))) % 250.10/36.75 % 250.10/36.75 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) % 250.10/36.76 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 250.10/36.76 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 250.10/36.76 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 250.10/36.76 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | hAPP(v4, v0) % 250.10/36.76 = v1)) % 250.10/36.76 % 250.10/36.76 (fact_degree__0) % 250.10/36.76 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.10/36.76 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 250.10/36.76 | ~ (c_Polynomial_Odegree(v1, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = % 250.10/36.76 v2) | ~ (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ % 250.10/36.76 class_Groups_Ozero(v1))) % 250.10/36.76 % 250.10/36.76 (fact_degree__1) % 250.10/36.76 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.10/36.76 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 250.10/36.76 | ~ (c_Polynomial_Odegree(v1, v3) = v4) | ~ % 250.10/36.76 (c_Groups_Oone__class_Oone(v2) = v3) | ~ (tc_Polynomial_Opoly(v1) = v2) | % 250.10/36.76 ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v1))) % 250.10/36.76 % 250.10/36.76 (fact_degree__pCons__0) % 250.10/36.76 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.10/36.76 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.10/36.76 $i] : ! [v6: $i] : (v6 = v0 | ~ (c_Polynomial_Odegree(v2, v5) = v6) | ~ % 250.10/36.76 (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ (tc_Polynomial_Opoly(v2) = v3) % 250.10/36.76 | ~ (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 250.10/36.76 class_Groups_Ozero(v2))) % 250.10/36.76 % 250.10/36.76 (fact_degree__pCons__eq__if) % 250.10/36.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.10/36.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.10/36.77 $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~ % 250.10/36.77 (c_Polynomial_OpCons(v3, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 250.10/36.77 | ~ class_Groups_Ozero(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 250.10/36.77 [v9: $i] : ((v5 = v0 | ( ~ (v7 = v2) & tc_Polynomial_Opoly(v3) = v6 & % 250.10/36.77 c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6))) & ((v9 = v5 % 250.10/36.77 & c_Nat_OSuc(v8) = v5 & c_Polynomial_Odegree(v3, v2) = v8 & $i(v8) & % 250.10/36.77 $i(v5)) | (v7 = v2 & tc_Polynomial_Opoly(v3) = v6 & % 250.10/36.77 c_Groups_Ozero__class_Ozero(v6) = v2 & $i(v6)))))) % 250.10/36.77 % 250.10/36.77 (fact_degree__smult__eq) % 250.10/36.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.10/36.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.10/36.77 $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~ % 250.10/36.77 (c_Polynomial_Osmult(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 250.10/36.77 | ~ class_Rings_Oidom(v3) | ? [v6: $i] : ? [v7: $i] : ((v5 = v0 | ( ~ % 250.10/36.77 (v6 = v2) & c_Groups_Ozero__class_Ozero(v3) = v6 & $i(v6))) & ((v7 = % 250.26/36.77 v5 & c_Polynomial_Odegree(v3, v1) = v5 & $i(v5)) | (v6 = v2 & % 250.26/36.77 c_Groups_Ozero__class_Ozero(v3) = v2))))) % 250.26/36.77 % 250.26/36.77 (fact_diff__0__eq__0) % 250.26/36.77 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.77 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 250.26/36.77 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 250.26/36.77 % 250.26/36.77 (fact_diff__Suc__1) % 250.26/36.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 250.26/36.78 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 250.26/36.78 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v1)) % 250.26/36.78 % 250.26/36.78 (fact_diff__Suc__eq__diff__pred) % 250.26/36.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 250.26/36.78 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 250.26/36.78 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 250.26/36.78 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ $i(v2) | ~ % 250.26/36.78 $i(v1) | ? [v5: $i] : (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) % 250.26/36.78 = v4 & c_Nat_OSuc(v1) = v5 & $i(v5) & $i(v4)))) % 250.26/36.78 % 250.26/36.78 (fact_diff__add__0) % 250.26/36.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 250.26/36.78 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 250.26/36.78 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 250.26/36.78 $i(v1))) % 250.26/36.78 % 250.26/36.78 (fact_diff__is__0__eq) % 250.26/36.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 250.26/36.78 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 250.26/36.78 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & ! % 250.26/36.78 [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 250.26/36.78 v1) = v0) | ~ $i(v2) | ~ $i(v1) | % 250.26/36.78 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 250.26/36.78 % 250.26/36.78 (fact_diff__is__0__eq_H) % 250.26/36.78 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.78 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 250.26/36.78 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 250.26/36.78 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 250.26/36.78 % 250.26/36.78 (fact_diff__less) % 250.26/36.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 250.26/36.79 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~ % 250.26/36.79 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 250.26/36.79 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 250.26/36.79 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1))) % 250.26/36.79 % 250.26/36.79 (fact_diff__self__eq__0) % 250.26/36.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 250.26/36.79 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ $i(v1))) % 250.26/36.79 % 250.26/36.79 (fact_diffs0__imp__equal) % 250.26/36.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 250.26/36.79 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ $i(v2) | ~ % 250.26/36.79 $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) & % 250.26/36.79 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & $i(v3)))) % 250.26/36.79 % 250.26/36.79 (fact_dvd__1__iff__1) % 250.26/36.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 250.26/36.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 250.26/36.79 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v1) & ! [v2: $i] : (v2 = v1 | ~ % 250.26/36.79 $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1))) % 250.26/36.79 % 250.26/36.79 (fact_dvd__1__left) % 250.26/36.79 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 250.26/36.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ? [v2: % 250.26/36.79 $i] : ( ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2))) % 250.26/36.79 % 250.26/36.79 (fact_dvd__imp__le) % 250.26/36.79 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.79 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 250.26/36.79 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~ % 250.26/36.79 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1) | % 250.26/36.79 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 250.26/36.79 % 250.26/36.79 (fact_dvd__mult__cancel) % 250.26/36.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.80 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.80 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.80 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) % 250.26/36.80 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 250.26/36.80 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 250.26/36.80 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2))) % 250.26/36.80 % 250.26/36.80 (fact_dvd__mult__cancel1) % 250.26/36.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 250.26/36.80 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 250.26/36.80 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.80 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ % 250.26/36.80 (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 250.26/36.80 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : ! [v4: $i] % 250.26/36.80 : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) % 250.26/36.80 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 250.26/36.80 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 250.26/36.80 % 250.26/36.80 (fact_dvd__mult__cancel2) % 250.26/36.80 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 250.26/36.80 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 250.26/36.80 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.80 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ % 250.26/36.80 (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 250.26/36.80 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : ! [v4: $i] % 250.26/36.80 : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ $i(v3) % 250.26/36.80 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 250.26/36.80 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 250.26/36.80 % 250.26/36.80 (fact_dvd__pos__nat) % 250.26/36.81 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.81 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 250.26/36.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 250.26/36.81 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) | % 250.26/36.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 250.26/36.81 % 250.26/36.81 (fact_dvd__power) % 250.26/36.81 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.81 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.81 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 250.26/36.81 (hAPP(v5, v2) = v6) | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.81 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 250.26/36.81 class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3, v1, v6)) % 250.26/36.81 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 250.26/36.81 [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v2) = % 250.26/36.81 v6) | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 250.26/36.81 class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3, v1, v6) % 250.26/36.81 | ? [v7: $i] : ( ~ (v7 = v1) & c_Groups_Oone__class_Oone(v3) = v7 & % 250.26/36.81 $i(v7)))) % 250.26/36.81 % 250.26/36.81 (fact_ex__least__nat__less) % 250.26/36.81 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.81 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 250.26/36.81 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.81 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) | ~ $i(v3) | ~ % 250.26/36.81 $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 250.26/36.81 $i] : ($i(v6) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 % 250.26/36.81 & hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) & % 250.26/36.81 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9: $i] : % 250.26/36.81 ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9) | ~ hBOOL(v10) | % 250.26/36.81 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) | % 250.26/36.81 (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5)))))) % 250.26/36.81 % 250.26/36.81 (fact_gcd__lcm__complete__lattice__nat_Obot__least) % 250.26/36.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 250.26/36.82 $i(v0) & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 250.26/36.82 v0, v1))) % 250.26/36.82 % 250.26/36.82 (fact_gcd__lcm__complete__lattice__nat_Otop__greatest) % 250.26/36.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.82 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 250.26/36.82 v1, v0))) % 250.26/36.82 % 250.26/36.82 (fact_gr0I) % 250.26/36.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.82 & $i(v0) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | % 250.26/36.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 250.26/36.82 % 250.26/36.82 (fact_gr0__conv__Suc) % 250.26/36.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.82 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2) % 250.26/36.82 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! % 250.26/36.82 [v1: $i] : ( ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 250.26/36.82 v1) | ? [v2: $i] : (c_Nat_OSuc(v2) = v1 & $i(v2)))) % 250.26/36.82 % 250.26/36.82 (fact_gr__implies__not0) % 250.26/36.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.82 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 250.26/36.82 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 250.26/36.82 % 250.26/36.82 (fact_le0) % 250.26/36.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.82 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) | % 250.26/36.82 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1))) % 250.26/36.82 % 250.26/36.82 (fact_le__0__eq) % 250.26/36.82 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.82 & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) & ! [v1: % 250.26/36.82 $i] : (v1 = v0 | ~ $i(v1) | ~ % 250.26/36.82 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))) % 250.26/36.82 % 250.26/36.82 (fact_less__Suc0) % 250.26/36.83 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 250.26/36.83 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] : (v2 = v0 % 250.26/36.83 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1))) % 250.26/36.83 % 250.26/36.83 (fact_less__Suc__eq) % 250.26/36.83 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 250.26/36.83 (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! [v1: % 250.26/36.83 $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)) & ! [v0: $i] : ! [v1: % 250.26/36.83 $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) % 250.26/36.83 % 250.26/36.83 (fact_less__Suc__eq__0__disj) % 250.26/36.83 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.83 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 250.26/36.83 (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~ $i(v2) | % 250.26/36.83 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) | % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v1: $i] : ! % 250.26/36.83 [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | % 250.26/36.83 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4: % 250.26/36.83 $i] : (c_Nat_OSuc(v4) = v2 & $i(v4) & % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1: $i] : ! % 250.26/36.83 [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 250.26/36.83 % 250.26/36.83 (fact_less__eq__nat_Osimps_I1_J) % 250.26/36.83 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.83 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) | % 250.26/36.83 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1))) % 250.26/36.83 % 250.26/36.83 (fact_less__nat__zero__code) % 250.26/36.83 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.83 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 250.26/36.83 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 250.26/36.83 % 250.26/36.83 (fact_less__zeroE) % 250.26/36.84 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.84 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 250.26/36.84 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 250.26/36.84 % 250.26/36.84 (fact_minus__nat_Odiff__0) % 250.26/36.84 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.84 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 250.26/36.84 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 250.26/36.84 % 250.26/36.84 (fact_mod__1) % 250.26/36.84 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 250.26/36.84 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.84 $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, % 250.26/36.84 v2, v1) = v3) | ~ $i(v2))) % 250.26/36.84 % 250.26/36.84 (fact_mod__Suc) % 250.26/36.84 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.84 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 250.26/36.84 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~ % 250.26/36.84 (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? [v6: $i] % 250.26/36.84 : ( ~ (v6 = v1) & c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v5 & % 250.26/36.84 c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5))) & ! [v1: $i] : ! [v2: $i] : ! % 250.26/36.84 [v3: $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, % 250.26/36.84 v1) = v4) | ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: % 250.26/36.84 $i] : ? [v6: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = % 250.26/36.84 v5 & c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5) & (v6 = v4 | v6 = v1)))) % 250.26/36.84 % 250.26/36.84 (fact_mod__eq__0__iff) % 250.26/36.85 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.85 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.85 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.85 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 250.26/36.85 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v4) | ~ $i(v3) | ~ % 250.26/36.85 $i(v2) | ? [v5: $i] : (hAPP(v1, v2) = v5 & $i(v5) & ! [v6: $i] : ( ~ % 250.26/36.85 (hAPP(v5, v6) = v3) | ~ $i(v6)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 250.26/36.85 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v0) | ~ $i(v3) | ~ % 250.26/36.85 $i(v2) | ? [v4: $i] : ? [v5: $i] : (hAPP(v4, v5) = v3 & hAPP(v1, v2) = % 250.26/36.85 v4 & $i(v5) & $i(v4)))) % 250.26/36.85 % 250.26/36.85 (fact_mod__le__divisor) % 250.26/36.85 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.85 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 250.26/36.85 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~ % 250.26/36.85 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 250.26/36.85 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2))) % 250.26/36.85 % 250.26/36.85 (fact_mod__less__divisor) % 250.26/36.85 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.85 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 250.26/36.85 (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~ % 250.26/36.85 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 250.26/36.85 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 250.26/36.85 % 250.26/36.85 (fact_monom__0) % 250.26/36.85 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.85 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.85 $i] : ( ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ % 250.26/36.85 (tc_Polynomial_Opoly(v2) = v3) | ~ (c_Groups_Ozero__class_Ozero(v3) = v4) % 250.26/36.85 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Ozero(v2) | % 250.26/36.85 (c_Polynomial_Omonom(v2, v1, v0) = v5 & $i(v5)))) % 250.26/36.85 % 250.26/36.85 (fact_mult__0) % 250.26/36.86 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 250.26/36.86 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) & % 250.26/36.86 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v2, v3) = % 250.26/36.86 v4) | ~ $i(v3))) % 250.26/36.86 % 250.26/36.86 (fact_mult__0__right) % 250.26/36.86 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.86 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.86 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = % 250.26/36.86 v1)) % 250.26/36.86 % 250.26/36.86 (fact_mult__cancel1) % 250.26/36.86 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.86 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.86 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | % 250.26/36.86 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | % 250.26/36.86 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.86 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ % 250.26/36.86 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.86 $i(v2))) % 250.26/36.86 % 250.26/36.86 (fact_mult__cancel2) % 250.26/36.86 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.86 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.86 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.86 : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, % 250.26/36.86 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 250.26/36.86 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.86 : (v4 = v2 | v3 = v1 | ~ (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ % 250.26/36.86 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.86 $i(v2))) % 250.26/36.86 % 250.26/36.86 (fact_mult__eq__1__iff) % 250.26/36.87 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 250.26/36.87 v2 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.87 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.87 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v3) = v2) | % 250.26/36.87 ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: % 250.26/36.87 $i] : ! [v5: $i] : (v3 = v2 | ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = % 250.26/36.87 v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 250.26/36.87 (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v2) = v3))) % 250.26/36.87 % 250.26/36.87 (fact_mult__eq__self__implies__10) % 250.26/36.87 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 250.26/36.87 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 250.26/36.87 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.87 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.87 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, % 250.26/36.87 v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 250.26/36.87 % 250.26/36.87 (fact_mult__is__0) % 250.26/36.88 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.88 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.88 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.88 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) = v4) | ~ % 250.26/36.88 (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 250.26/36.88 : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v0, v2) = v3) | ~ $i(v2)) & % 250.26/36.88 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, % 250.26/36.88 v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2))) % 250.26/36.88 % 250.26/36.88 (fact_mult__le__cancel1) % 250.26/36.88 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.88 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.88 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.88 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.88 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) % 250.26/36.88 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 250.26/36.88 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) | % 250.26/36.88 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 250.26/36.88 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 250.26/36.88 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 250.26/36.88 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.88 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 250.26/36.88 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : ! % 250.26/36.88 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 250.26/36.88 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 250.26/36.88 $i(v4) | ~ $i(v3) | ~ $i(v2) | % 250.26/36.88 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 250.26/36.88 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7))) % 250.26/36.88 % 250.26/36.88 (fact_mult__le__cancel2) % 250.26/36.89 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.89 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.89 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.89 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.89 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ % 250.26/36.89 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.89 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~ % 250.26/36.89 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) | % 250.26/36.89 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : ! % 250.26/36.89 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 250.26/36.89 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 250.26/36.89 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.89 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) | % 250.26/36.89 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)) & ! [v2: $i] : ! % 250.26/36.89 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 250.26/36.89 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 250.26/36.89 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 250.26/36.89 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 250.26/36.89 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8))) % 250.26/36.89 % 250.26/36.89 (fact_mult__less__cancel1) % 250.26/36.89 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.89 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.89 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.89 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.89 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) % 250.26/36.89 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.89 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 250.26/36.89 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 250.26/36.89 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 250.26/36.89 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 250.26/36.89 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.89 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 250.26/36.89 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i] : ! % 250.26/36.89 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 250.26/36.89 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 250.26/36.89 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.89 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 250.26/36.89 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 250.26/36.89 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 250.26/36.89 % 250.26/36.89 (fact_mult__less__cancel2) % 250.26/36.90 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.90 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.90 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.90 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.90 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ % 250.26/36.90 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.90 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : ! % 250.26/36.90 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 250.26/36.90 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 250.26/36.90 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] : ! % 250.26/36.90 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 250.26/36.90 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 250.26/36.90 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~ % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 250.26/36.90 % 250.26/36.90 (fact_mult__less__mono1) % 250.26/36.90 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.90 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.90 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.90 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.90 : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5, v2) = v6) | ~ % 250.26/36.90 (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.90 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 250.26/36.90 % 250.26/36.90 (fact_mult__less__mono2) % 250.26/36.90 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.90 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.90 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.90 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.90 : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ (hAPP(v1, v2) = v5) % 250.26/36.90 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 250.26/36.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 250.26/36.90 % 250.26/36.90 (fact_n__less__m__mult__n) % 250.26/36.91 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 250.26/36.91 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 250.26/36.91 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.91 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) = % 250.26/36.91 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 250.26/36.91 % 250.26/36.91 (fact_n__less__n__mult__m) % 250.26/36.91 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 250.26/36.91 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 250.26/36.91 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.91 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = % 250.26/36.91 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 250.26/36.91 % 250.26/36.91 (fact_nat_Osimps_I2_J) % 250.26/36.91 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.91 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 250.26/36.91 % 250.26/36.91 (fact_nat_Osimps_I3_J) % 250.26/36.91 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.91 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 250.26/36.91 % 250.26/36.91 (fact_nat__0__less__mult__iff) % 250.26/36.91 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.91 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.91 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.91 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | % 250.26/36.91 ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 250.26/36.91 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 250.26/36.91 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i] : ! % 250.26/36.91 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 250.26/36.91 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 250.26/36.91 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5))) % 250.26/36.91 % 250.26/36.91 (fact_nat__1__eq__mult__iff) % 250.26/36.92 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.92 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 250.26/36.92 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.92 $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = v0) | ~ % 250.26/36.92 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : % 250.26/36.92 ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | % 250.26/36.92 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 250.26/36.92 (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2))) % 250.26/36.92 % 250.26/36.92 (fact_nat__dvd__1__iff__1) % 250.26/36.92 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 250.26/36.92 $i(v0) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 = % 250.26/36.92 v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0))) % 250.26/36.92 % 250.26/36.92 (fact_nat__dvd__not__less) % 250.26/36.92 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.92 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 250.26/36.92 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ % 250.26/36.92 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 250.26/36.92 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2))) % 250.26/36.92 % 250.26/36.92 (fact_nat__lt__two__imp__zero__or__one) % 250.26/36.92 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 250.26/36.92 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 250.26/36.92 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ $i(v3) | ~ % 250.26/36.92 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 250.26/36.92 % 250.26/36.92 (fact_nat__mult__1) % 250.26/36.92 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 250.26/36.92 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 250.26/36.92 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 & $i(v2) % 250.26/36.92 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3) % 250.26/36.92 = v4) | ~ $i(v3))) % 250.26/36.92 % 250.26/36.92 (fact_nat__mult__1__right) % 250.26/36.92 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.92 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 250.26/36.92 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.92 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = % 250.26/36.92 v2)) % 250.26/36.92 % 250.26/36.92 (fact_nat__mult__dvd__cancel1) % 250.26/36.92 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.92 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.92 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.92 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 250.26/36.92 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.92 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 250.26/36.92 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 250.26/36.92 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i] % 250.26/36.92 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) % 250.26/36.92 = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ % 250.26/36.92 $i(v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) % 250.26/36.92 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 250.26/36.92 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7))) % 250.26/36.92 % 250.26/36.92 (fact_nat__mult__dvd__cancel__disj) % 250.26/36.93 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.93 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.93 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.93 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.93 : (v4 = v1 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, % 250.26/36.93 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.93 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 250.26/36.93 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i] % 250.26/36.93 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) % 250.26/36.93 = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 250.26/36.93 $i(v3) | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 250.26/36.93 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : ! [v3: $i] % 250.26/36.93 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ % 250.26/36.93 (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 250.26/36.93 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v6))) % 250.26/36.93 % 250.26/36.93 (fact_nat__mult__eq__1__iff) % 250.26/36.93 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.93 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 250.26/36.93 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.93 $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = v1) | ~ % 250.26/36.93 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : % 250.26/36.93 ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | % 250.26/36.93 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 250.26/36.93 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2))) % 250.26/36.93 % 250.26/36.93 (fact_nat__mult__eq__cancel1) % 250.26/36.93 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.93 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.93 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.93 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | % 250.26/36.93 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | % 250.26/36.93 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.93 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 250.26/36.93 % 250.26/36.93 (fact_nat__mult__eq__cancel__disj) % 250.26/36.93 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.93 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 250.26/36.93 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.93 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | % 250.26/36.93 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | % 250.26/36.93 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.93 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ % 250.26/36.93 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.93 $i(v2))) % 250.26/36.93 % 250.26/36.93 (fact_nat__mult__le__cancel1) % 250.26/36.94 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.94 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.94 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.94 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.94 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 250.26/36.94 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) | % 250.26/36.94 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 250.26/36.94 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 250.26/36.94 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ % 250.26/36.94 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 250.26/36.94 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7))) % 250.26/36.94 % 250.26/36.94 (fact_nat__mult__less__cancel1) % 250.26/36.94 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.94 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 250.26/36.94 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.94 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.94 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 250.26/36.94 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 250.26/36.94 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 250.26/36.94 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 250.26/36.94 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ % 250.26/36.94 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 250.26/36.94 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 250.26/36.94 % 250.26/36.94 (fact_nat__one__le__power) % 250.26/36.94 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 250.26/36.94 v1 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & % 250.26/36.94 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.94 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = % 250.26/36.94 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.94 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) | % 250.26/36.94 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6))) % 250.26/36.94 % 250.26/36.94 (fact_nat__power__eq__Suc__0__iff) % 250.26/36.94 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 250.26/36.94 v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 250.26/36.94 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.94 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v3) = v5) | % 250.26/36.94 ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.94 $i] : (v5 = v2 | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, v3) = v4) | ~ % 250.26/36.94 $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | % 250.26/36.94 ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 250.26/36.94 % 250.26/36.94 (fact_nat__power__less__imp__less) % 250.26/36.95 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.95 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 250.26/36.95 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.95 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.95 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 250.26/36.95 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.95 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 250.26/36.95 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 250.26/36.95 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 250.26/36.95 % 250.26/36.95 (fact_nat__zero__less__power__iff) % 250.26/36.95 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.95 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 250.26/36.95 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.95 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4, % 250.26/36.95 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.95 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 250.26/36.95 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 250.26/36.95 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 250.26/36.95 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.95 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 250.26/36.95 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : ! % 250.26/36.95 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) | % 250.26/36.95 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 250.26/36.95 % 250.26/36.95 (fact_neq0__conv) % 250.26/36.95 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.95 & $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1: % 250.26/36.95 $i] : (v1 = v0 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 250.26/36.95 v0, v1))) % 250.26/36.95 % 250.26/36.95 (fact_not__less0) % 250.26/36.95 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.95 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 250.26/36.95 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 250.26/36.95 % 250.26/36.95 (fact_not__one__le__zero) % 250.26/36.95 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 250.26/36.95 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 250.26/36.95 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~ % 250.26/36.95 c_Orderings_Oord__class_Oless__eq(v0, v1, v2))) % 250.26/36.95 % 250.26/36.95 (fact_not__one__less__zero) % 250.26/36.95 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 250.26/36.96 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 250.26/36.96 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~ % 250.26/36.96 c_Orderings_Oord__class_Oless(v0, v1, v2))) % 250.26/36.96 % 250.26/36.96 (fact_offset__poly__eq__0__lemma) % 250.26/36.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.96 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (c_Polynomial_Osmult(v3, v2, v1) = v5) % 250.26/36.96 | ~ (c_Groups_Oplus__class_Oplus(v4, v5, v6) = v7) | ~ % 250.26/36.96 (c_Polynomial_OpCons(v3, v0, v1) = v6) | ~ (tc_Polynomial_Opoly(v3) = v4) | % 250.26/36.96 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 250.26/36.96 class_Rings_Ocomm__semiring__0(v3) | ? [v8: $i] : % 250.26/36.96 (c_Groups_Ozero__class_Ozero(v4) = v8 & $i(v8) & ( ~ (v8 = v7) | v7 = v1))) % 250.26/36.96 % 250.26/36.96 (fact_offset__poly__pCons) % 250.26/36.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.96 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Polynomial_Osmult(v3, % 250.26/36.96 v0, v5) = v6) | ~ (c_Groups_Oplus__class_Oplus(v4, v6, v7) = v8) | ~ % 250.26/36.96 (c_Polynomial_OpCons(v3, v2, v5) = v7) | ~ (tc_Polynomial_Opoly(v3) = v4) | % 250.26/36.96 ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v3, v1, v0) = % 250.26/36.96 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 250.26/36.96 class_Rings_Ocomm__semiring__0(v3) | ? [v9: $i] : (c_Polynomial_OpCons(v3, % 250.26/36.96 v2, v1) = v9 & % 250.26/36.96 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v3, v9, v0) = v8 % 250.26/36.96 & $i(v9) & $i(v8))) % 250.26/36.96 % 250.26/36.96 (fact_offset__poly__single) % 250.26/36.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.96 $i] : ! [v6: $i] : (v6 = v5 | ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | % 250.26/36.96 ~ (tc_Polynomial_Opoly(v2) = v3) | ~ (c_Groups_Ozero__class_Ozero(v3) = v4) % 250.26/36.96 | ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v2, v5, v0) = % 250.26/36.96 v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 250.26/36.96 class_Rings_Ocomm__semiring__0(v2)) % 250.26/36.96 % 250.26/36.96 (fact_one__is__add) % 250.26/36.96 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 250.26/36.96 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.96 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 250.26/36.96 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 250.26/36.96 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~ % 250.26/36.96 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 250.26/36.96 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~ % 250.26/36.96 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 250.26/36.96 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~ % 250.26/36.96 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 250.26/36.96 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~ % 250.26/36.96 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] : % 250.26/36.96 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2))) % 250.26/36.96 % 250.26/36.96 (fact_one__le__mult__iff) % 250.26/36.97 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 250.26/36.97 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 250.26/36.97 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.97 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = % 250.26/36.97 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.97 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) | % 250.26/36.97 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)) & ! [v3: $i] : ! % 250.26/36.97 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ % 250.26/36.97 (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.97 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) | % 250.26/36.97 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) & ! [v3: $i] : ! % 250.26/36.97 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ % 250.26/36.97 (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.97 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) | ~ % 250.26/36.97 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | % 250.26/36.97 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6))) % 250.26/36.97 % 250.26/36.97 (fact_one__less__mult) % 250.26/36.97 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 250.26/36.97 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 250.26/36.97 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 250.26/36.97 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) = % 250.26/36.97 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 250.26/36.97 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 250.26/36.97 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 250.26/36.97 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6))) % 250.26/36.97 % 250.26/36.97 (fact_one__less__power) % 250.26/36.97 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.97 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.97 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 250.26/36.97 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.97 $i(v1) | ~ class_Rings_Olinordered__semidom(v3) | ~ % 250.26/36.97 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v7: $i] : % 250.26/36.97 (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~ % 250.26/36.97 c_Orderings_Oord__class_Oless(v3, v7, v2) | % 250.26/36.97 c_Orderings_Oord__class_Oless(v3, v7, v6))))) % 250.26/36.97 % 250.26/36.97 (fact_one__neq__zero) % 250.26/36.97 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 250.26/36.97 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) & % 250.26/36.97 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2))) % 250.26/36.97 % 250.26/36.97 (fact_order__root) % 250.26/36.97 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.97 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.97 $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~ % 250.26/36.97 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: $i] : % 250.26/36.97 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) & % 250.26/36.97 c_Polynomial_Oorder(v3, v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7 % 250.26/36.97 & c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | (v6 = v5 % 250.26/36.97 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & ((v8 = v2 & % 250.26/36.97 tc_Polynomial_Opoly(v3) = v7 & c_Groups_Ozero__class_Ozero(v7) = v2 % 250.26/36.98 & $i(v7)) | ( ~ (v9 = v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & % 250.26/36.98 $i(v9)) | ( ~ (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 & % 250.26/36.98 $i(v6)))))) % 250.26/36.98 % 250.26/36.98 (fact_pCons__eq__0__iff) % 250.26/36.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 250.26/36.98 (c_Polynomial_OpCons(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 250.26/36.98 ~ class_Groups_Ozero(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 250.26/36.98 (tc_Polynomial_Opoly(v2) = v4 & c_Groups_Ozero__class_Ozero(v4) = v5 & % 250.26/36.98 $i(v5) & $i(v4) & ( ~ (v5 = v3) | (v6 = v1 & v3 = v0 & % 250.26/36.98 c_Groups_Ozero__class_Ozero(v2) = v1)) & ( ~ (v5 = v0) | v3 = v0 | ( ~ % 250.26/36.98 (v6 = v1) & c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6))))) % 250.26/36.98 % 250.26/36.98 (fact_plus__nat_Oadd__0) % 250.26/36.98 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.98 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 250.26/36.98 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 250.26/36.98 % 250.26/36.98 (fact_pow__divides__eq__int) % 250.26/36.98 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.98 (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 & % 250.26/36.98 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.98 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.98 : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | % 250.26/36.98 ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 250.26/36.98 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) | % 250.26/36.98 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)) & ! [v2: $i] : ! [v3: $i] % 250.26/36.98 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 % 250.26/36.98 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) % 250.26/36.98 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.98 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2) | % 250.26/36.98 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8))) % 250.26/36.98 % 250.26/36.98 (fact_pow__divides__eq__nat) % 250.26/36.98 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.98 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 250.26/36.98 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.98 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.98 : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | % 250.26/36.98 ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 250.26/36.98 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) | % 250.26/36.98 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! [v3: $i] % 250.26/36.98 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 % 250.26/36.98 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) % 250.26/36.98 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.26/36.98 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 250.26/36.98 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8))) % 250.26/36.98 % 250.26/36.98 (fact_pow__divides__pow__int) % 250.26/36.99 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.99 (c_Power_Opower__class_Opower(tc_Int_Oint) = v0 & % 250.26/36.99 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.99 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.99 : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | % 250.26/36.99 ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 250.26/36.99 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) | % 250.26/36.99 c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v2))) % 250.26/36.99 % 250.26/36.99 (fact_pow__divides__pow__nat) % 250.26/36.99 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.26/36.99 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 250.26/36.99 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 250.26/36.99 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.26/36.99 : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | % 250.26/36.99 ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | % 250.26/36.99 ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) | % 250.26/36.99 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v2))) % 250.26/36.99 % 250.26/36.99 (fact_power_Opower_Opower__0) % 250.26/36.99 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.99 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.99 $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | ~ % 250.26/36.99 (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 250.26/36.99 hAPP(v6, v0) = v3)) % 250.26/36.99 % 250.26/36.99 (fact_power__0) % 250.26/36.99 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.99 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 250.26/36.99 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 250.26/36.99 $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] : % 250.26/36.99 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5)))) % 250.26/36.99 % 250.26/36.99 (fact_power__0__left) % 250.26/36.99 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.26/36.99 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.26/36.99 $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~ % 250.26/36.99 (c_Power_Opower__class_Opower(v2) = v3) | ~ % 250.26/36.99 (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | ~ % 250.26/36.99 (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | % 250.26/36.99 ~ class_Rings_Osemiring__0(v2)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 250.26/36.99 : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | % 250.26/36.99 ~ (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | ~ % 250.26/36.99 (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ class_Power_Opower(v1) | ~ % 250.26/36.99 class_Rings_Osemiring__0(v1) | (c_Groups_Oone__class_Oone(v1) = v5 & % 250.26/36.99 $i(v5)))) % 250.26/36.99 % 250.26/36.99 (fact_power__Suc__0) % 250.74/37.00 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 250.74/37.00 (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 250.74/37.00 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 & $i(v3) & % 250.74/37.00 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ % 250.74/37.00 (hAPP(v3, v4) = v5) | ~ $i(v4))) % 250.74/37.00 % 250.74/37.00 (fact_power__dvd__imp__le) % 250.74/37.00 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.74/37.00 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 250.74/37.00 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 250.74/37.00 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 250.74/37.00 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 250.74/37.00 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.74/37.00 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 250.74/37.00 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 250.74/37.00 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2))) % 250.74/37.00 % 250.74/37.00 (fact_power__eq__0__iff) % 250.74/37.00 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.74/37.00 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.74/37.00 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 250.74/37.00 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 250.74/37.00 $i(v1) | ~ class_Power_Opower(v3) | ~ class_Rings_Ozero__neq__one(v3) | % 250.74/37.00 ~ class_Rings_Ono__zero__divisors(v3) | ~ class_Rings_Omult__zero(v3) | % 250.74/37.00 ? [v7: $i] : (c_Groups_Ozero__class_Ozero(v3) = v7 & $i(v7) & ( ~ (v7 = % 250.74/37.00 v6) | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2) | v6 = v2 | v1 = % 250.74/37.00 v0)))) % 250.74/37.00 % 250.74/37.00 (fact_power__eq__imp__eq__base) % 250.74/37.00 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.74/37.00 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.74/37.00 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ % 250.74/37.00 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v2) = v7) | ~ % 250.74/37.00 (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v1) = v8) | ~ % 250.74/37.00 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 250.74/37.00 class_Rings_Olinordered__semidom(v4) | ~ % 250.74/37.00 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v9: $i] : % 250.74/37.00 (c_Groups_Ozero__class_Ozero(v4) = v9 & $i(v9) & ( ~ % 250.74/37.00 c_Orderings_Oord__class_Oless__eq(v4, v9, v3) | ~ % 250.74/37.00 c_Orderings_Oord__class_Oless__eq(v4, v9, v1))))) % 250.74/37.00 % 250.74/37.00 (fact_power__one__right) % 250.74/37.00 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 250.74/37.00 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 250.74/37.00 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 250.74/37.00 $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | hAPP(v4, v0) = % 250.74/37.00 v1)) % 250.74/37.00 % 250.74/37.00 (fact_power__strict__mono) % 250.74/37.01 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.74/37.01 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 250.74/37.01 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 250.74/37.01 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9) | ~ % 250.74/37.01 (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v8) | ~ % 250.74/37.01 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 250.74/37.01 class_Rings_Olinordered__semidom(v4) | ~ % 250.74/37.01 c_Orderings_Oord__class_Oless(v4, v3, v2) | ~ % 250.74/37.01 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 250.74/37.01 c_Orderings_Oord__class_Oless(v4, v7, v9) | ? [v10: $i] : % 250.74/37.01 (c_Groups_Ozero__class_Ozero(v4) = v10 & $i(v10) & ~ % 250.74/37.01 c_Orderings_Oord__class_Oless__eq(v4, v10, v3)))) % 250.74/37.01 % 250.74/37.01 (fact_realpow__minus__mult) % 250.74/37.01 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.74/37.01 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 250.74/37.01 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.74/37.01 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 250.74/37.01 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 250.74/37.01 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~ % 250.74/37.01 (c_Power_Opower__class_Opower(v4) = v6) | ~ % 250.74/37.01 (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = v11) | ~ % 250.74/37.01 (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v9) = v10) | % 250.74/37.01 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ class_Groups_Omonoid__mult(v4) | ~ % 250.74/37.01 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3) = v11 & % 250.74/37.01 $i(v11)))) % 250.74/37.01 % 250.74/37.01 (fact_realpow__two__disj) % 250.74/37.01 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 250.74/37.01 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 250.74/37.01 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 250.74/37.01 $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v5) = % 250.74/37.01 v6) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ % 250.74/37.01 $i(v4) | ~ $i(v3) | ~ class_Rings_Oidom(v5) | ? [v9: $i] : ? [v10: $i] % 250.74/37.01 : ? [v11: $i] : ((v4 = v3 | (v11 = v4 & % 250.74/37.01 c_Groups_Ouminus__class_Ouminus(v5, v3) = v4) | ( ~ (v10 = v9) & % 250.74/37.01 hAPP(v8, v2) = v10 & hAPP(v7, v2) = v9 & $i(v10) & $i(v9))) & ((v10 % 250.74/37.01 = v9 & hAPP(v8, v2) = v9 & hAPP(v7, v2) = v9 & $i(v9)) | ( ~ (v11 = % 250.74/37.01 v4) & ~ (v4 = v3) & c_Groups_Ouminus__class_Ouminus(v5, v3) = v11 % 250.74/37.01 & $i(v11)))))) % 250.74/37.01 % 250.74/37.01 (fact_synthetic__div__eq__0__iff) % 250.74/37.01 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.74/37.01 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 250.74/37.01 (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 250.74/37.01 ~ $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? [v5: $i] : ? [v6: % 250.74/37.01 $i] : ? [v7: $i] : (((v7 = v0 & c_Polynomial_Odegree(v3, v2) = v0) | ( % 250.74/37.01 ~ (v6 = v4) & tc_Polynomial_Opoly(v3) = v5 & % 250.74/37.01 c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) & ((v6 = v4 % 250.74/37.01 & tc_Polynomial_Opoly(v3) = v5 & c_Groups_Ozero__class_Ozero(v5) = % 250.74/37.01 v4 & $i(v5) & $i(v4)) | ( ~ (v7 = v0) & c_Polynomial_Odegree(v3, v2) % 250.74/37.01 = v7 & $i(v7)))))) % 250.74/37.01 % 250.74/37.01 (fact_zero__le__one) % 250.74/37.01 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 250.74/37.01 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 250.74/37.01 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & % 250.74/37.01 c_Orderings_Oord__class_Oless__eq(v0, v2, v1))) % 250.74/37.01 % 250.74/37.01 (fact_zero__less__Suc) % 250.74/37.02 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.74/37.02 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) % 250.74/37.02 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 250.74/37.02 % 250.74/37.02 (fact_zero__less__diff) % 250.74/37.02 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 250.74/37.02 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 250.74/37.02 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 250.74/37.02 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | % 250.74/37.02 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : ! % 250.74/37.02 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 250.74/37.02 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 250.74/37.02 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 250.74/37.02 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2))) % 250.74/37.02 % 250.74/37.02 (fact_zero__less__power__nat__eq) % 250.74/37.02 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 250.74/37.02 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 250.74/37.02 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 250.74/37.02 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4, % 250.74/37.02 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.74/37.02 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 250.74/37.02 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 250.74/37.02 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 250.74/37.02 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 250.74/37.02 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 250.74/37.02 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : ! % 250.74/37.02 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) | % 250.74/37.02 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 250.74/37.02 % 250.74/37.02 (fact_zero__neq__one) % 250.74/37.02 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 250.74/37.02 $i(v0) | ~ class_Rings_Ozero__neq__one(v0) | ? [v2: $i] : ( ~ (v2 = v1) & % 250.74/37.02 c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2))) % 250.74/37.02 % 251.42/37.02 (tfree_0) % 251.42/37.02 $i(t_a) & class_Rings_Ocomm__semiring__0(t_a) % 251.42/37.02 % 251.42/37.02 (function-axioms) % 251.42/37.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.42/37.03 $i] : ! [v6: $i] : (v1 = v0 | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, % 251.42/37.03 v2) = v1) | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, v2) = v0)) & ! % 251.42/37.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 251.42/37.03 : (v1 = v0 | ~ (c_If(v5, v4, v3, v2) = v1) | ~ (c_If(v5, v4, v3, v2) = v0)) % 251.42/37.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 251.42/37.03 v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 251.42/37.03 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 251.42/37.03 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 251.42/37.03 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v1) | ~ % 251.42/37.03 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 251.42/37.03 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 251.42/37.03 (c_Polynomial_Opoly__gcd(v4, v3, v2) = v1) | ~ (c_Polynomial_Opoly__gcd(v4, % 251.42/37.03 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 251.42/37.03 ! [v4: $i] : (v1 = v0 | ~ (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ % 251.42/37.03 (c_Power_Opower_Opower(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 251.42/37.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Omonom(v4, % 251.42/37.03 v3, v2) = v1) | ~ (c_Polynomial_Omonom(v4, v3, v2) = v0)) & ! [v0: $i] % 251.42/37.03 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 251.42/37.03 (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~ (c_Polynomial_Oorder(v4, v3, v2) % 251.42/37.03 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 251.42/37.03 $i] : (v1 = v0 | ~ (c_Polynomial_Osynthetic__div(v4, v3, v2) = v1) | ~ % 251.42/37.03 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 251.42/37.03 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 251.42/37.03 (c_Polynomial_Opcompose(v4, v3, v2) = v1) | ~ (c_Polynomial_Opcompose(v4, % 251.42/37.03 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 251.42/37.03 ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Osmult(v4, v3, v2) = v1) | ~ % 251.42/37.03 (c_Polynomial_Osmult(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 251.42/37.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 251.42/37.03 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~ % 251.42/37.03 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 251.42/37.03 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 251.42/37.03 (c_Polynomial_OpCons(v4, v3, v2) = v1) | ~ (c_Polynomial_OpCons(v4, v3, v2) % 251.42/37.03 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 251.42/37.03 $i] : (v1 = v0 | ~ % 251.42/37.03 (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v4, v3, v2) = v1) % 251.42/37.03 | ~ (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v4, v3, v2) = % 251.42/37.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 251.42/37.03 ~ (c_Rings_Oinverse__class_Oinverse(v3, v2) = v1) | ~ % 251.42/37.03 (c_Rings_Oinverse__class_Oinverse(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 251.42/37.03 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Polynomial_Ocoeff(v3, v2) = v1) % 251.42/37.03 | ~ (c_Polynomial_Ocoeff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 251.42/37.03 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Groups_Ouminus__class_Ouminus(v3, % 251.42/37.03 v2) = v1) | ~ (c_Groups_Ouminus__class_Ouminus(v3, v2) = v0)) & ! [v0: % 251.42/37.03 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 251.42/37.03 (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, v2) = % 251.42/37.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 251.42/37.03 ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 251.42/37.03 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Polynomial_Opoly(v3, v2) % 251.42/37.03 = v1) | ~ (c_Polynomial_Opoly(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 251.42/37.03 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_fequal(v3, v2) = v1) | ~ % 251.42/37.03 (c_fequal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 251.42/37.03 $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) & ! [v0: % 251.42/37.03 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Nat_OSuc(v2) = v1) | ~ % 251.42/37.03 (c_Nat_OSuc(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 251.42/37.03 | ~ (c_Power_Opower__class_Opower(v2) = v1) | ~ % 251.42/37.03 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 251.42/37.03 [v2: $i] : (v1 = v0 | ~ (c_Groups_Oone__class_Oone(v2) = v1) | ~ % 251.42/37.03 (c_Groups_Oone__class_Oone(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 251.42/37.03 $i] : (v1 = v0 | ~ (c_Groups_Otimes__class_Otimes(v2) = v1) | ~ % 251.42/37.03 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 251.42/37.03 [v2: $i] : (v1 = v0 | ~ (tc_Polynomial_Opoly(v2) = v1) | ~ % 251.42/37.03 (tc_Polynomial_Opoly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 251.42/37.03 (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 251.42/37.03 (c_Groups_Ozero__class_Ozero(v2) = v0)) % 251.42/37.03 % 251.42/37.03 Further assumptions not needed in the proof: % 251.42/37.03 -------------------------------------------- % 251.42/37.04 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Groups_Ouminus, % 251.42/37.04 arity_HOL__Obool__Lattices_Oboolean__algebra, arity_HOL__Obool__Orderings_Oord, % 251.42/37.04 arity_HOL__Obool__Orderings_Oorder, arity_HOL__Obool__Orderings_Opreorder, % 251.42/37.04 arity_Int__Oint__Divides_Oring__div, arity_Int__Oint__Divides_Osemiring__div, % 251.42/37.04 arity_Int__Oint__Groups_Oab__group__add, % 251.42/37.04 arity_Int__Oint__Groups_Oab__semigroup__add, % 251.42/37.04 arity_Int__Oint__Groups_Oab__semigroup__mult, % 251.42/37.04 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, % 251.42/37.04 arity_Int__Oint__Groups_Ocancel__comm__monoid__add, % 251.42/37.04 arity_Int__Oint__Groups_Ocancel__semigroup__add, % 251.42/37.04 arity_Int__Oint__Groups_Ocomm__monoid__add, % 251.42/37.04 arity_Int__Oint__Groups_Ocomm__monoid__mult, % 251.42/37.04 arity_Int__Oint__Groups_Ogroup__add, % 251.42/37.04 arity_Int__Oint__Groups_Olinordered__ab__group__add, % 251.42/37.04 arity_Int__Oint__Groups_Ominus, arity_Int__Oint__Groups_Omonoid__add, % 251.42/37.04 arity_Int__Oint__Groups_Omonoid__mult, arity_Int__Oint__Groups_Oone, % 251.42/37.04 arity_Int__Oint__Groups_Oordered__ab__group__add, % 251.42/37.04 arity_Int__Oint__Groups_Oordered__ab__semigroup__add, % 251.42/37.04 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, % 251.42/37.04 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, % 251.42/37.04 arity_Int__Oint__Groups_Oordered__comm__monoid__add, % 251.42/37.04 arity_Int__Oint__Groups_Oplus, arity_Int__Oint__Groups_Ouminus, % 251.42/37.04 arity_Int__Oint__Groups_Ozero, arity_Int__Oint__Int_Oring__char__0, % 251.42/37.04 arity_Int__Oint__Orderings_Olinorder, arity_Int__Oint__Orderings_Oord, % 251.42/37.04 arity_Int__Oint__Orderings_Oorder, arity_Int__Oint__Orderings_Opreorder, % 251.42/37.04 arity_Int__Oint__Power_Opower, arity_Int__Oint__Rings_Ocomm__ring, % 251.42/37.04 arity_Int__Oint__Rings_Ocomm__ring__1, arity_Int__Oint__Rings_Ocomm__semiring, % 251.42/37.04 arity_Int__Oint__Rings_Ocomm__semiring__0, % 251.42/37.04 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Odvd, % 251.42/37.04 arity_Int__Oint__Rings_Oidom, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__idom, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__ring, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__ring__strict, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__semidom, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__semiring, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__semiring__1, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__semiring__1__strict, % 251.42/37.04 arity_Int__Oint__Rings_Olinordered__semiring__strict, % 251.42/37.04 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors, % 251.42/37.04 arity_Int__Oint__Rings_Oordered__cancel__semiring, % 251.42/37.04 arity_Int__Oint__Rings_Oordered__comm__semiring, % 251.42/37.04 arity_Int__Oint__Rings_Oordered__ring, % 251.42/37.04 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring, % 251.42/37.04 arity_Int__Oint__Rings_Oring__1, % 251.42/37.04 arity_Int__Oint__Rings_Oring__1__no__zero__divisors, % 251.42/37.04 arity_Int__Oint__Rings_Oring__no__zero__divisors, % 251.42/37.04 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0, % 251.42/37.04 arity_Int__Oint__Rings_Ozero__neq__one, % 251.42/37.04 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 251.42/37.04 arity_Nat__Onat__Divides_Osemiring__div, % 251.42/37.04 arity_Nat__Onat__Groups_Oab__semigroup__add, % 251.42/37.04 arity_Nat__Onat__Groups_Oab__semigroup__mult, % 251.42/37.04 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, % 251.42/37.04 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, % 251.42/37.04 arity_Nat__Onat__Groups_Ocancel__semigroup__add, % 251.42/37.04 arity_Nat__Onat__Groups_Ocomm__monoid__add, % 251.42/37.04 arity_Nat__Onat__Groups_Ocomm__monoid__mult, arity_Nat__Onat__Groups_Ominus, % 251.42/37.04 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult, % 251.42/37.04 arity_Nat__Onat__Groups_Oone, % 251.42/37.04 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, % 251.42/37.04 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, % 251.42/37.04 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, % 251.42/37.04 arity_Nat__Onat__Groups_Oordered__comm__monoid__add, % 251.42/37.04 arity_Nat__Onat__Groups_Oplus, arity_Nat__Onat__Groups_Ozero, % 251.42/37.04 arity_Nat__Onat__Orderings_Olinorder, arity_Nat__Onat__Orderings_Oord, % 251.42/37.04 arity_Nat__Onat__Orderings_Oorder, arity_Nat__Onat__Orderings_Opreorder, % 251.42/37.04 arity_Nat__Onat__Rings_Ocomm__semiring, % 251.42/37.04 arity_Nat__Onat__Rings_Ocomm__semiring__0, % 251.42/37.04 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, % 251.42/37.04 arity_Nat__Onat__Rings_Olinordered__semiring, % 251.42/37.04 arity_Nat__Onat__Rings_Olinordered__semiring__strict, % 251.42/37.04 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors, % 251.42/37.04 arity_Nat__Onat__Rings_Oordered__cancel__semiring, % 251.42/37.04 arity_Nat__Onat__Rings_Oordered__comm__semiring, % 251.42/37.04 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring, % 251.42/37.04 arity_Nat__Onat__Rings_Osemiring__0, % 251.42/37.04 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 251.42/37.04 arity_Polynomial__Opoly__Divides_Oring__div, % 251.42/37.04 arity_Polynomial__Opoly__Divides_Osemiring__div, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oab__group__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oab__semigroup__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Ogroup__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Ominus, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Omonoid__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Omonoid__mult, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oone, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Oplus, arity_Polynomial__Opoly__Groups_Ouminus, % 251.42/37.04 arity_Polynomial__Opoly__Groups_Ozero, % 251.42/37.04 arity_Polynomial__Opoly__Int_Oring__char__0, % 251.42/37.04 arity_Polynomial__Opoly__Orderings_Olinorder, % 251.42/37.04 arity_Polynomial__Opoly__Orderings_Oord, % 251.42/37.04 arity_Polynomial__Opoly__Orderings_Oorder, % 251.42/37.04 arity_Polynomial__Opoly__Orderings_Opreorder, % 251.42/37.04 arity_Polynomial__Opoly__Power_Opower, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Ocomm__ring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Ocomm__ring__1, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Ocomm__semiring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Oidom, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__idom, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__ring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__semidom, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__semiring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Omult__zero, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Ono__zero__divisors, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Oordered__ring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Oordered__semiring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Osemiring, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Osemiring__0, % 251.42/37.04 arity_Polynomial__Opoly__Rings_Ozero__neq__one, % 251.42/37.04 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 251.42/37.04 arity_fun__Groups_Ominus, arity_fun__Groups_Ouminus, % 251.42/37.04 arity_fun__Lattices_Oboolean__algebra, arity_fun__Orderings_Oord, % 251.42/37.04 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Groups_Oab__semigroup__add, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Groups_Oab__semigroup__mult, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Groups_Omonoid__add, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Groups_Oplus, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Rings_Ocomm__semiring, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Rings_Omult__zero, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Rings_Osemiring, % 251.42/37.04 clrel_Rings_Ocomm__semiring__0__Rings_Osemiring__0, % 251.42/37.04 fact_Divides_Otransfer__nat__int__function__closures_I2_J, % 251.42/37.04 fact_Nat_Odiff__diff__eq, % 251.42/37.04 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, % 251.42/37.04 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, % 251.42/37.04 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, % 251.42/37.04 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, % 251.42/37.04 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, % 251.42/37.04 fact_Suc__diff__diff, fact_Suc__diff__le, fact_Suc__inject, fact_Suc__leD, % 251.42/37.04 fact_Suc__leI, fact_Suc__le__eq, fact_Suc__le__lessD, fact_Suc__le__mono, % 251.42/37.04 fact_Suc__lessD, fact_Suc__lessI, fact_Suc__less__SucD, fact_Suc__less__eq, % 251.42/37.04 fact_Suc__mono, fact_Suc__mult__cancel1, fact_Suc__mult__le__cancel1, % 251.42/37.04 fact_Suc__mult__less__cancel1, fact_Suc__n__not__le__n, fact_Suc__n__not__n, % 251.42/37.04 fact_ab__diff__minus, fact_ab__left__minus, % 251.42/37.04 fact_ab__semigroup__add__class_Oadd__ac_I1_J, % 251.42/37.04 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_add1__zle__eq, % 251.42/37.04 fact_add_Ocomm__neutral, fact_add__0, fact_add__0__iff, fact_add__0__left, % 251.42/37.04 fact_add__0__right, fact_add__Suc, fact_add__Suc__right, fact_add__Suc__shift, % 251.42/37.04 fact_add__diff__assoc, fact_add__diff__assoc2, fact_add__diff__cancel, % 251.42/37.04 fact_add__diff__inverse, fact_add__eq__0__iff, fact_add__imp__eq, % 251.42/37.04 fact_add__increasing, fact_add__increasing2, fact_add__leD1, fact_add__leD2, % 251.42/37.04 fact_add__leE, fact_add__le__cancel__left, fact_add__le__cancel__right, % 251.42/37.04 fact_add__le__imp__le__left, fact_add__le__imp__le__right, % 251.42/37.04 fact_add__le__less__mono, fact_add__le__mono, fact_add__le__mono1, % 251.42/37.04 fact_add__left__cancel, fact_add__left__imp__eq, fact_add__left__mono, % 251.42/37.04 fact_add__lessD1, fact_add__less__cancel__left, fact_add__less__cancel__right, % 251.42/37.04 fact_add__less__imp__less__left, fact_add__less__imp__less__right, % 251.42/37.04 fact_add__less__le__mono, fact_add__less__mono, fact_add__less__mono1, % 251.42/37.04 fact_add__minus__cancel, fact_add__mono, fact_add__monom, % 251.42/37.04 fact_add__mult__distrib, fact_add__mult__distrib2, fact_add__neg__neg, % 251.42/37.04 fact_add__neg__nonpos, fact_add__nonneg__eq__0__iff, fact_add__nonneg__nonneg, % 251.42/37.04 fact_add__nonneg__pos, fact_add__nonpos__neg, fact_add__nonpos__nonpos, % 251.42/37.04 fact_add__pCons, fact_add__poly__code_I1_J, fact_add__poly__code_I2_J, % 251.42/37.04 fact_add__pos__nonneg, fact_add__pos__pos, fact_add__right__cancel, % 251.42/37.04 fact_add__right__imp__eq, fact_add__right__mono, fact_add__scale__eq__noteq, % 251.42/37.04 fact_add__strict__increasing, fact_add__strict__increasing2, % 251.42/37.04 fact_add__strict__left__mono, fact_add__strict__mono, % 251.42/37.04 fact_add__strict__right__mono, fact_coeff__0, fact_coeff__add, fact_coeff__diff, % 251.42/37.04 fact_coeff__eq__0, fact_coeff__inject, fact_coeff__linear__power, % 251.42/37.04 fact_coeff__minus, fact_coeff__monom, fact_coeff__mult__degree__sum, % 251.42/37.04 fact_coeff__pCons__Suc, fact_coeff__smult, fact_combine__common__factor, % 251.42/37.04 fact_comm__mult__left__mono, fact_comm__mult__strict__left__mono, % 251.42/37.04 fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, % 251.42/37.04 fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, % 251.42/37.04 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, % 251.42/37.04 fact_comm__semiring__class_Odistrib, fact_compl__eq__compl__iff, % 251.42/37.04 fact_compl__le__compl__iff, fact_compl__mono, fact_convex__bound__le, % 251.42/37.04 fact_convex__bound__lt, fact_crossproduct__eq, fact_crossproduct__noteq, % 251.42/37.04 fact_degree__add__eq__left, fact_degree__add__eq__right, fact_degree__add__le, % 251.42/37.04 fact_degree__add__less, fact_degree__le, fact_degree__linear__power, % 251.42/37.04 fact_degree__minus, fact_degree__mod__less, fact_degree__monom__eq, % 251.42/37.04 fact_degree__monom__le, fact_degree__mult__eq, fact_degree__mult__le, % 251.42/37.04 fact_degree__pCons__eq, fact_degree__pCons__le, fact_degree__pcompose__le, % 251.42/37.04 fact_degree__power__le, fact_degree__smult__le, fact_diff__0, % 251.42/37.04 fact_diff__0__right, fact_diff__Suc__Suc, fact_diff__add__assoc, % 251.42/37.04 fact_diff__add__assoc2, fact_diff__add__cancel, fact_diff__add__inverse, % 251.42/37.04 fact_diff__add__inverse2, fact_diff__cancel, fact_diff__cancel2, % 251.42/37.04 fact_diff__commute, fact_diff__def, fact_diff__diff__cancel, % 251.42/37.04 fact_diff__diff__left, fact_diff__diff__right, fact_diff__eq__diff__eq, % 251.42/37.04 fact_diff__eq__diff__less, fact_diff__eq__diff__less__eq, fact_diff__le__mono, % 251.42/37.04 fact_diff__le__mono2, fact_diff__le__self, fact_diff__less__Suc, % 251.42/37.04 fact_diff__less__mono, fact_diff__less__mono2, fact_diff__minus__eq__add, % 251.42/37.04 fact_diff__monom, fact_diff__mult__distrib, fact_diff__mult__distrib2, % 251.42/37.04 fact_diff__pCons, fact_diff__self, fact_division__ring__inverse__add, % 251.42/37.04 fact_division__ring__inverse__diff, fact_divisors__zero, % 251.42/37.04 fact_double__add__le__zero__iff__single__add__le__zero, % 251.42/37.04 fact_double__add__less__zero__iff__single__add__less__zero, fact_double__compl, % 251.42/37.04 fact_double__eq__0__iff, fact_double__zero__sym, fact_dvdI, fact_dvd_Oantisym, % 251.42/37.04 fact_dvd_Oantisym__conv, fact_dvd_Oeq__iff, fact_dvd_Oeq__refl, % 251.42/37.04 fact_dvd_Ole__imp__less__or__eq, fact_dvd_Ole__less, fact_dvd_Ole__less__trans, % 251.42/37.04 fact_dvd_Ole__neq__trans, fact_dvd_Oless__asym, fact_dvd_Oless__asym_H, % 251.42/37.04 fact_dvd_Oless__imp__le, fact_dvd_Oless__imp__neq, fact_dvd_Oless__imp__not__eq, % 251.42/37.04 fact_dvd_Oless__imp__not__eq2, fact_dvd_Oless__imp__not__less, % 251.42/37.04 fact_dvd_Oless__le, fact_dvd_Oless__le__trans, fact_dvd_Oless__not__sym, % 251.42/37.04 fact_dvd_Oless__trans, fact_dvd_Oneq__le__trans, fact_dvd_Oord__eq__le__trans, % 251.42/37.04 fact_dvd_Oord__eq__less__trans, fact_dvd_Oord__le__eq__trans, % 251.42/37.04 fact_dvd_Oord__less__eq__trans, fact_dvd_Oorder__refl, fact_dvd_Oorder__trans, % 251.42/37.04 fact_dvd__0__left, fact_dvd__0__right, fact_dvd__add, fact_dvd__antisym, % 251.42/37.04 fact_dvd__diff, fact_dvd__diffD, fact_dvd__diffD1, fact_dvd__diff__nat, % 251.42/37.04 fact_dvd__eq__mod__eq__0, fact_dvd__iff__poly__eq__0, fact_dvd__imp__degree__le, % 251.42/37.04 fact_dvd__imp__mod__0, fact_dvd__minus__iff, fact_dvd__mod, fact_dvd__mod__iff, % 251.42/37.04 fact_dvd__mod__imp__dvd, fact_dvd__mult, fact_dvd__mult2, % 251.42/37.04 fact_dvd__mult__cancel__left, fact_dvd__mult__cancel__right, % 251.42/37.04 fact_dvd__mult__left, fact_dvd__mult__right, fact_dvd__poly__gcd__iff, % 251.42/37.04 fact_dvd__power__le, fact_dvd__power__same, fact_dvd__reduce, fact_dvd__refl, % 251.42/37.04 fact_dvd__smult, fact_dvd__smult__cancel, fact_dvd__smult__iff, fact_dvd__trans, % 251.42/37.04 fact_dvd__triv__left, fact_dvd__triv__right, fact_eq__add__iff1, % 251.42/37.04 fact_eq__add__iff2, fact_eq__diff__iff, fact_eq__iff__diff__eq__0, % 251.42/37.04 fact_eq__imp__le, fact_eq__neg__iff__add__eq__0, % 251.42/37.04 fact_eq__zero__or__degree__less, fact_equal__neg__zero, % 251.42/37.04 fact_equation__minus__iff, fact_even__less__0__iff, fact_expand__poly__eq, % 251.42/37.04 fact_ext, fact_field__inverse, fact_field__inverse__zero, % 251.42/37.04 fact_field__le__mult__one__interval, fact_field__power__not__zero, % 251.42/37.04 fact_incr__mult__lemma, fact_inf__period_I3_J, fact_inf__period_I4_J, % 251.42/37.04 fact_int__0__less__1, fact_int__0__neq__1, fact_int__one__le__iff__zero__less, % 251.42/37.04 fact_inverse__1, fact_inverse__add, fact_inverse__eq__1__iff, % 251.42/37.04 fact_inverse__eq__iff__eq, fact_inverse__eq__imp__eq, fact_inverse__inverse__eq, % 251.42/37.04 fact_inverse__le__1__iff, fact_inverse__le__imp__le, % 251.42/37.04 fact_inverse__le__imp__le__neg, fact_inverse__less__1__iff, % 251.42/37.04 fact_inverse__less__imp__less, fact_inverse__less__imp__less__neg, % 251.42/37.04 fact_inverse__minus__eq, fact_inverse__mult__distrib, % 251.42/37.04 fact_inverse__negative__iff__negative, fact_inverse__negative__imp__negative, % 251.42/37.04 fact_inverse__nonnegative__iff__nonnegative, % 251.42/37.04 fact_inverse__nonpositive__iff__nonpositive, % 251.42/37.04 fact_inverse__nonzero__iff__nonzero, fact_inverse__positive__iff__positive, % 251.42/37.04 fact_inverse__positive__imp__positive, fact_inverse__unique, fact_inverse__zero, % 251.42/37.04 fact_inverse__zero__imp__zero, fact_leD, fact_leI, fact_le__SucE, fact_le__SucI, % 251.42/37.04 fact_le__Suc__eq, fact_le__Suc__ex__iff, fact_le__add1, fact_le__add2, % 251.42/37.04 fact_le__add__diff, fact_le__add__diff__inverse, fact_le__add__diff__inverse2, % 251.42/37.04 fact_le__add__iff1, fact_le__add__iff2, fact_le__antisym, fact_le__cube, % 251.42/37.04 fact_le__degree, fact_le__diff__conv, fact_le__diff__conv2, fact_le__diff__iff, % 251.42/37.04 fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE, fact_le__fun__def, % 251.42/37.04 fact_le__iff__add, fact_le__iff__diff__le__0, fact_le__imp__0__less, % 251.42/37.04 fact_le__imp__diff__is__add, fact_le__imp__inverse__le, % 251.42/37.04 fact_le__imp__inverse__le__neg, fact_le__imp__less__Suc, fact_le__imp__neg__le, % 251.42/37.04 fact_le__imp__power__dvd, fact_le__less__Suc__eq, fact_le__minus__iff, % 251.42/37.04 fact_le__minus__self__iff, fact_le__mod__geq, fact_le__neq__implies__less, % 251.42/37.04 fact_le__refl, fact_le__square, fact_le__trans, fact_leading__coeff__0__iff, % 251.42/37.04 fact_leading__coeff__neq__0, fact_left__add__mult__distrib, fact_left__inverse, % 251.42/37.04 fact_left__minus, fact_lessI, fact_less__1__mult, fact_less__SucE, % 251.42/37.04 fact_less__SucI, fact_less__Suc__eq__le, fact_less__add__Suc1, % 251.42/37.04 fact_less__add__Suc2, fact_less__add__eq__less, fact_less__add__iff1, % 251.42/37.04 fact_less__add__iff2, fact_less__add__one, fact_less__antisym, % 251.42/37.04 fact_less__degree__imp, fact_less__diff__conv, fact_less__diff__iff, % 251.42/37.04 fact_less__eq__Suc__le, fact_less__fun__def, fact_less__iff__Suc__add, % 251.42/37.04 fact_less__iff__diff__less__0, fact_less__imp__diff__less, % 251.42/37.04 fact_less__imp__inverse__less, fact_less__imp__inverse__less__neg, % 251.42/37.04 fact_less__imp__le__nat, fact_less__imp__neq, fact_less__irrefl__nat, % 251.42/37.04 fact_less__le__not__le, fact_less__minus__iff, fact_less__minus__self__iff, % 251.42/37.04 fact_less__not__refl, fact_less__not__refl2, fact_less__not__refl3, % 251.42/37.04 fact_less__or__eq__imp__le, fact_less__trans__Suc, % 251.42/37.04 fact_linorder__antisym__conv1, fact_linorder__antisym__conv2, % 251.42/37.04 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases, % 251.42/37.04 fact_linorder__le__less__linear, fact_linorder__less__linear, % 251.42/37.04 fact_linorder__linear, fact_linorder__neqE, % 251.42/37.04 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat, % 251.42/37.04 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less, % 251.42/37.04 fact_minus__add, fact_minus__add__cancel, fact_minus__add__distrib, % 251.42/37.04 fact_minus__apply, fact_minus__diff__eq, fact_minus__dvd__iff, % 251.42/37.04 fact_minus__equation__iff, fact_minus__le__iff, fact_minus__le__self__iff, % 251.42/37.04 fact_minus__less__iff, fact_minus__minus, fact_minus__monom, % 251.42/37.04 fact_minus__mult__commute, fact_minus__mult__left, fact_minus__mult__minus, % 251.42/37.04 fact_minus__mult__right, fact_minus__pCons, fact_minus__poly__code_I1_J, % 251.42/37.04 fact_minus__poly__code_I2_J, fact_minus__unique, fact_minus__zero, fact_mod__0, % 251.42/37.04 fact_mod__Suc__eq__Suc__mod, fact_mod__add__cong, fact_mod__add__eq, % 251.42/37.04 fact_mod__add__left__eq, fact_mod__add__right__eq, fact_mod__add__self1, % 251.42/37.04 fact_mod__add__self2, fact_mod__by__0, fact_mod__by__1, fact_mod__diff__cong, % 251.42/37.04 fact_mod__diff__eq, fact_mod__diff__left__eq, fact_mod__diff__right__eq, % 251.42/37.04 fact_mod__geq, fact_mod__if, fact_mod__less, fact_mod__less__eq__dividend, % 251.42/37.04 fact_mod__minus__cong, fact_mod__minus__eq, fact_mod__mod__cancel, % 251.42/37.04 fact_mod__mod__trivial, fact_mod__mult__cong, fact_mod__mult__distrib, % 251.42/37.04 fact_mod__mult__distrib2, fact_mod__mult__eq, fact_mod__mult__left__eq, % 251.42/37.04 fact_mod__mult__mult1, fact_mod__mult__mult2, fact_mod__mult__right__eq, % 251.42/37.04 fact_mod__mult__self1, fact_mod__mult__self1__is__0, fact_mod__mult__self2, % 251.42/37.04 fact_mod__mult__self2__is__0, fact_mod__mult__self3, fact_mod__mult__self4, % 251.42/37.04 fact_mod__neg__neg__trivial, fact_mod__poly__eq, fact_mod__poly__less, % 251.42/37.04 fact_mod__self, fact_mod__smult__left, fact_mod__smult__right, fact_monom__Suc, % 251.42/37.04 fact_monom__eq__0, fact_monom__eq__0__iff, fact_monom__eq__iff, % 251.42/37.04 fact_mult_Oadd__left, fact_mult_Oadd__right, fact_mult_Ocomm__neutral, % 251.42/37.04 fact_mult_Odiff__left, fact_mult_Odiff__right, fact_mult_Ominus__left, % 251.42/37.04 fact_mult_Ominus__right, fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, % 251.42/37.04 fact_mult_Ozero__right, fact_mult__1, fact_mult__1__left, fact_mult__1__right, % 251.42/37.04 fact_mult__Suc, fact_mult__Suc__right, fact_mult__diff__mult, % 251.42/37.04 fact_mult__dvd__mono, fact_mult__eq__0__iff, fact_mult__idem, % 251.42/37.04 fact_mult__le__0__iff, fact_mult__le__cancel__left__neg, % 251.42/37.04 fact_mult__le__cancel__left__pos, fact_mult__le__less__imp__less, % 251.42/37.04 fact_mult__le__mono, fact_mult__le__mono1, fact_mult__le__mono2, % 251.42/37.04 fact_mult__left_Oadd, fact_mult__left_Odiff, fact_mult__left_Ominus, % 251.42/37.04 fact_mult__left_Ozero, fact_mult__left__idem, fact_mult__left__le__imp__le, % 251.42/37.04 fact_mult__left__le__one__le, fact_mult__left__less__imp__less, % 251.42/37.04 fact_mult__left__mono, fact_mult__left__mono__neg, % 251.42/37.04 fact_mult__less__cancel__left__disj, fact_mult__less__cancel__left__neg, % 251.42/37.04 fact_mult__less__cancel__left__pos, fact_mult__less__cancel__right__disj, % 251.42/37.04 fact_mult__less__imp__less__left, fact_mult__less__imp__less__right, % 251.42/37.04 fact_mult__less__le__imp__less, fact_mult__mono, fact_mult__mono_H, % 251.42/37.04 fact_mult__monom, fact_mult__neg__neg, fact_mult__neg__pos, % 251.42/37.04 fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos, % 251.42/37.04 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg, % 251.42/37.04 fact_mult__nonpos__nonpos, fact_mult__pCons__left, fact_mult__pCons__right, % 251.42/37.04 fact_mult__poly__0__left, fact_mult__poly__0__right, fact_mult__poly__add__left, % 251.42/37.04 fact_mult__pos__neg, fact_mult__pos__neg2, fact_mult__pos__pos, % 251.42/37.04 fact_mult__right_Oadd, fact_mult__right_Odiff, fact_mult__right_Ominus, % 251.42/37.04 fact_mult__right_Ozero, fact_mult__right__le__imp__le, % 251.42/37.04 fact_mult__right__le__one__le, fact_mult__right__less__imp__less, % 251.42/37.04 fact_mult__right__mono, fact_mult__right__mono__neg, fact_mult__smult__left, % 251.42/37.04 fact_mult__smult__right, fact_mult__strict__left__mono, % 251.42/37.04 fact_mult__strict__left__mono__neg, fact_mult__strict__mono, % 251.42/37.04 fact_mult__strict__mono_H, fact_mult__strict__right__mono, % 251.42/37.04 fact_mult__strict__right__mono__neg, fact_mult__zero__left, % 251.42/37.04 fact_mult__zero__right, fact_n__not__Suc__n, fact_nat_Oinject, % 251.42/37.04 fact_nat__add__assoc, fact_nat__add__commute, fact_nat__add__left__cancel, % 251.42/37.04 fact_nat__add__left__cancel__le, fact_nat__add__left__cancel__less, % 251.42/37.04 fact_nat__add__left__commute, fact_nat__add__right__cancel, % 251.42/37.04 fact_nat__le__linear, fact_nat__less__cases, fact_nat__less__le, % 251.42/37.04 fact_nat__mult__assoc, fact_nat__mult__commute, fact_nat__neq__iff, % 251.42/37.04 fact_neg__0__equal__iff__equal, fact_neg__0__le__iff__le, % 251.42/37.04 fact_neg__0__less__iff__less, fact_neg__equal__0__iff__equal, % 251.42/37.04 fact_neg__equal__iff__equal, fact_neg__equal__zero, fact_neg__le__0__iff__le, % 251.42/37.04 fact_neg__le__iff__le, fact_neg__less__0__iff__less, fact_neg__less__iff__less, % 251.42/37.04 fact_neg__less__nonneg, fact_neg__mod__bound, fact_neg__mod__conj, % 251.42/37.04 fact_neg__mod__sign, fact_negative__imp__inverse__negative, % 251.42/37.04 fact_no__zero__divisors, fact_nonzero__imp__inverse__nonzero, % 251.42/37.04 fact_nonzero__inverse__eq__imp__eq, fact_nonzero__inverse__inverse__eq, % 251.42/37.04 fact_nonzero__inverse__minus__eq, fact_nonzero__inverse__mult__distrib, % 251.42/37.04 fact_nonzero__power__inverse, fact_not__add__less1, fact_not__add__less2, % 251.42/37.04 fact_not__leE, fact_not__less__eq, fact_not__less__eq__eq, % 251.42/37.04 fact_not__less__iff__gr__or__eq, fact_not__less__less__Suc__eq, % 251.42/37.04 fact_not__pos__poly__0, fact_not__square__less__zero, % 251.42/37.04 fact_not__sum__squares__lt__zero, fact_odd__less__0, fact_odd__nonzero, % 251.42/37.04 fact_offset__poly__0, fact_one__dvd, fact_one__le__inverse, % 251.42/37.04 fact_one__le__inverse__iff, fact_one__le__power, fact_one__less__inverse, % 251.42/37.04 fact_one__less__inverse__iff, fact_one__poly__def, fact_one__reorient, % 251.42/37.04 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans, % 251.42/37.04 fact_ord__less__eq__trans, fact_order, fact_order__1, fact_order__2, % 251.42/37.04 fact_order__antisym, fact_order__antisym__conv, fact_order__degree, % 251.42/37.04 fact_order__eq__iff, fact_order__eq__refl, fact_order__le__imp__less__or__eq, % 251.42/37.04 fact_order__le__less, fact_order__le__less__trans, fact_order__le__neq__trans, % 251.42/37.04 fact_order__less__asym, fact_order__less__asym_H, fact_order__less__imp__le, % 251.42/37.04 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2, % 251.42/37.04 fact_order__less__imp__not__less, fact_order__less__irrefl, % 251.42/37.04 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym, % 251.42/37.04 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl, % 251.42/37.04 fact_order__trans, fact_pCons__0__0, fact_pCons__eq__iff, fact_pcompose__0, % 251.42/37.04 fact_pcompose__pCons, fact_pdivmod__rel__0, fact_pdivmod__rel__0__iff, % 251.42/37.04 fact_pdivmod__rel__by__0, fact_pdivmod__rel__by__0__iff, fact_pdivmod__rel__def, % 251.42/37.04 fact_pdivmod__rel__mult, fact_pdivmod__rel__smult__left, % 251.42/37.04 fact_pdivmod__rel__smult__right, fact_pdivmod__rel__unique, % 251.42/37.04 fact_pdivmod__rel__unique__div, fact_pdivmod__rel__unique__mod, fact_poly__0, % 251.42/37.04 fact_poly__1, fact_poly__add, fact_poly__diff, fact_poly__dvd__antisym, % 251.42/37.04 fact_poly__eq__0__iff__dvd, fact_poly__eq__iff, fact_poly__gcd_Oassoc, % 251.42/37.04 fact_poly__gcd_Ocommute, fact_poly__gcd_Oleft__commute, % 251.42/37.04 fact_poly__gcd_Osimps_I1_J, fact_poly__gcd_Osimps_I2_J, fact_poly__gcd__0__0, % 251.42/37.04 fact_poly__gcd__1__left, fact_poly__gcd__1__right, fact_poly__gcd__code, % 251.42/37.04 fact_poly__gcd__dvd1, fact_poly__gcd__dvd2, fact_poly__gcd__greatest, % 251.42/37.04 fact_poly__gcd__minus__left, fact_poly__gcd__minus__right, % 251.42/37.04 fact_poly__gcd__monic, fact_poly__gcd__unique, fact_poly__gcd__zero__iff, % 251.42/37.04 fact_poly__minus, fact_poly__mod__minus__left, fact_poly__mod__minus__right, % 251.42/37.04 fact_poly__monom, fact_poly__mult, fact_poly__offset__poly, fact_poly__pCons, % 251.42/37.04 fact_poly__pcompose, fact_poly__power, fact_poly__rec_Osimps, fact_poly__rec__0, % 251.42/37.04 fact_poly__rec__pCons, fact_poly__smult, fact_poly__zero, fact_pos__add__strict, % 251.42/37.04 fact_pos__mod__bound, fact_pos__poly__add, fact_pos__poly__def, % 251.42/37.04 fact_pos__poly__mult, fact_pos__poly__pCons, fact_pos__poly__total, % 251.42/37.04 fact_pos__zmult__eq__1__iff, fact_positive__imp__inverse__positive, % 251.42/37.04 fact_power_Opower_Opower__Suc, fact_power__0__Suc, fact_power__Suc, % 251.42/37.04 fact_power__Suc2, fact_power__Suc__less, fact_power__Suc__less__one, % 251.42/37.04 fact_power__add, fact_power__commutes, fact_power__decreasing, fact_power__gt1, % 251.42/37.04 fact_power__gt1__lemma, fact_power__increasing, fact_power__increasing__iff, % 251.42/37.04 fact_power__inject__base, fact_power__inject__exp, fact_power__inverse, % 251.42/37.04 fact_power__le__dvd, fact_power__le__imp__le__base, % 251.42/37.04 fact_power__le__imp__le__exp, fact_power__less__imp__less__base, % 251.42/37.04 fact_power__less__imp__less__exp, fact_power__less__power__Suc, % 251.42/37.04 fact_power__minus, fact_power__mono, fact_power__mult, % 251.42/37.04 fact_power__mult__distrib, fact_power__one, fact_power__power__power, % 251.42/37.04 fact_power__strict__decreasing, fact_power__strict__increasing, % 251.42/37.04 fact_power__strict__increasing__iff, fact_q__neg__lemma, fact_q__pos__lemma, % 251.42/37.04 fact_real__squared__diff__one__factored, fact_realpow__Suc__le__self, % 251.42/37.04 fact_right__inverse, fact_right__minus, fact_right__minus__eq, % 251.42/37.04 fact_self__quotient__aux1, fact_self__quotient__aux2, fact_smult__0__left, % 251.42/37.04 fact_smult__0__right, fact_smult__1__left, fact_smult__add__left, % 251.42/37.04 fact_smult__add__right, fact_smult__diff__left, fact_smult__dvd, % 251.42/37.04 fact_smult__dvd__cancel, fact_smult__dvd__iff, fact_smult__eq__0__iff, % 251.42/37.04 fact_smult__minus__left, fact_smult__minus__right, fact_smult__monom, % 251.42/37.04 fact_smult__pCons, fact_smult__smult, fact_split__mult__neg__le, % 251.42/37.04 fact_split__mult__pos__le, fact_square__eq__1__iff, fact_square__eq__iff, % 251.42/37.04 fact_sum__squares__eq__zero__iff, fact_sum__squares__ge__zero, % 251.42/37.04 fact_sum__squares__gt__zero__iff, fact_sum__squares__le__zero__iff, % 251.42/37.04 fact_synthetic__div__0, fact_synthetic__div__correct, % 251.42/37.04 fact_synthetic__div__correct_H, fact_synthetic__div__pCons, % 251.42/37.04 fact_synthetic__div__unique, fact_synthetic__div__unique__lemma, % 251.42/37.04 fact_termination__basic__simps_I1_J, fact_termination__basic__simps_I2_J, % 251.42/37.04 fact_termination__basic__simps_I3_J, fact_termination__basic__simps_I4_J, % 251.42/37.04 fact_termination__basic__simps_I5_J, fact_times_Oidem, fact_trans__le__add1, % 251.42/37.04 fact_trans__le__add2, fact_trans__less__add1, fact_trans__less__add2, % 251.42/37.04 fact_uminus__apply, fact_uminus__dvd__conv_I1_J, fact_uminus__dvd__conv_I2_J, % 251.42/37.04 fact_unique__quotient__lemma, fact_unique__quotient__lemma__neg, % 251.42/37.04 fact_unity__coeff__ex, fact_xt1_I10_J, fact_xt1_I11_J, fact_xt1_I12_J, % 251.42/37.04 fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J, fact_xt1_I5_J, % 251.42/37.04 fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J, fact_zadd__0, % 251.42/37.04 fact_zadd__0__right, fact_zadd__assoc, fact_zadd__commute, % 251.42/37.04 fact_zadd__left__commute, fact_zadd__left__mono, fact_zadd__strict__right__mono, % 251.42/37.04 fact_zadd__zless__mono, fact_zadd__zminus__inverse2, fact_zadd__zmult__distrib, % 251.42/37.04 fact_zadd__zmult__distrib2, fact_zdiv__mono2__lemma, % 251.42/37.04 fact_zdiv__mono2__neg__lemma, fact_zdvd__antisym__nonneg, fact_zdvd__imp__le, % 251.42/37.04 fact_zdvd__mono, fact_zdvd__mult__cancel, fact_zdvd__not__zless, % 251.42/37.04 fact_zdvd__period, fact_zdvd__reduce, fact_zdvd__zmod, % 251.42/37.04 fact_zdvd__zmod__imp__zdvd, % 251.42/37.04 fact_zero__le__double__add__iff__zero__le__single__add, % 251.42/37.04 fact_zero__le__mult__iff, fact_zero__le__power, fact_zero__le__square, % 251.42/37.04 fact_zero__less__double__add__iff__zero__less__single__add, % 251.42/37.04 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, fact_zero__less__one, % 251.42/37.04 fact_zero__less__power, fact_zero__less__two, fact_zero__reorient, % 251.42/37.04 fact_zle__add1__eq__le, fact_zle__antisym, fact_zle__linear, fact_zle__refl, % 251.42/37.04 fact_zle__trans, fact_zless__add1__eq, fact_zless__imp__add1__zle, % 251.42/37.04 fact_zless__le, fact_zless__linear, fact_zminus__0, fact_zminus__zadd__distrib, % 251.42/37.04 fact_zminus__zminus, fact_zminus__zmod, fact_zmod__eq__0__iff, % 251.42/37.04 fact_zmod__le__nonneg__dividend, fact_zmod__self, fact_zmod__simps_I1_J, % 251.42/37.04 fact_zmod__simps_I2_J, fact_zmod__simps_I3_J, fact_zmod__simps_I4_J, % 251.42/37.04 fact_zmod__zero, fact_zmod__zminus1__not__zero, fact_zmod__zminus2, % 251.42/37.04 fact_zmod__zminus2__not__zero, fact_zmod__zminus__zminus, fact_zmod__zmult1__eq, % 251.42/37.04 fact_zmult__1, fact_zmult__1__right, fact_zmult__assoc, fact_zmult__commute, % 251.42/37.04 fact_zmult__zless__mono2, fact_zmult__zminus, fact_zpower__zadd__distrib, % 251.42/37.04 fact_zpower__zmod, fact_zpower__zpower, help_c__fequal__1, help_c__fequal__2 % 251.42/37.04 % 251.42/37.04 Those formulas are unsatisfiable: % 251.42/37.04 --------------------------------- % 251.42/37.04 % 251.42/37.04 Begin of proof % 251.42/37.05 | % 251.42/37.05 | ALPHA: (fact_order__root) implies: % 251.42/37.05 | (1) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 251.42/37.05 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 251.42/37.05 | ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~ % 251.42/37.05 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: % 251.42/37.05 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (((v9 = v0 & ~ % 251.42/37.05 | (v8 = v2) & c_Polynomial_Oorder(v3, v1, v2) = v0 & % 251.42/37.05 | tc_Polynomial_Opoly(v3) = v7 & % 251.42/37.05 | c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | (v6 % 251.42/37.05 | = v5 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & ((v8 % 251.42/37.05 | = v2 & tc_Polynomial_Opoly(v3) = v7 & % 251.42/37.05 | c_Groups_Ozero__class_Ozero(v7) = v2 & $i(v7)) | ( ~ (v9 = % 251.42/37.05 | v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & $i(v9)) | ( ~ % 251.42/37.05 | (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 & % 251.42/37.05 | $i(v6)))))) % 251.42/37.05 | % 251.42/37.05 | ALPHA: (fact_monom__0) implies: % 251.42/37.05 | (2) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 251.42/37.05 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 251.42/37.05 | ( ~ (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ % 251.42/37.05 | (tc_Polynomial_Opoly(v2) = v3) | ~ % 251.42/37.05 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 251.42/37.05 | class_Groups_Ozero(v2) | (c_Polynomial_Omonom(v2, v1, v0) = v5 & % 251.42/37.05 | $i(v5)))) % 251.42/37.05 | % 251.42/37.05 | ALPHA: (fact_dvd__mult__cancel1) implies: % 251.42/37.06 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 251.42/37.06 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 251.42/37.06 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 251.42/37.06 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 % 251.42/37.06 | = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) % 251.42/37.06 | | ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) % 251.42/37.06 | | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : % 251.42/37.06 | ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, % 251.42/37.06 | v3) = v4) | ~ $i(v3) | ~ % 251.42/37.06 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 251.42/37.06 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_dvd__mult__cancel2) implies: % 251.42/37.06 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 251.42/37.06 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 251.42/37.06 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 251.42/37.06 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 % 251.42/37.06 | = v2 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) % 251.42/37.06 | | ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) % 251.42/37.06 | | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4)) & ! [v3: $i] : % 251.42/37.06 | ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, % 251.42/37.06 | v2) = v4) | ~ $i(v3) | ~ % 251.42/37.06 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 251.42/37.06 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_degree__1) implies: % 251.42/37.06 | (5) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 251.42/37.06 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 251.42/37.06 | (c_Polynomial_Odegree(v1, v3) = v4) | ~ % 251.42/37.06 | (c_Groups_Oone__class_Oone(v2) = v3) | ~ (tc_Polynomial_Opoly(v1) % 251.42/37.06 | = v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v1))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_mult__eq__self__implies__10) implies: % 251.42/37.06 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 251.42/37.06 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 251.42/37.06 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 251.42/37.06 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 % 251.42/37.06 | | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 251.42/37.06 | $i(v3))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_degree__0) implies: % 251.42/37.06 | (7) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 251.42/37.06 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 251.42/37.06 | (c_Polynomial_Odegree(v1, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = % 251.42/37.06 | v2) | ~ (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ % 251.42/37.06 | class_Groups_Ozero(v1))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_degree__smult__eq) implies: % 251.42/37.06 | (8) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 251.42/37.06 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 251.42/37.06 | ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~ (c_Polynomial_Osmult(v3, % 251.42/37.06 | v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 251.42/37.06 | class_Rings_Oidom(v3) | ? [v6: $i] : ? [v7: $i] : ((v5 = v0 | ( ~ % 251.42/37.06 | (v6 = v2) & c_Groups_Ozero__class_Ozero(v3) = v6 & $i(v6))) & % 251.42/37.06 | ((v7 = v5 & c_Polynomial_Odegree(v3, v1) = v5 & $i(v5)) | (v6 = % 251.42/37.06 | v2 & c_Groups_Ozero__class_Ozero(v3) = v2))))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_degree__pCons__0) implies: % 251.42/37.06 | (9) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) & % 251.42/37.06 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 251.42/37.06 | ! [v6: $i] : (v6 = v0 | ~ (c_Polynomial_Odegree(v2, v5) = v6) | ~ % 251.42/37.06 | (c_Polynomial_OpCons(v2, v1, v4) = v5) | ~ % 251.42/37.06 | (tc_Polynomial_Opoly(v2) = v3) | ~ % 251.42/37.06 | (c_Groups_Ozero__class_Ozero(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 251.42/37.06 | class_Groups_Ozero(v2))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_synthetic__div__eq__0__iff) implies: % 251.42/37.06 | (10) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.06 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 251.42/37.06 | (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ $i(v3) | ~ % 251.42/37.06 | $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? % 251.42/37.06 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (((v7 = v0 & % 251.42/37.06 | c_Polynomial_Odegree(v3, v2) = v0) | ( ~ (v6 = v4) & % 251.42/37.06 | tc_Polynomial_Opoly(v3) = v5 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) & % 251.42/37.06 | ((v6 = v4 & tc_Polynomial_Opoly(v3) = v5 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(v5) = v4 & $i(v5) & $i(v4)) | ( % 251.42/37.06 | ~ (v7 = v0) & c_Polynomial_Odegree(v3, v2) = v7 & % 251.42/37.06 | $i(v7)))))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_mult__0) implies: % 251.42/37.06 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 251.42/37.06 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & % 251.42/37.06 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ % 251.42/37.06 | (hAPP(v2, v3) = v4) | ~ $i(v3))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_mult__0__right) implies: % 251.42/37.06 | (12) ? [v0: $i] : ? [v1: $i] : % 251.42/37.06 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.42/37.06 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | % 251.42/37.06 | hAPP(v3, v1) = v1)) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_mult__is__0) implies: % 251.42/37.06 | (13) ? [v0: $i] : ? [v1: $i] : % 251.42/37.06 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.42/37.06 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) = % 251.42/37.06 | v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ! % 251.42/37.06 | [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~ % 251.42/37.06 | (hAPP(v0, v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! % 251.42/37.06 | [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ % 251.42/37.06 | (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_mult__cancel2) implies: % 251.42/37.06 | (14) ? [v0: $i] : ? [v1: $i] : % 251.42/37.06 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.06 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.42/37.06 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.06 | ! [v7: $i] : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = % 251.42/37.06 | v5) | ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ % 251.42/37.06 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 251.42/37.06 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v2 | v3 = v1 | ~ % 251.42/37.06 | (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 251.42/37.06 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 251.42/37.06 | $i(v2))) % 251.42/37.06 | % 251.42/37.06 | ALPHA: (fact_plus__nat_Oadd__0) implies: % 251.42/37.07 | (15) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ % 251.42/37.07 | $i(v1))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_Nat_Oadd__0__right) implies: % 251.42/37.07 | (16) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ % 251.42/37.07 | $i(v1))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_add__is__0) implies: % 251.42/37.07 | (17) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ % 251.42/37.07 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ % 251.42/37.07 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : (v1 = v0 | ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_add__eq__self__zero) implies: % 251.42/37.07 | (18) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ % 251.42/37.07 | $i(v2) | ~ $i(v1))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_gr0I) implies: % 251.42/37.07 | (19) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_dvd__imp__le) implies: % 251.42/37.07 | (20) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ~ % 251.42/37.07 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v1) | % 251.42/37.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_nat__dvd__not__less) implies: % 251.42/37.07 | (21) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 251.42/37.07 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_le__0__eq) implies: % 251.42/37.07 | (22) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) & ! [v1: % 251.42/37.07 | $i] : (v1 = v0 | ~ $i(v1) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_add__gr__0) implies: % 251.42/37.07 | (23) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.42/37.07 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 251.42/37.07 | v0, v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i] % 251.42/37.07 | : ! [v2: $i] : ! [v3: $i] : ( ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.42/37.07 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 251.42/37.07 | v0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & % 251.42/37.07 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 251.42/37.07 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.42/37.07 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 251.42/37.07 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_less__eq__nat_Osimps_I1_J) implies: % 251.42/37.07 | (24) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ? [v1: $i] : ( ~ $i(v1) | % 251.42/37.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_neq0__conv) implies: % 251.42/37.07 | (25) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1: % 251.42/37.07 | $i] : (v1 = v0 | ~ $i(v1) | % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_not__less0) implies: % 251.42/37.07 | (26) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.07 | & ! [v1: $i] : ( ~ $i(v1) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_dvd__mult__cancel) implies: % 251.42/37.07 | (27) ? [v0: $i] : ? [v1: $i] : % 251.42/37.07 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.42/37.07 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.07 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.07 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 251.42/37.07 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 251.42/37.07 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_mult__less__mono2) implies: % 251.42/37.07 | (28) ? [v0: $i] : ? [v1: $i] : % 251.42/37.07 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.42/37.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.42/37.07 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.07 | ! [v7: $i] : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ % 251.42/37.07 | (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_mult__less__mono1) implies: % 251.42/37.07 | (29) ? [v0: $i] : ? [v1: $i] : % 251.42/37.07 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.42/37.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.42/37.07 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.07 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5, % 251.42/37.07 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) | % 251.42/37.07 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 251.42/37.07 | % 251.42/37.07 | ALPHA: (fact_mult__le__cancel2) implies: % 251.42/37.07 | (30) ? [v0: $i] : ? [v1: $i] : % 251.42/37.07 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.07 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.42/37.07 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.07 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, % 251.42/37.07 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | % 251.42/37.07 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) | % 251.42/37.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2: % 251.42/37.07 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 251.42/37.07 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) % 251.42/37.07 | = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 251.42/37.07 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) | % 251.42/37.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)) & ! [v2: % 251.42/37.07 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 251.42/37.07 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) % 251.42/37.07 | = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 251.42/37.07 | $i(v4) | ~ $i(v3) | ~ $i(v2) | % 251.42/37.07 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 251.42/37.07 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8))) % 251.42/37.07 | % 251.42/37.08 | ALPHA: (fact_mult__le__cancel1) implies: % 251.42/37.08 | (31) ? [v0: $i] : ? [v1: $i] : % 251.42/37.08 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.42/37.08 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.08 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) | % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: % 251.42/37.08 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 251.42/37.08 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)) & ! [v2: % 251.42/37.08 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 251.42/37.08 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7))) % 251.42/37.08 | % 251.42/37.08 | ALPHA: (fact_mult__less__cancel2) implies: % 251.42/37.08 | (32) ? [v0: $i] : ? [v1: $i] : % 251.42/37.08 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.42/37.08 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.08 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, % 251.42/37.08 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | % 251.42/37.08 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] % 251.42/37.08 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 251.42/37.08 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = % 251.42/37.08 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 251.42/37.08 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] % 251.42/37.08 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 251.42/37.08 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = % 251.42/37.08 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 251.42/37.08 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 251.42/37.08 | % 251.42/37.08 | ALPHA: (fact_mult__less__cancel1) implies: % 251.42/37.08 | (33) ? [v0: $i] : ? [v1: $i] : % 251.42/37.08 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.42/37.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.42/37.08 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.08 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] % 251.42/37.08 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 251.42/37.08 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i] % 251.42/37.08 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 251.42/37.08 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 251.42/37.08 | % 251.42/37.08 | ALPHA: (fact_nat__0__less__mult__iff) implies: % 251.42/37.08 | (34) ? [v0: $i] : ? [v1: $i] : % 251.42/37.08 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.42/37.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.42/37.08 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, % 251.42/37.08 | v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 251.42/37.08 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] % 251.42/37.08 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 251.42/37.08 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i] % 251.42/37.08 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 251.42/37.08 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5))) % 251.42/37.08 | % 251.42/37.08 | ALPHA: (fact_nat__mult__le__cancel1) implies: % 251.42/37.08 | (35) ? [v0: $i] : ? [v1: $i] : % 251.42/37.08 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.42/37.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.42/37.08 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.08 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) | % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: % 251.42/37.08 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 251.42/37.08 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 251.42/37.08 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7))) % 251.42/37.08 | % 251.42/37.08 | ALPHA: (fact_dvd__pos__nat) implies: % 251.42/37.08 | (36) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.42/37.08 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 251.42/37.08 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v2) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 251.42/37.08 | % 251.42/37.08 | ALPHA: (fact_nat__mult__less__cancel1) implies: % 251.42/37.08 | (37) ? [v0: $i] : ? [v1: $i] : % 251.42/37.08 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.42/37.08 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.42/37.08 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.08 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] % 251.42/37.08 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 251.42/37.08 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.08 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 251.42/37.08 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 251.42/37.08 | % 251.42/37.08 | ALPHA: (fact_nat__mult__dvd__cancel1) implies: % 251.42/37.09 | (38) ? [v0: $i] : ? [v1: $i] : % 251.42/37.09 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.42/37.09 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.42/37.09 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.42/37.09 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 251.42/37.09 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 251.42/37.09 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 251.42/37.09 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 251.42/37.09 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 251.42/37.09 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) % 251.42/37.09 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.42/37.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 251.42/37.09 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 251.42/37.09 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7))) % 251.42/37.09 | % 251.42/37.09 | ALPHA: (fact_nat__dvd__1__iff__1) implies: % 251.42/37.09 | (39) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 251.42/37.09 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 = % 251.42/37.09 | v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, % 251.42/37.09 | v0))) % 251.42/37.09 | % 251.42/37.09 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Obot__least) implies: % 251.42/37.09 | (40) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 251.42/37.09 | ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, % 251.42/37.09 | v1))) % 251.42/37.09 | % 251.42/37.09 | ALPHA: (fact_nat__mult__eq__1__iff) implies: % 251.42/37.09 | (41) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 251.42/37.09 | v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & % 251.42/37.09 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ % 251.42/37.09 | (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ % 251.42/37.09 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ % 251.42/37.09 | (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ % 251.42/37.09 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (hAPP(v2, v1) % 251.42/37.09 | = v3) | ~ (hAPP(v0, v1) = v2))) % 251.42/37.09 | % 251.42/37.09 | ALPHA: (fact_nat__mult__1__right) implies: % 251.42/37.09 | (42) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 251.42/37.09 | v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & % 251.42/37.09 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ % 251.42/37.09 | $i(v2) | hAPP(v3, v1) = v2)) % 251.42/37.09 | % 251.42/37.09 | ALPHA: (fact_nat__1__eq__mult__iff) implies: % 251.42/37.09 | (43) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 251.42/37.09 | v0 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & % 251.42/37.09 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ % 251.42/37.09 | (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 251.42/37.09 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ % 251.42/37.09 | (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 251.42/37.09 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (hAPP(v2, v0) % 251.42/37.09 | = v3) | ~ (hAPP(v1, v0) = v2))) % 251.42/37.09 | % 251.42/37.09 | ALPHA: (fact_nat__mult__1) implies: % 251.71/37.09 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 251.71/37.09 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 251.71/37.09 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 % 251.71/37.09 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | % 251.71/37.09 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3))) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_nat__mult__dvd__cancel__disj) implies: % 251.71/37.09 | (45) ? [v0: $i] : ? [v1: $i] : % 251.71/37.09 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.71/37.09 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.71/37.09 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.71/37.09 | ! [v7: $i] : (v4 = v1 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 251.71/37.09 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 251.71/37.09 | | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 251.71/37.09 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 251.71/37.09 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 251.71/37.09 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) % 251.71/37.09 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.09 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 251.71/37.09 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : ! % 251.71/37.09 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, % 251.71/37.09 | v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | % 251.71/37.09 | ~ $i(v3) | ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, % 251.71/37.09 | v6))) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Otop__greatest) implies: % 251.71/37.09 | (46) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.09 | & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 251.71/37.09 | v1, v0))) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_nat__mult__eq__cancel__disj) implies: % 251.71/37.09 | (47) ? [v0: $i] : ? [v1: $i] : % 251.71/37.09 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.71/37.09 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 251.71/37.09 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.71/37.09 | (v6 = v5 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ % 251.71/37.09 | (hAPP(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! % 251.71/37.09 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | v3 = % 251.71/37.09 | v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ % 251.71/37.09 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_nat__mult__eq__cancel1) implies: % 251.71/37.09 | (48) ? [v0: $i] : ? [v1: $i] : % 251.71/37.09 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.71/37.09 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.71/37.09 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 251.71/37.09 | (v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ % 251.71/37.09 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_ex__least__nat__less) implies: % 251.71/37.09 | (49) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 251.71/37.09 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 251.71/37.09 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) % 251.71/37.09 | | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i] % 251.71/37.09 | : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 251.71/37.09 | ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 & % 251.71/37.09 | hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) & % 251.71/37.09 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9: % 251.71/37.09 | $i] : ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9) % 251.71/37.09 | | ~ hBOOL(v10) | ~ % 251.71/37.09 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) | % 251.71/37.09 | (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5)))))) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) % 251.71/37.09 | implies: % 251.71/37.09 | (50) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 251.71/37.09 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 251.71/37.09 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 251.71/37.09 | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | % 251.71/37.09 | hAPP(v4, v0) = v1)) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) % 251.71/37.09 | implies: % 251.71/37.09 | (51) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.09 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 251.71/37.09 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 251.71/37.09 | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | ? % 251.71/37.09 | [v5: $i] : (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 % 251.71/37.09 | & $i(v5)))) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_coeff__pCons__0) implies: % 251.71/37.09 | (52) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.09 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.09 | $i] : ( ~ (c_Polynomial_Ocoeff(v3, v4) = v5) | ~ % 251.71/37.09 | (c_Polynomial_OpCons(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 251.71/37.09 | ~ $i(v1) | ~ class_Groups_Ozero(v3) | hAPP(v5, v0) = v2)) % 251.71/37.09 | % 251.71/37.09 | ALPHA: (fact_coeff__1) implies: % 251.71/37.10 | (53) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.10 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.10 | $i] : ! [v6: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v4) = v5) | ~ % 251.71/37.10 | (c_Groups_Oone__class_Oone(v3) = v4) | ~ (tc_Polynomial_Opoly(v2) % 251.71/37.10 | = v3) | ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ~ % 251.71/37.10 | class_Rings_Ocomm__semiring__1(v2) | ? [v7: $i] : ? [v8: $i] : % 251.71/37.10 | (( ~ (v1 = v0) | (v7 = v6 & c_Groups_Oone__class_Oone(v2) = v6 & % 251.71/37.10 | $i(v6))) & (v1 = v0 | (v8 = v6 & % 251.71/37.10 | c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6)))))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_power__strict__mono) implies: % 251.71/37.10 | (54) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.10 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.10 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 251.71/37.10 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9) | % 251.71/37.10 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) % 251.71/37.10 | = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 251.71/37.10 | class_Rings_Olinordered__semidom(v4) | ~ % 251.71/37.10 | c_Orderings_Oord__class_Oless(v4, v3, v2) | ~ % 251.71/37.10 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 251.71/37.10 | c_Orderings_Oord__class_Oless(v4, v7, v9) | ? [v10: $i] : % 251.71/37.10 | (c_Groups_Ozero__class_Ozero(v4) = v10 & $i(v10) & ~ % 251.71/37.10 | c_Orderings_Oord__class_Oless__eq(v4, v10, v3)))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_dvd__power) implies: % 251.71/37.10 | (55) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.10 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.10 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 251.71/37.10 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ % 251.71/37.10 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 251.71/37.10 | v0, v2) | ~ class_Rings_Ocomm__semiring__1(v3) | % 251.71/37.10 | c_Rings_Odvd__class_Odvd(v3, v1, v6)) & ! [v1: $i] : ! [v2: $i] % 251.71/37.10 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 251.71/37.10 | (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v5, v2) = v6) | % 251.71/37.10 | ~ (hAPP(v4, v1) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 251.71/37.10 | class_Rings_Ocomm__semiring__1(v3) | c_Rings_Odvd__class_Odvd(v3, % 251.71/37.10 | v1, v6) | ? [v7: $i] : ( ~ (v7 = v1) & % 251.71/37.10 | c_Groups_Oone__class_Oone(v3) = v7 & $i(v7)))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_one__less__power) implies: % 251.71/37.10 | (56) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.10 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.10 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 251.71/37.10 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ % 251.71/37.10 | $i(v2) | ~ $i(v1) | ~ class_Rings_Olinordered__semidom(v3) | ~ % 251.71/37.10 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v7: $i] : % 251.71/37.10 | (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~ % 251.71/37.10 | c_Orderings_Oord__class_Oless(v3, v7, v2) | % 251.71/37.10 | c_Orderings_Oord__class_Oless(v3, v7, v6))))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_pow__divides__pow__int) implies: % 251.71/37.10 | (57) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Int_Oint) % 251.71/37.10 | = v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & % 251.71/37.10 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 251.71/37.10 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = % 251.71/37.10 | v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 251.71/37.10 | (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) | % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v2))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_pow__divides__eq__int) implies: % 251.71/37.10 | (58) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Int_Oint) % 251.71/37.10 | = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 251.71/37.10 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 251.71/37.10 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = % 251.71/37.10 | v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ % 251.71/37.10 | (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8) | % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2)) & ! [v2: $i] : ! % 251.71/37.10 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 251.71/37.10 | ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = % 251.71/37.10 | v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ % 251.71/37.10 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v3, v2) | % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v6, v8))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_nat__power__less__imp__less) implies: % 251.71/37.10 | (59) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 251.71/37.10 | = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 251.71/37.10 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 251.71/37.10 | [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) % 251.71/37.10 | = v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 251.71/37.10 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 251.71/37.10 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 251.71/37.10 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_pow__divides__pow__nat) implies: % 251.71/37.10 | (60) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 251.71/37.10 | = v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & % 251.71/37.10 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 251.71/37.10 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ (hAPP(v7, v3) = % 251.71/37.10 | v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 251.71/37.10 | (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) | % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v2))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_pow__divides__eq__nat) implies: % 251.71/37.10 | (61) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 251.71/37.10 | = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 251.71/37.10 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 251.71/37.10 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = % 251.71/37.10 | v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ % 251.71/37.10 | (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8) | % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 251.71/37.10 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 251.71/37.10 | ! [v8: $i] : (v4 = v0 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = % 251.71/37.10 | v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ % 251.71/37.10 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v2) | % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v8))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_power__dvd__imp__le) implies: % 251.71/37.10 | (62) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 251.71/37.10 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) % 251.71/37.10 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 251.71/37.10 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 251.71/37.10 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 251.71/37.10 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 251.71/37.10 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | % 251.71/37.10 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2))) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_power__one__right) implies: % 251.71/37.10 | (63) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 251.71/37.10 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 251.71/37.10 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 251.71/37.10 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | % 251.71/37.10 | hAPP(v4, v0) = v1)) % 251.71/37.10 | % 251.71/37.10 | ALPHA: (fact_power__eq__0__iff) implies: % 251.71/37.10 | (64) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.10 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.10 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 251.71/37.10 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ % 251.71/37.10 | $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v3) | ~ % 251.71/37.10 | class_Rings_Ozero__neq__one(v3) | ~ % 251.71/37.10 | class_Rings_Ono__zero__divisors(v3) | ~ % 251.71/37.11 | class_Rings_Omult__zero(v3) | ? [v7: $i] : % 251.71/37.11 | (c_Groups_Ozero__class_Ozero(v3) = v7 & $i(v7) & ( ~ (v7 = v6) | % 251.71/37.11 | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2) | v6 = v2 | v1 = % 251.71/37.11 | v0)))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_power__0) implies: % 251.71/37.11 | (65) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.11 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 251.71/37.11 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 251.71/37.11 | ~ $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] : % 251.71/37.11 | (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & % 251.71/37.11 | $i(v5)))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_power__0__left) implies: % 251.71/37.11 | (66) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.11 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.11 | $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~ % 251.71/37.11 | (c_Power_Opower__class_Opower(v2) = v3) | ~ % 251.71/37.11 | (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | % 251.71/37.11 | ~ (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 251.71/37.11 | class_Power_Opower(v2) | ~ class_Rings_Osemiring__0(v2)) & ! % 251.71/37.11 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 251.71/37.11 | ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ % 251.71/37.11 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | % 251.71/37.11 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ class_Power_Opower(v1) | ~ % 251.71/37.11 | class_Rings_Osemiring__0(v1) | (c_Groups_Oone__class_Oone(v1) = v5 % 251.71/37.11 | & $i(v5)))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_power__eq__imp__eq__base) implies: % 251.71/37.11 | (67) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.11 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.11 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ % 251.71/37.11 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v2) = v7) | % 251.71/37.11 | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v1) % 251.71/37.11 | = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 251.71/37.11 | class_Rings_Olinordered__semidom(v4) | ~ % 251.71/37.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v9: $i] : % 251.71/37.11 | (c_Groups_Ozero__class_Ozero(v4) = v9 & $i(v9) & ( ~ % 251.71/37.11 | c_Orderings_Oord__class_Oless__eq(v4, v9, v3) | ~ % 251.71/37.11 | c_Orderings_Oord__class_Oless__eq(v4, v9, v1))))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_zero__less__Suc) implies: % 251.71/37.11 | (68) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.11 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) % 251.71/37.11 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_dvd__1__left) implies: % 251.71/37.11 | (69) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ? % 251.71/37.11 | [v2: $i] : ( ~ $i(v2) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, % 251.71/37.11 | v2))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_nat__power__eq__Suc__0__iff) implies: % 251.71/37.11 | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 251.71/37.11 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 251.71/37.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 251.71/37.11 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ % 251.71/37.11 | (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & ! % 251.71/37.11 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v1) = % 251.71/37.11 | v5) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3)) & ! [v3: $i] : ! % 251.71/37.11 | [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3) = v2) % 251.71/37.11 | | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_power__Suc__0) implies: % 251.71/37.11 | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 251.71/37.11 | (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 % 251.71/37.11 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 % 251.71/37.11 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : % 251.71/37.11 | (v5 = v2 | ~ (hAPP(v3, v4) = v5) | ~ $i(v4))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_nat_Osimps_I3_J) implies: % 251.71/37.11 | (72) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.11 | & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_less__Suc__eq) implies: % 251.71/37.11 | (73) ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 251.71/37.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_gr0__conv__Suc) implies: % 251.71/37.11 | (74) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.11 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2) % 251.71/37.11 | | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) % 251.71/37.11 | & ! [v1: $i] : ( ~ $i(v1) | ~ % 251.71/37.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v2: $i] : % 251.71/37.11 | (c_Nat_OSuc(v2) = v1 & $i(v2)))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_less__Suc0) implies: % 251.71/37.11 | (75) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 251.71/37.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] : % 251.71/37.11 | (v2 = v0 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 251.71/37.11 | v2, v1))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_less__Suc__eq__0__disj) implies: % 251.71/37.11 | (76) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.11 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 251.71/37.11 | (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~ % 251.71/37.11 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 251.71/37.11 | v4, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & % 251.71/37.11 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ % 251.71/37.11 | (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 251.71/37.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4: $i] : % 251.71/37.11 | (c_Nat_OSuc(v4) = v2 & $i(v4) & % 251.71/37.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1: % 251.71/37.11 | $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 251.71/37.11 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_dvd__1__iff__1) implies: % 251.71/37.11 | (77) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 251.71/37.11 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v1) & ! [v2: $i] : (v2 = % 251.71/37.11 | v1 | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, % 251.71/37.11 | v1))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_one__is__add) implies: % 251.71/37.11 | (78) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.11 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.71/37.11 | [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 251.71/37.11 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ % 251.71/37.11 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = % 251.71/37.11 | v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | % 251.71/37.11 | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 % 251.71/37.11 | = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) % 251.71/37.11 | | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | % 251.71/37.11 | v2 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = % 251.71/37.11 | v1) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : (v2 = v1 | ~ % 251.71/37.11 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: % 251.71/37.11 | $i] : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, % 251.71/37.11 | v1) = v2))) % 251.71/37.11 | % 251.71/37.11 | ALPHA: (fact_nat__one__le__power) implies: % 251.71/37.12 | (79) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.12 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & % 251.71/37.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 251.71/37.12 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 251.71/37.12 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 251.71/37.12 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) % 251.71/37.12 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_mult__eq__1__iff) implies: % 251.71/37.12 | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 251.71/37.12 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 251.71/37.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 251.71/37.12 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ % 251.71/37.12 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 251.71/37.12 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v2 | ~ % 251.71/37.12 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 251.71/37.12 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (hAPP(v3, v2) % 251.71/37.12 | = v4) | ~ (hAPP(v0, v2) = v3))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_One__nat__def) implies: % 251.71/37.12 | (81) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & % 251.71/37.12 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 251.71/37.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_Suc__eq__plus1__left) implies: % 251.71/37.12 | (82) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 251.71/37.12 | ! [v1: $i] : ! [v2: $i] : ( ~ % 251.71/37.12 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ % 251.71/37.12 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_Suc__eq__plus1) implies: % 251.71/37.12 | (83) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 251.71/37.12 | ! [v1: $i] : ! [v2: $i] : ( ~ % 251.71/37.12 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ % 251.71/37.12 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_realpow__two__disj) implies: % 251.71/37.12 | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 251.71/37.12 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 251.71/37.12 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 251.71/37.12 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 251.71/37.12 | (c_Power_Opower__class_Opower(v5) = v6) | ~ (hAPP(v6, v4) = v7) | % 251.71/37.12 | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 251.71/37.12 | class_Rings_Oidom(v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] % 251.71/37.12 | : ((v4 = v3 | (v11 = v4 & c_Groups_Ouminus__class_Ouminus(v5, v3) % 251.71/37.12 | = v4) | ( ~ (v10 = v9) & hAPP(v8, v2) = v10 & hAPP(v7, v2) = % 251.71/37.12 | v9 & $i(v10) & $i(v9))) & ((v10 = v9 & hAPP(v8, v2) = v9 & % 251.71/37.12 | hAPP(v7, v2) = v9 & $i(v9)) | ( ~ (v11 = v4) & ~ (v4 = v3) % 251.71/37.12 | & c_Groups_Ouminus__class_Ouminus(v5, v3) = v11 & % 251.71/37.12 | $i(v11)))))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_n__less__m__mult__n) implies: % 251.71/37.12 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.12 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 251.71/37.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 251.71/37.12 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 251.71/37.12 | (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ % 251.71/37.12 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 251.71/37.12 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 251.71/37.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_n__less__n__mult__m) implies: % 251.71/37.12 | (86) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.12 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 251.71/37.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 251.71/37.12 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 251.71/37.12 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 251.71/37.12 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 251.71/37.12 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 251.71/37.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_one__less__mult) implies: % 251.71/37.12 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.12 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 251.71/37.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 251.71/37.12 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 251.71/37.12 | (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ % 251.71/37.12 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 251.71/37.12 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 251.71/37.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_power_Opower_Opower__0) implies: % 251.71/37.12 | (88) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.12 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.12 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | % 251.71/37.12 | ~ (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.12 | $i(v1) | hAPP(v6, v0) = v3)) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_one__le__mult__iff) implies: % 251.71/37.12 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.12 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 251.71/37.12 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 251.71/37.12 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 251.71/37.12 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 251.71/37.12 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) % 251.71/37.12 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)) & ! % 251.71/37.12 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, % 251.71/37.12 | v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 251.71/37.12 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) | % 251.71/37.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) & ! [v3: % 251.71/37.12 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) % 251.71/37.12 | = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 251.71/37.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) | ~ % 251.71/37.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | % 251.71/37.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_degree__pCons__eq__if) implies: % 251.71/37.12 | (90) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.12 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 251.71/37.12 | $i] : ( ~ (c_Polynomial_Odegree(v3, v4) = v5) | ~ % 251.71/37.12 | (c_Polynomial_OpCons(v3, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | % 251.71/37.12 | ~ $i(v1) | ~ class_Groups_Ozero(v3) | ? [v6: $i] : ? [v7: $i] : % 251.71/37.12 | ? [v8: $i] : ? [v9: $i] : ((v5 = v0 | ( ~ (v7 = v2) & % 251.71/37.12 | tc_Polynomial_Opoly(v3) = v6 & % 251.71/37.12 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6))) & % 251.71/37.12 | ((v9 = v5 & c_Nat_OSuc(v8) = v5 & c_Polynomial_Odegree(v3, v2) = % 251.71/37.12 | v8 & $i(v8) & $i(v5)) | (v7 = v2 & tc_Polynomial_Opoly(v3) = % 251.71/37.12 | v6 & c_Groups_Ozero__class_Ozero(v6) = v2 & $i(v6)))))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_zero__less__power__nat__eq) implies: % 251.71/37.12 | (91) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 251.71/37.12 | = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 251.71/37.12 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 % 251.71/37.12 | = v0 | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) % 251.71/37.12 | | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 251.71/37.12 | v5) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! % 251.71/37.12 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, % 251.71/37.12 | v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 251.71/37.12 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 251.71/37.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] % 251.71/37.12 | : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, % 251.71/37.12 | v2) = v3) | ~ $i(v2) | % 251.71/37.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 251.71/37.12 | % 251.71/37.12 | ALPHA: (fact_nat__lt__two__imp__zero__or__one) implies: % 251.71/37.13 | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 251.71/37.13 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 251.71/37.13 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 251.71/37.13 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_realpow__minus__mult) implies: % 251.71/37.13 | (93) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 251.71/37.13 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 251.71/37.13 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 251.71/37.13 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 251.71/37.13 | [v11: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) % 251.71/37.13 | = v8) | ~ (c_Power_Opower__class_Opower(v4) = v6) | ~ % 251.71/37.13 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = % 251.71/37.13 | v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ % 251.71/37.13 | (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 251.71/37.13 | class_Groups_Omonoid__mult(v4) | ~ % 251.71/37.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3) % 251.71/37.13 | = v11 & $i(v11)))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_mod__Suc) implies: % 251.71/37.13 | (94) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | % 251.71/37.13 | ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~ % 251.71/37.13 | (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? % 251.71/37.13 | [v6: $i] : ( ~ (v6 = v1) & c_Divides_Odiv__class_Omod(tc_Nat_Onat, % 251.71/37.13 | v2, v1) = v5 & c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5))) & ! % 251.71/37.13 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 251.71/37.13 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v1) = v4) | ~ % 251.71/37.13 | (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? % 251.71/37.13 | [v6: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v5 & % 251.71/37.13 | c_Nat_OSuc(v5) = v6 & $i(v6) & $i(v5) & (v6 = v4 | v6 = v1)))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_mod__1) implies: % 251.71/37.13 | (95) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 251.71/37.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.71/37.13 | [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 251.71/37.13 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.71/37.13 | $i(v2))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_mod__eq__0__iff) implies: % 251.71/37.13 | (96) ? [v0: $i] : ? [v1: $i] : % 251.71/37.13 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 251.71/37.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 251.71/37.13 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 251.71/37.13 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = v4) | ~ $i(v3) % 251.71/37.13 | | ~ $i(v2) | ? [v5: $i] : (hAPP(v1, v2) = v5 & $i(v5) & ! [v6: % 251.71/37.13 | $i] : ( ~ (hAPP(v5, v6) = v3) | ~ $i(v6)))) & ! [v2: $i] : % 251.71/37.13 | ! [v3: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v3, v2) = % 251.71/37.13 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 251.71/37.13 | (hAPP(v4, v5) = v3 & hAPP(v1, v2) = v4 & $i(v5) & $i(v4)))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_mod__less__divisor) implies: % 251.71/37.13 | (97) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 251.71/37.13 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) % 251.71/37.13 | | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 251.71/37.13 | v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diffs0__imp__equal) implies: % 251.71/37.13 | (98) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) & % 251.71/37.13 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & % 251.71/37.13 | $i(v3)))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diff__self__eq__0) implies: % 251.71/37.13 | (99) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ % 251.71/37.13 | $i(v1))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_minus__nat_Odiff__0) implies: % 251.71/37.13 | (100) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 251.71/37.13 | $i(v1))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diff__0__eq__0) implies: % 251.71/37.13 | (101) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 251.71/37.13 | $i(v1))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diff__less) implies: % 251.71/37.13 | (102) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1) | ~ % 251.71/37.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 251.71/37.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 251.71/37.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_zero__less__diff) implies: % 251.71/37.13 | (103) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1) | ~ % 251.71/37.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | % 251.71/37.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] % 251.71/37.13 | : ! [v2: $i] : ! [v3: $i] : ( ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1) | ~ % 251.71/37.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 251.71/37.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diff__add__0) implies: % 251.71/37.13 | (104) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 251.71/37.13 | | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | % 251.71/37.13 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diff__is__0__eq_H) implies: % 251.71/37.13 | (105) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1) | ~ % 251.71/37.13 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diff__is__0__eq) implies: % 251.71/37.13 | (106) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.13 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1) | ~ % 251.71/37.13 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & ! [v1: % 251.71/37.13 | $i] : ! [v2: $i] : ( ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v0) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1) | % 251.71/37.13 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diff__Suc__1) implies: % 251.71/37.13 | (107) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 251.71/37.13 | ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 251.71/37.13 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v1)) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_diff__Suc__eq__diff__pred) implies: % 251.71/37.13 | (108) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 251.71/37.13 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ % 251.71/37.13 | $i(v2) | ~ $i(v1) | ? [v5: $i] : % 251.71/37.13 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) = v4 & % 251.71/37.13 | c_Nat_OSuc(v1) = v5 & $i(v5) & $i(v4)))) % 251.71/37.13 | % 251.71/37.13 | ALPHA: (fact_mod__le__divisor) implies: % 251.71/37.14 | (109) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 251.71/37.14 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 251.71/37.14 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v2) = v3) | ~ % 251.71/37.14 | $i(v2) | ~ $i(v1) | ~ % 251.71/37.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 251.71/37.14 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2))) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (arity_Nat__Onat__Rings_Olinordered__semidom) implies: % 251.71/37.14 | (110) class_Rings_Olinordered__semidom(tc_Nat_Onat) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (arity_Nat__Onat__Rings_Ocomm__semiring__1) implies: % 251.71/37.14 | (111) class_Rings_Ocomm__semiring__1(tc_Nat_Onat) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (arity_Nat__Onat__Rings_Ozero__neq__one) implies: % 251.71/37.14 | (112) class_Rings_Ozero__neq__one(tc_Nat_Onat) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (arity_Nat__Onat__Power_Opower) implies: % 251.71/37.14 | (113) class_Power_Opower(tc_Nat_Onat) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (arity_Nat__Onat__Rings_Odvd) implies: % 251.71/37.14 | (114) $i(tc_Nat_Onat) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (conj_0) implies: % 251.71/37.14 | (115) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (tc_Polynomial_Opoly(t_a) = % 251.71/37.14 | v1 & c_Groups_Ozero__class_Ozero(v1) = v2 & $i(v2) & $i(v1) & (v2 = % 251.71/37.14 | v_p | ( ~ (v2 = v0) & % 251.71/37.14 | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, % 251.71/37.14 | v_p, v_h) = v0 & $i(v0)))) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (conj_1) implies: % 251.71/37.14 | (116) $i(v_h) % 251.71/37.14 | (117) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 251.71/37.14 | (c_Polynomial_Osmult(t_a, v_h, v1) = v2 & % 251.71/37.14 | c_Groups_Oplus__class_Oplus(v0, v2, v3) = v4 & % 251.71/37.14 | c_Polynomial_OpCons(t_a, v_a, v1) = v3 & tc_Polynomial_Opoly(t_a) = % 251.71/37.14 | v0 & c_Groups_Ozero__class_Ozero(v0) = v4 & % 251.71/37.14 | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, v_p, % 251.71/37.14 | v_h) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (tfree_0) implies: % 251.71/37.14 | (118) class_Rings_Ocomm__semiring__0(t_a) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (conj_2) implies: % 251.71/37.14 | (119) $i(t_a) % 251.71/37.14 | (120) $i(v_p) % 251.71/37.14 | (121) $i(v_a) % 251.71/37.14 | (122) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (( ~ (v2 = v_p) & % 251.71/37.14 | tc_Polynomial_Opoly(t_a) = v1 & c_Groups_Ozero__class_Ozero(v1) = % 251.71/37.14 | v2 & $i(v2) & $i(v1)) | ( ~ (v0 = v_a) & % 251.71/37.14 | c_Groups_Ozero__class_Ozero(t_a) = v0 & $i(v0))) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (function-axioms) implies: % 251.71/37.14 | (123) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 251.71/37.14 | (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 251.71/37.14 | (c_Groups_Ozero__class_Ozero(v2) = v0)) % 251.71/37.14 | (124) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 251.71/37.14 | (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0)) % 251.71/37.14 | (125) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 251.71/37.14 | (c_Groups_Oone__class_Oone(v2) = v1) | ~ % 251.71/37.14 | (c_Groups_Oone__class_Oone(v2) = v0)) % 251.71/37.14 | (126) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 251.71/37.14 | (c_Power_Opower__class_Opower(v2) = v1) | ~ % 251.71/37.14 | (c_Power_Opower__class_Opower(v2) = v0)) % 251.71/37.14 | (127) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 251.71/37.14 | (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0)) % 251.71/37.14 | (128) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 251.71/37.14 | (v1 = v0 | ~ % 251.71/37.14 | (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v4, v3, % 251.71/37.14 | v2) = v1) | ~ % 251.71/37.14 | (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v4, v3, % 251.71/37.14 | v2) = v0)) % 251.71/37.14 | (129) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 251.71/37.14 | (v1 = v0 | ~ (c_Polynomial_OpCons(v4, v3, v2) = v1) | ~ % 251.71/37.14 | (c_Polynomial_OpCons(v4, v3, v2) = v0)) % 251.71/37.14 | % 251.71/37.14 | DELTA: instantiating (72) with fresh symbol all_817_0 gives: % 251.71/37.14 | (130) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_817_0 & $i(all_817_0) % 251.71/37.14 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_817_0) | ~ $i(v0)) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (130) implies: % 251.71/37.14 | (131) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_817_0 % 251.71/37.14 | % 251.71/37.14 | DELTA: instantiating (72) with fresh symbol all_820_0 gives: % 251.71/37.14 | (132) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_820_0 & $i(all_820_0) % 251.71/37.14 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_820_0) | ~ $i(v0)) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (132) implies: % 251.71/37.14 | (133) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_820_0 % 251.71/37.14 | % 251.71/37.14 | DELTA: instantiating (72) with fresh symbol all_823_0 gives: % 251.71/37.14 | (134) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_823_0 & $i(all_823_0) % 251.71/37.14 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_823_0) | ~ $i(v0)) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (134) implies: % 251.71/37.14 | (135) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_823_0 % 251.71/37.14 | % 251.71/37.14 | DELTA: instantiating (26) with fresh symbol all_829_0 gives: % 251.71/37.14 | (136) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_829_0 & $i(all_829_0) % 251.71/37.14 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 251.71/37.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_829_0)) % 251.71/37.14 | % 251.71/37.14 | ALPHA: (136) implies: % 251.71/37.14 | (137) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_829_0 % 251.71/37.14 | % 251.71/37.14 | DELTA: instantiating (72) with fresh symbol all_832_0 gives: % 251.71/37.15 | (138) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_832_0 & $i(all_832_0) % 251.71/37.15 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_832_0) | ~ $i(v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (138) implies: % 251.71/37.15 | (139) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_832_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (26) with fresh symbol all_837_0 gives: % 251.71/37.15 | (140) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_837_0 & $i(all_837_0) % 251.71/37.15 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 251.71/37.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_837_0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (140) implies: % 251.71/37.15 | (141) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_837_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (46) with fresh symbol all_840_0 gives: % 251.71/37.15 | (142) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_840_0 & $i(all_840_0) % 251.71/37.15 | & ? [v0: $i] : ( ~ $i(v0) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 251.71/37.15 | v0, all_840_0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (142) implies: % 251.71/37.15 | (143) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_840_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (72) with fresh symbol all_842_0 gives: % 251.71/37.15 | (144) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_842_0 & $i(all_842_0) % 251.71/37.15 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_842_0) | ~ $i(v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (144) implies: % 251.71/37.15 | (145) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_842_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (26) with fresh symbol all_845_0 gives: % 251.71/37.15 | (146) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_845_0 & $i(all_845_0) % 251.71/37.15 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 251.71/37.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_845_0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (146) implies: % 251.71/37.15 | (147) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_845_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (24) with fresh symbol all_853_0 gives: % 251.71/37.15 | (148) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_853_0 & $i(all_853_0) % 251.71/37.15 | & ? [v0: $i] : ( ~ $i(v0) | % 251.71/37.15 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_853_0, v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (148) implies: % 251.71/37.15 | (149) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_853_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (26) with fresh symbol all_857_0 gives: % 251.71/37.15 | (150) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_857_0 & $i(all_857_0) % 251.71/37.15 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 251.71/37.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_857_0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (150) implies: % 251.71/37.15 | (151) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_857_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (24) with fresh symbol all_860_0 gives: % 251.71/37.15 | (152) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_860_0 & $i(all_860_0) % 251.71/37.15 | & ? [v0: $i] : ( ~ $i(v0) | % 251.71/37.15 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_860_0, v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (152) implies: % 251.71/37.15 | (153) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_860_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (72) with fresh symbol all_862_0 gives: % 251.71/37.15 | (154) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_862_0 & $i(all_862_0) % 251.71/37.15 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_862_0) | ~ $i(v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (154) implies: % 251.71/37.15 | (155) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_862_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (40) with fresh symbol all_865_0 gives: % 251.71/37.15 | (156) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_865_0 & $i(all_865_0) & % 251.71/37.15 | ? [v0: $i] : ( ~ $i(v0) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 251.71/37.15 | all_865_0, v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (156) implies: % 251.71/37.15 | (157) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_865_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (101) with fresh symbol all_867_0 gives: % 251.71/37.15 | (158) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_867_0 & $i(all_867_0) % 251.71/37.15 | & ! [v0: $i] : ! [v1: int] : (v1 = all_867_0 | ~ % 251.71/37.15 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, all_867_0, v0) = v1) | % 251.71/37.15 | ~ $i(v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (158) implies: % 251.71/37.15 | (159) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_867_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (81) with fresh symbols all_870_0, all_870_1 gives: % 251.71/37.15 | (160) c_Nat_OSuc(all_870_0) = all_870_1 & % 251.71/37.15 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_870_1 & % 251.71/37.15 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_870_0 & $i(all_870_0) % 251.71/37.15 | & $i(all_870_1) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (160) implies: % 251.71/37.15 | (161) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_870_0 % 251.71/37.15 | (162) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_870_1 % 251.71/37.15 | (163) c_Nat_OSuc(all_870_0) = all_870_1 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (100) with fresh symbol all_875_0 gives: % 251.71/37.15 | (164) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_875_0 & $i(all_875_0) % 251.71/37.15 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 251.71/37.15 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_875_0) = v1) | % 251.71/37.15 | ~ $i(v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (164) implies: % 251.71/37.15 | (165) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_875_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (107) with fresh symbol all_890_0 gives: % 251.71/37.15 | (166) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_890_0 & $i(all_890_0) & % 251.71/37.15 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 251.71/37.15 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_890_0) = v0) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (166) implies: % 251.71/37.15 | (167) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_890_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (16) with fresh symbol all_893_0 gives: % 251.71/37.15 | (168) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_893_0 & $i(all_893_0) % 251.71/37.15 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 251.71/37.15 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_893_0) = v1) | ~ % 251.71/37.15 | $i(v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (168) implies: % 251.71/37.15 | (169) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_893_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (68) with fresh symbol all_902_0 gives: % 251.71/37.15 | (170) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_902_0 & $i(all_902_0) % 251.71/37.15 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 251.71/37.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_902_0, v1)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (170) implies: % 251.71/37.15 | (171) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_902_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (99) with fresh symbol all_905_0 gives: % 251.71/37.15 | (172) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_905_0 & $i(all_905_0) % 251.71/37.15 | & ! [v0: $i] : ! [v1: int] : (v1 = all_905_0 | ~ % 251.71/37.15 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v0) = v1) | ~ % 251.71/37.15 | $i(v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (172) implies: % 251.71/37.15 | (173) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_905_0 % 251.71/37.15 | % 251.71/37.15 | DELTA: instantiating (19) with fresh symbol all_908_0 gives: % 251.71/37.15 | (174) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_908_0 & $i(all_908_0) % 251.71/37.15 | & ? [v0: any] : (v0 = all_908_0 | ~ $i(v0) | % 251.71/37.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_908_0, v0)) % 251.71/37.15 | % 251.71/37.15 | ALPHA: (174) implies: % 251.71/37.16 | (175) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_908_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (15) with fresh symbol all_917_0 gives: % 251.71/37.16 | (176) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_917_0 & $i(all_917_0) % 251.71/37.16 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 251.71/37.16 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_917_0, v0) = v1) | ~ % 251.71/37.16 | $i(v0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (176) implies: % 251.71/37.16 | (177) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_917_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (39) with fresh symbol all_927_0 gives: % 251.71/37.16 | (178) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_927_0 & $i(all_927_0) & % 251.71/37.16 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_927_0, all_927_0) & ! [v0: % 251.71/37.16 | any] : (v0 = all_927_0 | ~ $i(v0) | ~ % 251.71/37.16 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_927_0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (178) implies: % 251.71/37.16 | (179) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_927_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (83) with fresh symbol all_933_0 gives: % 251.71/37.16 | (180) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_933_0 & $i(all_933_0) & % 251.71/37.16 | ! [v0: $i] : ! [v1: $i] : ( ~ % 251.71/37.16 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_933_0) = v1) | ~ % 251.71/37.16 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1))) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (180) implies: % 251.71/37.16 | (181) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_933_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (69) with fresh symbols all_936_0, all_936_1 gives: % 251.71/37.16 | (182) c_Nat_OSuc(all_936_1) = all_936_0 & % 251.71/37.16 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_936_1 & $i(all_936_0) % 251.71/37.16 | & $i(all_936_1) & ? [v0: $i] : ( ~ $i(v0) | % 251.71/37.16 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_936_0, v0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (182) implies: % 251.71/37.16 | (183) $i(all_936_0) % 251.71/37.16 | (184) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_936_1 % 251.71/37.16 | (185) c_Nat_OSuc(all_936_1) = all_936_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (18) with fresh symbol all_944_0 gives: % 251.71/37.16 | (186) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_944_0 & $i(all_944_0) % 251.71/37.16 | & ! [v0: any] : ! [v1: $i] : (v0 = all_944_0 | ~ % 251.71/37.16 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v1) | ~ $i(v1) % 251.71/37.16 | | ~ $i(v0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (186) implies: % 251.71/37.16 | (187) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_944_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (82) with fresh symbol all_954_0 gives: % 251.71/37.16 | (188) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_954_0 & $i(all_954_0) & % 251.71/37.16 | ! [v0: $i] : ! [v1: $i] : ( ~ % 251.71/37.16 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_954_0, v0) = v1) | ~ % 251.71/37.16 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1))) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (188) implies: % 251.71/37.16 | (189) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_954_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (25) with fresh symbol all_957_0 gives: % 251.71/37.16 | (190) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_957_0 & $i(all_957_0) % 251.71/37.16 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_957_0, all_957_0) % 251.71/37.16 | & ? [v0: any] : (v0 = all_957_0 | ~ $i(v0) | % 251.71/37.16 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_957_0, v0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (190) implies: % 251.71/37.16 | (191) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_957_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (22) with fresh symbol all_959_0 gives: % 251.71/37.16 | (192) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_959_0 & $i(all_959_0) % 251.71/37.16 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_959_0, % 251.71/37.16 | all_959_0) & ! [v0: any] : (v0 = all_959_0 | ~ $i(v0) | ~ % 251.71/37.16 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, all_959_0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (192) implies: % 251.71/37.16 | (193) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_959_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (42) with fresh symbols all_979_0, all_979_1 gives: % 251.71/37.16 | (194) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_979_0 & % 251.71/37.16 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_979_1 & % 251.71/37.16 | $i(all_979_0) & $i(all_979_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 251.71/37.16 | (hAPP(all_979_1, v0) = v1) | ~ $i(v0) | hAPP(v1, all_979_0) = v0) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (194) implies: % 251.71/37.16 | (195) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_979_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (97) with fresh symbol all_982_0 gives: % 251.71/37.16 | (196) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_982_0 & $i(all_982_0) % 251.71/37.16 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 251.71/37.16 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) % 251.71/37.16 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 251.71/37.16 | all_982_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, % 251.71/37.16 | v1)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (196) implies: % 251.71/37.16 | (197) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_982_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (95) with fresh symbols all_985_0, all_985_1 gives: % 251.71/37.16 | (198) c_Nat_OSuc(all_985_1) = all_985_0 & % 251.71/37.16 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_985_1 & $i(all_985_0) % 251.71/37.16 | & $i(all_985_1) & ! [v0: $i] : ! [v1: int] : (v1 = all_985_1 | ~ % 251.71/37.16 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, all_985_0) = v1) | ~ % 251.71/37.16 | $i(v0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (198) implies: % 251.71/37.16 | (199) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_985_1 % 251.71/37.16 | (200) c_Nat_OSuc(all_985_1) = all_985_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (105) with fresh symbol all_996_0 gives: % 251.71/37.16 | (201) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_996_0 & $i(all_996_0) % 251.71/37.16 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_996_0 | ~ % 251.71/37.16 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 251.71/37.16 | $i(v1) | ~ $i(v0) | ~ % 251.71/37.16 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (201) implies: % 251.71/37.16 | (202) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_996_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (12) with fresh symbols all_999_0, all_999_1 gives: % 251.71/37.16 | (203) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_999_1 & % 251.71/37.16 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_999_0 & $i(all_999_0) % 251.71/37.16 | & $i(all_999_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_999_1, % 251.71/37.16 | v0) = v1) | ~ $i(v0) | hAPP(v1, all_999_0) = all_999_0) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (203) implies: % 251.71/37.16 | (204) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_999_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (20) with fresh symbol all_1008_0 gives: % 251.71/37.16 | (205) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1008_0 & % 251.71/37.16 | $i(all_1008_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 251.71/37.16 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1008_0, v0) | ~ % 251.71/37.16 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) | % 251.71/37.16 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (205) implies: % 251.71/37.16 | (206) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1008_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (36) with fresh symbol all_1016_0 gives: % 251.71/37.16 | (207) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1016_0 & % 251.71/37.16 | $i(all_1016_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 251.71/37.16 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1016_0, v1) | ~ % 251.71/37.16 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v1) | % 251.71/37.16 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1016_0, v0)) % 251.71/37.16 | % 251.71/37.16 | ALPHA: (207) implies: % 251.71/37.16 | (208) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1016_0 % 251.71/37.16 | % 251.71/37.16 | DELTA: instantiating (104) with fresh symbol all_1019_0 gives: % 251.71/37.17 | (209) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1019_0 & % 251.71/37.17 | $i(all_1019_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 251.71/37.17 | int] : (v3 = all_1019_0 | ~ % 251.71/37.17 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 251.71/37.17 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 251.71/37.17 | | ~ $i(v0)) % 251.71/37.17 | % 251.71/37.17 | ALPHA: (209) implies: % 251.71/37.17 | (210) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1019_0 % 251.71/37.17 | % 251.71/37.17 | DELTA: instantiating (21) with fresh symbol all_1022_0 gives: % 252.03/37.17 | (211) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1022_0 & % 252.03/37.17 | $i(all_1022_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 252.03/37.17 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~ % 252.03/37.17 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1022_0, v1) | ~ % 252.03/37.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v1)) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (211) implies: % 252.03/37.17 | (212) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1022_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (109) with fresh symbol all_1025_0 gives: % 252.03/37.17 | (213) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1025_0 & % 252.03/37.17 | $i(all_1025_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 252.03/37.17 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) % 252.03/37.17 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.03/37.17 | all_1025_0, v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 252.03/37.17 | v2, v1)) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (213) implies: % 252.03/37.17 | (214) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1025_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (63) with fresh symbol all_1040_0 gives: % 252.03/37.17 | (215) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1040_0 & $i(all_1040_0) % 252.03/37.17 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 252.03/37.17 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 252.03/37.17 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Omonoid__mult(v1) | hAPP(v3, % 252.03/37.17 | all_1040_0) = v0) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (215) implies: % 252.03/37.17 | (216) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1040_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (50) with fresh symbol all_1043_0 gives: % 252.03/37.17 | (217) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1043_0 & $i(all_1043_0) % 252.03/37.17 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 252.03/37.17 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 252.03/37.17 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | % 252.03/37.17 | hAPP(v3, all_1043_0) = v0) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (217) implies: % 252.03/37.17 | (218) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1043_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (102) with fresh symbol all_1046_0 gives: % 252.03/37.17 | (219) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1046_0 & % 252.03/37.17 | $i(all_1046_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 252.03/37.17 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 252.03/37.17 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.03/37.17 | all_1046_0, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.03/37.17 | all_1046_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, % 252.03/37.17 | v0)) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (219) implies: % 252.03/37.17 | (220) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1046_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (7) with fresh symbol all_1049_0 gives: % 252.03/37.17 | (221) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1049_0 & % 252.03/37.17 | $i(all_1049_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.03/37.17 | int] : (v3 = all_1049_0 | ~ (c_Polynomial_Odegree(v0, v2) = v3) | % 252.03/37.17 | ~ (tc_Polynomial_Opoly(v0) = v1) | ~ % 252.03/37.17 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ $i(v0) | ~ % 252.03/37.17 | class_Groups_Ozero(v0)) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (221) implies: % 252.03/37.17 | (222) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1049_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (75) with fresh symbols all_1054_0, all_1054_1 gives: % 252.03/37.17 | (223) c_Nat_OSuc(all_1054_1) = all_1054_0 & % 252.03/37.17 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1054_1 & % 252.03/37.17 | $i(all_1054_0) & $i(all_1054_1) & % 252.03/37.17 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1054_1, all_1054_0) & % 252.03/37.17 | ! [v0: any] : (v0 = all_1054_1 | ~ $i(v0) | ~ % 252.03/37.17 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1054_0)) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (223) implies: % 252.03/37.17 | (224) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1054_1 % 252.03/37.17 | (225) c_Nat_OSuc(all_1054_1) = all_1054_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (5) with fresh symbol all_1063_0 gives: % 252.03/37.17 | (226) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1063_0 & % 252.03/37.17 | $i(all_1063_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.03/37.17 | int] : (v3 = all_1063_0 | ~ (c_Polynomial_Odegree(v0, v2) = v3) | % 252.03/37.17 | ~ (c_Groups_Oone__class_Oone(v1) = v2) | ~ % 252.03/37.17 | (tc_Polynomial_Opoly(v0) = v1) | ~ $i(v0) | ~ % 252.03/37.17 | class_Rings_Ocomm__semiring__1(v0)) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (226) implies: % 252.03/37.17 | (227) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1063_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (77) with fresh symbols all_1066_0, all_1066_1 gives: % 252.03/37.17 | (228) c_Nat_OSuc(all_1066_1) = all_1066_0 & % 252.03/37.17 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1066_1 & % 252.03/37.17 | $i(all_1066_0) & $i(all_1066_1) & % 252.03/37.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_1066_0, all_1066_0) & ! % 252.03/37.17 | [v0: any] : (v0 = all_1066_0 | ~ $i(v0) | ~ % 252.03/37.17 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_1066_0)) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (228) implies: % 252.03/37.17 | (229) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1066_1 % 252.03/37.17 | (230) c_Nat_OSuc(all_1066_1) = all_1066_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (115) with fresh symbols all_1072_0, all_1072_1, % 252.03/37.17 | all_1072_2 gives: % 252.03/37.17 | (231) tc_Polynomial_Opoly(t_a) = all_1072_1 & % 252.03/37.17 | c_Groups_Ozero__class_Ozero(all_1072_1) = all_1072_0 & $i(all_1072_0) % 252.03/37.17 | & $i(all_1072_1) & (all_1072_0 = v_p | ( ~ (all_1072_0 = all_1072_2) % 252.03/37.17 | & c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, % 252.03/37.17 | v_p, v_h) = all_1072_2 & $i(all_1072_2))) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (231) implies: % 252.03/37.17 | (232) c_Groups_Ozero__class_Ozero(all_1072_1) = all_1072_0 % 252.03/37.17 | (233) tc_Polynomial_Opoly(t_a) = all_1072_1 % 252.03/37.17 | (234) all_1072_0 = v_p | ( ~ (all_1072_0 = all_1072_2) & % 252.03/37.17 | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, v_p, % 252.03/37.17 | v_h) = all_1072_2 & $i(all_1072_2)) % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (122) with fresh symbols all_1077_0, all_1077_1, % 252.03/37.17 | all_1077_2 gives: % 252.03/37.17 | (235) ( ~ (all_1077_0 = v_p) & tc_Polynomial_Opoly(t_a) = all_1077_1 & % 252.03/37.17 | c_Groups_Ozero__class_Ozero(all_1077_1) = all_1077_0 & % 252.03/37.17 | $i(all_1077_0) & $i(all_1077_1)) | ( ~ (all_1077_2 = v_a) & % 252.03/37.17 | c_Groups_Ozero__class_Ozero(t_a) = all_1077_2 & $i(all_1077_2)) % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (44) with fresh symbols all_1078_0, all_1078_1, % 252.03/37.17 | all_1078_2 gives: % 252.03/37.17 | (236) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1078_1 & % 252.03/37.17 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1078_2 & % 252.03/37.17 | hAPP(all_1078_2, all_1078_1) = all_1078_0 & $i(all_1078_0) & % 252.03/37.17 | $i(all_1078_1) & $i(all_1078_2) & ! [v0: $i] : ! [v1: $i] : (v1 = % 252.03/37.17 | v0 | ~ (hAPP(all_1078_0, v0) = v1) | ~ $i(v0)) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (236) implies: % 252.03/37.17 | (237) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1078_1 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (98) with fresh symbol all_1084_0 gives: % 252.03/37.17 | (238) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1084_0 & % 252.03/37.17 | $i(all_1084_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 252.03/37.17 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = all_1084_0) | % 252.03/37.17 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = all_1084_0) & % 252.03/37.17 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2 & % 252.03/37.17 | $i(v2))) % 252.03/37.17 | % 252.03/37.17 | ALPHA: (238) implies: % 252.03/37.17 | (239) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1084_0 % 252.03/37.17 | % 252.03/37.17 | DELTA: instantiating (11) with fresh symbols all_1091_0, all_1091_1, % 252.08/37.17 | all_1091_2 gives: % 252.08/37.17 | (240) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1091_2 & % 252.08/37.17 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1091_1 & % 252.08/37.17 | hAPP(all_1091_2, all_1091_1) = all_1091_0 & $i(all_1091_0) & % 252.08/37.17 | $i(all_1091_1) & $i(all_1091_2) & ! [v0: $i] : ! [v1: int] : (v1 = % 252.08/37.17 | all_1091_1 | ~ (hAPP(all_1091_0, v0) = v1) | ~ $i(v0)) % 252.08/37.17 | % 252.08/37.17 | ALPHA: (240) implies: % 252.08/37.17 | (241) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1091_1 % 252.08/37.17 | % 252.08/37.17 | DELTA: instantiating (52) with fresh symbol all_1094_0 gives: % 252.08/37.18 | (242) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1094_0 & % 252.08/37.18 | $i(all_1094_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.18 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v3) = v4) | ~ % 252.08/37.18 | (c_Polynomial_OpCons(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 252.08/37.18 | $i(v0) | ~ class_Groups_Ozero(v2) | hAPP(v4, all_1094_0) = v1) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (242) implies: % 252.08/37.18 | (243) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1094_0 % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (88) with fresh symbol all_1097_0 gives: % 252.08/37.18 | (244) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1097_0 & % 252.08/37.18 | $i(all_1097_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.18 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower_Opower(v3, % 252.08/37.18 | v2, v1) = v4) | ~ (hAPP(v4, v0) = v5) | ~ $i(v3) | ~ $i(v2) % 252.08/37.18 | | ~ $i(v1) | ~ $i(v0) | hAPP(v5, all_1097_0) = v2) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (244) implies: % 252.08/37.18 | (245) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1097_0 % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (65) with fresh symbol all_1102_0 gives: % 252.08/37.18 | (246) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1102_0 & % 252.08/37.18 | $i(all_1102_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.18 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, % 252.08/37.18 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ class_Power_Opower(v1) | % 252.08/37.18 | ? [v4: $i] : (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, % 252.08/37.18 | all_1102_0) = v4 & $i(v4))) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (246) implies: % 252.08/37.18 | (247) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1102_0 % 252.08/37.18 | (248) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 252.08/37.18 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 252.08/37.18 | ~ $i(v1) | ~ $i(v0) | ~ class_Power_Opower(v1) | ? [v4: $i] : % 252.08/37.18 | (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, all_1102_0) = v4 & % 252.08/37.18 | $i(v4))) % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (51) with fresh symbol all_1113_0 gives: % 252.08/37.18 | (249) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1113_0 & % 252.08/37.18 | $i(all_1113_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.18 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, % 252.08/37.18 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.18 | class_Rings_Ocomm__semiring__1(v1) | ? [v4: $i] : % 252.08/37.18 | (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, all_1113_0) = v4 & % 252.08/37.18 | $i(v4))) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (249) implies: % 252.08/37.18 | (250) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1113_0 % 252.08/37.18 | (251) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 252.08/37.18 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 252.08/37.18 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | ? % 252.08/37.18 | [v4: $i] : (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, % 252.08/37.18 | all_1113_0) = v4 & $i(v4))) % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (9) with fresh symbol all_1119_0 gives: % 252.08/37.18 | (252) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1119_0 & % 252.08/37.18 | $i(all_1119_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.18 | $i] : ! [v4: $i] : ! [v5: int] : (v5 = all_1119_0 | ~ % 252.08/37.18 | (c_Polynomial_Odegree(v1, v4) = v5) | ~ (c_Polynomial_OpCons(v1, % 252.08/37.18 | v0, v3) = v4) | ~ (tc_Polynomial_Opoly(v1) = v2) | ~ % 252.08/37.18 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.18 | class_Groups_Ozero(v1)) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (252) implies: % 252.08/37.18 | (253) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1119_0 % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (74) with fresh symbol all_1122_0 gives: % 252.08/37.18 | (254) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1122_0 & % 252.08/37.18 | $i(all_1122_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = % 252.08/37.18 | v0) | ~ $i(v1) | ~ $i(v0) | % 252.08/37.18 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1122_0, v0)) & ! % 252.08/37.18 | [v0: $i] : ( ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.08/37.18 | all_1122_0, v0) | ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & $i(v1))) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (254) implies: % 252.08/37.18 | (255) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1122_0 % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (92) with fresh symbols all_1125_0, all_1125_1, % 252.08/37.18 | all_1125_2 gives: % 252.08/37.18 | (256) c_Nat_OSuc(all_1125_1) = all_1125_0 & c_Nat_OSuc(all_1125_2) = % 252.08/37.18 | all_1125_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1125_2 & % 252.08/37.18 | $i(all_1125_0) & $i(all_1125_1) & $i(all_1125_2) & ! [v0: any] : (v0 % 252.08/37.18 | = all_1125_1 | v0 = all_1125_2 | ~ $i(v0) | ~ % 252.08/37.18 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1125_0)) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (256) implies: % 252.08/37.18 | (257) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1125_2 % 252.08/37.18 | (258) c_Nat_OSuc(all_1125_2) = all_1125_1 % 252.08/37.18 | (259) c_Nat_OSuc(all_1125_1) = all_1125_0 % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (2) with fresh symbol all_1134_0 gives: % 252.08/37.18 | (260) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1134_0 & % 252.08/37.18 | $i(all_1134_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.18 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_OpCons(v1, v0, v3) = v4) | ~ % 252.08/37.18 | (tc_Polynomial_Opoly(v1) = v2) | ~ % 252.08/37.18 | (c_Groups_Ozero__class_Ozero(v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.18 | class_Groups_Ozero(v1) | (c_Polynomial_Omonom(v1, v0, all_1134_0) = % 252.08/37.18 | v4 & $i(v4))) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (260) implies: % 252.08/37.18 | (261) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1134_0 % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (108) with fresh symbol all_1137_0 gives: % 252.08/37.18 | (262) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1137_0 & $i(all_1137_0) % 252.08/37.18 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 252.08/37.18 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ % 252.08/37.18 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1137_0) = v2) | % 252.08/37.18 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 252.08/37.18 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v4) = v3 & % 252.08/37.18 | c_Nat_OSuc(v0) = v4 & $i(v4) & $i(v3))) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (262) implies: % 252.08/37.18 | (263) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1137_0 % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (71) with fresh symbols all_1157_0, all_1157_1, % 252.08/37.18 | all_1157_2, all_1157_3 gives: % 252.08/37.18 | (264) c_Nat_OSuc(all_1157_2) = all_1157_1 & % 252.08/37.18 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1157_3 & % 252.08/37.18 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1157_2 & % 252.08/37.18 | hAPP(all_1157_3, all_1157_1) = all_1157_0 & $i(all_1157_0) & % 252.08/37.18 | $i(all_1157_1) & $i(all_1157_2) & $i(all_1157_3) & ! [v0: $i] : ! % 252.08/37.18 | [v1: int] : (v1 = all_1157_1 | ~ (hAPP(all_1157_0, v0) = v1) | ~ % 252.08/37.18 | $i(v0)) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (264) implies: % 252.08/37.18 | (265) hAPP(all_1157_3, all_1157_1) = all_1157_0 % 252.08/37.18 | (266) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1157_2 % 252.08/37.18 | (267) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1157_3 % 252.08/37.18 | (268) c_Nat_OSuc(all_1157_2) = all_1157_1 % 252.08/37.18 | % 252.08/37.18 | DELTA: instantiating (117) with fresh symbols all_1160_0, all_1160_1, % 252.08/37.18 | all_1160_2, all_1160_3, all_1160_4 gives: % 252.08/37.18 | (269) c_Polynomial_Osmult(t_a, v_h, all_1160_3) = all_1160_2 & % 252.08/37.18 | c_Groups_Oplus__class_Oplus(all_1160_4, all_1160_2, all_1160_1) = % 252.08/37.18 | all_1160_0 & c_Polynomial_OpCons(t_a, v_a, all_1160_3) = all_1160_1 & % 252.08/37.18 | tc_Polynomial_Opoly(t_a) = all_1160_4 & % 252.08/37.18 | c_Groups_Ozero__class_Ozero(all_1160_4) = all_1160_0 & % 252.08/37.18 | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, v_p, % 252.08/37.18 | v_h) = all_1160_3 & $i(all_1160_0) & $i(all_1160_1) & % 252.08/37.18 | $i(all_1160_2) & $i(all_1160_3) & $i(all_1160_4) % 252.08/37.18 | % 252.08/37.18 | ALPHA: (269) implies: % 252.08/37.19 | (270) $i(all_1160_3) % 252.08/37.19 | (271) c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, v_p, % 252.08/37.19 | v_h) = all_1160_3 % 252.08/37.19 | (272) c_Groups_Ozero__class_Ozero(all_1160_4) = all_1160_0 % 252.08/37.19 | (273) tc_Polynomial_Opoly(t_a) = all_1160_4 % 252.08/37.19 | (274) c_Polynomial_OpCons(t_a, v_a, all_1160_3) = all_1160_1 % 252.08/37.19 | (275) c_Groups_Oplus__class_Oplus(all_1160_4, all_1160_2, all_1160_1) = % 252.08/37.19 | all_1160_0 % 252.08/37.19 | (276) c_Polynomial_Osmult(t_a, v_h, all_1160_3) = all_1160_2 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (106) with fresh symbol all_1168_0 gives: % 252.08/37.19 | (277) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1168_0 & % 252.08/37.19 | $i(all_1168_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 252.08/37.19 | all_1168_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) % 252.08/37.19 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: % 252.08/37.19 | $i] : ! [v1: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 252.08/37.19 | v1, v0) = all_1168_0) | ~ $i(v1) | ~ $i(v0) | % 252.08/37.19 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (277) implies: % 252.08/37.19 | (278) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1168_0 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (6) with fresh symbols all_1171_0, all_1171_1, all_1171_2 % 252.08/37.19 | gives: % 252.08/37.19 | (279) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1171_1 & % 252.08/37.19 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1171_2 & % 252.08/37.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1171_0 & % 252.08/37.19 | $i(all_1171_0) & $i(all_1171_1) & $i(all_1171_2) & ! [v0: any] : ! % 252.08/37.19 | [v1: any] : ! [v2: $i] : (v1 = all_1171_0 | v0 = all_1171_1 | ~ % 252.08/37.19 | (hAPP(v2, v0) = v1) | ~ (hAPP(all_1171_2, v1) = v2) | ~ $i(v1) | % 252.08/37.19 | ~ $i(v0)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (279) implies: % 252.08/37.19 | (280) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1171_0 % 252.08/37.19 | (281) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1171_1 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (17) with fresh symbol all_1174_0 gives: % 252.08/37.19 | (282) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1174_0 & % 252.08/37.19 | $i(all_1174_0) & ! [v0: $i] : ! [v1: any] : (v1 = all_1174_0 | ~ % 252.08/37.19 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1174_0) | % 252.08/37.19 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 252.08/37.19 | all_1174_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = % 252.08/37.19 | all_1174_0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = % 252.08/37.19 | all_1174_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 252.08/37.19 | all_1174_0, all_1174_0) = v0)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (282) implies: % 252.08/37.19 | (283) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1174_0 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (103) with fresh symbol all_1183_0 gives: % 252.08/37.19 | (284) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1183_0 & % 252.08/37.19 | $i(all_1183_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 252.08/37.19 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 252.08/37.19 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.08/37.19 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1183_0, % 252.08/37.19 | v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 252.08/37.19 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 252.08/37.19 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.08/37.19 | all_1183_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 252.08/37.19 | v1)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (284) implies: % 252.08/37.19 | (285) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1183_0 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (48) with fresh symbols all_1186_0, all_1186_1 gives: % 252.08/37.19 | (286) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1186_0 & % 252.08/37.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_1 & % 252.08/37.19 | $i(all_1186_0) & $i(all_1186_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.08/37.19 | $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (hAPP(v3, v1) = v4) % 252.08/37.19 | | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1186_0, v2) = v3) | ~ % 252.08/37.19 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1186_1, v2)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (286) implies: % 252.08/37.19 | (287) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_1 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (79) with fresh symbols all_1189_0, all_1189_1, % 252.08/37.19 | all_1189_2 gives: % 252.08/37.19 | (288) c_Nat_OSuc(all_1189_2) = all_1189_1 & % 252.08/37.19 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1189_0 & % 252.08/37.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1189_2 & % 252.08/37.19 | $i(all_1189_0) & $i(all_1189_1) & $i(all_1189_2) & ! [v0: $i] : ! % 252.08/37.19 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ % 252.08/37.19 | (hAPP(all_1189_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1189_1, v1) | % 252.08/37.19 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1189_1, v3)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (288) implies: % 252.08/37.19 | (289) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1189_2 % 252.08/37.19 | (290) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1189_0 % 252.08/37.19 | (291) c_Nat_OSuc(all_1189_2) = all_1189_1 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (62) with fresh symbols all_1209_0, all_1209_1 gives: % 252.08/37.19 | (292) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1209_1 & % 252.08/37.19 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1209_0 & $i(all_1209_0) % 252.08/37.19 | & $i(all_1209_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.19 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ % 252.08/37.19 | (hAPP(v3, v0) = v5) | ~ (hAPP(all_1209_1, v2) = v3) | ~ $i(v2) | % 252.08/37.19 | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1209_0, v2) | ~ % 252.08/37.19 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) | % 252.08/37.19 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (292) implies: % 252.08/37.19 | (293) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1209_0 % 252.08/37.19 | (294) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1209_1 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (87) with fresh symbols all_1212_0, all_1212_1, % 252.08/37.19 | all_1212_2 gives: % 252.08/37.19 | (295) c_Nat_OSuc(all_1212_2) = all_1212_1 & % 252.08/37.19 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1212_0 & % 252.08/37.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1212_2 & % 252.08/37.19 | $i(all_1212_0) & $i(all_1212_1) & $i(all_1212_2) & ! [v0: $i] : ! % 252.08/37.19 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~ % 252.08/37.19 | (hAPP(all_1212_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1212_1, v1) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1212_1, v0) | % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1212_1, v3)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (295) implies: % 252.08/37.19 | (296) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1212_2 % 252.08/37.19 | (297) c_Nat_OSuc(all_1212_2) = all_1212_1 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (59) with fresh symbols all_1227_0, all_1227_1 gives: % 252.08/37.19 | (298) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1227_0 & % 252.08/37.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1227_1 & % 252.08/37.19 | $i(all_1227_0) & $i(all_1227_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.08/37.19 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 252.08/37.19 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1227_0, v2) = v3) | % 252.08/37.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1227_1, v2) | % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (298) implies: % 252.08/37.19 | (299) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1227_1 % 252.08/37.19 | (300) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1227_0 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (28) with fresh symbols all_1233_0, all_1233_1 gives: % 252.08/37.19 | (301) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1233_0 & % 252.08/37.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1233_1 & % 252.08/37.19 | $i(all_1233_0) & $i(all_1233_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.08/37.19 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v2) = % 252.08/37.19 | v4) | ~ (hAPP(v3, v1) = v5) | ~ (hAPP(all_1233_0, v0) = v3) | % 252.08/37.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1233_1, v0) | % 252.08/37.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 252.08/37.19 | % 252.08/37.19 | ALPHA: (301) implies: % 252.08/37.19 | (302) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1233_1 % 252.08/37.19 | % 252.08/37.19 | DELTA: instantiating (86) with fresh symbols all_1242_0, all_1242_1, % 252.08/37.19 | all_1242_2 gives: % 252.08/37.20 | (303) c_Nat_OSuc(all_1242_2) = all_1242_1 & % 252.08/37.20 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1242_0 & % 252.08/37.20 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1242_2 & % 252.08/37.20 | $i(all_1242_0) & $i(all_1242_1) & $i(all_1242_2) & ! [v0: $i] : ! % 252.08/37.20 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ % 252.08/37.20 | (hAPP(all_1242_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1242_1, v1) | ~ % 252.08/37.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1242_1, v0) | % 252.08/37.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (303) implies: % 252.08/37.20 | (304) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1242_2 % 252.08/37.20 | (305) c_Nat_OSuc(all_1242_2) = all_1242_1 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (85) with fresh symbols all_1245_0, all_1245_1, % 252.08/37.20 | all_1245_2 gives: % 252.08/37.20 | (306) c_Nat_OSuc(all_1245_2) = all_1245_1 & % 252.08/37.20 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1245_0 & % 252.08/37.20 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1245_2 & % 252.08/37.20 | $i(all_1245_0) & $i(all_1245_1) & $i(all_1245_2) & ! [v0: $i] : ! % 252.08/37.20 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~ % 252.08/37.20 | (hAPP(all_1245_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1245_1, v1) | ~ % 252.08/37.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1245_1, v0) | % 252.08/37.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (306) implies: % 252.08/37.20 | (307) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1245_2 % 252.08/37.20 | (308) c_Nat_OSuc(all_1245_2) = all_1245_1 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (27) with fresh symbols all_1248_0, all_1248_1 gives: % 252.08/37.20 | (309) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1248_1 & % 252.08/37.20 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1248_0 & % 252.08/37.20 | $i(all_1248_0) & $i(all_1248_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.08/37.20 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 252.08/37.20 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1248_1, v2) = v3) | % 252.08/37.20 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1248_0, v2) | ~ % 252.08/37.20 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) | % 252.08/37.20 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (309) implies: % 252.08/37.20 | (310) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1248_0 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (60) with fresh symbols all_1260_0, all_1260_1 gives: % 252.08/37.20 | (311) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1260_1 & % 252.08/37.20 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1260_0 & % 252.08/37.20 | $i(all_1260_0) & $i(all_1260_1) & ! [v0: $i] : ! [v1: any] : ! % 252.08/37.20 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 252.08/37.20 | (v1 = all_1260_0 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | % 252.08/37.20 | ~ (hAPP(all_1260_1, v2) = v3) | ~ (hAPP(all_1260_1, v0) = v5) | ~ % 252.08/37.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.20 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6) | % 252.08/37.20 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0)) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (311) implies: % 252.08/37.20 | (312) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1260_0 % 252.08/37.20 | (313) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1260_1 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (57) with fresh symbols all_1272_0, all_1272_1 gives: % 252.08/37.20 | (314) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1272_1 & % 252.08/37.20 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1272_0 & % 252.08/37.20 | $i(all_1272_0) & $i(all_1272_1) & ! [v0: $i] : ! [v1: any] : ! % 252.08/37.20 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 252.08/37.20 | (v1 = all_1272_0 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | % 252.08/37.20 | ~ (hAPP(all_1272_1, v2) = v3) | ~ (hAPP(all_1272_1, v0) = v5) | ~ % 252.08/37.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.20 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6) | % 252.08/37.20 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v2, v0)) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (314) implies: % 252.08/37.20 | (315) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1272_0 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (29) with fresh symbols all_1275_0, all_1275_1 gives: % 252.08/37.20 | (316) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1275_0 & % 252.08/37.20 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1275_1 & % 252.08/37.20 | $i(all_1275_0) & $i(all_1275_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.08/37.20 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 252.08/37.20 | (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1275_0, % 252.08/37.20 | v2) = v3) | ~ (hAPP(all_1275_0, v1) = v5) | ~ $i(v2) | ~ % 252.08/37.20 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.08/37.20 | v2, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.08/37.20 | all_1275_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, % 252.08/37.20 | v6)) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (316) implies: % 252.08/37.20 | (317) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1275_1 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (56) with fresh symbol all_1278_0 gives: % 252.08/37.20 | (318) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1278_0 & % 252.08/37.20 | $i(all_1278_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.20 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 252.08/37.20 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) | % 252.08/37.20 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.08/37.20 | class_Rings_Olinordered__semidom(v2) | ~ % 252.08/37.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1278_0, v0) | ? % 252.08/37.20 | [v6: $i] : (c_Groups_Oone__class_Oone(v2) = v6 & $i(v6) & ( ~ % 252.08/37.20 | c_Orderings_Oord__class_Oless(v2, v6, v1) | % 252.08/37.20 | c_Orderings_Oord__class_Oless(v2, v6, v5)))) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (318) implies: % 252.08/37.20 | (319) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1278_0 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (8) with fresh symbol all_1331_0 gives: % 252.08/37.20 | (320) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1331_0 & % 252.08/37.20 | $i(all_1331_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.08/37.20 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Odegree(v2, v3) = v4) | ~ % 252.08/37.20 | (c_Polynomial_Osmult(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 252.08/37.20 | $i(v0) | ~ class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] : % 252.08/37.20 | ((v4 = all_1331_0 | ( ~ (v5 = v1) & c_Groups_Ozero__class_Ozero(v2) % 252.08/37.20 | = v5 & $i(v5))) & ((v6 = v4 & c_Polynomial_Odegree(v2, v0) = % 252.08/37.20 | v4 & $i(v4)) | (v5 = v1 & c_Groups_Ozero__class_Ozero(v2) = % 252.08/37.20 | v1)))) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (320) implies: % 252.08/37.20 | (321) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1331_0 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (43) with fresh symbols all_1334_0, all_1334_1 gives: % 252.08/37.20 | (322) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1334_1 & % 252.08/37.20 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1334_0 & % 252.08/37.20 | $i(all_1334_0) & $i(all_1334_1) & ! [v0: $i] : ! [v1: any] : ! % 252.08/37.20 | [v2: $i] : (v1 = all_1334_1 | ~ (hAPP(v2, v0) = all_1334_1) | ~ % 252.08/37.20 | (hAPP(all_1334_0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] % 252.08/37.20 | : ! [v1: $i] : ! [v2: $i] : (v0 = all_1334_1 | ~ (hAPP(v2, v0) = % 252.08/37.20 | all_1334_1) | ~ (hAPP(all_1334_0, v1) = v2) | ~ $i(v1) | ~ % 252.08/37.20 | $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1334_1 | ~ % 252.08/37.20 | (hAPP(v0, all_1334_1) = v1) | ~ (hAPP(all_1334_0, all_1334_1) = % 252.08/37.20 | v0)) % 252.08/37.20 | % 252.08/37.20 | ALPHA: (322) implies: % 252.08/37.20 | (323) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1334_1 % 252.08/37.20 | % 252.08/37.20 | DELTA: instantiating (41) with fresh symbols all_1337_0, all_1337_1 gives: % 252.08/37.20 | (324) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1337_0 & % 252.08/37.20 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1337_1 & % 252.08/37.20 | $i(all_1337_0) & $i(all_1337_1) & ! [v0: $i] : ! [v1: any] : ! % 252.08/37.20 | [v2: $i] : (v1 = all_1337_0 | ~ (hAPP(v2, v0) = all_1337_0) | ~ % 252.08/37.20 | (hAPP(all_1337_1, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] % 252.08/37.20 | : ! [v1: $i] : ! [v2: $i] : (v0 = all_1337_0 | ~ (hAPP(v2, v0) = % 252.08/37.20 | all_1337_0) | ~ (hAPP(all_1337_1, v1) = v2) | ~ $i(v1) | ~ % 252.08/37.21 | $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1337_0 | ~ % 252.08/37.21 | (hAPP(v0, all_1337_0) = v1) | ~ (hAPP(all_1337_1, all_1337_0) = % 252.08/37.21 | v0)) % 252.08/37.21 | % 252.08/37.21 | ALPHA: (324) implies: % 252.21/37.21 | (325) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1337_0 % 252.21/37.21 | % 252.21/37.21 | DELTA: instantiating (53) with fresh symbol all_1340_0 gives: % 252.21/37.21 | (326) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1340_0 & % 252.21/37.21 | $i(all_1340_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.21/37.21 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Polynomial_Ocoeff(v1, v3) % 252.21/37.21 | = v4) | ~ (c_Groups_Oone__class_Oone(v2) = v3) | ~ % 252.21/37.21 | (tc_Polynomial_Opoly(v1) = v2) | ~ (hAPP(v4, v0) = v5) | ~ $i(v1) % 252.21/37.21 | | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | ? [v6: $i] : % 252.21/37.21 | ? [v7: $i] : (( ~ (v0 = all_1340_0) | (v6 = v5 & % 252.21/37.21 | c_Groups_Oone__class_Oone(v1) = v5 & $i(v5))) & (v0 = % 252.21/37.21 | all_1340_0 | (v7 = v5 & c_Groups_Ozero__class_Ozero(v1) = v5 & % 252.21/37.21 | $i(v5))))) % 252.21/37.21 | % 252.21/37.21 | ALPHA: (326) implies: % 252.21/37.21 | (327) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1340_0 % 252.21/37.21 | % 252.21/37.21 | DELTA: instantiating (54) with fresh symbol all_1346_0 gives: % 252.21/37.21 | (328) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1346_0 & % 252.21/37.21 | $i(all_1346_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.21/37.21 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 252.21/37.21 | [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7, % 252.21/37.21 | v0) = v8) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v2) = v5) | % 252.21/37.21 | ~ (hAPP(v4, v1) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 252.21/37.21 | $i(v0) | ~ class_Rings_Olinordered__semidom(v3) | ~ % 252.21/37.21 | c_Orderings_Oord__class_Oless(v3, v2, v1) | ~ % 252.21/37.21 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1346_0, v0) | % 252.21/37.21 | c_Orderings_Oord__class_Oless(v3, v6, v8) | ? [v9: $i] : % 252.21/37.21 | (c_Groups_Ozero__class_Ozero(v3) = v9 & $i(v9) & ~ % 252.21/37.21 | c_Orderings_Oord__class_Oless__eq(v3, v9, v2))) % 252.21/37.21 | % 252.21/37.21 | ALPHA: (328) implies: % 252.21/37.21 | (329) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1346_0 % 252.21/37.21 | % 252.21/37.21 | DELTA: instantiating (93) with fresh symbols all_1349_0, all_1349_1 gives: % 252.21/37.21 | (330) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1349_0 & % 252.21/37.21 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1349_1 & % 252.21/37.21 | $i(all_1349_0) & $i(all_1349_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.21/37.21 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 252.21/37.21 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 252.21/37.21 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1349_0) = v6) | % 252.21/37.21 | ~ (c_Power_Opower__class_Opower(v2) = v4) | ~ % 252.21/37.21 | (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v8, v0) = v9) | % 252.21/37.21 | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v3, v7) % 252.21/37.21 | = v8) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.21/37.21 | class_Groups_Omonoid__mult(v2) | ~ % 252.21/37.21 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1349_1, v1) | % 252.21/37.21 | (hAPP(v5, v1) = v9 & $i(v9))) % 252.21/37.21 | % 252.21/37.21 | ALPHA: (330) implies: % 252.21/37.21 | (331) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1349_1 % 252.21/37.21 | (332) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1349_0 % 252.21/37.21 | % 252.21/37.21 | DELTA: instantiating (3) with fresh symbols all_1352_0, all_1352_1, all_1352_2 % 252.21/37.21 | gives: % 252.21/37.21 | (333) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1352_0 & % 252.21/37.21 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1352_1 & % 252.21/37.21 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1352_2 & % 252.21/37.21 | $i(all_1352_0) & $i(all_1352_1) & $i(all_1352_2) & ! [v0: any] : ! % 252.21/37.21 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = all_1352_0 | ~ % 252.21/37.21 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1352_1, v1) = v2) | ~ $i(v1) | % 252.21/37.21 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.21 | all_1352_2, v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, % 252.21/37.21 | v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, % 252.21/37.21 | all_1352_0) = v2) | ~ (hAPP(all_1352_1, v0) = v1) | ~ $i(v0) % 252.21/37.21 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1352_2, v0) | % 252.21/37.21 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0)) % 252.21/37.21 | % 252.21/37.21 | ALPHA: (333) implies: % 252.21/37.21 | (334) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1352_2 % 252.21/37.21 | (335) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1352_0 % 252.21/37.21 | % 252.21/37.21 | DELTA: instantiating (47) with fresh symbols all_1355_0, all_1355_1 gives: % 252.21/37.21 | (336) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1355_1 & % 252.21/37.21 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1355_0 & % 252.21/37.21 | $i(all_1355_0) & $i(all_1355_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.21/37.21 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3) % 252.21/37.21 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1355_1, all_1355_0) = v2) | % 252.21/37.21 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 252.21/37.21 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1355_0 | v1 = v0 | ~ (hAPP(v3, % 252.21/37.21 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1355_1, v2) = % 252.21/37.21 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 252.21/37.21 | % 252.21/37.21 | ALPHA: (336) implies: % 252.21/37.21 | (337) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1355_0 % 252.21/37.21 | % 252.21/37.21 | DELTA: instantiating (23) with fresh symbol all_1363_0 gives: % 252.21/37.21 | (338) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1363_0 & % 252.21/37.21 | $i(all_1363_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 252.21/37.21 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 252.21/37.21 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.21 | all_1363_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.21 | all_1363_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.21 | all_1363_0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 252.21/37.21 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 252.21/37.21 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.21 | all_1363_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.21 | all_1363_0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 252.21/37.21 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 252.21/37.21 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.21 | all_1363_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.21 | all_1363_0, v2)) % 252.21/37.21 | % 252.21/37.21 | ALPHA: (338) implies: % 252.21/37.21 | (339) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1363_0 % 252.21/37.21 | % 252.21/37.21 | DELTA: instantiating (47) with fresh symbols all_1366_0, all_1366_1 gives: % 252.21/37.21 | (340) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1366_1 & % 252.21/37.21 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1366_0 & % 252.21/37.21 | $i(all_1366_0) & $i(all_1366_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.21/37.21 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3) % 252.21/37.21 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1366_1, all_1366_0) = v2) | % 252.21/37.21 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 252.21/37.21 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1366_0 | v1 = v0 | ~ (hAPP(v3, % 252.21/37.21 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1366_1, v2) = % 252.21/37.21 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 252.21/37.21 | % 252.21/37.21 | ALPHA: (340) implies: % 252.21/37.21 | (341) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1366_0 % 252.21/37.21 | % 252.21/37.21 | DELTA: instantiating (13) with fresh symbols all_1369_0, all_1369_1 gives: % 252.21/37.21 | (342) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1369_1 & % 252.21/37.21 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1369_0 & % 252.21/37.22 | $i(all_1369_0) & $i(all_1369_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.21/37.22 | int] : (v2 = all_1369_0 | ~ (hAPP(v1, v0) = v2) | ~ % 252.21/37.22 | (hAPP(all_1369_1, all_1369_0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! % 252.21/37.22 | [v1: $i] : ! [v2: int] : (v2 = all_1369_0 | ~ (hAPP(v1, all_1369_0) % 252.21/37.22 | = v2) | ~ (hAPP(all_1369_1, v0) = v1) | ~ $i(v0)) & ! [v0: % 252.21/37.22 | any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1369_0 | v0 = % 252.21/37.22 | all_1369_0 | ~ (hAPP(v2, v0) = all_1369_0) | ~ (hAPP(all_1369_1, % 252.21/37.22 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (342) implies: % 252.21/37.22 | (343) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1369_0 % 252.21/37.22 | % 252.21/37.22 | DELTA: instantiating (4) with fresh symbols all_1375_0, all_1375_1, all_1375_2 % 252.21/37.22 | gives: % 252.21/37.22 | (344) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1375_0 & % 252.21/37.22 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1375_1 & % 252.21/37.22 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1375_2 & % 252.21/37.22 | $i(all_1375_0) & $i(all_1375_1) & $i(all_1375_2) & ! [v0: any] : ! % 252.21/37.22 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = all_1375_0 | ~ % 252.21/37.22 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1375_1, v0) = v2) | ~ $i(v1) | % 252.21/37.22 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.21/37.22 | all_1375_2, v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, % 252.21/37.22 | v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, % 252.21/37.22 | v0) = v2) | ~ (hAPP(all_1375_1, all_1375_0) = v1) | ~ $i(v0) % 252.21/37.22 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1375_2, v0) | % 252.21/37.22 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0)) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (344) implies: % 252.21/37.22 | (345) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1375_2 % 252.21/37.22 | (346) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1375_0 % 252.21/37.22 | % 252.21/37.22 | DELTA: instantiating (67) with fresh symbol all_1384_0 gives: % 252.21/37.22 | (347) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1384_0 & % 252.21/37.22 | $i(all_1384_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.21/37.22 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v2 = % 252.21/37.22 | v0 | ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7, v1) % 252.21/37.22 | = v6) | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ % 252.21/37.22 | (hAPP(v4, v0) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 252.21/37.22 | | ~ class_Rings_Olinordered__semidom(v3) | ~ % 252.21/37.22 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1384_0, v1) | ? % 252.21/37.22 | [v8: $i] : (c_Groups_Ozero__class_Ozero(v3) = v8 & $i(v8) & ( ~ % 252.21/37.22 | c_Orderings_Oord__class_Oless__eq(v3, v8, v2) | ~ % 252.21/37.22 | c_Orderings_Oord__class_Oless__eq(v3, v8, v0)))) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (347) implies: % 252.21/37.22 | (348) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1384_0 % 252.21/37.22 | % 252.21/37.22 | DELTA: instantiating (96) with fresh symbols all_1390_0, all_1390_1 gives: % 252.21/37.22 | (349) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1390_0 & % 252.21/37.22 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1390_1 & % 252.21/37.22 | $i(all_1390_0) & $i(all_1390_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.21/37.22 | int] : (v2 = all_1390_1 | ~ % 252.21/37.22 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 252.21/37.22 | | ~ $i(v0) | ? [v3: $i] : (hAPP(all_1390_0, v0) = v3 & $i(v3) & % 252.21/37.22 | ! [v4: $i] : ( ~ (hAPP(v3, v4) = v1) | ~ $i(v4)))) & ! [v0: $i] % 252.21/37.22 | : ! [v1: $i] : ( ~ (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) % 252.21/37.22 | = all_1390_1) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 252.21/37.22 | : (hAPP(v2, v3) = v1 & hAPP(all_1390_0, v0) = v2 & $i(v3) & % 252.21/37.22 | $i(v2))) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (349) implies: % 252.21/37.22 | (350) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1390_1 % 252.21/37.22 | % 252.21/37.22 | DELTA: instantiating (80) with fresh symbols all_1393_0, all_1393_1, % 252.21/37.22 | all_1393_2 gives: % 252.21/37.22 | (351) c_Nat_OSuc(all_1393_1) = all_1393_0 & % 252.21/37.22 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1393_2 & % 252.21/37.22 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1393_1 & % 252.21/37.22 | $i(all_1393_0) & $i(all_1393_1) & $i(all_1393_2) & ! [v0: $i] : ! % 252.21/37.22 | [v1: any] : ! [v2: $i] : (v1 = all_1393_0 | ~ (hAPP(v2, v0) = % 252.21/37.22 | all_1393_0) | ~ (hAPP(all_1393_2, v1) = v2) | ~ $i(v1) | ~ % 252.21/37.22 | $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 = % 252.21/37.22 | all_1393_0 | ~ (hAPP(v2, v0) = all_1393_0) | ~ (hAPP(all_1393_2, % 252.21/37.22 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int] % 252.21/37.22 | : (v1 = all_1393_0 | ~ (hAPP(v0, all_1393_0) = v1) | ~ % 252.21/37.22 | (hAPP(all_1393_2, all_1393_0) = v0)) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (351) implies: % 252.21/37.22 | (352) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1393_1 % 252.21/37.22 | (353) c_Nat_OSuc(all_1393_1) = all_1393_0 % 252.21/37.22 | % 252.21/37.22 | DELTA: instantiating (14) with fresh symbols all_1402_0, all_1402_1 gives: % 252.21/37.22 | (354) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1402_1 & % 252.21/37.22 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1402_0 & % 252.21/37.22 | $i(all_1402_0) & $i(all_1402_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.21/37.22 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 252.21/37.22 | (hAPP(v4, all_1402_0) = v5) | ~ (hAPP(v2, all_1402_0) = v3) | ~ % 252.21/37.22 | (hAPP(all_1402_1, v1) = v2) | ~ (hAPP(all_1402_1, v0) = v4) | ~ % 252.21/37.22 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! % 252.21/37.22 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | v1 = all_1402_0 | % 252.21/37.22 | ~ (hAPP(v5, v1) = v4) | ~ (hAPP(v3, v1) = v4) | ~ % 252.21/37.22 | (hAPP(all_1402_1, v2) = v3) | ~ (hAPP(all_1402_1, v0) = v5) | ~ % 252.21/37.22 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (354) implies: % 252.21/37.22 | (355) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1402_0 % 252.21/37.22 | % 252.21/37.22 | DELTA: instantiating (64) with fresh symbol all_1405_0 gives: % 252.21/37.22 | (356) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1405_0 & % 252.21/37.22 | $i(all_1405_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.21/37.22 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 252.21/37.22 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) | % 252.21/37.22 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.21/37.22 | class_Power_Opower(v2) | ~ class_Rings_Ozero__neq__one(v2) | ~ % 252.21/37.22 | class_Rings_Ono__zero__divisors(v2) | ~ % 252.21/37.22 | class_Rings_Omult__zero(v2) | ? [v6: $i] : % 252.21/37.22 | (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = v5) | % 252.21/37.22 | (v5 = v1 & ~ (v0 = all_1405_0))) & ( ~ (v6 = v1) | v5 = v1 | % 252.21/37.22 | v0 = all_1405_0))) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (356) implies: % 252.21/37.22 | (357) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1405_0 % 252.21/37.22 | % 252.21/37.22 | DELTA: instantiating (76) with fresh symbol all_1411_0 gives: % 252.21/37.22 | (358) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1411_0 & % 252.21/37.22 | $i(all_1411_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.21/37.22 | $i] : ( ~ (c_Nat_OSuc(v3) = v1) | ~ (c_Nat_OSuc(v0) = v2) | ~ % 252.21/37.22 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 252.21/37.22 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0) | % 252.21/37.22 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)) & ! [v0: $i] : % 252.21/37.22 | ! [v1: any] : ! [v2: $i] : (v1 = all_1411_0 | ~ (c_Nat_OSuc(v0) = % 252.21/37.22 | v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.21/37.22 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v3: $i] : % 252.21/37.22 | (c_Nat_OSuc(v3) = v1 & $i(v3) & % 252.21/37.22 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))) & ! [v0: % 252.21/37.22 | $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 252.21/37.22 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1411_0, v1)) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (358) implies: % 252.21/37.22 | (359) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1411_0 % 252.21/37.22 | (360) ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = all_1411_0 | ~ % 252.21/37.22 | (c_Nat_OSuc(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.21/37.22 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v3: $i] : % 252.21/37.22 | (c_Nat_OSuc(v3) = v1 & $i(v3) & % 252.21/37.22 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))) % 252.21/37.22 | % 252.21/37.22 | DELTA: instantiating (70) with fresh symbols all_1423_0, all_1423_1, % 252.21/37.22 | all_1423_2 gives: % 252.21/37.22 | (361) c_Nat_OSuc(all_1423_1) = all_1423_0 & % 252.21/37.22 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1423_2 & % 252.21/37.22 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1423_1 & % 252.21/37.22 | $i(all_1423_0) & $i(all_1423_1) & $i(all_1423_2) & ! [v0: $i] : ! % 252.21/37.22 | [v1: $i] : ! [v2: int] : (v2 = all_1423_0 | ~ (hAPP(v1, v0) = v2) | % 252.21/37.22 | ~ (hAPP(all_1423_2, all_1423_0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 252.21/37.22 | ! [v1: $i] : ! [v2: int] : (v2 = all_1423_0 | ~ (hAPP(v1, % 252.21/37.22 | all_1423_1) = v2) | ~ (hAPP(all_1423_2, v0) = v1) | ~ $i(v0)) % 252.21/37.22 | & ! [v0: any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1423_0 | v0 = % 252.21/37.22 | all_1423_1 | ~ (hAPP(v2, v0) = all_1423_0) | ~ (hAPP(all_1423_2, % 252.21/37.22 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 252.21/37.22 | % 252.21/37.22 | ALPHA: (361) implies: % 252.21/37.23 | (362) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1423_1 % 252.21/37.23 | (363) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1423_2 % 252.21/37.23 | (364) c_Nat_OSuc(all_1423_1) = all_1423_0 % 252.21/37.23 | % 252.21/37.23 | DELTA: instantiating (91) with fresh symbols all_1426_0, all_1426_1 gives: % 252.21/37.23 | (365) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1426_0 & % 252.21/37.23 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1426_1 & % 252.21/37.23 | $i(all_1426_0) & $i(all_1426_1) & ! [v0: any] : ! [v1: $i] : ! % 252.21/37.23 | [v2: $i] : ! [v3: $i] : (v0 = all_1426_1 | ~ (hAPP(v2, v0) = v3) | % 252.21/37.23 | ~ (hAPP(all_1426_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.21/37.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_1, v3) | % 252.21/37.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_1, v1)) & ! % 252.21/37.23 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 252.21/37.23 | v0) = v3) | ~ (hAPP(all_1426_0, v1) = v2) | ~ $i(v1) | ~ % 252.21/37.23 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_1, % 252.21/37.23 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_1, v3)) % 252.21/37.23 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1426_1) % 252.21/37.23 | = v2) | ~ (hAPP(all_1426_0, v0) = v1) | ~ $i(v0) | % 252.21/37.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_1, v2)) % 252.21/37.23 | % 252.21/37.23 | ALPHA: (365) implies: % 252.21/37.23 | (366) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1426_1 % 252.21/37.23 | (367) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1426_0 % 252.21/37.23 | % 252.21/37.23 | DELTA: instantiating (91) with fresh symbols all_1429_0, all_1429_1 gives: % 252.30/37.23 | (368) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1429_0 & % 252.30/37.23 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1429_1 & % 252.30/37.23 | $i(all_1429_0) & $i(all_1429_1) & ! [v0: any] : ! [v1: $i] : ! % 252.30/37.23 | [v2: $i] : ! [v3: $i] : (v0 = all_1429_1 | ~ (hAPP(v2, v0) = v3) | % 252.30/37.23 | ~ (hAPP(all_1429_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1429_1, v3) | % 252.30/37.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1429_1, v1)) & ! % 252.30/37.23 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 252.30/37.23 | v0) = v3) | ~ (hAPP(all_1429_0, v1) = v2) | ~ $i(v1) | ~ % 252.30/37.23 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1429_1, % 252.30/37.23 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1429_1, v3)) % 252.30/37.23 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1429_1) % 252.30/37.23 | = v2) | ~ (hAPP(all_1429_0, v0) = v1) | ~ $i(v0) | % 252.30/37.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1429_1, v2)) % 252.30/37.23 | % 252.30/37.23 | ALPHA: (368) implies: % 252.30/37.23 | (369) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1429_1 % 252.30/37.23 | (370) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1429_0 % 252.30/37.23 | % 252.30/37.23 | DELTA: instantiating (66) with fresh symbol all_1432_0 gives: % 252.30/37.23 | (371) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1432_0 & % 252.30/37.23 | $i(all_1432_0) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.30/37.23 | $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | v0 = all_1432_0 | ~ % 252.30/37.23 | (c_Power_Opower__class_Opower(v1) = v2) | ~ % 252.30/37.23 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | % 252.30/37.23 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.23 | class_Power_Opower(v1) | ~ class_Rings_Osemiring__0(v1)) & ! [v0: % 252.30/37.23 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 252.30/37.23 | (c_Power_Opower__class_Opower(v0) = v1) | ~ % 252.30/37.23 | (c_Groups_Ozero__class_Ozero(v0) = v2) | ~ (hAPP(v3, all_1432_0) = % 252.30/37.23 | v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v0) | ~ % 252.30/37.23 | class_Power_Opower(v0) | ~ class_Rings_Osemiring__0(v0) | % 252.30/37.23 | (c_Groups_Oone__class_Oone(v0) = v4 & $i(v4))) % 252.30/37.23 | % 252.30/37.23 | ALPHA: (371) implies: % 252.30/37.23 | (372) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1432_0 % 252.30/37.23 | % 252.30/37.23 | DELTA: instantiating (10) with fresh symbol all_1438_0 gives: % 252.30/37.23 | (373) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1438_0 & % 252.30/37.23 | $i(all_1438_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.30/37.23 | $i] : ( ~ (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3) | ~ % 252.30/37.23 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.23 | class_Rings_Ocomm__semiring__0(v2) | ? [v4: $i] : ? [v5: $i] : ? % 252.30/37.23 | [v6: any] : (((v6 = all_1438_0 & c_Polynomial_Odegree(v2, v1) = % 252.30/37.23 | all_1438_0) | ( ~ (v5 = v3) & tc_Polynomial_Opoly(v2) = v4 & % 252.30/37.23 | c_Groups_Ozero__class_Ozero(v4) = v5 & $i(v5) & $i(v4))) & % 252.30/37.23 | ((v5 = v3 & tc_Polynomial_Opoly(v2) = v4 & % 252.30/37.23 | c_Groups_Ozero__class_Ozero(v4) = v3 & $i(v4) & $i(v3)) | ( ~ % 252.30/37.23 | (v6 = all_1438_0) & c_Polynomial_Odegree(v2, v1) = v6 & % 252.30/37.23 | $i(v6))))) % 252.30/37.23 | % 252.30/37.23 | ALPHA: (373) implies: % 252.30/37.23 | (374) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1438_0 % 252.30/37.23 | % 252.30/37.23 | DELTA: instantiating (38) with fresh symbols all_1444_0, all_1444_1 gives: % 252.30/37.23 | (375) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1444_0 & % 252.30/37.23 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1444_1 & % 252.30/37.23 | $i(all_1444_0) & $i(all_1444_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.23 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 252.30/37.23 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1444_0, v2) = v3) | % 252.30/37.23 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1444_1, v2) | ~ % 252.30/37.23 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) | % 252.30/37.23 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! % 252.30/37.23 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 252.30/37.23 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.23 | (hAPP(all_1444_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.23 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1444_1, v2) | ~ % 252.30/37.23 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) | % 252.30/37.23 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5)) % 252.30/37.23 | % 252.30/37.23 | ALPHA: (375) implies: % 252.30/37.23 | (376) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1444_1 % 252.30/37.23 | % 252.30/37.23 | DELTA: instantiating (35) with fresh symbols all_1450_0, all_1450_1 gives: % 252.30/37.23 | (377) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1450_0 & % 252.30/37.23 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1450_1 & % 252.30/37.23 | $i(all_1450_0) & $i(all_1450_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.23 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 252.30/37.23 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1450_0, v2) = v3) | % 252.30/37.23 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1450_1, v2) | ~ % 252.30/37.23 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) | % 252.30/37.23 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: % 252.30/37.23 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 252.30/37.23 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.23 | (hAPP(all_1450_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.23 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1450_1, v2) | ~ % 252.30/37.23 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 252.30/37.23 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)) % 252.30/37.23 | % 252.30/37.23 | ALPHA: (377) implies: % 252.30/37.23 | (378) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1450_1 % 252.30/37.23 | % 252.30/37.23 | DELTA: instantiating (49) with fresh symbols all_1453_0, all_1453_1 gives: % 252.30/37.23 | (379) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1453_0 & % 252.30/37.23 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1453_1 & % 252.30/37.23 | $i(all_1453_0) & $i(all_1453_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.23 | $i] : ( ~ (hAPP(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.23 | hBOOL(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 252.30/37.23 | ($i(v4) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, % 252.30/37.23 | all_1453_0) = v5 & hAPP(v1, v5) = v6 & $i(v6) & $i(v5) & % 252.30/37.23 | hBOOL(v6) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, % 252.30/37.23 | v0) & ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v1, v7) = v8) | % 252.30/37.23 | ~ $i(v7) | ~ hBOOL(v8) | ~ % 252.30/37.23 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v7, v4))) | % 252.30/37.23 | (hAPP(v1, all_1453_1) = v3 & $i(v3) & hBOOL(v3))))) % 252.30/37.23 | % 252.30/37.23 | ALPHA: (379) implies: % 252.30/37.23 | (380) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1453_1 % 252.30/37.23 | (381) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1453_0 % 252.30/37.23 | % 252.30/37.24 | DELTA: instantiating (37) with fresh symbols all_1456_0, all_1456_1 gives: % 252.30/37.24 | (382) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1456_0 & % 252.30/37.24 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1456_1 & % 252.30/37.24 | $i(all_1456_0) & $i(all_1456_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.24 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 252.30/37.24 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1456_0, v2) = v3) | % 252.30/37.24 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~ % 252.30/37.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1456_1, v2) | % 252.30/37.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : % 252.30/37.24 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 252.30/37.24 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.24 | (hAPP(all_1456_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.24 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~ % 252.30/37.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1456_1, v2) | % 252.30/37.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 252.30/37.24 | % 252.30/37.24 | ALPHA: (382) implies: % 252.30/37.24 | (383) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1456_1 % 252.30/37.24 | % 252.30/37.24 | DELTA: instantiating (55) with fresh symbol all_1459_0 gives: % 252.30/37.24 | (384) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1459_0 & % 252.30/37.24 | $i(all_1459_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.30/37.24 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 252.30/37.24 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v1) = v5) | % 252.30/37.24 | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1459_0, v1) | ~ % 252.30/37.24 | class_Rings_Ocomm__semiring__1(v2) | c_Rings_Odvd__class_Odvd(v2, % 252.30/37.24 | v0, v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 252.30/37.24 | : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = % 252.30/37.24 | v3) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) % 252.30/37.24 | | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v2) | % 252.30/37.24 | c_Rings_Odvd__class_Odvd(v2, v0, v5) | ? [v6: $i] : ( ~ (v6 = v0) % 252.30/37.24 | & c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))) % 252.30/37.24 | % 252.30/37.24 | ALPHA: (384) implies: % 252.30/37.24 | (385) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1459_0 % 252.30/37.24 | % 252.30/37.24 | DELTA: instantiating (94) with fresh symbol all_1462_0 gives: % 252.30/37.24 | (386) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1462_0 & % 252.30/37.24 | $i(all_1462_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.30/37.24 | int] : (v3 = all_1462_0 | ~ % 252.30/37.24 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v0) = v3) | ~ % 252.30/37.24 | (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 252.30/37.24 | [v5: $i] : ( ~ (v5 = v0) & c_Divides_Odiv__class_Omod(tc_Nat_Onat, % 252.30/37.24 | v1, v0) = v4 & c_Nat_OSuc(v4) = v5 & $i(v5) & $i(v4))) & ! % 252.30/37.24 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 252.30/37.24 | (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v2, v0) = v3) | ~ % 252.30/37.24 | (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 252.30/37.24 | [v5: $i] : (c_Divides_Odiv__class_Omod(tc_Nat_Onat, v1, v0) = v4 & % 252.30/37.24 | c_Nat_OSuc(v4) = v5 & $i(v5) & $i(v4) & (v5 = v3 | v5 = v0))) % 252.30/37.24 | % 252.30/37.24 | ALPHA: (386) implies: % 252.30/37.24 | (387) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1462_0 % 252.30/37.24 | % 252.30/37.24 | DELTA: instantiating (34) with fresh symbols all_1468_0, all_1468_1 gives: % 252.30/37.24 | (388) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1468_0 & % 252.30/37.24 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1468_1 & % 252.30/37.24 | $i(all_1468_0) & $i(all_1468_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.24 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1468_0, % 252.30/37.24 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1468_1, v3) | % 252.30/37.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1468_1, v1)) & ! % 252.30/37.24 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 252.30/37.24 | v0) = v3) | ~ (hAPP(all_1468_0, v1) = v2) | ~ $i(v1) | ~ % 252.30/37.24 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1468_1, % 252.30/37.24 | v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1468_1, v0)) % 252.30/37.24 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 252.30/37.24 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1468_0, v1) = v2) | ~ $i(v1) | % 252.30/37.24 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.30/37.24 | all_1468_1, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.30/37.24 | all_1468_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.30/37.24 | all_1468_1, v3)) % 252.30/37.24 | % 252.30/37.24 | ALPHA: (388) implies: % 252.30/37.24 | (389) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1468_1 % 252.30/37.24 | % 252.30/37.24 | DELTA: instantiating (90) with fresh symbol all_1471_0 gives: % 252.30/37.24 | (390) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1471_0 & % 252.30/37.24 | $i(all_1471_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.30/37.24 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Odegree(v2, v3) = v4) | ~ % 252.30/37.24 | (c_Polynomial_OpCons(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 252.30/37.24 | $i(v0) | ~ class_Groups_Ozero(v2) | ? [v5: $i] : ? [v6: $i] : ? % 252.30/37.24 | [v7: $i] : ? [v8: $i] : ((v4 = all_1471_0 | ( ~ (v6 = v1) & % 252.30/37.24 | tc_Polynomial_Opoly(v2) = v5 & % 252.30/37.24 | c_Groups_Ozero__class_Ozero(v5) = v6 & $i(v6) & $i(v5))) & % 252.30/37.24 | ((v8 = v4 & c_Nat_OSuc(v7) = v4 & c_Polynomial_Odegree(v2, v1) = % 252.30/37.24 | v7 & $i(v7) & $i(v4)) | (v6 = v1 & tc_Polynomial_Opoly(v2) = % 252.30/37.24 | v5 & c_Groups_Ozero__class_Ozero(v5) = v1 & $i(v5))))) % 252.30/37.24 | % 252.30/37.24 | ALPHA: (390) implies: % 252.30/37.24 | (391) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1471_0 % 252.30/37.24 | % 252.30/37.24 | DELTA: instantiating (61) with fresh symbols all_1474_0, all_1474_1 gives: % 252.30/37.24 | (392) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1474_0 & % 252.30/37.24 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1474_1 & % 252.30/37.24 | $i(all_1474_0) & $i(all_1474_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.24 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2 % 252.30/37.24 | = all_1474_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ % 252.30/37.24 | (hAPP(all_1474_0, v1) = v3) | ~ (hAPP(all_1474_0, v0) = v5) | ~ % 252.30/37.24 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.24 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6) | % 252.30/37.24 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! % 252.30/37.24 | [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 252.30/37.24 | ! [v6: $i] : (v2 = all_1474_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, % 252.30/37.24 | v2) = v4) | ~ (hAPP(all_1474_0, v1) = v3) | ~ % 252.30/37.24 | (hAPP(all_1474_0, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.24 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) | % 252.30/37.24 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v6)) % 252.30/37.24 | % 252.30/37.24 | ALPHA: (392) implies: % 252.30/37.24 | (393) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1474_1 % 252.30/37.24 | (394) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1474_0 % 252.30/37.24 | % 252.30/37.24 | DELTA: instantiating (58) with fresh symbols all_1477_0, all_1477_1 gives: % 252.30/37.24 | (395) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1477_0 & % 252.30/37.24 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1477_1 & % 252.30/37.24 | $i(all_1477_0) & $i(all_1477_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.24 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2 % 252.30/37.24 | = all_1477_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ % 252.30/37.24 | (hAPP(all_1477_0, v1) = v3) | ~ (hAPP(all_1477_0, v0) = v5) | ~ % 252.30/37.24 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.24 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6) | % 252.30/37.24 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0)) & ! [v0: $i] : ! % 252.30/37.24 | [v1: $i] : ! [v2: any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 252.30/37.24 | ! [v6: $i] : (v2 = all_1477_1 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, % 252.30/37.24 | v2) = v4) | ~ (hAPP(all_1477_0, v1) = v3) | ~ % 252.30/37.24 | (hAPP(all_1477_0, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.24 | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint, v1, v0) | % 252.30/37.24 | c_Rings_Odvd__class_Odvd(tc_Int_Oint, v4, v6)) % 252.30/37.24 | % 252.30/37.24 | ALPHA: (395) implies: % 252.30/37.24 | (396) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1477_1 % 252.30/37.24 | % 252.30/37.24 | DELTA: instantiating (89) with fresh symbols all_1480_0, all_1480_1, % 252.30/37.24 | all_1480_2 gives: % 252.30/37.25 | (397) c_Nat_OSuc(all_1480_2) = all_1480_1 & % 252.30/37.25 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1480_0 & % 252.30/37.25 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1480_2 & % 252.30/37.25 | $i(all_1480_0) & $i(all_1480_1) & $i(all_1480_2) & ! [v0: $i] : ! % 252.30/37.25 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ % 252.30/37.25 | (hAPP(all_1480_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1480_1, v3) | % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1480_1, v1)) & % 252.30/37.25 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 252.30/37.25 | v0) = v3) | ~ (hAPP(all_1480_0, v1) = v2) | ~ $i(v1) | ~ % 252.30/37.25 | $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 252.30/37.25 | all_1480_1, v3) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 252.30/37.25 | all_1480_1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 252.30/37.25 | [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1480_0, v1) = v2) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1480_1, v1) | ~ % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1480_1, v0) | % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1480_1, v3)) % 252.30/37.25 | % 252.30/37.25 | ALPHA: (397) implies: % 252.30/37.25 | (398) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1480_2 % 252.30/37.25 | (399) c_Nat_OSuc(all_1480_2) = all_1480_1 % 252.30/37.25 | % 252.30/37.25 | DELTA: instantiating (45) with fresh symbols all_1488_0, all_1488_1 gives: % 252.30/37.25 | (400) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1488_1 & % 252.30/37.25 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1488_0 & % 252.30/37.25 | $i(all_1488_0) & $i(all_1488_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.25 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1488_0 | % 252.30/37.25 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.25 | (hAPP(all_1488_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.25 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5) | % 252.30/37.25 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! % 252.30/37.25 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 252.30/37.25 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.25 | (hAPP(all_1488_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.25 | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0) | % 252.30/37.25 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, v5)) & ! [v0: $i] : ! % 252.30/37.25 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v2, % 252.30/37.25 | v1) = v3) | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1488_1, % 252.30/37.25 | all_1488_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.25 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v4)) % 252.30/37.25 | % 252.30/37.25 | ALPHA: (400) implies: % 252.30/37.25 | (401) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1488_0 % 252.30/37.25 | % 252.30/37.25 | DELTA: instantiating (1) with fresh symbol all_1491_0 gives: % 252.30/37.25 | (402) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1491_0 & % 252.30/37.25 | $i(all_1491_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 252.30/37.25 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(v2, v1) = v3) | ~ % 252.30/37.25 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.25 | class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 252.30/37.25 | ? [v8: any] : (((v8 = all_1491_0 & ~ (v7 = v1) & % 252.30/37.25 | c_Polynomial_Oorder(v2, v0, v1) = all_1491_0 & % 252.30/37.25 | tc_Polynomial_Opoly(v2) = v6 & % 252.30/37.25 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6)) | (v5 % 252.30/37.25 | = v4 & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) & ((v7 % 252.30/37.25 | = v1 & tc_Polynomial_Opoly(v2) = v6 & % 252.30/37.25 | c_Groups_Ozero__class_Ozero(v6) = v1 & $i(v6)) | ( ~ (v8 = % 252.30/37.25 | all_1491_0) & c_Polynomial_Oorder(v2, v0, v1) = v8 & % 252.30/37.25 | $i(v8)) | ( ~ (v5 = v4) & c_Groups_Ozero__class_Ozero(v2) = % 252.30/37.25 | v5 & $i(v5))))) % 252.30/37.25 | % 252.30/37.25 | ALPHA: (402) implies: % 252.30/37.25 | (403) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1491_0 % 252.30/37.25 | % 252.30/37.25 | DELTA: instantiating (78) with fresh symbols all_1494_0, all_1494_1 gives: % 252.30/37.25 | (404) c_Nat_OSuc(all_1494_1) = all_1494_0 & % 252.30/37.25 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1494_1 & % 252.30/37.25 | $i(all_1494_0) & $i(all_1494_1) & ! [v0: $i] : ! [v1: any] : (v1 = % 252.30/37.25 | all_1494_0 | v1 = all_1494_1 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1494_0) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 252.30/37.25 | all_1494_0 | v0 = all_1494_0 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1494_0) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 252.30/37.25 | all_1494_1 | v0 = all_1494_1 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1494_0) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 252.30/37.25 | all_1494_0 | v0 = all_1494_1 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1494_0) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1494_0 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1494_0, all_1494_1) = % 252.30/37.25 | v0)) & ! [v0: int] : (v0 = all_1494_0 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1494_1, all_1494_0) = % 252.30/37.25 | v0)) % 252.30/37.25 | % 252.30/37.25 | ALPHA: (404) implies: % 252.30/37.25 | (405) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1494_1 % 252.30/37.25 | (406) c_Nat_OSuc(all_1494_1) = all_1494_0 % 252.30/37.25 | % 252.30/37.25 | DELTA: instantiating (78) with fresh symbols all_1497_0, all_1497_1 gives: % 252.30/37.25 | (407) c_Nat_OSuc(all_1497_1) = all_1497_0 & % 252.30/37.25 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1497_1 & % 252.30/37.25 | $i(all_1497_0) & $i(all_1497_1) & ! [v0: $i] : ! [v1: any] : (v1 = % 252.30/37.25 | all_1497_0 | v1 = all_1497_1 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1497_0) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 252.30/37.25 | all_1497_0 | v0 = all_1497_0 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1497_0) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 252.30/37.25 | all_1497_1 | v0 = all_1497_1 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1497_0) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 252.30/37.25 | all_1497_0 | v0 = all_1497_1 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1497_0) | % 252.30/37.25 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1497_0 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1497_0, all_1497_1) = % 252.30/37.25 | v0)) & ! [v0: int] : (v0 = all_1497_0 | ~ % 252.30/37.25 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1497_1, all_1497_0) = % 252.30/37.25 | v0)) % 252.30/37.25 | % 252.30/37.25 | ALPHA: (407) implies: % 252.30/37.25 | (408) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1497_1 % 252.30/37.25 | (409) c_Nat_OSuc(all_1497_1) = all_1497_0 % 252.30/37.25 | % 252.30/37.25 | DELTA: instantiating (84) with fresh symbols all_1500_0, all_1500_1, % 252.30/37.25 | all_1500_2 gives: % 252.30/37.25 | (410) c_Nat_OSuc(all_1500_1) = all_1500_0 & c_Nat_OSuc(all_1500_2) = % 252.30/37.25 | all_1500_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1500_2 & % 252.30/37.25 | $i(all_1500_0) & $i(all_1500_1) & $i(all_1500_2) & ! [v0: $i] : ! % 252.30/37.25 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 252.30/37.25 | ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) % 252.30/37.25 | | ~ (hAPP(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.25 | class_Rings_Oidom(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 252.30/37.25 | ((v1 = v0 | (v8 = v1 & c_Groups_Ouminus__class_Ouminus(v2, v0) = % 252.30/37.25 | v1) | ( ~ (v7 = v6) & hAPP(v5, all_1500_0) = v7 & hAPP(v4, % 252.30/37.25 | all_1500_0) = v6 & $i(v7) & $i(v6))) & ((v7 = v6 & hAPP(v5, % 252.30/37.25 | all_1500_0) = v6 & hAPP(v4, all_1500_0) = v6 & $i(v6)) | ( % 252.30/37.25 | ~ (v8 = v1) & ~ (v1 = v0) & % 252.30/37.25 | c_Groups_Ouminus__class_Ouminus(v2, v0) = v8 & $i(v8))))) % 252.30/37.25 | % 252.30/37.25 | ALPHA: (410) implies: % 252.30/37.25 | (411) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1500_2 % 252.30/37.25 | (412) c_Nat_OSuc(all_1500_2) = all_1500_1 % 252.30/37.25 | (413) c_Nat_OSuc(all_1500_1) = all_1500_0 % 252.30/37.25 | % 252.30/37.25 | DELTA: instantiating (31) with fresh symbols all_1503_0, all_1503_1 gives: % 252.30/37.25 | (414) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1503_1 & % 252.30/37.25 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1503_0 & % 252.30/37.25 | $i(all_1503_0) & $i(all_1503_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.25 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 252.30/37.25 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1503_1, v2) = v3) | % 252.30/37.25 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.25 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1503_0, v2) | ~ % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) | % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: % 252.30/37.25 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 252.30/37.25 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.25 | (hAPP(all_1503_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.25 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)) & ! [v0: % 252.30/37.25 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 252.30/37.25 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.25 | (hAPP(all_1503_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.25 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1503_0, v2) | % 252.30/37.25 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)) % 252.30/37.25 | % 252.30/37.25 | ALPHA: (414) implies: % 252.30/37.25 | (415) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1503_0 % 252.30/37.25 | % 252.30/37.25 | DELTA: instantiating (33) with fresh symbols all_1506_0, all_1506_1 gives: % 252.30/37.26 | (416) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1506_1 & % 252.30/37.26 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1506_0 & % 252.30/37.26 | $i(all_1506_0) & $i(all_1506_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.26 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 252.30/37.26 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1506_1, v2) = v3) | % 252.30/37.26 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : % 252.30/37.26 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 252.30/37.26 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.26 | (hAPP(all_1506_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.26 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1506_0, v2)) & ! % 252.30/37.26 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 252.30/37.26 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 252.30/37.26 | (hAPP(all_1506_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.26 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~ % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1506_0, v2) | % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 252.30/37.26 | % 252.30/37.26 | ALPHA: (416) implies: % 252.30/37.26 | (417) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1506_0 % 252.30/37.26 | % 252.30/37.26 | DELTA: instantiating (32) with fresh symbols all_1509_0, all_1509_1 gives: % 252.30/37.26 | (418) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1509_1 & % 252.30/37.26 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1509_0 & % 252.30/37.26 | $i(all_1509_0) & $i(all_1509_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.26 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 252.30/37.26 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1509_1, % 252.30/37.26 | v2) = v3) | ~ (hAPP(all_1509_1, v0) = v5) | ~ $i(v2) | ~ % 252.30/37.26 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.30/37.26 | v4, v6) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0)) & % 252.30/37.26 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 252.30/37.26 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) % 252.30/37.26 | = v4) | ~ (hAPP(all_1509_1, v2) = v3) | ~ (hAPP(all_1509_1, v0) % 252.30/37.26 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) | % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1509_0, v1)) & ! % 252.30/37.26 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 252.30/37.26 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = % 252.30/37.26 | v4) | ~ (hAPP(all_1509_1, v2) = v3) | ~ (hAPP(all_1509_1, v0) = % 252.30/37.26 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0) | ~ % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1509_0, v1) | % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)) % 252.30/37.26 | % 252.30/37.26 | ALPHA: (418) implies: % 252.30/37.26 | (419) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1509_0 % 252.30/37.26 | % 252.30/37.26 | DELTA: instantiating (30) with fresh symbols all_1512_0, all_1512_1 gives: % 252.30/37.26 | (420) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1512_1 & % 252.30/37.26 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1512_0 & % 252.30/37.26 | $i(all_1512_0) & $i(all_1512_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 252.30/37.26 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 252.30/37.26 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1512_1, % 252.30/37.26 | v2) = v3) | ~ (hAPP(all_1512_1, v0) = v5) | ~ $i(v2) | ~ % 252.30/37.26 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.30/37.26 | all_1512_0, v1) | ~ % 252.30/37.26 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6) | % 252.30/37.26 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0)) & ! [v0: % 252.30/37.26 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 252.30/37.26 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = % 252.30/37.26 | v4) | ~ (hAPP(all_1512_1, v2) = v3) | ~ (hAPP(all_1512_1, v0) = % 252.30/37.26 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 252.30/37.26 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) | % 252.30/37.26 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6)) & ! [v0: % 252.30/37.26 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 252.30/37.26 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = % 252.30/37.26 | v4) | ~ (hAPP(all_1512_1, v2) = v3) | ~ (hAPP(all_1512_1, v0) = % 252.30/37.26 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 252.30/37.26 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1512_0, v1) | % 252.30/37.26 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6)) % 252.30/37.26 | % 252.30/37.26 | ALPHA: (420) implies: % 252.30/37.26 | (421) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1512_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_820_0, all_829_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (133), (137) gives: % 252.30/37.26 | (422) all_829_0 = all_820_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_817_0, all_829_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (131), (137) gives: % 252.30/37.26 | (423) all_829_0 = all_817_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_829_0, all_832_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (137), (139) gives: % 252.30/37.26 | (424) all_832_0 = all_829_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_832_0, all_837_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (139), (141) gives: % 252.30/37.26 | (425) all_837_0 = all_832_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_853_0, all_857_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (149), (151) gives: % 252.30/37.26 | (426) all_857_0 = all_853_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_857_0, all_860_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (151), (153) gives: % 252.30/37.26 | (427) all_860_0 = all_857_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_860_0, all_862_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (153), (155) gives: % 252.30/37.26 | (428) all_862_0 = all_860_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_862_0, all_867_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (155), (159) gives: % 252.30/37.26 | (429) all_867_0 = all_862_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_867_0, all_870_0, tc_Nat_Onat, % 252.30/37.26 | simplifying with (159), (161) gives: % 252.30/37.26 | (430) all_870_0 = all_867_0 % 252.30/37.26 | % 252.30/37.26 | GROUND_INST: instantiating (123) with all_893_0, all_902_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (169), (171) gives: % 252.30/37.27 | (431) all_902_0 = all_893_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_902_0, all_905_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (171), (173) gives: % 252.30/37.27 | (432) all_905_0 = all_902_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_905_0, all_908_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (173), (175) gives: % 252.30/37.27 | (433) all_908_0 = all_905_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_908_0, all_917_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (175), (177) gives: % 252.30/37.27 | (434) all_917_0 = all_908_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_917_0, all_936_1, tc_Nat_Onat, % 252.30/37.27 | simplifying with (177), (184) gives: % 252.30/37.27 | (435) all_936_1 = all_917_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_842_0, all_957_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (145), (191) gives: % 252.30/37.27 | (436) all_957_0 = all_842_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_840_0, all_957_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (143), (191) gives: % 252.30/37.27 | (437) all_957_0 = all_840_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_837_0, all_957_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (141), (191) gives: % 252.30/37.27 | (438) all_957_0 = all_837_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_985_1, all_996_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (199), (202) gives: % 252.30/37.27 | (439) all_996_0 = all_985_1 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_996_0, all_999_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (202), (204) gives: % 252.30/37.27 | (440) all_999_0 = all_996_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_959_0, all_1008_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (193), (206) gives: % 252.30/37.27 | (441) all_1008_0 = all_959_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_944_0, all_1008_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (187), (206) gives: % 252.30/37.27 | (442) all_1008_0 = all_944_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_936_1, all_1008_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (184), (206) gives: % 252.30/37.27 | (443) all_1008_0 = all_936_1 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1019_0, all_1022_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (210), (212) gives: % 252.30/37.27 | (444) all_1022_0 = all_1019_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_985_1, all_1025_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (199), (214) gives: % 252.30/37.27 | (445) all_1025_0 = all_985_1 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_959_0, all_1025_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (193), (214) gives: % 252.30/37.27 | (446) all_1025_0 = all_959_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1022_0, all_1046_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (212), (220) gives: % 252.30/37.27 | (447) all_1046_0 = all_1022_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1019_0, all_1049_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (210), (222) gives: % 252.30/37.27 | (448) all_1049_0 = all_1019_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_999_0, all_1049_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (204), (222) gives: % 252.30/37.27 | (449) all_1049_0 = all_999_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1046_0, all_1054_1, tc_Nat_Onat, % 252.30/37.27 | simplifying with (220), (224) gives: % 252.30/37.27 | (450) all_1054_1 = all_1046_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1054_1, all_1063_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (224), (227) gives: % 252.30/37.27 | (451) all_1063_0 = all_1054_1 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1063_0, all_1066_1, tc_Nat_Onat, % 252.30/37.27 | simplifying with (227), (229) gives: % 252.30/37.27 | (452) all_1066_1 = all_1063_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1066_1, all_1084_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (229), (239) gives: % 252.30/37.27 | (453) all_1084_0 = all_1066_1 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1084_0, all_1091_1, tc_Nat_Onat, % 252.30/37.27 | simplifying with (239), (241) gives: % 252.30/37.27 | (454) all_1091_1 = all_1084_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1091_1, all_1094_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (241), (243) gives: % 252.30/37.27 | (455) all_1094_0 = all_1091_1 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1094_0, all_1097_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (243), (245) gives: % 252.30/37.27 | (456) all_1097_0 = all_1094_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1097_0, all_1102_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (245), (247) gives: % 252.30/37.27 | (457) all_1102_0 = all_1097_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1102_0, all_1113_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (247), (250) gives: % 252.30/37.27 | (458) all_1113_0 = all_1102_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1113_0, all_1119_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (250), (253) gives: % 252.30/37.27 | (459) all_1119_0 = all_1113_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1119_0, all_1122_0, tc_Nat_Onat, % 252.30/37.27 | simplifying with (253), (255) gives: % 252.30/37.27 | (460) all_1122_0 = all_1119_0 % 252.30/37.27 | % 252.30/37.27 | GROUND_INST: instantiating (123) with all_1122_0, all_1125_2, tc_Nat_Onat, % 252.30/37.27 | simplifying with (255), (257) gives: % 252.30/37.27 | (461) all_1125_2 = all_1122_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1125_2, all_1134_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (257), (261) gives: % 252.30/37.28 | (462) all_1134_0 = all_1125_2 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1134_0, all_1157_2, tc_Nat_Onat, % 252.30/37.28 | simplifying with (261), (266) gives: % 252.30/37.28 | (463) all_1157_2 = all_1134_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1157_2, all_1168_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (266), (278) gives: % 252.30/37.28 | (464) all_1168_0 = all_1157_2 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1168_0, all_1171_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (278), (280) gives: % 252.30/37.28 | (465) all_1171_0 = all_1168_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1171_0, all_1174_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (280), (283) gives: % 252.30/37.28 | (466) all_1174_0 = all_1171_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1174_0, all_1183_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (283), (285) gives: % 252.30/37.28 | (467) all_1183_0 = all_1174_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1183_0, all_1186_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (285), (287) gives: % 252.30/37.28 | (468) all_1186_1 = all_1183_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1186_1, all_1189_2, tc_Nat_Onat, % 252.30/37.28 | simplifying with (287), (289) gives: % 252.30/37.28 | (469) all_1189_2 = all_1186_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1189_2, all_1212_2, tc_Nat_Onat, % 252.30/37.28 | simplifying with (289), (296) gives: % 252.30/37.28 | (470) all_1212_2 = all_1189_2 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1212_2, all_1227_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (296), (299) gives: % 252.30/37.28 | (471) all_1227_1 = all_1212_2 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1227_1, all_1233_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (299), (302) gives: % 252.30/37.28 | (472) all_1233_1 = all_1227_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1233_1, all_1242_2, tc_Nat_Onat, % 252.30/37.28 | simplifying with (302), (304) gives: % 252.30/37.28 | (473) all_1242_2 = all_1233_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1242_2, all_1245_2, tc_Nat_Onat, % 252.30/37.28 | simplifying with (304), (307) gives: % 252.30/37.28 | (474) all_1245_2 = all_1242_2 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1245_2, all_1248_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (307), (310) gives: % 252.30/37.28 | (475) all_1248_0 = all_1245_2 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1248_0, all_1260_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (310), (312) gives: % 252.30/37.28 | (476) all_1260_0 = all_1248_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1260_0, all_1272_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (312), (315) gives: % 252.30/37.28 | (477) all_1272_0 = all_1260_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1272_0, all_1275_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (315), (317) gives: % 252.30/37.28 | (478) all_1275_1 = all_1272_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1275_1, all_1278_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (317), (319) gives: % 252.30/37.28 | (479) all_1278_0 = all_1275_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1278_0, all_1331_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (319), (321) gives: % 252.30/37.28 | (480) all_1331_0 = all_1278_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1331_0, all_1340_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (321), (327) gives: % 252.30/37.28 | (481) all_1340_0 = all_1331_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1340_0, all_1346_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (327), (329) gives: % 252.30/37.28 | (482) all_1346_0 = all_1340_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_893_0, all_1349_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (169), (331) gives: % 252.30/37.28 | (483) all_1349_1 = all_893_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_870_0, all_1349_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (161), (331) gives: % 252.30/37.28 | (484) all_1349_1 = all_870_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1346_0, all_1352_2, tc_Nat_Onat, % 252.30/37.28 | simplifying with (329), (334) gives: % 252.30/37.28 | (485) all_1352_2 = all_1346_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1363_0, all_1366_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (339), (341) gives: % 252.30/37.28 | (486) all_1366_0 = all_1363_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1366_0, all_1369_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (341), (343) gives: % 252.30/37.28 | (487) all_1369_0 = all_1366_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1349_1, all_1375_2, tc_Nat_Onat, % 252.30/37.28 | simplifying with (331), (345) gives: % 252.30/37.28 | (488) all_1375_2 = all_1349_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_875_0, all_1375_2, tc_Nat_Onat, % 252.30/37.28 | simplifying with (165), (345) gives: % 252.30/37.28 | (489) all_1375_2 = all_875_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1363_0, all_1402_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (339), (355) gives: % 252.30/37.28 | (490) all_1402_0 = all_1363_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1352_2, all_1402_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (334), (355) gives: % 252.30/37.28 | (491) all_1402_0 = all_1352_2 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1393_1, all_1411_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (352), (359) gives: % 252.30/37.28 | (492) all_1411_0 = all_1393_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_823_0, all_1411_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (135), (359) gives: % 252.30/37.28 | (493) all_1411_0 = all_823_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1411_0, all_1423_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (359), (362) gives: % 252.30/37.28 | (494) all_1423_1 = all_1411_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1423_1, all_1426_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (362), (366) gives: % 252.30/37.28 | (495) all_1426_1 = all_1423_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1426_1, all_1429_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (366), (369) gives: % 252.30/37.28 | (496) all_1429_1 = all_1426_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1429_1, all_1432_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (369), (372) gives: % 252.30/37.28 | (497) all_1432_0 = all_1429_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1049_0, all_1438_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (222), (374) gives: % 252.30/37.28 | (498) all_1438_0 = all_1049_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1402_0, all_1444_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (355), (376) gives: % 252.30/37.28 | (499) all_1444_1 = all_1402_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1444_1, all_1450_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (376), (378) gives: % 252.30/37.28 | (500) all_1450_1 = all_1444_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1450_1, all_1453_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (378), (380) gives: % 252.30/37.28 | (501) all_1453_1 = all_1450_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1393_1, all_1456_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (352), (383) gives: % 252.30/37.28 | (502) all_1456_1 = all_1393_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1390_1, all_1456_1, tc_Nat_Onat, % 252.30/37.28 | simplifying with (350), (383) gives: % 252.30/37.28 | (503) all_1456_1 = all_1390_1 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1432_0, all_1459_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (372), (385) gives: % 252.30/37.28 | (504) all_1459_0 = all_1432_0 % 252.30/37.28 | % 252.30/37.28 | GROUND_INST: instantiating (123) with all_1459_0, all_1462_0, tc_Nat_Onat, % 252.30/37.28 | simplifying with (385), (387) gives: % 252.30/37.28 | (505) all_1462_0 = all_1459_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1453_1, all_1468_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (380), (389) gives: % 252.30/37.29 | (506) all_1468_1 = all_1453_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1468_1, all_1471_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (389), (391) gives: % 252.30/37.29 | (507) all_1471_0 = all_1468_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1462_0, all_1474_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (387), (393) gives: % 252.30/37.29 | (508) all_1474_1 = all_1462_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1456_1, all_1477_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (383), (396) gives: % 252.30/37.29 | (509) all_1477_1 = all_1456_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1384_0, all_1477_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (348), (396) gives: % 252.30/37.29 | (510) all_1477_1 = all_1384_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1369_0, all_1477_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (343), (396) gives: % 252.30/37.29 | (511) all_1477_1 = all_1369_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1471_0, all_1480_2, tc_Nat_Onat, % 252.30/37.29 | simplifying with (391), (398) gives: % 252.30/37.29 | (512) all_1480_2 = all_1471_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1025_0, all_1488_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (214), (401) gives: % 252.30/37.29 | (513) all_1488_0 = all_1025_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1480_2, all_1491_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (398), (403) gives: % 252.30/37.29 | (514) all_1491_0 = all_1480_2 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1491_0, all_1494_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (403), (405) gives: % 252.30/37.29 | (515) all_1494_1 = all_1491_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1494_1, all_1497_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (405), (408) gives: % 252.30/37.29 | (516) all_1497_1 = all_1494_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1438_0, all_1500_2, tc_Nat_Onat, % 252.30/37.29 | simplifying with (374), (411) gives: % 252.30/37.29 | (517) all_1500_2 = all_1438_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1016_0, all_1500_2, tc_Nat_Onat, % 252.30/37.29 | simplifying with (208), (411) gives: % 252.30/37.29 | (518) all_1500_2 = all_1016_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_853_0, all_1503_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (149), (415) gives: % 252.30/37.29 | (519) all_1503_0 = all_853_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_845_0, all_1503_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (147), (415) gives: % 252.30/37.29 | (520) all_1503_0 = all_845_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_842_0, all_1503_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (145), (415) gives: % 252.30/37.29 | (521) all_1503_0 = all_842_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1474_1, all_1506_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (393), (417) gives: % 252.30/37.29 | (522) all_1506_0 = all_1474_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1405_0, all_1506_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (357), (417) gives: % 252.30/37.29 | (523) all_1506_0 = all_1405_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1488_0, all_1509_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (401), (419) gives: % 252.30/37.29 | (524) all_1509_0 = all_1488_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_982_0, all_1509_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (197), (419) gives: % 252.30/37.29 | (525) all_1509_0 = all_982_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1497_1, all_1512_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (408), (421) gives: % 252.30/37.29 | (526) all_1512_0 = all_1497_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (123) with all_1355_0, all_1512_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (337), (421) gives: % 252.30/37.29 | (527) all_1512_0 = all_1355_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (124) with all_1072_1, all_1160_4, t_a, simplifying % 252.30/37.29 | with (233), (273) gives: % 252.30/37.29 | (528) all_1160_4 = all_1072_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_865_0, all_890_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (157), (167) gives: % 252.30/37.29 | (529) all_890_0 = all_865_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_890_0, all_927_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (167), (179) gives: % 252.30/37.29 | (530) all_927_0 = all_890_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_927_0, all_933_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (179), (181) gives: % 252.30/37.29 | (531) all_933_0 = all_927_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_933_0, all_954_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (181), (189) gives: % 252.30/37.29 | (532) all_954_0 = all_933_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_979_0, all_1043_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (195), (218) gives: % 252.30/37.29 | (533) all_1043_0 = all_979_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_954_0, all_1043_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (189), (218) gives: % 252.30/37.29 | (534) all_1043_0 = all_954_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_870_1, all_1043_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (162), (218) gives: % 252.30/37.29 | (535) all_1043_0 = all_870_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1043_0, all_1078_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (218), (237) gives: % 252.30/37.29 | (536) all_1078_1 = all_1043_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1078_1, all_1137_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (237), (263) gives: % 252.30/37.29 | (537) all_1137_0 = all_1078_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1137_0, all_1171_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (263), (281) gives: % 252.30/37.29 | (538) all_1171_1 = all_1137_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1171_1, all_1209_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (281), (293) gives: % 252.30/37.29 | (539) all_1209_0 = all_1171_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1337_0, all_1349_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (325), (332) gives: % 252.30/37.29 | (540) all_1349_0 = all_1337_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1352_0, all_1375_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (335), (346) gives: % 252.30/37.29 | (541) all_1375_0 = all_1352_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1349_0, all_1375_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (332), (346) gives: % 252.30/37.29 | (542) all_1375_0 = all_1349_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1040_0, all_1375_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (216), (346) gives: % 252.30/37.29 | (543) all_1375_0 = all_1040_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1337_0, all_1453_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (325), (381) gives: % 252.30/37.29 | (544) all_1453_0 = all_1337_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1334_1, all_1453_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (323), (381) gives: % 252.30/37.29 | (545) all_1453_0 = all_1334_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (125) with all_1209_0, all_1453_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (293), (381) gives: % 252.30/37.29 | (546) all_1453_0 = all_1209_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (126) with all_1189_0, all_1209_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (290), (294) gives: % 252.30/37.29 | (547) all_1209_1 = all_1189_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (126) with all_1209_1, all_1227_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (294), (300) gives: % 252.30/37.29 | (548) all_1227_0 = all_1209_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (126) with all_1227_0, all_1260_1, tc_Nat_Onat, % 252.30/37.29 | simplifying with (300), (313) gives: % 252.30/37.29 | (549) all_1260_1 = all_1227_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (126) with all_1260_1, all_1423_2, tc_Nat_Onat, % 252.30/37.29 | simplifying with (313), (363) gives: % 252.30/37.29 | (550) all_1423_2 = all_1260_1 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (126) with all_1423_2, all_1426_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (363), (367) gives: % 252.30/37.29 | (551) all_1426_0 = all_1423_2 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (126) with all_1426_0, all_1429_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (367), (370) gives: % 252.30/37.29 | (552) all_1429_0 = all_1426_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (126) with all_1429_0, all_1474_0, tc_Nat_Onat, % 252.30/37.29 | simplifying with (370), (394) gives: % 252.30/37.29 | (553) all_1474_0 = all_1429_0 % 252.30/37.29 | % 252.30/37.29 | GROUND_INST: instantiating (126) with all_1157_3, all_1474_0, tc_Nat_Onat, % 252.30/37.30 | simplifying with (267), (394) gives: % 252.30/37.30 | (554) all_1474_0 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (526), (527) imply: % 252.30/37.30 | (555) all_1497_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (555) implies: % 252.30/37.30 | (556) all_1497_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (524), (525) imply: % 252.30/37.30 | (557) all_1488_0 = all_982_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (557) implies: % 252.30/37.30 | (558) all_1488_0 = all_982_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (522), (523) imply: % 252.30/37.30 | (559) all_1474_1 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (559) implies: % 252.30/37.30 | (560) all_1474_1 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (519), (520) imply: % 252.30/37.30 | (561) all_853_0 = all_845_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (561) implies: % 252.30/37.30 | (562) all_853_0 = all_845_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (520), (521) imply: % 252.30/37.30 | (563) all_845_0 = all_842_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (517), (518) imply: % 252.30/37.30 | (564) all_1438_0 = all_1016_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (564) implies: % 252.30/37.30 | (565) all_1438_0 = all_1016_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (516), (556) imply: % 252.30/37.30 | (566) all_1494_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (566) implies: % 252.30/37.30 | (567) all_1494_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (515), (567) imply: % 252.30/37.30 | (568) all_1491_0 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (568) implies: % 252.30/37.30 | (569) all_1491_0 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (514), (569) imply: % 252.30/37.30 | (570) all_1480_2 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (570) implies: % 252.30/37.30 | (571) all_1480_2 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (513), (558) imply: % 252.30/37.30 | (572) all_1025_0 = all_982_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (572) implies: % 252.30/37.30 | (573) all_1025_0 = all_982_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (512), (571) imply: % 252.30/37.30 | (574) all_1471_0 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (574) implies: % 252.30/37.30 | (575) all_1471_0 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (509), (510) imply: % 252.30/37.30 | (576) all_1456_1 = all_1384_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (576) implies: % 252.30/37.30 | (577) all_1456_1 = all_1384_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (510), (511) imply: % 252.30/37.30 | (578) all_1384_0 = all_1369_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (553), (554) imply: % 252.30/37.30 | (579) all_1429_0 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | SIMP: (579) implies: % 252.30/37.30 | (580) all_1429_0 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (508), (560) imply: % 252.30/37.30 | (581) all_1462_0 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (581) implies: % 252.30/37.30 | (582) all_1462_0 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (507), (575) imply: % 252.30/37.30 | (583) all_1468_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (583) implies: % 252.30/37.30 | (584) all_1468_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (506), (584) imply: % 252.30/37.30 | (585) all_1453_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (585) implies: % 252.30/37.30 | (586) all_1453_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (505), (582) imply: % 252.30/37.30 | (587) all_1459_0 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (587) implies: % 252.30/37.30 | (588) all_1459_0 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (504), (588) imply: % 252.30/37.30 | (589) all_1432_0 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (589) implies: % 252.30/37.30 | (590) all_1432_0 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (502), (503) imply: % 252.30/37.30 | (591) all_1393_1 = all_1390_1 % 252.30/37.30 | % 252.30/37.30 | SIMP: (591) implies: % 252.30/37.30 | (592) all_1393_1 = all_1390_1 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (503), (577) imply: % 252.30/37.30 | (593) all_1390_1 = all_1384_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (544), (545) imply: % 252.30/37.30 | (594) all_1337_0 = all_1334_1 % 252.30/37.30 | % 252.30/37.30 | SIMP: (594) implies: % 252.30/37.30 | (595) all_1337_0 = all_1334_1 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (545), (546) imply: % 252.30/37.30 | (596) all_1334_1 = all_1209_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (501), (586) imply: % 252.30/37.30 | (597) all_1450_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (597) implies: % 252.30/37.30 | (598) all_1450_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (500), (598) imply: % 252.30/37.30 | (599) all_1444_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (599) implies: % 252.30/37.30 | (600) all_1444_1 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (499), (600) imply: % 252.30/37.30 | (601) all_1402_0 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (601) implies: % 252.30/37.30 | (602) all_1402_0 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (498), (565) imply: % 252.30/37.30 | (603) all_1049_0 = all_1016_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (603) implies: % 252.30/37.30 | (604) all_1049_0 = all_1016_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (497), (590) imply: % 252.30/37.30 | (605) all_1429_1 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (605) implies: % 252.30/37.30 | (606) all_1429_1 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (552), (580) imply: % 252.30/37.30 | (607) all_1426_0 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | SIMP: (607) implies: % 252.30/37.30 | (608) all_1426_0 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (496), (606) imply: % 252.30/37.30 | (609) all_1426_1 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (609) implies: % 252.30/37.30 | (610) all_1426_1 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (551), (608) imply: % 252.30/37.30 | (611) all_1423_2 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | SIMP: (611) implies: % 252.30/37.30 | (612) all_1423_2 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (495), (610) imply: % 252.30/37.30 | (613) all_1423_1 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (613) implies: % 252.30/37.30 | (614) all_1423_1 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (494), (614) imply: % 252.30/37.30 | (615) all_1411_0 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (615) implies: % 252.30/37.30 | (616) all_1411_0 = all_1405_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (550), (612) imply: % 252.30/37.30 | (617) all_1260_1 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | SIMP: (617) implies: % 252.30/37.30 | (618) all_1260_1 = all_1157_3 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (493), (616) imply: % 252.30/37.30 | (619) all_1405_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (492), (616) imply: % 252.30/37.30 | (620) all_1405_0 = all_1393_1 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (619), (620) imply: % 252.30/37.30 | (621) all_1393_1 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (621) implies: % 252.30/37.30 | (622) all_1393_1 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (491), (602) imply: % 252.30/37.30 | (623) all_1355_0 = all_1352_2 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (490), (602) imply: % 252.30/37.30 | (624) all_1363_0 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (624) implies: % 252.30/37.30 | (625) all_1363_0 = all_1355_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (592), (622) imply: % 252.30/37.30 | (626) all_1390_1 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (626) implies: % 252.30/37.30 | (627) all_1390_1 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (593), (627) imply: % 252.30/37.30 | (628) all_1384_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (628) implies: % 252.30/37.30 | (629) all_1384_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (578), (629) imply: % 252.30/37.30 | (630) all_1369_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (630) implies: % 252.30/37.30 | (631) all_1369_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (541), (542) imply: % 252.30/37.30 | (632) all_1352_0 = all_1349_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (541), (543) imply: % 252.30/37.30 | (633) all_1352_0 = all_1040_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (488), (489) imply: % 252.30/37.30 | (634) all_1349_1 = all_875_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (634) implies: % 252.30/37.30 | (635) all_1349_1 = all_875_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (487), (631) imply: % 252.30/37.30 | (636) all_1366_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (636) implies: % 252.30/37.30 | (637) all_1366_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (486), (637) imply: % 252.30/37.30 | (638) all_1363_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (638) implies: % 252.30/37.30 | (639) all_1363_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (625), (639) imply: % 252.30/37.30 | (640) all_1355_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (640) implies: % 252.30/37.30 | (641) all_1355_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (623), (641) imply: % 252.30/37.30 | (642) all_1352_2 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (642) implies: % 252.30/37.30 | (643) all_1352_2 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (632), (633) imply: % 252.30/37.30 | (644) all_1349_0 = all_1040_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (644) implies: % 252.30/37.30 | (645) all_1349_0 = all_1040_0 % 252.30/37.30 | % 252.30/37.30 | COMBINE_EQS: (485), (643) imply: % 252.30/37.30 | (646) all_1346_0 = all_823_0 % 252.30/37.30 | % 252.30/37.30 | SIMP: (646) implies: % 252.30/37.30 | (647) all_1346_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (540), (645) imply: % 252.30/37.31 | (648) all_1337_0 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (648) implies: % 252.30/37.31 | (649) all_1337_0 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (484), (635) imply: % 252.30/37.31 | (650) all_875_0 = all_870_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (483), (635) imply: % 252.30/37.31 | (651) all_893_0 = all_875_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (651) implies: % 252.30/37.31 | (652) all_893_0 = all_875_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (482), (647) imply: % 252.30/37.31 | (653) all_1340_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (653) implies: % 252.30/37.31 | (654) all_1340_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (481), (654) imply: % 252.30/37.31 | (655) all_1331_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (655) implies: % 252.30/37.31 | (656) all_1331_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (595), (649) imply: % 252.30/37.31 | (657) all_1334_1 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (657) implies: % 252.30/37.31 | (658) all_1334_1 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (596), (658) imply: % 252.30/37.31 | (659) all_1209_0 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (659) implies: % 252.30/37.31 | (660) all_1209_0 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (480), (656) imply: % 252.30/37.31 | (661) all_1278_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (661) implies: % 252.30/37.31 | (662) all_1278_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (479), (662) imply: % 252.30/37.31 | (663) all_1275_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (663) implies: % 252.30/37.31 | (664) all_1275_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (478), (664) imply: % 252.30/37.31 | (665) all_1272_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (665) implies: % 252.30/37.31 | (666) all_1272_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (477), (666) imply: % 252.30/37.31 | (667) all_1260_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (667) implies: % 252.30/37.31 | (668) all_1260_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (476), (668) imply: % 252.30/37.31 | (669) all_1248_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (669) implies: % 252.30/37.31 | (670) all_1248_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (549), (618) imply: % 252.30/37.31 | (671) all_1227_0 = all_1157_3 % 252.30/37.31 | % 252.30/37.31 | SIMP: (671) implies: % 252.30/37.31 | (672) all_1227_0 = all_1157_3 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (475), (670) imply: % 252.30/37.31 | (673) all_1245_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (673) implies: % 252.30/37.31 | (674) all_1245_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (474), (674) imply: % 252.30/37.31 | (675) all_1242_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (675) implies: % 252.30/37.31 | (676) all_1242_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (473), (676) imply: % 252.30/37.31 | (677) all_1233_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (677) implies: % 252.30/37.31 | (678) all_1233_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (472), (678) imply: % 252.30/37.31 | (679) all_1227_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (679) implies: % 252.30/37.31 | (680) all_1227_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (548), (672) imply: % 252.30/37.31 | (681) all_1209_1 = all_1157_3 % 252.30/37.31 | % 252.30/37.31 | SIMP: (681) implies: % 252.30/37.31 | (682) all_1209_1 = all_1157_3 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (471), (680) imply: % 252.30/37.31 | (683) all_1212_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (683) implies: % 252.30/37.31 | (684) all_1212_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (470), (684) imply: % 252.30/37.31 | (685) all_1189_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (685) implies: % 252.30/37.31 | (686) all_1189_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (539), (660) imply: % 252.30/37.31 | (687) all_1171_1 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (687) implies: % 252.30/37.31 | (688) all_1171_1 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (547), (682) imply: % 252.30/37.31 | (689) all_1189_0 = all_1157_3 % 252.30/37.31 | % 252.30/37.31 | SIMP: (689) implies: % 252.30/37.31 | (690) all_1189_0 = all_1157_3 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (469), (686) imply: % 252.30/37.31 | (691) all_1186_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (691) implies: % 252.30/37.31 | (692) all_1186_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (468), (692) imply: % 252.30/37.31 | (693) all_1183_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (693) implies: % 252.30/37.31 | (694) all_1183_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (467), (694) imply: % 252.30/37.31 | (695) all_1174_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (695) implies: % 252.30/37.31 | (696) all_1174_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (466), (696) imply: % 252.30/37.31 | (697) all_1171_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (697) implies: % 252.30/37.31 | (698) all_1171_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (465), (698) imply: % 252.30/37.31 | (699) all_1168_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (699) implies: % 252.30/37.31 | (700) all_1168_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (538), (688) imply: % 252.30/37.31 | (701) all_1137_0 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (701) implies: % 252.30/37.31 | (702) all_1137_0 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (464), (700) imply: % 252.30/37.31 | (703) all_1157_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (703) implies: % 252.30/37.31 | (704) all_1157_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (463), (704) imply: % 252.30/37.31 | (705) all_1134_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (705) implies: % 252.30/37.31 | (706) all_1134_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (537), (702) imply: % 252.30/37.31 | (707) all_1078_1 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (707) implies: % 252.30/37.31 | (708) all_1078_1 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (462), (706) imply: % 252.30/37.31 | (709) all_1125_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (709) implies: % 252.30/37.31 | (710) all_1125_2 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (461), (710) imply: % 252.30/37.31 | (711) all_1122_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (711) implies: % 252.30/37.31 | (712) all_1122_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (460), (712) imply: % 252.30/37.31 | (713) all_1119_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (713) implies: % 252.30/37.31 | (714) all_1119_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (459), (714) imply: % 252.30/37.31 | (715) all_1113_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (715) implies: % 252.30/37.31 | (716) all_1113_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (458), (716) imply: % 252.30/37.31 | (717) all_1102_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (717) implies: % 252.30/37.31 | (718) all_1102_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (457), (718) imply: % 252.30/37.31 | (719) all_1097_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (719) implies: % 252.30/37.31 | (720) all_1097_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (456), (720) imply: % 252.30/37.31 | (721) all_1094_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (721) implies: % 252.30/37.31 | (722) all_1094_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (455), (722) imply: % 252.30/37.31 | (723) all_1091_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (723) implies: % 252.30/37.31 | (724) all_1091_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (454), (724) imply: % 252.30/37.31 | (725) all_1084_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (725) implies: % 252.30/37.31 | (726) all_1084_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (453), (726) imply: % 252.30/37.31 | (727) all_1066_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (727) implies: % 252.30/37.31 | (728) all_1066_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (536), (708) imply: % 252.30/37.31 | (729) all_1043_0 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (729) implies: % 252.30/37.31 | (730) all_1043_0 = all_1040_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (452), (728) imply: % 252.30/37.31 | (731) all_1063_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (731) implies: % 252.30/37.31 | (732) all_1063_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (451), (732) imply: % 252.30/37.31 | (733) all_1054_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (733) implies: % 252.30/37.31 | (734) all_1054_1 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (450), (734) imply: % 252.30/37.31 | (735) all_1046_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (735) implies: % 252.30/37.31 | (736) all_1046_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (448), (604) imply: % 252.30/37.31 | (737) all_1019_0 = all_1016_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (737) implies: % 252.30/37.31 | (738) all_1019_0 = all_1016_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (449), (604) imply: % 252.30/37.31 | (739) all_1016_0 = all_999_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (447), (736) imply: % 252.30/37.31 | (740) all_1022_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (740) implies: % 252.30/37.31 | (741) all_1022_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (533), (730) imply: % 252.30/37.31 | (742) all_1040_0 = all_979_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (534), (730) imply: % 252.30/37.31 | (743) all_1040_0 = all_954_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (535), (730) imply: % 252.30/37.31 | (744) all_1040_0 = all_870_1 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (742), (744) imply: % 252.30/37.31 | (745) all_979_0 = all_870_1 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (742), (743) imply: % 252.30/37.31 | (746) all_979_0 = all_954_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (445), (573) imply: % 252.30/37.31 | (747) all_985_1 = all_982_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (747) implies: % 252.30/37.31 | (748) all_985_1 = all_982_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (446), (573) imply: % 252.30/37.31 | (749) all_982_0 = all_959_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (444), (741) imply: % 252.30/37.31 | (750) all_1019_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (750) implies: % 252.30/37.31 | (751) all_1019_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (738), (751) imply: % 252.30/37.31 | (752) all_1016_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (752) implies: % 252.30/37.31 | (753) all_1016_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (739), (753) imply: % 252.30/37.31 | (754) all_999_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (754) implies: % 252.30/37.31 | (755) all_999_0 = all_823_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (442), (443) imply: % 252.30/37.31 | (756) all_944_0 = all_936_1 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (441), (442) imply: % 252.30/37.31 | (757) all_959_0 = all_944_0 % 252.30/37.31 | % 252.30/37.31 | SIMP: (757) implies: % 252.30/37.31 | (758) all_959_0 = all_944_0 % 252.30/37.31 | % 252.30/37.31 | COMBINE_EQS: (440), (755) imply: % 252.30/37.31 | (759) all_996_0 = all_823_0 % 252.30/37.31 | % 252.30/37.32 | SIMP: (759) implies: % 252.30/37.32 | (760) all_996_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (439), (760) imply: % 252.30/37.32 | (761) all_985_1 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (761) implies: % 252.30/37.32 | (762) all_985_1 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (748), (762) imply: % 252.30/37.32 | (763) all_982_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (763) implies: % 252.30/37.32 | (764) all_982_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (749), (764) imply: % 252.30/37.32 | (765) all_959_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (765) implies: % 252.30/37.32 | (766) all_959_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (745), (746) imply: % 252.30/37.32 | (767) all_954_0 = all_870_1 % 252.30/37.32 | % 252.30/37.32 | SIMP: (767) implies: % 252.30/37.32 | (768) all_954_0 = all_870_1 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (758), (766) imply: % 252.30/37.32 | (769) all_944_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (769) implies: % 252.30/37.32 | (770) all_944_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (436), (437) imply: % 252.30/37.32 | (771) all_842_0 = all_840_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (771) implies: % 252.30/37.32 | (772) all_842_0 = all_840_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (437), (438) imply: % 252.30/37.32 | (773) all_840_0 = all_837_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (532), (768) imply: % 252.30/37.32 | (774) all_933_0 = all_870_1 % 252.30/37.32 | % 252.30/37.32 | SIMP: (774) implies: % 252.30/37.32 | (775) all_933_0 = all_870_1 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (756), (770) imply: % 252.30/37.32 | (776) all_936_1 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (776) implies: % 252.30/37.32 | (777) all_936_1 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (435), (777) imply: % 252.30/37.32 | (778) all_917_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (778) implies: % 252.30/37.32 | (779) all_917_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (531), (775) imply: % 252.30/37.32 | (780) all_927_0 = all_870_1 % 252.30/37.32 | % 252.30/37.32 | SIMP: (780) implies: % 252.30/37.32 | (781) all_927_0 = all_870_1 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (530), (781) imply: % 252.30/37.32 | (782) all_890_0 = all_870_1 % 252.30/37.32 | % 252.30/37.32 | SIMP: (782) implies: % 252.30/37.32 | (783) all_890_0 = all_870_1 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (434), (779) imply: % 252.30/37.32 | (784) all_908_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (784) implies: % 252.30/37.32 | (785) all_908_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (433), (785) imply: % 252.30/37.32 | (786) all_905_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (786) implies: % 252.30/37.32 | (787) all_905_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (432), (787) imply: % 252.30/37.32 | (788) all_902_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (788) implies: % 252.30/37.32 | (789) all_902_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (431), (789) imply: % 252.30/37.32 | (790) all_893_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (790) implies: % 252.30/37.32 | (791) all_893_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (652), (791) imply: % 252.30/37.32 | (792) all_875_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (792) implies: % 252.30/37.32 | (793) all_875_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (529), (783) imply: % 252.30/37.32 | (794) all_870_1 = all_865_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (650), (793) imply: % 252.30/37.32 | (795) all_870_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (795) implies: % 252.30/37.32 | (796) all_870_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (430), (796) imply: % 252.30/37.32 | (797) all_867_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (797) implies: % 252.30/37.32 | (798) all_867_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (429), (798) imply: % 252.30/37.32 | (799) all_862_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (799) implies: % 252.30/37.32 | (800) all_862_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (428), (800) imply: % 252.30/37.32 | (801) all_860_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (801) implies: % 252.30/37.32 | (802) all_860_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (427), (802) imply: % 252.30/37.32 | (803) all_857_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (803) implies: % 252.30/37.32 | (804) all_857_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (426), (804) imply: % 252.30/37.32 | (805) all_853_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (805) implies: % 252.30/37.32 | (806) all_853_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (562), (806) imply: % 252.30/37.32 | (807) all_845_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (807) implies: % 252.30/37.32 | (808) all_845_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (563), (808) imply: % 252.30/37.32 | (809) all_842_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (809) implies: % 252.30/37.32 | (810) all_842_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (772), (810) imply: % 252.30/37.32 | (811) all_840_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (811) implies: % 252.30/37.32 | (812) all_840_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | COMBINE_EQS: (773), (812) imply: % 252.30/37.32 | (813) all_837_0 = all_823_0 % 252.30/37.32 | % 252.30/37.32 | SIMP: (813) implies: % 252.71/37.32 | (814) all_837_0 = all_823_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (425), (814) imply: % 252.71/37.32 | (815) all_832_0 = all_823_0 % 252.71/37.32 | % 252.71/37.32 | SIMP: (815) implies: % 252.71/37.32 | (816) all_832_0 = all_823_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (424), (816) imply: % 252.71/37.32 | (817) all_829_0 = all_823_0 % 252.71/37.32 | % 252.71/37.32 | SIMP: (817) implies: % 252.71/37.32 | (818) all_829_0 = all_823_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (422), (818) imply: % 252.71/37.32 | (819) all_823_0 = all_820_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (423), (818) imply: % 252.71/37.32 | (820) all_823_0 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (819), (820) imply: % 252.71/37.32 | (821) all_820_0 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | SIMP: (821) implies: % 252.71/37.32 | (822) all_820_0 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (796), (820) imply: % 252.71/37.32 | (823) all_870_0 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (777), (820) imply: % 252.71/37.32 | (824) all_936_1 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (762), (820) imply: % 252.71/37.32 | (825) all_985_1 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (753), (820) imply: % 252.71/37.32 | (826) all_1016_0 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (734), (820) imply: % 252.71/37.32 | (827) all_1054_1 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (728), (820) imply: % 252.71/37.32 | (828) all_1066_1 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (710), (820) imply: % 252.71/37.32 | (829) all_1125_2 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (704), (820) imply: % 252.71/37.32 | (830) all_1157_2 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (686), (820) imply: % 252.71/37.32 | (831) all_1189_2 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (684), (820) imply: % 252.71/37.32 | (832) all_1212_2 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (676), (820) imply: % 252.71/37.32 | (833) all_1242_2 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (674), (820) imply: % 252.71/37.32 | (834) all_1245_2 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (641), (820) imply: % 252.71/37.32 | (835) all_1355_0 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (622), (820) imply: % 252.71/37.32 | (836) all_1393_1 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (619), (820) imply: % 252.71/37.32 | (837) all_1405_0 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (616), (837) imply: % 252.71/37.32 | (838) all_1411_0 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (614), (837) imply: % 252.71/37.32 | (839) all_1423_1 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (571), (835) imply: % 252.71/37.32 | (840) all_1480_2 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (567), (835) imply: % 252.71/37.32 | (841) all_1494_1 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (556), (835) imply: % 252.71/37.32 | (842) all_1497_1 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | COMBINE_EQS: (518), (826) imply: % 252.71/37.32 | (843) all_1500_2 = all_817_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (412), (843) imply: % 252.71/37.32 | (844) c_Nat_OSuc(all_817_0) = all_1500_1 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (409), (842) imply: % 252.71/37.32 | (845) c_Nat_OSuc(all_817_0) = all_1497_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (406), (841) imply: % 252.71/37.32 | (846) c_Nat_OSuc(all_817_0) = all_1494_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (399), (840) imply: % 252.71/37.32 | (847) c_Nat_OSuc(all_817_0) = all_1480_1 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (364), (839) imply: % 252.71/37.32 | (848) c_Nat_OSuc(all_817_0) = all_1423_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (353), (836) imply: % 252.71/37.32 | (849) c_Nat_OSuc(all_817_0) = all_1393_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (308), (834) imply: % 252.71/37.32 | (850) c_Nat_OSuc(all_817_0) = all_1245_1 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (305), (833) imply: % 252.71/37.32 | (851) c_Nat_OSuc(all_817_0) = all_1242_1 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (297), (832) imply: % 252.71/37.32 | (852) c_Nat_OSuc(all_817_0) = all_1212_1 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (291), (831) imply: % 252.71/37.32 | (853) c_Nat_OSuc(all_817_0) = all_1189_1 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (268), (830) imply: % 252.71/37.32 | (854) c_Nat_OSuc(all_817_0) = all_1157_1 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (258), (829) imply: % 252.71/37.32 | (855) c_Nat_OSuc(all_817_0) = all_1125_1 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (230), (828) imply: % 252.71/37.32 | (856) c_Nat_OSuc(all_817_0) = all_1066_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (225), (827) imply: % 252.71/37.32 | (857) c_Nat_OSuc(all_817_0) = all_1054_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (200), (825) imply: % 252.71/37.32 | (858) c_Nat_OSuc(all_817_0) = all_985_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (185), (824) imply: % 252.71/37.32 | (859) c_Nat_OSuc(all_817_0) = all_936_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (163), (794), (823) imply: % 252.71/37.32 | (860) c_Nat_OSuc(all_817_0) = all_865_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (275), (528) imply: % 252.71/37.32 | (861) c_Groups_Oplus__class_Oplus(all_1072_1, all_1160_2, all_1160_1) = % 252.71/37.32 | all_1160_0 % 252.71/37.32 | % 252.71/37.32 | REDUCE: (272), (528) imply: % 252.71/37.32 | (862) c_Groups_Ozero__class_Ozero(all_1072_1) = all_1160_0 % 252.71/37.32 | % 252.71/37.32 | GROUND_INST: instantiating (123) with all_1072_0, all_1160_0, all_1072_1, % 252.71/37.32 | simplifying with (232), (862) gives: % 252.71/37.32 | (863) all_1160_0 = all_1072_0 % 252.71/37.32 | % 252.71/37.32 | GROUND_INST: instantiating (127) with all_936_0, all_1054_0, all_817_0, % 252.71/37.32 | simplifying with (857), (859) gives: % 252.71/37.32 | (864) all_1054_0 = all_936_0 % 252.71/37.32 | % 252.71/37.32 | GROUND_INST: instantiating (127) with all_1054_0, all_1066_0, all_817_0, % 252.71/37.32 | simplifying with (856), (857) gives: % 252.71/37.32 | (865) all_1066_0 = all_1054_0 % 252.71/37.32 | % 252.71/37.32 | GROUND_INST: instantiating (127) with all_1066_0, all_1125_1, all_817_0, % 252.71/37.32 | simplifying with (855), (856) gives: % 252.71/37.32 | (866) all_1125_1 = all_1066_0 % 252.71/37.32 | % 252.71/37.32 | GROUND_INST: instantiating (127) with all_1125_1, all_1157_1, all_817_0, % 252.71/37.32 | simplifying with (854), (855) gives: % 252.71/37.32 | (867) all_1157_1 = all_1125_1 % 252.71/37.32 | % 252.71/37.32 | GROUND_INST: instantiating (127) with all_1157_1, all_1189_1, all_817_0, % 252.71/37.32 | simplifying with (853), (854) gives: % 252.71/37.32 | (868) all_1189_1 = all_1157_1 % 252.71/37.32 | % 252.71/37.32 | GROUND_INST: instantiating (127) with all_1054_0, all_1242_1, all_817_0, % 252.71/37.32 | simplifying with (851), (857) gives: % 252.71/37.32 | (869) all_1242_1 = all_1054_0 % 252.71/37.32 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_985_0, all_1242_1, all_817_0, % 252.71/37.33 | simplifying with (851), (858) gives: % 252.71/37.33 | (870) all_1242_1 = all_985_0 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1242_1, all_1393_0, all_817_0, % 252.71/37.33 | simplifying with (849), (851) gives: % 252.71/37.33 | (871) all_1393_0 = all_1242_1 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1212_1, all_1393_0, all_817_0, % 252.71/37.33 | simplifying with (849), (852) gives: % 252.71/37.33 | (872) all_1393_0 = all_1212_1 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1423_0, all_1480_1, all_817_0, % 252.71/37.33 | simplifying with (847), (848) gives: % 252.71/37.33 | (873) all_1480_1 = all_1423_0 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1189_1, all_1480_1, all_817_0, % 252.71/37.33 | simplifying with (847), (853) gives: % 252.71/37.33 | (874) all_1480_1 = all_1189_1 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1480_1, all_1494_0, all_817_0, % 252.71/37.33 | simplifying with (846), (847) gives: % 252.71/37.33 | (875) all_1494_0 = all_1480_1 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1393_0, all_1497_0, all_817_0, % 252.71/37.33 | simplifying with (845), (849) gives: % 252.71/37.33 | (876) all_1497_0 = all_1393_0 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1245_1, all_1497_0, all_817_0, % 252.71/37.33 | simplifying with (845), (850) gives: % 252.71/37.33 | (877) all_1497_0 = all_1245_1 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1494_0, all_1500_1, all_817_0, % 252.71/37.33 | simplifying with (844), (846) gives: % 252.71/37.33 | (878) all_1500_1 = all_1494_0 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_865_0, all_1500_1, all_817_0, % 252.71/37.33 | simplifying with (844), (860) gives: % 252.71/37.33 | (879) all_1500_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (878), (879) imply: % 252.71/37.33 | (880) all_1494_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (880) implies: % 252.71/37.33 | (881) all_1494_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (876), (877) imply: % 252.71/37.33 | (882) all_1393_0 = all_1245_1 % 252.71/37.33 | % 252.71/37.33 | SIMP: (882) implies: % 252.71/37.33 | (883) all_1393_0 = all_1245_1 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (875), (881) imply: % 252.71/37.33 | (884) all_1480_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (884) implies: % 252.71/37.33 | (885) all_1480_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (873), (874) imply: % 252.71/37.33 | (886) all_1423_0 = all_1189_1 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (873), (885) imply: % 252.71/37.33 | (887) all_1423_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (886), (887) imply: % 252.71/37.33 | (888) all_1189_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (888) implies: % 252.71/37.33 | (889) all_1189_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (872), (883) imply: % 252.71/37.33 | (890) all_1245_1 = all_1212_1 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (871), (883) imply: % 252.71/37.33 | (891) all_1245_1 = all_1242_1 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (890), (891) imply: % 252.71/37.33 | (892) all_1242_1 = all_1212_1 % 252.71/37.33 | % 252.71/37.33 | SIMP: (892) implies: % 252.71/37.33 | (893) all_1242_1 = all_1212_1 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (870), (893) imply: % 252.71/37.33 | (894) all_1212_1 = all_985_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (869), (893) imply: % 252.71/37.33 | (895) all_1212_1 = all_1054_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (894), (895) imply: % 252.71/37.33 | (896) all_1054_0 = all_985_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (896) implies: % 252.71/37.33 | (897) all_1054_0 = all_985_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (868), (889) imply: % 252.71/37.33 | (898) all_1157_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (898) implies: % 252.71/37.33 | (899) all_1157_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (867), (899) imply: % 252.71/37.33 | (900) all_1125_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (900) implies: % 252.71/37.33 | (901) all_1125_1 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (866), (901) imply: % 252.71/37.33 | (902) all_1066_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (902) implies: % 252.71/37.33 | (903) all_1066_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (865), (903) imply: % 252.71/37.33 | (904) all_1054_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (904) implies: % 252.71/37.33 | (905) all_1054_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (864), (897) imply: % 252.71/37.33 | (906) all_985_0 = all_936_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (897), (905) imply: % 252.71/37.33 | (907) all_985_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | COMBINE_EQS: (906), (907) imply: % 252.71/37.33 | (908) all_936_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | SIMP: (908) implies: % 252.71/37.33 | (909) all_936_0 = all_865_0 % 252.71/37.33 | % 252.71/37.33 | REDUCE: (413), (879) imply: % 252.71/37.33 | (910) c_Nat_OSuc(all_865_0) = all_1500_0 % 252.71/37.33 | % 252.71/37.33 | REDUCE: (259), (901) imply: % 252.71/37.33 | (911) c_Nat_OSuc(all_865_0) = all_1125_0 % 252.71/37.33 | % 252.71/37.33 | REDUCE: (861), (863) imply: % 252.71/37.33 | (912) c_Groups_Oplus__class_Oplus(all_1072_1, all_1160_2, all_1160_1) = % 252.71/37.33 | all_1072_0 % 252.71/37.33 | % 252.71/37.33 | REDUCE: (265), (899) imply: % 252.71/37.33 | (913) hAPP(all_1157_3, all_865_0) = all_1157_0 % 252.71/37.33 | % 252.71/37.33 | REDUCE: (183), (909) imply: % 252.71/37.33 | (914) $i(all_865_0) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (127) with all_1125_0, all_1500_0, all_865_0, % 252.71/37.33 | simplifying with (910), (911) gives: % 252.71/37.33 | (915) all_1500_0 = all_1125_0 % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (clrel_Rings_Ocomm__semiring__0__Groups_Ozero) with % 252.71/37.33 | t_a, simplifying with (118), (119) gives: % 252.71/37.33 | (916) class_Groups_Ozero(t_a) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (fact_offset__poly__pCons) with v_h, v_p, v_a, t_a, % 252.71/37.33 | all_1072_1, all_1160_3, all_1160_2, all_1160_1, all_1072_0, % 252.71/37.33 | simplifying with (116), (118), (119), (120), (121), (233), (271), % 252.71/37.33 | (274), (276), (912) gives: % 252.71/37.33 | (917) ? [v0: $i] : (c_Polynomial_OpCons(t_a, v_a, v_p) = v0 & % 252.71/37.33 | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, v0, % 252.71/37.33 | v_h) = all_1072_0 & $i(v0) & $i(all_1072_0)) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (fact_offset__poly__eq__0__lemma) with v_a, % 252.71/37.33 | all_1160_3, v_h, t_a, all_1072_1, all_1160_2, all_1160_1, % 252.71/37.33 | all_1072_0, simplifying with (116), (118), (119), (121), (233), % 252.71/37.33 | (270), (274), (276), (912) gives: % 252.71/37.33 | (918) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(all_1072_1) = v0 & $i(v0) % 252.71/37.33 | & ( ~ (v0 = all_1072_0) | all_1160_3 = all_1072_0)) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (fact_zero__neq__one) with tc_Nat_Onat, all_865_0, % 252.71/37.33 | simplifying with (112), (114), (157) gives: % 252.71/37.33 | (919) ? [v0: any] : ( ~ (v0 = all_865_0) & % 252.71/37.33 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0)) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (fact_zero__le__one) with tc_Nat_Onat, all_865_0, % 252.71/37.33 | simplifying with (110), (114), (157) gives: % 252.71/37.33 | (920) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 252.71/37.33 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, all_865_0)) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_Nat_Onat, % 252.71/37.33 | all_865_0, simplifying with (110), (114), (157) gives: % 252.71/37.33 | (921) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 252.71/37.33 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_865_0, v0)) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (fact_not__one__le__zero) with tc_Nat_Onat, % 252.71/37.33 | all_865_0, simplifying with (110), (114), (157) gives: % 252.71/37.33 | (922) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 252.71/37.33 | & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_865_0, v0)) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (248) with all_865_0, tc_Nat_Onat, all_1157_3, % 252.71/37.33 | all_1157_0, simplifying with (113), (114), (267), (913), (914) % 252.71/37.33 | gives: % 252.71/37.33 | (923) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.71/37.33 | hAPP(all_1157_0, all_1102_0) = v0 & $i(v0)) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (251) with all_865_0, tc_Nat_Onat, all_1157_3, % 252.71/37.33 | all_1157_0, simplifying with (111), (114), (267), (913), (914) % 252.71/37.33 | gives: % 252.71/37.33 | (924) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.71/37.33 | hAPP(all_1157_0, all_1113_0) = v0 & $i(v0)) % 252.71/37.33 | % 252.71/37.33 | GROUND_INST: instantiating (73) with all_865_0, all_1125_0, simplifying with % 252.71/37.33 | (911), (914) gives: % 252.71/37.33 | (925) c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_865_0, all_1125_0) % 252.71/37.33 | % 252.71/37.33 | DELTA: instantiating (923) with fresh symbol all_1546_0 gives: % 252.71/37.33 | (926) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1546_0 & % 252.71/37.33 | hAPP(all_1157_0, all_1102_0) = all_1546_0 & $i(all_1546_0) % 252.71/37.33 | % 252.71/37.33 | ALPHA: (926) implies: % 252.71/37.33 | (927) $i(all_1546_0) % 252.71/37.33 | (928) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1546_0 % 252.71/37.33 | % 252.71/37.33 | DELTA: instantiating (924) with fresh symbol all_1548_0 gives: % 252.71/37.33 | (929) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1548_0 & % 252.71/37.33 | hAPP(all_1157_0, all_1113_0) = all_1548_0 & $i(all_1548_0) % 252.71/37.33 | % 252.71/37.33 | ALPHA: (929) implies: % 252.71/37.33 | (930) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1548_0 % 252.71/37.33 | % 252.71/37.33 | DELTA: instantiating (919) with fresh symbol all_1550_0 gives: % 252.71/37.33 | (931) ~ (all_1550_0 = all_865_0) & % 252.71/37.33 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1550_0 & % 252.71/37.33 | $i(all_1550_0) % 252.71/37.33 | % 252.71/37.33 | ALPHA: (931) implies: % 252.71/37.33 | (932) ~ (all_1550_0 = all_865_0) % 252.71/37.33 | (933) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1550_0 % 252.71/37.33 | % 252.71/37.33 | DELTA: instantiating (922) with fresh symbol all_1556_0 gives: % 252.71/37.33 | (934) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1556_0 & % 252.71/37.33 | $i(all_1556_0) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 252.71/37.33 | all_865_0, all_1556_0) % 252.71/37.33 | % 252.71/37.33 | ALPHA: (934) implies: % 252.71/37.33 | (935) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1556_0 % 252.71/37.33 | % 252.71/37.33 | DELTA: instantiating (921) with fresh symbol all_1558_0 gives: % 252.71/37.33 | (936) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1558_0 & % 252.71/37.33 | $i(all_1558_0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 252.71/37.33 | all_865_0, all_1558_0) % 252.71/37.33 | % 252.71/37.33 | ALPHA: (936) implies: % 252.71/37.33 | (937) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1558_0 % 252.71/37.33 | % 252.71/37.33 | DELTA: instantiating (920) with fresh symbol all_1560_0 gives: % 252.71/37.33 | (938) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1560_0 & % 252.71/37.33 | $i(all_1560_0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 252.71/37.33 | all_1560_0, all_865_0) % 252.71/37.33 | % 252.71/37.33 | ALPHA: (938) implies: % 252.71/37.33 | (939) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1560_0 % 252.71/37.33 | % 252.71/37.33 | DELTA: instantiating (918) with fresh symbol all_1562_0 gives: % 252.71/37.34 | (940) c_Groups_Ozero__class_Ozero(all_1072_1) = all_1562_0 & $i(all_1562_0) % 252.71/37.34 | & ( ~ (all_1562_0 = all_1072_0) | all_1160_3 = all_1072_0) % 252.71/37.34 | % 252.71/37.34 | ALPHA: (940) implies: % 252.71/37.34 | (941) c_Groups_Ozero__class_Ozero(all_1072_1) = all_1562_0 % 252.71/37.34 | (942) ~ (all_1562_0 = all_1072_0) | all_1160_3 = all_1072_0 % 252.71/37.34 | % 252.71/37.34 | DELTA: instantiating (917) with fresh symbol all_1566_0 gives: % 252.71/37.34 | (943) c_Polynomial_OpCons(t_a, v_a, v_p) = all_1566_0 & % 252.71/37.34 | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, % 252.71/37.34 | all_1566_0, v_h) = all_1072_0 & $i(all_1566_0) & $i(all_1072_0) % 252.71/37.34 | % 252.71/37.34 | ALPHA: (943) implies: % 252.71/37.34 | (944) c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, % 252.71/37.34 | all_1566_0, v_h) = all_1072_0 % 252.71/37.34 | (945) c_Polynomial_OpCons(t_a, v_a, v_p) = all_1566_0 % 252.71/37.34 | % 252.71/37.34 | GROUND_INST: instantiating (123) with all_1556_0, all_1558_0, tc_Nat_Onat, % 252.71/37.34 | simplifying with (935), (937) gives: % 252.71/37.34 | (946) all_1558_0 = all_1556_0 % 252.71/37.34 | % 252.71/37.34 | GROUND_INST: instantiating (123) with all_1550_0, all_1558_0, tc_Nat_Onat, % 252.71/37.34 | simplifying with (933), (937) gives: % 252.71/37.34 | (947) all_1558_0 = all_1550_0 % 252.71/37.34 | % 252.71/37.34 | GROUND_INST: instantiating (123) with all_817_0, all_1560_0, tc_Nat_Onat, % 252.71/37.34 | simplifying with (131), (939) gives: % 252.71/37.34 | (948) all_1560_0 = all_817_0 % 252.71/37.34 | % 252.71/37.34 | GROUND_INST: instantiating (123) with all_1556_0, all_1560_0, tc_Nat_Onat, % 252.71/37.34 | simplifying with (935), (939) gives: % 252.71/37.34 | (949) all_1560_0 = all_1556_0 % 252.71/37.34 | % 252.71/37.34 | GROUND_INST: instantiating (123) with all_1072_0, all_1562_0, all_1072_1, % 252.71/37.34 | simplifying with (232), (941) gives: % 252.71/37.34 | (950) all_1562_0 = all_1072_0 % 252.71/37.34 | % 252.71/37.34 | GROUND_INST: instantiating (125) with all_865_0, all_1548_0, tc_Nat_Onat, % 252.71/37.34 | simplifying with (157), (930) gives: % 252.71/37.34 | (951) all_1548_0 = all_865_0 % 252.71/37.34 | % 252.71/37.34 | GROUND_INST: instantiating (125) with all_1546_0, all_1548_0, tc_Nat_Onat, % 252.71/37.34 | simplifying with (928), (930) gives: % 252.71/37.34 | (952) all_1548_0 = all_1546_0 % 252.71/37.34 | % 252.71/37.34 | COMBINE_EQS: (948), (949) imply: % 252.71/37.34 | (953) all_1556_0 = all_817_0 % 252.71/37.34 | % 252.71/37.34 | SIMP: (953) implies: % 252.71/37.34 | (954) all_1556_0 = all_817_0 % 252.71/37.34 | % 252.71/37.34 | COMBINE_EQS: (946), (947) imply: % 252.71/37.34 | (955) all_1556_0 = all_1550_0 % 252.71/37.34 | % 252.71/37.34 | SIMP: (955) implies: % 252.71/37.34 | (956) all_1556_0 = all_1550_0 % 252.71/37.34 | % 252.71/37.34 | COMBINE_EQS: (954), (956) imply: % 252.71/37.34 | (957) all_1550_0 = all_817_0 % 252.71/37.34 | % 252.71/37.34 | SIMP: (957) implies: % 252.71/37.34 | (958) all_1550_0 = all_817_0 % 252.71/37.34 | % 252.71/37.34 | COMBINE_EQS: (951), (952) imply: % 252.71/37.34 | (959) all_1546_0 = all_865_0 % 252.71/37.34 | % 252.71/37.34 | REDUCE: (932), (958) imply: % 252.71/37.34 | (960) ~ (all_865_0 = all_817_0) % 252.71/37.34 | % 252.71/37.34 | SIMP: (960) implies: % 252.71/37.34 | (961) ~ (all_865_0 = all_817_0) % 252.71/37.34 | % 252.71/37.34 | BETA: splitting (942) gives: % 252.71/37.34 | % 252.71/37.34 | Case 1: % 252.71/37.34 | | % 252.71/37.34 | | (962) ~ (all_1562_0 = all_1072_0) % 252.71/37.34 | | % 252.71/37.34 | | REDUCE: (950), (962) imply: % 252.71/37.34 | | (963) $false % 252.71/37.34 | | % 252.71/37.34 | | CLOSE: (963) is inconsistent. % 252.71/37.34 | | % 252.71/37.34 | Case 2: % 252.71/37.34 | | % 252.71/37.34 | | (964) all_1160_3 = all_1072_0 % 252.71/37.34 | | % 252.71/37.34 | | REDUCE: (274), (964) imply: % 252.71/37.34 | | (965) c_Polynomial_OpCons(t_a, v_a, all_1072_0) = all_1160_1 % 252.71/37.34 | | % 252.71/37.34 | | REDUCE: (271), (964) imply: % 252.71/37.34 | | (966) c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, v_p, % 252.71/37.34 | | v_h) = all_1072_0 % 252.71/37.34 | | % 252.71/37.34 | | REDUCE: (270), (964) imply: % 252.71/37.34 | | (967) $i(all_1072_0) % 252.71/37.34 | | % 252.71/37.34 | | BETA: splitting (234) gives: % 252.71/37.34 | | % 252.71/37.34 | | Case 1: % 252.71/37.34 | | | % 252.71/37.34 | | | (968) all_1072_0 = v_p % 252.71/37.34 | | | % 252.71/37.34 | | | REDUCE: (965), (968) imply: % 252.71/37.34 | | | (969) c_Polynomial_OpCons(t_a, v_a, v_p) = all_1160_1 % 252.71/37.34 | | | % 252.71/37.34 | | | REDUCE: (232), (968) imply: % 252.71/37.34 | | | (970) c_Groups_Ozero__class_Ozero(all_1072_1) = v_p % 252.71/37.34 | | | % 252.71/37.34 | | | REDUCE: (944), (968) imply: % 252.71/37.34 | | | (971) c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, % 252.71/37.34 | | | all_1566_0, v_h) = v_p % 252.71/37.34 | | | % 252.71/37.34 | | | BETA: splitting (235) gives: % 252.71/37.34 | | | % 252.71/37.34 | | | Case 1: % 252.71/37.34 | | | | % 252.71/37.34 | | | | (972) ~ (all_1077_0 = v_p) & tc_Polynomial_Opoly(t_a) = all_1077_1 & % 252.71/37.34 | | | | c_Groups_Ozero__class_Ozero(all_1077_1) = all_1077_0 & % 252.71/37.34 | | | | $i(all_1077_0) & $i(all_1077_1) % 252.71/37.34 | | | | % 252.71/37.34 | | | | ALPHA: (972) implies: % 252.71/37.34 | | | | (973) ~ (all_1077_0 = v_p) % 252.71/37.34 | | | | (974) c_Groups_Ozero__class_Ozero(all_1077_1) = all_1077_0 % 252.71/37.34 | | | | (975) tc_Polynomial_Opoly(t_a) = all_1077_1 % 252.71/37.34 | | | | % 252.71/37.34 | | | | GROUND_INST: instantiating (124) with all_1072_1, all_1077_1, t_a, % 252.71/37.34 | | | | simplifying with (233), (975) gives: % 252.71/37.34 | | | | (976) all_1077_1 = all_1072_1 % 252.71/37.34 | | | | % 252.71/37.34 | | | | REDUCE: (974), (976) imply: % 252.71/37.34 | | | | (977) c_Groups_Ozero__class_Ozero(all_1072_1) = all_1077_0 % 252.71/37.34 | | | | % 252.71/37.34 | | | | GROUND_INST: instantiating (123) with v_p, all_1077_0, all_1072_1, % 252.71/37.34 | | | | simplifying with (970), (977) gives: % 252.71/37.34 | | | | (978) all_1077_0 = v_p % 252.71/37.34 | | | | % 252.71/37.34 | | | | REDUCE: (973), (978) imply: % 252.71/37.34 | | | | (979) $false % 252.71/37.34 | | | | % 252.71/37.34 | | | | CLOSE: (979) is inconsistent. % 252.71/37.34 | | | | % 252.71/37.34 | | | Case 2: % 252.71/37.34 | | | | % 252.71/37.34 | | | | (980) ~ (all_1077_2 = v_a) & c_Groups_Ozero__class_Ozero(t_a) = % 252.71/37.34 | | | | all_1077_2 & $i(all_1077_2) % 252.71/37.34 | | | | % 252.71/37.34 | | | | ALPHA: (980) implies: % 252.71/37.34 | | | | (981) ~ (all_1077_2 = v_a) % 252.71/37.34 | | | | (982) c_Groups_Ozero__class_Ozero(t_a) = all_1077_2 % 252.71/37.34 | | | | % 252.71/37.34 | | | | GROUND_INST: instantiating (129) with all_1566_0, all_1160_1, v_p, v_a, % 252.71/37.34 | | | | t_a, simplifying with (945), (969) gives: % 252.71/37.34 | | | | (983) all_1566_0 = all_1160_1 % 252.71/37.34 | | | | % 252.71/37.34 | | | | REDUCE: (971), (983) imply: % 252.71/37.34 | | | | (984) c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, % 252.71/37.34 | | | | all_1160_1, v_h) = v_p % 252.71/37.34 | | | | % 252.71/37.35 | | | | GROUND_INST: instantiating (360) with all_865_0, all_865_0, all_1125_0, % 252.71/37.35 | | | | simplifying with (911), (914), (925) gives: % 252.71/37.35 | | | | (985) all_1411_0 = all_865_0 | ? [v0: $i] : (c_Nat_OSuc(v0) = % 252.71/37.35 | | | | all_865_0 & $i(v0) & % 252.71/37.35 | | | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_865_0)) % 252.71/37.35 | | | | % 252.71/37.35 | | | | GROUND_INST: instantiating (fact_offset__poly__single) with v_h, v_a, % 252.71/37.35 | | | | t_a, all_1072_1, v_p, all_1160_1, v_p, simplifying with % 252.71/37.35 | | | | (116), (118), (119), (121), (233), (969), (970), (984) % 252.71/37.35 | | | | gives: % 252.71/37.35 | | | | (986) all_1160_1 = v_p % 252.71/37.35 | | | | % 252.71/37.35 | | | | GROUND_INST: instantiating (fact_pCons__eq__0__iff) with v_p, v_a, t_a, % 252.71/37.35 | | | | all_1160_1, simplifying with (119), (120), (121), (916), % 252.71/37.35 | | | | (969) gives: % 252.71/37.35 | | | | (987) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.71/37.35 | | | | (tc_Polynomial_Opoly(t_a) = v0 & % 252.71/37.35 | | | | c_Groups_Ozero__class_Ozero(v0) = v1 & $i(v1) & $i(v0) & ( ~ % 252.71/37.35 | | | | (v1 = all_1160_1) | (v2 = v_a & all_1160_1 = v_p & % 252.71/37.35 | | | | c_Groups_Ozero__class_Ozero(t_a) = v_a)) & ( ~ (v1 = v_p) % 252.71/37.35 | | | | | all_1160_1 = v_p | ( ~ (v2 = v_a) & % 252.71/37.35 | | | | c_Groups_Ozero__class_Ozero(t_a) = v2 & $i(v2)))) % 252.71/37.35 | | | | % 252.71/37.35 | | | | DELTA: instantiating (987) with fresh symbols all_1742_0, all_1742_1, % 252.71/37.35 | | | | all_1742_2 gives: % 252.71/37.35 | | | | (988) tc_Polynomial_Opoly(t_a) = all_1742_2 & % 252.71/37.35 | | | | c_Groups_Ozero__class_Ozero(all_1742_2) = all_1742_1 & % 252.71/37.35 | | | | $i(all_1742_1) & $i(all_1742_2) & ( ~ (all_1742_1 = all_1160_1) % 252.71/37.35 | | | | | (all_1742_0 = v_a & all_1160_1 = v_p & % 252.71/37.35 | | | | c_Groups_Ozero__class_Ozero(t_a) = v_a)) & ( ~ (all_1742_1 % 252.71/37.35 | | | | = v_p) | all_1160_1 = v_p | ( ~ (all_1742_0 = v_a) & % 252.71/37.35 | | | | c_Groups_Ozero__class_Ozero(t_a) = all_1742_0 & % 252.71/37.35 | | | | $i(all_1742_0))) % 252.71/37.35 | | | | % 252.71/37.35 | | | | ALPHA: (988) implies: % 252.71/37.35 | | | | (989) c_Groups_Ozero__class_Ozero(all_1742_2) = all_1742_1 % 252.71/37.35 | | | | (990) tc_Polynomial_Opoly(t_a) = all_1742_2 % 252.71/37.35 | | | | (991) ~ (all_1742_1 = all_1160_1) | (all_1742_0 = v_a & all_1160_1 = % 252.71/37.35 | | | | v_p & c_Groups_Ozero__class_Ozero(t_a) = v_a) % 252.71/37.35 | | | | % 252.71/37.35 | | | | BETA: splitting (991) gives: % 252.71/37.35 | | | | % 252.71/37.35 | | | | Case 1: % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | (992) ~ (all_1742_1 = all_1160_1) % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | REDUCE: (986), (992) imply: % 252.71/37.35 | | | | | (993) ~ (all_1742_1 = v_p) % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | BETA: splitting (985) gives: % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | Case 1: % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | (994) all_1411_0 = all_865_0 % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | COMBINE_EQS: (838), (994) imply: % 252.71/37.35 | | | | | | (995) all_865_0 = all_817_0 % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | REDUCE: (961), (995) imply: % 252.71/37.35 | | | | | | (996) $false % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | CLOSE: (996) is inconsistent. % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | Case 2: % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | GROUND_INST: instantiating (124) with all_1072_1, all_1742_2, t_a, % 252.71/37.35 | | | | | | simplifying with (233), (990) gives: % 252.71/37.35 | | | | | | (997) all_1742_2 = all_1072_1 % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | REDUCE: (989), (997) imply: % 252.71/37.35 | | | | | | (998) c_Groups_Ozero__class_Ozero(all_1072_1) = all_1742_1 % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | GROUND_INST: instantiating (123) with v_p, all_1742_1, all_1072_1, % 252.71/37.35 | | | | | | simplifying with (970), (998) gives: % 252.71/37.35 | | | | | | (999) all_1742_1 = v_p % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | REDUCE: (993), (999) imply: % 252.71/37.35 | | | | | | (1000) $false % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | | CLOSE: (1000) is inconsistent. % 252.71/37.35 | | | | | | % 252.71/37.35 | | | | | End of split % 252.71/37.35 | | | | | % 252.71/37.35 | | | | Case 2: % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | (1001) all_1742_0 = v_a & all_1160_1 = v_p & % 252.71/37.35 | | | | | c_Groups_Ozero__class_Ozero(t_a) = v_a % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | ALPHA: (1001) implies: % 252.71/37.35 | | | | | (1002) c_Groups_Ozero__class_Ozero(t_a) = v_a % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | GROUND_INST: instantiating (123) with all_1077_2, v_a, t_a, % 252.71/37.35 | | | | | simplifying with (982), (1002) gives: % 252.71/37.35 | | | | | (1003) all_1077_2 = v_a % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | REDUCE: (981), (1003) imply: % 252.71/37.35 | | | | | (1004) $false % 252.71/37.35 | | | | | % 252.71/37.35 | | | | | CLOSE: (1004) is inconsistent. % 252.71/37.35 | | | | | % 252.71/37.35 | | | | End of split % 252.71/37.35 | | | | % 252.71/37.35 | | | End of split % 252.71/37.35 | | | % 252.71/37.35 | | Case 2: % 252.71/37.35 | | | % 252.71/37.35 | | | (1005) ~ (all_1072_0 = all_1072_2) & % 252.71/37.35 | | | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, % 252.71/37.35 | | | v_p, v_h) = all_1072_2 & $i(all_1072_2) % 252.71/37.35 | | | % 252.71/37.35 | | | ALPHA: (1005) implies: % 252.71/37.35 | | | (1006) ~ (all_1072_0 = all_1072_2) % 252.71/37.35 | | | (1007) c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a, % 252.71/37.35 | | | v_p, v_h) = all_1072_2 % 252.71/37.35 | | | % 252.71/37.35 | | | GROUND_INST: instantiating (128) with all_1072_2, all_1072_0, v_h, v_p, % 252.71/37.35 | | | t_a, simplifying with (966), (1007) gives: % 252.71/37.35 | | | (1008) all_1072_0 = all_1072_2 % 252.71/37.35 | | | % 252.71/37.35 | | | REDUCE: (1006), (1008) imply: % 252.71/37.35 | | | (1009) $false % 252.71/37.35 | | | % 252.71/37.35 | | | CLOSE: (1009) is inconsistent. % 252.71/37.35 | | | % 252.71/37.35 | | End of split % 252.71/37.35 | | % 252.71/37.35 | End of split % 252.71/37.35 | % 252.71/37.35 End of proof % 252.71/37.35 % SZS output end Proof for theBenchmark % 252.71/37.35 % 252.71/37.35 36689ms %------------------------------------------------------------------------------