%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW215+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 : n027.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 00:49:27 EDT 2023 % Result : Theorem 107.03s 15.23s % Output : Proof 253.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWW215+1 : TPTP v8.1.2. Released v5.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.33 % Computer : n027.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Sun Aug 27 22:36:21 EDT 2023 % 0.17/0.33 % CPUTime : % 0.17/0.61 ________ _____ % 0.17/0.61 ___ __ \_________(_)________________________________ % 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.61 % 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.61 (2023-06-19) % 0.17/0.61 % 0.17/0.61 (c) Philipp Rümmer, 2009-2023 % 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.61 Amanda Stjerna. % 0.17/0.61 Free software under BSD-3-Clause. % 0.17/0.61 % 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.61 % 0.17/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.63 Running up to 7 provers in parallel. % 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 24.95/4.25 Prover 4: Preprocessing ... % 24.95/4.31 Prover 0: Preprocessing ... % 25.62/4.32 Prover 6: Preprocessing ... % 25.62/4.32 Prover 5: Preprocessing ... % 26.18/4.41 Prover 1: Preprocessing ... % 26.18/4.45 Prover 3: Preprocessing ... % 26.18/4.51 Prover 2: Preprocessing ... % 70.39/10.38 Prover 1: Warning: ignoring some quantifiers % 74.21/10.84 Prover 3: Warning: ignoring some quantifiers % 75.19/10.99 Prover 6: Proving ... % 76.11/11.08 Prover 1: Constructing countermodel ... % 76.77/11.16 Prover 3: Constructing countermodel ... % 78.37/11.54 Prover 4: Warning: ignoring some quantifiers % 86.98/12.59 Prover 4: Constructing countermodel ... % 90.67/13.17 Prover 0: Proving ... % 94.33/13.56 Prover 5: Proving ... % 96.73/14.00 Prover 5: stopped % 98.38/14.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 107.03/15.16 Prover 7: Preprocessing ... % 107.03/15.23 Prover 3: proved (14580ms) % 107.03/15.23 % 107.03/15.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 107.03/15.23 % 107.64/15.24 Prover 6: stopped % 107.64/15.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 107.64/15.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 107.64/15.25 Prover 0: stopped % 107.64/15.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 107.64/15.47 Prover 2: Proving ... % 107.64/15.47 Prover 2: stopped % 107.64/15.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 112.90/16.00 Prover 1: stopped % 112.90/16.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 122.42/17.28 Prover 10: Preprocessing ... % 123.09/17.32 Prover 11: Preprocessing ... % 123.66/17.40 Prover 8: Preprocessing ... % 126.75/17.89 Prover 16: Preprocessing ... % 126.75/17.89 Prover 13: Preprocessing ... % 133.66/18.84 Prover 7: Warning: ignoring some quantifiers % 136.49/19.15 Prover 7: Constructing countermodel ... % 136.91/19.39 Prover 13: stopped % 136.91/19.40 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 141.90/19.86 Prover 10: Warning: ignoring some quantifiers % 143.36/20.16 Prover 8: Warning: ignoring some quantifiers % 143.36/20.22 Prover 10: Constructing countermodel ... % 143.36/20.22 Prover 16: Warning: ignoring some quantifiers % 146.29/20.44 Prover 16: Constructing countermodel ... % 146.83/20.51 Prover 8: Constructing countermodel ... % 148.64/20.77 Prover 16: stopped % 149.42/20.89 Prover 19: Preprocessing ... % 153.84/21.45 Prover 11: Warning: ignoring some quantifiers % 155.12/21.80 Prover 11: Constructing countermodel ... % 168.08/23.53 Prover 19: Warning: ignoring some quantifiers % 170.92/23.79 Prover 19: Constructing countermodel ... % 200.73/27.98 Prover 4: stopped % 201.94/28.21 Prover 19: stopped % 230.55/32.74 Prover 7: stopped % 251.12/36.08 Prover 10: Found proof (size 378) % 251.12/36.08 Prover 10: proved (20833ms) % 251.12/36.08 Prover 11: stopped % 251.12/36.09 Prover 8: stopped % 251.12/36.09 % 251.12/36.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 251.12/36.09 % 252.02/36.17 % SZS output start Proof for theBenchmark % 252.02/36.20 Assumptions after simplification: % 252.02/36.20 --------------------------------- % 252.02/36.20 % 252.02/36.20 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) % 252.02/36.20 $i(tc_Complex_Ocomplex) & % 252.02/36.20 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) % 252.02/36.20 % 252.02/36.20 (arity_RealDef__Oreal__Orderings_Oorder) % 252.02/36.20 $i(tc_RealDef_Oreal) & class_Orderings_Oorder(tc_RealDef_Oreal) % 252.02/36.20 % 252.02/36.20 (conj_0) % 252.25/36.23 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & $i(v_w____) & $i(v_z) & ? % 252.25/36.23 [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.25/36.23 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0 & % 252.25/36.23 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 & % 252.25/36.23 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & $i(v2) & $i(v1) & $i(v0) % 252.25/36.23 & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) % 252.25/36.23 % 252.25/36.23 (fact_H_I2_J) % 252.25/36.23 $i(v_da____) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.25/36.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & % 252.25/36.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, v0)) % 252.25/36.23 % 252.25/36.23 (fact_H_I3_J) % 252.25/36.23 $i(v_m____) & $i(v_e) & $i(v_da____) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.25/36.23 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____) = v0 & $i(v0) % 252.25/36.23 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, v0)) % 252.25/36.23 % 252.25/36.23 (fact_H_I5_J) % 252.25/36.23 $i(tc_Complex_Ocomplex) & $i(v_da____) & $i(tc_RealDef_Oreal) & $i(v_w____) & % 252.25/36.23 $i(v_z) & ? [v0: $i] : ? [v1: $i] : % 252.25/36.23 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0 & % 252.25/36.23 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 & $i(v1) & % 252.25/36.23 $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v_da____)) % 252.25/36.23 % 252.25/36.23 (fact_LIMSEQ__inverse__realpow__zero__lemma) % 252.25/36.23 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 252.25/36.23 $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 & % 252.25/36.23 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 252.25/36.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.25/36.23 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & $i(v3) & $i(v2) & $i(v1) % 252.25/36.23 & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 252.25/36.23 $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) | % 252.25/36.23 ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ $i(v4) | % 252.25/36.23 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) | ? [v9: % 252.25/36.23 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : % 252.25/36.23 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 & % 252.25/36.23 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & hAPP(v10, % 252.25/36.23 v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & $i(v10) & $i(v9) % 252.25/36.23 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8)))) % 252.25/36.23 % 252.25/36.23 (fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096) % 252.25/36.24 $i(v_m____) & $i(v_e) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? % 252.25/36.24 [v2: $i] : ? [v3: $i] : (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, % 252.25/36.24 v_e, v_m____) = v2 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.25/36.24 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & $i(v1) % 252.25/36.24 & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) & % 252.25/36.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1) & % 252.25/36.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) % 252.25/36.24 % 252.25/36.24 (fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_A1_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_096) % 252.25/36.24 $i(v_cs____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.25/36.24 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 252.25/36.24 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v2 & % 252.25/36.24 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.25/36.24 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & $i(v1) % 252.25/36.24 & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: % 252.25/36.24 $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? % 252.25/36.24 [v7: $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7 % 252.25/36.24 & $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, % 252.25/36.24 v3)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = % 252.25/36.24 v6 & $i(v6) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 252.25/36.24 v6, v1))))) % 252.25/36.24 % 252.25/36.24 (fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) % 252.25/36.24 $i(v_m____) & $i(v_e) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? % 252.25/36.24 [v2: $i] : ? [v3: $i] : (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, % 252.25/36.24 v_e, v_m____) = v2 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.25/36.24 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & $i(v1) % 252.25/36.24 & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) & % 252.25/36.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1) & % 252.25/36.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) % 252.25/36.24 % 252.25/36.24 (fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_A_B_Bz_O_Acmod_Az_A_060_061_A1_A_061_061_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) % 252.25/36.25 $i(v_cs____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.25/36.25 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 252.25/36.25 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v2 & % 252.25/36.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.25/36.25 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & $i(v1) % 252.25/36.25 & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: % 252.25/36.25 $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? % 252.25/36.25 [v7: $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7 % 252.25/36.25 & $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, % 252.25/36.25 v3)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = % 252.25/36.25 v6 & $i(v6) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 252.25/36.25 v6, v1))))) % 252.25/36.25 % 252.25/36.25 (fact_abs__add__one__gt__zero) % 252.25/36.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.25/36.25 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.25/36.25 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2: % 252.25/36.25 $i] : ! [v3: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = % 252.25/36.25 v3) | ~ $i(v2) | ? [v4: $i] : % 252.25/36.25 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v3) = v4 & $i(v4) & % 252.25/36.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))) % 252.25/36.25 % 252.25/36.25 (fact_abs__add__one__not__less__self) % 252.25/36.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.25/36.25 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.25/36.25 [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ % 252.25/36.25 $i(v1) | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 252.25/36.25 v0) = v3 & $i(v3) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 252.25/36.25 v3, v1)))) % 252.25/36.25 % 252.25/36.25 (fact_abs__real__of__nat__cancel) % 252.25/36.25 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ( ~ % 252.25/36.25 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | % 252.25/36.25 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v1 & $i(v1))) % 252.25/36.25 % 252.25/36.25 (fact_arctan__add) % 252.41/36.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.26 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 252.41/36.26 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2: % 252.41/36.26 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 252.41/36.26 : ! [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v2) = % 252.41/36.26 v4) | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v4, v7) = % 252.41/36.26 v8) | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, v6) = v7) % 252.41/36.26 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2) % 252.41/36.26 | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] % 252.41/36.26 : ? [v14: $i] : ((v14 = v13 & c_Transcendental_Oarctan(v8) = v13 & % 252.41/36.26 c_Transcendental_Oarctan(v3) = v11 & c_Transcendental_Oarctan(v2) = % 252.41/36.26 v12 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v12) = v13 & % 252.41/36.26 $i(v13) & $i(v12) & $i(v11)) | % 252.41/36.26 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v9 & $i(v9) & ~ % 252.41/36.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v0)) | % 252.41/36.26 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v10 & $i(v10) & ~ % 252.41/36.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10, v0))))) % 252.41/36.26 % 252.41/36.26 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) % 252.41/36.26 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.41/36.26 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 252.41/36.26 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 252.41/36.26 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | hAPP(v4, v0) % 252.41/36.26 = v1)) % 252.41/36.26 % 252.41/36.26 (fact_d_I2_J) % 252.41/36.26 $i(v_d____) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & % 252.41/36.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_d____, v0)) % 252.41/36.26 % 252.41/36.26 (fact_degree__synthetic__div) % 252.41/36.26 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.41/36.26 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 252.41/36.26 : ( ~ (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ % 252.41/36.26 (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 252.41/36.26 ~ class_Rings_Ocomm__semiring__0(v3) | ? [v6: $i] : % 252.41/36.26 (c_Polynomial_Odegree(v3, v2) = v6 & % 252.41/36.26 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v0) = v5 & $i(v6) & % 252.41/36.26 $i(v5)))) % 252.41/36.26 % 252.41/36.26 (fact_div__less__dividend) % 252.41/36.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.26 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 252.41/36.26 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] % 252.41/36.26 : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, % 252.41/36.26 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 252.41/36.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~ % 252.41/36.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 252.41/36.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 252.41/36.26 % 252.41/36.26 (fact_dvd__mult__cancel1) % 252.41/36.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.41/36.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 252.41/36.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 252.41/36.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 252.41/36.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ (hAPP(v5, % 252.41/36.27 v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 252.41/36.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) | ~ % 252.41/36.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3: $i] : ! % 252.41/36.27 [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | % 252.41/36.27 ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 252.41/36.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 252.41/36.27 % 252.41/36.27 (fact_dvd__mult__cancel2) % 252.41/36.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.41/36.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 252.41/36.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 252.41/36.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 252.41/36.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ (hAPP(v5, % 252.41/36.27 v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 252.41/36.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) | ~ % 252.41/36.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3: $i] : ! % 252.41/36.27 [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) | % 252.41/36.27 ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 252.41/36.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 252.41/36.27 % 252.41/36.27 (fact_ex__least__nat__less) % 252.41/36.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.27 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 252.41/36.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 252.41/36.27 : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) | ~ $i(v3) | ~ % 252.41/36.27 $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 252.41/36.27 $i] : ($i(v6) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 % 252.41/36.27 & hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) & % 252.41/36.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9: $i] : % 252.41/36.27 ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9) | ~ hBOOL(v10) | % 252.41/36.27 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) | % 252.41/36.27 (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5)))))) % 252.41/36.27 % 252.41/36.27 (fact_gcd__lcm__complete__lattice__nat_Obot__least) % 252.41/36.28 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.41/36.28 $i(v0) & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 252.41/36.28 v0, v1))) % 252.41/36.28 % 252.41/36.28 (fact_ge__natfloor__plus__one__imp__gt) % 252.41/36.28 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.28 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 252.41/36.28 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = % 252.41/36.28 v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 252.41/36.28 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5: $i] : % 252.41/36.28 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 & $i(v5) & ~ % 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v1)))) % 252.41/36.28 % 252.41/36.28 (fact_le__natfloor__eq__one) % 252.41/36.28 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.28 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.41/36.28 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2: % 252.41/36.28 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ % 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) | % 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & ! [v2: $i] % 252.41/36.28 : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ % 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) | % 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3))) % 252.41/36.28 % 252.41/36.28 (fact_lemmaCauchy) % 252.41/36.28 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.28 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.41/36.28 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 252.41/36.28 (c_RealVector_Onorm__class_Onorm(v4, v5) = v6) | ~ (hAPP(v1, v2) = v5) | % 252.41/36.28 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Orderings_Oord(v3) % 252.41/36.28 | ~ class_RealVector_Oreal__normed__vector(v4) | ? [v7: $i] : ? [v8: % 252.41/36.28 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & % 252.41/36.28 ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 & $i(v7) & % 252.41/36.28 ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ % 252.41/36.28 (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~ (hAPP(v1, % 252.41/36.28 v12) = v13) | ~ $i(v12) | ~ % 252.41/36.28 c_Orderings_Oord__class_Oless__eq(v3, v2, v12) | % 252.41/36.28 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v7))) | % 252.41/36.28 (c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 & % 252.41/36.28 c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1, v8) = v9 & % 252.41/36.28 $i(v11) & $i(v10) & $i(v9) & c_Orderings_Oord__class_Oless__eq(v3, % 252.41/36.28 v2, v8) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, % 252.41/36.28 v0)))))) % 252.41/36.28 % 252.41/36.28 (fact_m_I2_J) % 252.41/36.29 $i(v_cs____) & $i(v_m____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & % 252.41/36.29 ? [v0: $i] : ? [v1: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) % 252.41/36.29 = v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & % 252.41/36.29 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i] % 252.41/36.29 : ? [v5: $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) % 252.41/36.29 = v5 & $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 252.41/36.29 v5, v_m____)) | % 252.41/36.29 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 & $i(v4) % 252.41/36.29 & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0))))) % 252.41/36.29 % 252.41/36.29 (fact_mult__eq__if) % 252.41/36.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.41/36.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 252.41/36.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 252.41/36.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 252.41/36.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 252.41/36.29 $i] : (v4 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = % 252.41/36.29 v8) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~ % 252.41/36.29 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ? % 252.41/36.29 [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & $i(v9) & $i(v8))) & ! % 252.41/36.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v0 | ~ (hAPP(v4, v3) = v5) | % 252.41/36.29 ~ (hAPP(v1, v0) = v4) | ~ $i(v3))) % 252.41/36.29 % 252.41/36.29 (fact_mult__eq__self__implies__10) % 252.41/36.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.41/36.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 252.41/36.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & % 252.41/36.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & ! % 252.41/36.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3) % 252.41/36.29 = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 252.41/36.29 % 252.41/36.29 (fact_nat__1__eq__mult__iff) % 252.41/36.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 252.41/36.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] % 252.41/36.29 : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = v0) | ~ % 252.41/36.29 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : % 252.41/36.29 ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | % 252.41/36.29 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 252.41/36.29 (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2))) % 252.41/36.29 % 252.41/36.29 (fact_nat__dvd__1__iff__1) % 252.41/36.29 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.41/36.29 $i(v0) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 = % 252.41/36.29 v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0))) % 252.41/36.29 % 252.41/36.29 (fact_nat__le__real__less) % 252.41/36.30 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.30 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.41/36.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) % 252.41/36.30 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ % 252.41/36.30 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? % 252.41/36.30 [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 & % 252.41/36.30 $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))) & ! % 252.41/36.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 252.41/36.30 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, % 252.41/36.30 v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 252.41/36.30 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: $i] : % 252.41/36.30 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 & $i(v5) & ~ % 252.41/36.30 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5)))) % 252.41/36.30 % 252.41/36.30 (fact_nat__less__real__le) % 252.41/36.30 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.30 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.41/36.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) % 252.41/36.30 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ % 252.41/36.30 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: % 252.41/36.30 $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & % 252.41/36.30 $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))) & % 252.41/36.30 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 252.41/36.30 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, % 252.41/36.30 v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 252.41/36.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] : % 252.41/36.30 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) & ~ % 252.41/36.30 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4)))) % 252.41/36.30 % 252.41/36.30 (fact_nat__mult__1) % 252.41/36.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.41/36.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 252.41/36.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) & % 252.41/36.30 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3) = % 252.41/36.30 v4) | ~ $i(v3))) % 252.41/36.30 % 252.41/36.30 (fact_nat__mult__1__right) % 252.41/36.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 252.41/36.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 252.41/36.30 : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = v2)) % 252.41/36.30 % 252.41/36.30 (fact_nat__mult__eq__1__iff) % 252.41/36.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 252.41/36.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 252.41/36.30 : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = v1) | ~ % 252.41/36.30 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : % 252.41/36.30 ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | % 252.41/36.30 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 252.41/36.30 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2))) % 252.41/36.30 % 252.41/36.30 (fact_natceiling__add__one) % 252.41/36.30 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 252.41/36.30 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.41/36.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 252.41/36.30 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) & $i(v0) % 252.41/36.30 & ! [v3: $i] : ! [v4: $i] : ( ~ % 252.41/36.30 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) | % 252.41/36.30 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5: % 252.41/36.30 $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 & % 252.41/36.30 c_RComplete_Onatceiling(v3) = v6 & % 252.41/36.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) & % 252.41/36.31 $i(v5)))) % 252.41/36.31 % 252.41/36.31 (fact_natceiling__eq) % 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 252.41/36.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2: % 252.41/36.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 252.41/36.31 (c_RComplete_Onatceiling(v2) = v4) | ~ % 252.41/36.31 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~ $i(v3) | ~ % 252.41/36.31 $i(v2) | ? [v6: $i] : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v3) = % 252.41/36.31 v6 & $i(v6) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, % 252.41/36.31 v2) | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 & % 252.41/36.31 $i(v7) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 252.41/36.31 v7)))))) % 252.41/36.31 % 252.41/36.31 (fact_natceiling__le__eq__one) % 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.41/36.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2: % 252.41/36.31 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | % 252.41/36.31 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) | % 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i] % 252.41/36.31 : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ % 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | % 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0))) % 252.41/36.31 % 252.41/36.31 (fact_natceiling__one) % 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.31 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 252.41/36.31 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 252.41/36.31 % 252.41/36.31 (fact_natfloor__add__one) % 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 252.41/36.31 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.41/36.31 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 252.41/36.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) & $i(v0) % 252.41/36.31 & ! [v3: $i] : ! [v4: $i] : ( ~ % 252.41/36.31 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) | % 252.41/36.31 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5: % 252.41/36.31 $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 & % 252.41/36.31 c_RComplete_Onatfloor(v3) = v6 & % 252.41/36.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) & % 252.41/36.31 $i(v5)))) % 252.41/36.31 % 252.41/36.31 (fact_natfloor__div__nat) % 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.31 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 252.41/36.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2: % 252.41/36.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 252.41/36.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v4) | ~ % 252.41/36.31 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 252.41/36.31 $i(v3) | ~ $i(v2) | ~ % 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~ % 252.41/36.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v6: $i] : ? [v7: % 252.41/36.31 $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v2) = v6 & % 252.41/36.31 c_RComplete_Onatfloor(v5) = v6 & c_RComplete_Onatfloor(v3) = v7 & $i(v7) % 252.41/36.31 & $i(v6)))) % 252.41/36.31 % 252.41/36.31 (fact_natfloor__eq) % 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.31 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.41/36.31 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 252.41/36.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RComplete_Onatfloor(v1) = % 252.41/36.31 v4) | ~ $i(v2) | ~ $i(v1) | ~ % 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? [v5: $i] % 252.41/36.31 : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) & % 252.41/36.31 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5)))) % 252.41/36.31 % 252.41/36.31 (fact_natfloor__one) % 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.31 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 % 252.41/36.31 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 252.41/36.31 % 252.41/36.31 (fact_norm__minus__commute) % 252.41/36.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 252.41/36.31 (c_Groups_Ominus__class_Ominus(v2, v0, v1) = v3) | ~ % 252.41/36.31 (c_RealVector_Onorm__class_Onorm(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 252.41/36.31 $i(v0) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : % 252.41/36.31 (c_Groups_Ominus__class_Ominus(v2, v1, v0) = v5 & % 252.41/36.31 c_RealVector_Onorm__class_Onorm(v2, v5) = v4 & $i(v5) & $i(v4))) % 252.41/36.31 % 252.41/36.31 (fact_norm__one) % 252.41/36.32 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.41/36.32 [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_RealVector_Onorm__class_Onorm(v1, % 252.41/36.32 v2) = v3) | ~ (c_Groups_Oone__class_Oone(v1) = v2) | ~ $i(v1) | ~ % 252.41/36.32 class_RealVector_Oreal__normed__algebra__1(v1))) % 252.41/36.32 % 252.41/36.32 (fact_one0) % 252.41/36.32 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.41/36.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & % 252.41/36.32 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)) % 252.41/36.32 % 252.41/36.32 (fact_order__less__le) % 252.41/36.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ $i(v2) | ~ $i(v1) | % 252.41/36.32 ~ $i(v0) | ~ class_Orderings_Oorder(v2) | ~ % 252.41/36.32 c_Orderings_Oord__class_Oless__eq(v2, v1, v0) | % 252.41/36.32 c_Orderings_Oord__class_Oless(v2, v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! % 252.41/36.32 [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ class_Orderings_Oorder(v2) % 252.41/36.32 | ~ c_Orderings_Oord__class_Oless(v2, v1, v0) | % 252.41/36.32 c_Orderings_Oord__class_Oless__eq(v2, v1, v0)) & ! [v0: $i] : ! [v1: $i] : % 252.41/36.32 ( ~ $i(v1) | ~ $i(v0) | ~ class_Orderings_Oorder(v1) | ~ % 252.41/36.32 c_Orderings_Oord__class_Oless(v1, v0, v0)) % 252.41/36.32 % 252.41/36.32 (fact_power__dvd__imp__le) % 252.41/36.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.32 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 252.41/36.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 252.41/36.32 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 252.41/36.32 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 252.41/36.32 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 252.41/36.32 v6, v7) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 252.41/36.32 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2))) % 252.41/36.32 % 252.41/36.32 (fact_power__eq__if) % 252.41/36.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 252.41/36.32 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 252.41/36.32 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 & % 252.41/36.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 252.41/36.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v3) & $i(v2) & $i(v1) & % 252.41/36.32 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 252.41/36.32 : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~ % 252.41/36.32 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ (hAPP(v7, % 252.41/36.32 v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = v7) | ~ % 252.41/36.32 (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, v5) = v10 & % 252.41/36.32 $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | ~ % 252.41/36.32 (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4))) % 252.41/36.32 % 252.41/36.32 (fact_power__one__right) % 252.41/36.32 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.41/36.32 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 252.41/36.32 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 252.41/36.32 $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | hAPP(v4, v0) = % 252.41/36.32 v1)) % 252.41/36.32 % 252.41/36.32 (fact_real__le__trans) % 252.41/36.32 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | % 252.41/36.32 ~ $i(v1) | ~ $i(v0) | ~ % 252.41/36.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | ~ % 252.41/36.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | % 252.41/36.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)) % 252.41/36.32 % 252.41/36.32 (fact_real__mult__1) % 252.41/36.32 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.41/36.32 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 252.41/36.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & hAPP(v0, v1) = v2 & % 252.41/36.32 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ % 252.41/36.32 (hAPP(v2, v3) = v4) | ~ $i(v3))) % 252.41/36.32 % 252.41/36.32 (fact_real__natfloor__add__one__gt) % 252.41/36.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.41/36.32 [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 252.41/36.32 ? [v4: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & % 252.41/36.32 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 & $i(v4) & % 252.41/36.32 $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4)))) % 252.41/36.32 % 252.41/36.32 (fact_real__natfloor__gt__diff__one) % 252.41/36.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.41/36.32 [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = % 252.41/36.32 v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : % 252.41/36.32 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1) = v3 & % 252.41/36.32 $i(v4) & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, % 252.41/36.32 v4)))) % 252.41/36.32 % 252.41/36.32 (fact_real__of__nat__1) % 252.41/36.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.32 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 & % 252.41/36.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 252.41/36.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)) % 252.41/36.32 % 252.41/36.32 (fact_real__of__nat__div3) % 252.41/36.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 252.41/36.33 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 252.41/36.33 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 252.41/36.33 $i] : ! [v8: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = % 252.41/36.33 v6) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~ % 252.41/36.33 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, % 252.41/36.33 v1) = v4) | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, % 252.41/36.33 v4) = v5) | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5, % 252.41/36.33 v7) = v8) | ~ $i(v2) | ~ $i(v1) | % 252.41/36.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v0))) % 252.41/36.33 % 252.41/36.33 (fact_real__zero__not__eq__one) % 252.41/36.33 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 252.41/36.33 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.41/36.33 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)) % 252.41/36.33 % 252.41/36.33 (fact_realpow__minus__mult) % 252.41/36.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.33 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 252.41/36.33 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 252.41/36.33 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 252.41/36.33 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 252.41/36.33 (c_Power_Opower__class_Opower(v4) = v6) | ~ % 252.41/36.33 (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ % 252.41/36.33 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~ (hAPP(v10, % 252.41/36.33 v2) = v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ % 252.41/36.33 (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 252.41/36.33 class_Groups_Omonoid__mult(v4) | ~ % 252.41/36.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3) = v11 & % 252.41/36.33 $i(v11)))) % 252.41/36.33 % 252.41/36.33 (fact_realpow__num__eq__if) % 252.41/36.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 252.41/36.33 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 252.41/36.33 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 252.41/36.33 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 252.41/36.33 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 252.41/36.33 (c_Power_Opower__class_Opower(v4) = v5) | ~ % 252.41/36.33 (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ % 252.41/36.33 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~ (hAPP(v8, % 252.41/36.33 v10) = v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ % 252.41/36.33 (hAPP(v5, v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 252.41/36.33 class_Power_Opower(v4) | ? [v12: $i] : ? [v13: $i] : (( ~ (v3 = v0) | % 252.41/36.33 (v13 = v12 & c_Groups_Oone__class_Oone(v4) = v12 & hAPP(v6, v0) = v12 % 252.41/36.33 & $i(v12))) & (v3 = v0 | (v12 = v11 & hAPP(v6, v3) = v11 & % 252.41/36.33 $i(v11)))))) % 252.41/36.33 % 252.41/36.33 (fact_reals__Archimedean6) % 252.80/36.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 252.80/36.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.80/36.33 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 252.80/36.33 : ( ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 252.80/36.33 v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 252.80/36.33 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v3) % 252.80/36.33 = v6 & c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & $i(v6) % 252.80/36.33 & $i(v5) & $i(v4) & $i(v3) & % 252.80/36.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2) & % 252.80/36.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6)))) % 252.80/36.33 % 252.80/36.33 (fact_reduce__poly__simple) % 252.80/36.33 $i(tc_Nat_Onat) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] % 252.80/36.33 : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 252.80/36.33 (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v4 & % 252.80/36.33 c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 & % 252.80/36.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 252.80/36.33 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & % 252.80/36.33 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 & % 252.80/36.33 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v5 & $i(v5) & $i(v4) & $i(v3) % 252.80/36.33 & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v7 = % 252.80/36.33 v0 | v6 = v1 | ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | ~ $i(v6) | ? [v9: % 252.80/36.33 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 252.80/36.33 [v14: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v12) = % 252.80/36.33 v13 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v13) = v14 & % 252.80/36.33 hAPP(v10, v6) = v11 & hAPP(v8, v11) = v12 & hAPP(v4, v9) = v10 & $i(v14) % 252.80/36.33 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & % 252.80/36.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v5)))) % 252.80/36.33 % 252.80/36.33 (fact_unimodular__reduce__norm) % 252.80/36.34 $i(c_Complex_Oii) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: % 252.80/36.34 $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v1 & % 252.80/36.34 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2: % 252.80/36.34 $i] : ! [v3: $i] : ( ~ % 252.80/36.34 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, v1) = v3) | ~ % 252.80/36.34 $i(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 252.80/36.34 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v4 = v0) & % 252.80/36.34 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 & % 252.80/36.34 $i(v4)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v1) = % 252.80/36.34 v5 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v6 & % 252.80/36.34 $i(v6) & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, % 252.80/36.34 v0)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, % 252.80/36.34 c_Complex_Oii) = v8 & % 252.80/36.34 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9 & $i(v9) % 252.80/36.34 & $i(v8) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v0)) | % 252.80/36.34 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, c_Complex_Oii) = % 252.80/36.34 v10 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10) = v11 % 252.80/36.34 & $i(v11) & $i(v10) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 252.80/36.34 v11, v0)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, % 252.80/36.34 v3) = v7 & $i(v7) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 252.80/36.34 v7, v0))))) % 252.80/36.34 % 252.80/36.34 (function-axioms) % 252.80/36.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 252.80/36.34 | ~ (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ % 252.80/36.34 (c_Power_Opower_Opower(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 252.80/36.34 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v1) | ~ % 252.80/36.34 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 252.80/36.34 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v1) | ~ % 252.80/36.34 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 252.80/36.34 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~ % 252.80/36.34 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 252.80/36.34 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Polynomial_Opcompose(v4, v3, v2) = v1) | ~ (c_Polynomial_Opcompose(v4, % 252.80/36.34 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 252.80/36.34 ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~ % 252.80/36.34 (c_Polynomial_Oorder(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 252.80/36.34 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~ % 252.80/36.34 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 252.80/36.34 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v1) | ~ % 252.80/36.34 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 252.80/36.34 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 252.80/36.34 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 252.80/36.34 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_RealDef_Oreal(v3, v2) = % 252.80/36.34 v1) | ~ (c_RealDef_Oreal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 252.80/36.34 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v1) | ~ % 252.80/36.34 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v0)) & ! [v0: % 252.80/36.34 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, v2) = % 252.80/36.34 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 252.80/36.34 ~ (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) = v0)) % 252.80/36.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Groups_Oabs__class_Oabs(v3, v2) = v1) | ~ (c_Groups_Oabs__class_Oabs(v3, % 252.80/36.34 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 252.80/36.34 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) = v0)) & ! [v0: $i] : % 252.80/36.34 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~ % 252.80/36.34 (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 252.80/36.34 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3, % 252.80/36.34 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Power_Opower__class_Opower(v2) = v1) | ~ % 252.80/36.34 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 252.80/36.34 [v2: $i] : (v1 = v0 | ~ (c_Complex_Oexpi(v2) = v1) | ~ (c_Complex_Oexpi(v2) % 252.80/36.34 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_RComplete_Onatfloor(v2) = v1) | ~ (c_RComplete_Onatfloor(v2) = v0)) & ! % 252.80/36.34 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_RComplete_Onatceiling(v2) = v1) | ~ (c_RComplete_Onatceiling(v2) = v0)) % 252.80/36.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 252.80/36.34 (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0)) & ! % 252.80/36.34 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Transcendental_Oarctan(v2) = v1) | ~ (c_Transcendental_Oarctan(v2) = % 252.80/36.34 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 252.80/36.34 (c_Groups_Otimes__class_Otimes(v2) = v1) | ~ % 252.80/36.34 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 252.80/36.34 [v2: $i] : (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 252.80/36.34 (c_Groups_Ozero__class_Ozero(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 252.80/36.34 [v2: $i] : (v1 = v0 | ~ (c_Groups_Oone__class_Oone(v2) = v1) | ~ % 252.80/36.34 (c_Groups_Oone__class_Oone(v2) = v0)) % 252.80/36.34 % 252.80/36.34 Further assumptions not needed in the proof: % 252.80/36.34 -------------------------------------------- % 252.80/36.35 arity_Complex__Ocomplex__Fields_Ofield, % 252.80/36.35 arity_Complex__Ocomplex__Fields_Ofield__inverse__zero, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Oab__group__add, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Oab__semigroup__add, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Ogroup__add, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Ominus, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Omonoid__add, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Omonoid__mult, % 252.80/36.35 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ozero, % 252.80/36.35 arity_Complex__Ocomplex__Int_Oring__char__0, % 252.80/36.35 arity_Complex__Ocomplex__Power_Opower, % 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__field, % 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, % 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, % 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, % 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__normed__field, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__ring, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__ring__1, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__semiring, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Odivision__ring, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Odvd, arity_Complex__Ocomplex__Rings_Oidom, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Omult__zero, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Ono__zero__divisors, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Osemiring, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Osemiring__0, % 252.80/36.35 arity_Complex__Ocomplex__Rings_Ozero__neq__one, % 252.80/36.35 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 252.80/36.35 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Orderings_Oord, % 252.80/36.35 arity_HOL__Obool__Orderings_Oorder, arity_HOL__Obool__Orderings_Opreorder, % 252.80/36.35 arity_Int__Oint__Divides_Oring__div, arity_Int__Oint__Divides_Osemiring__div, % 252.80/36.35 arity_Int__Oint__Groups_Oab__group__add, % 252.80/36.35 arity_Int__Oint__Groups_Oab__semigroup__add, % 252.80/36.35 arity_Int__Oint__Groups_Oab__semigroup__mult, % 252.80/36.35 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, % 252.80/36.35 arity_Int__Oint__Groups_Ocancel__comm__monoid__add, % 252.80/36.35 arity_Int__Oint__Groups_Ocancel__semigroup__add, % 252.80/36.35 arity_Int__Oint__Groups_Ocomm__monoid__add, % 252.80/36.35 arity_Int__Oint__Groups_Ocomm__monoid__mult, % 252.80/36.35 arity_Int__Oint__Groups_Ogroup__add, % 252.80/36.35 arity_Int__Oint__Groups_Olinordered__ab__group__add, % 252.80/36.35 arity_Int__Oint__Groups_Ominus, arity_Int__Oint__Groups_Omonoid__add, % 252.80/36.35 arity_Int__Oint__Groups_Omonoid__mult, arity_Int__Oint__Groups_Oone, % 252.80/36.35 arity_Int__Oint__Groups_Oordered__ab__group__add, % 252.80/36.35 arity_Int__Oint__Groups_Oordered__ab__group__add__abs, % 252.80/36.35 arity_Int__Oint__Groups_Oordered__ab__semigroup__add, % 252.80/36.35 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, % 252.80/36.35 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, % 252.80/36.35 arity_Int__Oint__Groups_Oordered__comm__monoid__add, % 252.80/36.35 arity_Int__Oint__Groups_Ozero, arity_Int__Oint__Int_Oring__char__0, % 252.80/36.35 arity_Int__Oint__Orderings_Olinorder, arity_Int__Oint__Orderings_Oord, % 252.80/36.35 arity_Int__Oint__Orderings_Oorder, arity_Int__Oint__Orderings_Opreorder, % 252.80/36.35 arity_Int__Oint__Power_Opower, arity_Int__Oint__Rings_Ocomm__ring, % 252.80/36.35 arity_Int__Oint__Rings_Ocomm__ring__1, arity_Int__Oint__Rings_Ocomm__semiring, % 252.80/36.35 arity_Int__Oint__Rings_Ocomm__semiring__0, % 252.80/36.35 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Odvd, % 252.80/36.35 arity_Int__Oint__Rings_Oidom, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__idom, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__ring, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__ring__strict, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semidom, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semiring, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semiring__1, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semiring__1__strict, % 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semiring__strict, % 252.80/36.35 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors, % 252.80/36.35 arity_Int__Oint__Rings_Oordered__cancel__semiring, % 252.80/36.35 arity_Int__Oint__Rings_Oordered__comm__semiring, % 252.80/36.35 arity_Int__Oint__Rings_Oordered__ring, % 252.80/36.35 arity_Int__Oint__Rings_Oordered__ring__abs, % 252.80/36.35 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring, % 252.80/36.35 arity_Int__Oint__Rings_Oring__1, % 252.80/36.35 arity_Int__Oint__Rings_Oring__1__no__zero__divisors, % 252.80/36.35 arity_Int__Oint__Rings_Oring__no__zero__divisors, % 252.80/36.35 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0, % 252.80/36.35 arity_Int__Oint__Rings_Ozero__neq__one, % 252.80/36.35 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 252.80/36.35 arity_Nat__Onat__Divides_Osemiring__div, % 252.80/36.35 arity_Nat__Onat__Groups_Oab__semigroup__add, % 252.80/36.35 arity_Nat__Onat__Groups_Oab__semigroup__mult, % 252.80/36.35 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, % 252.80/36.35 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, % 252.80/36.35 arity_Nat__Onat__Groups_Ocancel__semigroup__add, % 252.80/36.35 arity_Nat__Onat__Groups_Ocomm__monoid__add, % 252.80/36.35 arity_Nat__Onat__Groups_Ocomm__monoid__mult, arity_Nat__Onat__Groups_Ominus, % 252.80/36.35 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult, % 252.80/36.35 arity_Nat__Onat__Groups_Oone, % 252.80/36.35 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, % 252.80/36.35 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, % 252.80/36.35 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, % 252.80/36.35 arity_Nat__Onat__Groups_Oordered__comm__monoid__add, % 252.80/36.35 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Orderings_Olinorder, % 252.80/36.35 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder, % 252.80/36.35 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Power_Opower, % 252.80/36.35 arity_Nat__Onat__Rings_Ocomm__semiring, % 252.80/36.35 arity_Nat__Onat__Rings_Ocomm__semiring__0, % 252.80/36.35 arity_Nat__Onat__Rings_Ocomm__semiring__1, arity_Nat__Onat__Rings_Odvd, % 252.80/36.35 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, % 252.80/36.35 arity_Nat__Onat__Rings_Olinordered__semidom, % 252.80/36.35 arity_Nat__Onat__Rings_Olinordered__semiring, % 252.80/36.35 arity_Nat__Onat__Rings_Olinordered__semiring__strict, % 252.80/36.35 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors, % 252.80/36.35 arity_Nat__Onat__Rings_Oordered__cancel__semiring, % 252.80/36.35 arity_Nat__Onat__Rings_Oordered__comm__semiring, % 252.80/36.35 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring, % 252.80/36.35 arity_Nat__Onat__Rings_Osemiring__0, arity_Nat__Onat__Rings_Ozero__neq__one, % 252.80/36.35 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 252.80/36.35 arity_Polynomial__Opoly__Divides_Oring__div, % 252.80/36.35 arity_Polynomial__Opoly__Divides_Osemiring__div, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oab__group__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oab__semigroup__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Ogroup__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Ominus, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Omonoid__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Omonoid__mult, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oone, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, % 252.80/36.35 arity_Polynomial__Opoly__Groups_Ozero, % 252.80/36.35 arity_Polynomial__Opoly__Int_Oring__char__0, % 252.80/36.35 arity_Polynomial__Opoly__Orderings_Olinorder, % 252.80/36.35 arity_Polynomial__Opoly__Orderings_Oord, % 252.80/36.35 arity_Polynomial__Opoly__Orderings_Oorder, % 252.80/36.35 arity_Polynomial__Opoly__Orderings_Opreorder, % 252.80/36.35 arity_Polynomial__Opoly__Power_Opower, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__ring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__ring__1, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__semiring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Oidom, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__idom, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__ring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semidom, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semiring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Omult__zero, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Ono__zero__divisors, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__ring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__ring__abs, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__semiring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Osemiring, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Osemiring__0, % 252.80/36.35 arity_Polynomial__Opoly__Rings_Ozero__neq__one, % 252.80/36.35 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 252.80/36.35 arity_RealDef__Oreal__Fields_Ofield, % 252.80/36.35 arity_RealDef__Oreal__Fields_Ofield__inverse__zero, % 252.80/36.35 arity_RealDef__Oreal__Fields_Olinordered__field, % 252.80/36.35 arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oab__group__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oab__semigroup__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oab__semigroup__mult, % 252.80/36.35 arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Ocomm__monoid__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, % 252.80/36.35 arity_RealDef__Oreal__Groups_Ogroup__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Ominus, arity_RealDef__Oreal__Groups_Omonoid__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Omonoid__mult, arity_RealDef__Oreal__Groups_Oone, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__ab__group__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, % 252.80/36.35 arity_RealDef__Oreal__Groups_Ozero, arity_RealDef__Oreal__Int_Oring__char__0, % 252.80/36.35 arity_RealDef__Oreal__Orderings_Odense__linorder, % 252.80/36.35 arity_RealDef__Oreal__Orderings_Olinorder, arity_RealDef__Oreal__Orderings_Oord, % 252.80/36.35 arity_RealDef__Oreal__Orderings_Opreorder, arity_RealDef__Oreal__Power_Opower, % 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__field, % 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, % 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, % 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, % 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__field, % 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__vector, % 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__ring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__ring__1, % 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__semiring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__semiring__0, % 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__semiring__1, % 252.80/36.35 arity_RealDef__Oreal__Rings_Odivision__ring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero, % 252.80/36.35 arity_RealDef__Oreal__Rings_Odvd, arity_RealDef__Oreal__Rings_Oidom, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__idom, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__ring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__ring__strict, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semidom, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semiring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semiring__1, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, % 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semiring__strict, % 252.80/36.35 arity_RealDef__Oreal__Rings_Omult__zero, % 252.80/36.35 arity_RealDef__Oreal__Rings_Ono__zero__divisors, % 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__cancel__semiring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__comm__semiring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__ring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__ring__abs, % 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__semiring, % 252.80/36.35 arity_RealDef__Oreal__Rings_Oring, arity_RealDef__Oreal__Rings_Oring__1, % 252.80/36.35 arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, % 252.80/36.35 arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, % 252.80/36.35 arity_RealDef__Oreal__Rings_Osemiring, arity_RealDef__Oreal__Rings_Osemiring__0, % 252.80/36.35 arity_RealDef__Oreal__Rings_Ozero__neq__one, % 252.80/36.35 arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 252.80/36.35 arity_fun__Groups_Ominus, arity_fun__Orderings_Oord, % 252.80/36.35 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, % 252.80/36.35 fact_DERIV__mult__lemma, fact_DIVISION__BY__ZERO, fact_Deriv_Oadd__diff__add, % 252.80/36.35 fact_Divides_Omod__div__equality_H, % 252.80/36.35 fact_Divides_Otransfer__nat__int__function__closures_I2_J, fact_H_I1_J, % 252.80/36.35 fact_H_I4_J, fact_Nat_Oadd__0__right, fact_Nat_Odiff__diff__eq, % 252.80/36.35 fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Adegree_Aq_A_061_Adegree_Ap_059_A_B_Bx_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Iz_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, % 252.80/36.35 fact_ab__semigroup__add__class_Oadd__ac_I1_J, % 252.80/36.35 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_abs__add__abs, % 252.80/36.35 fact_abs__diff__less__iff, fact_abs__diff__triangle__ineq, fact_abs__div, % 252.80/36.35 fact_abs__div__pos, fact_abs__divide, fact_abs__dvd__iff, fact_abs__eq__0, % 252.80/36.35 fact_abs__eq__mult, fact_abs__ge__self, fact_abs__ge__zero, % 252.80/36.35 fact_abs__idempotent, fact_abs__le__D1, fact_abs__le__zero__iff, % 252.80/36.35 fact_abs__minus__commute, fact_abs__mult, fact_abs__mult__less, % 252.80/36.35 fact_abs__mult__pos, fact_abs__mult__self, fact_abs__norm__cancel, % 252.80/36.35 fact_abs__not__less__zero, fact_abs__of__nonneg, fact_abs__of__pos, % 252.80/36.35 fact_abs__one, fact_abs__triangle__ineq, fact_abs__triangle__ineq2, % 252.80/36.35 fact_abs__triangle__ineq2__sym, fact_abs__triangle__ineq3, % 252.80/36.35 fact_abs__triangle__ineq4, fact_abs__zero, fact_add_Ocomm__neutral, fact_add__0, % 252.80/36.35 fact_add__0__iff, fact_add__0__left, fact_add__0__right, fact_add__diff__assoc, % 252.80/36.35 fact_add__diff__assoc2, fact_add__diff__cancel, fact_add__diff__inverse, % 252.80/36.35 fact_add__divide__distrib, fact_add__divide__eq__iff, fact_add__eq__self__zero, % 252.80/36.35 fact_add__frac__eq, fact_add__frac__num, fact_add__gr__0, fact_add__imp__eq, % 252.80/36.35 fact_add__increasing, fact_add__increasing2, fact_add__is__0, fact_add__leD1, % 252.80/36.35 fact_add__leD2, fact_add__leE, fact_add__le__cancel__left, % 252.80/36.35 fact_add__le__cancel__right, fact_add__le__imp__le__left, % 252.80/36.35 fact_add__le__imp__le__right, fact_add__le__less__mono, fact_add__le__mono, % 252.80/36.35 fact_add__le__mono1, fact_add__left__cancel, fact_add__left__imp__eq, % 252.80/36.35 fact_add__left__mono, fact_add__lessD1, fact_add__less__cancel__left, % 252.80/36.35 fact_add__less__cancel__right, fact_add__less__imp__less__left, % 252.80/36.35 fact_add__less__imp__less__right, fact_add__less__le__mono, % 252.80/36.35 fact_add__less__mono, fact_add__less__mono1, fact_add__mono, % 252.80/36.35 fact_add__mult__distrib, fact_add__mult__distrib2, fact_add__neg__neg, % 252.80/36.35 fact_add__neg__nonpos, fact_add__nonneg__eq__0__iff, fact_add__nonneg__nonneg, % 252.80/36.35 fact_add__nonneg__pos, fact_add__nonpos__neg, fact_add__nonpos__nonpos, % 252.80/36.35 fact_add__num__frac, fact_add__poly__code_I1_J, fact_add__poly__code_I2_J, % 252.80/36.35 fact_add__pos__nonneg, fact_add__pos__pos, fact_add__right__cancel, % 252.80/36.35 fact_add__right__imp__eq, fact_add__right__mono, fact_add__scale__eq__noteq, % 252.80/36.35 fact_add__strict__increasing, fact_add__strict__increasing2, % 252.80/36.35 fact_add__strict__left__mono, fact_add__strict__mono, % 252.80/36.35 fact_add__strict__right__mono, fact_arctan__monotone, fact_arctan__monotone_H, % 252.80/36.35 fact_arctan__zero__zero, fact_assms, fact_combine__common__factor, % 252.80/36.35 fact_comm__mult__left__mono, fact_comm__mult__strict__left__mono, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, % 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, % 252.80/36.35 fact_comm__semiring__class_Odistrib, fact_complex__i__not__one, % 252.80/36.35 fact_complex__i__not__zero, fact_complex__mod__triangle__ineq2, % 252.80/36.35 fact_complex__mod__triangle__sub, fact_convex__bound__le, % 252.80/36.35 fact_convex__bound__lt, fact_crossproduct__eq, fact_crossproduct__noteq, % 252.80/36.35 fact_d_I1_J, fact_d_I3_J, fact_decseq__def, fact_degree__0, fact_degree__1, % 252.80/36.35 fact_degree__add__eq__left, fact_degree__add__eq__right, fact_degree__add__le, % 252.80/36.35 fact_degree__add__less, fact_degree__diff__le, fact_degree__diff__less, % 252.80/36.35 fact_degree__mod__less, fact_degree__mult__eq, fact_degree__mult__le, % 252.80/36.35 fact_degree__pcompose__le, fact_degree__power__le, fact_dense__le, % 252.80/36.35 fact_dense__le__bounded, fact_diff__0__eq__0, fact_diff__0__right, % 252.80/36.35 fact_diff__add__0, fact_diff__add__assoc, fact_diff__add__assoc2, % 252.80/36.35 fact_diff__add__cancel, fact_diff__add__inverse, fact_diff__add__inverse2, % 252.80/36.35 fact_diff__cancel, fact_diff__cancel2, fact_diff__commute, % 252.80/36.35 fact_diff__diff__cancel, fact_diff__diff__left, fact_diff__diff__right, % 252.80/36.35 fact_diff__divide__distrib, fact_diff__divide__eq__iff, fact_diff__eq__diff__eq, % 252.80/36.35 fact_diff__eq__diff__less, fact_diff__eq__diff__less__eq, fact_diff__frac__eq, % 252.80/36.35 fact_diff__is__0__eq, fact_diff__is__0__eq_H, fact_diff__le__mono, % 252.80/36.35 fact_diff__le__mono2, fact_diff__le__self, fact_diff__less, % 252.80/36.35 fact_diff__less__mono, fact_diff__less__mono2, fact_diff__mult__distrib, % 252.80/36.35 fact_diff__mult__distrib2, fact_diff__poly__code_I2_J, fact_diff__self, % 252.80/36.35 fact_diff__self__eq__0, fact_diffs0__imp__equal, fact_div__0, fact_div__add, % 252.80/36.35 fact_div__add1__eq, fact_div__add__self1, fact_div__add__self2, fact_div__by__0, % 252.80/36.35 fact_div__by__1, fact_div__dvd__div, fact_div__le__dividend, fact_div__le__mono, % 252.80/36.35 fact_div__le__mono2, fact_div__less, fact_div__mod__equality, % 252.80/36.35 fact_div__mod__equality2, fact_div__mod__equality_H, fact_div__mult1__eq, % 252.80/36.35 fact_div__mult2__eq, fact_div__mult__div__if__dvd, fact_div__mult__mult1, % 252.80/36.35 fact_div__mult__mult1__if, fact_div__mult__mult2, fact_div__mult__self1, % 252.80/36.35 fact_div__mult__self1__is__id, fact_div__mult__self1__is__m, % 252.80/36.35 fact_div__mult__self2, fact_div__mult__self2__is__id, % 252.80/36.35 fact_div__mult__self__is__m, fact_div__mult__swap, fact_div__poly__eq, % 252.80/36.35 fact_div__poly__less, fact_div__power, fact_div__self, fact_divide_Oadd, % 252.80/36.35 fact_divide_Odiff, fact_divide_Ononneg__bounded, fact_divide_Opos__bounded, % 252.80/36.35 fact_divide_Ozero, fact_divide__1, fact_divide__add__eq__iff, % 252.80/36.35 fact_divide__diff__eq__iff, fact_divide__eq__eq, fact_divide__eq__imp, % 252.80/36.35 fact_divide__le__0__iff, fact_divide__le__eq, fact_divide__left__mono, % 252.80/36.35 fact_divide__left__mono__neg, fact_divide__less__0__iff, fact_divide__less__eq, % 252.80/36.35 fact_divide__neg__neg, fact_divide__neg__pos, fact_divide__nonneg__neg, % 252.80/36.35 fact_divide__nonneg__pos, fact_divide__nonpos__neg, fact_divide__nonpos__pos, % 252.80/36.35 fact_divide__pos__neg, fact_divide__pos__pos, fact_divide__right__mono, % 252.80/36.35 fact_divide__right__mono__neg, fact_divide__self, fact_divide__self__if, % 252.80/36.35 fact_divide__strict__left__mono, fact_divide__strict__left__mono__neg, % 252.80/36.35 fact_divide__strict__right__mono, fact_divide__strict__right__mono__neg, % 252.80/36.35 fact_divide__zero, fact_divide__zero__left, fact_divisors__zero, % 252.80/36.35 fact_divmod__int__rel__div__eq, fact_divmod__int__rel__mod__eq, fact_dm_I1_J, % 252.80/36.35 fact_dm_I2_J, fact_double__add__le__zero__iff__single__add__le__zero, % 252.80/36.35 fact_double__add__less__zero__iff__single__add__less__zero, % 252.80/36.35 fact_double__eq__0__iff, fact_double__zero__sym, fact_dvdI, fact_dvd_Oantisym, % 252.80/36.35 fact_dvd_Oantisym__conv, fact_dvd_Oeq__iff, fact_dvd_Oeq__refl, % 252.80/36.35 fact_dvd_Ole__imp__less__or__eq, fact_dvd_Ole__less, fact_dvd_Ole__less__trans, % 252.80/36.35 fact_dvd_Ole__neq__trans, fact_dvd_Oless__asym, fact_dvd_Oless__asym_H, % 252.80/36.35 fact_dvd_Oless__imp__le, fact_dvd_Oless__imp__neq, fact_dvd_Oless__imp__not__eq, % 252.80/36.35 fact_dvd_Oless__imp__not__eq2, fact_dvd_Oless__imp__not__less, % 252.80/36.35 fact_dvd_Oless__le, fact_dvd_Oless__le__trans, fact_dvd_Oless__not__sym, % 252.80/36.35 fact_dvd_Oless__trans, fact_dvd_Oneq__le__trans, fact_dvd_Oord__eq__le__trans, % 252.80/36.35 fact_dvd_Oord__eq__less__trans, fact_dvd_Oord__le__eq__trans, % 252.80/36.35 fact_dvd_Oord__less__eq__trans, fact_dvd_Oorder__refl, fact_dvd_Oorder__trans, % 252.80/36.35 fact_dvd__0__left, fact_dvd__0__right, fact_dvd__abs__iff, fact_dvd__add, % 252.80/36.35 fact_dvd__antisym, fact_dvd__diff, fact_dvd__diffD, fact_dvd__diffD1, % 252.80/36.35 fact_dvd__diff__nat, fact_dvd__div__div__eq__mult, fact_dvd__div__eq__mult, % 252.80/36.35 fact_dvd__div__mult, fact_dvd__div__mult__self, fact_dvd__eq__mod__eq__0, % 252.80/36.35 fact_dvd__if__abs__eq, fact_dvd__imp__degree__le, fact_dvd__imp__le, % 252.80/36.35 fact_dvd__imp__le__int, fact_dvd__imp__mod__0, fact_dvd__mod, % 252.80/36.35 fact_dvd__mod__iff, fact_dvd__mod__imp__dvd, fact_dvd__mult, fact_dvd__mult2, % 252.80/36.35 fact_dvd__mult__cancel, fact_dvd__mult__cancel__left, % 252.80/36.35 fact_dvd__mult__cancel__right, fact_dvd__mult__div__cancel, % 252.80/36.35 fact_dvd__mult__left, fact_dvd__mult__right, fact_dvd__pos__nat, % 252.80/36.35 fact_dvd__power, fact_dvd__power__le, fact_dvd__power__same, fact_dvd__reduce, % 252.80/36.35 fact_dvd__refl, fact_dvd__trans, fact_dvd__triv__left, fact_dvd__triv__right, % 252.80/36.35 fact_em0, fact_eq__add__iff1, fact_eq__add__iff2, fact_eq__diff__iff, % 252.80/36.35 fact_eq__divide__eq, fact_eq__divide__imp, fact_eq__iff__diff__eq__0, % 252.80/36.35 fact_eq__imp__le, fact_even__less__0__iff, fact_expi__add, fact_expi__zero, % 252.80/36.35 fact_ext, fact_field__le__mult__one__interval, fact_field__power__not__zero, % 252.80/36.35 fact_frac__eq__eq, fact_frac__le, fact_frac__less, fact_frac__less2, % 252.80/36.35 fact_gcd__lcm__complete__lattice__nat_Otop__greatest, fact_gr0I, % 252.80/36.35 fact_gr__implies__not0, fact_gt__half__sum, fact_inf__period_I3_J, % 252.80/36.35 fact_inf__period_I4_J, fact_le0, fact_leD, fact_leI, fact_le__0__eq, % 252.80/36.35 fact_le__Suc__ex__iff, fact_le__add1, fact_le__add2, fact_le__add__diff, % 252.80/36.35 fact_le__add__diff__inverse, fact_le__add__diff__inverse2, fact_le__add__iff1, % 252.80/36.35 fact_le__add__iff2, fact_le__antisym, fact_le__cube, fact_le__diff__conv, % 252.80/36.35 fact_le__diff__conv2, fact_le__diff__iff, fact_le__divide__eq, % 252.80/36.35 fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE, fact_le__fun__def, % 252.80/36.35 fact_le__iff__add, fact_le__iff__diff__le__0, fact_le__imp__diff__is__add, % 252.80/36.35 fact_le__imp__power__dvd, fact_le__mod__geq, fact_le__mult__natfloor, % 252.80/36.35 fact_le__natfloor, fact_le__natfloor__eq, fact_le__neq__implies__less, % 252.80/36.35 fact_le__refl, fact_le__square, fact_le__trans, fact_left__add__mult__distrib, % 252.80/36.35 fact_lemma__MVT, fact_lemma__interval, fact_lemma__interval__lt, % 252.80/36.35 fact_less__1__mult, fact_less__add__eq__less, fact_less__add__iff1, % 252.80/36.35 fact_less__add__iff2, fact_less__add__one, fact_less__diff__conv, % 252.80/36.35 fact_less__diff__iff, fact_less__divide__eq, fact_less__eq__nat_Osimps_I1_J, % 252.80/36.35 fact_less__eq__real__def, fact_less__fun__def, fact_less__half__sum, % 252.80/36.35 fact_less__iff__diff__less__0, fact_less__imp__diff__less, % 252.80/36.35 fact_less__imp__le__nat, fact_less__imp__neq, fact_less__irrefl__nat, % 252.80/36.35 fact_less__le__not__le, fact_less__nat__zero__code, fact_less__natfloor, % 252.80/36.35 fact_less__not__refl, fact_less__not__refl2, fact_less__not__refl3, % 252.80/36.35 fact_less__or__eq__imp__le, fact_less__real__def, fact_less__zeroE, % 252.80/36.35 fact_linorder__antisym__conv1, fact_linorder__antisym__conv2, % 252.80/36.35 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases, % 252.80/36.35 fact_linorder__le__less__linear, fact_linorder__less__linear, % 252.80/36.35 fact_linorder__linear, fact_linorder__neqE, % 252.80/36.35 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat, % 252.80/36.35 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less, % 252.80/36.35 fact_m_I1_J, fact_minus__apply, fact_minus__nat_Odiff__0, fact_mod__0, % 252.80/36.35 fact_mod__add__cong, fact_mod__add__eq, fact_mod__add__left__eq, % 252.80/36.35 fact_mod__add__right__eq, fact_mod__add__self1, fact_mod__add__self2, % 252.80/36.35 fact_mod__by__0, fact_mod__by__1, fact_mod__diff__cong, fact_mod__diff__eq, % 252.80/36.35 fact_mod__diff__left__eq, fact_mod__diff__right__eq, fact_mod__div__equality, % 252.80/36.35 fact_mod__div__equality2, fact_mod__div__trivial, fact_mod__eq__0__iff, % 252.80/36.35 fact_mod__geq, fact_mod__if, fact_mod__le__divisor, fact_mod__lemma, % 252.80/36.35 fact_mod__less, fact_mod__less__divisor, fact_mod__less__eq__dividend, % 252.80/36.35 fact_mod__mod__cancel, fact_mod__mod__trivial, fact_mod__mult2__eq, % 252.80/36.35 fact_mod__mult__cong, fact_mod__mult__distrib, fact_mod__mult__distrib2, % 252.80/36.35 fact_mod__mult__eq, fact_mod__mult__left__eq, fact_mod__mult__mult1, % 252.80/36.35 fact_mod__mult__mult2, fact_mod__mult__right__eq, fact_mod__mult__self1, % 252.80/36.35 fact_mod__mult__self1__is__0, fact_mod__mult__self2, % 252.80/36.35 fact_mod__mult__self2__is__0, fact_mod__mult__self3, % 252.80/36.35 fact_mod__neg__neg__trivial, fact_mod__poly__eq, fact_mod__poly__less, % 252.80/36.35 fact_mod__pos__pos__trivial, fact_mod__self, fact_mult_Oadd__left, % 252.80/36.35 fact_mult_Oadd__right, fact_mult_Ocomm__neutral, fact_mult_Odiff__left, % 252.80/36.35 fact_mult_Odiff__right, fact_mult_Ononneg__bounded, fact_mult_Opos__bounded, % 252.80/36.35 fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, fact_mult_Ozero__right, % 252.80/36.35 fact_mult__0, fact_mult__0__right, fact_mult__1, fact_mult__1__left, % 252.80/36.35 fact_mult__1__right, fact_mult__cancel1, fact_mult__cancel2, % 252.80/36.35 fact_mult__diff__mult, fact_mult__div__cancel, % 252.80/36.35 fact_mult__divide__mult__cancel__left, fact_mult__divide__mult__cancel__right, % 252.80/36.35 fact_mult__dvd__mono, fact_mult__eq__0__iff, fact_mult__idem, % 252.80/36.35 fact_mult__imp__div__pos__le, fact_mult__imp__div__pos__less, % 252.80/36.35 fact_mult__imp__le__div__pos, fact_mult__imp__less__div__pos, fact_mult__is__0, % 252.80/36.35 fact_mult__le__0__iff, fact_mult__le__cancel1, fact_mult__le__cancel2, % 252.80/36.35 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos, % 252.80/36.35 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1, % 252.80/36.35 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Odiff, % 252.80/36.35 fact_mult__left_Ononneg__bounded, fact_mult__left_Opos__bounded, % 252.80/36.35 fact_mult__left_Ozero, fact_mult__left__idem, fact_mult__left__le__imp__le, % 252.80/36.35 fact_mult__left__le__one__le, fact_mult__left__less__imp__less, % 252.80/36.35 fact_mult__left__mono, fact_mult__left__mono__neg, fact_mult__less__cancel1, % 252.80/36.35 fact_mult__less__cancel2, fact_mult__less__cancel__left__disj, % 252.80/36.35 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos, % 252.80/36.35 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left, % 252.80/36.35 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less, % 252.80/36.35 fact_mult__less__mono1, fact_mult__less__mono2, fact_mult__mono, % 252.80/36.35 fact_mult__mono_H, fact_mult__neg__neg, fact_mult__neg__pos, % 252.80/36.35 fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos, % 252.80/36.35 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg, % 252.80/36.35 fact_mult__nonpos__nonpos, fact_mult__poly__0__left, fact_mult__poly__0__right, % 252.80/36.35 fact_mult__poly__add__left, fact_mult__pos__neg, fact_mult__pos__neg2, % 252.80/36.35 fact_mult__pos__pos, fact_mult__right_Oadd, fact_mult__right_Odiff, % 252.80/36.35 fact_mult__right_Ononneg__bounded, fact_mult__right_Opos__bounded, % 252.80/36.35 fact_mult__right_Ozero, fact_mult__right__le__imp__le, % 252.80/36.35 fact_mult__right__le__one__le, fact_mult__right__less__imp__less, % 252.80/36.35 fact_mult__right__mono, fact_mult__right__mono__neg, % 252.80/36.35 fact_mult__strict__left__mono, fact_mult__strict__left__mono__neg, % 252.80/36.35 fact_mult__strict__mono, fact_mult__strict__mono_H, % 252.80/36.35 fact_mult__strict__right__mono, fact_mult__strict__right__mono__neg, % 252.80/36.35 fact_mult__zero__left, fact_mult__zero__right, fact_nat__0__less__mult__iff, % 252.80/36.35 fact_nat__add__assoc, fact_nat__add__commute, fact_nat__add__left__cancel, % 252.80/36.35 fact_nat__add__left__cancel__le, fact_nat__add__left__cancel__less, % 252.80/36.35 fact_nat__add__left__commute, fact_nat__add__right__cancel, % 252.80/36.35 fact_nat__diff__add__eq1, fact_nat__diff__add__eq2, fact_nat__diff__split, % 252.80/36.35 fact_nat__diff__split__asm, fact_nat__dvd__not__less, fact_nat__eq__add__iff1, % 252.80/36.35 fact_nat__eq__add__iff2, fact_nat__le__add__iff1, fact_nat__le__add__iff2, % 252.80/36.35 fact_nat__le__linear, fact_nat__less__add__iff1, fact_nat__less__add__iff2, % 252.80/36.35 fact_nat__less__cases, fact_nat__less__le, fact_nat__mult__assoc, % 252.80/36.35 fact_nat__mult__commute, fact_nat__mult__div__cancel1, % 252.80/36.35 fact_nat__mult__div__cancel__disj, fact_nat__mult__dvd__cancel1, % 252.80/36.35 fact_nat__mult__dvd__cancel__disj, fact_nat__mult__eq__cancel1, % 252.80/36.35 fact_nat__mult__eq__cancel__disj, fact_nat__mult__le__cancel1, % 252.80/36.35 fact_nat__mult__less__cancel1, fact_nat__neq__iff, % 252.80/36.35 fact_nat__power__less__imp__less, fact_nat__zero__less__power__iff, % 252.80/36.35 fact_natceiling__add, fact_natceiling__le, fact_natceiling__le__eq, % 252.80/36.35 fact_natceiling__mono, fact_natceiling__neg, fact_natceiling__real__of__nat, % 252.80/36.35 fact_natceiling__subtract, fact_natceiling__zero, fact_natfloor__add, % 252.80/36.35 fact_natfloor__mono, fact_natfloor__neg, fact_natfloor__power, % 252.80/36.35 fact_natfloor__real__of__nat, fact_natfloor__subtract, fact_natfloor__zero, % 252.80/36.35 fact_neg__divide__le__eq, fact_neg__divide__less__eq, fact_neg__le__divide__eq, % 252.80/36.35 fact_neg__less__divide__eq, fact_neg__mod__bound, fact_neg__mod__conj, % 252.80/36.35 fact_neg__mod__sign, fact_neq0__conv, fact_no__zero__divisors, % 252.80/36.35 fact_nonzero__abs__divide, fact_nonzero__divide__eq__eq, % 252.80/36.35 fact_nonzero__eq__divide__eq, fact_nonzero__norm__divide, % 252.80/36.35 fact_nonzero__power__divide, fact_norm__add__less, fact_norm__diff__ineq, % 252.80/36.35 fact_norm__diff__triangle__ineq, fact_norm__divide, fact_norm__eq__zero, % 252.80/36.35 fact_norm__ge__zero, fact_norm__le__zero__iff, fact_norm__mult, % 252.80/36.35 fact_norm__mult__ineq, fact_norm__mult__less, fact_norm__not__less__zero, % 252.80/36.35 fact_norm__power, fact_norm__power__ineq, fact_norm__ratiotest__lemma, % 252.80/36.35 fact_norm__triangle__ineq, fact_norm__triangle__ineq2, % 252.80/36.35 fact_norm__triangle__ineq3, fact_norm__triangle__ineq4, fact_norm__zero, % 252.80/36.35 fact_not__add__less1, fact_not__add__less2, fact_not__leE, fact_not__less0, % 252.80/36.35 fact_not__less__iff__gr__or__eq, fact_not__one__le__zero, % 252.80/36.35 fact_not__one__less__zero, fact_not__real__of__nat__less__zero, % 252.80/36.35 fact_not__real__square__gt__zero, fact_not__square__less__zero, % 252.80/36.35 fact_not__sum__squares__lt__zero, fact_one__dvd, fact_one__le__power, % 252.80/36.35 fact_one__less__power, fact_one__neq__zero, fact_one__reorient, % 252.80/36.35 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans, % 252.80/36.35 fact_ord__less__eq__trans, fact_order__antisym, fact_order__antisym__conv, % 252.80/36.35 fact_order__degree, fact_order__eq__iff, fact_order__eq__refl, % 252.80/36.35 fact_order__le__imp__less__or__eq, fact_order__le__less, % 252.80/36.35 fact_order__le__less__trans, fact_order__le__neq__trans, fact_order__less__asym, % 252.80/36.35 fact_order__less__asym_H, fact_order__less__imp__le, % 252.80/36.35 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2, % 252.80/36.35 fact_order__less__imp__not__less, fact_order__less__irrefl, % 252.80/36.35 fact_order__less__le__trans, fact_order__less__not__sym, % 252.80/36.35 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl, % 252.80/36.35 fact_order__root, fact_order__trans, fact_pCons, fact_pcompose__0, % 252.80/36.35 fact_pdivmod__rel, fact_pdivmod__rel__0, fact_pdivmod__rel__0__iff, % 252.80/36.35 fact_pdivmod__rel__by__0, fact_pdivmod__rel__by__0__iff, fact_pdivmod__rel__def, % 252.80/36.35 fact_pdivmod__rel__mult, fact_pdivmod__rel__unique, % 252.80/36.35 fact_pdivmod__rel__unique__div, fact_pdivmod__rel__unique__mod, % 252.80/36.35 fact_plus__nat_Oadd__0, fact_poly__0, fact_poly__1, fact_poly__add, % 252.80/36.35 fact_poly__bound__exists, fact_poly__diff, fact_poly__div__mult__right, % 252.80/36.35 fact_poly__eq__iff, fact_poly__mod__mult__right, fact_poly__mult, % 252.80/36.35 fact_poly__pcompose, fact_poly__power, fact_poly__zero, fact_pos__add__strict, % 252.80/36.35 fact_pos__divide__le__eq, fact_pos__divide__less__eq, fact_pos__le__divide__eq, % 252.80/36.35 fact_pos__less__divide__eq, fact_pos__mod__bound, fact_pos__mod__conj, % 252.80/36.35 fact_pos__mod__sign, fact_positive__add, fact_positive__mult, % 252.80/36.35 fact_positive__zero, fact_pow__divides__eq__int, fact_pow__divides__eq__nat, % 252.80/36.35 fact_pow__divides__pow__int, fact_pow__divides__pow__nat, fact_power__0, % 252.80/36.35 fact_power__0__left, fact_power__Suc__less, fact_power__abs, fact_power__add, % 252.80/36.35 fact_power__commutes, fact_power__decreasing, fact_power__diff, % 252.80/36.35 fact_power__divide, fact_power__eq__0__iff, fact_power__eq__imp__eq__base, % 252.80/36.35 fact_power__gt1__lemma, fact_power__increasing, fact_power__increasing__iff, % 252.80/36.35 fact_power__inject__exp, fact_power__le__dvd, fact_power__le__imp__le__exp, % 252.80/36.35 fact_power__less__imp__less__base, fact_power__less__imp__less__exp, % 252.80/36.35 fact_power__less__power__Suc, fact_power__mono, fact_power__mult, % 252.80/36.35 fact_power__mult__distrib, fact_power__one, fact_power__one__over, % 252.80/36.35 fact_power__power__power, fact_power__real__of__nat, % 252.80/36.35 fact_power__strict__decreasing, fact_power__strict__increasing, % 252.80/36.35 fact_power__strict__increasing__iff, fact_power__strict__mono, % 252.80/36.35 fact_psize__eq__0__iff, fact_q_I1_J, fact_q_I2_J, fact_rabs__ratiotest__lemma, % 252.80/36.35 fact_real__0__le__divide__iff, fact_real__add__left__mono, % 252.80/36.35 fact_real__add__mult__distrib, fact_real__divide__square__eq, % 252.80/36.35 fact_real__le__antisym, fact_real__le__eq__diff, fact_real__le__linear, % 252.80/36.35 fact_real__le__refl, fact_real__less__def, fact_real__mult__assoc, % 252.80/36.35 fact_real__mult__commute, fact_real__mult__le__cancel__iff1, % 252.80/36.35 fact_real__mult__le__cancel__iff2, fact_real__mult__left__cancel, % 252.80/36.35 fact_real__mult__less__iff1, fact_real__mult__less__mono2, % 252.80/36.35 fact_real__mult__order, fact_real__mult__right__cancel, % 252.80/36.35 fact_real__natceiling__ge, fact_real__natfloor__le, fact_real__norm__def, % 252.80/36.35 fact_real__of__nat__add, fact_real__of__nat__diff, fact_real__of__nat__div, % 252.80/36.35 fact_real__of__nat__div2, fact_real__of__nat__div4, % 252.80/36.35 fact_real__of__nat__div__aux, fact_real__of__nat__ge__zero, % 252.80/36.35 fact_real__of__nat__gt__zero__cancel__iff, fact_real__of__nat__inject, % 252.80/36.35 fact_real__of__nat__le__iff, fact_real__of__nat__le__zero__cancel__iff, % 252.80/36.35 fact_real__of__nat__less__iff, fact_real__of__nat__mult, % 252.80/36.35 fact_real__of__nat__power, fact_real__of__nat__zero, % 252.80/36.35 fact_real__of__nat__zero__iff, fact_real__squared__diff__one__factored, % 252.80/36.35 fact_real__two__squares__add__zero__iff, fact_right__inverse__eq, % 252.80/36.35 fact_right__minus__eq, fact_semiring__div__class_Omod__div__equality_H, % 252.80/36.35 fact_split__div, fact_split__mod, fact_split__mult__neg__le, % 252.80/36.35 fact_split__mult__pos__le, fact_split__neg__lemma, fact_split__pos__lemma, % 252.80/36.35 fact_split__zdiv, fact_split__zmod, fact_sum__squares__eq__zero__iff, % 252.80/36.35 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff, % 252.80/36.35 fact_sum__squares__le__zero__iff, fact_synthetic__div__0, % 252.80/36.35 fact_synthetic__div__eq__0__iff, fact_termination__basic__simps_I1_J, % 252.80/36.35 fact_termination__basic__simps_I2_J, fact_termination__basic__simps_I3_J, % 252.80/36.35 fact_termination__basic__simps_I4_J, fact_termination__basic__simps_I5_J, % 252.80/36.35 fact_th, fact_times_Oidem, fact_times__divide__eq__right, % 252.80/36.35 fact_times__divide__times__eq, fact_trans__le__add1, fact_trans__le__add2, % 252.80/36.35 fact_trans__less__add1, fact_trans__less__add2, fact_unity__coeff__ex, % 252.80/36.35 fact_xt1_I10_J, fact_xt1_I11_J, fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, % 252.80/36.35 fact_xt1_I3_J, fact_xt1_I4_J, fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J, % 252.80/36.35 fact_xt1_I8_J, fact_xt1_I9_J, fact_xt5, fact_xt7, fact_zdiv__zmod__equality, % 252.80/36.35 fact_zdiv__zmod__equality2, fact_zdiv__zmult1__eq, fact_zdiv__zmult2__eq, % 252.80/36.35 fact_zdvd1__eq, fact_zdvd__antisym__abs, fact_zdvd__antisym__nonneg, % 252.80/36.35 fact_zdvd__imp__le, fact_zdvd__mono, fact_zdvd__mult__cancel, % 252.80/36.35 fact_zdvd__mult__cancel1, fact_zdvd__mult__div__cancel, fact_zdvd__not__zless, % 252.80/36.35 fact_zdvd__period, fact_zdvd__reduce, fact_zdvd__zdiffD, fact_zdvd__zmod, % 252.80/36.35 fact_zdvd__zmod__imp__zdvd, fact_zero__le__divide__iff, % 252.80/36.35 fact_zero__le__double__add__iff__zero__le__single__add, % 252.80/36.35 fact_zero__le__mult__iff, fact_zero__le__natceiling, fact_zero__le__natfloor, % 252.80/36.35 fact_zero__le__one, fact_zero__le__power, fact_zero__le__power__abs, % 252.80/36.35 fact_zero__le__square, fact_zero__le__zpower__abs, fact_zero__less__abs__iff, % 252.80/36.35 fact_zero__less__diff, fact_zero__less__divide__iff, % 252.80/36.35 fact_zero__less__double__add__iff__zero__less__single__add, % 252.80/36.35 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, % 252.80/36.35 fact_zero__less__norm__iff, fact_zero__less__one, fact_zero__less__power, % 252.80/36.35 fact_zero__less__two, fact_zero__less__zpower__abs__iff, fact_zero__neq__one, % 252.80/36.35 fact_zero__reorient, fact_zmod__eq__0__iff, fact_zmod__eq__dvd__iff, % 252.80/36.35 fact_zmod__le__nonneg__dividend, fact_zmod__self, fact_zmod__simps_I1_J, % 252.80/36.35 fact_zmod__simps_I2_J, fact_zmod__simps_I3_J, fact_zmod__simps_I4_J, % 252.80/36.35 fact_zmod__zdiv__equality, fact_zmod__zdiv__equality_H, % 252.80/36.35 fact_zmod__zdiv__trivial, fact_zmod__zero, fact_zmod__zmult1__eq, % 252.80/36.35 fact_zmod__zmult2__eq, fact_zmult2__lemma__aux1, fact_zmult2__lemma__aux2, % 252.80/36.35 fact_zmult2__lemma__aux3, fact_zmult2__lemma__aux4, fact_zmult__div__cancel, % 252.80/36.35 fact_zpower__zadd__distrib, fact_zpower__zmod, fact_zpower__zpower % 252.80/36.35 % 252.80/36.35 Those formulas are unsatisfiable: % 252.80/36.35 --------------------------------- % 252.80/36.35 % 252.80/36.35 Begin of proof % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_H_I2_J) implies: % 252.80/36.36 | (1) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 252.80/36.36 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, % 252.80/36.36 | v0)) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_H_I5_J) implies: % 252.80/36.36 | (2) ? [v0: $i] : ? [v1: $i] : % 252.80/36.36 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0 % 252.80/36.36 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 & % 252.80/36.36 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, % 252.80/36.36 | v_da____)) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_norm__one) implies: % 252.80/36.36 | (3) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 252.80/36.36 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 252.80/36.36 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ % 252.80/36.36 | (c_Groups_Oone__class_Oone(v1) = v2) | ~ $i(v1) | ~ % 252.80/36.36 | class_RealVector_Oreal__normed__algebra__1(v1))) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_real__le__trans) implies: % 252.80/36.36 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 252.80/36.36 | $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 252.80/36.36 | v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, % 252.80/36.36 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_d_I2_J) implies: % 252.80/36.36 | (5) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 252.80/36.36 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_d____, % 252.80/36.36 | v0)) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_order__less__le) implies: % 252.80/36.36 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 252.80/36.36 | $i(v0) | ~ class_Orderings_Oorder(v2) | ~ % 252.80/36.36 | c_Orderings_Oord__class_Oless(v2, v1, v0) | % 252.80/36.36 | c_Orderings_Oord__class_Oless__eq(v2, v1, v0)) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_one0) implies: % 252.80/36.36 | (7) ? [v0: $i] : ? [v1: $i] : % 252.80/36.36 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.80/36.36 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & % 252.80/36.36 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_H_I3_J) implies: % 252.80/36.36 | (8) $i(v_da____) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_abs__add__one__gt__zero) implies: % 252.80/36.36 | (9) ? [v0: $i] : ? [v1: $i] : % 252.80/36.36 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.80/36.36 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & % 252.80/36.36 | ! [v2: $i] : ! [v3: $i] : ( ~ % 252.80/36.36 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2) % 252.80/36.36 | | ? [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, % 252.80/36.36 | v3) = v4 & $i(v4) & % 252.80/36.36 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_abs__add__one__not__less__self) implies: % 252.80/36.36 | (10) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 252.80/36.36 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 252.80/36.36 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1) % 252.80/36.36 | | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 252.80/36.36 | v0) = v3 & $i(v3) & ~ % 252.80/36.36 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1)))) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_real__zero__not__eq__one) implies: % 252.80/36.36 | (11) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 252.80/36.36 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.80/36.36 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) % 252.80/36.36 | implies: % 252.80/36.36 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 252.80/36.36 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____) = v2 % 252.80/36.36 | & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.80/36.36 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & % 252.80/36.36 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 252.80/36.36 | v3, v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1) % 252.80/36.36 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) % 252.80/36.36 | % 252.80/36.36 | ALPHA: (fact_real__mult__1) implies: % 252.80/36.37 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 252.80/36.37 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 252.80/36.37 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & hAPP(v0, v1) = v2 % 252.80/36.37 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | % 252.80/36.37 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3))) % 252.80/36.37 | % 252.80/36.37 | ALPHA: (fact_unimodular__reduce__norm) implies: % 252.80/36.37 | (14) ? [v0: $i] : ? [v1: $i] : % 252.80/36.37 | (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v1 & % 252.80/36.37 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & % 252.80/36.37 | ! [v2: $i] : ! [v3: $i] : ( ~ % 252.80/36.37 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, v1) = v3) % 252.80/36.37 | | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 252.80/36.37 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 252.80/36.37 | (( ~ (v4 = v0) & % 252.80/36.37 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 % 252.80/36.37 | & $i(v4)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, % 252.80/36.37 | v2, v1) = v5 & % 252.80/36.37 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v6 % 252.80/36.37 | & $i(v6) & $i(v5) & % 252.80/36.37 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v0)) | % 252.80/36.37 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, % 252.80/36.37 | c_Complex_Oii) = v8 & % 252.80/36.37 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9 % 252.80/36.37 | & $i(v9) & $i(v8) & % 252.80/36.37 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v0)) | % 252.80/36.37 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, % 252.80/36.37 | c_Complex_Oii) = v10 & % 252.80/36.37 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10) = % 252.80/36.37 | v11 & $i(v11) & $i(v10) & % 252.80/36.37 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v0)) | % 252.80/36.37 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v7 & % 252.80/36.37 | $i(v7) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, % 252.80/36.37 | v0))))) % 252.80/36.37 | % 252.80/36.37 | ALPHA: (fact_arctan__add) implies: % 252.80/36.37 | (15) ? [v0: $i] : ? [v1: $i] : % 252.80/36.37 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 252.80/36.37 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & % 252.80/36.37 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 252.80/36.37 | : ! [v7: $i] : ! [v8: $i] : ( ~ % 252.80/36.37 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v2) = v4) | ~ % 252.80/36.37 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v4, v7) = v8) | % 252.80/36.37 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, v6) = v7) % 252.80/36.37 | | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v3) | ~ % 252.80/36.37 | $i(v2) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] % 252.80/36.37 | : ? [v13: $i] : ? [v14: $i] : ((v14 = v13 & % 252.80/36.37 | c_Transcendental_Oarctan(v8) = v13 & % 252.80/36.37 | c_Transcendental_Oarctan(v3) = v11 & % 252.80/36.37 | c_Transcendental_Oarctan(v2) = v12 & % 252.80/36.37 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v12) = v13 % 252.80/36.37 | & $i(v13) & $i(v12) & $i(v11)) | % 252.80/36.37 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v9 & $i(v9) & % 252.80/36.37 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, % 252.80/36.37 | v0)) | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = % 252.80/36.37 | v10 & $i(v10) & ~ % 252.80/36.37 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10, v0))))) % 252.80/36.37 | % 252.80/36.37 | ALPHA: (fact_m_I2_J) implies: % 252.80/36.37 | (16) ? [v0: $i] : ? [v1: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, % 252.80/36.37 | v_cs____) = v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 % 252.80/36.37 | & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = % 252.80/36.37 | v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 252.80/36.37 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v5 & % 252.80/36.37 | $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 252.80/36.37 | v5, v_m____)) | % 252.80/36.37 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 & % 252.80/36.37 | $i(v4) & ~ % 252.80/36.37 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, % 252.80/36.37 | v0))))) % 252.80/36.37 | % 252.80/36.37 | ALPHA: (fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_A_B_Bz_O_Acmod_Az_A_060_061_A1_A_061_061_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) % 252.80/36.37 | implies: % 252.80/36.37 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 252.80/36.37 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v2 & % 252.80/36.37 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 252.80/36.37 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & % 252.80/36.37 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 252.80/36.37 | v0, v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ % 252.80/36.37 | $i(v4) | ? [v6: $i] : ? [v7: $i] : % 252.80/36.37 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7 & % 252.80/36.37 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 252.80/36.37 | v7, v3)) | % 252.80/36.37 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = v6 & % 252.80/36.37 | $i(v6) & ~ % 252.80/36.37 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, % 252.80/36.37 | v1))))) % 252.80/36.37 | % 252.80/36.37 | ALPHA: (fact_mult__eq__if) implies: % 253.02/36.38 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 253.02/36.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 253.02/36.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 253.02/36.38 | [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ % 253.02/36.38 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~ % 253.02/36.38 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~ % 253.02/36.38 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ % 253.02/36.38 | $i(v3) | ? [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & % 253.02/36.38 | $i(v9) & $i(v8))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 253.02/36.38 | (v5 = v0 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v0) = v4) | ~ % 253.02/36.38 | $i(v3))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_nat__mult__eq__1__iff) implies: % 253.02/36.38 | (19) ? [v0: $i] : ? [v1: $i] : % 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 253.02/36.38 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = % 253.02/36.38 | v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 253.02/36.38 | $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = % 253.02/36.38 | v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 253.02/36.38 | $i] : ! [v3: $i] : (v3 = v1 | ~ (hAPP(v2, v1) = v3) | ~ % 253.02/36.38 | (hAPP(v0, v1) = v2))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_nat__mult__1__right) implies: % 253.02/36.38 | (20) ? [v0: $i] : ? [v1: $i] : % 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 253.02/36.38 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | % 253.02/36.38 | hAPP(v3, v1) = v2)) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_nat__1__eq__mult__iff) implies: % 253.02/36.38 | (21) ? [v0: $i] : ? [v1: $i] : % 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 253.02/36.38 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = % 253.02/36.38 | v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 253.02/36.38 | $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = % 253.02/36.38 | v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 253.02/36.38 | $i] : ! [v3: $i] : (v3 = v0 | ~ (hAPP(v2, v0) = v3) | ~ % 253.02/36.38 | (hAPP(v1, v0) = v2))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_nat__mult__1) implies: % 253.02/36.38 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & % 253.02/36.38 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ % 253.02/36.38 | (hAPP(v2, v3) = v4) | ~ $i(v3))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_mult__eq__self__implies__10) implies: % 253.02/36.38 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 253.02/36.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 253.02/36.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = % 253.02/36.38 | v1 | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | % 253.02/36.38 | ~ $i(v3))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_natceiling__add__one) implies: % 253.02/36.38 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 253.02/36.38 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) & % 253.02/36.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 253.02/36.38 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ % 253.02/36.38 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.38 | v0, v3) | ? [v5: $i] : ? [v6: $i] : % 253.02/36.38 | (c_RComplete_Onatceiling(v4) = v5 & c_RComplete_Onatceiling(v3) = % 253.02/36.38 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & % 253.02/36.38 | $i(v6) & $i(v5)))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_natfloor__add__one) implies: % 253.02/36.38 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 253.02/36.38 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) & % 253.02/36.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 253.02/36.38 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ % 253.02/36.38 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.38 | v0, v3) | ? [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) % 253.02/36.38 | = v5 & c_RComplete_Onatfloor(v3) = v6 & % 253.02/36.38 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) & % 253.02/36.38 | $i(v5)))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_natfloor__one) implies: % 253.02/36.38 | (26) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_natceiling__one) implies: % 253.02/36.38 | (27) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 253.02/36.38 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_le__natfloor__eq__one) implies: % 253.02/36.38 | (28) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 253.02/36.38 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & % 253.02/36.38 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) % 253.02/36.38 | = v3) | ~ $i(v2) | ~ % 253.02/36.38 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) | % 253.02/36.38 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & ! % 253.02/36.38 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ % 253.02/36.38 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.38 | v1, v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, % 253.02/36.38 | v3))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_natceiling__le__eq__one) implies: % 253.02/36.38 | (29) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 253.02/36.38 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & % 253.02/36.38 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 253.02/36.38 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ % 253.02/36.38 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) | % 253.02/36.38 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! % 253.02/36.38 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ % 253.02/36.38 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.38 | v2, v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, % 253.02/36.38 | v0))) % 253.02/36.38 | % 253.02/36.38 | ALPHA: (fact_natceiling__eq) implies: % 253.02/36.38 | (30) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 253.02/36.38 | v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & % 253.02/36.38 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 % 253.02/36.38 | = v4 | ~ (c_RComplete_Onatceiling(v2) = v4) | ~ % 253.02/36.38 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~ % 253.02/36.38 | $i(v3) | ~ $i(v2) | ? [v6: $i] : ? [v7: $i] : % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & $i(v6) & ( ~ % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v2) | % 253.02/36.39 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 & % 253.02/36.39 | $i(v7) & ~ % 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 253.02/36.39 | v7)))))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_ex__least__nat__less) implies: % 253.02/36.39 | (31) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 253.02/36.39 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) % 253.02/36.39 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) % 253.02/36.39 | | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i] % 253.02/36.39 | : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 253.02/36.39 | ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 & % 253.02/36.39 | hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) & % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9: % 253.02/36.39 | $i] : ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9) % 253.02/36.39 | | ~ hBOOL(v10) | ~ % 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) | % 253.02/36.39 | (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5)))))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_abs__real__of__nat__cancel) implies: % 253.02/36.39 | (32) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = % 253.02/36.39 | v1) | ~ $i(v0) | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) % 253.02/36.39 | = v1 & $i(v1))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_real__of__nat__1) implies: % 253.02/36.39 | (33) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 & % 253.02/36.39 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 253.02/36.39 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_nat__less__real__le) implies: % 253.02/36.39 | (34) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 253.02/36.39 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] % 253.02/36.39 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & % 253.02/36.39 | $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, % 253.02/36.39 | v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 253.02/36.39 | : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] : % 253.02/36.39 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & % 253.02/36.39 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.39 | v5, v4)))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_nat__le__real__less) implies: % 253.02/36.39 | (35) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 253.02/36.39 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: % 253.02/36.39 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = % 253.02/36.39 | v5 & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 253.02/36.39 | v3, v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 253.02/36.39 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: % 253.02/36.39 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = % 253.02/36.39 | v5 & $i(v5) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 253.02/36.39 | v3, v5)))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_real__natfloor__add__one__gt) implies: % 253.02/36.39 | (36) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) % 253.02/36.39 | = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & % 253.02/36.39 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 & % 253.02/36.39 | $i(v4) & $i(v3) & % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4)))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_real__natfloor__gt__diff__one) implies: % 253.02/36.39 | (37) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 253.02/36.39 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | % 253.02/36.39 | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1) % 253.02/36.39 | = v3 & $i(v4) & $i(v3) & % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4)))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_ge__natfloor__plus__one__imp__gt) implies: % 253.02/36.39 | (38) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 253.02/36.39 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ % 253.02/36.39 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5: % 253.02/36.39 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 & % 253.02/36.39 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, % 253.02/36.39 | v1)))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_natfloor__eq) implies: % 253.02/36.39 | (39) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 % 253.02/36.39 | = v2 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 253.02/36.39 | (c_RComplete_Onatfloor(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? % 253.02/36.39 | [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) % 253.02/36.39 | = v5 & $i(v5) & ~ % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5)))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_reals__Archimedean6) implies: % 253.02/36.39 | (40) ? [v0: $i] : ? [v1: $i] : % 253.02/36.39 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 253.02/36.39 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 253.02/36.39 | [v2: $i] : ( ~ $i(v2) | ~ % 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? % 253.02/36.39 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & % 253.02/36.39 | c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & % 253.02/36.39 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & $i(v6) % 253.02/36.39 | & $i(v5) & $i(v4) & $i(v3) & % 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2) & % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6)))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_natfloor__div__nat) implies: % 253.02/36.39 | (41) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 253.02/36.39 | = v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & % 253.02/36.39 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v4) | ~ % 253.02/36.39 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) | % 253.02/36.39 | ~ $i(v3) | ~ $i(v2) | ~ % 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~ % 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v6: $i] : % 253.02/36.39 | ? [v7: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v2) = % 253.02/36.39 | v6 & c_RComplete_Onatfloor(v5) = v6 & c_RComplete_Onatfloor(v3) % 253.02/36.39 | = v7 & $i(v7) & $i(v6)))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_real__of__nat__div3) implies: % 253.02/36.39 | (42) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 253.02/36.39 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 253.02/36.39 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v6) | ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ % 253.02/36.39 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) | % 253.02/36.39 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5, v7) = v8) % 253.02/36.39 | | ~ $i(v2) | ~ $i(v1) | % 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v0))) % 253.02/36.39 | % 253.02/36.39 | ALPHA: (fact_div__less__dividend) implies: % 253.02/36.40 | (43) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 253.02/36.40 | = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) % 253.02/36.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 253.02/36.40 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v3) % 253.02/36.40 | | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 253.02/36.40 | v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_degree__synthetic__div) implies: % 253.02/36.40 | (44) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 253.02/36.40 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 253.02/36.40 | ( ~ (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~ % 253.02/36.40 | (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 253.02/36.40 | $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? [v6: $i] : % 253.02/36.40 | (c_Polynomial_Odegree(v3, v2) = v6 & % 253.02/36.40 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v0) = v5 & $i(v6) % 253.02/36.40 | & $i(v5)))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_lemmaCauchy) implies: % 253.02/36.40 | (45) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 253.02/36.40 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 253.02/36.40 | [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v4, % 253.02/36.40 | v5) = v6) | ~ (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 253.02/36.40 | ~ $i(v2) | ~ $i(v1) | ~ class_Orderings_Oord(v3) | ~ % 253.02/36.40 | class_RealVector_Oreal__normed__vector(v4) | ? [v7: $i] : ? [v8: % 253.02/36.40 | $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & % 253.02/36.40 | ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 & % 253.02/36.40 | $i(v7) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ % 253.02/36.40 | (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~ % 253.02/36.40 | (hAPP(v1, v12) = v13) | ~ $i(v12) | ~ % 253.02/36.40 | c_Orderings_Oord__class_Oless__eq(v3, v2, v12) | % 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v7))) % 253.02/36.40 | | (c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 & % 253.02/36.40 | c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1, % 253.02/36.40 | v8) = v9 & $i(v11) & $i(v10) & $i(v9) & % 253.02/36.40 | c_Orderings_Oord__class_Oless__eq(v3, v2, v8) & ~ % 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, % 253.02/36.40 | v0)))))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_nat__dvd__1__iff__1) implies: % 253.02/36.40 | (46) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 253.02/36.40 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 = % 253.02/36.40 | v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, % 253.02/36.40 | v0))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_dvd__mult__cancel1) implies: % 253.02/36.40 | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 253.02/36.40 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 253.02/36.40 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 253.02/36.40 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 253.02/36.40 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 % 253.02/36.40 | = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) % 253.02/36.40 | | ~ $i(v3) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) | % 253.02/36.40 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3: % 253.02/36.40 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 253.02/36.40 | (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 253.02/36.40 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_dvd__mult__cancel2) implies: % 253.02/36.40 | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 253.02/36.40 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 253.02/36.40 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 253.02/36.40 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 253.02/36.40 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 % 253.02/36.40 | = v2 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) % 253.02/36.40 | | ~ $i(v3) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) | % 253.02/36.40 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3: % 253.02/36.40 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ % 253.02/36.40 | (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ % 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 253.02/36.40 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Obot__least) implies: % 253.02/36.40 | (49) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 253.02/36.40 | ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, % 253.02/36.40 | v1))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_LIMSEQ__inverse__realpow__zero__lemma) implies: % 253.02/36.40 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 253.02/36.40 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 & % 253.02/36.40 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 253.02/36.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 253.02/36.40 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & $i(v3) & $i(v2) & % 253.02/36.40 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 253.02/36.40 | $i] : ! [v8: $i] : ( ~ % 253.02/36.40 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) | ~ % 253.02/36.40 | (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ % 253.02/36.40 | $i(v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.40 | v0, v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 253.02/36.40 | $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 & % 253.02/36.40 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & % 253.02/36.40 | hAPP(v10, v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & % 253.02/36.40 | $i(v10) & $i(v9) & % 253.02/36.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8)))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) % 253.02/36.40 | implies: % 253.02/36.40 | (51) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 253.02/36.40 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 253.02/36.40 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 253.02/36.40 | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | % 253.02/36.40 | hAPP(v4, v0) = v1)) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_realpow__num__eq__if) implies: % 253.02/36.40 | (52) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 253.02/36.40 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) % 253.02/36.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 253.02/36.40 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 253.02/36.40 | [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v4) = v5) | ~ % 253.02/36.40 | (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ % 253.02/36.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~ % 253.02/36.40 | (hAPP(v8, v10) = v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) % 253.02/36.40 | = v10) | ~ (hAPP(v5, v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~ % 253.02/36.40 | $i(v2) | ~ class_Power_Opower(v4) | ? [v12: $i] : ? [v13: $i] : % 253.02/36.40 | (( ~ (v3 = v0) | (v13 = v12 & c_Groups_Oone__class_Oone(v4) = v12 % 253.02/36.40 | & hAPP(v6, v0) = v12 & $i(v12))) & (v3 = v0 | (v12 = v11 & % 253.02/36.40 | hAPP(v6, v3) = v11 & $i(v11)))))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_realpow__minus__mult) implies: % 253.02/36.40 | (53) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 253.02/36.40 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) % 253.02/36.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 253.02/36.40 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 253.02/36.40 | [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v4) = v6) | ~ % 253.02/36.40 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ % 253.02/36.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~ % 253.02/36.40 | (hAPP(v10, v2) = v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) % 253.02/36.40 | = v7) | ~ (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ % 253.02/36.40 | $i(v2) | ~ class_Groups_Omonoid__mult(v4) | ~ % 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3) % 253.02/36.40 | = v11 & $i(v11)))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_power__dvd__imp__le) implies: % 253.02/36.40 | (54) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat) % 253.02/36.40 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) % 253.02/36.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 253.02/36.40 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 253.02/36.40 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 253.02/36.40 | | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | ~ % 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 253.02/36.40 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2))) % 253.02/36.40 | % 253.02/36.40 | ALPHA: (fact_power__eq__if) implies: % 253.02/36.41 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 253.02/36.41 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 253.02/36.41 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 & % 253.02/36.41 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v3) & $i(v2) & % 253.02/36.41 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 253.02/36.41 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~ % 253.02/36.41 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ % 253.02/36.41 | (hAPP(v7, v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = % 253.02/36.41 | v7) | ~ (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, % 253.02/36.41 | v5) = v10 & $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 253.02/36.41 | $i] : (v6 = v2 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | % 253.02/36.41 | ~ $i(v4))) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (fact_power__one__right) implies: % 253.02/36.41 | (56) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 253.02/36.41 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 253.02/36.41 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | % 253.02/36.41 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | % 253.02/36.41 | hAPP(v4, v0) = v1)) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (fact_reduce__poly__simple) implies: % 253.02/36.41 | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 253.02/36.41 | ? [v5: $i] : (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v4 & % 253.02/36.41 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 & % 253.02/36.41 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 253.02/36.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v5 & $i(v5) & $i(v4) & % 253.02/36.41 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ! [v7: $i] : ! % 253.02/36.41 | [v8: $i] : (v7 = v0 | v6 = v1 | ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | % 253.02/36.41 | ~ $i(v6) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 253.02/36.41 | $i] : ? [v13: $i] : ? [v14: $i] : % 253.02/36.41 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v12) = v13 & % 253.02/36.41 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v13) = v14 % 253.02/36.41 | & hAPP(v10, v6) = v11 & hAPP(v8, v11) = v12 & hAPP(v4, v9) = v10 % 253.02/36.41 | & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & % 253.02/36.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v5)))) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (arity_RealDef__Oreal__Orderings_Oorder) implies: % 253.02/36.41 | (58) class_Orderings_Oorder(tc_RealDef_Oreal) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) implies: % 253.02/36.41 | (59) class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (conj_0) implies: % 253.02/36.41 | (60) $i(v_z) % 253.02/36.41 | (61) $i(v_w____) % 253.02/36.41 | (62) $i(tc_RealDef_Oreal) % 253.02/36.41 | (63) $i(tc_Complex_Ocomplex) % 253.02/36.41 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 253.02/36.41 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0 % 253.02/36.41 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & $i(v2) & $i(v1) & % 253.02/36.41 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, % 253.02/36.41 | v2)) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (function-axioms) implies: % 253.02/36.41 | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 253.02/36.41 | (c_Groups_Oone__class_Oone(v2) = v1) | ~ % 253.02/36.41 | (c_Groups_Oone__class_Oone(v2) = v0)) % 253.02/36.41 | (66) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 253.02/36.41 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~ % 253.02/36.41 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) % 253.02/36.41 | (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 253.02/36.41 | (v1 = v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 253.02/36.41 | (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (1) with fresh symbol all_713_0 gives: % 253.02/36.41 | (68) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_713_0 & % 253.02/36.41 | $i(all_713_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 253.02/36.41 | v_da____, all_713_0) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (68) implies: % 253.02/36.41 | (69) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, all_713_0) % 253.02/36.41 | (70) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_713_0 % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (5) with fresh symbol all_729_0 gives: % 253.02/36.41 | (71) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_729_0 & % 253.02/36.41 | $i(all_729_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 253.02/36.41 | v_d____, all_729_0) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (71) implies: % 253.02/36.41 | (72) $i(all_729_0) % 253.02/36.41 | (73) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_729_0 % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (49) with fresh symbol all_742_0 gives: % 253.02/36.41 | (74) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_742_0 & $i(all_742_0) & % 253.02/36.41 | ? [v0: $i] : ( ~ $i(v0) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, % 253.02/36.41 | all_742_0, v0)) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (74) implies: % 253.02/36.41 | (75) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_742_0 % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (27) with fresh symbols all_773_0, all_773_1 gives: % 253.02/36.41 | (76) c_RComplete_Onatceiling(all_773_1) = all_773_0 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_773_0 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_773_1 & % 253.02/36.41 | $i(all_773_0) & $i(all_773_1) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (76) implies: % 253.02/36.41 | (77) $i(all_773_0) % 253.02/36.41 | (78) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_773_1 % 253.02/36.41 | (79) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_773_0 % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (7) with fresh symbols all_797_0, all_797_1 gives: % 253.02/36.41 | (80) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_797_1 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_797_0 & % 253.02/36.41 | $i(all_797_0) & $i(all_797_1) & % 253.02/36.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_797_1, all_797_0) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (80) implies: % 253.02/36.41 | (81) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_797_0 % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (26) with fresh symbols all_799_0, all_799_1 gives: % 253.02/36.41 | (82) c_RComplete_Onatfloor(all_799_1) = all_799_0 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_799_0 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_799_1 & % 253.02/36.41 | $i(all_799_0) & $i(all_799_1) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (82) implies: % 253.02/36.41 | (83) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_799_1 % 253.02/36.41 | (84) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_799_0 % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (2) with fresh symbols all_818_0, all_818_1 gives: % 253.02/36.41 | (85) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = % 253.02/36.41 | all_818_1 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, % 253.02/36.41 | all_818_1) = all_818_0 & $i(all_818_0) & $i(all_818_1) & % 253.02/36.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_818_0, v_da____) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (85) implies: % 253.02/36.41 | (86) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_818_0, v_da____) % 253.02/36.41 | (87) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_818_1) = % 253.02/36.41 | all_818_0 % 253.02/36.41 | (88) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = % 253.02/36.41 | all_818_1 % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (11) with fresh symbols all_824_0, all_824_1 gives: % 253.02/36.41 | (89) ~ (all_824_0 = all_824_1) & % 253.02/36.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_824_1 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_824_0 & % 253.02/36.41 | $i(all_824_0) & $i(all_824_1) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (89) implies: % 253.02/36.41 | (90) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_824_0 % 253.02/36.41 | % 253.02/36.41 | DELTA: instantiating (33) with fresh symbols all_826_0, all_826_1 gives: % 253.02/36.41 | (91) c_RealDef_Oreal(tc_Nat_Onat, all_826_1) = all_826_0 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_826_1 & % 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_826_0 & % 253.02/36.41 | $i(all_826_0) & $i(all_826_1) % 253.02/36.41 | % 253.02/36.41 | ALPHA: (91) implies: % 253.02/36.41 | (92) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_826_0 % 253.02/36.41 | (93) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_826_1 % 253.02/36.42 | (94) c_RealDef_Oreal(tc_Nat_Onat, all_826_1) = all_826_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (46) with fresh symbol all_855_0 gives: % 253.02/36.42 | (95) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_855_0 & $i(all_855_0) & % 253.02/36.42 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_855_0, all_855_0) & ! [v0: % 253.02/36.42 | any] : (v0 = all_855_0 | ~ $i(v0) | ~ % 253.02/36.42 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_855_0)) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (95) implies: % 253.02/36.42 | (96) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_855_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (10) with fresh symbol all_912_0 gives: % 253.02/36.42 | (97) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_912_0 & % 253.02/36.42 | $i(all_912_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.02/36.42 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) | % 253.02/36.42 | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, % 253.02/36.42 | all_912_0) = v2 & $i(v2) & ~ % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0))) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (97) implies: % 253.02/36.42 | (98) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_912_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (64) with fresh symbols all_915_0, all_915_1, all_915_2 % 253.02/36.42 | gives: % 253.02/36.42 | (99) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = % 253.02/36.42 | all_915_2 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, % 253.02/36.42 | all_915_2) = all_915_1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) % 253.02/36.42 | = all_915_0 & $i(all_915_0) & $i(all_915_1) & $i(all_915_2) & ~ % 253.02/36.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_915_1, % 253.02/36.42 | all_915_0) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (99) implies: % 253.02/36.42 | (100) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_915_1, % 253.02/36.42 | all_915_0) % 253.02/36.42 | (101) $i(all_915_1) % 253.02/36.42 | (102) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_915_0 % 253.02/36.42 | (103) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_915_2) = % 253.02/36.42 | all_915_1 % 253.02/36.42 | (104) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = % 253.02/36.42 | all_915_2 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (3) with fresh symbol all_939_0 gives: % 253.02/36.42 | (105) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_939_0 & % 253.02/36.42 | $i(all_939_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 253.02/36.42 | all_939_0 | ~ (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~ % 253.02/36.42 | (c_Groups_Oone__class_Oone(v0) = v1) | ~ $i(v0) | ~ % 253.02/36.42 | class_RealVector_Oreal__normed__algebra__1(v0)) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (105) implies: % 253.02/36.42 | (106) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_939_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (20) with fresh symbols all_945_0, all_945_1 gives: % 253.02/36.42 | (107) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_945_1 & % 253.02/36.42 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_945_0 & $i(all_945_0) & % 253.02/36.42 | $i(all_945_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_945_1, v0) % 253.02/36.42 | = v1) | ~ $i(v0) | hAPP(v1, all_945_0) = v0) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (107) implies: % 253.02/36.42 | (108) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_945_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (51) with fresh symbol all_957_0 gives: % 253.02/36.42 | (109) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_957_0 & $i(all_957_0) & % 253.02/36.42 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 253.02/36.42 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 253.02/36.42 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | % 253.02/36.42 | hAPP(v3, all_957_0) = v0) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (109) implies: % 253.02/36.42 | (110) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_957_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (56) with fresh symbol all_986_0 gives: % 253.02/36.42 | (111) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_986_0 & $i(all_986_0) & % 253.02/36.42 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 253.02/36.42 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 253.02/36.42 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Omonoid__mult(v1) | hAPP(v3, % 253.02/36.42 | all_986_0) = v0) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (111) implies: % 253.02/36.42 | (112) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_986_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (9) with fresh symbols all_992_0, all_992_1 gives: % 253.02/36.42 | (113) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_992_1 & % 253.02/36.42 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_992_0 & % 253.02/36.42 | $i(all_992_0) & $i(all_992_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.02/36.42 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 253.02/36.42 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, % 253.02/36.42 | all_992_0, v1) = v2 & $i(v2) & % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_992_1, v2))) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (113) implies: % 253.02/36.42 | (114) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_992_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (22) with fresh symbols all_1001_0, all_1001_1, % 253.02/36.42 | all_1001_2 gives: % 253.02/36.42 | (115) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1001_2 & % 253.02/36.42 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1001_1 & % 253.02/36.42 | hAPP(all_1001_2, all_1001_1) = all_1001_0 & $i(all_1001_0) & % 253.02/36.42 | $i(all_1001_1) & $i(all_1001_2) & ! [v0: $i] : ! [v1: $i] : (v1 = % 253.02/36.42 | v0 | ~ (hAPP(all_1001_0, v0) = v1) | ~ $i(v0)) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (115) implies: % 253.02/36.42 | (116) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1001_1 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (36) with fresh symbol all_1004_0 gives: % 253.02/36.42 | (117) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1004_0 & % 253.02/36.42 | $i(all_1004_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.02/36.42 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 253.02/36.42 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & % 253.02/36.42 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1004_0) = % 253.02/36.42 | v3 & $i(v3) & $i(v2) & % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (117) implies: % 253.02/36.42 | (118) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1004_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (37) with fresh symbol all_1021_0 gives: % 253.02/36.42 | (119) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1021_0 & % 253.02/36.42 | $i(all_1021_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.02/36.42 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, all_1021_0) = % 253.02/36.42 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 253.02/36.42 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & c_RComplete_Onatfloor(v0) % 253.02/36.42 | = v2 & $i(v3) & $i(v2) & % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3))) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (119) implies: % 253.02/36.42 | (120) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1021_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (13) with fresh symbols all_1027_0, all_1027_1, % 253.02/36.42 | all_1027_2 gives: % 253.02/36.42 | (121) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1027_2 & % 253.02/36.42 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1027_1 & % 253.02/36.42 | hAPP(all_1027_2, all_1027_1) = all_1027_0 & $i(all_1027_0) & % 253.02/36.42 | $i(all_1027_1) & $i(all_1027_2) & ! [v0: $i] : ! [v1: $i] : (v1 = % 253.02/36.42 | v0 | ~ (hAPP(all_1027_0, v0) = v1) | ~ $i(v0)) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (121) implies: % 253.02/36.42 | (122) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1027_1 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (12) with fresh symbols all_1043_0, all_1043_1, % 253.02/36.42 | all_1043_2, all_1043_3 gives: % 253.02/36.42 | (123) c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____) = % 253.02/36.42 | all_1043_1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = % 253.02/36.42 | all_1043_3 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1043_2 % 253.02/36.42 | & $i(all_1043_0) & $i(all_1043_1) & $i(all_1043_2) & $i(all_1043_3) & % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1043_0, % 253.02/36.42 | all_1043_1) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 253.02/36.42 | all_1043_0, all_1043_2) & % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1043_3, % 253.02/36.42 | all_1043_0) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (123) implies: % 253.02/36.42 | (124) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1043_2 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (38) with fresh symbol all_1057_0 gives: % 253.02/36.42 | (125) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1057_0 & $i(all_1057_0) % 253.02/36.42 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 253.02/36.42 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ % 253.02/36.42 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v4: % 253.02/36.42 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, all_1057_0) = % 253.02/36.42 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 253.02/36.42 | v4, v0))) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (125) implies: % 253.02/36.42 | (126) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1057_0 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (12) with fresh symbols all_1081_0, all_1081_1, % 253.02/36.42 | all_1081_2, all_1081_3 gives: % 253.02/36.42 | (127) c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____) = % 253.02/36.42 | all_1081_1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = % 253.02/36.42 | all_1081_3 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1081_2 % 253.02/36.42 | & $i(all_1081_0) & $i(all_1081_1) & $i(all_1081_2) & $i(all_1081_3) & % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1081_0, % 253.02/36.42 | all_1081_1) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 253.02/36.42 | all_1081_0, all_1081_2) & % 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1081_3, % 253.02/36.42 | all_1081_0) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (127) implies: % 253.02/36.42 | (128) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1081_2 % 253.02/36.42 | % 253.02/36.42 | DELTA: instantiating (43) with fresh symbols all_1083_0, all_1083_1 gives: % 253.02/36.42 | (129) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1083_0 & % 253.02/36.42 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1083_1 & $i(all_1083_0) % 253.02/36.42 | & $i(all_1083_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 253.02/36.42 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) % 253.02/36.42 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 253.02/36.42 | all_1083_0, v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 253.02/36.42 | all_1083_1, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, % 253.02/36.42 | v0)) % 253.02/36.42 | % 253.02/36.42 | ALPHA: (129) implies: % 253.02/36.42 | (130) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1083_1 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (42) with fresh symbol all_1092_0 gives: % 253.02/36.43 | (131) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1092_0 & % 253.02/36.43 | $i(all_1092_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.02/36.43 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 253.02/36.43 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v5) | ~ % 253.02/36.43 | (c_RealDef_Oreal(tc_Nat_Onat, v5) = v6) | ~ % 253.02/36.43 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 253.02/36.43 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ % 253.02/36.43 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v3) = v4) | % 253.02/36.43 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v4, v6) = v7) | % 253.02/36.43 | ~ $i(v1) | ~ $i(v0) | % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, % 253.02/36.43 | all_1092_0)) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (131) implies: % 253.02/36.43 | (132) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1092_0 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (39) with fresh symbol all_1104_0 gives: % 253.02/36.43 | (133) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1104_0 & % 253.02/36.43 | $i(all_1104_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.02/36.43 | $i] : (v3 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 253.02/36.43 | (c_RComplete_Onatfloor(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ? % 253.02/36.43 | [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 253.02/36.43 | all_1104_0) = v4 & $i(v4) & ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (133) implies: % 253.02/36.43 | (134) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1104_0 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (23) with fresh symbols all_1145_0, all_1145_1, % 253.02/36.43 | all_1145_2 gives: % 253.02/36.43 | (135) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1145_2 & % 253.02/36.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1145_0 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1145_1 & $i(all_1145_0) % 253.02/36.43 | & $i(all_1145_1) & $i(all_1145_2) & ! [v0: any] : ! [v1: any] : ! % 253.02/36.43 | [v2: $i] : (v1 = all_1145_0 | v0 = all_1145_1 | ~ (hAPP(v2, v0) = % 253.02/36.43 | v1) | ~ (hAPP(all_1145_2, v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (135) implies: % 253.02/36.43 | (136) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1145_1 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (28) with fresh symbols all_1148_0, all_1148_1 gives: % 253.02/36.43 | (137) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1148_1 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1148_0 & % 253.02/36.43 | $i(all_1148_0) & $i(all_1148_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.02/36.43 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1148_1, v1) | % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1148_0, % 253.02/36.43 | v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0) % 253.02/36.43 | = v1) | ~ $i(v0) | ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1148_0, v0) % 253.02/36.43 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1148_1, v1)) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (137) implies: % 253.02/36.43 | (138) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1148_0 % 253.02/36.43 | (139) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1148_1 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (44) with fresh symbol all_1156_0 gives: % 253.02/36.43 | (140) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1156_0 & $i(all_1156_0) % 253.02/36.43 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 253.02/36.43 | : ( ~ (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3) | ~ % 253.02/36.43 | (c_Polynomial_Odegree(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 253.02/36.43 | $i(v0) | ~ class_Rings_Ocomm__semiring__0(v2) | ? [v5: $i] : % 253.02/36.43 | (c_Polynomial_Odegree(v2, v1) = v5 & % 253.02/36.43 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, all_1156_0) = v4 & % 253.02/36.43 | $i(v5) & $i(v4))) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (140) implies: % 253.02/36.43 | (141) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1156_0 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (16) with fresh symbols all_1168_0, all_1168_1 gives: % 253.02/36.43 | (142) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1168_0 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1168_1 & % 253.02/36.43 | $i(all_1168_0) & $i(all_1168_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.02/36.43 | (hAPP(all_1168_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 253.02/36.43 | : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 & % 253.02/36.43 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.43 | v3, v_m____)) | % 253.02/36.43 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 & % 253.02/36.43 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.43 | v2, all_1168_1)))) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (142) implies: % 253.02/36.43 | (143) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1168_1 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (29) with fresh symbols all_1171_0, all_1171_1 gives: % 253.02/36.43 | (144) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1171_1 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1171_0 & % 253.02/36.43 | $i(all_1171_0) & $i(all_1171_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.02/36.43 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1171_1) | % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 253.02/36.43 | all_1171_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.02/36.43 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_1171_0) % 253.02/36.43 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1171_1)) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (144) implies: % 253.02/36.43 | (145) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1171_0 % 253.02/36.43 | (146) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1171_1 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (54) with fresh symbols all_1240_0, all_1240_1 gives: % 253.02/36.43 | (147) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1240_1 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1240_0 & $i(all_1240_0) % 253.02/36.43 | & $i(all_1240_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.02/36.43 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ % 253.02/36.43 | (hAPP(v3, v0) = v5) | ~ (hAPP(all_1240_1, v2) = v3) | ~ $i(v2) | % 253.02/36.43 | ~ $i(v1) | ~ $i(v0) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4, % 253.02/36.43 | v5) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1240_0, % 253.02/36.43 | v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (147) implies: % 253.02/36.43 | (148) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1240_0 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (25) with fresh symbols all_1263_0, all_1263_1, % 253.02/36.43 | all_1263_2 gives: % 253.02/36.43 | (149) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1263_2 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1263_0 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1263_1 & % 253.02/36.43 | $i(all_1263_0) & $i(all_1263_1) & $i(all_1263_2) & ! [v0: $i] : ! % 253.02/36.43 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, % 253.02/36.43 | all_1263_1) = v1) | ~ $i(v0) | ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1263_2, v0) % 253.02/36.43 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatfloor(v1) = v2 & % 253.02/36.43 | c_RComplete_Onatfloor(v0) = v3 & % 253.02/36.43 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1263_0) = v2 & % 253.02/36.43 | $i(v3) & $i(v2))) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (149) implies: % 253.02/36.43 | (150) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1263_1 % 253.02/36.43 | (151) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1263_0 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (24) with fresh symbols all_1266_0, all_1266_1, % 253.02/36.43 | all_1266_2 gives: % 253.02/36.43 | (152) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1266_2 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1266_0 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1266_1 & % 253.02/36.43 | $i(all_1266_0) & $i(all_1266_1) & $i(all_1266_2) & ! [v0: $i] : ! % 253.02/36.43 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, % 253.02/36.43 | all_1266_1) = v1) | ~ $i(v0) | ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1266_2, v0) % 253.02/36.43 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatceiling(v1) = v2 & % 253.02/36.43 | c_RComplete_Onatceiling(v0) = v3 & % 253.02/36.43 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1266_0) = v2 & % 253.02/36.43 | $i(v3) & $i(v2))) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (152) implies: % 253.02/36.43 | (153) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1266_1 % 253.02/36.43 | (154) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1266_0 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (30) with fresh symbols all_1285_0, all_1285_1 gives: % 253.02/36.43 | (155) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1285_0 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1285_1 & % 253.02/36.43 | $i(all_1285_0) & $i(all_1285_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 253.02/36.43 | $i] : ! [v3: $i] : (v3 = v2 | ~ (c_RComplete_Onatceiling(v0) = % 253.02/36.43 | v2) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, % 253.02/36.43 | all_1285_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 253.02/36.43 | [v5: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 & $i(v4) & ( ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0) | % 253.02/36.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, all_1285_1) % 253.02/36.43 | = v5 & $i(v5) & ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 253.02/36.43 | v5))))) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (155) implies: % 253.02/36.43 | (156) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1285_1 % 253.02/36.43 | (157) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1285_0 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (41) with fresh symbols all_1288_0, all_1288_1 gives: % 253.02/36.43 | (158) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1288_0 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1288_1 & % 253.02/36.43 | $i(all_1288_0) & $i(all_1288_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 253.02/36.43 | $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | % 253.02/36.43 | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v2) = v3) % 253.02/36.43 | | ~ $i(v1) | ~ $i(v0) | ~ % 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1288_1, v1) % 253.02/36.43 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1288_0, v0) | % 253.02/36.43 | ? [v4: $i] : ? [v5: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, % 253.02/36.43 | v5, v0) = v4 & c_RComplete_Onatfloor(v3) = v4 & % 253.02/36.43 | c_RComplete_Onatfloor(v1) = v5 & $i(v5) & $i(v4))) % 253.02/36.43 | % 253.02/36.43 | ALPHA: (158) implies: % 253.02/36.43 | (159) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1288_1 % 253.02/36.43 | % 253.02/36.43 | DELTA: instantiating (40) with fresh symbols all_1306_0, all_1306_1 gives: % 253.02/36.43 | (160) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1306_1 & % 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1306_0 & $i(all_1306_0) % 253.02/36.43 | & $i(all_1306_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 253.02/36.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1306_1, v0) % 253.02/36.44 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 253.02/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & % 253.02/36.44 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 & % 253.02/36.44 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1306_0) = v2 & % 253.02/36.44 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 253.02/36.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) & % 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))) % 253.02/36.44 | % 253.02/36.44 | ALPHA: (160) implies: % 253.02/36.44 | (161) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1306_0 % 253.02/36.44 | % 253.02/36.44 | DELTA: instantiating (17) with fresh symbols all_1331_0, all_1331_1, % 253.02/36.44 | all_1331_2, all_1331_3 gives: % 253.02/36.44 | (162) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1331_1 & % 253.02/36.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1331_3 & % 253.02/36.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1331_2 & % 253.02/36.44 | $i(all_1331_0) & $i(all_1331_1) & $i(all_1331_2) & $i(all_1331_3) & % 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1331_3, % 253.02/36.44 | all_1331_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1331_1, v0) % 253.02/36.44 | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 253.02/36.44 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 & % 253.02/36.44 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.44 | v3, all_1331_0)) | % 253.02/36.44 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 & % 253.02/36.44 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.44 | v2, all_1331_2)))) % 253.02/36.44 | % 253.02/36.44 | ALPHA: (162) implies: % 253.02/36.44 | (163) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1331_2 % 253.02/36.44 | % 253.02/36.44 | DELTA: instantiating (17) with fresh symbols all_1343_0, all_1343_1, % 253.02/36.44 | all_1343_2, all_1343_3 gives: % 253.02/36.44 | (164) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1343_1 & % 253.02/36.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1343_3 & % 253.02/36.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1343_2 & % 253.02/36.44 | $i(all_1343_0) & $i(all_1343_1) & $i(all_1343_2) & $i(all_1343_3) & % 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1343_3, % 253.02/36.44 | all_1343_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1343_1, v0) % 253.02/36.44 | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 253.02/36.44 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 & % 253.02/36.44 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.44 | v3, all_1343_0)) | % 253.02/36.44 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 & % 253.02/36.44 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.02/36.44 | v2, all_1343_2)))) % 253.02/36.44 | % 253.02/36.44 | ALPHA: (164) implies: % 253.02/36.44 | (165) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1343_2 % 253.02/36.44 | % 253.02/36.44 | DELTA: instantiating (19) with fresh symbols all_1370_0, all_1370_1 gives: % 253.02/36.44 | (166) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1370_1 & % 253.02/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1370_0 & $i(all_1370_0) % 253.02/36.44 | & $i(all_1370_1) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = % 253.02/36.44 | all_1370_0 | ~ (hAPP(v2, v0) = all_1370_0) | ~ (hAPP(all_1370_1, % 253.02/36.44 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] % 253.02/36.44 | : ! [v2: $i] : (v0 = all_1370_0 | ~ (hAPP(v2, v0) = all_1370_0) | % 253.02/36.44 | ~ (hAPP(all_1370_1, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: % 253.02/36.44 | $i] : ! [v1: int] : (v1 = all_1370_0 | ~ (hAPP(v0, all_1370_0) = % 253.02/36.44 | v1) | ~ (hAPP(all_1370_1, all_1370_0) = v0)) % 253.02/36.44 | % 253.02/36.44 | ALPHA: (166) implies: % 253.02/36.44 | (167) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1370_0 % 253.02/36.44 | % 253.02/36.44 | DELTA: instantiating (21) with fresh symbols all_1376_0, all_1376_1 gives: % 253.02/36.44 | (168) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1376_0 & % 253.02/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1376_1 & $i(all_1376_0) % 253.02/36.44 | & $i(all_1376_1) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = % 253.02/36.44 | all_1376_1 | ~ (hAPP(v2, v0) = all_1376_1) | ~ (hAPP(all_1376_0, % 253.02/36.44 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] % 253.02/36.44 | : ! [v2: $i] : (v0 = all_1376_1 | ~ (hAPP(v2, v0) = all_1376_1) | % 253.02/36.44 | ~ (hAPP(all_1376_0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: % 253.02/36.44 | $i] : ! [v1: int] : (v1 = all_1376_1 | ~ (hAPP(v0, all_1376_1) = % 253.02/36.44 | v1) | ~ (hAPP(all_1376_0, all_1376_1) = v0)) % 253.02/36.44 | % 253.02/36.44 | ALPHA: (168) implies: % 253.02/36.44 | (169) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1376_1 % 253.02/36.44 | % 253.02/36.44 | DELTA: instantiating (48) with fresh symbols all_1400_0, all_1400_1, % 253.02/36.44 | all_1400_2 gives: % 253.02/36.44 | (170) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1400_1 & % 253.02/36.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1400_2 & % 253.02/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1400_0 & $i(all_1400_0) % 253.02/36.44 | & $i(all_1400_1) & $i(all_1400_2) & ! [v0: any] : ! [v1: $i] : ! % 253.02/36.44 | [v2: $i] : ! [v3: $i] : (v0 = all_1400_0 | ~ (hAPP(v2, v1) = v3) | % 253.02/36.44 | ~ (hAPP(all_1400_1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 253.02/36.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v1) | ~ % 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1400_2, v1)) & ! % 253.02/36.44 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, v0) = v2) | ~ % 253.02/36.44 | (hAPP(all_1400_1, all_1400_0) = v1) | ~ $i(v0) | ~ % 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1400_2, v0) | % 253.02/36.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0)) % 253.02/36.44 | % 253.02/36.44 | ALPHA: (170) implies: % 253.02/36.44 | (171) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1400_0 % 253.02/36.44 | % 253.02/36.44 | DELTA: instantiating (47) with fresh symbols all_1426_0, all_1426_1, % 253.02/36.44 | all_1426_2 gives: % 253.02/36.44 | (172) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1426_1 & % 253.02/36.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1426_2 & % 253.02/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1426_0 & $i(all_1426_0) % 253.02/36.44 | & $i(all_1426_1) & $i(all_1426_2) & ! [v0: any] : ! [v1: $i] : ! % 253.02/36.44 | [v2: $i] : ! [v3: $i] : (v0 = all_1426_0 | ~ (hAPP(v2, v0) = v3) | % 253.02/36.44 | ~ (hAPP(all_1426_1, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 253.02/36.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v1) | ~ % 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_2, v1)) & ! % 253.02/36.44 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1426_0) = % 253.02/36.44 | v2) | ~ (hAPP(all_1426_1, v0) = v1) | ~ $i(v0) | ~ % 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_2, v0) | % 253.02/36.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0)) % 253.02/36.44 | % 253.02/36.44 | ALPHA: (172) implies: % 253.02/36.44 | (173) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1426_0 % 253.02/36.44 | % 253.02/36.44 | DELTA: instantiating (34) with fresh symbol all_1445_0 gives: % 253.33/36.44 | (174) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1445_0 & % 253.33/36.44 | $i(all_1445_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.33/36.44 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 253.33/36.44 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] % 253.33/36.44 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1445_0) = % 253.33/36.44 | v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.33/36.44 | v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.33/36.44 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 253.33/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] : % 253.33/36.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1445_0) = v4 % 253.33/36.44 | & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 253.33/36.44 | v4, v3))) % 253.33/36.44 | % 253.33/36.44 | ALPHA: (174) implies: % 253.33/36.44 | (175) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1445_0 % 253.33/36.44 | % 253.33/36.44 | DELTA: instantiating (35) with fresh symbol all_1448_0 gives: % 253.33/36.44 | (176) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1448_0 & % 253.33/36.44 | $i(all_1448_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.33/36.44 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 253.33/36.44 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4: % 253.33/36.44 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, % 253.33/36.44 | all_1448_0) = v4 & $i(v4) & % 253.33/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) & ! % 253.33/36.44 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 253.33/36.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4: % 253.33/36.44 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, % 253.33/36.44 | all_1448_0) = v4 & $i(v4) & ~ % 253.33/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) % 253.33/36.44 | % 253.33/36.44 | ALPHA: (176) implies: % 253.33/36.44 | (177) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1448_0 % 253.33/36.44 | % 253.33/36.44 | DELTA: instantiating (53) with fresh symbols all_1451_0, all_1451_1 gives: % 253.33/36.44 | (178) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1451_1 & % 253.33/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1451_0 & $i(all_1451_0) % 253.33/36.44 | & $i(all_1451_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.33/36.44 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 253.33/36.44 | [v8: $i] : ! [v9: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = v4) % 253.33/36.44 | | ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ % 253.33/36.44 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1451_0) = v6) | % 253.33/36.44 | ~ (hAPP(v8, v0) = v9) | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v4, v0) % 253.33/36.44 | = v5) | ~ (hAPP(v3, v7) = v8) | ~ $i(v2) | ~ $i(v1) | ~ % 253.33/36.44 | $i(v0) | ~ class_Groups_Omonoid__mult(v2) | ~ % 253.33/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1451_1, v1) | % 253.33/36.44 | (hAPP(v5, v1) = v9 & $i(v9))) % 253.33/36.44 | % 253.33/36.44 | ALPHA: (178) implies: % 253.33/36.44 | (179) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1451_0 % 253.33/36.44 | % 253.33/36.44 | DELTA: instantiating (18) with fresh symbols all_1503_0, all_1503_1, % 253.33/36.44 | all_1503_2 gives: % 253.33/36.44 | (180) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1503_1 & % 253.33/36.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1503_2 & % 253.33/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1503_0 & $i(all_1503_0) % 253.33/36.44 | & $i(all_1503_1) & $i(all_1503_2) & ! [v0: $i] : ! [v1: any] : ! % 253.33/36.44 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = all_1503_2 % 253.33/36.44 | | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v4) = v5) | ~ % 253.33/36.44 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1503_0) = v2) | % 253.33/36.44 | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1503_1, v2) = v3) | ~ $i(v1) % 253.33/36.44 | | ~ $i(v0) | ? [v6: $i] : (hAPP(v6, v0) = v5 & hAPP(all_1503_1, % 253.33/36.44 | v1) = v6 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! % 253.33/36.44 | [v2: int] : (v2 = all_1503_2 | ~ (hAPP(v1, v0) = v2) | ~ % 253.33/36.44 | (hAPP(all_1503_1, all_1503_2) = v1) | ~ $i(v0)) % 253.33/36.44 | % 253.33/36.44 | ALPHA: (180) implies: % 253.33/36.44 | (181) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1503_0 % 253.33/36.44 | % 253.33/36.44 | DELTA: instantiating (55) with fresh symbols all_1518_0, all_1518_1, % 253.33/36.44 | all_1518_2, all_1518_3 gives: % 253.33/36.45 | (182) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1518_2 & % 253.33/36.45 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1518_0 & % 253.33/36.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1518_3 & % 253.33/36.45 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1518_1 & $i(all_1518_0) % 253.33/36.45 | & $i(all_1518_1) & $i(all_1518_2) & $i(all_1518_3) & ! [v0: $i] : ! % 253.33/36.45 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 253.33/36.45 | ! [v6: $i] : (v1 = all_1518_3 | ~ % 253.33/36.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1518_1) = v4) | % 253.33/36.45 | ~ (hAPP(v3, v5) = v6) | ~ (hAPP(v2, v4) = v5) | ~ % 253.33/36.45 | (hAPP(all_1518_0, v0) = v3) | ~ (hAPP(all_1518_2, v0) = v2) | ~ % 253.33/36.45 | $i(v1) | ~ $i(v0) | (hAPP(v2, v1) = v6 & $i(v6))) & ! [v0: $i] : % 253.33/36.45 | ! [v1: $i] : ! [v2: int] : (v2 = all_1518_1 | ~ (hAPP(v1, % 253.33/36.45 | all_1518_3) = v2) | ~ (hAPP(all_1518_2, v0) = v1) | ~ $i(v0)) % 253.33/36.45 | % 253.33/36.45 | ALPHA: (182) implies: % 253.33/36.45 | (183) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1518_1 % 253.33/36.45 | % 253.33/36.45 | DELTA: instantiating (31) with fresh symbols all_1527_0, all_1527_1 gives: % 253.33/36.45 | (184) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1527_1 & % 253.33/36.45 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1527_0 & $i(all_1527_0) % 253.33/36.45 | & $i(all_1527_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 253.33/36.45 | (hAPP(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v2) | ? % 253.33/36.45 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) & % 253.33/36.45 | ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, all_1527_0) = v5 & % 253.33/36.45 | hAPP(v1, v5) = v6 & $i(v6) & $i(v5) & hBOOL(v6) & % 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v0) & ! [v7: % 253.33/36.45 | $i] : ! [v8: $i] : ( ~ (hAPP(v1, v7) = v8) | ~ $i(v7) | % 253.33/36.45 | ~ hBOOL(v8) | ~ % 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v7, v4))) | % 253.33/36.45 | (hAPP(v1, all_1527_1) = v3 & $i(v3) & hBOOL(v3))))) % 253.33/36.45 | % 253.33/36.45 | ALPHA: (184) implies: % 253.33/36.45 | (185) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1527_0 % 253.33/36.45 | % 253.33/36.45 | DELTA: instantiating (50) with fresh symbols all_1542_0, all_1542_1, % 253.33/36.45 | all_1542_2, all_1542_3 gives: % 253.33/36.45 | (186) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1542_0 & % 253.33/36.45 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1542_2 & % 253.33/36.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1542_3 & % 253.33/36.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1542_1 & % 253.33/36.45 | $i(all_1542_0) & $i(all_1542_1) & $i(all_1542_2) & $i(all_1542_3) & % 253.33/36.45 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 253.33/36.45 | ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1542_1) = % 253.33/36.45 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1542_0, v2) = v3) | % 253.33/36.45 | ~ $i(v1) | ~ $i(v0) | ~ % 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1542_3, v1) % 253.33/36.45 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 253.33/36.45 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v5 & % 253.33/36.45 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, all_1542_1) = % 253.33/36.45 | v8 & hAPP(v6, v1) = v7 & hAPP(all_1542_2, v5) = v6 & $i(v8) & % 253.33/36.45 | $i(v7) & $i(v6) & $i(v5) & % 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v4))) % 253.33/36.45 | % 253.33/36.45 | ALPHA: (186) implies: % 253.33/36.45 | (187) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1542_1 % 253.33/36.45 | % 253.33/36.45 | DELTA: instantiating (52) with fresh symbols all_1557_0, all_1557_1 gives: % 253.33/36.45 | (188) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1557_1 & % 253.33/36.45 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1557_0 & $i(all_1557_0) % 253.33/36.45 | & $i(all_1557_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.33/36.45 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 253.33/36.45 | [v8: $i] : ! [v9: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = v3) % 253.33/36.45 | | ~ (c_Groups_Otimes__class_Otimes(v2) = v5) | ~ % 253.33/36.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1557_0) = v7) | % 253.33/36.45 | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v7) % 253.33/36.45 | = v8) | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 253.33/36.45 | $i(v0) | ~ class_Power_Opower(v2) | ? [v10: $i] : ? [v11: $i] : % 253.33/36.45 | (( ~ (v1 = all_1557_1) | (v11 = v10 & c_Groups_Oone__class_Oone(v2) % 253.33/36.45 | = v10 & hAPP(v4, all_1557_1) = v10 & $i(v10))) & (v1 = % 253.33/36.45 | all_1557_1 | (v10 = v9 & hAPP(v4, v1) = v9 & $i(v9))))) % 253.33/36.45 | % 253.33/36.45 | ALPHA: (188) implies: % 253.33/36.45 | (189) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1557_0 % 253.33/36.45 | % 253.33/36.45 | DELTA: instantiating (15) with fresh symbols all_1578_0, all_1578_1 gives: % 253.33/36.45 | (190) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1578_0 & % 253.33/36.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1578_1 & % 253.33/36.45 | $i(all_1578_0) & $i(all_1578_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 253.33/36.45 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 253.33/36.45 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 253.33/36.45 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v5) = v6) | % 253.33/36.45 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, all_1578_1, v4) % 253.33/36.45 | = v5) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1578_0, v1) = v3) | % 253.33/36.45 | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 253.33/36.45 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ((v12 = v11 & % 253.33/36.45 | c_Transcendental_Oarctan(v6) = v11 & % 253.33/36.45 | c_Transcendental_Oarctan(v1) = v9 & % 253.33/36.45 | c_Transcendental_Oarctan(v0) = v10 & % 253.33/36.45 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v9, v10) = v11 & % 253.33/36.45 | $i(v11) & $i(v10) & $i(v9)) | % 253.33/36.45 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v7 & $i(v7) & % 253.33/36.45 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, % 253.33/36.45 | all_1578_1)) | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, % 253.33/36.45 | v0) = v8 & $i(v8) & ~ % 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, % 253.33/36.45 | all_1578_1)))) % 253.33/36.45 | % 253.33/36.45 | ALPHA: (190) implies: % 253.33/36.45 | (191) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1578_1 % 253.33/36.45 | % 253.33/36.45 | DELTA: instantiating (45) with fresh symbol all_1584_0 gives: % 253.33/36.45 | (192) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1584_0 & % 253.33/36.45 | $i(all_1584_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 253.33/36.45 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 253.33/36.45 | (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ (hAPP(v0, v1) = % 253.33/36.45 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 253.33/36.45 | class_Orderings_Oord(v2) | ~ % 253.33/36.45 | class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ? [v7: % 253.33/36.45 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v7) & % 253.33/36.45 | ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1584_0, v5) = % 253.33/36.45 | v6 & $i(v6) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( % 253.33/36.45 | ~ (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ % 253.33/36.45 | (hAPP(v0, v11) = v12) | ~ $i(v11) | ~ % 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(v2, v1, v11) | % 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v6))) % 253.33/36.45 | | (c_Groups_Ominus__class_Ominus(v3, v4, v8) = v9 & % 253.33/36.45 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & hAPP(v0, v7) % 253.33/36.45 | = v8 & $i(v10) & $i(v9) & $i(v8) & % 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(v2, v1, v7) & ~ % 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10, % 253.33/36.45 | all_1584_0))))) % 253.33/36.45 | % 253.33/36.45 | ALPHA: (192) implies: % 253.33/36.45 | (193) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1584_0 % 253.33/36.45 | % 253.33/36.45 | DELTA: instantiating (14) with fresh symbols all_1587_0, all_1587_1 gives: % 253.33/36.45 | (194) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1587_0 & % 253.33/36.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1587_1 & % 253.33/36.45 | $i(all_1587_0) & $i(all_1587_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 253.33/36.45 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v0, all_1587_0) % 253.33/36.45 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? % 253.33/36.45 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 253.33/36.45 | (( ~ (v2 = all_1587_1) & % 253.33/36.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 & % 253.33/36.45 | $i(v2)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v0, % 253.33/36.45 | all_1587_0) = v3 & % 253.33/36.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4 & % 253.33/36.45 | $i(v4) & $i(v3) & % 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, % 253.33/36.45 | all_1587_1)) | % 253.33/36.45 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v0, % 253.33/36.45 | c_Complex_Oii) = v6 & % 253.33/36.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) = v7 & % 253.33/36.45 | $i(v7) & $i(v6) & % 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, % 253.33/36.45 | all_1587_1)) | % 253.33/36.45 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v0, % 253.33/36.45 | c_Complex_Oii) = v8 & % 253.33/36.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9 & % 253.33/36.45 | $i(v9) & $i(v8) & % 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, % 253.33/36.45 | all_1587_1)) | % 253.33/36.45 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v5 & % 253.33/36.45 | $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v5, % 253.33/36.45 | all_1587_1)))) % 253.33/36.45 | % 253.33/36.45 | ALPHA: (194) implies: % 253.33/36.45 | (195) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1587_1 % 253.33/36.45 | % 253.33/36.45 | DELTA: instantiating (57) with fresh symbols all_1602_0, all_1602_1, % 253.33/36.45 | all_1602_2, all_1602_3, all_1602_4, all_1602_5 gives: % 253.33/36.45 | (196) c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = all_1602_1 & % 253.33/36.45 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1602_2 & % 253.33/36.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1602_4 & % 253.33/36.45 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1602_5 & % 253.33/36.45 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1602_3 & % 253.33/36.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1602_0 & % 253.33/36.45 | $i(all_1602_0) & $i(all_1602_1) & $i(all_1602_2) & $i(all_1602_3) & % 253.33/36.45 | $i(all_1602_4) & $i(all_1602_5) & ? [v0: any] : ! [v1: any] : ! % 253.33/36.45 | [v2: $i] : (v1 = all_1602_5 | v0 = all_1602_4 | ~ (hAPP(all_1602_2, % 253.33/36.45 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 253.33/36.45 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 253.33/36.45 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, all_1602_3, v6) = % 253.33/36.45 | v7 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v7) = % 253.33/36.45 | v8 & hAPP(v4, v0) = v5 & hAPP(v2, v5) = v6 & hAPP(all_1602_1, v3) % 253.33/36.45 | = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, all_1602_0))) % 253.33/36.45 | % 253.33/36.45 | ALPHA: (196) implies: % 253.33/36.45 | (197) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1602_0 % 253.33/36.45 | % 253.33/36.45 | GROUND_INST: instantiating (65) with all_773_1, all_797_0, tc_RealDef_Oreal, % 253.33/36.45 | simplifying with (78), (81) gives: % 253.33/36.45 | (198) all_797_0 = all_773_1 % 253.33/36.45 | % 253.33/36.45 | GROUND_INST: instantiating (65) with all_773_1, all_799_1, tc_RealDef_Oreal, % 253.33/36.45 | simplifying with (78), (83) gives: % 253.33/36.45 | (199) all_799_1 = all_773_1 % 253.33/36.45 | % 253.33/36.45 | GROUND_INST: instantiating (65) with all_799_1, all_824_0, tc_RealDef_Oreal, % 253.33/36.45 | simplifying with (83), (90) gives: % 253.33/36.45 | (200) all_824_0 = all_799_1 % 253.33/36.45 | % 253.33/36.45 | GROUND_INST: instantiating (65) with all_797_0, all_826_0, tc_RealDef_Oreal, % 253.33/36.45 | simplifying with (81), (92) gives: % 253.33/36.45 | (201) all_826_0 = all_797_0 % 253.33/36.45 | % 253.33/36.45 | GROUND_INST: instantiating (65) with all_826_0, all_912_0, tc_RealDef_Oreal, % 253.33/36.45 | simplifying with (92), (98) gives: % 253.33/36.46 | (202) all_912_0 = all_826_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_912_0, all_915_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (98), (102) gives: % 253.33/36.46 | (203) all_915_0 = all_912_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_824_0, all_939_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (90), (106) gives: % 253.33/36.46 | (204) all_939_0 = all_824_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_939_0, all_992_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (106), (114) gives: % 253.33/36.46 | (205) all_992_0 = all_939_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_992_0, all_1004_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (114), (118) gives: % 253.33/36.46 | (206) all_1004_0 = all_992_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1004_0, all_1021_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (118), (120) gives: % 253.33/36.46 | (207) all_1021_0 = all_1004_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1021_0, all_1027_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (120), (122) gives: % 253.33/36.46 | (208) all_1027_1 = all_1021_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1027_1, all_1043_2, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (122), (124) gives: % 253.33/36.46 | (209) all_1043_2 = all_1027_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_915_0, all_1081_2, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (102), (128) gives: % 253.33/36.46 | (210) all_1081_2 = all_915_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1043_2, all_1148_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (124), (138) gives: % 253.33/36.46 | (211) all_1148_0 = all_1043_2 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_729_0, all_1148_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (73), (138) gives: % 253.33/36.46 | (212) all_1148_0 = all_729_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1148_0, all_1171_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (138), (145) gives: % 253.33/36.46 | (213) all_1171_0 = all_1148_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1171_0, all_1263_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (145), (150) gives: % 253.33/36.46 | (214) all_1263_1 = all_1171_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1263_1, all_1266_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (150), (153) gives: % 253.33/36.46 | (215) all_1266_1 = all_1263_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1266_1, all_1285_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (153), (156) gives: % 253.33/36.46 | (216) all_1285_1 = all_1266_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1288_1, all_1331_2, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (159), (163) gives: % 253.33/36.46 | (217) all_1331_2 = all_1288_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1081_2, all_1331_2, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (128), (163) gives: % 253.33/36.46 | (218) all_1331_2 = all_1081_2 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1288_1, all_1343_2, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (159), (165) gives: % 253.33/36.46 | (219) all_1343_2 = all_1288_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1285_1, all_1445_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (156), (175) gives: % 253.33/36.46 | (220) all_1445_0 = all_1285_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1445_0, all_1448_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (175), (177) gives: % 253.33/36.46 | (221) all_1448_0 = all_1445_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1331_2, all_1542_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (163), (187) gives: % 253.33/36.46 | (222) all_1542_1 = all_1331_2 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1168_1, all_1542_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (143), (187) gives: % 253.33/36.46 | (223) all_1542_1 = all_1168_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1448_0, all_1578_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (177), (191) gives: % 253.33/36.46 | (224) all_1578_1 = all_1448_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1331_2, all_1584_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (163), (193) gives: % 253.33/36.46 | (225) all_1584_0 = all_1331_2 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1092_0, all_1584_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (132), (193) gives: % 253.33/36.46 | (226) all_1584_0 = all_1092_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1343_2, all_1587_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (165), (195) gives: % 253.33/36.46 | (227) all_1587_1 = all_1343_2 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_713_0, all_1587_1, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (70), (195) gives: % 253.33/36.46 | (228) all_1587_1 = all_713_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1578_1, all_1602_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (191), (197) gives: % 253.33/36.46 | (229) all_1602_0 = all_1578_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1104_0, all_1602_0, tc_RealDef_Oreal, % 253.33/36.46 | simplifying with (134), (197) gives: % 253.33/36.46 | (230) all_1602_0 = all_1104_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_742_0, all_799_0, tc_Nat_Onat, % 253.33/36.46 | simplifying with (75), (84) gives: % 253.33/36.46 | (231) all_799_0 = all_742_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_957_0, all_1001_1, tc_Nat_Onat, % 253.33/36.46 | simplifying with (110), (116) gives: % 253.33/36.46 | (232) all_1001_1 = all_957_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1001_1, all_1083_1, tc_Nat_Onat, % 253.33/36.46 | simplifying with (116), (130) gives: % 253.33/36.46 | (233) all_1083_1 = all_1001_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1083_1, all_1145_1, tc_Nat_Onat, % 253.33/36.46 | simplifying with (130), (136) gives: % 253.33/36.46 | (234) all_1145_1 = all_1083_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1083_1, all_1148_1, tc_Nat_Onat, % 253.33/36.46 | simplifying with (130), (139) gives: % 253.33/36.46 | (235) all_1148_1 = all_1083_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1145_1, all_1171_1, tc_Nat_Onat, % 253.33/36.46 | simplifying with (136), (146) gives: % 253.33/36.46 | (236) all_1171_1 = all_1145_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1171_1, all_1240_0, tc_Nat_Onat, % 253.33/36.46 | simplifying with (146), (148) gives: % 253.33/36.46 | (237) all_1240_0 = all_1171_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1240_0, all_1263_0, tc_Nat_Onat, % 253.33/36.46 | simplifying with (148), (151) gives: % 253.33/36.46 | (238) all_1263_0 = all_1240_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1148_1, all_1266_0, tc_Nat_Onat, % 253.33/36.46 | simplifying with (139), (154) gives: % 253.33/36.46 | (239) all_1266_0 = all_1148_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1001_1, all_1306_0, tc_Nat_Onat, % 253.33/36.46 | simplifying with (116), (161) gives: % 253.33/36.46 | (240) all_1306_0 = all_1001_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_945_0, all_1306_0, tc_Nat_Onat, % 253.33/36.46 | simplifying with (108), (161) gives: % 253.33/36.46 | (241) all_1306_0 = all_945_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_855_0, all_1306_0, tc_Nat_Onat, % 253.33/36.46 | simplifying with (96), (161) gives: % 253.33/36.46 | (242) all_1306_0 = all_855_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1001_1, all_1376_1, tc_Nat_Onat, % 253.33/36.46 | simplifying with (116), (169) gives: % 253.33/36.46 | (243) all_1376_1 = all_1001_1 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_986_0, all_1376_1, tc_Nat_Onat, % 253.33/36.46 | simplifying with (112), (169) gives: % 253.33/36.46 | (244) all_1376_1 = all_986_0 % 253.33/36.46 | % 253.33/36.46 | GROUND_INST: instantiating (65) with all_1370_0, all_1400_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (167), (171) gives: % 253.42/36.46 | (245) all_1400_0 = all_1370_0 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_1285_0, all_1400_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (157), (171) gives: % 253.42/36.46 | (246) all_1400_0 = all_1285_0 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_1266_0, all_1400_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (154), (171) gives: % 253.42/36.46 | (247) all_1400_0 = all_1266_0 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_1057_0, all_1400_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (126), (171) gives: % 253.42/36.46 | (248) all_1400_0 = all_1057_0 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_1376_1, all_1426_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (169), (173) gives: % 253.42/36.46 | (249) all_1426_0 = all_1376_1 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_855_0, all_1451_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (96), (179) gives: % 253.42/36.46 | (250) all_1451_0 = all_855_0 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_826_1, all_1451_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (93), (179) gives: % 253.42/36.46 | (251) all_1451_0 = all_826_1 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_799_0, all_1451_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (84), (179) gives: % 253.42/36.46 | (252) all_1451_0 = all_799_0 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_1426_0, all_1503_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (173), (181) gives: % 253.42/36.46 | (253) all_1503_0 = all_1426_0 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_1503_0, all_1518_1, tc_Nat_Onat, % 253.42/36.46 | simplifying with (181), (183) gives: % 253.42/36.46 | (254) all_1518_1 = all_1503_0 % 253.42/36.46 | % 253.42/36.46 | GROUND_INST: instantiating (65) with all_1263_0, all_1527_0, tc_Nat_Onat, % 253.42/36.46 | simplifying with (151), (185) gives: % 253.42/36.47 | (255) all_1527_0 = all_1263_0 % 253.42/36.47 | % 253.42/36.47 | GROUND_INST: instantiating (65) with all_773_0, all_1527_0, tc_Nat_Onat, % 253.42/36.47 | simplifying with (79), (185) gives: % 253.42/36.47 | (256) all_1527_0 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | GROUND_INST: instantiating (65) with all_1518_1, all_1557_0, tc_Nat_Onat, % 253.42/36.47 | simplifying with (183), (189) gives: % 253.42/36.47 | (257) all_1557_0 = all_1518_1 % 253.42/36.47 | % 253.42/36.47 | GROUND_INST: instantiating (65) with all_1156_0, all_1557_0, tc_Nat_Onat, % 253.42/36.47 | simplifying with (141), (189) gives: % 253.42/36.47 | (258) all_1557_0 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | GROUND_INST: instantiating (67) with all_818_1, all_915_2, v_z, v_w____, % 253.42/36.47 | tc_Complex_Ocomplex, simplifying with (88), (104) gives: % 253.42/36.47 | (259) all_915_2 = all_818_1 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (229), (230) imply: % 253.42/36.47 | (260) all_1578_1 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (260) implies: % 253.42/36.47 | (261) all_1578_1 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (227), (228) imply: % 253.42/36.47 | (262) all_1343_2 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (262) implies: % 253.42/36.47 | (263) all_1343_2 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (225), (226) imply: % 253.42/36.47 | (264) all_1331_2 = all_1092_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (264) implies: % 253.42/36.47 | (265) all_1331_2 = all_1092_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (224), (261) imply: % 253.42/36.47 | (266) all_1448_0 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (266) implies: % 253.42/36.47 | (267) all_1448_0 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (257), (258) imply: % 253.42/36.47 | (268) all_1518_1 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (268) implies: % 253.42/36.47 | (269) all_1518_1 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (222), (223) imply: % 253.42/36.47 | (270) all_1331_2 = all_1168_1 % 253.42/36.47 | % 253.42/36.47 | SIMP: (270) implies: % 253.42/36.47 | (271) all_1331_2 = all_1168_1 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (255), (256) imply: % 253.42/36.47 | (272) all_1263_0 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (272) implies: % 253.42/36.47 | (273) all_1263_0 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (254), (269) imply: % 253.42/36.47 | (274) all_1503_0 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (274) implies: % 253.42/36.47 | (275) all_1503_0 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (253), (275) imply: % 253.42/36.47 | (276) all_1426_0 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (276) implies: % 253.42/36.47 | (277) all_1426_0 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (250), (251) imply: % 253.42/36.47 | (278) all_855_0 = all_826_1 % 253.42/36.47 | % 253.42/36.47 | SIMP: (278) implies: % 253.42/36.47 | (279) all_855_0 = all_826_1 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (251), (252) imply: % 253.42/36.47 | (280) all_826_1 = all_799_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (221), (267) imply: % 253.42/36.47 | (281) all_1445_0 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (281) implies: % 253.42/36.47 | (282) all_1445_0 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (220), (282) imply: % 253.42/36.47 | (283) all_1285_1 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (283) implies: % 253.42/36.47 | (284) all_1285_1 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (249), (277) imply: % 253.42/36.47 | (285) all_1376_1 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (285) implies: % 253.42/36.47 | (286) all_1376_1 = all_1156_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (245), (248) imply: % 253.42/36.47 | (287) all_1370_0 = all_1057_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (245), (246) imply: % 253.42/36.47 | (288) all_1370_0 = all_1285_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (245), (247) imply: % 253.42/36.47 | (289) all_1370_0 = all_1266_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (244), (286) imply: % 253.42/36.47 | (290) all_1156_0 = all_986_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (243), (286) imply: % 253.42/36.47 | (291) all_1156_0 = all_1001_1 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (288), (289) imply: % 253.42/36.47 | (292) all_1285_0 = all_1266_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (287), (288) imply: % 253.42/36.47 | (293) all_1285_0 = all_1057_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (219), (263) imply: % 253.42/36.47 | (294) all_1288_1 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (294) implies: % 253.42/36.47 | (295) all_1288_1 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (218), (271) imply: % 253.42/36.47 | (296) all_1168_1 = all_1081_2 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (217), (271) imply: % 253.42/36.47 | (297) all_1288_1 = all_1168_1 % 253.42/36.47 | % 253.42/36.47 | SIMP: (297) implies: % 253.42/36.47 | (298) all_1288_1 = all_1168_1 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (265), (271) imply: % 253.42/36.47 | (299) all_1168_1 = all_1092_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (240), (241) imply: % 253.42/36.47 | (300) all_1001_1 = all_945_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (300) implies: % 253.42/36.47 | (301) all_1001_1 = all_945_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (241), (242) imply: % 253.42/36.47 | (302) all_945_0 = all_855_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (295), (298) imply: % 253.42/36.47 | (303) all_1168_1 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (303) implies: % 253.42/36.47 | (304) all_1168_1 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (292), (293) imply: % 253.42/36.47 | (305) all_1266_0 = all_1057_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (305) implies: % 253.42/36.47 | (306) all_1266_0 = all_1057_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (216), (284) imply: % 253.42/36.47 | (307) all_1266_1 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (307) implies: % 253.42/36.47 | (308) all_1266_1 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (239), (306) imply: % 253.42/36.47 | (309) all_1148_1 = all_1057_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (309) implies: % 253.42/36.47 | (310) all_1148_1 = all_1057_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (215), (308) imply: % 253.42/36.47 | (311) all_1263_1 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (311) implies: % 253.42/36.47 | (312) all_1263_1 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (238), (273) imply: % 253.42/36.47 | (313) all_1240_0 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (313) implies: % 253.42/36.47 | (314) all_1240_0 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (214), (312) imply: % 253.42/36.47 | (315) all_1171_0 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (315) implies: % 253.42/36.47 | (316) all_1171_0 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (237), (314) imply: % 253.42/36.47 | (317) all_1171_1 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (317) implies: % 253.42/36.47 | (318) all_1171_1 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (213), (316) imply: % 253.42/36.47 | (319) all_1148_0 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (319) implies: % 253.42/36.47 | (320) all_1148_0 = all_1104_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (236), (318) imply: % 253.42/36.47 | (321) all_1145_1 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (321) implies: % 253.42/36.47 | (322) all_1145_1 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (299), (304) imply: % 253.42/36.47 | (323) all_1092_0 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (296), (299) imply: % 253.42/36.47 | (324) all_1092_0 = all_1081_2 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (290), (291) imply: % 253.42/36.47 | (325) all_1001_1 = all_986_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (325) implies: % 253.42/36.47 | (326) all_1001_1 = all_986_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (211), (320) imply: % 253.42/36.47 | (327) all_1104_0 = all_1043_2 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (212), (320) imply: % 253.42/36.47 | (328) all_1104_0 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (235), (310) imply: % 253.42/36.47 | (329) all_1083_1 = all_1057_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (329) implies: % 253.42/36.47 | (330) all_1083_1 = all_1057_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (234), (322) imply: % 253.42/36.47 | (331) all_1083_1 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (331) implies: % 253.42/36.47 | (332) all_1083_1 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (327), (328) imply: % 253.42/36.47 | (333) all_1043_2 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (333) implies: % 253.42/36.47 | (334) all_1043_2 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (323), (324) imply: % 253.42/36.47 | (335) all_1081_2 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (335) implies: % 253.42/36.47 | (336) all_1081_2 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (233), (330) imply: % 253.42/36.47 | (337) all_1057_0 = all_1001_1 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (330), (332) imply: % 253.42/36.47 | (338) all_1057_0 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (210), (336) imply: % 253.42/36.47 | (339) all_915_0 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (339) implies: % 253.42/36.47 | (340) all_915_0 = all_713_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (337), (338) imply: % 253.42/36.47 | (341) all_1001_1 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (341) implies: % 253.42/36.47 | (342) all_1001_1 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (209), (334) imply: % 253.42/36.47 | (343) all_1027_1 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (343) implies: % 253.42/36.47 | (344) all_1027_1 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (208), (344) imply: % 253.42/36.47 | (345) all_1021_0 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (345) implies: % 253.42/36.47 | (346) all_1021_0 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (207), (346) imply: % 253.42/36.47 | (347) all_1004_0 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (347) implies: % 253.42/36.47 | (348) all_1004_0 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (206), (348) imply: % 253.42/36.47 | (349) all_992_0 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (349) implies: % 253.42/36.47 | (350) all_992_0 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (232), (326) imply: % 253.42/36.47 | (351) all_986_0 = all_957_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (301), (326) imply: % 253.42/36.47 | (352) all_986_0 = all_945_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (326), (342) imply: % 253.42/36.47 | (353) all_986_0 = all_773_0 % 253.42/36.47 | % 253.42/36.47 | COMBINE_EQS: (205), (350) imply: % 253.42/36.47 | (354) all_939_0 = all_729_0 % 253.42/36.47 | % 253.42/36.47 | SIMP: (354) implies: % 253.42/36.48 | (355) all_939_0 = all_729_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (351), (352) imply: % 253.42/36.48 | (356) all_957_0 = all_945_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (351), (353) imply: % 253.42/36.48 | (357) all_957_0 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (356), (357) imply: % 253.42/36.48 | (358) all_945_0 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (358) implies: % 253.42/36.48 | (359) all_945_0 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (302), (359) imply: % 253.42/36.48 | (360) all_855_0 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (360) implies: % 253.42/36.48 | (361) all_855_0 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (204), (355) imply: % 253.42/36.48 | (362) all_824_0 = all_729_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (362) implies: % 253.42/36.48 | (363) all_824_0 = all_729_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (203), (340) imply: % 253.42/36.48 | (364) all_912_0 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (364) implies: % 253.42/36.48 | (365) all_912_0 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (202), (365) imply: % 253.42/36.48 | (366) all_826_0 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (366) implies: % 253.42/36.48 | (367) all_826_0 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (279), (361) imply: % 253.42/36.48 | (368) all_826_1 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (368) implies: % 253.42/36.48 | (369) all_826_1 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (201), (367) imply: % 253.42/36.48 | (370) all_797_0 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (370) implies: % 253.42/36.48 | (371) all_797_0 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (280), (369) imply: % 253.42/36.48 | (372) all_799_0 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (372) implies: % 253.42/36.48 | (373) all_799_0 = all_773_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (200), (363) imply: % 253.42/36.48 | (374) all_799_1 = all_729_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (374) implies: % 253.42/36.48 | (375) all_799_1 = all_729_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (231), (373) imply: % 253.42/36.48 | (376) all_773_0 = all_742_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (199), (375) imply: % 253.42/36.48 | (377) all_773_1 = all_729_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (377) implies: % 253.42/36.48 | (378) all_773_1 = all_729_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (198), (371) imply: % 253.42/36.48 | (379) all_773_1 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | SIMP: (379) implies: % 253.42/36.48 | (380) all_773_1 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (378), (380) imply: % 253.42/36.48 | (381) all_729_0 = all_713_0 % 253.42/36.48 | % 253.42/36.48 | COMBINE_EQS: (369), (376) imply: % 253.42/36.48 | (382) all_826_1 = all_742_0 % 253.42/36.48 | % 253.42/36.48 | REDUCE: (94), (367), (382) imply: % 253.42/36.48 | (383) c_RealDef_Oreal(tc_Nat_Onat, all_742_0) = all_713_0 % 253.42/36.48 | % 253.42/36.48 | REDUCE: (103), (259) imply: % 253.42/36.48 | (384) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_818_1) = % 253.42/36.48 | all_915_1 % 253.42/36.48 | % 253.42/36.48 | REDUCE: (77), (376) imply: % 253.42/36.48 | (385) $i(all_742_0) % 253.42/36.48 | % 253.42/36.48 | REDUCE: (72), (381) imply: % 253.42/36.48 | (386) $i(all_713_0) % 253.42/36.48 | % 253.42/36.48 | REDUCE: (100), (340) imply: % 253.42/36.48 | (387) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_915_1, % 253.42/36.48 | all_713_0) % 253.42/36.48 | % 253.42/36.48 | GROUND_INST: instantiating (66) with all_818_0, all_915_1, all_818_1, % 253.42/36.48 | tc_Complex_Ocomplex, simplifying with (87), (384) gives: % 253.42/36.48 | (388) all_915_1 = all_818_0 % 253.42/36.48 | % 253.42/36.48 | REDUCE: (101), (388) imply: % 253.42/36.48 | (389) $i(all_818_0) % 253.42/36.48 | % 253.42/36.48 | REDUCE: (387), (388) imply: % 253.42/36.48 | (390) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_818_0, % 253.42/36.48 | all_713_0) % 253.42/36.48 | % 253.42/36.48 | GROUND_INST: instantiating (6) with v_da____, all_818_0, tc_RealDef_Oreal, % 253.42/36.48 | simplifying with (8), (58), (62), (86), (389) gives: % 253.42/36.48 | (391) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_818_0, % 253.42/36.48 | v_da____) % 253.42/36.48 | % 253.42/36.48 | GROUND_INST: instantiating (6) with all_713_0, v_da____, tc_RealDef_Oreal, % 253.42/36.48 | simplifying with (8), (58), (62), (69), (386) gives: % 253.42/36.48 | (392) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____, % 253.42/36.48 | all_713_0) % 253.42/36.48 | % 253.42/36.48 | GROUND_INST: instantiating (fact_norm__minus__commute) with v_w____, v_z, % 253.42/36.48 | tc_Complex_Ocomplex, all_818_1, all_818_0, simplifying with (59), % 253.42/36.48 | (60), (61), (63), (87), (88) gives: % 253.42/36.48 | (393) ? [v0: $i] : (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, % 253.42/36.48 | v_z, v_w____) = v0 & % 253.42/36.48 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = % 253.42/36.48 | all_818_0 & $i(v0) & $i(all_818_0)) % 253.42/36.48 | % 253.42/36.48 | GROUND_INST: instantiating (32) with all_742_0, all_713_0, simplifying with % 253.42/36.48 | (383), (385) gives: % 253.42/36.48 | (394) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_713_0) = all_713_0 & % 253.42/36.48 | $i(all_713_0) % 253.42/36.48 | % 253.42/36.48 | DELTA: instantiating (393) with fresh symbol all_1739_0 gives: % 253.42/36.48 | (395) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_z, v_w____) = % 253.42/36.48 | all_1739_0 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, % 253.42/36.48 | all_1739_0) = all_818_0 & $i(all_1739_0) & $i(all_818_0) % 253.42/36.48 | % 253.42/36.48 | GROUND_INST: instantiating (4) with all_713_0, v_da____, all_818_0, % 253.42/36.48 | simplifying with (8), (386), (389), (390), (391), (392) gives: % 253.42/36.48 | (396) $false % 253.42/36.48 | % 253.42/36.48 | CLOSE: (396) is inconsistent. % 253.42/36.48 | % 253.42/36.48 End of proof % 253.42/36.48 % SZS output end Proof for theBenchmark % 253.42/36.48 % 253.42/36.48 35864ms %------------------------------------------------------------------------------