%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW179+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 : n009.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 00:49:20 EDT 2023 % Result : Theorem 78.51s 10.98s % Output : Proof 232.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWW179+1 : TPTP v8.1.2. Released v5.2.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Aug 27 18:35:05 EDT 2023 % 0.12/0.34 % CPUTime : % 0.56/0.60 ________ _____ % 0.56/0.60 ___ __ \_________(_)________________________________ % 0.56/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.56/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.56/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.56/0.60 % 0.56/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.56/0.60 (2023-06-19) % 0.56/0.60 % 0.56/0.60 (c) Philipp Rümmer, 2009-2023 % 0.56/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.56/0.60 Amanda Stjerna. % 0.56/0.60 Free software under BSD-3-Clause. % 0.56/0.60 % 0.56/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.56/0.60 % 0.56/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.56/0.61 Running up to 7 provers in parallel. % 0.56/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.56/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.56/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.56/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.56/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.56/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.56/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 18.31/3.23 Prover 1: Preprocessing ... % 19.23/3.33 Prover 6: Preprocessing ... % 19.23/3.33 Prover 0: Preprocessing ... % 19.23/3.34 Prover 3: Preprocessing ... % 19.58/3.37 Prover 5: Preprocessing ... % 19.58/3.37 Prover 2: Preprocessing ... % 19.58/3.39 Prover 4: Preprocessing ... % 51.32/7.47 Prover 3: Warning: ignoring some quantifiers % 51.32/7.50 Prover 1: Warning: ignoring some quantifiers % 52.55/7.63 Prover 3: Constructing countermodel ... % 52.87/7.71 Prover 1: Constructing countermodel ... % 56.08/8.08 Prover 6: Proving ... % 60.71/8.69 Prover 4: Warning: ignoring some quantifiers % 62.98/8.99 Prover 4: Constructing countermodel ... % 63.56/9.10 Prover 5: Proving ... % 68.34/9.70 Prover 0: Proving ... % 73.82/10.43 Prover 2: Proving ... % 74.64/10.48 Prover 2: stopped % 74.64/10.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 78.51/10.97 Prover 3: proved (10351ms) % 78.51/10.97 % 78.51/10.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 78.51/10.98 % 78.51/10.98 Prover 6: stopped % 78.51/10.98 Prover 5: stopped % 78.51/10.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 78.51/10.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 78.51/11.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 79.38/11.08 Prover 0: stopped % 79.38/11.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 83.79/11.67 Prover 7: Preprocessing ... % 87.96/12.20 Prover 13: Preprocessing ... % 87.96/12.20 Prover 10: Preprocessing ... % 87.96/12.22 Prover 8: Preprocessing ... % 88.52/12.28 Prover 11: Preprocessing ... % 100.32/13.82 Prover 10: Warning: ignoring some quantifiers % 101.18/13.89 Prover 7: Warning: ignoring some quantifiers % 101.73/13.96 Prover 8: Warning: ignoring some quantifiers % 102.66/14.07 Prover 10: Constructing countermodel ... % 103.52/14.17 Prover 7: Constructing countermodel ... % 103.52/14.23 Prover 8: Constructing countermodel ... % 107.93/14.74 Prover 13: Warning: ignoring some quantifiers % 109.83/15.00 Prover 13: Constructing countermodel ... % 111.44/15.24 Prover 13: stopped % 111.99/15.25 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 112.56/15.34 Prover 11: Warning: ignoring some quantifiers % 113.86/15.51 Prover 11: Constructing countermodel ... % 121.96/16.63 Prover 16: Preprocessing ... % 133.52/18.08 Prover 16: Warning: ignoring some quantifiers % 134.43/18.22 Prover 16: Constructing countermodel ... % 150.03/20.27 Prover 16: stopped % 150.03/20.27 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 154.89/20.94 Prover 19: Preprocessing ... % 169.50/22.85 Prover 19: Warning: ignoring some quantifiers % 170.68/22.97 Prover 19: Constructing countermodel ... % 184.41/24.77 Prover 19: stopped % 206.77/27.96 Prover 4: stopped % 225.57/31.01 Prover 10: Found proof (size 2351) % 225.57/31.01 Prover 10: proved (20028ms) % 225.57/31.02 Prover 7: stopped % 225.57/31.02 Prover 1: stopped % 225.57/31.02 Prover 8: stopped % 225.57/31.02 Prover 11: stopped % 225.57/31.02 % 225.57/31.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 225.57/31.03 % 228.96/34.07 % SZS output start Proof for theBenchmark % 229.07/34.09 Assumptions after simplification: % 229.07/34.09 --------------------------------- % 229.07/34.09 % 229.07/34.09 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) % 229.07/34.10 $i(tc_Complex_Ocomplex) & % 229.07/34.10 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) % 229.07/34.10 % 229.07/34.10 (arity_RealDef__Oreal__Groups_Ogroup__add) % 229.07/34.10 $i(tc_RealDef_Oreal) & class_Groups_Ogroup__add(tc_RealDef_Oreal) % 229.07/34.10 % 229.07/34.10 (arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) % 229.15/34.10 $i(tc_RealDef_Oreal) & % 229.15/34.10 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Groups_Oordered__ab__group__add) % 229.15/34.10 $i(tc_RealDef_Oreal) & class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) % 229.15/34.10 $i(tc_RealDef_Oreal) & % 229.15/34.10 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) % 229.15/34.10 $i(tc_RealDef_Oreal) & % 229.15/34.10 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Rings_Ocomm__semiring__1) % 229.15/34.10 $i(tc_RealDef_Oreal) & class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Rings_Olinordered__ring__strict) % 229.15/34.10 $i(tc_RealDef_Oreal) & class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Rings_Olinordered__semidom) % 229.15/34.10 $i(tc_RealDef_Oreal) & class_Rings_Olinordered__semidom(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) % 229.15/34.10 $i(tc_RealDef_Oreal) & % 229.15/34.10 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Rings_Ono__zero__divisors) % 229.15/34.10 $i(tc_RealDef_Oreal) & class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) % 229.15/34.10 $i(tc_RealDef_Oreal) & % 229.15/34.10 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Rings_Oordered__ring) % 229.15/34.10 $i(tc_RealDef_Oreal) & class_Rings_Oordered__ring(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) % 229.15/34.10 $i(tc_RealDef_Oreal) & class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) % 229.15/34.10 % 229.15/34.10 (conj_0) % 229.26/34.12 $i(v_m____) & $i(v_r) & $i(v_c____) & $i(tc_Complex_Ocomplex) & % 229.26/34.12 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 229.26/34.12 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 229.26/34.12 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.26/34.12 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v7) = v8 & % 229.26/34.12 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3 & % 229.26/34.12 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v4 & % 229.26/34.12 c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 & % 229.26/34.12 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 229.26/34.12 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____) = v2 & % 229.26/34.12 hAPP(v5, v_m____) = v6 & hAPP(v4, v_r) = v5 & $i(v8) & $i(v7) & $i(v6) & % 229.26/34.12 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 229.26/34.12 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v8)) % 229.26/34.12 % 229.26/34.12 (fact_BseqD) % 229.26/34.13 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.26/34.13 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.26/34.13 ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~ % 229.26/34.13 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3) & % 229.26/34.13 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: $i] : % 229.26/34.13 ! [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5) % 229.26/34.13 = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | % 229.26/34.13 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))))) % 229.26/34.13 % 229.26/34.13 (fact_BseqI) % 229.26/34.13 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.26/34.13 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] : % 229.26/34.13 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.13 class_RealVector_Oreal__normed__vector(v3) | ~ % 229.26/34.13 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | c_SEQ_OBseq(v3, % 229.26/34.13 v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 229.26/34.13 (c_RealVector_Onorm__class_Onorm(v3, v5) = v6 & hAPP(v1, v4) = v5 & $i(v6) % 229.26/34.13 & $i(v5) & $i(v4) & ~ % 229.26/34.13 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v2)))) % 229.26/34.13 % 229.26/34.13 (fact_Bseq__def) % 229.26/34.13 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.26/34.13 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] : % 229.26/34.13 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.13 class_RealVector_Oreal__normed__vector(v2) | ~ % 229.26/34.13 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | c_SEQ_OBseq(v2, % 229.26/34.13 v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 229.26/34.13 (c_RealVector_Onorm__class_Onorm(v2, v5) = v6 & hAPP(v1, v4) = v5 & $i(v6) % 229.26/34.13 & $i(v5) & $i(v4) & ~ % 229.26/34.13 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))) & ! [v1: % 229.26/34.13 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~ % 229.26/34.13 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3) & % 229.26/34.13 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: $i] : % 229.26/34.13 ! [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5) % 229.26/34.13 = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | % 229.26/34.13 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))))) % 229.26/34.13 % 229.26/34.13 (fact_Bseq__iff2) % 229.26/34.14 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.26/34.14 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] : % 229.26/34.14 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 229.26/34.14 (c_Groups_Ouminus__class_Ouminus(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 229.26/34.14 ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ~ % 229.26/34.14 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | c_SEQ_OBseq(v2, % 229.26/34.14 v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 229.26/34.14 (c_Groups_Oplus__class_Oplus(v2, v7, v5) = v8 & % 229.26/34.14 c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v6) = v7 & % 229.26/34.14 $i(v9) & $i(v8) & $i(v7) & $i(v6) & ~ % 229.26/34.14 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3))) & ! [v1: % 229.26/34.14 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~ % 229.26/34.14 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? [v4: $i] : % 229.26/34.14 ? [v5: $i] : (c_Groups_Ouminus__class_Ouminus(v2, v4) = v5 & $i(v5) & % 229.26/34.14 $i(v4) & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 229.26/34.14 v3) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 229.26/34.14 (c_Groups_Oplus__class_Oplus(v2, v7, v5) = v8) | ~ % 229.26/34.14 (c_RealVector_Onorm__class_Onorm(v2, v8) = v9) | ~ (hAPP(v1, v6) = % 229.26/34.14 v7) | ~ $i(v6) | % 229.26/34.14 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3))))) % 229.26/34.14 % 229.26/34.14 (fact_Bseq__iff3) % 229.26/34.14 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.26/34.14 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.26/34.14 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 229.26/34.14 (c_Groups_Ouminus__class_Ouminus(v2, v5) = v6) | ~ (hAPP(v1, v4) = v5) | % 229.26/34.14 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.14 class_RealVector_Oreal__normed__vector(v2) | ~ % 229.26/34.14 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | c_SEQ_OBseq(v2, % 229.26/34.14 v1) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 229.26/34.14 (c_Groups_Oplus__class_Oplus(v2, v8, v6) = v9 & % 229.26/34.14 c_RealVector_Onorm__class_Onorm(v2, v9) = v10 & hAPP(v1, v7) = v8 & % 229.26/34.14 $i(v10) & $i(v9) & $i(v8) & $i(v7) & ~ % 229.26/34.14 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v3))) & ! [v1: % 229.26/34.14 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~ % 229.26/34.14 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? [v4: $i] : % 229.26/34.14 ? [v5: $i] : ? [v6: $i] : (c_Groups_Ouminus__class_Ouminus(v2, v5) = v6 & % 229.26/34.14 hAPP(v1, v4) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 229.26/34.14 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v7: $i] : % 229.26/34.14 ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 229.26/34.14 (c_Groups_Oplus__class_Oplus(v2, v8, v6) = v9) | ~ % 229.26/34.14 (c_RealVector_Onorm__class_Onorm(v2, v9) = v10) | ~ (hAPP(v1, v7) = % 229.26/34.14 v8) | ~ $i(v7) | % 229.26/34.14 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v3))))) % 229.26/34.14 % 229.26/34.14 (fact_LIMSEQ__inverse__realpow__zero__lemma) % 229.26/34.15 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 229.26/34.15 $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 & % 229.26/34.15 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & % 229.26/34.15 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.26/34.15 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) & $i(v2) & % 229.26/34.15 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 229.26/34.15 [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) % 229.26/34.15 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ $i(v4) % 229.26/34.15 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) | ? [v9: % 229.26/34.15 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : % 229.26/34.15 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 & % 229.26/34.15 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & hAPP(v10, % 229.26/34.15 v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & $i(v10) & $i(v9) % 229.26/34.15 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8)))) % 229.26/34.15 % 229.26/34.15 (fact_Nat_Oadd__0__right) % 229.26/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.15 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 229.26/34.15 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 229.26/34.15 % 229.26/34.15 (fact_One__nat__def) % 229.26/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & % 229.26/34.15 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 229.26/34.15 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)) % 229.26/34.15 % 229.26/34.15 (fact_Suc__diff__1) % 229.26/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.26/34.15 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 229.26/34.15 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.15 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 229.26/34.15 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 229.26/34.15 v0, v2) | c_Nat_OSuc(v3) = v2)) % 229.26/34.15 % 229.26/34.15 (fact_Suc__eq__plus1) % 229.26/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 229.26/34.15 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 229.26/34.15 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) | % 229.26/34.15 (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 229.26/34.15 % 229.26/34.15 (fact_Suc__eq__plus1__left) % 229.26/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 229.26/34.15 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 229.26/34.15 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) | % 229.26/34.15 (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 229.26/34.15 % 229.26/34.15 (fact_Suc__neq__Zero) % 229.26/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.15 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 229.26/34.15 % 229.26/34.15 (fact_Suc__not__Zero) % 229.26/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.15 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 229.26/34.15 % 229.26/34.15 (fact_Suc__pred) % 229.26/34.15 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 229.26/34.15 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.15 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 229.26/34.15 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 229.26/34.15 v0, v2) | c_Nat_OSuc(v3) = v2)) % 229.26/34.15 % 229.26/34.15 (fact_Suc__pred_H) % 229.26/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.26/34.16 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 229.26/34.16 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.16 $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 229.26/34.16 v1) = v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 229.26/34.16 v0, v2) | c_Nat_OSuc(v3) = v2)) % 229.26/34.16 % 229.26/34.16 (fact_Zero__neq__Suc) % 229.26/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.16 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 229.26/34.16 % 229.26/34.16 (fact_Zero__not__Suc) % 229.26/34.16 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.16 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 229.26/34.16 % 229.26/34.16 (fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096) % 229.26/34.16 $i(v_m____) & $i(v_r) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? % 229.26/34.16 [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 229.26/34.16 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.26/34.16 c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v4 & % 229.26/34.16 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & hAPP(v2, v_m____) = v3 % 229.26/34.16 & hAPP(v1, v_r) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 229.26/34.16 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4)) % 229.26/34.16 % 229.26/34.16 (fact__0960_A_060_061_Acmod_Ac_096) % 229.26/34.16 $i(v_c____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.26/34.16 ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 229.26/34.16 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____) = v1 & $i(v1) % 229.26/34.16 & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1)) % 229.26/34.16 % 229.26/34.16 (fact_abs__add__one__gt__zero) % 229.26/34.16 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.26/34.16 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.26/34.16 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.26/34.16 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, % 229.26/34.16 v2) = v3) | ~ $i(v2) | ? [v4: $i] : % 229.26/34.16 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v3) = v4 & $i(v4) & % 229.26/34.16 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))) % 229.26/34.16 % 229.26/34.16 (fact_abs__add__one__not__less__self) % 229.26/34.16 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.26/34.16 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 229.26/34.16 [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ % 229.26/34.16 $i(v1) | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 229.26/34.16 v0) = v3 & $i(v3) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 229.26/34.16 v3, v1)))) % 229.26/34.16 % 229.26/34.16 (fact_abs__eq__0) % 229.26/34.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1, % 229.26/34.16 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.26/34.16 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] : % 229.26/34.16 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) & % 229.26/34.16 ( ~ (v3 = v0) | v2 = v0))) % 229.26/34.16 % 229.26/34.16 (fact_abs__le__zero__iff) % 229.26/34.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1, % 229.26/34.16 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.26/34.16 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] : % 229.26/34.16 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v0) | % 229.26/34.16 c_Orderings_Oord__class_Oless__eq(v1, v2, v0)) & (v3 = v0 | ~ % 229.26/34.16 c_Orderings_Oord__class_Oless__eq(v1, v2, v3)))) % 229.26/34.16 % 229.26/34.16 (fact_abs__norm__cancel) % 229.26/34.17 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 229.26/34.17 (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.26/34.17 class_RealVector_Oreal__normed__vector(v1) | % 229.26/34.17 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v2 & $i(v2))) % 229.26/34.17 % 229.26/34.17 (fact_abs__not__less__zero) % 229.26/34.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1, % 229.26/34.17 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.26/34.17 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] : % 229.26/34.17 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ~ % 229.26/34.17 c_Orderings_Oord__class_Oless(v1, v2, v3))) % 229.26/34.17 % 229.26/34.17 (fact_abs__real__def) % 229.26/34.17 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.26/34.17 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.26/34.17 ! [v2: $i] : (v2 = v1 | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) % 229.26/34.17 = v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, % 229.26/34.17 v0)) & ! [v1: $i] : ! [v2: $i] : ( ~ % 229.26/34.17 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1) | ~ % 229.26/34.17 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | % 229.26/34.17 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 & $i(v2)))) % 229.26/34.17 % 229.26/34.17 (fact_add__eq__if) % 229.26/34.17 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.26/34.17 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 229.26/34.17 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.17 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | ~ % 229.26/34.17 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 229.26/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = v5) | ~ $i(v3) | ~ % 229.26/34.17 $i(v2) | ? [v6: $i] : (c_Nat_OSuc(v5) = v6 & % 229.26/34.17 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v6 & $i(v6))) & ! % 229.26/34.17 [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 229.26/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = v3) | ~ $i(v2))) % 229.26/34.17 % 229.26/34.17 (fact_add__eq__self__zero) % 229.26/34.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 229.26/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ $i(v2) | ~ % 229.26/34.17 $i(v1))) % 229.26/34.17 % 229.26/34.17 (fact_add__gr__0) % 229.26/34.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 229.26/34.17 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 229.26/34.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 229.26/34.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i] : ! % 229.26/34.17 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, % 229.26/34.17 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 229.26/34.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : ! % 229.26/34.17 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, % 229.26/34.17 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 229.26/34.17 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 229.26/34.17 % 229.26/34.17 (fact_add__is__0) % 229.26/34.17 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.17 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 229.26/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~ % 229.26/34.17 $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 229.26/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ $i(v2) | ~ % 229.26/34.17 $i(v1)) & ! [v1: $i] : (v1 = v0 | ~ % 229.26/34.17 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1))) % 229.26/34.17 % 229.26/34.17 (fact_add__is__1) % 229.26/34.18 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 229.26/34.18 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.18 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 229.26/34.18 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 229.26/34.18 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 229.26/34.18 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 229.26/34.18 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] : % 229.26/34.18 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2))) % 229.26/34.18 % 229.26/34.18 (fact_add__neg__neg) % 229.26/34.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.18 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.18 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v1, v4) | ~ % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v0, v4) | % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v3, v4)))) % 229.26/34.18 % 229.26/34.18 (fact_add__neg__nonpos) % 229.26/34.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.18 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.18 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v1, v4) | ~ % 229.26/34.18 c_Orderings_Oord__class_Oless__eq(v2, v0, v4) | % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v3, v4)))) % 229.26/34.18 % 229.26/34.18 (fact_add__nonneg__eq__0__iff) % 229.26/34.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.18 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.18 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.18 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) | ~ % 229.26/34.18 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) | (( ~ (v4 = v3) | (v3 = % 229.26/34.18 v0 & v1 = v0)) & ( ~ (v4 = v0) | ~ (v1 = v0) | v3 = v0))))) % 229.26/34.18 % 229.26/34.18 (fact_add__nonneg__nonneg) % 229.26/34.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.18 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.18 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.18 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) | ~ % 229.26/34.18 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) | % 229.26/34.18 c_Orderings_Oord__class_Oless__eq(v2, v4, v3)))) % 229.26/34.18 % 229.26/34.18 (fact_add__nonneg__pos) % 229.26/34.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.18 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.18 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v4, v0) | ~ % 229.26/34.18 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) | % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v4, v3)))) % 229.26/34.18 % 229.26/34.18 (fact_add__nonpos__neg) % 229.26/34.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.18 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.18 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.18 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v0, v4) | ~ % 229.26/34.18 c_Orderings_Oord__class_Oless__eq(v2, v1, v4) | % 229.26/34.18 c_Orderings_Oord__class_Oless(v2, v3, v4)))) % 229.26/34.18 % 229.26/34.18 (fact_add__nonpos__nonpos) % 229.26/34.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.19 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.19 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.19 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.19 c_Orderings_Oord__class_Oless__eq(v2, v1, v4) | ~ % 229.26/34.19 c_Orderings_Oord__class_Oless__eq(v2, v0, v4) | % 229.26/34.19 c_Orderings_Oord__class_Oless__eq(v2, v3, v4)))) % 229.26/34.19 % 229.26/34.19 (fact_add__pos__nonneg) % 229.26/34.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.19 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.19 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.19 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.19 c_Orderings_Oord__class_Oless(v2, v4, v1) | ~ % 229.26/34.19 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) | % 229.26/34.19 c_Orderings_Oord__class_Oless(v2, v4, v3)))) % 229.26/34.19 % 229.26/34.19 (fact_add__pos__pos) % 229.26/34.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.19 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.19 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] : % 229.26/34.19 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ % 229.26/34.19 c_Orderings_Oord__class_Oless(v2, v4, v1) | ~ % 229.26/34.19 c_Orderings_Oord__class_Oless(v2, v4, v0) | % 229.26/34.19 c_Orderings_Oord__class_Oless(v2, v4, v3)))) % 229.26/34.19 % 229.26/34.19 (fact_add__strict__increasing) % 229.26/34.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.26/34.19 (c_Groups_Oplus__class_Oplus(v3, v2, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.26/34.19 $i(v1) | ~ $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v3) | ~ % 229.26/34.19 c_Orderings_Oord__class_Oless__eq(v3, v1, v0) | % 229.26/34.19 c_Orderings_Oord__class_Oless(v3, v1, v4) | ? [v5: $i] : % 229.26/34.19 (c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5) & ~ % 229.26/34.19 c_Orderings_Oord__class_Oless(v3, v5, v2))) % 229.26/34.19 % 229.26/34.19 (fact_coeff__1) % 229.26/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.19 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.26/34.19 $i] : ! [v6: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v4) = v5) | ~ % 229.26/34.19 (tc_Polynomial_Opoly(v2) = v3) | ~ (c_Groups_Oone__class_Oone(v3) = v4) | % 229.26/34.19 ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.19 class_Rings_Ocomm__semiring__1(v2) | ? [v7: $i] : ? [v8: $i] : (( ~ (v1 % 229.26/34.19 = v0) | (v7 = v6 & c_Groups_Oone__class_Oone(v2) = v6 & $i(v6))) & % 229.26/34.19 (v1 = v0 | (v8 = v6 & c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6)))))) % 229.26/34.19 % 229.26/34.19 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) % 229.26/34.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.19 (c_Groups_Oplus__class_Oplus(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.19 $i(v0) | ~ class_Rings_Ocomm__semiring__1(v2) | % 229.26/34.19 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3 & $i(v3))) % 229.26/34.19 % 229.26/34.19 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) % 229.26/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.19 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.26/34.19 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 229.26/34.19 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | ? [v5: $i] : % 229.26/34.19 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5)))) % 229.26/34.19 % 229.26/34.19 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) % 229.26/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 229.26/34.19 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.26/34.19 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 229.26/34.19 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | hAPP(v4, v0) % 229.26/34.19 = v1)) % 229.26/34.19 % 229.26/34.19 (fact_diff__0__eq__0) % 229.26/34.19 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.19 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 229.26/34.19 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 229.26/34.19 % 229.26/34.20 (fact_diff__Suc__eq__diff__pred) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 229.26/34.20 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.26/34.20 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 229.26/34.20 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ $i(v2) | ~ % 229.26/34.20 $i(v1) | ? [v5: $i] : (c_Nat_OSuc(v1) = v5 & % 229.26/34.20 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) = v4 & $i(v5) & % 229.26/34.20 $i(v4)))) % 229.26/34.20 % 229.26/34.20 (fact_diff__Suc__less) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.20 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.26/34.20 (c_Nat_OSuc(v1) = v3) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 229.26/34.20 v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 229.26/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 229.26/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 229.26/34.20 % 229.26/34.20 (fact_diff__add__0) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.20 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 % 229.26/34.20 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 229.26/34.20 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 229.26/34.20 $i(v1))) % 229.26/34.20 % 229.26/34.20 (fact_diff__is__0__eq) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.20 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 229.26/34.20 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 229.26/34.20 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & ! % 229.26/34.20 [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 229.26/34.20 v1) = v0) | ~ $i(v2) | ~ $i(v1) | % 229.26/34.20 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 229.26/34.20 % 229.26/34.20 (fact_diff__is__0__eq_H) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.20 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 229.26/34.20 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 229.26/34.20 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 229.26/34.20 % 229.26/34.20 (fact_diff__less) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.20 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.26/34.20 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~ % 229.26/34.20 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ~ % 229.26/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 229.26/34.20 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1))) % 229.26/34.20 % 229.26/34.20 (fact_diff__self__eq__0) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.20 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 229.26/34.20 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ $i(v1))) % 229.26/34.20 % 229.26/34.20 (fact_diffs0__imp__equal) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.20 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 229.26/34.20 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ $i(v2) | ~ % 229.26/34.20 $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) & % 229.26/34.20 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & $i(v3)))) % 229.26/34.20 % 229.26/34.20 (fact_div__1) % 229.26/34.20 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 229.26/34.20 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.20 $i] : ! [v3: $i] : (v3 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, % 229.26/34.20 v2, v1) = v3) | ~ $i(v2))) % 229.26/34.20 % 229.26/34.20 (fact_div__geq) % 229.26/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.21 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.26/34.21 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~ % 229.26/34.21 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~ % 229.26/34.21 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 229.26/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v5: $i] : % 229.26/34.21 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 & c_Nat_OSuc(v4) = % 229.26/34.21 v5 & $i(v5)))) % 229.26/34.21 % 229.26/34.21 (fact_div__if) % 229.26/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.21 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.26/34.21 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~ % 229.26/34.21 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ $i(v2) | ~ % 229.26/34.21 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v5: % 229.26/34.21 $i] : ? [v6: $i] : (( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 229.26/34.21 v2) | (v5 = v0 & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = % 229.26/34.21 v0)) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | (v6 = % 229.26/34.21 v5 & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 & % 229.26/34.21 c_Nat_OSuc(v4) = v5 & $i(v5)))))) % 229.26/34.21 % 229.26/34.21 (fact_div__le__mono2) % 229.26/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.21 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.26/34.21 $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v3) = v5) | ~ % 229.26/34.21 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v4) | ~ $i(v3) | ~ % 229.26/34.21 $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) % 229.26/34.21 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 229.26/34.21 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5))) % 229.26/34.21 % 229.26/34.21 (fact_div__less) % 229.26/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.26/34.21 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 229.26/34.21 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 229.26/34.21 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1))) % 229.26/34.21 % 229.26/34.21 (fact_div__less__dividend) % 229.26/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.26/34.21 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 229.26/34.21 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.21 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.26/34.21 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v3) | ~ % 229.26/34.21 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~ % 229.26/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 229.26/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 229.26/34.21 % 229.26/34.21 (fact_div__mult__self1__is__m) % 229.26/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.26/34.21 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 229.26/34.21 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.21 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | % 229.26/34.21 ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = v6) | ~ (hAPP(v4, % 229.26/34.21 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.26/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 229.26/34.21 % 229.26/34.21 (fact_div__mult__self__is__m) % 229.26/34.21 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.26/34.21 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 229.26/34.21 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.26/34.21 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | % 229.26/34.21 ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = v6) | ~ (hAPP(v4, % 229.26/34.21 v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.26/34.21 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 229.26/34.21 % 229.26/34.21 (fact_divisors__zero) % 229.26/34.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.26/34.22 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 229.26/34.22 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.26/34.22 class_Rings_Ono__zero__divisors(v2) | ? [v6: $i] : % 229.26/34.22 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = v5) | v5 = v1 | % 229.26/34.22 v5 = v0))) % 229.26/34.22 % 229.26/34.22 (fact_equal__neg__zero) % 229.26/34.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 229.26/34.22 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.26/34.22 class_Groups_Olinordered__ab__group__add(v1) | ? [v3: $i] : (( ~ (v2 = v0) % 229.26/34.22 | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1) = v0)) & (v2 = v0 | ( ~ (v3 % 229.26/34.22 = v0) & c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3))))) % 229.26/34.22 % 229.26/34.22 (fact_ex__least__nat__less) % 229.76/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.22 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 229.76/34.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.22 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) | ~ $i(v3) | ~ % 229.76/34.22 $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 229.76/34.22 $i] : ($i(v6) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 % 229.76/34.22 & hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) & % 229.76/34.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9: $i] : % 229.76/34.22 ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9) | ~ hBOOL(v10) | % 229.76/34.22 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) | % 229.76/34.22 (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5)))))) % 229.76/34.22 % 229.76/34.22 (fact_ge__natfloor__plus__one__imp__gt) % 229.76/34.22 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.22 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 229.76/34.22 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = % 229.76/34.22 v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 229.76/34.22 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5: $i] : % 229.76/34.22 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 & $i(v5) & ~ % 229.76/34.22 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v1)))) % 229.76/34.22 % 229.76/34.22 (fact_gr0I) % 229.76/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.22 & $i(v0) & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | % 229.76/34.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 229.76/34.22 % 229.76/34.22 (fact_gr0__conv__Suc) % 229.76/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.22 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2) % 229.76/34.22 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! % 229.76/34.22 [v1: $i] : ( ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 229.76/34.22 v1) | ? [v2: $i] : (c_Nat_OSuc(v2) = v1 & $i(v2)))) % 229.76/34.22 % 229.76/34.22 (fact_gr__implies__not0) % 229.76/34.22 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.22 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 229.76/34.22 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 229.76/34.22 % 229.76/34.22 (fact_int__power__div__base) % 229.76/34.23 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.76/34.23 ? [v3: $i] : (c_Nat_OSuc(v0) = v3 & c_Power_Opower__class_Opower(tc_Int_Oint) % 229.76/34.23 = v2 & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & % 229.76/34.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) & % 229.76/34.23 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 229.76/34.23 : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v3) = v7) | ~ % 229.76/34.23 (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v9: $i] : % 229.76/34.23 (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v9, v4) = v8 & hAPP(v6, v5) = v9 % 229.76/34.23 & $i(v9) & $i(v8)))) % 229.76/34.23 % 229.76/34.23 (fact_int__val__lemma) % 229.76/34.23 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.76/34.23 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 & % 229.76/34.23 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 229.76/34.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & % 229.76/34.23 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, v5) = % 229.76/34.23 v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v6) | ? [v7: $i] : ? % 229.76/34.23 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 229.76/34.23 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ($i(v10) & $i(v8) & ((v9 = v3 & % 229.76/34.23 hAPP(v4, v8) = v3 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 229.76/34.23 v8, v5)) | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v12, v13) = % 229.76/34.23 v14 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v10, v0) = v11 & % 229.76/34.23 c_Groups_Oabs__class_Oabs(tc_Int_Oint, v14) = v15 & hAPP(v4, v11) = % 229.76/34.23 v12 & hAPP(v4, v10) = v13 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 229.76/34.23 $i(v11) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v5) & ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v15, v1)) | (hAPP(v4, % 229.76/34.23 v2) = v7 & $i(v7) & ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v7, v3)))))) % 229.76/34.23 % 229.76/34.23 (fact_le0) % 229.76/34.23 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.23 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) | % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1))) % 229.76/34.23 % 229.76/34.23 (fact_le__0__eq) % 229.76/34.23 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.23 & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) & ! [v1: % 229.76/34.23 $i] : (v1 = v0 | ~ $i(v1) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))) % 229.76/34.23 % 229.76/34.23 (fact_le__mult__natfloor) % 229.76/34.23 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 229.76/34.23 $i] : (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 229.76/34.23 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & % 229.76/34.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) & % 229.76/34.23 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.23 : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~ % 229.76/34.23 (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v1, % 229.76/34.23 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v9: $i] % 229.76/34.23 : ? [v10: $i] : ? [v11: $i] : (c_RComplete_Onatfloor(v10) = v11 & % 229.76/34.23 hAPP(v9, v3) = v10 & hAPP(v2, v4) = v9 & $i(v11) & $i(v10) & $i(v9) & % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11)))) % 229.76/34.23 % 229.76/34.23 (fact_le__natfloor__eq) % 229.76/34.23 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.23 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.23 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, % 229.76/34.23 v1) = v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ % 229.76/34.23 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)) & ! [v1: $i] % 229.76/34.23 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.76/34.23 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ (c_RComplete_Onatfloor(v2) = % 229.76/34.23 v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3))) % 229.76/34.23 % 229.76/34.23 (fact_le__natfloor__eq__one) % 229.76/34.23 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.23 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 229.76/34.23 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.23 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) | % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & ! [v2: $i] % 229.76/34.23 : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) | % 229.76/34.23 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3))) % 229.76/34.23 % 229.76/34.23 (fact_lemmaCauchy) % 229.76/34.24 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.24 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 229.76/34.24 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 229.76/34.24 (c_RealVector_Onorm__class_Onorm(v4, v5) = v6) | ~ (hAPP(v1, v2) = v5) | % 229.76/34.24 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Orderings_Oord(v3) % 229.76/34.24 | ~ class_RealVector_Oreal__normed__vector(v4) | ? [v7: $i] : ? [v8: % 229.76/34.24 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & % 229.76/34.24 ((c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 & % 229.76/34.24 c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1, v8) = v9 & % 229.76/34.24 $i(v11) & $i(v10) & $i(v9) & c_Orderings_Oord__class_Oless__eq(v3, % 229.76/34.24 v2, v8) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, % 229.76/34.24 v0)) | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 % 229.76/34.24 & $i(v7) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ % 229.76/34.24 (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~ (hAPP(v1, % 229.76/34.24 v12) = v13) | ~ $i(v12) | ~ % 229.76/34.24 c_Orderings_Oord__class_Oless__eq(v3, v2, v12) | % 229.76/34.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v7))))))) % 229.76/34.24 % 229.76/34.24 (fact_lemma__NBseq__def) % 229.76/34.24 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.24 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] : % 229.76/34.24 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Nat_OSuc(v3) = v4) | ~ % 229.76/34.24 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.24 class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ? [v6: $i] : % 229.76/34.24 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v5) & % 229.76/34.24 ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 & % 229.76/34.24 c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 & % 229.76/34.24 $i(v9) & $i(v8) & $i(v6) & ~ % 229.76/34.24 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v6)) | % 229.76/34.24 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v10: % 229.76/34.24 $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 229.76/34.24 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1, % 229.76/34.24 v10) = v11) | ~ $i(v10) | % 229.76/34.24 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v5)))))) % 229.76/34.24 & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.24 $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ~ % 229.76/34.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: $i] : ? % 229.76/34.24 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) % 229.76/34.24 & $i(v4) & ((c_Nat_OSuc(v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 % 229.76/34.24 & $i(v6) & $i(v5) & ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 229.76/34.24 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1, % 229.76/34.24 v10) = v11) | ~ $i(v10) | % 229.76/34.24 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v6))) | % 229.76/34.24 (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 & % 229.76/34.24 $i(v9) & $i(v8) & ~ % 229.76/34.24 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3)))))) % 229.76/34.24 % 229.76/34.24 (fact_lemma__NBseq__def2) % 229.76/34.24 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.24 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] : % 229.76/34.24 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Nat_OSuc(v3) = v4) | ~ % 229.76/34.24 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.24 class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ? [v6: $i] : % 229.76/34.24 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v5) & % 229.76/34.24 ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 & % 229.76/34.24 c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 & % 229.76/34.24 $i(v9) & $i(v8) & $i(v6) & ~ % 229.76/34.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v6)) | % 229.76/34.24 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v10: % 229.76/34.24 $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 229.76/34.24 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1, % 229.76/34.24 v10) = v11) | ~ $i(v10) | % 229.76/34.24 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v5)))))) % 229.76/34.24 & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.24 $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ~ % 229.76/34.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: $i] : ? % 229.76/34.24 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) % 229.76/34.24 & $i(v4) & ((c_Nat_OSuc(v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 % 229.76/34.24 & $i(v6) & $i(v5) & ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 229.76/34.24 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1, % 229.76/34.24 v10) = v11) | ~ $i(v10) | % 229.76/34.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v6))) | % 229.76/34.24 (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 & % 229.76/34.24 $i(v9) & $i(v8) & ~ % 229.76/34.24 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3)))))) % 229.76/34.24 % 229.76/34.24 (fact_lemma__interval) % 229.76/34.24 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.24 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.24 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~ % 229.76/34.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4: $i] : % 229.76/34.24 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! % 229.76/34.24 [v5: $i] : ! [v6: $i] : ( ~ % 229.76/34.24 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~ % 229.76/34.24 $i(v5) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1) | % 229.76/34.24 ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 & % 229.76/34.24 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, % 229.76/34.24 v4))) & ! [v5: $i] : ! [v6: $i] : ( ~ % 229.76/34.24 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~ % 229.76/34.24 $i(v5) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5) | % 229.76/34.24 ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 & % 229.76/34.24 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, % 229.76/34.24 v4)))))) % 229.76/34.24 % 229.76/34.24 (fact_lemma__interval__lt) % 229.76/34.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.25 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.25 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4: $i] : % 229.76/34.25 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! % 229.76/34.25 [v5: $i] : ! [v6: $i] : ( ~ % 229.76/34.25 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~ % 229.76/34.25 $i(v5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v5, v1) | ? % 229.76/34.25 [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 & % 229.76/34.25 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, % 229.76/34.25 v4))) & ! [v5: $i] : ! [v6: $i] : ( ~ % 229.76/34.25 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~ % 229.76/34.25 $i(v5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5) | ? % 229.76/34.25 [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 & % 229.76/34.25 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, % 229.76/34.25 v4)))))) % 229.76/34.25 % 229.76/34.25 (fact_less__Suc0) % 229.76/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 229.76/34.25 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] : (v2 = v0 % 229.76/34.25 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1))) % 229.76/34.25 % 229.76/34.25 (fact_less__Suc__eq__0__disj) % 229.76/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.25 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.76/34.25 (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~ $i(v2) | % 229.76/34.25 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) | % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v1: $i] : ! % 229.76/34.25 [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v2) | % 229.76/34.25 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4: % 229.76/34.25 $i] : (c_Nat_OSuc(v4) = v2 & $i(v4) & % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1: $i] : ! % 229.76/34.25 [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 229.76/34.25 % 229.76/34.25 (fact_less__eq__nat_Osimps_I1_J) % 229.76/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.25 & $i(v0) & ? [v1: $i] : ( ~ $i(v1) | % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1))) % 229.76/34.25 % 229.76/34.25 (fact_less__nat__zero__code) % 229.76/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.25 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 229.76/34.25 % 229.76/34.25 (fact_less__natfloor) % 229.76/34.25 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.25 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.25 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, % 229.76/34.25 v1) = v3) | ~ (c_RComplete_Onatfloor(v2) = v4) | ~ $i(v2) | ~ % 229.76/34.25 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) % 229.76/34.25 % 229.76/34.25 (fact_less__zeroE) % 229.76/34.25 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.25 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 229.76/34.25 % 229.76/34.25 (fact_ln__add__one__self__le__self) % 229.76/34.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.25 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.76/34.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.25 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, % 229.76/34.25 v1, v2) = v3) | ~ $i(v2) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v4: $i] % 229.76/34.25 : (c_Transcendental_Oln(v3) = v4 & $i(v4) & % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)))) % 229.76/34.25 % 229.76/34.25 (fact_ln__eq__zero__iff) % 229.76/34.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.25 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.76/34.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.25 [v2: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = v0) | ~ $i(v2) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)) & ! [v2: $i] : % 229.76/34.25 (v2 = v0 | ~ (c_Transcendental_Oln(v1) = v2) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1))) % 229.76/34.25 % 229.76/34.25 (fact_ln__ge__zero) % 229.76/34.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.25 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 229.76/34.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! % 229.76/34.25 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | % 229.76/34.25 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3))) % 229.76/34.25 % 229.76/34.25 (fact_ln__ge__zero__iff) % 229.76/34.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.25 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.76/34.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.25 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | % 229.76/34.25 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) | % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] % 229.76/34.25 : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2))) % 229.76/34.25 % 229.76/34.25 (fact_ln__ge__zero__imp__ge__one) % 229.76/34.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.25 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.76/34.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.25 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | % 229.76/34.25 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 229.76/34.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2))) % 229.76/34.25 % 229.76/34.25 (fact_ln__gt__zero) % 229.76/34.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.25 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 229.76/34.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! % 229.76/34.25 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | % 229.76/34.25 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 229.76/34.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3))) % 229.76/34.25 % 229.76/34.25 (fact_ln__gt__zero__iff) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.76/34.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | % 229.76/34.26 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] : % 229.76/34.26 ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2))) % 229.76/34.26 % 229.76/34.26 (fact_ln__gt__zero__imp__gt__one) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.76/34.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | % 229.76/34.26 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2))) % 229.76/34.26 % 229.76/34.26 (fact_ln__inj__iff) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.26 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.26 ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = v3) | % 229.76/34.26 ~ (c_Transcendental_Oln(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1))) % 229.76/34.26 % 229.76/34.26 (fact_ln__le__cancel__iff) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.26 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.26 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) % 229.76/34.26 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) | % 229.76/34.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v1: $i] % 229.76/34.26 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = % 229.76/34.26 v3) | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | % 229.76/34.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4))) % 229.76/34.26 % 229.76/34.26 (fact_ln__less__cancel__iff) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.26 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.26 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) % 229.76/34.26 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! [v1: $i] : % 229.76/34.26 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) % 229.76/34.26 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4))) % 229.76/34.26 % 229.76/34.26 (fact_ln__less__self) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.26 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.26 ! [v2: $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~ $i(v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1))) % 229.76/34.26 % 229.76/34.26 (fact_ln__less__zero) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.76/34.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | % 229.76/34.26 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0))) % 229.76/34.26 % 229.76/34.26 (fact_ln__less__zero__iff) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.76/34.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.26 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | % 229.76/34.26 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i] : % 229.76/34.26 ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0))) % 229.76/34.26 % 229.76/34.26 (fact_ln__mult) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.26 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.76/34.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.26 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 229.76/34.26 (c_Transcendental_Oln(v3) = v4) | ~ (c_Transcendental_Oln(v2) = v5) | ~ % 229.76/34.26 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~ $i(v3) | % 229.76/34.26 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | % 229.76/34.26 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7: $i] : % 229.76/34.26 ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7, v2) = v8 & hAPP(v1, % 229.76/34.26 v3) = v7 & $i(v8) & $i(v7) & $i(v6)))) % 229.76/34.26 % 229.76/34.26 (fact_ln__one) % 229.76/34.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : (c_Transcendental_Oln(v0) = % 229.76/34.26 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 229.76/34.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)) % 229.76/34.26 % 229.76/34.26 (fact_ln__realpow) % 229.76/34.26 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 229.76/34.26 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 & % 229.76/34.26 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & % 229.76/34.26 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) & % 229.76/34.26 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.26 : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) = v7) | ~ % 229.76/34.26 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6, v7) = v8) | ~ % 229.76/34.26 (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ % 229.76/34.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v9: $i] : ? % 229.76/34.26 [v10: $i] : (c_Transcendental_Oln(v10) = v8 & hAPP(v9, v3) = v10 & % 229.76/34.26 hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & $i(v8)))) % 229.76/34.26 % 229.76/34.26 (fact_minus__nat_Odiff__0) % 229.76/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 229.76/34.27 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 229.76/34.27 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1))) % 229.76/34.27 % 229.76/34.27 (fact_mult_Obounded) % 229.76/34.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.27 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 229.76/34.27 ! [v2: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~ % 229.76/34.27 class_RealVector_Oreal__normed__algebra(v1) | ? [v3: $i] : ($i(v3) & ! % 229.76/34.27 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! % 229.76/34.27 [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 229.76/34.27 (c_RealVector_Onorm__class_Onorm(v1, v5) = v8) | ~ % 229.76/34.27 (c_RealVector_Onorm__class_Onorm(v1, v4) = v6) | ~ (hAPP(v10, v3) = % 229.76/34.27 v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v0, v9) = v10) | ~ % 229.76/34.27 (hAPP(v0, v6) = v7) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i] : ? [v13: % 229.76/34.27 $i] : ? [v14: $i] : (c_RealVector_Onorm__class_Onorm(v1, v13) = v14 % 229.76/34.27 & hAPP(v12, v5) = v13 & hAPP(v2, v4) = v12 & $i(v14) & $i(v13) & % 229.76/34.27 $i(v12) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v14, % 229.76/34.27 v11)))))) % 229.76/34.27 % 229.76/34.27 (fact_mult_Ononneg__bounded) % 229.76/34.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.27 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.76/34.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.27 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ % 229.76/34.27 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] : % 229.76/34.27 ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & ! % 229.76/34.27 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 229.76/34.27 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 229.76/34.27 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~ % 229.76/34.27 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) = % 229.76/34.27 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~ % 229.76/34.27 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14: % 229.76/34.27 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 % 229.76/34.27 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) & % 229.76/34.27 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15, % 229.76/34.27 v12)))))) % 229.76/34.27 % 229.76/34.27 (fact_mult_Opos__bounded) % 229.76/34.27 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.27 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.76/34.27 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 229.76/34.27 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ % 229.76/34.27 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] : % 229.76/34.27 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! % 229.76/34.27 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 229.76/34.27 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 229.76/34.27 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~ % 229.76/34.27 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) = % 229.76/34.27 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~ % 229.76/34.27 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14: % 229.76/34.27 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 % 229.76/34.27 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) & % 229.76/34.27 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15, % 229.76/34.27 v12)))))) % 229.76/34.27 % 229.76/34.27 (fact_mult__0) % 229.76/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.76/34.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) & % 229.76/34.27 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v2, v3) = % 229.76/34.27 v4) | ~ $i(v3))) % 229.76/34.27 % 229.76/34.27 (fact_mult__0__right) % 229.76/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.27 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = % 229.76/34.27 v1)) % 229.76/34.27 % 229.76/34.27 (fact_mult__cancel1) % 229.76/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.27 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | % 229.76/34.27 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | % 229.76/34.27 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.27 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ % 229.76/34.27 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 229.76/34.27 $i(v2))) % 229.76/34.27 % 229.76/34.27 (fact_mult__cancel2) % 229.76/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.27 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.27 : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, % 229.76/34.27 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 229.76/34.27 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.27 : (v4 = v2 | v3 = v1 | ~ (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ % 229.76/34.27 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 229.76/34.27 $i(v2))) % 229.76/34.27 % 229.76/34.27 (fact_mult__eq__0__iff) % 229.76/34.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.27 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 229.76/34.27 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.76/34.27 class_Rings_Oring__no__zero__divisors(v2) | ? [v6: $i] : % 229.76/34.27 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = v5) | v5 = v1 | % 229.76/34.27 v5 = v0) & (v6 = v5 | ( ~ (v6 = v1) & ~ (v6 = v0))))) % 229.76/34.27 % 229.76/34.27 (fact_mult__eq__1__iff) % 229.76/34.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 229.76/34.27 v2 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & % 229.76/34.27 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v3) = v2) | % 229.76/34.27 ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: % 229.76/34.27 $i] : ! [v5: $i] : (v3 = v2 | ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = % 229.76/34.27 v5) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 229.76/34.27 (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v2) = v3))) % 229.76/34.27 % 229.76/34.27 (fact_mult__eq__if) % 229.76/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.76/34.28 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 229.76/34.28 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 229.76/34.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 229.76/34.28 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 229.76/34.28 $i] : (v4 = v0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = % 229.76/34.28 v5) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~ % 229.76/34.28 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ? % 229.76/34.28 [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & $i(v9) & $i(v8))) & ! % 229.76/34.28 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v0 | ~ (hAPP(v4, v3) = v5) | % 229.76/34.28 ~ (hAPP(v1, v0) = v4) | ~ $i(v3))) % 229.76/34.28 % 229.76/34.28 (fact_mult__eq__self__implies__10) % 229.76/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.76/34.28 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 229.76/34.28 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & % 229.76/34.28 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, % 229.76/34.28 v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 229.76/34.28 % 229.76/34.28 (fact_mult__is__0) % 229.76/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.28 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.28 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) = v4) | ~ % 229.76/34.28 (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 229.76/34.28 : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v0, v2) = v3) | ~ $i(v2)) & % 229.76/34.28 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, % 229.76/34.28 v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2))) % 229.76/34.28 % 229.76/34.28 (fact_mult__le__0__iff) % 229.76/34.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.28 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 229.76/34.28 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.76/34.28 class_Rings_Olinordered__ring__strict(v2) | ? [v6: $i] : % 229.76/34.28 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(v2, v5, v6) | % 229.76/34.28 (c_Orderings_Oord__class_Oless__eq(v2, v6, v1) & % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(v2, v0, v6)) | % 229.76/34.28 (c_Orderings_Oord__class_Oless__eq(v2, v6, v0) & % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(v2, v1, v6))) & % 229.76/34.28 (c_Orderings_Oord__class_Oless__eq(v2, v5, v6) | (( ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(v2, v6, v1) | ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(v2, v0, v6)) & ( ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(v2, v6, v0) | ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(v2, v1, v6)))))) % 229.76/34.28 % 229.76/34.28 (fact_mult__le__cancel1) % 229.76/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.28 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.28 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.28 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) % 229.76/34.28 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) | % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 229.76/34.28 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 229.76/34.28 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 229.76/34.28 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)) & ! [v2: $i] : ! % 229.76/34.28 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 229.76/34.28 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 229.76/34.28 $i(v4) | ~ $i(v3) | ~ $i(v2) | % 229.76/34.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7))) % 229.76/34.28 % 229.76/34.28 (fact_mult__le__cancel2) % 229.76/34.28 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.28 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.28 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.28 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ % 229.76/34.28 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 229.76/34.28 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) | % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : ! % 229.76/34.28 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 229.76/34.28 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 229.76/34.28 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) | % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)) & ! [v2: $i] : ! % 229.76/34.28 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 229.76/34.28 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 229.76/34.28 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 229.76/34.28 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 229.76/34.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8))) % 229.76/34.28 % 229.76/34.28 (fact_mult__left_Obounded) % 229.76/34.28 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 229.76/34.28 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] : % 229.76/34.28 ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | % 229.76/34.28 ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? % 229.76/34.28 [v4: $i] : ($i(v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 229.76/34.28 : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v7, v4) % 229.76/34.28 = v8) | ~ (hAPP(v0, v6) = v7) | ~ $i(v5) | ? [v9: $i] : ? [v10: % 229.76/34.28 $i] : ? [v11: $i] : (c_RealVector_Onorm__class_Onorm(v2, v10) = v11 % 229.76/34.28 & hAPP(v9, v1) = v10 & hAPP(v3, v5) = v9 & $i(v11) & $i(v10) & % 229.76/34.28 $i(v9) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 229.76/34.28 v8)))))) % 229.76/34.28 % 229.76/34.28 (fact_mult__left_Ononneg__bounded) % 229.76/34.29 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.29 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.76/34.29 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ? % 229.76/34.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.76/34.29 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.29 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) & % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) & ! [v6: % 229.76/34.29 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 229.76/34.29 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) = % 229.76/34.29 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11: % 229.76/34.29 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 % 229.76/34.29 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) & % 229.76/34.29 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 229.76/34.29 v9)))))) % 229.76/34.29 % 229.76/34.29 (fact_mult__left_Opos__bounded) % 229.76/34.29 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.29 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.76/34.29 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ? % 229.76/34.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.76/34.29 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.29 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) & % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v6: $i] : % 229.76/34.29 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 229.76/34.29 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) = % 229.76/34.29 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11: % 229.76/34.29 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 % 229.76/34.29 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) & % 229.76/34.29 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 229.76/34.29 v9)))))) % 229.76/34.29 % 229.76/34.29 (fact_mult__less__cancel1) % 229.76/34.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.29 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) % 229.76/34.29 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 229.76/34.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 229.76/34.29 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 229.76/34.29 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i] : ! % 229.76/34.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 229.76/34.29 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~ % 229.76/34.29 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 229.76/34.29 % 229.76/34.29 (fact_mult__less__cancel2) % 229.76/34.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 229.76/34.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.29 : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ % 229.76/34.29 (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 229.76/34.29 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : ! % 229.76/34.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 229.76/34.29 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 229.76/34.29 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] : ! % 229.76/34.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 229.76/34.29 $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) % 229.76/34.29 = v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 229.76/34.29 % 229.76/34.29 (fact_mult__less__mono1) % 229.76/34.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 229.76/34.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.29 : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5, v2) = v6) | ~ % 229.76/34.29 (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 229.76/34.29 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 229.76/34.29 % 229.76/34.29 (fact_mult__less__mono2) % 229.76/34.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 229.76/34.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 229.76/34.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 229.76/34.29 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 229.76/34.29 : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ (hAPP(v1, v2) = v5) % 229.76/34.29 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 229.76/34.29 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 229.76/34.29 % 229.76/34.29 (fact_mult__neg__neg) % 229.76/34.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.29 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 229.76/34.29 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.76/34.29 class_Rings_Olinordered__ring__strict(v2) | ? [v6: $i] : % 229.76/34.29 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(v2, v1, v6) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless(v2, v0, v6) | % 229.76/34.29 c_Orderings_Oord__class_Oless(v2, v6, v5)))) % 229.76/34.29 % 229.76/34.29 (fact_mult__nonneg__nonneg) % 229.76/34.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.29 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 229.76/34.29 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.76/34.29 class_Rings_Oordered__cancel__semiring(v2) | ? [v6: $i] : % 229.76/34.29 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v6, v1) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v6, v0) | % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v6, v5)))) % 229.76/34.29 % 229.76/34.29 (fact_mult__nonneg__nonpos) % 229.76/34.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.29 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 229.76/34.29 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.76/34.29 class_Rings_Oordered__cancel__semiring(v2) | ? [v6: $i] : % 229.76/34.29 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v6, v1) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v0, v6) | % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v5, v6)))) % 229.76/34.29 % 229.76/34.29 (fact_mult__nonneg__nonpos2) % 229.76/34.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.29 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v1) = v5) % 229.76/34.29 | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.76/34.29 class_Rings_Oordered__cancel__semiring(v2) | ? [v6: $i] : % 229.76/34.29 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v6, v1) | ~ % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v0, v6) | % 229.76/34.29 c_Orderings_Oord__class_Oless__eq(v2, v5, v6)))) % 229.76/34.29 % 229.76/34.29 (fact_mult__nonpos__nonpos) % 229.76/34.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.30 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 229.76/34.30 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.76/34.30 class_Rings_Oordered__ring(v2) | ? [v6: $i] : % 229.76/34.30 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 229.76/34.30 c_Orderings_Oord__class_Oless__eq(v2, v1, v6) | ~ % 229.76/34.30 c_Orderings_Oord__class_Oless__eq(v2, v0, v6) | % 229.76/34.30 c_Orderings_Oord__class_Oless__eq(v2, v6, v5)))) % 229.76/34.30 % 229.76/34.30 (fact_mult__pos__neg) % 229.76/34.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 229.76/34.30 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 229.76/34.30 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.76/34.30 class_Rings_Olinordered__semiring__strict(v2) | ? [v6: $i] : % 229.76/34.30 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 229.76/34.30 c_Orderings_Oord__class_Oless(v2, v6, v1) | ~ % 229.76/34.30 c_Orderings_Oord__class_Oless(v2, v0, v6) | % 229.76/34.30 c_Orderings_Oord__class_Oless(v2, v5, v6)))) % 229.76/34.30 % 229.76/34.30 (fact_mult__pos__neg2) % 230.10/34.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.30 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v1) = v5) % 230.10/34.30 | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.30 class_Rings_Olinordered__semiring__strict(v2) | ? [v6: $i] : % 230.10/34.30 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 230.10/34.30 c_Orderings_Oord__class_Oless(v2, v6, v1) | ~ % 230.10/34.30 c_Orderings_Oord__class_Oless(v2, v0, v6) | % 230.10/34.30 c_Orderings_Oord__class_Oless(v2, v5, v6)))) % 230.10/34.30 % 230.10/34.30 (fact_mult__pos__pos) % 230.10/34.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.30 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 230.10/34.30 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.30 class_Rings_Olinordered__semiring__strict(v2) | ? [v6: $i] : % 230.10/34.30 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 230.10/34.30 c_Orderings_Oord__class_Oless(v2, v6, v1) | ~ % 230.10/34.30 c_Orderings_Oord__class_Oless(v2, v6, v0) | % 230.10/34.30 c_Orderings_Oord__class_Oless(v2, v6, v5)))) % 230.10/34.30 % 230.10/34.30 (fact_mult__right_Obounded) % 230.10/34.30 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.30 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.30 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.10/34.30 (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 230.10/34.30 $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? % 230.10/34.30 [v5: $i] : ($i(v5) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 230.10/34.30 : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v6) = v7) | ~ (hAPP(v8, v5) % 230.10/34.30 = v9) | ~ (hAPP(v0, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11: % 230.10/34.30 $i] : (c_RealVector_Onorm__class_Onorm(v2, v10) = v11 & hAPP(v4, v6) % 230.10/34.30 = v10 & $i(v11) & $i(v10) & % 230.10/34.30 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, v9)))))) % 230.10/34.30 % 230.10/34.30 (fact_mult__right_Ononneg__bounded) % 230.10/34.30 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.30 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.10/34.30 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.10/34.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.30 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~ % 230.10/34.30 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ? % 230.10/34.30 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.10/34.30 v0, v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 230.10/34.30 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) = % 230.10/34.30 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12: % 230.10/34.30 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7) % 230.10/34.30 = v11 & $i(v12) & $i(v11) & % 230.10/34.30 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10)))))) % 230.10/34.30 % 230.10/34.30 (fact_mult__right_Opos__bounded) % 230.10/34.30 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.30 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.10/34.30 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.10/34.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.30 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~ % 230.10/34.30 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ? % 230.10/34.30 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 230.10/34.30 v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 230.10/34.30 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) = % 230.10/34.30 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12: % 230.10/34.30 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7) % 230.10/34.30 = v11 & $i(v12) & $i(v11) & % 230.10/34.30 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10)))))) % 230.10/34.30 % 230.10/34.30 (fact_n__less__m__mult__n) % 230.10/34.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 230.10/34.30 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 230.10/34.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 230.10/34.30 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) = % 230.10/34.30 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 230.10/34.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 230.10/34.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 230.10/34.30 % 230.10/34.30 (fact_n__less__n__mult__m) % 230.10/34.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 230.10/34.30 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 230.10/34.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 230.10/34.30 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = % 230.10/34.30 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 230.10/34.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 230.10/34.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 230.10/34.30 % 230.10/34.30 (fact_nat0__intermed__int__val) % 230.10/34.30 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.10/34.30 (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 & % 230.10/34.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 230.10/34.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & % 230.10/34.30 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v4, v5) = % 230.10/34.30 v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v6) | ? [v7: $i] : ? % 230.10/34.30 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 230.10/34.30 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ($i(v10) & $i(v8) & ((v9 = v3 & % 230.10/34.30 hAPP(v4, v8) = v3 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 230.10/34.30 v8, v5)) | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v12, v13) = % 230.10/34.30 v14 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v10, v0) = v11 & % 230.10/34.30 c_Groups_Oabs__class_Oabs(tc_Int_Oint, v14) = v15 & hAPP(v4, v11) = % 230.10/34.30 v12 & hAPP(v4, v10) = v13 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 230.10/34.30 $i(v11) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v5) & ~ % 230.10/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v15, v1)) | (hAPP(v4, % 230.10/34.30 v2) = v7 & $i(v7) & ~ % 230.10/34.30 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v7, v3)))))) % 230.10/34.30 % 230.10/34.30 (fact_nat_Osimps_I2_J) % 230.10/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.31 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 230.10/34.31 % 230.10/34.31 (fact_nat_Osimps_I3_J) % 230.10/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.31 & $i(v0) & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 230.10/34.31 % 230.10/34.31 (fact_nat__0__less__mult__iff) % 230.10/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.31 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.10/34.31 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | % 230.10/34.31 ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 230.10/34.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 230.10/34.31 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i] : ! % 230.10/34.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 230.10/34.31 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5))) % 230.10/34.31 % 230.10/34.31 (fact_nat__1__eq__mult__iff) % 230.10/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 230.10/34.31 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.31 $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = v0) | ~ % 230.10/34.31 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : % 230.10/34.31 ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | % 230.10/34.31 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.10/34.31 (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2))) % 230.10/34.31 % 230.10/34.31 (fact_nat__diff__split) % 230.10/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.31 $i] : ! [v6: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 230.10/34.31 v1) = v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2) % 230.10/34.31 | ~ (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 230.10/34.31 ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) & hBOOL(v7))) & % 230.10/34.31 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.31 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 230.10/34.31 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v5) | ~ % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] : % 230.10/34.31 (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! [v1: $i] : ! [v2: $i] : ! % 230.10/34.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.31 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 230.10/34.31 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] : ? [v7: % 230.10/34.31 $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3, % 230.10/34.31 v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : ! [v2: % 230.10/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.31 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 230.10/34.31 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | ? [v6: % 230.10/34.31 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ((v8 = v2 & % 230.10/34.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v7) = v2 & hAPP(v3, v7) % 230.10/34.31 = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, v0) = v6 & $i(v6) & ~ % 230.10/34.31 hBOOL(v6)))))) % 230.10/34.31 % 230.10/34.31 (fact_nat__diff__split__asm) % 230.10/34.31 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.31 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.31 $i] : ! [v6: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 230.10/34.31 v1) = v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2) % 230.10/34.31 | ~ (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 230.10/34.31 ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) & hBOOL(v7))) & % 230.10/34.31 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.31 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 230.10/34.31 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v5) | ~ % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] : % 230.10/34.31 (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! [v1: $i] : ! [v2: $i] : ! % 230.10/34.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.31 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 230.10/34.31 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v6: $i] : ? [v7: % 230.10/34.31 $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3, % 230.10/34.31 v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : ! [v2: % 230.10/34.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.31 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ (hAPP(v3, % 230.10/34.31 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v5) | ? [v6: % 230.10/34.31 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ((v8 = v2 & % 230.10/34.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v7) = v2 & hAPP(v3, v7) % 230.10/34.31 = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, v0) = v6 & $i(v6) & ~ % 230.10/34.31 hBOOL(v6)))))) % 230.10/34.31 % 230.10/34.31 (fact_nat__le__real__less) % 230.10/34.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.31 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 230.10/34.31 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) % 230.10/34.31 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ % 230.10/34.31 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? % 230.10/34.31 [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 & % 230.10/34.31 $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))) & ! % 230.10/34.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.10/34.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, % 230.10/34.31 v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 230.10/34.31 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: $i] : % 230.10/34.31 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 & $i(v5) & ~ % 230.10/34.31 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5)))) % 230.10/34.31 % 230.10/34.31 (fact_nat__less__real__le) % 230.10/34.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 230.10/34.32 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) % 230.10/34.32 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ % 230.10/34.32 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: % 230.10/34.32 $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & % 230.10/34.32 $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))) & % 230.10/34.32 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.10/34.32 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, % 230.10/34.32 v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] : % 230.10/34.32 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) & ~ % 230.10/34.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4)))) % 230.10/34.32 % 230.10/34.32 (fact_nat__lt__two__imp__zero__or__one) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 230.10/34.32 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.10/34.32 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ $i(v3) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__1) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.10/34.32 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.10/34.32 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 & $i(v2) % 230.10/34.32 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3) % 230.10/34.32 = v4) | ~ $i(v3))) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__1__right) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.32 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.10/34.32 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = % 230.10/34.32 v2)) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__div__cancel1) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.32 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.10/34.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.10/34.32 : ! [v8: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) | % 230.10/34.32 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | % 230.10/34.32 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.10/34.32 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8)))) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__div__cancel__disj) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.32 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.10/34.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.10/34.32 : ! [v8: $i] : (v4 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, % 230.10/34.32 v7) = v8) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.10/34.32 (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 230.10/34.32 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8))) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.10/34.32 : (v7 = v0 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v6) = v7) | ~ % 230.10/34.32 (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v1, v0) = v4) | ~ % 230.10/34.32 $i(v3) | ~ $i(v2))) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__eq__1__iff) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.32 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.10/34.32 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = v1) | ~ % 230.10/34.32 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : % 230.10/34.32 ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | % 230.10/34.32 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 230.10/34.32 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2))) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__eq__cancel1) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.32 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.10/34.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | % 230.10/34.32 ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | % 230.10/34.32 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__eq__cancel__disj) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.32 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.10/34.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | % 230.10/34.32 ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v0, v1) = v4) | % 230.10/34.32 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.32 $i] : ! [v6: $i] : (v4 = v1 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ % 230.10/34.32 (hAPP(v5, v2) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.32 $i(v2))) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__le__cancel1) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.32 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.10/34.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.10/34.32 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 230.10/34.32 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) | % 230.10/34.32 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 230.10/34.32 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 230.10/34.32 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ % 230.10/34.32 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 230.10/34.32 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7))) % 230.10/34.32 % 230.10/34.32 (fact_nat__mult__less__cancel1) % 230.10/34.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.32 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.10/34.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.32 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.10/34.32 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 230.10/34.32 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] : ! % 230.10/34.32 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 230.10/34.32 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ % 230.10/34.32 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.10/34.32 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 230.10/34.32 % 230.10/34.32 (fact_nat__one__le__power) % 230.10/34.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 230.10/34.33 v1 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & % 230.10/34.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 230.10/34.33 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = % 230.10/34.33 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) | % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6))) % 230.10/34.33 % 230.10/34.33 (fact_nat__power__eq__Suc__0__iff) % 230.10/34.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 230.10/34.33 v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 230.10/34.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & % 230.10/34.33 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v3) = v5) | % 230.10/34.33 ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.33 $i] : (v5 = v2 | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, v3) = v4) | ~ % 230.10/34.33 $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | % 230.10/34.33 ~ (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 230.10/34.33 % 230.10/34.33 (fact_nat__power__less__imp__less) % 230.10/34.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.33 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 230.10/34.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.33 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.10/34.33 : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) % 230.10/34.33 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.10/34.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 230.10/34.33 % 230.10/34.33 (fact_nat__zero__less__power__iff) % 230.10/34.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.33 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 230.10/34.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.33 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4, % 230.10/34.33 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 230.10/34.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 230.10/34.33 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 230.10/34.33 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 230.10/34.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : ! % 230.10/34.33 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) | % 230.10/34.33 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 230.10/34.33 % 230.10/34.33 (fact_natceiling__add) % 230.10/34.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.33 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, % 230.10/34.33 v1) = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) % 230.10/34.33 = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v5: $i] % 230.10/34.33 : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 & % 230.10/34.33 c_RComplete_Onatceiling(v2) = v6 & % 230.10/34.33 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) & % 230.10/34.33 $i(v5)))) % 230.10/34.33 % 230.10/34.33 (fact_natceiling__add__one) % 230.10/34.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 230.10/34.33 $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 230.10/34.33 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.10/34.33 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) & % 230.10/34.33 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 230.10/34.33 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) | % 230.10/34.33 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5: % 230.10/34.33 $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 & % 230.10/34.33 c_RComplete_Onatceiling(v3) = v6 & % 230.10/34.33 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) & % 230.10/34.33 $i(v5)))) % 230.10/34.33 % 230.10/34.33 (fact_natceiling__eq) % 230.10/34.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.33 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.10/34.33 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.33 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 230.10/34.33 (c_RComplete_Onatceiling(v2) = v4) | ~ % 230.10/34.33 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~ $i(v3) | ~ % 230.10/34.33 $i(v2) | ? [v6: $i] : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v3) = % 230.10/34.33 v6 & $i(v6) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, % 230.10/34.33 v2) | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 & % 230.10/34.33 $i(v7) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 230.10/34.33 v7)))))) % 230.10/34.33 % 230.10/34.33 (fact_natceiling__le__eq) % 230.10/34.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.33 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, % 230.10/34.33 v1) = v4) | ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ % 230.10/34.33 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4)) & ! [v1: $i] % 230.10/34.33 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.10/34.33 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ (c_RComplete_Onatceiling(v2) % 230.10/34.33 = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1))) % 230.10/34.33 % 230.10/34.33 (fact_natceiling__le__eq__one) % 230.10/34.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.33 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 230.10/34.33 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.33 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | % 230.10/34.33 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) | % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i] % 230.10/34.33 : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | % 230.10/34.33 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0))) % 230.10/34.33 % 230.10/34.33 (fact_natceiling__neg) % 230.10/34.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.33 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 230.10/34.33 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.10/34.33 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_RComplete_Onatceiling(v2) = v3) | % 230.10/34.33 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 230.10/34.33 v0))) % 230.10/34.33 % 230.10/34.33 (fact_natceiling__one) % 230.10/34.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.33 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.10/34.33 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 230.10/34.33 % 230.10/34.33 (fact_natceiling__zero) % 230.10/34.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.33 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = % 230.10/34.33 v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 230.10/34.33 % 230.10/34.33 (fact_natfloor__add) % 230.10/34.34 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.34 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, % 230.10/34.34 v1) = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) % 230.10/34.34 = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v5: $i] % 230.10/34.34 : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 & % 230.10/34.34 c_RComplete_Onatfloor(v2) = v6 & % 230.10/34.34 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) & % 230.10/34.34 $i(v5)))) % 230.10/34.34 % 230.10/34.34 (fact_natfloor__add__one) % 230.10/34.34 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 230.10/34.34 $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 230.10/34.34 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.10/34.34 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) & % 230.10/34.34 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 230.10/34.34 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) | % 230.10/34.34 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5: % 230.10/34.34 $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 & % 230.10/34.34 c_RComplete_Onatfloor(v3) = v6 & % 230.10/34.34 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) & % 230.10/34.34 $i(v5)))) % 230.10/34.34 % 230.10/34.34 (fact_natfloor__eq) % 230.10/34.34 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.34 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 230.10/34.34 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 230.10/34.34 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RComplete_Onatfloor(v1) = % 230.10/34.34 v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? [v5: $i] % 230.10/34.34 : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) & % 230.10/34.34 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5)))) % 230.10/34.34 % 230.10/34.34 (fact_natfloor__neg) % 230.10/34.34 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 230.10/34.34 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.10/34.34 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ % 230.10/34.34 $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 230.10/34.34 % 230.10/34.34 (fact_natfloor__one) % 230.10/34.34 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.34 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 % 230.10/34.34 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 230.10/34.34 % 230.10/34.34 (fact_natfloor__zero) % 230.10/34.34 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.34 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = % 230.10/34.34 v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 230.10/34.34 % 230.10/34.34 (fact_neg__0__equal__iff__equal) % 230.10/34.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 230.10/34.34 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.34 class_Groups_Ogroup__add(v1) | ? [v3: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) & % 230.10/34.34 ( ~ (v3 = v0) | v2 = v0))) % 230.10/34.34 % 230.10/34.34 (fact_neg__0__le__iff__le) % 230.10/34.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 230.10/34.34 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.34 class_Groups_Oordered__ab__group__add(v1) | ? [v3: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(v1, v3, v2) | % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(v1, v0, v3)) & ( ~ % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(v1, v0, v3) | % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(v1, v3, v2)))) % 230.10/34.34 % 230.10/34.34 (fact_neg__0__less__iff__less) % 230.10/34.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 230.10/34.34 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.34 class_Groups_Oordered__ab__group__add(v1) | ? [v3: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ % 230.10/34.34 c_Orderings_Oord__class_Oless(v1, v3, v2) | % 230.10/34.34 c_Orderings_Oord__class_Oless(v1, v0, v3)) & ( ~ % 230.10/34.34 c_Orderings_Oord__class_Oless(v1, v0, v3) | % 230.10/34.34 c_Orderings_Oord__class_Oless(v1, v3, v2)))) % 230.10/34.34 % 230.10/34.34 (fact_neg__equal__0__iff__equal) % 230.10/34.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 230.10/34.34 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.34 class_Groups_Ogroup__add(v1) | ? [v3: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v2) | v2 = v0) & % 230.10/34.34 ( ~ (v3 = v0) | v2 = v0))) % 230.10/34.34 % 230.10/34.34 (fact_neg__equal__zero) % 230.10/34.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 230.10/34.34 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.34 class_Groups_Olinordered__ab__group__add(v1) | ? [v3: $i] : (( ~ (v2 = v0) % 230.10/34.34 | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1) = v0)) & (v2 = v0 | ( ~ (v3 % 230.10/34.34 = v0) & c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3))))) % 230.10/34.34 % 230.10/34.34 (fact_neg__le__0__iff__le) % 230.10/34.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 230.10/34.34 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.34 class_Groups_Oordered__ab__group__add(v1) | ? [v3: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(v1, v3, v0) | % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(v1, v2, v3)) & ( ~ % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(v1, v2, v3) | % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(v1, v3, v0)))) % 230.10/34.34 % 230.10/34.34 (fact_neg__less__0__iff__less) % 230.10/34.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 230.10/34.34 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.34 class_Groups_Oordered__ab__group__add(v1) | ? [v3: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ % 230.10/34.34 c_Orderings_Oord__class_Oless(v1, v3, v0) | % 230.10/34.34 c_Orderings_Oord__class_Oless(v1, v2, v3)) & ( ~ % 230.10/34.34 c_Orderings_Oord__class_Oless(v1, v2, v3) | % 230.10/34.34 c_Orderings_Oord__class_Oless(v1, v3, v0)))) % 230.10/34.34 % 230.10/34.34 (fact_neq0__conv) % 230.10/34.34 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.34 & $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1: % 230.10/34.34 $i] : (v1 = v0 | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 230.10/34.34 v0, v1))) % 230.10/34.34 % 230.10/34.34 (fact_no__zero__divisors) % 230.10/34.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.34 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 230.10/34.34 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.10/34.34 class_Rings_Ono__zero__divisors(v2) | ? [v6: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = v5) | v5 = v1 | % 230.10/34.34 v5 = v0))) % 230.10/34.34 % 230.10/34.34 (fact_norm__eq__zero) % 230.10/34.34 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.34 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) = % 230.10/34.34 v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.34 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~ (v3 = v0) % 230.10/34.34 | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = v1)) & (v3 = v0 | ( ~ % 230.10/34.34 (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4)))))) % 230.10/34.34 % 230.10/34.34 (fact_norm__ge__zero) % 230.10/34.34 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.34 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.34 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) = % 230.10/34.34 v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.34 class_RealVector_Oreal__normed__vector(v2) | % 230.10/34.34 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3))) % 230.10/34.34 % 230.10/34.34 (fact_norm__le__zero__iff) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.35 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.35 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) = % 230.10/34.35 v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.35 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~ % 230.10/34.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | (v4 = v1 % 230.10/34.35 & c_Groups_Ozero__class_Ozero(v2) = v1)) & % 230.10/34.35 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | ( ~ (v4 = % 230.10/34.35 v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4)))))) % 230.10/34.35 % 230.10/34.35 (fact_norm__mult) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.35 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.10/34.35 [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v2) = v4) | ~ % 230.10/34.35 (c_RealVector_Onorm__class_Onorm(v3, v1) = v6) | ~ (hAPP(v5, v6) = v7) | % 230.10/34.35 ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.35 class_RealVector_Oreal__normed__div__algebra(v3) | ? [v8: $i] : ? [v9: % 230.10/34.35 $i] : ? [v10: $i] : (c_Groups_Otimes__class_Otimes(v3) = v8 & % 230.10/34.35 c_RealVector_Onorm__class_Onorm(v3, v10) = v7 & hAPP(v9, v1) = v10 & % 230.10/34.35 hAPP(v8, v2) = v9 & $i(v10) & $i(v9) & $i(v8) & $i(v7)))) % 230.10/34.35 % 230.10/34.35 (fact_norm__mult__ineq) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.35 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.10/34.35 [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v2) = v4) | ~ % 230.10/34.35 (c_RealVector_Onorm__class_Onorm(v3, v1) = v6) | ~ (hAPP(v5, v6) = v7) | % 230.10/34.35 ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.35 class_RealVector_Oreal__normed__algebra(v3) | ? [v8: $i] : ? [v9: $i] : % 230.10/34.35 ? [v10: $i] : ? [v11: $i] : (c_Groups_Otimes__class_Otimes(v3) = v8 & % 230.10/34.35 c_RealVector_Onorm__class_Onorm(v3, v10) = v11 & hAPP(v9, v1) = v10 & % 230.10/34.35 hAPP(v8, v2) = v9 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 230.10/34.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, v7)))) % 230.10/34.35 % 230.10/34.35 (fact_norm__mult__less) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.35 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.10/34.35 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 230.10/34.35 (c_Groups_Otimes__class_Otimes(v5) = v6) | ~ % 230.10/34.35 (c_RealVector_Onorm__class_Onorm(v5, v8) = v9) | ~ (hAPP(v10, v1) = v11) % 230.10/34.35 | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v0, v3) = % 230.10/34.35 v10) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.35 class_RealVector_Oreal__normed__algebra(v5) | % 230.10/34.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v11) | ? [v12: $i] : % 230.10/34.35 ? [v13: $i] : ((c_RealVector_Onorm__class_Onorm(v5, v4) = v12 & $i(v12) & % 230.10/34.35 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v3)) | % 230.10/34.35 (c_RealVector_Onorm__class_Onorm(v5, v2) = v13 & $i(v13) & ~ % 230.10/34.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v1))))) % 230.10/34.35 % 230.10/34.35 (fact_norm__not__less__zero) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.35 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.35 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) = % 230.10/34.35 v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.35 class_RealVector_Oreal__normed__vector(v2) | ~ % 230.10/34.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0))) % 230.10/34.35 % 230.10/34.35 (fact_norm__one) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.35 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 230.10/34.35 [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Groups_Oone__class_Oone(v1) = v2) % 230.10/34.35 | ~ (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~ % 230.10/34.35 class_RealVector_Oreal__normed__algebra__1(v1))) % 230.10/34.35 % 230.10/34.35 (fact_norm__ratiotest__lemma) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.35 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.10/34.35 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.10/34.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.10/34.35 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v5, % 230.10/34.35 v3) = v6) | ~ (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~ % 230.10/34.35 (hAPP(v7, v8) = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~ % 230.10/34.35 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v5) | ~ % 230.10/34.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) | ~ % 230.10/34.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) | % 230.10/34.35 c_Groups_Ozero__class_Ozero(v5) = v3)) % 230.10/34.35 % 230.10/34.35 (fact_norm__sgn) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.35 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.10/34.35 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.10/34.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.35 (c_Groups_Osgn__class_Osgn(v3, v2) = v4) | ~ % 230.10/34.35 (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | % 230.10/34.35 ~ class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ((v5 = v1 | % 230.10/34.35 (v6 = v2 & c_Groups_Ozero__class_Ozero(v3) = v2)) & (v5 = v0 | ( ~ (v6 % 230.10/34.35 = v2) & c_Groups_Ozero__class_Ozero(v3) = v6 & $i(v6)))))) % 230.10/34.35 % 230.10/34.35 (fact_norm__zero) % 230.10/34.35 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.35 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.35 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Groups_Ozero__class_Ozero(v1) = % 230.10/34.35 v2) | ~ (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~ % 230.10/34.35 class_RealVector_Oreal__normed__vector(v1))) % 230.10/34.35 % 230.10/34.35 (fact_not__less0) % 230.10/34.35 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.35 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 230.10/34.35 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 230.10/34.35 % 230.10/34.35 (fact_not__one__le__zero) % 230.10/34.35 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 230.10/34.35 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 230.10/34.35 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~ % 230.10/34.35 c_Orderings_Oord__class_Oless__eq(v0, v1, v2))) % 230.10/34.35 % 230.10/34.35 (fact_not__one__less__zero) % 230.10/34.35 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 230.10/34.35 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 230.10/34.35 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~ % 230.10/34.35 c_Orderings_Oord__class_Oless(v0, v1, v2))) % 230.10/34.35 % 230.10/34.35 (fact_not__real__of__nat__less__zero) % 230.10/34.35 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.35 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.35 ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ~ % 230.10/34.35 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0))) % 230.10/34.35 % 230.10/34.35 (fact_not__real__square__gt__zero) % 230.10/34.36 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.36 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.10/34.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.10/34.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3, v2) = v4) | % 230.10/34.36 ~ (hAPP(v1, v2) = v3) | ~ $i(v2) | % 230.10/34.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2: $i] : % 230.10/34.36 ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2) | ~ % 230.10/34.36 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))) % 230.10/34.36 % 230.10/34.36 (fact_one__is__add) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 230.10/34.36 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.10/34.36 $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 230.10/34.36 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 230.10/34.36 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = v1 | ~ % 230.10/34.36 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 230.10/34.36 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | v2 = v0 | ~ % 230.10/34.36 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 230.10/34.36 $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v2 = v0 | ~ % 230.10/34.36 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ $i(v3) | ~ % 230.10/34.36 $i(v2)) & ! [v2: $i] : (v2 = v1 | ~ % 230.10/34.36 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! [v2: $i] : % 230.10/34.36 (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2))) % 230.10/34.36 % 230.10/34.36 (fact_one__le__mult__iff) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 230.10/34.36 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 230.10/34.36 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 230.10/34.36 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = % 230.10/34.36 v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.36 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) | % 230.10/34.36 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)) & ! [v3: $i] : ! % 230.10/34.36 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ % 230.10/34.36 (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.36 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6) | % 230.10/34.36 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) & ! [v3: $i] : ! % 230.10/34.36 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ % 230.10/34.36 (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.36 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4) | ~ % 230.10/34.36 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | % 230.10/34.36 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6))) % 230.10/34.36 % 230.10/34.36 (fact_one__less__mult) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = % 230.10/34.36 v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 230.10/34.36 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & % 230.10/34.36 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v4) = % 230.10/34.36 v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.10/34.36 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 230.10/34.36 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 230.10/34.36 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6))) % 230.10/34.36 % 230.10/34.36 (fact_one__less__power) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.36 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.36 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 230.10/34.36 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.36 $i(v1) | ~ class_Rings_Olinordered__semidom(v3) | ~ % 230.10/34.36 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v7: $i] : % 230.10/34.36 (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~ % 230.10/34.36 c_Orderings_Oord__class_Oless(v3, v7, v2) | % 230.10/34.36 c_Orderings_Oord__class_Oless(v3, v7, v6))))) % 230.10/34.36 % 230.10/34.36 (fact_order__root) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.36 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.36 $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = v5) | ~ % 230.10/34.36 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Oidom(v3) | ? [v6: $i] : % 230.10/34.36 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) & % 230.10/34.36 c_Polynomial_Oorder(v3, v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7 % 230.10/34.36 & c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | (v6 = v5 % 230.10/34.36 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & ((v8 = v2 & % 230.10/34.36 tc_Polynomial_Opoly(v3) = v7 & c_Groups_Ozero__class_Ozero(v7) = v2 % 230.10/34.36 & $i(v7)) | ( ~ (v9 = v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & % 230.10/34.36 $i(v9)) | ( ~ (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 & % 230.10/34.36 $i(v6)))))) % 230.10/34.36 % 230.10/34.36 (fact_pCons) % 230.10/34.36 $i(v_cs____) & $i(v_r) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? % 230.10/34.36 [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.10/34.36 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v1 & % 230.10/34.36 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) & % 230.10/34.36 $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) & ! [v3: % 230.10/34.36 $i] : ! [v4: $i] : ( ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? % 230.10/34.36 [v6: $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = v6 % 230.10/34.36 & $i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, % 230.10/34.36 v2)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = % 230.10/34.36 v5 & $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.10/34.36 v5, v_r))))) % 230.10/34.36 % 230.10/34.36 (fact_plus__nat_Oadd__0) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.36 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 230.10/34.36 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1))) % 230.10/34.36 % 230.10/34.36 (fact_power_Opower_Opower__0) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.36 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.36 $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) | ~ % 230.10/34.36 (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 230.10/34.36 hAPP(v6, v0) = v3)) % 230.10/34.36 % 230.10/34.36 (fact_power__0) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.36 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.10/34.36 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 230.10/34.36 $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] : % 230.10/34.36 (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & $i(v5)))) % 230.10/34.36 % 230.10/34.36 (fact_power__0__left) % 230.10/34.36 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.36 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.36 $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~ % 230.10/34.36 (c_Power_Opower__class_Opower(v2) = v3) | ~ % 230.10/34.36 (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | ~ % 230.10/34.36 (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.36 class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2)) & ! [v1: $i] : % 230.10/34.36 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.10/34.36 (c_Power_Opower__class_Opower(v1) = v2) | ~ % 230.10/34.36 (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | ~ % 230.10/34.36 (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ class_Rings_Osemiring__0(v1) | ~ % 230.10/34.36 class_Power_Opower(v1) | (c_Groups_Oone__class_Oone(v1) = v5 & $i(v5)))) % 230.10/34.36 % 230.10/34.36 (fact_power__Suc__0) % 230.10/34.37 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 230.10/34.37 (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 230.10/34.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 & $i(v3) & % 230.10/34.37 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ % 230.10/34.37 (hAPP(v3, v4) = v5) | ~ $i(v4))) % 230.10/34.37 % 230.10/34.37 (fact_power__eq__0__iff) % 230.10/34.37 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.37 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.37 $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ % 230.10/34.37 (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.37 $i(v1) | ~ class_Power_Opower(v3) | ~ class_Rings_Ozero__neq__one(v3) | % 230.10/34.37 ~ class_Rings_Omult__zero(v3) | ~ class_Rings_Ono__zero__divisors(v3) | % 230.10/34.37 ? [v7: $i] : (c_Groups_Ozero__class_Ozero(v3) = v7 & $i(v7) & ( ~ (v7 = % 230.10/34.37 v6) | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2) | v6 = v2 | v1 = % 230.10/34.37 v0)))) % 230.10/34.37 % 230.10/34.37 (fact_power__eq__if) % 230.10/34.37 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 230.10/34.37 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 230.10/34.37 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 230.10/34.37 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 & % 230.10/34.37 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & $i(v1) & % 230.10/34.37 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 230.10/34.37 : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~ % 230.10/34.37 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ (hAPP(v7, % 230.10/34.37 v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = v7) | ~ % 230.10/34.37 (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, v5) = v10 & % 230.10/34.37 $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | ~ % 230.10/34.37 (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4))) % 230.10/34.37 % 230.10/34.37 (fact_power__eq__imp__eq__base) % 230.10/34.37 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.37 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.37 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ % 230.10/34.37 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v2) = v7) | ~ % 230.10/34.37 (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v1) = v8) | ~ % 230.10/34.37 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.37 class_Rings_Olinordered__semidom(v4) | ~ % 230.10/34.37 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v9: $i] : % 230.10/34.37 (c_Groups_Ozero__class_Ozero(v4) = v9 & $i(v9) & ( ~ % 230.10/34.37 c_Orderings_Oord__class_Oless__eq(v4, v9, v3) | ~ % 230.10/34.37 c_Orderings_Oord__class_Oless__eq(v4, v9, v1))))) % 230.10/34.37 % 230.10/34.37 (fact_power__strict__mono) % 230.10/34.37 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.10/34.37 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.10/34.37 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 230.10/34.37 (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9) | ~ % 230.10/34.37 (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v8) | ~ % 230.10/34.37 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.10/34.37 class_Rings_Olinordered__semidom(v4) | ~ % 230.10/34.37 c_Orderings_Oord__class_Oless(v4, v3, v2) | ~ % 230.10/34.37 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 230.10/34.37 c_Orderings_Oord__class_Oless(v4, v7, v9) | ? [v10: $i] : % 230.10/34.37 (c_Groups_Ozero__class_Ozero(v4) = v10 & $i(v10) & ~ % 230.10/34.37 c_Orderings_Oord__class_Oless__eq(v4, v10, v3)))) % 230.10/34.37 % 230.10/34.37 (fact_rabs__ratiotest__lemma) % 230.10/34.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.10/34.37 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.10/34.37 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.10/34.37 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.10/34.37 $i] : ! [v8: $i] : (v3 = v0 | ~ % 230.10/34.37 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v5) | ~ % 230.10/34.37 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v7) | ~ (hAPP(v6, v7) % 230.10/34.37 = v8) | ~ (hAPP(v1, v4) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.10/34.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v8) | ~ % 230.10/34.37 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0))) % 230.10/34.37 % 230.10/34.37 (fact_real__0__le__add__iff) % 230.10/34.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.37 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.37 ! [v2: $i] : ! [v3: $i] : ( ~ % 230.10/34.37 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.10/34.37 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) % 230.10/34.37 | ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = % 230.10/34.37 v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, % 230.10/34.37 v1))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.10/34.37 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.10/34.37 ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 230.10/34.37 ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & % 230.10/34.37 $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, % 230.10/34.37 v1)))) % 230.10/34.37 % 230.10/34.37 (fact_real__0__less__add__iff) % 230.10/34.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.10/34.37 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.10/34.37 ! [v2: $i] : ! [v3: $i] : ( ~ % 230.10/34.37 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.10/34.37 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | % 230.10/34.37 ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & % 230.10/34.37 $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v1))) & ! % 230.10/34.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.10/34.37 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.10/34.37 ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? % 230.10/34.37 [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & % 230.10/34.37 $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v1)))) % 230.10/34.37 % 230.10/34.37 (fact_real__abs__def) % 230.41/34.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.37 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.37 ! [v2: $i] : (v2 = v1 | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) % 230.41/34.37 = v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, % 230.41/34.37 v0)) & ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.37 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1) | ~ % 230.41/34.37 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | % 230.41/34.37 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 & $i(v2)))) % 230.41/34.37 % 230.41/34.37 (fact_real__add__eq__0__iff) % 230.41/34.37 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.37 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.37 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.41/34.37 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.41/34.37 ~ $i(v1) | ? [v4: $i] : ( ~ (v4 = v1) & % 230.41/34.37 c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & $i(v4))) & % 230.41/34.37 ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.37 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v0) | ~ $i(v2) | % 230.41/34.37 ~ $i(v1) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v1)) % 230.41/34.37 % 230.41/34.37 (fact_real__add__le__0__iff) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.38 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.38 ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.38 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.41/34.38 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) % 230.41/34.38 | ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = % 230.41/34.38 v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, % 230.41/34.38 v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.38 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.41/34.38 ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | % 230.41/34.38 ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & % 230.41/34.38 $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, % 230.41/34.38 v4)))) % 230.41/34.38 % 230.41/34.38 (fact_real__add__less__0__iff) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.38 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.38 ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.38 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.41/34.38 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | % 230.41/34.38 ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & % 230.41/34.38 $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))) & ! % 230.41/34.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.38 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) | % 230.41/34.38 ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ? % 230.41/34.38 [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & % 230.41/34.38 $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4)))) % 230.41/34.38 % 230.41/34.38 (fact_real__add__minus__iff) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.38 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.38 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.41/34.38 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2) | ~ % 230.41/34.38 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~ $i(v1)) % 230.41/34.38 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 230.41/34.38 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v3) | ~ % 230.41/34.38 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v0) | ~ $i(v2) | % 230.41/34.38 ~ $i(v1))) % 230.41/34.38 % 230.41/34.38 (fact_real__add__mult__distrib) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.38 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.38 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.38 [v7: $i] : ! [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, % 230.41/34.38 v5, v7) = v8) | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~ % 230.41/34.38 (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.38 $i(v1) | ? [v9: $i] : ? [v10: $i] : % 230.41/34.38 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v2) = v9 & hAPP(v10, % 230.41/34.38 v1) = v8 & hAPP(v0, v9) = v10 & $i(v10) & $i(v9) & $i(v8)))) % 230.41/34.38 % 230.41/34.38 (fact_real__le__eq__diff) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.38 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.38 ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.38 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) % 230.41/34.38 | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, % 230.41/34.38 v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! % 230.41/34.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.38 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) % 230.41/34.38 | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 230.41/34.38 v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0))) % 230.41/34.38 % 230.41/34.38 (fact_real__minus__mult__self__le) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.38 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.38 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 230.41/34.38 (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v2) = v3) | ~ % 230.41/34.38 (hAPP(v0, v1) = v5) | ~ $i(v2) | ~ $i(v1) | ? [v7: $i] : % 230.41/34.38 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v4) = v7 & $i(v7) & % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v6)))) % 230.41/34.38 % 230.41/34.38 (fact_real__mult__1) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.38 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.38 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v0, v1) = v2 & % 230.41/34.38 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ % 230.41/34.38 (hAPP(v2, v3) = v4) | ~ $i(v3))) % 230.41/34.38 % 230.41/34.38 (fact_real__mult__assoc) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.38 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.38 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.38 [v7: $i] : ( ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v0, % 230.41/34.38 v5) = v6) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 230.41/34.38 | ? [v8: $i] : ? [v9: $i] : (hAPP(v8, v1) = v9 & hAPP(v4, v9) = v7 & % 230.41/34.38 hAPP(v0, v2) = v8 & $i(v9) & $i(v8) & $i(v7)))) % 230.41/34.38 % 230.41/34.38 (fact_real__mult__commute) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.38 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.38 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) | ~ % 230.41/34.38 (hAPP(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : (hAPP(v5, v1) % 230.41/34.38 = v4 & hAPP(v0, v2) = v5 & $i(v5) & $i(v4)))) % 230.41/34.38 % 230.41/34.38 (fact_real__mult__le__cancel__iff1) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.38 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.38 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.38 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ % 230.41/34.38 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 230.41/34.38 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) | % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i] % 230.41/34.38 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 230.41/34.38 [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, % 230.41/34.38 v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 230.41/34.38 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8))) % 230.41/34.38 % 230.41/34.38 (fact_real__mult__le__cancel__iff2) % 230.41/34.38 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.38 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.38 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.38 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) % 230.41/34.38 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) | % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i] % 230.41/34.38 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 230.41/34.38 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~ % 230.41/34.38 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.38 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | % 230.41/34.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7))) % 230.41/34.38 % 230.41/34.38 (fact_real__mult__left__cancel) % 230.41/34.39 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.39 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.39 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.39 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v0 % 230.41/34.39 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, % 230.41/34.39 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 230.41/34.39 % 230.41/34.39 (fact_real__mult__less__iff1) % 230.41/34.39 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.39 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.39 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.39 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.39 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ % 230.41/34.39 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 230.41/34.39 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i] : % 230.41/34.39 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 230.41/34.39 $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) % 230.41/34.39 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8))) % 230.41/34.39 % 230.41/34.39 (fact_real__mult__less__mono2) % 230.41/34.39 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.39 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.39 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.39 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.39 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) % 230.41/34.39 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7))) % 230.41/34.39 % 230.41/34.39 (fact_real__mult__order) % 230.41/34.39 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.39 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.39 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.39 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 230.41/34.39 | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5))) % 230.41/34.39 % 230.41/34.39 (fact_real__mult__right__cancel) % 230.41/34.39 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.39 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.39 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.39 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.39 $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) | ~ (hAPP(v5, v4) = v6) % 230.41/34.39 | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) % 230.41/34.39 | ~ $i(v2))) % 230.41/34.39 % 230.41/34.39 (fact_real__natceiling__ge) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ( ~ % 230.41/34.39 (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 230.41/34.39 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v2) & % 230.41/34.39 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2))) % 230.41/34.39 % 230.41/34.39 (fact_real__natfloor__add__one__gt) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.39 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 230.41/34.39 [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 230.41/34.39 ? [v4: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & % 230.41/34.39 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 & $i(v4) & % 230.41/34.39 $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4)))) % 230.41/34.39 % 230.41/34.39 (fact_real__natfloor__gt__diff__one) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.39 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 230.41/34.39 [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = % 230.41/34.39 v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : % 230.41/34.39 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1) = v3 & % 230.41/34.39 $i(v4) & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, % 230.41/34.39 v4)))) % 230.41/34.39 % 230.41/34.39 (fact_real__natfloor__le) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.39 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.39 ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ? [v3: $i] % 230.41/34.39 : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) & % 230.41/34.39 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)))) % 230.41/34.39 % 230.41/34.39 (fact_real__of__nat__1) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.39 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 & % 230.41/34.39 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 230.41/34.39 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)) % 230.41/34.39 % 230.41/34.39 (fact_real__of__nat__Suc) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.39 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ! % 230.41/34.39 [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ? [v3: % 230.41/34.39 $i] : ? [v4: $i] : (c_Nat_OSuc(v1) = v3 & c_RealDef_Oreal(tc_Nat_Onat, % 230.41/34.39 v3) = v4 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v0) = v4 % 230.41/34.39 & $i(v4) & $i(v3)))) % 230.41/34.39 % 230.41/34.39 (fact_real__of__nat__Suc__gt__zero) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.39 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.39 ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 230.41/34.39 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) & % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))) % 230.41/34.39 % 230.41/34.39 (fact_real__of__nat__ge__zero) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.39 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.39 ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | % 230.41/34.39 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2))) % 230.41/34.39 % 230.41/34.39 (fact_real__of__nat__gt__zero__cancel__iff) % 230.41/34.39 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.39 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 230.41/34.39 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.39 [v2: $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 230.41/34.39 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] : % 230.41/34.39 ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~ % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | % 230.41/34.39 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2))) % 230.41/34.39 % 230.41/34.39 (fact_real__of__nat__le__zero__cancel__iff) % 230.41/34.40 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.40 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.40 [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = % 230.41/34.40 v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.40 v3, v0)) & ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | % 230.41/34.40 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 230.41/34.40 % 230.41/34.40 (fact_real__of__nat__mult) % 230.41/34.40 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.40 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.40 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.40 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.40 $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4) | ~ % 230.41/34.40 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v6) | ~ (hAPP(v5, v6) = v7) | ~ % 230.41/34.40 (hAPP(v1, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ? [v8: $i] : ? [v9: $i] : % 230.41/34.40 (c_RealDef_Oreal(tc_Nat_Onat, v9) = v7 & hAPP(v8, v2) = v9 & hAPP(v0, v3) % 230.41/34.40 = v8 & $i(v9) & $i(v8) & $i(v7)))) % 230.41/34.40 % 230.41/34.40 (fact_real__of__nat__one) % 230.41/34.40 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 230.41/34.40 $i] : (c_Nat_OSuc(v0) = v1 & c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & % 230.41/34.40 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0)) % 230.41/34.40 % 230.41/34.40 (fact_real__of__nat__zero) % 230.41/34.40 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.40 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)) % 230.41/34.40 % 230.41/34.40 (fact_real__of__nat__zero__iff) % 230.41/34.40 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.40 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.40 [v2: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v0) | ~ % 230.41/34.40 $i(v2)) & ! [v2: $i] : (v2 = v0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = % 230.41/34.40 v2))) % 230.41/34.40 % 230.41/34.40 (fact_real__sgn__def) % 230.41/34.40 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.40 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 & % 230.41/34.40 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) & % 230.41/34.40 $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | v3 = v0 | ~ % 230.41/34.40 (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v3) = v4) | ~ $i(v3) | % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v3: $i] : % 230.41/34.40 ! [v4: $i] : (v4 = v1 | v3 = v0 | ~ % 230.41/34.40 (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v3) = v4) | ~ $i(v3) | ~ % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v3: $i] : % 230.41/34.40 (v3 = v0 | ~ (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) = v3))) % 230.41/34.40 % 230.41/34.40 (fact_real__sgn__pos) % 230.41/34.40 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.40 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.40 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 230.41/34.40 (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2) | ~ % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2))) % 230.41/34.40 % 230.41/34.40 (fact_real__two__squares__add__zero__iff) % 230.41/34.40 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.40 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.40 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.40 $i] : (v3 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) % 230.41/34.40 = v1) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, % 230.41/34.40 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 230.41/34.40 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.41/34.40 : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) % 230.41/34.40 | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) = v4) % 230.41/34.40 | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: % 230.41/34.40 $i] : ! [v4: $i] : (v4 = v1 | ~ % 230.41/34.40 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~ % 230.41/34.40 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2))) % 230.41/34.40 % 230.41/34.40 (fact_real__zero__not__eq__one) % 230.41/34.40 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 230.41/34.40 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 230.41/34.40 % 230.41/34.40 (fact_realpow__minus__mult) % 230.41/34.40 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.40 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.41/34.40 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.41/34.40 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 230.41/34.40 (c_Power_Opower__class_Opower(v4) = v6) | ~ % 230.41/34.40 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~ % 230.41/34.40 (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = v11) | ~ % 230.41/34.40 (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v9) = v10) | % 230.41/34.40 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ class_Groups_Omonoid__mult(v4) | ~ % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3) = v11 & % 230.41/34.40 $i(v11)))) % 230.41/34.40 % 230.41/34.40 (fact_realpow__num__eq__if) % 230.41/34.40 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.40 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.41/34.40 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 230.41/34.40 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 230.41/34.40 (c_Power_Opower__class_Opower(v4) = v5) | ~ % 230.41/34.40 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~ % 230.41/34.40 (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ (hAPP(v8, v10) = v11) | ~ % 230.41/34.40 (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ (hAPP(v5, v2) = v6) | % 230.41/34.40 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ class_Power_Opower(v4) | ? [v12: % 230.41/34.40 $i] : ? [v13: $i] : (( ~ (v3 = v0) | (v13 = v12 & % 230.41/34.40 c_Groups_Oone__class_Oone(v4) = v12 & hAPP(v6, v0) = v12 & $i(v12))) % 230.41/34.40 & (v3 = v0 | (v12 = v11 & hAPP(v6, v3) = v11 & $i(v11)))))) % 230.41/34.40 % 230.41/34.40 (fact_realpow__pos__nth) % 230.41/34.40 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 230.41/34.40 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) & % 230.41/34.40 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v5: $i] : ? % 230.41/34.40 [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) & % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5)))) % 230.41/34.40 % 230.41/34.40 (fact_realpow__pos__nth__unique) % 230.41/34.40 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 230.41/34.40 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.41/34.40 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) & % 230.41/34.40 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v5: $i] : ? % 230.41/34.40 [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) & % 230.41/34.40 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & ! [v7: $i] : % 230.41/34.40 ! [v8: $i] : (v7 = v5 | ~ (hAPP(v8, v4) = v3) | ~ (hAPP(v2, v7) = v8) % 230.41/34.40 | ~ $i(v7) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, % 230.41/34.40 v7))))) % 230.41/34.40 % 230.41/34.40 (fact_realpow__two__diff) % 230.41/34.40 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 230.41/34.40 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.41/34.40 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.40 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: % 230.41/34.40 $i] : ( ~ (c_Power_Opower__class_Opower(v5) = v6) | ~ % 230.41/34.40 (c_Groups_Ominus__class_Ominus(v5, v8, v10) = v11) | ~ (hAPP(v9, v2) = % 230.41/34.40 v10) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, % 230.41/34.40 v3) = v9) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.41/34.40 class_Rings_Ocomm__ring__1(v5) | ? [v12: $i] : ? [v13: $i] : ? [v14: % 230.41/34.40 $i] : ? [v15: $i] : (c_Groups_Ominus__class_Ominus(v5, v4, v3) = v13 & % 230.41/34.40 c_Groups_Oplus__class_Oplus(v5, v4, v3) = v15 & % 230.41/34.40 c_Groups_Otimes__class_Otimes(v5) = v12 & hAPP(v14, v15) = v11 & % 230.41/34.40 hAPP(v12, v13) = v14 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 230.41/34.40 $i(v11)))) % 230.41/34.40 % 230.41/34.40 (fact_realpow__two__disj) % 230.41/34.41 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = % 230.41/34.41 v2 & c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.41/34.41 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.41 $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v5) = % 230.41/34.41 v6) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ % 230.41/34.41 $i(v4) | ~ $i(v3) | ~ class_Rings_Oidom(v5) | ? [v9: $i] : ? [v10: $i] % 230.41/34.41 : ? [v11: $i] : ((v4 = v3 | (v11 = v4 & % 230.41/34.41 c_Groups_Ouminus__class_Ouminus(v5, v3) = v4) | ( ~ (v10 = v9) & % 230.41/34.41 hAPP(v8, v2) = v10 & hAPP(v7, v2) = v9 & $i(v10) & $i(v9))) & ((v10 % 230.41/34.41 = v9 & hAPP(v8, v2) = v9 & hAPP(v7, v2) = v9 & $i(v9)) | ( ~ (v11 = % 230.41/34.41 v4) & ~ (v4 = v3) & c_Groups_Ouminus__class_Ouminus(v5, v3) = v11 % 230.41/34.41 & $i(v11)))))) % 230.41/34.41 % 230.41/34.41 (fact_reals__Archimedean3) % 230.41/34.41 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.41 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ? % 230.41/34.41 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: $i] : ? % 230.41/34.41 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) = % 230.41/34.41 v5 & hAPP(v6, v3) = v7 & hAPP(v1, v5) = v6 & $i(v7) & $i(v6) & $i(v5) & % 230.41/34.41 $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v7)))) % 230.41/34.41 % 230.41/34.41 (fact_reals__Archimedean4) % 230.41/34.41 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.41 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.41 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v4: $i] % 230.41/34.41 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 230.41/34.41 [v10: $i] : ? [v11: $i] : (c_Nat_OSuc(v4) = v8 & % 230.41/34.41 c_RealDef_Oreal(tc_Nat_Onat, v8) = v9 & c_RealDef_Oreal(tc_Nat_Onat, v4) % 230.41/34.41 = v5 & hAPP(v10, v3) = v11 & hAPP(v6, v3) = v7 & hAPP(v1, v9) = v10 & % 230.41/34.41 hAPP(v1, v5) = v6 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 230.41/34.41 $i(v6) & $i(v5) & $i(v4) & % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v11) & % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v2)))) % 230.41/34.41 % 230.41/34.41 (fact_reals__Archimedean6) % 230.41/34.41 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.41 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.41 [v2: $i] : ( ~ $i(v2) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v3: $i] % 230.41/34.41 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (c_RealDef_Oreal(tc_Nat_Onat, % 230.41/34.41 v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & % 230.41/34.41 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & $i(v6) & % 230.41/34.41 $i(v5) & $i(v4) & $i(v3) & % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6) & % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2)))) % 230.41/34.41 % 230.41/34.41 (fact_reals__Archimedean6a) % 230.41/34.41 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : ( % 230.41/34.41 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) % 230.41/34.41 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (c_Nat_OSuc(v2) % 230.41/34.41 = v4 & c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & % 230.41/34.41 c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v5) & $i(v4) & $i(v3) & % 230.41/34.41 $i(v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)))) % 230.41/34.41 % 230.41/34.41 (fact_sgn__real__def) % 230.41/34.41 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.41 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 & % 230.41/34.41 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) & % 230.41/34.41 $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | v3 = v0 | ~ % 230.41/34.41 (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v3) = v4) | ~ $i(v3) | % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v3: $i] : % 230.41/34.41 ! [v4: $i] : (v4 = v1 | v3 = v0 | ~ % 230.41/34.41 (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v3) = v4) | ~ $i(v3) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v3: $i] : % 230.41/34.41 (v3 = v0 | ~ (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) = v3))) % 230.41/34.41 % 230.41/34.41 (fact_split__div) % 230.41/34.41 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.41 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.41/34.41 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 230.41/34.41 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5) % 230.41/34.41 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ? [v7: $i] : % 230.41/34.41 ? [v8: $i] : (( ~ (v2 = v0) | (hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7))) & % 230.41/34.41 (v2 = v0 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : ! % 230.41/34.41 [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) % 230.41/34.41 = v3) | ~ (hAPP(v8, v9) = v11) | ~ $i(v10) | ~ $i(v9) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) | ? [v12: $i] % 230.41/34.41 : (hAPP(v4, v9) = v12 & $i(v12) & hBOOL(v12))))))) & ! [v2: $i] : % 230.41/34.41 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 230.41/34.41 (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ (hAPP(v4, v5) % 230.41/34.41 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | hBOOL(v6) | ? [v7: $i] : ? % 230.41/34.41 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 230.41/34.41 [v13: $i] : ($i(v10) & $i(v9) & ((v12 = v3 & ~ (v2 = v0) & % 230.41/34.41 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) = v3 & hAPP(v8, % 230.41/34.41 v9) = v11 & hAPP(v4, v9) = v13 & hAPP(v1, v2) = v8 & $i(v13) & % 230.41/34.41 $i(v11) & $i(v8) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, % 230.41/34.41 v2) & ~ hBOOL(v13)) | (v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & ~ % 230.41/34.41 hBOOL(v7)))))) % 230.41/34.41 % 230.41/34.41 (fact_split__mult__neg__le) % 230.41/34.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.41 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 230.41/34.41 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.41/34.41 class_Rings_Oordered__cancel__semiring(v2) | ? [v6: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & % 230.41/34.41 (c_Orderings_Oord__class_Oless__eq(v2, v5, v6) | (( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v6, v1) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v0, v6)) & ( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v6, v0) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v1, v6)))))) % 230.41/34.41 % 230.41/34.41 (fact_split__mult__pos__le) % 230.41/34.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.41 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 230.41/34.41 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.41/34.41 class_Rings_Oordered__ring(v2) | ? [v6: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & % 230.41/34.41 (c_Orderings_Oord__class_Oless__eq(v2, v6, v5) | (( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v6, v1) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v6, v0)) & ( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v1, v6) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v0, v6)))))) % 230.41/34.41 % 230.41/34.41 (fact_zero__le__mult__iff) % 230.41/34.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.41 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 230.41/34.41 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.41/34.41 class_Rings_Olinordered__ring__strict(v2) | ? [v6: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v6, v5) | % 230.41/34.41 (c_Orderings_Oord__class_Oless__eq(v2, v6, v1) & % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v6, v0)) | % 230.41/34.41 (c_Orderings_Oord__class_Oless__eq(v2, v1, v6) & % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v0, v6))) & % 230.41/34.41 (c_Orderings_Oord__class_Oless__eq(v2, v6, v5) | (( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v6, v1) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v6, v0)) & ( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v1, v6) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v2, v0, v6)))))) % 230.41/34.41 % 230.41/34.41 (fact_zero__le__natceiling) % 230.41/34.41 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.41/34.41 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatceiling(v1) = % 230.41/34.41 v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, % 230.41/34.41 v2))) % 230.41/34.41 % 230.41/34.41 (fact_zero__le__natfloor) % 230.41/34.41 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.41/34.41 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) % 230.41/34.41 | ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2))) % 230.41/34.41 % 230.41/34.41 (fact_zero__le__one) % 230.41/34.41 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 230.41/34.41 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & % 230.41/34.41 c_Orderings_Oord__class_Oless__eq(v0, v2, v1))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__Suc) % 230.41/34.41 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.41/34.41 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) % 230.41/34.41 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__abs__iff) % 230.41/34.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(v1, % 230.41/34.41 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.41/34.41 class_Groups_Oordered__ab__group__add__abs(v1) | ? [v3: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3) & ( ~ (v3 = v0) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(v1, v0, v2)) & (v3 = v0 | % 230.41/34.41 c_Orderings_Oord__class_Oless(v1, v3, v2)))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__diff) % 230.41/34.41 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 230.41/34.41 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.41 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ $i(v2) | ~ % 230.41/34.41 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v1: $i] : ! % 230.41/34.41 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, % 230.41/34.41 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__mult__pos) % 230.41/34.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.41 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 230.41/34.41 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.41/34.41 class_Rings_Olinordered__semiring__strict(v2) | ? [v6: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(v2, v6, v5) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(v2, v6, v1) | % 230.41/34.41 c_Orderings_Oord__class_Oless(v2, v6, v0)))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__mult__pos2) % 230.41/34.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.41 $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v4, v0) = v5) % 230.41/34.41 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 230.41/34.41 class_Rings_Olinordered__semiring__strict(v2) | ? [v6: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(v2, v6, v5) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(v2, v6, v0) | % 230.41/34.41 c_Orderings_Oord__class_Oless(v2, v6, v1)))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__norm__iff) % 230.41/34.41 $i(tc_RealDef_Oreal) & ? [v0: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : % 230.41/34.41 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) = % 230.41/34.41 v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.41 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ( ~ (v4 = % 230.41/34.41 v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) & % 230.41/34.41 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | (v4 = v1 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(v2) = v1))))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__one) % 230.41/34.41 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 230.41/34.41 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] : % 230.41/34.41 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & % 230.41/34.41 c_Orderings_Oord__class_Oless(v0, v2, v1))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__power__nat__eq) % 230.41/34.41 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 230.41/34.41 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: % 230.41/34.41 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | ~ (hAPP(v4, % 230.41/34.41 v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] : ! % 230.41/34.41 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ % 230.41/34.41 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] : ! % 230.41/34.41 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ (hAPP(v1, v2) = v3) | % 230.41/34.41 ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 230.41/34.41 % 230.41/34.41 (fact_zero__less__zpower__abs__iff) % 230.41/34.41 $i(tc_Int_Oint) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.41 (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & % 230.41/34.41 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & % 230.41/34.41 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = % 230.41/34.41 v0 | ~ (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v4) = v5) | ~ (hAPP(v6, % 230.41/34.41 v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v7)) & ! [v3: $i] : ! % 230.41/34.41 [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ % 230.41/34.41 (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v0) = v4) | ~ (hAPP(v5, v3) = v6) % 230.41/34.41 | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ~ % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v6)) & ! [v3: $i] : ! % 230.41/34.41 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 230.41/34.41 (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v3) = v4) | ~ (hAPP(v5, v2) = v6) % 230.41/34.41 | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | % 230.41/34.41 c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v6))) % 230.41/34.41 % 230.41/34.41 (function-axioms) % 230.41/34.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.42 $i] : ! [v6: $i] : (v1 = v0 | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, % 230.41/34.42 v2) = v1) | ~ (c_Polynomial_Opoly__rec(v6, v5, v4, v3, v2) = v0)) & ! % 230.41/34.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 230.41/34.42 ~ (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~ % 230.41/34.42 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 230.41/34.42 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 230.41/34.42 (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ (c_Power_Opower_Opower(v4, v3, % 230.41/34.42 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 230.41/34.42 [v4: $i] : (v1 = v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 230.41/34.42 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 230.41/34.42 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 230.41/34.42 (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~ (c_Polynomial_Oorder(v4, v3, v2) % 230.41/34.42 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 230.41/34.42 $i] : (v1 = v0 | ~ (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~ % 230.41/34.42 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 230.41/34.42 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_SMT_Oz3div(v3, v2) = v1) | ~ % 230.41/34.42 (c_SMT_Oz3div(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 230.41/34.42 [v3: $i] : (v1 = v0 | ~ (c_Nat__Transfer_Otsub(v3, v2) = v1) | ~ % 230.41/34.42 (c_Nat__Transfer_Otsub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 230.41/34.42 $i] : ! [v3: $i] : (v1 = v0 | ~ (c_RealDef_Oreal(v3, v2) = v1) | ~ % 230.41/34.42 (c_RealDef_Oreal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 230.41/34.42 ! [v3: $i] : (v1 = v0 | ~ (c_Groups_Ouminus__class_Ouminus(v3, v2) = v1) | ~ % 230.41/34.42 (c_Groups_Ouminus__class_Ouminus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 230.41/34.42 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Polynomial_Ocoeff(v3, v2) = v1) % 230.41/34.42 | ~ (c_Polynomial_Ocoeff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 230.41/34.42 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Groups_Osgn__class_Osgn(v3, v2) = % 230.41/34.42 v1) | ~ (c_Groups_Osgn__class_Osgn(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 230.41/34.42 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ % 230.41/34.42 (tc_fun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 230.41/34.42 $i] : (v1 = v0 | ~ (c_Polynomial_Opoly(v3, v2) = v1) | ~ % 230.41/34.42 (c_Polynomial_Opoly(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 230.41/34.42 : ! [v3: $i] : (v1 = v0 | ~ (c_Groups_Oabs__class_Oabs(v3, v2) = v1) | ~ % 230.41/34.42 (c_Groups_Oabs__class_Oabs(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 230.41/34.42 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_RealVector_Onorm__class_Onorm(v3, % 230.41/34.42 v2) = v1) | ~ (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) & ! [v0: % 230.41/34.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) % 230.41/34.42 = v1) | ~ (hAPP(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 230.41/34.42 : (v1 = v0 | ~ (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0)) & ! [v0: % 230.41/34.42 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Transcendental_Oln(v2) = % 230.41/34.42 v1) | ~ (c_Transcendental_Oln(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 230.41/34.42 [v2: $i] : (v1 = v0 | ~ (c_Power_Opower__class_Opower(v2) = v1) | ~ % 230.41/34.42 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 230.41/34.42 [v2: $i] : (v1 = v0 | ~ (c_RComplete_Onatfloor(v2) = v1) | ~ % 230.41/34.42 (c_RComplete_Onatfloor(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 230.41/34.42 : (v1 = v0 | ~ (c_RComplete_Onatceiling(v2) = v1) | ~ % 230.41/34.42 (c_RComplete_Onatceiling(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 230.41/34.42 $i] : (v1 = v0 | ~ (tc_Polynomial_Opoly(v2) = v1) | ~ % 230.41/34.42 (tc_Polynomial_Opoly(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 230.41/34.42 (v1 = v0 | ~ (c_Groups_Oone__class_Oone(v2) = v1) | ~ % 230.41/34.42 (c_Groups_Oone__class_Oone(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 230.41/34.42 $i] : (v1 = v0 | ~ (c_Groups_Otimes__class_Otimes(v2) = v1) | ~ % 230.41/34.42 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 230.41/34.42 [v2: $i] : (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 230.41/34.42 (c_Groups_Ozero__class_Ozero(v2) = v0)) % 230.41/34.42 % 230.41/34.42 Further assumptions not needed in the proof: % 230.41/34.42 -------------------------------------------- % 230.41/34.42 arity_Complex__Ocomplex__Fields_Ofield, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Oab__group__add, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Oab__semigroup__add, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Ogroup__add, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Ominus, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Omonoid__add, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Omonoid__mult, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ouminus, % 230.41/34.42 arity_Complex__Ocomplex__Groups_Ozero, % 230.41/34.42 arity_Complex__Ocomplex__Int_Oring__char__0, % 230.41/34.42 arity_Complex__Ocomplex__Power_Opower, % 230.41/34.42 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, % 230.41/34.42 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, % 230.41/34.42 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Ocomm__ring, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Ocomm__ring__1, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Ocomm__semiring, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Oidom, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Omult__zero, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Ono__zero__divisors, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Osemiring, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Osemiring__0, % 230.41/34.42 arity_Complex__Ocomplex__Rings_Ozero__neq__one, % 230.41/34.42 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 230.41/34.42 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Groups_Ouminus, % 230.41/34.42 arity_HOL__Obool__Lattices_Oboolean__algebra, arity_HOL__Obool__Orderings_Oord, % 230.41/34.42 arity_HOL__Obool__Orderings_Oorder, arity_HOL__Obool__Orderings_Opreorder, % 230.41/34.42 arity_Int__Oint__Divides_Osemiring__div, % 230.41/34.42 arity_Int__Oint__Groups_Oab__group__add, % 230.41/34.42 arity_Int__Oint__Groups_Oab__semigroup__add, % 230.41/34.42 arity_Int__Oint__Groups_Oab__semigroup__mult, arity_Int__Oint__Groups_Oabs__if, % 230.41/34.42 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, % 230.41/34.42 arity_Int__Oint__Groups_Ocancel__comm__monoid__add, % 230.41/34.42 arity_Int__Oint__Groups_Ocancel__semigroup__add, % 230.41/34.42 arity_Int__Oint__Groups_Ocomm__monoid__add, % 230.41/34.42 arity_Int__Oint__Groups_Ocomm__monoid__mult, % 230.41/34.42 arity_Int__Oint__Groups_Ogroup__add, % 230.41/34.42 arity_Int__Oint__Groups_Olinordered__ab__group__add, % 230.41/34.42 arity_Int__Oint__Groups_Ominus, arity_Int__Oint__Groups_Omonoid__add, % 230.41/34.42 arity_Int__Oint__Groups_Omonoid__mult, arity_Int__Oint__Groups_Oone, % 230.41/34.42 arity_Int__Oint__Groups_Oordered__ab__group__add, % 230.41/34.42 arity_Int__Oint__Groups_Oordered__ab__group__add__abs, % 230.41/34.42 arity_Int__Oint__Groups_Oordered__ab__semigroup__add, % 230.41/34.42 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, % 230.41/34.42 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, % 230.41/34.42 arity_Int__Oint__Groups_Oordered__comm__monoid__add, % 230.41/34.42 arity_Int__Oint__Groups_Osgn__if, arity_Int__Oint__Groups_Ouminus, % 230.41/34.42 arity_Int__Oint__Groups_Ozero, arity_Int__Oint__Int_Oring__char__0, % 230.41/34.42 arity_Int__Oint__Orderings_Olinorder, arity_Int__Oint__Orderings_Oord, % 230.41/34.42 arity_Int__Oint__Orderings_Oorder, arity_Int__Oint__Orderings_Opreorder, % 230.41/34.42 arity_Int__Oint__Power_Opower, arity_Int__Oint__Rings_Ocomm__ring, % 230.41/34.42 arity_Int__Oint__Rings_Ocomm__ring__1, arity_Int__Oint__Rings_Ocomm__semiring, % 230.41/34.42 arity_Int__Oint__Rings_Ocomm__semiring__0, % 230.41/34.42 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Oidom, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__idom, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__ring, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__ring__strict, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__semidom, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__semiring, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__semiring__1, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__semiring__1__strict, % 230.41/34.42 arity_Int__Oint__Rings_Olinordered__semiring__strict, % 230.41/34.42 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors, % 230.41/34.42 arity_Int__Oint__Rings_Oordered__cancel__semiring, % 230.41/34.42 arity_Int__Oint__Rings_Oordered__comm__semiring, % 230.41/34.42 arity_Int__Oint__Rings_Oordered__ring, % 230.41/34.42 arity_Int__Oint__Rings_Oordered__ring__abs, % 230.41/34.42 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring, % 230.41/34.42 arity_Int__Oint__Rings_Oring__1, % 230.41/34.42 arity_Int__Oint__Rings_Oring__1__no__zero__divisors, % 230.41/34.42 arity_Int__Oint__Rings_Oring__no__zero__divisors, % 230.41/34.42 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0, % 230.41/34.42 arity_Int__Oint__Rings_Ozero__neq__one, % 230.41/34.42 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 230.41/34.42 arity_Nat__Onat__Divides_Osemiring__div, % 230.41/34.42 arity_Nat__Onat__Groups_Oab__semigroup__add, % 230.41/34.42 arity_Nat__Onat__Groups_Oab__semigroup__mult, % 230.41/34.42 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, % 230.41/34.42 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, % 230.41/34.42 arity_Nat__Onat__Groups_Ocancel__semigroup__add, % 230.41/34.42 arity_Nat__Onat__Groups_Ocomm__monoid__add, % 230.41/34.42 arity_Nat__Onat__Groups_Ocomm__monoid__mult, arity_Nat__Onat__Groups_Ominus, % 230.41/34.42 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult, % 230.41/34.42 arity_Nat__Onat__Groups_Oone, % 230.41/34.42 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, % 230.41/34.42 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, % 230.41/34.42 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, % 230.41/34.42 arity_Nat__Onat__Groups_Oordered__comm__monoid__add, % 230.41/34.42 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Orderings_Olinorder, % 230.41/34.42 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder, % 230.41/34.42 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Power_Opower, % 230.41/34.42 arity_Nat__Onat__Rings_Ocomm__semiring, % 230.41/34.42 arity_Nat__Onat__Rings_Ocomm__semiring__0, % 230.41/34.42 arity_Nat__Onat__Rings_Ocomm__semiring__1, % 230.41/34.42 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, % 230.41/34.42 arity_Nat__Onat__Rings_Olinordered__semidom, % 230.41/34.42 arity_Nat__Onat__Rings_Olinordered__semiring, % 230.41/34.42 arity_Nat__Onat__Rings_Olinordered__semiring__strict, % 230.41/34.42 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors, % 230.41/34.42 arity_Nat__Onat__Rings_Oordered__cancel__semiring, % 230.41/34.42 arity_Nat__Onat__Rings_Oordered__comm__semiring, % 230.41/34.42 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring, % 230.41/34.42 arity_Nat__Onat__Rings_Osemiring__0, arity_Nat__Onat__Rings_Ozero__neq__one, % 230.41/34.42 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 230.41/34.42 arity_Polynomial__Opoly__Divides_Osemiring__div, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oab__group__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oab__semigroup__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oabs__if, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Ogroup__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Ominus, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Omonoid__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Omonoid__mult, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oone, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Osgn__if, % 230.41/34.42 arity_Polynomial__Opoly__Groups_Ouminus, arity_Polynomial__Opoly__Groups_Ozero, % 230.41/34.42 arity_Polynomial__Opoly__Int_Oring__char__0, % 230.41/34.42 arity_Polynomial__Opoly__Orderings_Olinorder, % 230.41/34.42 arity_Polynomial__Opoly__Orderings_Oord, % 230.41/34.42 arity_Polynomial__Opoly__Orderings_Oorder, % 230.41/34.42 arity_Polynomial__Opoly__Orderings_Opreorder, % 230.41/34.42 arity_Polynomial__Opoly__Power_Opower, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Ocomm__ring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Ocomm__ring__1, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Ocomm__semiring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oidom, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__idom, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__ring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__semidom, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__semiring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Omult__zero, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Ono__zero__divisors, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oordered__ring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oordered__ring__abs, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oordered__semiring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Osemiring, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Osemiring__0, % 230.41/34.42 arity_Polynomial__Opoly__Rings_Ozero__neq__one, % 230.41/34.42 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 230.41/34.42 arity_RealDef__Oreal__Fields_Ofield, % 230.41/34.42 arity_RealDef__Oreal__Fields_Olinordered__field, % 230.41/34.42 arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, % 230.41/34.42 arity_RealDef__Oreal__Groups_Oab__group__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Oab__semigroup__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Oab__semigroup__mult, % 230.41/34.42 arity_RealDef__Oreal__Groups_Oabs__if, % 230.41/34.42 arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Ocomm__monoid__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, % 230.41/34.42 arity_RealDef__Oreal__Groups_Ominus, arity_RealDef__Oreal__Groups_Omonoid__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Omonoid__mult, arity_RealDef__Oreal__Groups_Oone, % 230.41/34.42 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, % 230.41/34.42 arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add, % 230.41/34.42 arity_RealDef__Oreal__Groups_Osgn__if, arity_RealDef__Oreal__Groups_Ouminus, % 230.41/34.42 arity_RealDef__Oreal__Groups_Ozero, arity_RealDef__Oreal__Int_Oring__char__0, % 230.41/34.42 arity_RealDef__Oreal__Orderings_Olinorder, arity_RealDef__Oreal__Orderings_Oord, % 230.41/34.42 arity_RealDef__Oreal__Orderings_Oorder, % 230.41/34.42 arity_RealDef__Oreal__Orderings_Opreorder, arity_RealDef__Oreal__Power_Opower, % 230.41/34.42 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, % 230.41/34.42 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, % 230.41/34.42 arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, % 230.41/34.42 arity_RealDef__Oreal__RealVector_Oreal__normed__vector, % 230.41/34.42 arity_RealDef__Oreal__Rings_Ocomm__ring, % 230.41/34.42 arity_RealDef__Oreal__Rings_Ocomm__ring__1, % 230.41/34.42 arity_RealDef__Oreal__Rings_Ocomm__semiring, % 230.41/34.42 arity_RealDef__Oreal__Rings_Ocomm__semiring__0, % 230.41/34.42 arity_RealDef__Oreal__Rings_Oidom, % 230.41/34.42 arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict, % 230.41/34.42 arity_RealDef__Oreal__Rings_Olinordered__idom, % 230.41/34.42 arity_RealDef__Oreal__Rings_Olinordered__ring, % 230.41/34.42 arity_RealDef__Oreal__Rings_Olinordered__semiring, % 230.41/34.42 arity_RealDef__Oreal__Rings_Olinordered__semiring__1, % 230.41/34.42 arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, % 230.41/34.42 arity_RealDef__Oreal__Rings_Omult__zero, % 230.41/34.42 arity_RealDef__Oreal__Rings_Oordered__comm__semiring, % 230.41/34.42 arity_RealDef__Oreal__Rings_Oordered__ring__abs, % 230.41/34.42 arity_RealDef__Oreal__Rings_Oordered__semiring, % 230.41/34.42 arity_RealDef__Oreal__Rings_Oring, arity_RealDef__Oreal__Rings_Oring__1, % 230.41/34.42 arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, % 230.41/34.42 arity_RealDef__Oreal__Rings_Osemiring, arity_RealDef__Oreal__Rings_Osemiring__0, % 230.41/34.42 arity_RealDef__Oreal__Rings_Ozero__neq__one, % 230.41/34.42 arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 230.41/34.42 arity_fun__Groups_Ominus, arity_fun__Groups_Ouminus, % 230.41/34.42 arity_fun__Lattices_Oboolean__algebra, arity_fun__Orderings_Oord, % 230.41/34.42 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, fact_BseqI2_H, % 230.41/34.42 fact_Bseq__iff, fact_Bseq__iff1a, fact_Deriv_Oadd__diff__add, % 230.41/34.42 fact_Divides_Otransfer__nat__int__function__closures_I1_J, % 230.41/34.42 fact_Limits_Ominus__diff__minus, fact_Nat_Odiff__diff__eq, % 230.41/34.42 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, % 230.41/34.42 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, % 230.41/34.42 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, % 230.41/34.42 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, % 230.41/34.42 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, % 230.41/34.42 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, % 230.41/34.42 fact_Suc__diff__diff, fact_Suc__diff__le, fact_Suc__inject, fact_Suc__leD, % 230.41/34.42 fact_Suc__leI, fact_Suc__le__eq, fact_Suc__le__lessD, fact_Suc__le__mono, % 230.41/34.42 fact_Suc__lessD, fact_Suc__lessI, fact_Suc__less__SucD, fact_Suc__less__eq, % 230.41/34.42 fact_Suc__mono, fact_Suc__mult__cancel1, fact_Suc__mult__le__cancel1, % 230.41/34.42 fact_Suc__mult__less__cancel1, fact_Suc__n__not__le__n, fact_Suc__n__not__n, % 230.41/34.42 fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, % 230.41/34.42 fact_ab__diff__minus, fact_ab__left__minus, % 230.41/34.42 fact_ab__semigroup__add__class_Oadd__ac_I1_J, % 230.41/34.42 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_abs__add__abs, % 230.41/34.42 fact_abs__diff__less__iff, fact_abs__diff__triangle__ineq, fact_abs__eq__mult, % 230.41/34.42 fact_abs__ge__minus__self, fact_abs__ge__self, fact_abs__ge__zero, % 230.41/34.42 fact_abs__idempotent, fact_abs__if, fact_abs__leI, fact_abs__le__D1, % 230.41/34.42 fact_abs__le__D2, fact_abs__le__iff, fact_abs__le__interval__iff, % 230.41/34.42 fact_abs__less__iff, fact_abs__minus__add__cancel, fact_abs__minus__cancel, % 230.41/34.42 fact_abs__minus__commute, fact_abs__minus__le__zero, fact_abs__mult, % 230.41/34.42 fact_abs__mult__less, fact_abs__mult__pos, fact_abs__mult__self, % 230.41/34.42 fact_abs__of__neg, fact_abs__of__nonneg, fact_abs__of__nonpos, % 230.41/34.42 fact_abs__of__pos, fact_abs__one, fact_abs__poly__def, fact_abs__power__minus, % 230.41/34.42 fact_abs__real__of__nat__cancel, fact_abs__sgn, fact_abs__sum__triangle__ineq, % 230.41/34.42 fact_abs__triangle__ineq, fact_abs__triangle__ineq2, % 230.41/34.42 fact_abs__triangle__ineq2__sym, fact_abs__triangle__ineq3, % 230.41/34.42 fact_abs__triangle__ineq4, fact_abs__zero, fact_abs__zmult__eq__1, % 230.41/34.42 fact_add1__zle__eq, fact_add_Ocomm__neutral, fact_add__0, fact_add__0__iff, % 230.41/34.42 fact_add__0__left, fact_add__0__right, fact_add__Suc, fact_add__Suc__right, % 230.41/34.42 fact_add__Suc__shift, fact_add__diff__assoc, fact_add__diff__assoc2, % 230.41/34.42 fact_add__diff__cancel, fact_add__diff__inverse, fact_add__eq__0__iff, % 230.41/34.42 fact_add__imp__eq, fact_add__increasing, fact_add__increasing2, fact_add__leD1, % 230.41/34.42 fact_add__leD2, fact_add__leE, fact_add__le__cancel__left, % 230.41/34.42 fact_add__le__cancel__right, fact_add__le__imp__le__left, % 230.41/34.42 fact_add__le__imp__le__right, fact_add__le__less__mono, fact_add__le__mono, % 230.41/34.42 fact_add__le__mono1, fact_add__left__cancel, fact_add__left__imp__eq, % 230.41/34.42 fact_add__left__mono, fact_add__lessD1, fact_add__less__cancel__left, % 230.41/34.42 fact_add__less__cancel__right, fact_add__less__imp__less__left, % 230.41/34.42 fact_add__less__imp__less__right, fact_add__less__le__mono, % 230.41/34.42 fact_add__less__mono, fact_add__less__mono1, fact_add__minus__cancel, % 230.41/34.42 fact_add__mono, fact_add__mult__distrib, fact_add__mult__distrib2, % 230.41/34.42 fact_add__poly__code_I1_J, fact_add__poly__code_I2_J, fact_add__right__cancel, % 230.41/34.42 fact_add__right__imp__eq, fact_add__right__mono, fact_add__scale__eq__noteq, % 230.41/34.42 fact_add__strict__increasing2, fact_add__strict__left__mono, % 230.41/34.42 fact_add__strict__mono, fact_add__strict__right__mono, fact_coeff__0, % 230.41/34.42 fact_coeff__add, fact_coeff__diff, fact_coeff__inject, fact_coeff__minus, % 230.41/34.42 fact_combine__common__factor, fact_comm__mult__left__mono, % 230.41/34.42 fact_comm__mult__strict__left__mono, % 230.41/34.42 fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, % 230.41/34.42 fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, % 230.41/34.42 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, % 230.41/34.42 fact_comm__semiring__class_Odistrib, fact_compl__eq__compl__iff, % 230.41/34.42 fact_compl__le__compl__iff, fact_compl__mono, fact_complex__diff__def, % 230.41/34.42 fact_complex__mod__minus__le__complex__mod, fact_complex__mod__triangle__ineq2, % 230.41/34.42 fact_complex__mod__triangle__sub, fact_convex__bound__le, % 230.41/34.42 fact_convex__bound__lt, fact_crossproduct__eq, fact_crossproduct__noteq, % 230.41/34.42 fact_decr__lemma, fact_decr__mult__lemma, fact_decseq__def, fact_diff__0, % 230.41/34.42 fact_diff__0__right, fact_diff__Suc__1, fact_diff__Suc__Suc, % 230.41/34.42 fact_diff__Suc__diff__eq1, fact_diff__Suc__diff__eq2, fact_diff__add__assoc, % 230.41/34.42 fact_diff__add__assoc2, fact_diff__add__cancel, fact_diff__add__inverse, % 230.41/34.42 fact_diff__add__inverse2, fact_diff__cancel, fact_diff__cancel2, % 230.41/34.42 fact_diff__commute, fact_diff__def, fact_diff__diff__cancel, % 230.41/34.42 fact_diff__diff__left, fact_diff__diff__right, fact_diff__eq__diff__eq, % 230.41/34.42 fact_diff__eq__diff__less, fact_diff__eq__diff__less__eq, fact_diff__int__def, % 230.41/34.42 fact_diff__int__def__symmetric, fact_diff__le__mono, fact_diff__le__mono2, % 230.41/34.42 fact_diff__le__self, fact_diff__less__Suc, fact_diff__less__mono, % 230.41/34.42 fact_diff__less__mono2, fact_diff__minus__eq__add, fact_diff__mult__distrib, % 230.41/34.42 fact_diff__mult__distrib2, fact_diff__poly__code_I1_J, % 230.41/34.42 fact_diff__poly__code_I2_J, fact_diff__self, fact_div__0, fact_div__add__self1, % 230.41/34.42 fact_div__add__self2, fact_div__by__0, fact_div__by__1, fact_div__le__dividend, % 230.41/34.42 fact_div__le__mono, fact_div__mult2__eq, fact_div__mult__mult1, % 230.41/34.42 fact_div__mult__mult1__if, fact_div__mult__mult2, fact_div__mult__self1, % 230.41/34.42 fact_div__mult__self1__is__id, fact_div__mult__self2, % 230.41/34.42 fact_div__mult__self2__is__id, fact_div__neg__neg__trivial, % 230.41/34.42 fact_div__neg__pos__less0, fact_div__nonneg__neg__le0, % 230.41/34.42 fact_div__nonpos__pos__le0, fact_div__pos__pos__trivial, fact_div__self, % 230.41/34.42 fact_divmod__int__rel__div__eq, % 230.41/34.42 fact_double__add__le__zero__iff__single__add__le__zero, % 230.41/34.42 fact_double__add__less__zero__iff__single__add__less__zero, fact_double__compl, % 230.41/34.42 fact_double__eq__0__iff, fact_double__zero__sym, fact_eq__add__iff1, % 230.41/34.42 fact_eq__add__iff2, fact_eq__diff__iff, fact_eq__iff__diff__eq__0, % 230.41/34.42 fact_eq__imp__le, fact_eq__neg__iff__add__eq__0, fact_equation__minus__iff, % 230.41/34.42 fact_even__less__0__iff, fact_expand__poly__eq, fact_ext, % 230.41/34.42 fact_field__le__epsilon, fact_field__le__mult__one__interval, % 230.41/34.42 fact_field__power__not__zero, fact_incr__lemma, fact_incr__mult__lemma, % 230.41/34.42 fact_incseq__def, fact_int__0__less__1, fact_int__0__neq__1, % 230.41/34.42 fact_int__div__less__self, fact_int__one__le__iff__zero__less, fact_leD, % 230.41/34.42 fact_leI, fact_le__SucE, fact_le__SucI, fact_le__Suc__eq, fact_le__Suc__ex__iff, % 230.41/34.42 fact_le__add1, fact_le__add2, fact_le__add__diff, fact_le__add__diff__inverse, % 230.41/34.42 fact_le__add__diff__inverse2, fact_le__add__iff1, fact_le__add__iff2, % 230.41/34.42 fact_le__antisym, fact_le__cube, fact_le__diff__conv, fact_le__diff__conv2, % 230.41/34.42 fact_le__diff__iff, fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE, % 230.41/34.42 fact_le__fun__def, fact_le__iff__add, fact_le__iff__diff__le__0, % 230.41/34.42 fact_le__imp__0__less, fact_le__imp__diff__is__add, fact_le__imp__less__Suc, % 230.41/34.42 fact_le__imp__neg__le, fact_le__less__Suc__eq, fact_le__minus__iff, % 230.41/34.42 fact_le__minus__self__iff, fact_le__natfloor, fact_le__neq__implies__less, % 230.41/34.42 fact_le__refl, fact_le__square, fact_le__trans, fact_left__add__mult__distrib, % 230.41/34.42 fact_left__minus, fact_lemma__realpow__diff, fact_lessI, fact_less__1__mult, % 230.41/34.42 fact_less__SucE, fact_less__SucI, fact_less__Suc__eq, fact_less__Suc__eq__le, % 230.41/34.42 fact_less__add__Suc1, fact_less__add__Suc2, fact_less__add__eq__less, % 230.41/34.42 fact_less__add__iff1, fact_less__add__iff2, fact_less__add__one, % 230.41/34.42 fact_less__antisym, fact_less__bin__lemma, fact_less__diff__conv, % 230.41/34.42 fact_less__diff__iff, fact_less__eq__Suc__le, fact_less__eq__poly__def, % 230.41/34.42 fact_less__eq__real__def, fact_less__fun__def, fact_less__iff__Suc__add, % 230.41/34.42 fact_less__iff__diff__less__0, fact_less__imp__diff__less, % 230.41/34.42 fact_less__imp__le__nat, fact_less__imp__neq, fact_less__irrefl__nat, % 230.41/34.42 fact_less__le__not__le, fact_less__minus__iff, fact_less__minus__self__iff, % 230.41/34.42 fact_less__not__refl, fact_less__not__refl2, fact_less__not__refl3, % 230.41/34.42 fact_less__or__eq__imp__le, fact_less__poly__def, fact_less__trans__Suc, % 230.41/34.42 fact_linorder__antisym__conv1, fact_linorder__antisym__conv2, % 230.41/34.42 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases, % 230.41/34.42 fact_linorder__le__less__linear, fact_linorder__less__linear, % 230.41/34.42 fact_linorder__linear, fact_linorder__neqE, % 230.41/34.42 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat, % 230.41/34.42 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less, % 230.41/34.42 fact_m, fact_minus__add, fact_minus__add__cancel, fact_minus__add__distrib, % 230.41/34.42 fact_minus__apply, fact_minus__diff__eq, fact_minus__equation__iff, % 230.41/34.42 fact_minus__le__iff, fact_minus__le__self__iff, fact_minus__less__iff, % 230.41/34.42 fact_minus__minus, fact_minus__mult__commute, fact_minus__mult__left, % 230.41/34.42 fact_minus__mult__minus, fact_minus__mult__right, fact_minus__poly__code_I1_J, % 230.41/34.42 fact_minus__real__def, fact_minus__unique, fact_minus__zero, % 230.41/34.42 fact_mult_Oadd__left, fact_mult_Oadd__right, fact_mult_Ocomm__neutral, % 230.41/34.42 fact_mult_Odiff__left, fact_mult_Odiff__right, fact_mult_Ominus__left, % 230.41/34.42 fact_mult_Ominus__right, fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, % 230.41/34.42 fact_mult_Ozero__right, fact_mult__1, fact_mult__1__left, fact_mult__1__right, % 230.41/34.42 fact_mult__Suc, fact_mult__Suc__right, fact_mult__diff__mult, fact_mult__idem, % 230.41/34.42 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos, % 230.41/34.42 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1, % 230.41/34.42 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Odiff, % 230.41/34.42 fact_mult__left_Ominus, fact_mult__left_Ozero, fact_mult__left__idem, % 230.41/34.42 fact_mult__left__le__imp__le, fact_mult__left__le__one__le, % 230.41/34.42 fact_mult__left__less__imp__less, fact_mult__left__mono, % 230.41/34.42 fact_mult__left__mono__neg, fact_mult__less__cancel__left__disj, % 230.41/34.42 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos, % 230.41/34.42 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left, % 230.41/34.42 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less, % 230.41/34.42 fact_mult__mono, fact_mult__mono_H, fact_mult__neg__pos, % 230.41/34.42 fact_mult__nonpos__nonneg, fact_mult__poly__0__left, fact_mult__poly__0__right, % 230.41/34.42 fact_mult__poly__add__left, fact_mult__right_Oadd, fact_mult__right_Odiff, % 230.41/34.42 fact_mult__right_Ominus, fact_mult__right_Ozero, fact_mult__right__le__imp__le, % 230.41/34.42 fact_mult__right__le__one__le, fact_mult__right__less__imp__less, % 230.41/34.42 fact_mult__right__mono, fact_mult__right__mono__neg, fact_mult__sgn__abs, % 230.41/34.42 fact_mult__strict__left__mono, fact_mult__strict__left__mono__neg, % 230.41/34.42 fact_mult__strict__mono, fact_mult__strict__mono_H, % 230.41/34.42 fact_mult__strict__right__mono, fact_mult__strict__right__mono__neg, % 230.41/34.42 fact_mult__zero__left, fact_mult__zero__right, fact_n__not__Suc__n, % 230.41/34.42 fact_nat_Oinject, fact_nat__add__assoc, fact_nat__add__commute, % 230.41/34.42 fact_nat__add__left__cancel, fact_nat__add__left__cancel__le, % 230.41/34.42 fact_nat__add__left__cancel__less, fact_nat__add__left__commute, % 230.41/34.42 fact_nat__add__right__cancel, fact_nat__diff__add__eq1, % 230.41/34.42 fact_nat__diff__add__eq2, fact_nat__eq__add__iff1, fact_nat__eq__add__iff2, % 230.41/34.42 fact_nat__le__add__iff1, fact_nat__le__add__iff2, fact_nat__le__linear, % 230.41/34.42 fact_nat__less__add__iff1, fact_nat__less__add__iff2, fact_nat__less__cases, % 230.41/34.42 fact_nat__less__le, fact_nat__mult__assoc, fact_nat__mult__commute, % 230.41/34.42 fact_nat__neq__iff, fact_natceiling__le, fact_natceiling__mono, % 230.41/34.42 fact_natceiling__real__of__nat, fact_natceiling__subtract, fact_natfloor__mono, % 230.41/34.42 fact_natfloor__power, fact_natfloor__real__of__nat, fact_natfloor__subtract, % 230.41/34.42 fact_neg__equal__iff__equal, fact_neg__imp__zdiv__neg__iff, % 230.41/34.42 fact_neg__imp__zdiv__nonneg__iff, fact_neg__le__iff__le, % 230.41/34.42 fact_neg__less__iff__less, fact_neg__less__nonneg, % 230.41/34.42 fact_nonneg1__imp__zdiv__pos__iff, fact_norm__add__less, fact_norm__diff__ineq, % 230.41/34.42 fact_norm__diff__triangle__ineq, fact_norm__minus__cancel, % 230.41/34.42 fact_norm__minus__commute, fact_norm__power, fact_norm__power__ineq, % 230.41/34.42 fact_norm__triangle__ineq, fact_norm__triangle__ineq2, % 230.41/34.42 fact_norm__triangle__ineq3, fact_norm__triangle__ineq4, fact_not__add__less1, % 230.41/34.42 fact_not__add__less2, fact_not__leE, fact_not__less__eq, fact_not__less__eq__eq, % 230.41/34.42 fact_not__less__iff__gr__or__eq, fact_not__less__less__Suc__eq, % 230.41/34.42 fact_not__pos__poly__0, fact_not__square__less__zero, % 230.41/34.42 fact_not__sum__squares__lt__zero, fact_odd__less__0, fact_odd__nonzero, % 230.41/34.42 fact_one__le__power, fact_one__neq__zero, fact_one__reorient, % 230.41/34.42 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans, % 230.41/34.42 fact_ord__less__eq__trans, fact_order__antisym, fact_order__antisym__conv, % 230.41/34.42 fact_order__eq__iff, fact_order__eq__refl, fact_order__le__imp__less__or__eq, % 230.41/34.42 fact_order__le__less, fact_order__le__less__trans, fact_order__le__neq__trans, % 230.41/34.42 fact_order__less__asym, fact_order__less__asym_H, fact_order__less__imp__le, % 230.41/34.42 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2, % 230.41/34.42 fact_order__less__imp__not__less, fact_order__less__irrefl, % 230.41/34.42 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym, % 230.41/34.42 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl, % 230.41/34.42 fact_order__trans, fact_poly__0, fact_poly__1, fact_poly__add, fact_poly__diff, % 230.41/34.42 fact_poly__div__minus__left, fact_poly__div__minus__right, % 230.41/34.42 fact_poly__div__mult__right, fact_poly__eq__iff, fact_poly__minus, % 230.41/34.42 fact_poly__mult, fact_poly__power, fact_poly__rec__0, fact_poly__zero, % 230.41/34.42 fact_pos__add__strict, fact_pos__imp__zdiv__neg__iff, % 230.41/34.42 fact_pos__imp__zdiv__nonneg__iff, fact_pos__imp__zdiv__pos__iff, % 230.41/34.42 fact_pos__poly__add, fact_pos__poly__mult, fact_pos__poly__total, % 230.41/34.42 fact_pos__zmult__eq__1__iff, fact_power_Opower_Opower__Suc, fact_power__0__Suc, % 230.41/34.42 fact_power__Suc, fact_power__Suc2, fact_power__Suc__less, % 230.41/34.42 fact_power__Suc__less__one, fact_power__abs, fact_power__add, % 230.41/34.42 fact_power__commutes, fact_power__decreasing, fact_power__gt1, % 230.41/34.42 fact_power__gt1__lemma, fact_power__increasing, fact_power__increasing__iff, % 230.41/34.42 fact_power__inject__base, fact_power__inject__exp, % 230.41/34.42 fact_power__le__imp__le__base, fact_power__le__imp__le__exp, % 230.41/34.42 fact_power__less__imp__less__base, fact_power__less__imp__less__exp, % 230.41/34.42 fact_power__less__power__Suc, fact_power__minus, fact_power__mono, % 230.41/34.42 fact_power__mult, fact_power__mult__distrib, fact_power__one, % 230.41/34.42 fact_power__one__right, fact_power__power__power, fact_power__real__of__nat, % 230.41/34.42 fact_power__strict__decreasing, fact_power__strict__increasing, % 230.41/34.42 fact_power__strict__increasing__iff, fact_q__neg__lemma, fact_q__pos__lemma, % 230.41/34.42 fact_real__add__left__mono, fact_real__diff__def, fact_real__le__antisym, % 230.41/34.42 fact_real__le__linear, fact_real__le__refl, fact_real__le__trans, % 230.41/34.42 fact_real__less__def, fact_real__norm__def, fact_real__of__nat__add, % 230.41/34.42 fact_real__of__nat__diff, fact_real__of__nat__inject, % 230.41/34.42 fact_real__of__nat__le__iff, fact_real__of__nat__less__iff, % 230.41/34.42 fact_real__of__nat__power, fact_real__squared__diff__one__factored, % 230.41/34.42 fact_realpow__Suc__le__self, fact_right__minus, fact_right__minus__eq, % 230.41/34.42 fact_self__quotient__aux1, fact_self__quotient__aux2, fact_sgn0, fact_sgn__0__0, % 230.41/34.42 fact_sgn__1__neg, fact_sgn__1__pos, fact_sgn__greater, fact_sgn__if, % 230.41/34.42 fact_sgn__less, fact_sgn__minus, fact_sgn__mult, fact_sgn__neg, fact_sgn__one, % 230.41/34.42 fact_sgn__poly__def, fact_sgn__pos, fact_sgn__sgn, fact_sgn__times, % 230.41/34.42 fact_sgn__zero, fact_sgn__zero__iff, fact_split__zdiv, fact_square__eq__1__iff, % 230.41/34.42 fact_square__eq__iff, fact_sum__squares__eq__zero__iff, % 230.41/34.42 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff, % 230.41/34.42 fact_sum__squares__le__zero__iff, fact_termination__basic__simps_I1_J, % 230.41/34.42 fact_termination__basic__simps_I2_J, fact_termination__basic__simps_I3_J, % 230.41/34.42 fact_termination__basic__simps_I4_J, fact_termination__basic__simps_I5_J, % 230.41/34.42 fact_times_Oidem, fact_trans__le__add1, fact_trans__le__add2, % 230.41/34.42 fact_trans__less__add1, fact_trans__less__add2, fact_tsub__def, fact_tsub__eq, % 230.41/34.42 fact_uminus__apply, fact_unique__quotient__lemma, % 230.41/34.42 fact_unique__quotient__lemma__neg, fact_xt1_I10_J, fact_xt1_I11_J, % 230.41/34.42 fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J, % 230.41/34.42 fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J, % 230.41/34.42 fact_z3div__def, fact_zabs__def, fact_zabs__less__one__iff, fact_zadd__0, % 230.41/34.42 fact_zadd__0__right, fact_zadd__assoc, fact_zadd__commute, % 230.41/34.42 fact_zadd__left__commute, fact_zadd__left__mono, fact_zadd__strict__right__mono, % 230.41/34.42 fact_zadd__zless__mono, fact_zadd__zminus__inverse2, fact_zadd__zmult__distrib, % 230.41/34.42 fact_zadd__zmult__distrib2, fact_zdiff__zmult__distrib, % 230.41/34.42 fact_zdiff__zmult__distrib2, fact_zdiv__eq__0__iff, fact_zdiv__mono1, % 230.41/34.42 fact_zdiv__mono1__neg, fact_zdiv__mono2, fact_zdiv__mono2__lemma, % 230.41/34.42 fact_zdiv__mono2__neg, fact_zdiv__mono2__neg__lemma, fact_zdiv__self, % 230.41/34.42 fact_zdiv__zero, fact_zdiv__zminus2, fact_zdiv__zminus__zminus, % 230.41/34.42 fact_zdiv__zmult2__eq, fact_zero__le__double__add__iff__zero__le__single__add, % 230.41/34.42 fact_zero__le__power, fact_zero__le__power__abs, fact_zero__le__square, % 230.41/34.42 fact_zero__le__zpower__abs, % 230.41/34.42 fact_zero__less__double__add__iff__zero__less__single__add, % 230.41/34.42 fact_zero__less__power, fact_zero__less__two, fact_zero__neq__one, % 230.41/34.42 fact_zero__reorient, fact_zle__add1__eq__le, fact_zle__antisym, % 230.41/34.42 fact_zle__diff1__eq, fact_zle__linear, fact_zle__refl, fact_zle__trans, % 230.41/34.42 fact_zless__add1__eq, fact_zless__imp__add1__zle, fact_zless__le, % 230.41/34.42 fact_zless__linear, fact_zminus__0, fact_zminus__zadd__distrib, % 230.41/34.42 fact_zminus__zminus, fact_zmult__1, fact_zmult__1__right, fact_zmult__assoc, % 230.41/34.42 fact_zmult__commute, fact_zmult__zless__mono2, fact_zmult__zminus, % 230.41/34.42 fact_zpower__zadd__distrib, fact_zpower__zpower, fact_zsgn__def % 230.41/34.42 % 230.41/34.42 Those formulas are unsatisfiable: % 230.41/34.42 --------------------------------- % 230.41/34.42 % 230.41/34.42 Begin of proof % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact__0960_A_060_061_Acmod_Ac_096) implies: % 230.41/34.43 | (1) ? [v0: $i] : ? [v1: $i] : % 230.41/34.43 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.43 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____) = v1 & % 230.41/34.43 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.43 | v0, v1)) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096) implies: % 230.41/34.43 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 230.41/34.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.43 | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v4 & % 230.41/34.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & hAPP(v2, % 230.41/34.43 | v_m____) = v3 & hAPP(v1, v_r) = v2 & $i(v4) & $i(v3) & $i(v2) & % 230.41/34.43 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.43 | v0, v4)) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact_abs__add__one__gt__zero) implies: % 230.41/34.43 | (3) ? [v0: $i] : ? [v1: $i] : % 230.41/34.43 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.43 | & ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.43 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2) % 230.41/34.43 | | ? [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, % 230.41/34.43 | v3) = v4 & $i(v4) & % 230.41/34.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact_abs__add__one__not__less__self) implies: % 230.41/34.43 | (4) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.41/34.43 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.43 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1) % 230.41/34.43 | | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 230.41/34.43 | v0) = v3 & $i(v3) & ~ % 230.41/34.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1)))) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact_norm__mult__less) implies: % 230.41/34.43 | (5) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.43 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.41/34.43 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 230.41/34.43 | [v10: $i] : ! [v11: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v5) = % 230.41/34.43 | v6) | ~ (c_RealVector_Onorm__class_Onorm(v5, v8) = v9) | ~ % 230.41/34.43 | (hAPP(v10, v1) = v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = % 230.41/34.43 | v7) | ~ (hAPP(v0, v3) = v10) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 230.41/34.43 | | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.43 | class_RealVector_Oreal__normed__algebra(v5) | % 230.41/34.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v11) | ? [v12: % 230.41/34.43 | $i] : ? [v13: $i] : ((c_RealVector_Onorm__class_Onorm(v5, v4) = % 230.41/34.43 | v12 & $i(v12) & ~ % 230.41/34.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v3)) | % 230.41/34.43 | (c_RealVector_Onorm__class_Onorm(v5, v2) = v13 & $i(v13) & ~ % 230.41/34.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v1))))) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact_zero__less__norm__iff) implies: % 230.41/34.43 | (6) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.43 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.43 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~ % 230.41/34.43 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4: % 230.41/34.43 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 230.41/34.43 | v3) | ( ~ (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & % 230.41/34.43 | $i(v4))) & (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.41/34.43 | v0, v3) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = % 230.41/34.43 | v1))))) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact_real__two__squares__add__zero__iff) implies: % 230.41/34.43 | (7) ? [v0: $i] : ? [v1: $i] : % 230.41/34.43 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.43 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) % 230.41/34.43 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 230.41/34.43 | : ! [v7: $i] : (v3 = v1 | ~ % 230.41/34.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~ % 230.41/34.43 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) = % 230.41/34.43 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 230.41/34.43 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.43 | [v7: $i] : (v2 = v1 | ~ % 230.41/34.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~ % 230.41/34.43 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) = % 230.41/34.43 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: % 230.41/34.43 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ % 230.41/34.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~ % 230.41/34.43 | (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2))) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact_norm__one) implies: % 230.41/34.43 | (8) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.41/34.43 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.41/34.43 | (c_Groups_Oone__class_Oone(v1) = v2) | ~ % 230.41/34.43 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~ % 230.41/34.43 | class_RealVector_Oreal__normed__algebra__1(v1))) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact_norm__not__less__zero) implies: % 230.41/34.43 | (9) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.43 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.43 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~ % 230.41/34.43 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ~ % 230.41/34.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0))) % 230.41/34.43 | % 230.41/34.43 | ALPHA: (fact_not__real__square__gt__zero) implies: % 230.41/34.44 | (10) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3, % 230.41/34.44 | v2) = v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v2) | % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2: % 230.41/34.44 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = % 230.41/34.44 | v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 230.41/34.44 | v3))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_norm__ge__zero) implies: % 230.41/34.44 | (11) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~ % 230.41/34.44 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_norm__le__zero__iff) implies: % 230.41/34.44 | (12) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~ % 230.41/34.44 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4: % 230.41/34.44 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.44 | v3, v0) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = v1)) % 230.41/34.44 | & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | % 230.41/34.44 | ( ~ (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & % 230.41/34.44 | $i(v4)))))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_norm__mult__ineq) implies: % 230.41/34.44 | (13) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.41/34.44 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v4) | ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v3, v1) = v6) | ~ (hAPP(v5, v6) % 230.41/34.44 | = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.44 | $i(v1) | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v8: % 230.41/34.44 | $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(v3) = v8 & % 230.41/34.44 | c_RealVector_Onorm__class_Onorm(v3, v10) = v11 & hAPP(v9, v1) = % 230.41/34.44 | v10 & hAPP(v8, v2) = v9 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, v7)))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__le__cancel__iff2) implies: % 230.41/34.44 | (14) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.44 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 230.41/34.44 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 230.41/34.44 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) | % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! % 230.41/34.44 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.44 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.44 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__le__cancel__iff1) implies: % 230.41/34.44 | (15) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.44 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ % 230.41/34.44 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = % 230.41/34.44 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) | % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! % 230.41/34.44 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.44 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, % 230.41/34.44 | v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | % 230.41/34.44 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__assoc) implies: % 230.41/34.44 | (16) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.41/34.44 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v6, v1) = v7) | ~ % 230.41/34.44 | (hAPP(v4, v2) = v5) | ~ (hAPP(v0, v5) = v6) | ~ (hAPP(v0, v3) = % 230.41/34.44 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v8: $i] : ? [v9: % 230.41/34.44 | $i] : (hAPP(v8, v1) = v9 & hAPP(v4, v9) = v7 & hAPP(v0, v2) = v8 % 230.41/34.44 | & $i(v9) & $i(v8) & $i(v7)))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__commute) implies: % 230.41/34.44 | (17) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.44 | (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2) | ~ % 230.41/34.44 | $i(v1) | ? [v5: $i] : (hAPP(v5, v1) = v4 & hAPP(v0, v2) = v5 & % 230.41/34.44 | $i(v5) & $i(v4)))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__left__cancel) implies: % 230.41/34.44 | (18) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.44 | $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, % 230.41/34.44 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 230.41/34.44 | ~ $i(v2))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__right__cancel) implies: % 230.41/34.44 | (19) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.44 | $i] : ! [v7: $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) | % 230.41/34.44 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) % 230.41/34.44 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__zero__not__eq__one) implies: % 230.41/34.44 | (20) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 230.41/34.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.41/34.44 | $i(v0)) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__1) implies: % 230.41/34.44 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.44 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v0, v1) % 230.41/34.44 | = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = % 230.41/34.44 | v3 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__add__mult__distrib) implies: % 230.41/34.44 | (22) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.41/34.44 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 230.41/34.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v8) | ~ % 230.41/34.44 | (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, v3) = % 230.41/34.44 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 230.41/34.44 | | ? [v9: $i] : ? [v10: $i] : % 230.41/34.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v2) = v9 & % 230.41/34.44 | hAPP(v10, v1) = v8 & hAPP(v0, v9) = v10 & $i(v10) & $i(v9) & % 230.41/34.44 | $i(v8)))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_abs__norm__cancel) implies: % 230.41/34.44 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ % 230.41/34.44 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | % 230.41/34.44 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v2 & $i(v2))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_norm__eq__zero) implies: % 230.41/34.44 | (24) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~ % 230.41/34.44 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4: % 230.41/34.44 | $i] : (( ~ (v3 = v0) | (v4 = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(v2) = v1)) & (v3 = v0 | ( ~ (v4 % 230.41/34.44 | = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4)))))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_norm__zero) implies: % 230.41/34.44 | (25) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.41/34.44 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~ % 230.41/34.44 | class_RealVector_Oreal__normed__vector(v1))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_norm__mult) implies: % 230.41/34.44 | (26) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.44 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.41/34.44 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v4) | ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v3, v1) = v6) | ~ (hAPP(v5, v6) % 230.41/34.44 | = v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.44 | $i(v1) | ~ class_RealVector_Oreal__normed__div__algebra(v3) | ? % 230.41/34.44 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(v3) = v8 & % 230.41/34.44 | c_RealVector_Onorm__class_Onorm(v3, v10) = v7 & hAPP(v9, v1) = % 230.41/34.44 | v10 & hAPP(v8, v2) = v9 & $i(v10) & $i(v9) & $i(v8) & $i(v7)))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__less__mono2) implies: % 230.41/34.44 | (27) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.44 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = % 230.41/34.44 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 230.41/34.44 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__order) implies: % 230.41/34.44 | (28) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.41/34.44 | (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 230.41/34.44 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 230.41/34.44 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) % 230.41/34.44 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_real__mult__less__iff1) implies: % 230.41/34.44 | (29) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.44 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ % 230.41/34.44 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = % 230.41/34.44 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2: % 230.41/34.44 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.44 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) % 230.41/34.44 | = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ % 230.41/34.44 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | % 230.41/34.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_norm__ratiotest__lemma) implies: % 230.41/34.44 | (30) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.44 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v5, v3) = v6) | ~ % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~ (hAPP(v7, v8) % 230.41/34.44 | = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~ % 230.41/34.44 | $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v5) % 230.41/34.44 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) | % 230.41/34.44 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) | % 230.41/34.44 | c_Groups_Ozero__class_Ozero(v5) = v3)) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_rabs__ratiotest__lemma) implies: % 230.41/34.44 | (31) ? [v0: $i] : ? [v1: $i] : % 230.41/34.44 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.44 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.44 | $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v0 | ~ % 230.41/34.44 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v5) | ~ % 230.41/34.44 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v7) | ~ % 230.41/34.44 | (hAPP(v6, v7) = v8) | ~ (hAPP(v1, v4) = v6) | ~ $i(v4) | ~ % 230.41/34.44 | $i(v3) | ~ $i(v2) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v8) | ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_pCons) implies: % 230.41/34.44 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.44 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v1 & % 230.41/34.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) % 230.41/34.44 | & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) & % 230.41/34.44 | ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ? % 230.41/34.44 | [v5: $i] : ? [v6: $i] : % 230.41/34.44 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = v6 & % 230.41/34.44 | $i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.44 | v6, v2)) | % 230.41/34.44 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v5 & % 230.41/34.44 | $i(v5) & ~ % 230.41/34.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, % 230.41/34.44 | v_r))))) % 230.41/34.44 | % 230.41/34.44 | ALPHA: (fact_mult__left_Opos__bounded) implies: % 230.41/34.45 | (33) ? [v0: $i] : ? [v1: $i] : % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.45 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 230.41/34.45 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : % 230.41/34.45 | ($i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) % 230.41/34.45 | & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, % 230.41/34.45 | v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: % 230.41/34.45 | $i] : ? [v11: $i] : ? [v12: $i] : % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10, % 230.41/34.45 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) & % 230.41/34.45 | $i(v10) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 230.41/34.45 | v9)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_mult__right_Opos__bounded) implies: % 230.41/34.45 | (34) ? [v0: $i] : ? [v1: $i] : % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.45 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) % 230.41/34.45 | | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.45 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] : % 230.41/34.45 | ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6) % 230.41/34.45 | & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, % 230.41/34.45 | v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: % 230.41/34.45 | $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, % 230.41/34.45 | v11) = v12 & hAPP(v5, v7) = v11 & $i(v12) & $i(v11) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 230.41/34.45 | v10)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_mult_Opos__bounded) implies: % 230.41/34.45 | (35) ? [v0: $i] : ? [v1: $i] : % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.45 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) % 230.41/34.45 | = v3) | ~ $i(v2) | ~ % 230.41/34.45 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] : % 230.41/34.45 | ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) % 230.41/34.45 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! % 230.41/34.45 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, % 230.41/34.45 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = % 230.41/34.45 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? % 230.41/34.45 | [v13: $i] : ? [v14: $i] : ? [v15: $i] : % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13, % 230.41/34.45 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) & % 230.41/34.45 | $i(v13) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15, % 230.41/34.45 | v12)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_mult__left_Ononneg__bounded) implies: % 230.41/34.45 | (36) ? [v0: $i] : ? [v1: $i] : % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.45 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 230.41/34.45 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : % 230.41/34.45 | ($i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 230.41/34.45 | v5) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 230.41/34.45 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ % 230.41/34.45 | (hAPP(v8, v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? % 230.41/34.45 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10, % 230.41/34.45 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) & % 230.41/34.45 | $i(v10) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 230.41/34.45 | v9)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_mult__right_Ononneg__bounded) implies: % 230.41/34.45 | (37) ? [v0: $i] : ? [v1: $i] : % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.45 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) % 230.41/34.45 | | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.45 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] : % 230.41/34.45 | ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 230.41/34.45 | v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 230.41/34.45 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ % 230.41/34.45 | (hAPP(v9, v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? % 230.41/34.45 | [v11: $i] : ? [v12: $i] : % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7) % 230.41/34.45 | = v11 & $i(v12) & $i(v11) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 230.41/34.45 | v10)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_mult_Ononneg__bounded) implies: % 230.41/34.45 | (38) ? [v0: $i] : ? [v1: $i] : % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.45 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) % 230.41/34.45 | = v3) | ~ $i(v2) | ~ % 230.41/34.45 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] : % 230.41/34.45 | ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 230.41/34.45 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : % 230.41/34.45 | ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, % 230.41/34.45 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = % 230.41/34.45 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? % 230.41/34.45 | [v13: $i] : ? [v14: $i] : ? [v15: $i] : % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13, % 230.41/34.45 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) & % 230.41/34.45 | $i(v13) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15, % 230.41/34.45 | v12)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_mult__left_Obounded) implies: % 230.41/34.45 | (39) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.45 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 230.41/34.45 | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] : % 230.41/34.45 | ($i(v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : % 230.41/34.45 | ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ % 230.41/34.45 | (hAPP(v7, v4) = v8) | ~ (hAPP(v0, v6) = v7) | ~ $i(v5) | ? % 230.41/34.45 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v2, v10) = v11 & hAPP(v9, v1) % 230.41/34.45 | = v10 & hAPP(v3, v5) = v9 & $i(v11) & $i(v10) & $i(v9) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 230.41/34.45 | v8)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_order__root) implies: % 230.41/34.45 | (40) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.45 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.45 | $i] : ( ~ (c_Polynomial_Opoly(v3, v2) = v4) | ~ (hAPP(v4, v1) = % 230.41/34.45 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.45 | class_Rings_Oidom(v3) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 230.41/34.45 | ? [v9: $i] : (((v9 = v0 & ~ (v8 = v2) & c_Polynomial_Oorder(v3, % 230.41/34.45 | v1, v2) = v0 & tc_Polynomial_Opoly(v3) = v7 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(v7) = v8 & $i(v8) & $i(v7)) | % 230.41/34.45 | (v6 = v5 & c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5))) & % 230.41/34.45 | ((v8 = v2 & tc_Polynomial_Opoly(v3) = v7 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(v7) = v2 & $i(v7)) | ( ~ (v9 = % 230.41/34.45 | v0) & c_Polynomial_Oorder(v3, v1, v2) = v9 & $i(v9)) | ( ~ % 230.41/34.45 | (v6 = v5) & c_Groups_Ozero__class_Ozero(v3) = v6 & % 230.41/34.45 | $i(v6)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_mult_Obounded) implies: % 230.41/34.45 | (41) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~ % 230.41/34.45 | class_RealVector_Oreal__normed__algebra(v1) | ? [v3: $i] : % 230.41/34.45 | ($i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 230.41/34.45 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v8) | ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v6) | ~ (hAPP(v10, % 230.41/34.45 | v3) = v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v0, v9) = % 230.41/34.45 | v10) | ~ (hAPP(v0, v6) = v7) | ~ $i(v5) | ~ $i(v4) | ? % 230.41/34.45 | [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v1, v13) = v14 & hAPP(v12, % 230.41/34.45 | v5) = v13 & hAPP(v2, v4) = v12 & $i(v14) & $i(v13) & % 230.41/34.45 | $i(v12) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v14, % 230.41/34.45 | v11)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_mult__right_Obounded) implies: % 230.41/34.45 | (42) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.45 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.45 | (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v3, v1) = v4) % 230.41/34.45 | | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.45 | class_RealVector_Oreal__normed__algebra(v2) | ? [v5: $i] : % 230.41/34.45 | ($i(v5) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 230.41/34.45 | ( ~ (c_RealVector_Onorm__class_Onorm(v2, v6) = v7) | ~ % 230.41/34.45 | (hAPP(v8, v5) = v9) | ~ (hAPP(v0, v7) = v8) | ~ $i(v6) | ? % 230.41/34.45 | [v10: $i] : ? [v11: $i] : % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v2, v10) = v11 & hAPP(v4, v6) % 230.41/34.45 | = v10 & $i(v11) & $i(v10) & % 230.41/34.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 230.41/34.45 | v9)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_norm__sgn) implies: % 230.41/34.45 | (43) ? [v0: $i] : ? [v1: $i] : % 230.41/34.45 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.45 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.41/34.45 | (c_Groups_Osgn__class_Osgn(v3, v2) = v4) | ~ % 230.41/34.45 | (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ $i(v3) | ~ % 230.41/34.45 | $i(v2) | ~ class_RealVector_Oreal__normed__vector(v3) | ? [v6: % 230.41/34.45 | $i] : ((v5 = v1 | (v6 = v2 & c_Groups_Ozero__class_Ozero(v3) = % 230.41/34.45 | v2)) & (v5 = v0 | ( ~ (v6 = v2) & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(v3) = v6 & $i(v6)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_real__sgn__pos) implies: % 230.41/34.45 | (44) ? [v0: $i] : ? [v1: $i] : % 230.41/34.45 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) % 230.41/34.45 | & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 230.41/34.45 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2) % 230.41/34.45 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_coeff__1) implies: % 230.41/34.45 | (45) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.45 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.45 | $i] : ! [v6: $i] : ( ~ (c_Polynomial_Ocoeff(v2, v4) = v5) | ~ % 230.41/34.45 | (tc_Polynomial_Opoly(v2) = v3) | ~ (c_Groups_Oone__class_Oone(v3) % 230.41/34.45 | = v4) | ~ (hAPP(v5, v1) = v6) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.45 | class_Rings_Ocomm__semiring__1(v2) | ? [v7: $i] : ? [v8: $i] : % 230.41/34.45 | (( ~ (v1 = v0) | (v7 = v6 & c_Groups_Oone__class_Oone(v2) = v6 & % 230.41/34.45 | $i(v6))) & (v1 = v0 | (v8 = v6 & % 230.41/34.45 | c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_nat__diff__split__asm) implies: % 230.41/34.45 | (46) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.45 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.41/34.45 | $i] : ! [v6: $i] : ( ~ % 230.41/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 230.41/34.45 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2) | ~ % 230.41/34.45 | (hAPP(v3, v4) = v5) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.45 | $i(v1) | ~ hBOOL(v5) | ? [v7: $i] : (hAPP(v3, v6) = v7 & $i(v7) % 230.41/34.45 | & hBOOL(v7))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 230.41/34.45 | [v4: $i] : ! [v5: $i] : ( ~ % 230.41/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 230.41/34.45 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.45 | hBOOL(v5) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) % 230.41/34.45 | | ? [v6: $i] : (hAPP(v3, v0) = v6 & $i(v6) & hBOOL(v6))) & ! % 230.41/34.45 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 230.41/34.45 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 230.41/34.45 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 230.41/34.45 | hBOOL(v5) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | % 230.41/34.45 | ? [v6: $i] : ? [v7: $i] : % 230.41/34.45 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v6) = v2 & hAPP(v3, % 230.41/34.45 | v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))) & ! [v1: $i] : ! % 230.41/34.45 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 230.41/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v4) | ~ % 230.41/34.45 | (hAPP(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 230.41/34.45 | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 230.41/34.45 | : ($i(v7) & ((v8 = v2 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 230.41/34.45 | v1, v7) = v2 & hAPP(v3, v7) = v9 & $i(v9) & ~ hBOOL(v9)) % 230.41/34.45 | | (hAPP(v3, v0) = v6 & $i(v6) & ~ hBOOL(v6)))))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_diff__add__0) implies: % 230.41/34.45 | (47) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.45 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | % 230.41/34.45 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 230.41/34.45 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 230.41/34.45 | $i(v2) | ~ $i(v1))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_diff__0__eq__0) implies: % 230.41/34.45 | (48) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.45 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 230.41/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 230.41/34.45 | $i(v1))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_zero__less__diff) implies: % 230.41/34.45 | (49) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.45 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 230.41/34.45 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 230.41/34.45 | v1, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & % 230.41/34.45 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 230.41/34.45 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 230.41/34.45 | v0, v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_minus__nat_Odiff__0) implies: % 230.41/34.45 | (50) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.45 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 230.41/34.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 230.41/34.45 | $i(v1))) % 230.41/34.45 | % 230.41/34.45 | ALPHA: (fact_diff__self__eq__0) implies: % 230.41/34.46 | (51) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.46 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v1) = v2) | ~ % 230.41/34.46 | $i(v1))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_diff__less) implies: % 230.41/34.46 | (52) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.46 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 230.41/34.46 | v0, v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) % 230.41/34.46 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v1))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_diffs0__imp__equal) implies: % 230.41/34.46 | (53) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.46 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v0) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ? [v3: $i] : ( ~ (v3 = v0) & % 230.41/34.46 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3 & % 230.41/34.46 | $i(v3)))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_diff__is__0__eq_H) implies: % 230.41/34.46 | (54) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.46 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_diff__is__0__eq) implies: % 230.41/34.46 | (55) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.46 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & ! [v1: % 230.41/34.46 | $i] : ! [v2: $i] : ( ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v0) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_mult__eq__if) implies: % 230.41/34.46 | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.46 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 230.41/34.46 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 230.41/34.46 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.46 | [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~ % 230.41/34.46 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ % 230.41/34.46 | $i(v3) | ? [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & % 230.41/34.46 | $i(v9) & $i(v8))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 230.41/34.46 | (v5 = v0 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v0) = v4) | ~ % 230.41/34.46 | $i(v3))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__le__eq__diff) implies: % 230.41/34.46 | (57) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | % 230.41/34.46 | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! % 230.41/34.46 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | % 230.41/34.46 | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__minus__mult__self__le) implies: % 230.41/34.46 | (58) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.41/34.46 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v2) % 230.41/34.46 | = v4) | ~ (hAPP(v0, v2) = v3) | ~ (hAPP(v0, v1) = v5) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ? [v7: $i] : % 230.41/34.46 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v4) = v7 & % 230.41/34.46 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, % 230.41/34.46 | v6)))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__add__eq__0__iff) implies: % 230.41/34.46 | (59) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ? [v4: $i] : ( ~ (v4 = v1) & % 230.41/34.46 | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & % 230.41/34.46 | $i(v4))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v0) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | % 230.41/34.46 | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v1)) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__add__minus__iff) implies: % 230.41/34.46 | (60) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 230.41/34.46 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2) | ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~ % 230.41/34.46 | $i(v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 230.41/34.46 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v3) | ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v0) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__0__le__add__iff) implies: % 230.41/34.46 | (61) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? % 230.41/34.46 | [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) % 230.41/34.46 | = v4 & $i(v4) & % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v1))) & % 230.41/34.46 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? % 230.41/34.46 | [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) % 230.41/34.46 | = v4 & $i(v4) & ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v1)))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__add__le__0__iff) implies: % 230.41/34.46 | (62) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | ? % 230.41/34.46 | [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) % 230.41/34.46 | = v4 & $i(v4) & % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v4))) & % 230.41/34.46 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | ? % 230.41/34.46 | [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) % 230.41/34.46 | = v4 & $i(v4) & ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v4)))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_sgn__real__def) implies: % 230.41/34.46 | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.46 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 & % 230.41/34.46 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.46 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) % 230.41/34.46 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | v3 = v0 | ~ % 230.41/34.46 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v3) = v4) | ~ $i(v3) % 230.41/34.46 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! % 230.41/34.46 | [v3: $i] : ! [v4: $i] : (v4 = v1 | v3 = v0 | ~ % 230.41/34.46 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v3) = v4) | ~ $i(v3) % 230.41/34.46 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! % 230.41/34.46 | [v3: $i] : (v3 = v0 | ~ % 230.41/34.46 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) = v3))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__0__less__add__iff) implies: % 230.41/34.46 | (64) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: % 230.41/34.46 | $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = % 230.41/34.46 | v4 & $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.41/34.46 | v4, v1))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: % 230.41/34.46 | $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = % 230.41/34.46 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.41/34.46 | v4, v1)))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__add__less__0__iff) implies: % 230.41/34.46 | (65) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ? [v4: % 230.41/34.46 | $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = % 230.41/34.46 | v4 & $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.41/34.46 | v1, v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ % 230.41/34.46 | $i(v2) | ~ $i(v1) | % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ? [v4: % 230.41/34.46 | $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = % 230.41/34.46 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.41/34.46 | v1, v4)))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_real__abs__def) implies: % 230.41/34.46 | (66) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.46 | $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 230.41/34.46 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1) % 230.41/34.46 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! % 230.41/34.46 | [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.46 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1) % 230.41/34.46 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | % 230.41/34.46 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 & % 230.41/34.46 | $i(v2)))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_less__eq__nat_Osimps_I1_J) implies: % 230.41/34.46 | (67) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.46 | & ? [v1: $i] : ( ~ $i(v1) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_le__0__eq) implies: % 230.41/34.46 | (68) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.46 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v0) & ! [v1: % 230.41/34.46 | $i] : (v1 = v0 | ~ $i(v1) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_mult__le__cancel1) implies: % 230.41/34.46 | (69) ? [v0: $i] : ? [v1: $i] : % 230.41/34.46 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.46 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.46 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.46 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: % 230.41/34.46 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.46 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.46 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7)) & ! [v2: % 230.41/34.46 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.46 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.46 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_mult__le__cancel2) implies: % 230.41/34.46 | (70) ? [v0: $i] : ? [v1: $i] : % 230.41/34.46 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.46 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.46 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, % 230.41/34.46 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | % 230.41/34.46 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2: % 230.41/34.46 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.46 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) % 230.41/34.46 | = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 230.41/34.46 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8)) & ! [v2: % 230.41/34.46 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.46 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) % 230.41/34.46 | = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 230.41/34.46 | $i(v4) | ~ $i(v3) | ~ $i(v2) | % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 230.41/34.46 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v8))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_gr0I) implies: % 230.41/34.46 | (71) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.46 | & ? [v1: $i] : (v1 = v0 | ~ $i(v1) | % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_mult__less__mono2) implies: % 230.41/34.46 | (72) ? [v0: $i] : ? [v1: $i] : % 230.41/34.46 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.46 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.46 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.46 | ! [v7: $i] : ( ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v5, v3) = v7) | ~ % 230.41/34.46 | (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 230.41/34.46 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 230.41/34.46 | % 230.41/34.46 | ALPHA: (fact_mult__less__mono1) implies: % 230.41/34.47 | (73) ? [v0: $i] : ? [v1: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.47 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v5, % 230.41/34.47 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ (hAPP(v1, v3) = v7) | % 230.41/34.47 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v3) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_mult__cancel2) implies: % 230.41/34.47 | (74) ? [v0: $i] : ? [v1: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.47 | ! [v7: $i] : (v7 = v5 | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = % 230.41/34.47 | v5) | ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ % 230.41/34.47 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.41/34.47 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = v2 | v3 = v1 | ~ % 230.41/34.47 | (hAPP(v7, v3) = v6) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v0, v4) = % 230.41/34.47 | v5) | ~ (hAPP(v0, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 230.41/34.47 | $i(v2))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_mult__less__cancel2) implies: % 230.41/34.47 | (75) ? [v0: $i] : ? [v1: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.47 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, % 230.41/34.47 | v3) = v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | % 230.41/34.47 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)) & ! [v2: $i] % 230.41/34.47 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.47 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = % 230.41/34.47 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 230.41/34.47 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) & ! [v2: $i] % 230.41/34.47 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.47 | $i] : ! [v8: $i] : ( ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v5, v3) = % 230.41/34.47 | v6) | ~ (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v2) = v7) | ~ % 230.41/34.47 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v8))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_mult__less__cancel1) implies: % 230.41/34.47 | (76) ? [v0: $i] : ? [v1: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.47 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.47 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] % 230.41/34.47 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.47 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.47 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4)) & ! [v2: $i] % 230.41/34.47 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.47 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.47 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_mult__is__0) implies: % 230.41/34.47 | (77) ? [v0: $i] : ? [v1: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v2) = % 230.41/34.47 | v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ! % 230.41/34.47 | [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ (hAPP(v3, v1) = v4) | ~ % 230.41/34.47 | (hAPP(v0, v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! % 230.41/34.47 | [v4: $i] : (v3 = v1 | v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ % 230.41/34.47 | (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_mult__0__right) implies: % 230.41/34.47 | (78) ? [v0: $i] : ? [v1: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.47 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | % 230.41/34.47 | hAPP(v3, v1) = v1)) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_nat__0__less__mult__iff) implies: % 230.41/34.47 | (79) ? [v0: $i] : ? [v1: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, % 230.41/34.47 | v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 230.41/34.47 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] % 230.41/34.47 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 230.41/34.47 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2)) & ! [v2: $i] % 230.41/34.47 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 230.41/34.47 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_mult__0) implies: % 230.41/34.47 | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & % 230.41/34.47 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~ % 230.41/34.47 | (hAPP(v2, v3) = v4) | ~ $i(v3))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_neq0__conv) implies: % 230.41/34.47 | (81) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.47 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v0) & ? [v1: % 230.41/34.47 | $i] : (v1 = v0 | ~ $i(v1) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_not__less0) implies: % 230.41/34.47 | (82) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.47 | & ! [v1: $i] : ( ~ $i(v1) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_mult__eq__self__implies__10) implies: % 230.41/34.47 | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.47 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.41/34.47 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 230.41/34.47 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = % 230.41/34.47 | v1 | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | % 230.41/34.47 | ~ $i(v3))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_add__eq__self__zero) implies: % 230.41/34.47 | (84) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.47 | & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v2) | ~ % 230.41/34.47 | $i(v2) | ~ $i(v1))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_add__is__0) implies: % 230.41/34.47 | (85) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.47 | & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ % 230.41/34.47 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v0) | ~ % 230.41/34.47 | $i(v2) | ~ $i(v1)) & ! [v1: $i] : (v1 = v0 | ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v0) = v1))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_Nat_Oadd__0__right) implies: % 230.41/34.47 | (86) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.47 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ % 230.41/34.47 | $i(v1))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_add__gr__0) implies: % 230.41/34.47 | (87) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.47 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 230.41/34.47 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 230.41/34.47 | v0, v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) & ! [v1: $i] % 230.41/34.47 | : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 230.41/34.47 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 230.41/34.47 | v0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & % 230.41/34.47 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v3) | ~ % 230.41/34.47 | $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 230.41/34.47 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_plus__nat_Oadd__0) implies: % 230.41/34.47 | (88) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.47 | & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 230.41/34.47 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ % 230.41/34.47 | $i(v1))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_nat__mult__le__cancel1) implies: % 230.41/34.47 | (89) ? [v0: $i] : ? [v1: $i] : % 230.41/34.47 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.47 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.47 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.47 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.47 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7) | % 230.41/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)) & ! [v2: % 230.41/34.47 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.41/34.47 | [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.47 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~ % 230.41/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 230.41/34.47 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v7))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_nat__mult__1) implies: % 230.41/34.47 | (90) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.47 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.41/34.47 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 % 230.41/34.47 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | % 230.41/34.47 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_nat__1__eq__mult__iff) implies: % 230.41/34.47 | (91) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.41/34.47 | v0 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & $i(v1) & % 230.41/34.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ % 230.41/34.47 | (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 230.41/34.47 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ % 230.41/34.47 | (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 230.41/34.47 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (hAPP(v2, v0) % 230.41/34.47 | = v3) | ~ (hAPP(v1, v0) = v2))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_nat__mult__1__right) implies: % 230.41/34.47 | (92) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.41/34.47 | v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & % 230.41/34.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ % 230.41/34.47 | $i(v2) | hAPP(v3, v1) = v2)) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_nat__mult__eq__1__iff) implies: % 230.41/34.47 | (93) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.41/34.47 | v1 & c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & $i(v1) & % 230.41/34.47 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ % 230.41/34.47 | (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ % 230.41/34.47 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ % 230.41/34.47 | (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ % 230.41/34.47 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (hAPP(v2, v1) % 230.41/34.47 | = v3) | ~ (hAPP(v0, v1) = v2))) % 230.41/34.47 | % 230.41/34.47 | ALPHA: (fact_nat__mult__eq__cancel__disj) implies: % 230.41/34.48 | (94) ? [v0: $i] : ? [v1: $i] : % 230.41/34.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! % 230.41/34.48 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.48 | (v6 = v5 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ % 230.41/34.48 | (hAPP(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! % 230.41/34.48 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | v3 = % 230.41/34.48 | v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ % 230.41/34.48 | (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_nat__mult__eq__cancel1) implies: % 230.41/34.48 | (95) ? [v0: $i] : ? [v1: $i] : % 230.41/34.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.48 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.48 | (v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ % 230.41/34.48 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_nat__mult__less__cancel1) implies: % 230.41/34.48 | (96) ? [v0: $i] : ? [v1: $i] : % 230.41/34.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! % 230.41/34.48 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 230.41/34.48 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.48 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2)) & ! [v2: $i] % 230.41/34.48 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.41/34.48 | $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ % 230.41/34.48 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natceiling__add__one) implies: % 230.41/34.48 | (97) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.48 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 230.41/34.48 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) % 230.41/34.48 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.48 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ % 230.41/34.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.48 | v0, v3) | ? [v5: $i] : ? [v6: $i] : % 230.41/34.48 | (c_RComplete_Onatceiling(v4) = v5 & c_RComplete_Onatceiling(v3) = % 230.41/34.48 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & % 230.41/34.48 | $i(v6) & $i(v5)))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natfloor__add__one) implies: % 230.41/34.48 | (98) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.48 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 230.41/34.48 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) % 230.41/34.48 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.48 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ % 230.41/34.48 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.48 | v0, v3) | ? [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) % 230.41/34.48 | = v5 & c_RComplete_Onatfloor(v3) = v6 & % 230.41/34.48 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) & % 230.41/34.48 | $i(v5)))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natfloor__zero) implies: % 230.41/34.48 | (99) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.41/34.48 | $i(v0)) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_zero__le__natfloor) implies: % 230.41/34.48 | (100) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.48 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) % 230.41/34.48 | | ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, % 230.41/34.48 | v2))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natfloor__one) implies: % 230.41/34.48 | (101) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 & % 230.41/34.48 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.41/34.48 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natceiling__zero) implies: % 230.41/34.48 | (102) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.41/34.48 | $i(v0)) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_zero__le__natceiling) implies: % 230.41/34.48 | (103) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.41/34.48 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatceiling(v1) = % 230.41/34.48 | v2) | ~ $i(v1) | % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natceiling__one) implies: % 230.41/34.48 | (104) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 & % 230.41/34.48 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 230.41/34.48 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natfloor__neg) implies: % 230.41/34.48 | (105) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 230.41/34.48 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) % 230.41/34.48 | & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 230.41/34.48 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natceiling__neg) implies: % 230.41/34.48 | (106) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 230.41/34.48 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) % 230.41/34.48 | & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 230.41/34.48 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_le__natfloor__eq__one) implies: % 230.41/34.48 | (107) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.41/34.48 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & % 230.41/34.48 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) % 230.41/34.48 | = v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) | % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & ! % 230.41/34.48 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ % 230.41/34.48 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.48 | v1, v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, % 230.41/34.48 | v3))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natceiling__le__eq__one) implies: % 230.41/34.48 | (108) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.41/34.48 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & % 230.41/34.48 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.48 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) | % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! % 230.41/34.48 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | % 230.41/34.48 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.48 | v2, v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, % 230.41/34.48 | v0))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_le__mult__natfloor) implies: % 230.41/34.48 | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.41/34.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 230.41/34.48 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & % 230.41/34.48 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.41/34.48 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) % 230.41/34.48 | = v5) | ~ (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) % 230.41/34.48 | = v8) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? % 230.41/34.48 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 230.41/34.48 | (c_RComplete_Onatfloor(v10) = v11 & hAPP(v9, v3) = v10 & hAPP(v2, % 230.41/34.48 | v4) = v9 & $i(v11) & $i(v10) & $i(v9) & % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11)))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_natceiling__eq) implies: % 230.41/34.48 | (110) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.41/34.48 | v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.41/34.48 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 230.41/34.48 | (v5 = v4 | ~ (c_RComplete_Onatceiling(v2) = v4) | ~ % 230.41/34.48 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~ % 230.41/34.48 | $i(v3) | ~ $i(v2) | ? [v6: $i] : ? [v7: $i] : % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & $i(v6) & ( ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v2) | % 230.41/34.48 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 & % 230.41/34.48 | $i(v7) & ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 230.41/34.48 | v7)))))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__of__nat__ge__zero) implies: % 230.41/34.48 | (111) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.48 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__of__nat__zero) implies: % 230.41/34.48 | (112) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.41/34.48 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & % 230.41/34.48 | $i(v0)) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__of__nat__zero__iff) implies: % 230.41/34.48 | (113) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 230.41/34.48 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) % 230.41/34.48 | & $i(v0) & ! [v2: $i] : (v2 = v1 | ~ % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v0) | ~ $i(v2)) & ! [v2: % 230.41/34.48 | $i] : (v2 = v0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_not__real__of__nat__less__zero) implies: % 230.41/34.48 | (114) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.48 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__of__nat__mult) implies: % 230.41/34.48 | (115) ? [v0: $i] : ? [v1: $i] : % 230.41/34.48 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 230.41/34.48 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & $i(v1) & % 230.41/34.48 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 230.41/34.48 | [v6: $i] : ! [v7: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = % 230.41/34.48 | v4) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v6) | ~ (hAPP(v5, % 230.41/34.48 | v6) = v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ~ $i(v2) | % 230.41/34.48 | ? [v8: $i] : ? [v9: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v9) = v7 % 230.41/34.48 | & hAPP(v8, v2) = v9 & hAPP(v0, v3) = v8 & $i(v9) & $i(v8) & % 230.41/34.48 | $i(v7)))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__of__nat__1) implies: % 230.41/34.48 | (116) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 & % 230.41/34.48 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 230.41/34.48 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__natceiling__ge) implies: % 230.41/34.48 | (117) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatceiling(v0) = v1) | % 230.41/34.48 | ~ $i(v0) | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & % 230.41/34.48 | $i(v2) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 230.41/34.48 | v2))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__of__nat__le__zero__cancel__iff) implies: % 230.41/34.48 | (118) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 230.41/34.48 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) % 230.41/34.48 | & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)) & ! % 230.41/34.48 | [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__natfloor__le) implies: % 230.41/34.48 | (119) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.48 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) % 230.41/34.48 | = v2) | ~ $i(v1) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ? % 230.41/34.48 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) & % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_real__of__nat__gt__zero__cancel__iff) implies: % 230.41/34.48 | (120) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 230.41/34.48 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) % 230.41/34.48 | & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! % 230.41/34.48 | [v2: $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = % 230.41/34.48 | v3) | ~ $i(v2) | ~ % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_nat__less__real__le) implies: % 230.41/34.48 | (121) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.41/34.48 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.41/34.48 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 230.41/34.48 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: % 230.41/34.48 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = % 230.41/34.48 | v5 & $i(v5) & % 230.41/34.48 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))) & % 230.41/34.48 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 230.41/34.48 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 230.41/34.48 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] % 230.41/34.48 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & % 230.41/34.48 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.41/34.48 | v5, v4)))) % 230.41/34.48 | % 230.41/34.48 | ALPHA: (fact_nat__le__real__less) implies: % 230.41/34.49 | (122) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.41/34.49 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 230.41/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 230.41/34.49 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? % 230.41/34.49 | [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) % 230.41/34.49 | = v5 & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.41/34.49 | v3, v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 230.41/34.49 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 230.41/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: % 230.41/34.49 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = % 230.41/34.49 | v5 & $i(v5) & ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5)))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_le__natfloor__eq) implies: % 230.41/34.49 | (123) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.41/34.49 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ % 230.41/34.49 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)) & ! % 230.41/34.49 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ % 230.41/34.49 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_natceiling__le__eq) implies: % 230.41/34.49 | (124) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.41/34.49 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ % 230.41/34.49 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4)) & ! % 230.41/34.49 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ % 230.41/34.49 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_real__natfloor__add__one__gt) implies: % 230.41/34.49 | (125) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) % 230.41/34.49 | = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : % 230.41/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & % 230.41/34.49 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 & % 230.41/34.49 | $i(v4) & $i(v3) & % 230.41/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4)))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_real__natfloor__gt__diff__one) implies: % 230.41/34.49 | (126) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 230.41/34.49 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | % 230.41/34.49 | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : % 230.41/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & % 230.41/34.49 | c_RComplete_Onatfloor(v1) = v3 & $i(v4) & $i(v3) & % 230.41/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4)))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_less__natfloor) implies: % 230.41/34.49 | (127) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.41/34.49 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~ % 230.41/34.49 | (c_RComplete_Onatfloor(v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 230.41/34.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_natfloor__add) implies: % 230.41/34.49 | (128) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.41/34.49 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~ % 230.41/34.49 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~ % 230.41/34.49 | $i(v2) | ~ $i(v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? % 230.41/34.49 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 & % 230.41/34.49 | c_RComplete_Onatfloor(v2) = v6 & % 230.41/34.49 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) % 230.41/34.49 | & $i(v5)))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_ge__natfloor__plus__one__imp__gt) implies: % 230.41/34.49 | (129) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 230.41/34.49 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.41/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ % 230.41/34.49 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 230.41/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5: % 230.41/34.49 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 & % 230.41/34.49 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, % 230.41/34.49 | v1)))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_natfloor__eq) implies: % 230.41/34.49 | (130) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 230.41/34.49 | (v4 = v2 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ % 230.41/34.49 | (c_RComplete_Onatfloor(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? % 230.41/34.49 | [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) % 230.41/34.49 | = v5 & $i(v5) & ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5)))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_natceiling__add) implies: % 230.41/34.49 | (131) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.41/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.41/34.49 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~ % 230.41/34.49 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~ % 230.41/34.49 | $i(v2) | ~ $i(v1) | ~ % 230.41/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? % 230.41/34.49 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 & % 230.41/34.49 | c_RComplete_Onatceiling(v2) = v6 & % 230.41/34.49 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) % 230.41/34.49 | & $i(v5)))) % 230.41/34.49 | % 230.41/34.49 | ALPHA: (fact_reals__Archimedean6) implies: % 230.88/34.49 | (132) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.88/34.49 | v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.49 | $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? % 230.88/34.49 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 230.88/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & % 230.88/34.49 | c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & % 230.88/34.49 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & % 230.88/34.49 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6) & % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2)))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_lemma__interval) implies: % 230.88/34.49 | (133) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 230.88/34.49 | $i(v2) | ~ $i(v1) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4: % 230.88/34.49 | $i] : ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.88/34.49 | v0, v4) & ! [v5: $i] : ! [v6: $i] : ( ~ % 230.88/34.49 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = % 230.88/34.49 | v6) | ~ $i(v5) | % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1) | % 230.88/34.49 | ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, % 230.88/34.49 | v6) = v7 & $i(v7) & ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v4))) & % 230.88/34.49 | ! [v5: $i] : ! [v6: $i] : ( ~ % 230.88/34.49 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = % 230.88/34.49 | v6) | ~ $i(v5) | % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5) | % 230.88/34.49 | ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, % 230.88/34.49 | v6) = v7 & $i(v7) & ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, % 230.88/34.49 | v4)))))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_ex__least__nat__less) implies: % 230.88/34.49 | (134) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.88/34.49 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 230.88/34.49 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, % 230.88/34.49 | v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v4) | ? [v5: % 230.88/34.49 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 230.88/34.49 | ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 & % 230.88/34.49 | hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) & % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! % 230.88/34.49 | [v9: $i] : ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ % 230.88/34.49 | $i(v9) | ~ hBOOL(v10) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) % 230.88/34.49 | | (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5)))))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_lemma__interval__lt) implies: % 230.88/34.49 | (135) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 230.88/34.49 | $i(v2) | ~ $i(v1) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4: % 230.88/34.49 | $i] : ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.88/34.49 | v0, v4) & ! [v5: $i] : ! [v6: $i] : ( ~ % 230.88/34.49 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = % 230.88/34.49 | v6) | ~ $i(v5) | % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v5, v1) | ? % 230.88/34.49 | [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = % 230.88/34.49 | v7 & $i(v7) & ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v4))) & % 230.88/34.49 | ! [v5: $i] : ! [v6: $i] : ( ~ % 230.88/34.49 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = % 230.88/34.49 | v6) | ~ $i(v5) | % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5) | ? % 230.88/34.49 | [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = % 230.88/34.49 | v7 & $i(v7) & ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, % 230.88/34.49 | v4)))))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_lemmaCauchy) implies: % 230.88/34.49 | (136) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.88/34.49 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.88/34.49 | [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v4, % 230.88/34.49 | v5) = v6) | ~ (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 230.88/34.49 | ~ $i(v2) | ~ $i(v1) | ~ class_Orderings_Oord(v3) | ~ % 230.88/34.49 | class_RealVector_Oreal__normed__vector(v4) | ? [v7: $i] : ? % 230.88/34.49 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & % 230.88/34.49 | ((c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 & % 230.88/34.49 | c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1, % 230.88/34.49 | v8) = v9 & $i(v11) & $i(v10) & $i(v9) & % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(v3, v2, v8) & ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v0)) | % 230.88/34.49 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 & % 230.88/34.49 | $i(v7) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ % 230.88/34.49 | (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~ % 230.88/34.49 | (hAPP(v1, v12) = v13) | ~ $i(v12) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(v3, v2, v12) | % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, % 230.88/34.49 | v7))))))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_reals__Archimedean3) implies: % 230.88/34.49 | (137) ? [v0: $i] : ? [v1: $i] : % 230.88/34.49 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.88/34.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.49 | $i(v0) & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: % 230.88/34.49 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 230.88/34.49 | (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & hAPP(v6, v3) = v7 & % 230.88/34.49 | hAPP(v1, v5) = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v7)))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_LIMSEQ__inverse__realpow__zero__lemma) implies: % 230.88/34.49 | (138) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 230.88/34.49 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 & % 230.88/34.49 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & % 230.88/34.49 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.88/34.49 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) & % 230.88/34.49 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 230.88/34.49 | : ! [v7: $i] : ! [v8: $i] : ( ~ % 230.88/34.49 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) | ~ % 230.88/34.49 | (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ % 230.88/34.49 | $i(v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.88/34.49 | v0, v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 230.88/34.49 | $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 & % 230.88/34.49 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & % 230.88/34.49 | hAPP(v10, v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & % 230.88/34.49 | $i(v10) & $i(v9) & % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8)))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_Bseq__def) implies: % 230.88/34.49 | (139) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.49 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 230.88/34.49 | $i(v2) | ~ $i(v1) | ~ % 230.88/34.49 | class_RealVector_Oreal__normed__vector(v2) | ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | % 230.88/34.49 | c_SEQ_OBseq(v2, v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 230.88/34.49 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6 & hAPP(v1, v4) = v5 % 230.88/34.49 | & $i(v6) & $i(v5) & $i(v4) & ~ % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))) & % 230.88/34.49 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.49 | c_SEQ_OBseq(v2, v1) | ~ % 230.88/34.49 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : % 230.88/34.49 | ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) % 230.88/34.49 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 230.88/34.49 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v1, % 230.88/34.49 | v4) = v5) | ~ $i(v4) | % 230.88/34.49 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, % 230.88/34.49 | v3))))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) % 230.88/34.49 | implies: % 230.88/34.49 | (140) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.88/34.49 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.88/34.49 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) % 230.88/34.49 | | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | % 230.88/34.49 | ? [v5: $i] : (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) % 230.88/34.49 | = v5 & $i(v5)))) % 230.88/34.49 | % 230.88/34.49 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) % 230.88/34.49 | implies: % 230.88/34.49 | (141) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 230.88/34.49 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.88/34.49 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) % 230.88/34.49 | | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | % 230.88/34.49 | hAPP(v4, v0) = v1)) % 230.88/34.49 | % 230.88/34.50 | ALPHA: (fact_realpow__minus__mult) implies: % 230.88/34.50 | (142) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.88/34.50 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 230.88/34.50 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 230.88/34.50 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 230.88/34.50 | ! [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v4) = v6) | ~ % 230.88/34.50 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~ % 230.88/34.50 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ (hAPP(v10, v2) = % 230.88/34.50 | v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~ % 230.88/34.50 | (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.88/34.50 | class_Groups_Omonoid__mult(v4) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, % 230.88/34.50 | v3) = v11 & $i(v11)))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_realpow__num__eq__if) implies: % 230.88/34.50 | (143) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 230.88/34.50 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 230.88/34.50 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 230.88/34.50 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 230.88/34.50 | ! [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v4) = v5) | ~ % 230.88/34.50 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~ % 230.88/34.50 | (c_Groups_Otimes__class_Otimes(v4) = v7) | ~ (hAPP(v8, v10) = % 230.88/34.50 | v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~ % 230.88/34.50 | (hAPP(v5, v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.88/34.50 | class_Power_Opower(v4) | ? [v12: $i] : ? [v13: $i] : (( ~ (v3 = % 230.88/34.50 | v0) | (v13 = v12 & c_Groups_Oone__class_Oone(v4) = v12 & % 230.88/34.50 | hAPP(v6, v0) = v12 & $i(v12))) & (v3 = v0 | (v12 = v11 & % 230.88/34.50 | hAPP(v6, v3) = v11 & $i(v11)))))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_power__strict__mono) implies: % 230.88/34.50 | (144) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.88/34.50 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.88/34.50 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 230.88/34.50 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v1) = v9) % 230.88/34.50 | | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, % 230.88/34.50 | v2) = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 230.88/34.50 | ~ class_Rings_Olinordered__semidom(v4) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(v4, v3, v2) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | % 230.88/34.50 | c_Orderings_Oord__class_Oless(v4, v7, v9) | ? [v10: $i] : % 230.88/34.50 | (c_Groups_Ozero__class_Ozero(v4) = v10 & $i(v10) & ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(v4, v10, v3)))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_one__less__power) implies: % 230.88/34.50 | (145) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.88/34.50 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.88/34.50 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 230.88/34.50 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ % 230.88/34.50 | $i(v2) | ~ $i(v1) | ~ class_Rings_Olinordered__semidom(v3) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v7: $i] % 230.88/34.50 | : (c_Groups_Oone__class_Oone(v3) = v7 & $i(v7) & ( ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(v3, v7, v2) | % 230.88/34.50 | c_Orderings_Oord__class_Oless(v3, v7, v6))))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_nat__power__less__imp__less) implies: % 230.88/34.50 | (146) ? [v0: $i] : ? [v1: $i] : % 230.88/34.50 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 230.88/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 230.88/34.50 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 230.88/34.50 | : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | % 230.88/34.50 | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v7) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_zero__less__zpower__abs__iff) implies: % 230.88/34.50 | (147) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.88/34.50 | (c_Power_Opower__class_Opower(tc_Int_Oint) = v1 & % 230.88/34.50 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v0 & % 230.88/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 230.88/34.50 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 230.88/34.50 | [v7: $i] : (v4 = v0 | ~ (c_Groups_Oabs__class_Oabs(tc_Int_Oint, % 230.88/34.50 | v4) = v5) | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | % 230.88/34.50 | ~ $i(v4) | ~ $i(v3) | % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v7)) & ! [v3: $i] % 230.88/34.50 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ % 230.88/34.50 | (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v0) = v4) | ~ (hAPP(v5, % 230.88/34.50 | v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v6)) & ! [v3: $i] % 230.88/34.50 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 230.88/34.50 | (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v3) = v4) | ~ (hAPP(v5, % 230.88/34.50 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Int_Oint, v0, v6))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_power__eq__if) implies: % 230.88/34.50 | (148) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 230.88/34.50 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 230.88/34.50 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 230.88/34.50 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 & % 230.88/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & % 230.88/34.50 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 230.88/34.50 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~ % 230.88/34.50 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ % 230.88/34.50 | (hAPP(v7, v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) % 230.88/34.50 | = v7) | ~ (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | % 230.88/34.50 | (hAPP(v6, v5) = v10 & $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! % 230.88/34.50 | [v6: $i] : (v6 = v2 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = % 230.88/34.50 | v5) | ~ $i(v4))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_power__eq__0__iff) implies: % 230.88/34.50 | (149) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.88/34.50 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.88/34.50 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | % 230.88/34.50 | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ $i(v3) | ~ % 230.88/34.50 | $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v3) | ~ % 230.88/34.50 | class_Rings_Ozero__neq__one(v3) | ~ class_Rings_Omult__zero(v3) % 230.88/34.50 | | ~ class_Rings_Ono__zero__divisors(v3) | ? [v7: $i] : % 230.88/34.50 | (c_Groups_Ozero__class_Ozero(v3) = v7 & $i(v7) & ( ~ (v7 = v6) | % 230.88/34.50 | (v6 = v2 & ~ (v1 = v0))) & ( ~ (v7 = v2) | v6 = v2 | v1 = % 230.88/34.50 | v0)))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_power__0) implies: % 230.88/34.50 | (150) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.88/34.50 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.88/34.50 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) % 230.88/34.50 | | ~ $i(v2) | ~ $i(v1) | ~ class_Power_Opower(v2) | ? [v5: $i] % 230.88/34.50 | : (c_Groups_Oone__class_Oone(v2) = v5 & hAPP(v4, v0) = v5 & % 230.88/34.50 | $i(v5)))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_power__0__left) implies: % 230.88/34.50 | (151) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.88/34.50 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.88/34.50 | $i] : ! [v6: $i] : (v6 = v4 | v1 = v0 | ~ % 230.88/34.50 | (c_Power_Opower__class_Opower(v2) = v3) | ~ % 230.88/34.50 | (c_Groups_Ozero__class_Ozero(v2) = v4) | ~ (hAPP(v5, v1) = v6) | % 230.88/34.50 | ~ (hAPP(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.50 | class_Rings_Osemiring__0(v2) | ~ class_Power_Opower(v2)) & ! % 230.88/34.50 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 230.88/34.50 | ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ % 230.88/34.50 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | % 230.88/34.50 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ % 230.88/34.50 | class_Rings_Osemiring__0(v1) | ~ class_Power_Opower(v1) | % 230.88/34.50 | (c_Groups_Oone__class_Oone(v1) = v5 & $i(v5)))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_power__eq__imp__eq__base) implies: % 230.88/34.50 | (152) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.88/34.50 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.88/34.50 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v1 | ~ % 230.88/34.50 | (c_Power_Opower__class_Opower(v4) = v5) | ~ (hAPP(v8, v2) = v7) % 230.88/34.50 | | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, % 230.88/34.50 | v1) = v8) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 230.88/34.50 | ~ class_Rings_Olinordered__semidom(v4) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v9: $i] % 230.88/34.50 | : (c_Groups_Ozero__class_Ozero(v4) = v9 & $i(v9) & ( ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(v4, v9, v3) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(v4, v9, v1))))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_Bseq__iff2) implies: % 230.88/34.50 | (153) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.50 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.88/34.50 | [v5: $i] : ( ~ (c_Groups_Ouminus__class_Ouminus(v2, v4) = v5) | ~ % 230.88/34.50 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.50 | class_RealVector_Oreal__normed__vector(v2) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | % 230.88/34.50 | c_SEQ_OBseq(v2, v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 230.88/34.50 | ? [v9: $i] : (c_Groups_Oplus__class_Oplus(v2, v7, v5) = v8 & % 230.88/34.50 | c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v6) = % 230.88/34.50 | v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3))) & % 230.88/34.50 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.50 | c_SEQ_OBseq(v2, v1) | ~ % 230.88/34.50 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? % 230.88/34.50 | [v4: $i] : ? [v5: $i] : (c_Groups_Ouminus__class_Ouminus(v2, v4) % 230.88/34.50 | = v5 & $i(v5) & $i(v4) & $i(v3) & % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! % 230.88/34.50 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 230.88/34.50 | (c_Groups_Oplus__class_Oplus(v2, v7, v5) = v8) | ~ % 230.88/34.50 | (c_RealVector_Onorm__class_Onorm(v2, v8) = v9) | ~ (hAPP(v1, % 230.88/34.50 | v6) = v7) | ~ $i(v6) | % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, % 230.88/34.50 | v3))))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_Bseq__iff3) implies: % 230.88/34.50 | (154) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.50 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 230.88/34.50 | [v5: $i] : ! [v6: $i] : ( ~ (c_Groups_Ouminus__class_Ouminus(v2, % 230.88/34.50 | v5) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 230.88/34.50 | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.50 | class_RealVector_Oreal__normed__vector(v2) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | % 230.88/34.50 | c_SEQ_OBseq(v2, v1) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 230.88/34.50 | ? [v10: $i] : (c_Groups_Oplus__class_Oplus(v2, v8, v6) = v9 & % 230.88/34.50 | c_RealVector_Onorm__class_Onorm(v2, v9) = v10 & hAPP(v1, v7) = % 230.88/34.50 | v8 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v3))) % 230.88/34.50 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.50 | c_SEQ_OBseq(v2, v1) | ~ % 230.88/34.50 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? % 230.88/34.50 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 230.88/34.50 | (c_Groups_Ouminus__class_Ouminus(v2, v5) = v6 & hAPP(v1, v4) = v5 % 230.88/34.50 | & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! % 230.88/34.50 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 230.88/34.50 | (c_Groups_Oplus__class_Oplus(v2, v8, v6) = v9) | ~ % 230.88/34.50 | (c_RealVector_Onorm__class_Onorm(v2, v9) = v10) | ~ % 230.88/34.50 | (hAPP(v1, v7) = v8) | ~ $i(v7) | % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 230.88/34.50 | v3))))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_power_Opower_Opower__0) implies: % 230.88/34.50 | (155) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 230.88/34.50 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 230.88/34.50 | $i] : ! [v6: $i] : ( ~ (c_Power_Opower_Opower(v4, v3, v2) = v5) % 230.88/34.50 | | ~ (hAPP(v5, v1) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.88/34.50 | $i(v1) | hAPP(v6, v0) = v3)) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_zero__less__power__nat__eq) implies: % 230.88/34.50 | (156) ? [v0: $i] : ? [v1: $i] : % 230.88/34.50 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 230.88/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 230.88/34.50 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | % 230.88/34.50 | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 230.88/34.50 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3)) & ! [v2: $i] % 230.88/34.50 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) % 230.88/34.50 | | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5)) & ! [v2: $i] % 230.88/34.50 | : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ % 230.88/34.50 | (hAPP(v1, v2) = v3) | ~ $i(v2) | % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_BseqI) implies: % 230.88/34.50 | (157) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.50 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 230.88/34.50 | $i(v2) | ~ $i(v1) | ~ % 230.88/34.50 | class_RealVector_Oreal__normed__vector(v3) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 230.88/34.50 | c_SEQ_OBseq(v3, v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 230.88/34.50 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6 & hAPP(v1, v4) = v5 % 230.88/34.50 | & $i(v6) & $i(v5) & $i(v4) & ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v2)))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_BseqD) implies: % 230.88/34.50 | (158) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.50 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.50 | c_SEQ_OBseq(v2, v1) | ~ % 230.88/34.50 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : % 230.88/34.50 | ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) % 230.88/34.50 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 230.88/34.50 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v1, % 230.88/34.50 | v4) = v5) | ~ $i(v4) | % 230.88/34.50 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, % 230.88/34.50 | v3))))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_realpow__pos__nth__unique) implies: % 230.88/34.50 | (159) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.88/34.50 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 & % 230.88/34.50 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.88/34.50 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & % 230.88/34.50 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ % 230.88/34.50 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.88/34.50 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? % 230.88/34.50 | [v5: $i] : ? [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & % 230.88/34.50 | $i(v6) & $i(v5) & % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & ! % 230.88/34.50 | [v7: $i] : ! [v8: $i] : (v7 = v5 | ~ (hAPP(v8, v4) = v3) | ~ % 230.88/34.50 | (hAPP(v2, v7) = v8) | ~ $i(v7) | ~ % 230.88/34.50 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v7))))) % 230.88/34.50 | % 230.88/34.50 | ALPHA: (fact_realpow__pos__nth) implies: % 230.88/34.51 | (160) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.88/34.51 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & % 230.88/34.51 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ % 230.88/34.51 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 230.88/34.51 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? % 230.88/34.51 | [v5: $i] : ? [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & % 230.88/34.51 | $i(v6) & $i(v5) & % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5)))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__realpow) implies: % 230.88/34.51 | (161) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.88/34.51 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & % 230.88/34.51 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 230.88/34.51 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) = % 230.88/34.51 | v7) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6, % 230.88/34.51 | v7) = v8) | ~ (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 230.88/34.51 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? % 230.88/34.51 | [v9: $i] : ? [v10: $i] : (c_Transcendental_Oln(v10) = v8 & % 230.88/34.51 | hAPP(v9, v3) = v10 & hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & % 230.88/34.51 | $i(v8)))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__one) implies: % 230.88/34.51 | (162) ? [v0: $i] : ? [v1: $i] : (c_Transcendental_Oln(v0) = v1 & % 230.88/34.51 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & % 230.88/34.51 | $i(v0)) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__less__self) implies: % 230.88/34.51 | (163) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.51 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Transcendental_Oln(v1) % 230.88/34.51 | = v2) | ~ $i(v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__inj__iff) implies: % 230.88/34.51 | (164) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.51 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 230.88/34.51 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) = % 230.88/34.51 | v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__less__cancel__iff) implies: % 230.88/34.51 | (165) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.51 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.88/34.51 | ~ (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) % 230.88/34.51 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! % 230.88/34.51 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.88/34.51 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) = % 230.88/34.51 | v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__le__cancel__iff) implies: % 230.88/34.51 | (166) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.51 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.88/34.51 | ~ (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) % 230.88/34.51 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) | % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! % 230.88/34.51 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 230.88/34.51 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) = % 230.88/34.51 | v4) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__ge__zero) implies: % 230.88/34.51 | (167) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) % 230.88/34.51 | = v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__gt__zero) implies: % 230.88/34.51 | (168) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) % 230.88/34.51 | = v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__gt__zero__iff) implies: % 230.88/34.51 | (169) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) % 230.88/34.51 | = v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! % 230.88/34.51 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ % 230.88/34.51 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 230.88/34.51 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 230.88/34.51 | v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__eq__zero__iff) implies: % 230.88/34.51 | (170) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = % 230.88/34.51 | v0) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)) & ! % 230.88/34.51 | [v2: $i] : (v2 = v0 | ~ (c_Transcendental_Oln(v1) = v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__less__zero__iff) implies: % 230.88/34.51 | (171) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) % 230.88/34.51 | = v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! % 230.88/34.51 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ % 230.88/34.51 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, % 230.88/34.51 | v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 230.88/34.51 | v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__less__zero) implies: % 230.88/34.51 | (172) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) % 230.88/34.51 | = v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__gt__zero__imp__gt__one) implies: % 230.88/34.51 | (173) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) % 230.88/34.51 | = v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__ge__zero__iff) implies: % 230.88/34.51 | (174) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) % 230.88/34.51 | = v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) | % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & ! % 230.88/34.51 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ % 230.88/34.51 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 230.88/34.51 | v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.88/34.51 | v0, v3) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.88/34.51 | v1, v2))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__ge__zero__imp__ge__one) implies: % 230.88/34.51 | (175) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) % 230.88/34.51 | = v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__mult) implies: % 230.88/34.51 | (176) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 230.88/34.51 | [v6: $i] : ( ~ (c_Transcendental_Oln(v3) = v4) | ~ % 230.88/34.51 | (c_Transcendental_Oln(v2) = v5) | ~ % 230.88/34.51 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~ % 230.88/34.51 | $i(v3) | ~ $i(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7: % 230.88/34.51 | $i] : ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7, % 230.88/34.51 | v2) = v8 & hAPP(v1, v3) = v7 & $i(v8) & $i(v7) & $i(v6)))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_ln__add__one__self__le__self) implies: % 230.88/34.51 | (177) ? [v0: $i] : ? [v1: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 230.88/34.51 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~ % 230.88/34.51 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 230.88/34.51 | v0, v2) | ? [v4: $i] : (c_Transcendental_Oln(v3) = v4 & $i(v4) % 230.88/34.51 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, % 230.88/34.51 | v2)))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_nat0__intermed__int__val) implies: % 230.88/34.51 | (178) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 230.88/34.51 | (c_Groups_Oone__class_Oone(tc_Int_Oint) = v1 & % 230.88/34.51 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 230.88/34.51 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & % 230.88/34.51 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 230.88/34.51 | ~ (hAPP(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v3, v6) | ? [v7: % 230.88/34.51 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : % 230.88/34.51 | ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : % 230.88/34.51 | ($i(v10) & $i(v8) & ((v9 = v3 & hAPP(v4, v8) = v3 & % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v5)) | % 230.88/34.51 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v12, v13) = v14 & % 230.88/34.51 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v10, v0) = v11 & % 230.88/34.51 | c_Groups_Oabs__class_Oabs(tc_Int_Oint, v14) = v15 & % 230.88/34.51 | hAPP(v4, v11) = v12 & hAPP(v4, v10) = v13 & $i(v15) & % 230.88/34.51 | $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v5) & ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v15, v1)) | % 230.88/34.51 | (hAPP(v4, v2) = v7 & $i(v7) & ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v7, v3)))))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_lemma__NBseq__def) implies: % 230.88/34.51 | (179) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 230.88/34.51 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 230.88/34.51 | ~ (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.51 | class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ? % 230.88/34.51 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & % 230.88/34.51 | $i(v5) & ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 & % 230.88/34.51 | c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) % 230.88/34.51 | = v8 & $i(v9) & $i(v8) & $i(v6) & ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, % 230.88/34.51 | v6)) | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 230.88/34.51 | v0, v5) & ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( % 230.88/34.51 | ~ (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ % 230.88/34.51 | (hAPP(v1, v10) = v11) | ~ $i(v10) | % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 230.88/34.51 | v5)))))) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 230.88/34.51 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 230.88/34.51 | class_RealVector_Oreal__normed__vector(v2) | ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: % 230.88/34.51 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 230.88/34.51 | ? [v9: $i] : ($i(v7) & $i(v4) & ((c_Nat_OSuc(v4) = v5 & % 230.88/34.51 | c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 & $i(v6) & $i(v5) & % 230.88/34.51 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 230.88/34.51 | (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ % 230.88/34.51 | (hAPP(v1, v10) = v11) | ~ $i(v10) | % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 230.88/34.51 | v6))) | (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & % 230.88/34.51 | hAPP(v1, v7) = v8 & $i(v9) & $i(v8) & ~ % 230.88/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, % 230.88/34.51 | v3)))))) % 230.88/34.51 | % 230.88/34.51 | ALPHA: (fact_lemma__NBseq__def2) implies: % 231.00/34.51 | (180) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.00/34.51 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 231.00/34.51 | ~ (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 231.00/34.51 | class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ? % 231.00/34.51 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & % 231.00/34.51 | $i(v5) & ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 & % 231.00/34.51 | c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) % 231.00/34.51 | = v8 & $i(v9) & $i(v8) & $i(v6) & ~ % 231.00/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v6)) | % 231.00/34.51 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! % 231.00/34.51 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 231.00/34.51 | (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ % 231.00/34.51 | (hAPP(v1, v10) = v11) | ~ $i(v10) | % 231.00/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, % 231.00/34.51 | v5)))))) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 231.00/34.51 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 231.00/34.51 | class_RealVector_Oreal__normed__vector(v2) | ~ % 231.00/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: % 231.00/34.51 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 231.00/34.51 | ? [v9: $i] : ($i(v7) & $i(v4) & ((c_Nat_OSuc(v4) = v5 & % 231.00/34.51 | c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 & $i(v6) & $i(v5) & % 231.00/34.51 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 231.00/34.51 | (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ % 231.00/34.51 | (hAPP(v1, v10) = v11) | ~ $i(v10) | % 231.00/34.51 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, % 231.00/34.51 | v6))) | (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & % 231.00/34.51 | hAPP(v1, v7) = v8 & $i(v9) & $i(v8) & ~ % 231.00/34.51 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, % 231.00/34.51 | v3)))))) % 231.00/34.51 | % 231.00/34.51 | ALPHA: (fact_zero__less__Suc) implies: % 231.00/34.51 | (181) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.51 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) % 231.00/34.51 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_nat__lt__two__imp__zero__or__one) implies: % 231.00/34.52 | (182) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 231.00/34.52 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 231.00/34.52 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 231.00/34.52 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_One__nat__def) implies: % 231.00/34.52 | (183) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & % 231.00/34.52 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_one__is__add) implies: % 231.00/34.52 | (184) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.52 | ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 231.00/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | ~ % 231.00/34.52 | $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v2 = % 231.00/34.52 | v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v1) | % 231.00/34.52 | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | % 231.00/34.52 | v2 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = % 231.00/34.52 | v1) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 % 231.00/34.52 | = v1 | v2 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, % 231.00/34.52 | v2) = v1) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : (v2 = v1 | % 231.00/34.52 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2)) & ! % 231.00/34.52 | [v2: $i] : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 231.00/34.52 | v0, v1) = v2))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_diff__Suc__eq__diff__pred) implies: % 231.00/34.52 | (185) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 231.00/34.52 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.00/34.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4) | ~ % 231.00/34.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ % 231.00/34.52 | $i(v2) | ~ $i(v1) | ? [v5: $i] : (c_Nat_OSuc(v1) = v5 & % 231.00/34.52 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v5) = v4 & % 231.00/34.52 | $i(v5) & $i(v4)))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_Suc__eq__plus1) implies: % 231.00/34.52 | (186) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 231.00/34.52 | ! [v1: $i] : ! [v2: $i] : ( ~ % 231.00/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ % 231.00/34.52 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_Suc__eq__plus1__left) implies: % 231.00/34.52 | (187) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & % 231.00/34.52 | ! [v1: $i] : ! [v2: $i] : ( ~ % 231.00/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ % 231.00/34.52 | $i(v1) | (c_Nat_OSuc(v1) = v2 & $i(v2)))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_nat_Osimps_I3_J) implies: % 231.00/34.52 | (188) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.52 | & ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = v0) | ~ $i(v1))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_less__Suc__eq__0__disj) implies: % 231.00/34.52 | (189) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.52 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.00/34.52 | (c_Nat_OSuc(v4) = v2) | ~ (c_Nat_OSuc(v1) = v3) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v2) | ~ $i(v1) | ~ % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1) | % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v1: $i] % 231.00/34.52 | : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~ (c_Nat_OSuc(v1) = v3) | % 231.00/34.52 | ~ $i(v2) | ~ $i(v1) | ~ % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | ? [v4: $i] % 231.00/34.52 | : (c_Nat_OSuc(v4) = v2 & $i(v4) & % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1))) & ! [v1: % 231.00/34.52 | $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ $i(v1) | % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_less__Suc0) implies: % 231.00/34.52 | (190) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) & ! [v2: $i] : % 231.00/34.52 | (v2 = v0 | ~ $i(v2) | ~ % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_gr0__conv__Suc) implies: % 231.00/34.52 | (191) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.52 | & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v2) = v1) | ~ $i(v2) % 231.00/34.52 | | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1)) % 231.00/34.52 | & ! [v1: $i] : ( ~ $i(v1) | ~ % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | ? [v2: $i] % 231.00/34.52 | : (c_Nat_OSuc(v2) = v1 & $i(v2)))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_mult__eq__1__iff) implies: % 231.00/34.52 | (192) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 231.00/34.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ % 231.00/34.52 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v2 | ~ % 231.00/34.52 | (hAPP(v5, v3) = v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (hAPP(v3, v2) % 231.00/34.52 | = v4) | ~ (hAPP(v0, v2) = v3))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_power__Suc__0) implies: % 231.00/34.52 | (193) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 231.00/34.52 | (c_Nat_OSuc(v1) = v2 & c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 % 231.00/34.52 | & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & hAPP(v0, v2) = v3 % 231.00/34.52 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : % 231.00/34.52 | (v5 = v2 | ~ (hAPP(v3, v4) = v5) | ~ $i(v4))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_nat__power__eq__Suc__0__iff) implies: % 231.00/34.52 | (194) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 231.00/34.52 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ % 231.00/34.52 | (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v2) = v4) | ~ $i(v3)) & ! % 231.00/34.52 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v2 | ~ (hAPP(v4, v1) % 231.00/34.52 | = v5) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3)) & ! [v3: $i] : ! % 231.00/34.52 | [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3) = % 231.00/34.52 | v2) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_realpow__two__disj) implies: % 231.00/34.52 | (195) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 231.00/34.52 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 231.00/34.52 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 231.00/34.52 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 231.00/34.52 | (c_Power_Opower__class_Opower(v5) = v6) | ~ (hAPP(v6, v4) = v7) % 231.00/34.52 | | ~ (hAPP(v6, v3) = v8) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 231.00/34.52 | class_Rings_Oidom(v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] % 231.00/34.52 | : ((v4 = v3 | (v11 = v4 & c_Groups_Ouminus__class_Ouminus(v5, v3) % 231.00/34.52 | = v4) | ( ~ (v10 = v9) & hAPP(v8, v2) = v10 & hAPP(v7, v2) % 231.00/34.52 | = v9 & $i(v10) & $i(v9))) & ((v10 = v9 & hAPP(v8, v2) = v9 % 231.00/34.52 | & hAPP(v7, v2) = v9 & $i(v9)) | ( ~ (v11 = v4) & ~ (v4 = % 231.00/34.52 | v3) & c_Groups_Ouminus__class_Ouminus(v5, v3) = v11 & % 231.00/34.52 | $i(v11)))))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_one__less__mult) implies: % 231.00/34.52 | (196) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 231.00/34.52 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 231.00/34.52 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v6))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_n__less__n__mult__m) implies: % 231.00/34.52 | (197) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 231.00/34.52 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 231.00/34.52 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_n__less__m__mult__n) implies: % 231.00/34.52 | (198) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 231.00/34.52 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) | % 231.00/34.52 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_diff__Suc__less) implies: % 231.00/34.52 | (199) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.52 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.00/34.52 | (c_Nat_OSuc(v1) = v3) | ~ % 231.00/34.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v3) = v4) | ~ % 231.00/34.52 | $i(v2) | ~ $i(v1) | ~ % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 231.00/34.52 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_Suc__pred) implies: % 231.00/34.52 | (200) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.52 | ! [v2: $i] : ! [v3: $i] : ( ~ % 231.00/34.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 231.00/34.52 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 231.00/34.52 | c_Nat_OSuc(v3) = v2)) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_one__le__mult__iff) implies: % 231.00/34.52 | (201) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v2 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 231.00/34.52 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, % 231.00/34.52 | v6) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v4)) & % 231.00/34.52 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.00/34.52 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, % 231.00/34.52 | v6) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) & % 231.00/34.52 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.00/34.52 | (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, % 231.00/34.52 | v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) % 231.00/34.52 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_real__of__nat__Suc__gt__zero) implies: % 231.00/34.52 | (202) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.00/34.52 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ % 231.00/34.52 | $i(v1) | ? [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & % 231.00/34.52 | $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.00/34.52 | v3)))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_real__of__nat__one) implies: % 231.00/34.52 | (203) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & % 231.00/34.52 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 231.00/34.52 | $i(v0)) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_real__of__nat__Suc) implies: % 231.00/34.52 | (204) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 231.00/34.52 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 231.00/34.52 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ? [v3: $i] % 231.00/34.52 | : ? [v4: $i] : (c_Nat_OSuc(v1) = v3 & % 231.00/34.52 | c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & % 231.00/34.52 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v0) = v4 & % 231.00/34.52 | $i(v4) & $i(v3)))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_nat__one__le__power) implies: % 231.00/34.52 | (205) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.52 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & % 231.00/34.52 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 231.00/34.52 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ~ % 231.00/34.52 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, % 231.00/34.52 | v4) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v6))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_Suc__pred_H) implies: % 231.00/34.52 | (206) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 231.00/34.52 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 231.00/34.52 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v1) = v3) | ~ % 231.00/34.52 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 231.00/34.52 | c_Nat_OSuc(v3) = v2)) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_add__eq__if) implies: % 231.00/34.52 | (207) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 231.00/34.52 | v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & % 231.00/34.52 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 231.00/34.52 | (v3 = v0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = % 231.00/34.52 | v4) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = % 231.00/34.52 | v5) | ~ $i(v3) | ~ $i(v2) | ? [v6: $i] : (c_Nat_OSuc(v5) = % 231.00/34.52 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v2) = v6 & % 231.00/34.52 | $i(v6))) & ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 231.00/34.52 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v2) = v3) | ~ % 231.00/34.52 | $i(v2))) % 231.00/34.52 | % 231.00/34.52 | ALPHA: (fact_realpow__two__diff) implies: % 231.00/34.53 | (208) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Nat_OSuc(v1) = v2 & % 231.00/34.53 | c_Nat_OSuc(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 % 231.00/34.53 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 231.00/34.53 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 231.00/34.53 | [v10: $i] : ! [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v5) = % 231.00/34.53 | v6) | ~ (c_Groups_Ominus__class_Ominus(v5, v8, v10) = v11) | % 231.00/34.53 | ~ (hAPP(v9, v2) = v10) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, % 231.00/34.53 | v4) = v7) | ~ (hAPP(v6, v3) = v9) | ~ $i(v5) | ~ $i(v4) | % 231.00/34.53 | ~ $i(v3) | ~ class_Rings_Ocomm__ring__1(v5) | ? [v12: $i] : ? % 231.00/34.53 | [v13: $i] : ? [v14: $i] : ? [v15: $i] : % 231.00/34.53 | (c_Groups_Ominus__class_Ominus(v5, v4, v3) = v13 & % 231.00/34.53 | c_Groups_Oplus__class_Oplus(v5, v4, v3) = v15 & % 231.00/34.53 | c_Groups_Otimes__class_Otimes(v5) = v12 & hAPP(v14, v15) = v11 % 231.00/34.53 | & hAPP(v12, v13) = v14 & $i(v15) & $i(v14) & $i(v13) & $i(v12) % 231.00/34.53 | & $i(v11)))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_reals__Archimedean4) implies: % 231.00/34.53 | (209) ? [v0: $i] : ? [v1: $i] : % 231.00/34.53 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & % 231.00/34.53 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? % 231.00/34.53 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 231.00/34.53 | : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (c_Nat_OSuc(v4) = % 231.00/34.53 | v8 & c_RealDef_Oreal(tc_Nat_Onat, v8) = v9 & % 231.00/34.53 | c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & hAPP(v10, v3) = v11 & % 231.00/34.53 | hAPP(v6, v3) = v7 & hAPP(v1, v9) = v10 & hAPP(v1, v5) = v6 & % 231.00/34.53 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) % 231.00/34.53 | & $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, % 231.00/34.53 | v11) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.00/34.53 | v7, v2)))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_int__power__div__base) implies: % 231.00/34.53 | (210) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 231.00/34.53 | (c_Nat_OSuc(v0) = v3 & c_Power_Opower__class_Opower(tc_Int_Oint) = v2 % 231.00/34.53 | & c_Groups_Ozero__class_Ozero(tc_Int_Oint) = v1 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v3) & $i(v2) & % 231.00/34.53 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 231.00/34.53 | $i] : ! [v8: $i] : ( ~ % 231.00/34.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v3) = v7) | ~ % 231.00/34.53 | (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v4) = v6) | ~ $i(v5) | ~ % 231.00/34.53 | $i(v4) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, v1, v4) | % 231.00/34.53 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v5) | ? [v9: % 231.00/34.53 | $i] : (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v9, v4) = v8 & % 231.00/34.53 | hAPP(v6, v5) = v9 & $i(v9) & $i(v8)))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_reals__Archimedean6a) implies: % 231.00/34.53 | (211) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.00/34.53 | $i(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ? % 231.00/34.53 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 231.00/34.53 | (c_Nat_OSuc(v2) = v4 & c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & % 231.00/34.53 | c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v5) & $i(v4) & % 231.00/34.53 | $i(v3) & $i(v2) & % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & % 231.00/34.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_div__1) implies: % 231.00/34.53 | (212) ? [v0: $i] : ? [v1: $i] : (c_Nat_OSuc(v0) = v1 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.53 | ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~ % 231.00/34.53 | $i(v2))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_div__less) implies: % 231.00/34.53 | (213) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.53 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | ~ % 231.00/34.53 | $i(v2) | ~ $i(v1) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_nat__mult__div__cancel__disj) implies: % 231.00/34.53 | (214) ? [v0: $i] : ? [v1: $i] : % 231.00/34.53 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.53 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 231.00/34.53 | : ! [v7: $i] : ! [v8: $i] : (v4 = v0 | ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) | ~ % 231.00/34.53 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = % 231.00/34.53 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8))) % 231.00/34.53 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 231.00/34.53 | $i] : ! [v7: $i] : (v7 = v0 | ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v6) = v7) | ~ % 231.00/34.53 | (hAPP(v4, v3) = v5) | ~ (hAPP(v4, v2) = v6) | ~ (hAPP(v1, v0) = % 231.00/34.53 | v4) | ~ $i(v3) | ~ $i(v2))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_div__le__mono2) implies: % 231.00/34.53 | (215) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.53 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 231.00/34.53 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v3) = v5) % 231.00/34.53 | | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v4) | ~ % 231.00/34.53 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 231.00/34.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_nat__mult__div__cancel1) implies: % 231.00/34.53 | (216) ? [v0: $i] : ? [v1: $i] : % 231.00/34.53 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.53 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 231.00/34.53 | : ! [v7: $i] : ! [v8: $i] : ( ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v6, v7) = v8) | ~ % 231.00/34.53 | (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = % 231.00/34.53 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v8 & $i(v8)))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_div__mult__self__is__m) implies: % 231.00/34.53 | (217) ? [v0: $i] : ? [v1: $i] : % 231.00/34.53 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.53 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 231.00/34.53 | : (v6 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = % 231.00/34.53 | v6) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ % 231.00/34.53 | $i(v3) | ~ $i(v2) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_div__mult__self1__is__m) implies: % 231.00/34.53 | (218) ? [v0: $i] : ? [v1: $i] : % 231.00/34.53 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.53 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 231.00/34.53 | : (v6 = v2 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v3) = % 231.00/34.53 | v6) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ % 231.00/34.53 | $i(v3) | ~ $i(v2) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_div__less__dividend) implies: % 231.00/34.53 | (219) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 231.00/34.53 | v0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & $i(v1) & % 231.00/34.53 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ % 231.00/34.53 | $i(v3) | ~ $i(v2) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_div__if) implies: % 231.00/34.53 | (220) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.53 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~ % 231.00/34.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 231.00/34.53 | $i(v2) | ~ $i(v1) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | ? [v5: $i] % 231.00/34.53 | : ? [v6: $i] : (( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.00/34.53 | v1, v2) | (v5 = v0 & % 231.00/34.53 | c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v0)) & % 231.00/34.53 | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | (v6 = v5 % 231.00/34.53 | & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 & % 231.00/34.53 | c_Nat_OSuc(v4) = v5 & $i(v5)))))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_div__geq) implies: % 231.00/34.53 | (221) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v0) % 231.00/34.53 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v4) | ~ % 231.00/34.53 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 231.00/34.53 | $i(v2) | ~ $i(v1) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v2) | % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v5: $i] % 231.00/34.53 | : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v2) = v5 & % 231.00/34.53 | c_Nat_OSuc(v4) = v5 & $i(v5)))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (fact_split__div) implies: % 231.00/34.53 | (222) ? [v0: $i] : ? [v1: $i] : % 231.00/34.53 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & % 231.00/34.53 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 231.00/34.53 | : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ % 231.00/34.53 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 231.00/34.53 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : (( ~ (v2 = v0) | % 231.00/34.53 | (hAPP(v4, v0) = v7 & $i(v7) & hBOOL(v7))) & (v2 = v0 | % 231.00/34.53 | (hAPP(v1, v2) = v8 & $i(v8) & ! [v9: $i] : ! [v10: $i] : ! % 231.00/34.53 | [v11: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 231.00/34.53 | v11, v10) = v3) | ~ (hAPP(v8, v9) = v11) | ~ % 231.00/34.53 | $i(v10) | ~ $i(v9) | ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) | ? % 231.00/34.53 | [v12: $i] : (hAPP(v4, v9) = v12 & $i(v12) & % 231.00/34.53 | hBOOL(v12))))))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 231.00/34.53 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.00/34.53 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v2) = v5) | ~ % 231.00/34.53 | (hAPP(v4, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 231.00/34.53 | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 231.00/34.53 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v10) & % 231.00/34.53 | $i(v9) & ((v12 = v3 & ~ (v2 = v0) & % 231.00/34.53 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v11, v10) = v3 & % 231.00/34.53 | hAPP(v8, v9) = v11 & hAPP(v4, v9) = v13 & hAPP(v1, v2) = v8 % 231.00/34.53 | & $i(v13) & $i(v11) & $i(v8) & % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v10, v2) & ~ % 231.00/34.53 | hBOOL(v13)) | (v2 = v0 & hAPP(v4, v0) = v7 & $i(v7) & ~ % 231.00/34.53 | hBOOL(v7)))))) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) implies: % 231.00/34.53 | (223) class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) implies: % 231.00/34.53 | (224) class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) implies: % 231.00/34.53 | (225) class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) implies: % 231.00/34.53 | (226) class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) implies: % 231.00/34.53 | (227) class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Rings_Olinordered__ring__strict) implies: % 231.00/34.53 | (228) class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) implies: % 231.00/34.53 | (229) class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Groups_Oordered__ab__group__add) implies: % 231.00/34.53 | (230) class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Rings_Olinordered__semidom) implies: % 231.00/34.53 | (231) class_Rings_Olinordered__semidom(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Rings_Ono__zero__divisors) implies: % 231.00/34.53 | (232) class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Rings_Ocomm__semiring__1) implies: % 231.00/34.53 | (233) class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Rings_Oordered__ring) implies: % 231.00/34.53 | (234) class_Rings_Oordered__ring(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_RealDef__Oreal__Groups_Ogroup__add) implies: % 231.00/34.53 | (235) class_Groups_Ogroup__add(tc_RealDef_Oreal) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) implies: % 231.00/34.53 | (236) class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (conj_0) implies: % 231.00/34.53 | (237) $i(tc_RealDef_Oreal) % 231.00/34.53 | (238) $i(tc_Complex_Ocomplex) % 231.00/34.53 | (239) $i(v_c____) % 231.00/34.53 | (240) $i(v_r) % 231.00/34.53 | (241) $i(v_m____) % 231.00/34.53 | (242) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 231.00/34.53 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 231.00/34.53 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 231.00/34.53 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v7) = v8 & % 231.00/34.53 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3 & % 231.00/34.53 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v4 & % 231.00/34.53 | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 & % 231.00/34.53 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.00/34.53 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____) = v2 % 231.00/34.53 | & hAPP(v5, v_m____) = v6 & hAPP(v4, v_r) = v5 & $i(v8) & $i(v7) & % 231.00/34.53 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 231.00/34.53 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v8)) % 231.00/34.53 | % 231.00/34.53 | ALPHA: (function-axioms) implies: % 231.00/34.53 | (243) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 231.00/34.53 | (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ % 231.00/34.53 | (c_Groups_Ozero__class_Ozero(v2) = v0)) % 231.00/34.53 | (244) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 231.00/34.53 | (c_Groups_Otimes__class_Otimes(v2) = v1) | ~ % 231.00/34.53 | (c_Groups_Otimes__class_Otimes(v2) = v0)) % 231.00/34.53 | (245) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 231.00/34.53 | (c_Groups_Oone__class_Oone(v2) = v1) | ~ % 231.00/34.53 | (c_Groups_Oone__class_Oone(v2) = v0)) % 231.00/34.53 | (246) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 231.00/34.53 | (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0)) % 231.00/34.54 | (247) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 231.00/34.54 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) % 231.00/34.54 | (248) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 231.00/34.54 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~ % 231.00/34.54 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) % 231.00/34.54 | (249) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 231.00/34.54 | (c_Groups_Oabs__class_Oabs(v3, v2) = v1) | ~ % 231.00/34.54 | (c_Groups_Oabs__class_Oabs(v3, v2) = v0)) % 231.00/34.54 | (250) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 231.00/34.54 | (c_Groups_Ouminus__class_Ouminus(v3, v2) = v1) | ~ % 231.00/34.54 | (c_Groups_Ouminus__class_Ouminus(v3, v2) = v0)) % 231.00/34.54 | (251) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 231.00/34.54 | (c_RealDef_Oreal(v3, v2) = v1) | ~ (c_RealDef_Oreal(v3, v2) = v0)) % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (188) with fresh symbol all_691_0 gives: % 231.00/34.54 | (252) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_691_0 & $i(all_691_0) % 231.00/34.54 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_691_0) | ~ $i(v0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (252) implies: % 231.00/34.54 | (253) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_691_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (188) with fresh symbol all_694_0 gives: % 231.00/34.54 | (254) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_694_0 & $i(all_694_0) % 231.00/34.54 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_694_0) | ~ $i(v0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (254) implies: % 231.00/34.54 | (255) $i(all_694_0) % 231.00/34.54 | (256) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_694_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (188) with fresh symbol all_697_0 gives: % 231.00/34.54 | (257) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_697_0 & $i(all_697_0) % 231.00/34.54 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_697_0) | ~ $i(v0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (257) implies: % 231.00/34.54 | (258) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_697_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (67) with fresh symbol all_705_0 gives: % 231.00/34.54 | (259) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_705_0 & $i(all_705_0) % 231.00/34.54 | & ? [v0: $i] : ( ~ $i(v0) | % 231.00/34.54 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_705_0, v0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (259) implies: % 231.00/34.54 | (260) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_705_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (67) with fresh symbol all_707_0 gives: % 231.00/34.54 | (261) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_707_0 & $i(all_707_0) % 231.00/34.54 | & ? [v0: $i] : ( ~ $i(v0) | % 231.00/34.54 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_707_0, v0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (261) implies: % 231.00/34.54 | (262) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_707_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (82) with fresh symbol all_710_0 gives: % 231.00/34.54 | (263) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_710_0 & $i(all_710_0) % 231.00/34.54 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 231.00/34.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_710_0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (263) implies: % 231.00/34.54 | (264) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_710_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (82) with fresh symbol all_715_0 gives: % 231.00/34.54 | (265) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_715_0 & $i(all_715_0) % 231.00/34.54 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 231.00/34.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_715_0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (265) implies: % 231.00/34.54 | (266) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_715_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (82) with fresh symbol all_718_0 gives: % 231.00/34.54 | (267) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_718_0 & $i(all_718_0) % 231.00/34.54 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 231.00/34.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_718_0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (267) implies: % 231.00/34.54 | (268) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_718_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (82) with fresh symbol all_724_0 gives: % 231.00/34.54 | (269) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_724_0 & $i(all_724_0) % 231.00/34.54 | & ! [v0: $i] : ( ~ $i(v0) | ~ % 231.00/34.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_724_0)) % 231.00/34.54 | % 231.00/34.54 | ALPHA: (269) implies: % 231.00/34.54 | (270) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_724_0 % 231.00/34.54 | % 231.00/34.54 | DELTA: instantiating (188) with fresh symbol all_727_0 gives: % 231.11/34.54 | (271) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_727_0 & $i(all_727_0) % 231.11/34.54 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_727_0) | ~ $i(v0)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (271) implies: % 231.11/34.54 | (272) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_727_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (188) with fresh symbol all_730_0 gives: % 231.11/34.54 | (273) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_730_0 & $i(all_730_0) % 231.11/34.54 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_730_0) | ~ $i(v0)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (273) implies: % 231.11/34.54 | (274) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_730_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (188) with fresh symbol all_733_0 gives: % 231.11/34.54 | (275) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_733_0 & $i(all_733_0) % 231.11/34.54 | & ! [v0: $i] : ( ~ (c_Nat_OSuc(v0) = all_733_0) | ~ $i(v0)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (275) implies: % 231.11/34.54 | (276) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_733_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (50) with fresh symbol all_739_0 gives: % 231.11/34.54 | (277) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_739_0 & $i(all_739_0) % 231.11/34.54 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 231.11/34.54 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_739_0) = v1) | % 231.11/34.54 | ~ $i(v0)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (277) implies: % 231.11/34.54 | (278) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_739_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (51) with fresh symbol all_742_0 gives: % 231.11/34.54 | (279) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_742_0 & $i(all_742_0) % 231.11/34.54 | & ! [v0: $i] : ! [v1: int] : (v1 = all_742_0 | ~ % 231.11/34.54 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v0) = v1) | ~ % 231.11/34.54 | $i(v0)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (279) implies: % 231.11/34.54 | (280) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_742_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (100) with fresh symbol all_745_0 gives: % 231.11/34.54 | (281) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_745_0 & $i(all_745_0) % 231.11/34.54 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0) = v1) | % 231.11/34.54 | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 231.11/34.54 | all_745_0, v1)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (281) implies: % 231.11/34.54 | (282) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_745_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (101) with fresh symbols all_748_0, all_748_1 gives: % 231.11/34.54 | (283) c_RComplete_Onatfloor(all_748_1) = all_748_0 & % 231.11/34.54 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_748_0 & % 231.11/34.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_748_1 & % 231.11/34.54 | $i(all_748_0) & $i(all_748_1) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (283) implies: % 231.11/34.54 | (284) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_748_1 % 231.11/34.54 | (285) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_748_0 % 231.11/34.54 | (286) c_RComplete_Onatfloor(all_748_1) = all_748_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (71) with fresh symbol all_752_0 gives: % 231.11/34.54 | (287) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_752_0 & $i(all_752_0) % 231.11/34.54 | & ? [v0: any] : (v0 = all_752_0 | ~ $i(v0) | % 231.11/34.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_752_0, v0)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (287) implies: % 231.11/34.54 | (288) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_752_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (112) with fresh symbols all_757_0, all_757_1 gives: % 231.11/34.54 | (289) c_RealDef_Oreal(tc_Nat_Onat, all_757_1) = all_757_0 & % 231.11/34.54 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_757_1 & % 231.11/34.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_757_0 & % 231.11/34.54 | $i(all_757_0) & $i(all_757_1) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (289) implies: % 231.11/34.54 | (290) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_757_0 % 231.11/34.54 | (291) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_757_1 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (103) with fresh symbol all_762_0 gives: % 231.11/34.54 | (292) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_762_0 & $i(all_762_0) % 231.11/34.54 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatceiling(v0) = v1) % 231.11/34.54 | | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 231.11/34.54 | all_762_0, v1)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (292) implies: % 231.11/34.54 | (293) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_762_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (116) with fresh symbols all_765_0, all_765_1 gives: % 231.11/34.54 | (294) c_RealDef_Oreal(tc_Nat_Onat, all_765_1) = all_765_0 & % 231.11/34.54 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_765_1 & % 231.11/34.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_765_0 & % 231.11/34.54 | $i(all_765_0) & $i(all_765_1) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (294) implies: % 231.11/34.54 | (295) $i(all_765_0) % 231.11/34.54 | (296) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_765_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (86) with fresh symbol all_767_0 gives: % 231.11/34.54 | (297) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_767_0 & $i(all_767_0) % 231.11/34.54 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 231.11/34.54 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_767_0) = v1) | ~ % 231.11/34.54 | $i(v0)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (297) implies: % 231.11/34.54 | (298) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_767_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (104) with fresh symbols all_770_0, all_770_1 gives: % 231.11/34.54 | (299) c_RComplete_Onatceiling(all_770_1) = all_770_0 & % 231.11/34.54 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_770_0 & % 231.11/34.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_770_1 & % 231.11/34.54 | $i(all_770_0) & $i(all_770_1) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (299) implies: % 231.11/34.54 | (300) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_770_1 % 231.11/34.54 | (301) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_770_0 % 231.11/34.54 | (302) c_RComplete_Onatceiling(all_770_1) = all_770_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (20) with fresh symbols all_772_0, all_772_1 gives: % 231.11/34.54 | (303) ~ (all_772_0 = all_772_1) & % 231.11/34.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_772_0 & % 231.11/34.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_772_1 & % 231.11/34.54 | $i(all_772_0) & $i(all_772_1) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (303) implies: % 231.11/34.54 | (304) ~ (all_772_0 = all_772_1) % 231.11/34.54 | (305) $i(all_772_1) % 231.11/34.54 | (306) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_772_1 % 231.11/34.54 | (307) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_772_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (162) with fresh symbols all_781_0, all_781_1 gives: % 231.11/34.54 | (308) c_Transcendental_Oln(all_781_1) = all_781_0 & % 231.11/34.54 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_781_1 & % 231.11/34.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_781_0 & % 231.11/34.54 | $i(all_781_0) & $i(all_781_1) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (308) implies: % 231.11/34.54 | (309) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_781_0 % 231.11/34.54 | (310) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_781_1 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (99) with fresh symbols all_783_0, all_783_1 gives: % 231.11/34.54 | (311) c_RComplete_Onatfloor(all_783_1) = all_783_0 & % 231.11/34.54 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_783_0 & % 231.11/34.54 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_783_1 & % 231.11/34.54 | $i(all_783_0) & $i(all_783_1) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (311) implies: % 231.11/34.54 | (312) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_783_1 % 231.11/34.54 | (313) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_783_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (88) with fresh symbol all_788_0 gives: % 231.11/34.54 | (314) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_788_0 & $i(all_788_0) % 231.11/34.54 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 231.11/34.54 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_788_0, v0) = v1) | ~ % 231.11/34.54 | $i(v0)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (314) implies: % 231.11/34.54 | (315) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_788_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (181) with fresh symbol all_791_0 gives: % 231.11/34.54 | (316) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_791_0 & $i(all_791_0) % 231.11/34.54 | & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 231.11/34.54 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_791_0, v1)) % 231.11/34.54 | % 231.11/34.54 | ALPHA: (316) implies: % 231.11/34.54 | (317) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_791_0 % 231.11/34.54 | % 231.11/34.54 | DELTA: instantiating (48) with fresh symbol all_794_0 gives: % 231.11/34.54 | (318) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_794_0 & $i(all_794_0) % 231.11/34.54 | & ! [v0: $i] : ! [v1: int] : (v1 = all_794_0 | ~ % 231.11/34.54 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, all_794_0, v0) = v1) | % 231.11/34.54 | ~ $i(v0)) % 231.11/34.54 | % 231.11/34.55 | ALPHA: (318) implies: % 231.11/34.55 | (319) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_794_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (1) with fresh symbols all_797_0, all_797_1 gives: % 231.11/34.55 | (320) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_797_1 & % 231.11/34.55 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____) = % 231.11/34.55 | all_797_0 & $i(all_797_0) & $i(all_797_1) & % 231.11/34.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_797_1, % 231.11/34.55 | all_797_0) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (320) implies: % 231.11/34.55 | (321) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_797_1, % 231.11/34.55 | all_797_0) % 231.11/34.55 | (322) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____) = % 231.11/34.55 | all_797_0 % 231.11/34.55 | (323) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_797_1 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (114) with fresh symbol all_800_0 gives: % 231.11/34.55 | (324) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_800_0 & % 231.11/34.55 | $i(all_800_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ~ % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_800_0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (324) implies: % 231.11/34.55 | (325) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_800_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (111) with fresh symbol all_803_0 gives: % 231.11/34.55 | (326) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_803_0 & % 231.11/34.55 | $i(all_803_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | % 231.11/34.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_803_0, v1)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (326) implies: % 231.11/34.55 | (327) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_803_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (102) with fresh symbols all_809_0, all_809_1 gives: % 231.11/34.55 | (328) c_RComplete_Onatceiling(all_809_1) = all_809_0 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_809_0 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_809_1 & % 231.11/34.55 | $i(all_809_0) & $i(all_809_1) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (328) implies: % 231.11/34.55 | (329) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_809_1 % 231.11/34.55 | (330) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_809_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (183) with fresh symbols all_813_0, all_813_1 gives: % 231.11/34.55 | (331) c_Nat_OSuc(all_813_0) = all_813_1 & % 231.11/34.55 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_813_1 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_813_0 & $i(all_813_0) % 231.11/34.55 | & $i(all_813_1) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (331) implies: % 231.11/34.55 | (332) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_813_0 % 231.11/34.55 | (333) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_813_1 % 231.11/34.55 | (334) c_Nat_OSuc(all_813_0) = all_813_1 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (81) with fresh symbol all_822_0 gives: % 231.11/34.55 | (335) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_822_0 & $i(all_822_0) % 231.11/34.55 | & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_822_0, all_822_0) % 231.11/34.55 | & ? [v0: any] : (v0 = all_822_0 | ~ $i(v0) | % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_822_0, v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (335) implies: % 231.11/34.55 | (336) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_822_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (163) with fresh symbol all_830_0 gives: % 231.11/34.55 | (337) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_830_0 & % 231.11/34.55 | $i(all_830_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_830_0, v0) | % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (337) implies: % 231.11/34.55 | (338) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_830_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (84) with fresh symbol all_833_0 gives: % 231.11/34.55 | (339) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_833_0 & $i(all_833_0) % 231.11/34.55 | & ! [v0: any] : ! [v1: $i] : (v0 = all_833_0 | ~ % 231.11/34.55 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v1) | ~ $i(v1) % 231.11/34.55 | | ~ $i(v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (339) implies: % 231.11/34.55 | (340) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_833_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (186) with fresh symbol all_839_0 gives: % 231.11/34.55 | (341) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_839_0 & $i(all_839_0) & % 231.11/34.55 | ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, all_839_0) = v1) | ~ % 231.11/34.55 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1))) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (341) implies: % 231.11/34.55 | (342) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_839_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (187) with fresh symbol all_842_0 gives: % 231.11/34.55 | (343) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_842_0 & $i(all_842_0) & % 231.11/34.55 | ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_842_0, v0) = v1) | ~ % 231.11/34.55 | $i(v0) | (c_Nat_OSuc(v0) = v1 & $i(v1))) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (343) implies: % 231.11/34.55 | (344) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_842_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (68) with fresh symbol all_849_0 gives: % 231.11/34.55 | (345) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_849_0 & $i(all_849_0) % 231.11/34.55 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_849_0, % 231.11/34.55 | all_849_0) & ! [v0: any] : (v0 = all_849_0 | ~ $i(v0) | ~ % 231.11/34.55 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, all_849_0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (345) implies: % 231.11/34.55 | (346) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_849_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (203) with fresh symbols all_856_0, all_856_1, all_856_2 % 231.11/34.55 | gives: % 231.11/34.55 | (347) c_Nat_OSuc(all_856_2) = all_856_1 & c_RealDef_Oreal(tc_Nat_Onat, % 231.11/34.55 | all_856_1) = all_856_0 & % 231.11/34.55 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_856_0 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_856_2 & $i(all_856_0) % 231.11/34.55 | & $i(all_856_1) & $i(all_856_2) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (347) implies: % 231.11/34.55 | (348) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_856_2 % 231.11/34.55 | (349) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_856_0 % 231.11/34.55 | (350) c_RealDef_Oreal(tc_Nat_Onat, all_856_1) = all_856_0 % 231.11/34.55 | (351) c_Nat_OSuc(all_856_2) = all_856_1 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (8) with fresh symbol all_858_0 gives: % 231.11/34.55 | (352) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_858_0 & % 231.11/34.55 | $i(all_858_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 231.11/34.55 | all_858_0 | ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~ % 231.11/34.55 | (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~ $i(v0) | ~ % 231.11/34.55 | class_RealVector_Oreal__normed__algebra__1(v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (352) implies: % 231.11/34.55 | (353) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_858_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (4) with fresh symbol all_865_0 gives: % 231.11/34.55 | (354) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_865_0 & % 231.11/34.55 | $i(all_865_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 231.11/34.55 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, % 231.11/34.55 | all_865_0) = v2 & $i(v2) & ~ % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0))) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (354) implies: % 231.11/34.55 | (355) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_865_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (213) with fresh symbol all_868_0 gives: % 231.11/34.55 | (356) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_868_0 & $i(all_868_0) % 231.11/34.55 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_868_0 | ~ % 231.11/34.55 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 231.11/34.55 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, % 231.11/34.55 | v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (356) implies: % 231.11/34.55 | (357) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_868_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (92) with fresh symbols all_871_0, all_871_1 gives: % 231.11/34.55 | (358) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_871_0 & % 231.11/34.55 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_871_1 & % 231.11/34.55 | $i(all_871_0) & $i(all_871_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (hAPP(all_871_1, v0) = v1) | ~ $i(v0) | hAPP(v1, all_871_0) = v0) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (358) implies: % 231.11/34.55 | (359) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_871_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (54) with fresh symbol all_879_0 gives: % 231.11/34.55 | (360) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_879_0 & $i(all_879_0) % 231.11/34.55 | & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = all_879_0 | ~ % 231.11/34.55 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 231.11/34.55 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.55 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (360) implies: % 231.11/34.55 | (361) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_879_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (78) with fresh symbols all_884_0, all_884_1 gives: % 231.11/34.55 | (362) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_884_1 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_884_0 & $i(all_884_0) % 231.11/34.55 | & $i(all_884_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_884_1, % 231.11/34.55 | v0) = v1) | ~ $i(v0) | hAPP(v1, all_884_0) = all_884_0) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (362) implies: % 231.11/34.55 | (363) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_884_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (202) with fresh symbol all_890_0 gives: % 231.11/34.55 | (364) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_890_0 & % 231.11/34.55 | $i(all_890_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) % 231.11/34.55 | | ~ $i(v0) | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 % 231.11/34.55 | & $i(v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.55 | all_890_0, v2))) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (364) implies: % 231.11/34.55 | (365) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_890_0 % 231.11/34.55 | (366) ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 231.11/34.55 | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v2) & % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_890_0, v2))) % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (47) with fresh symbol all_893_0 gives: % 231.11/34.55 | (367) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_893_0 & $i(all_893_0) % 231.11/34.55 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 231.11/34.55 | all_893_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) % 231.11/34.55 | = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = % 231.11/34.55 | v2) | ~ $i(v1) | ~ $i(v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (367) implies: % 231.11/34.55 | (368) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_893_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (212) with fresh symbols all_896_0, all_896_1 gives: % 231.11/34.55 | (369) c_Nat_OSuc(all_896_1) = all_896_0 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_896_1 & $i(all_896_0) % 231.11/34.55 | & $i(all_896_1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 231.11/34.55 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, all_896_0) = v1) | ~ % 231.11/34.55 | $i(v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (369) implies: % 231.11/34.55 | (370) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_896_1 % 231.11/34.55 | (371) c_Nat_OSuc(all_896_1) = all_896_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (9) with fresh symbol all_902_0 gives: % 231.11/34.55 | (372) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_902_0 & % 231.11/34.55 | $i(all_902_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.55 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ % 231.11/34.55 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ~ % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, all_902_0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (372) implies: % 231.11/34.55 | (373) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_902_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (25) with fresh symbol all_905_0 gives: % 231.11/34.55 | (374) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_905_0 & % 231.11/34.55 | $i(all_905_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 231.11/34.55 | all_905_0 | ~ (c_Groups_Ozero__class_Ozero(v0) = v1) | ~ % 231.11/34.55 | (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~ $i(v0) | ~ % 231.11/34.55 | class_RealVector_Oreal__normed__vector(v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (374) implies: % 231.11/34.55 | (375) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_905_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (11) with fresh symbol all_911_0 gives: % 231.11/34.55 | (376) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_911_0 & % 231.11/34.55 | $i(all_911_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.55 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ % 231.11/34.55 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | % 231.11/34.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_911_0, v2)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (376) implies: % 231.11/34.55 | (377) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_911_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (200) with fresh symbols all_919_0, all_919_1 gives: % 231.11/34.55 | (378) c_Nat_OSuc(all_919_1) = all_919_0 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_919_1 & $i(all_919_0) % 231.11/34.55 | & $i(all_919_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_919_0) = v1) | % 231.11/34.55 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_919_1, % 231.11/34.55 | v0) | c_Nat_OSuc(v1) = v0) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (378) implies: % 231.11/34.55 | (379) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_919_1 % 231.11/34.55 | (380) c_Nat_OSuc(all_919_1) = all_919_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (106) with fresh symbols all_922_0, all_922_1 gives: % 231.11/34.55 | (381) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_922_0 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_922_1 & % 231.11/34.55 | $i(all_922_0) & $i(all_922_1) & ! [v0: $i] : ! [v1: int] : (v1 = % 231.11/34.55 | all_922_0 | ~ (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_922_1)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (381) implies: % 231.11/34.55 | (382) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_922_1 % 231.11/34.55 | (383) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_922_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (190) with fresh symbols all_931_0, all_931_1 gives: % 231.11/34.55 | (384) c_Nat_OSuc(all_931_1) = all_931_0 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_931_1 & $i(all_931_0) % 231.11/34.55 | & $i(all_931_1) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.55 | all_931_1, all_931_0) & ! [v0: any] : (v0 = all_931_1 | ~ $i(v0) % 231.11/34.55 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_931_0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (384) implies: % 231.11/34.55 | (385) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_931_1 % 231.11/34.55 | (386) c_Nat_OSuc(all_931_1) = all_931_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (52) with fresh symbol all_937_0 gives: % 231.11/34.55 | (387) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_937_0 & $i(all_937_0) % 231.11/34.55 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.55 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 231.11/34.55 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.55 | all_937_0, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.55 | all_937_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, % 231.11/34.55 | v0)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (387) implies: % 231.11/34.55 | (388) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_937_0 % 231.11/34.55 | % 231.11/34.55 | DELTA: instantiating (168) with fresh symbols all_940_0, all_940_1 gives: % 231.11/34.55 | (389) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_940_1 & % 231.11/34.55 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_940_0 & % 231.11/34.55 | $i(all_940_0) & $i(all_940_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.55 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_940_1, v0) | % 231.11/34.55 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_940_0, v1)) % 231.11/34.55 | % 231.11/34.55 | ALPHA: (389) implies: % 231.11/34.55 | (390) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_940_0 % 231.11/34.56 | (391) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_940_1 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (206) with fresh symbols all_943_0, all_943_1 gives: % 231.11/34.56 | (392) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_943_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_943_1 & $i(all_943_0) % 231.11/34.56 | & $i(all_943_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_943_0) = v1) | % 231.11/34.56 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_943_1, % 231.11/34.56 | v0) | c_Nat_OSuc(v1) = v0) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (392) implies: % 231.11/34.56 | (393) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_943_1 % 231.11/34.56 | (394) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_943_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (105) with fresh symbols all_946_0, all_946_1 gives: % 231.11/34.56 | (395) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_946_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_946_1 & % 231.11/34.56 | $i(all_946_0) & $i(all_946_1) & ! [v0: $i] : ! [v1: int] : (v1 = % 231.11/34.56 | all_946_0 | ~ (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_946_1)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (395) implies: % 231.11/34.56 | (396) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_946_1 % 231.11/34.56 | (397) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_946_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (44) with fresh symbols all_949_0, all_949_1 gives: % 231.11/34.56 | (398) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_949_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_949_1 & % 231.11/34.56 | $i(all_949_0) & $i(all_949_1) & ! [v0: $i] : ! [v1: int] : (v1 = % 231.11/34.56 | all_949_0 | ~ (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) = % 231.11/34.56 | v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_949_1, v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (398) implies: % 231.11/34.56 | (399) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_949_1 % 231.11/34.56 | (400) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_949_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (199) with fresh symbol all_961_0 gives: % 231.11/34.56 | (401) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_961_0 & $i(all_961_0) % 231.11/34.56 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.56 | (c_Nat_OSuc(v0) = v2) | ~ % 231.11/34.56 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v3) | ~ % 231.11/34.56 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.56 | all_961_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, % 231.11/34.56 | v1)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (401) implies: % 231.11/34.56 | (402) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_961_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (206) with fresh symbols all_967_0, all_967_1 gives: % 231.11/34.56 | (403) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_967_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_967_1 & $i(all_967_0) % 231.11/34.56 | & $i(all_967_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, all_967_0) = v1) | % 231.11/34.56 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_967_1, % 231.11/34.56 | v0) | c_Nat_OSuc(v1) = v0) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (403) implies: % 231.11/34.56 | (404) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_967_1 % 231.11/34.56 | (405) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_967_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (141) with fresh symbol all_975_0 gives: % 231.11/34.56 | (406) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_975_0 & $i(all_975_0) & % 231.11/34.56 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.56 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) | % 231.11/34.56 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | % 231.11/34.56 | hAPP(v3, all_975_0) = v0) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (406) implies: % 231.11/34.56 | (407) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_975_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (119) with fresh symbol all_978_0 gives: % 231.11/34.56 | (408) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_978_0 & % 231.11/34.56 | $i(all_978_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_978_0, v0) % 231.11/34.56 | | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v2) & % 231.11/34.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (408) implies: % 231.11/34.56 | (409) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_978_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (167) with fresh symbols all_987_0, all_987_1 gives: % 231.11/34.56 | (410) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_987_1 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_987_0 & % 231.11/34.56 | $i(all_987_0) & $i(all_987_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_987_1, v0) % 231.11/34.56 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_987_0, % 231.11/34.56 | v1)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (410) implies: % 231.11/34.56 | (411) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_987_0 % 231.11/34.56 | (412) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_987_1 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (126) with fresh symbol all_991_0 gives: % 231.11/34.56 | (413) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_991_0 & % 231.11/34.56 | $i(all_991_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, all_991_0) = % 231.11/34.56 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 231.11/34.56 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & c_RComplete_Onatfloor(v0) % 231.11/34.56 | = v2 & $i(v3) & $i(v2) & % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3))) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (413) implies: % 231.11/34.56 | (414) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_991_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (80) with fresh symbols all_994_0, all_994_1, all_994_2 % 231.11/34.56 | gives: % 231.11/34.56 | (415) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_994_2 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_994_1 & % 231.11/34.56 | hAPP(all_994_2, all_994_1) = all_994_0 & $i(all_994_0) & % 231.11/34.56 | $i(all_994_1) & $i(all_994_2) & ! [v0: $i] : ! [v1: int] : (v1 = % 231.11/34.56 | all_994_1 | ~ (hAPP(all_994_0, v0) = v1) | ~ $i(v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (415) implies: % 231.11/34.56 | (416) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_994_1 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (127) with fresh symbol all_997_0 gives: % 231.11/34.56 | (417) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_997_0 & % 231.11/34.56 | $i(all_997_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 231.11/34.56 | : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ % 231.11/34.56 | (c_RComplete_Onatfloor(v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_997_0, v1) % 231.11/34.56 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (417) implies: % 231.11/34.56 | (418) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_997_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (113) with fresh symbols all_1000_0, all_1000_1 gives: % 231.11/34.56 | (419) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1000_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1000_1 & % 231.11/34.56 | $i(all_1000_0) & $i(all_1000_1) & ! [v0: any] : (v0 = all_1000_0 | % 231.11/34.56 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = all_1000_1) | ~ $i(v0)) & ! % 231.11/34.56 | [v0: int] : (v0 = all_1000_1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, % 231.11/34.56 | all_1000_0) = v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (419) implies: % 231.11/34.56 | (420) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1000_1 % 231.11/34.56 | (421) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1000_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (90) with fresh symbols all_1003_0, all_1003_1, % 231.11/34.56 | all_1003_2 gives: % 231.11/34.56 | (422) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1003_1 & % 231.11/34.56 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1003_2 & % 231.11/34.56 | hAPP(all_1003_2, all_1003_1) = all_1003_0 & $i(all_1003_0) & % 231.11/34.56 | $i(all_1003_1) & $i(all_1003_2) & ! [v0: $i] : ! [v1: $i] : (v1 = % 231.11/34.56 | v0 | ~ (hAPP(all_1003_0, v0) = v1) | ~ $i(v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (422) implies: % 231.11/34.56 | (423) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1003_1 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (21) with fresh symbols all_1006_0, all_1006_1, % 231.11/34.56 | all_1006_2 gives: % 231.11/34.56 | (424) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1006_1 & % 231.11/34.56 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1006_2 & % 231.11/34.56 | hAPP(all_1006_2, all_1006_1) = all_1006_0 & $i(all_1006_0) & % 231.11/34.56 | $i(all_1006_1) & $i(all_1006_2) & ! [v0: $i] : ! [v1: $i] : (v1 = % 231.11/34.56 | v0 | ~ (hAPP(all_1006_0, v0) = v1) | ~ $i(v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (424) implies: % 231.11/34.56 | (425) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1006_2 % 231.11/34.56 | (426) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1006_1 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (125) with fresh symbol all_1009_0 gives: % 231.11/34.56 | (427) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1009_0 & % 231.11/34.56 | $i(all_1009_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 231.11/34.56 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & % 231.11/34.56 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1009_0) = % 231.11/34.56 | v3 & $i(v3) & $i(v2) & % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (427) implies: % 231.11/34.56 | (428) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1009_0 % 231.11/34.56 | (429) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0) = v1) | ~ % 231.11/34.56 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, % 231.11/34.56 | v1) = v2 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 231.11/34.56 | all_1009_0) = v3 & $i(v3) & $i(v2) & % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))) % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (3) with fresh symbols all_1015_0, all_1015_1 gives: % 231.11/34.56 | (430) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1015_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1015_1 & % 231.11/34.56 | $i(all_1015_0) & $i(all_1015_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 231.11/34.56 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, % 231.11/34.56 | all_1015_0, v1) = v2 & $i(v2) & % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1015_1, v2))) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (430) implies: % 231.11/34.56 | (431) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1015_1 % 231.11/34.56 | (432) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1015_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (53) with fresh symbol all_1018_0 gives: % 231.11/34.56 | (433) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1018_0 & % 231.11/34.56 | $i(all_1018_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 231.11/34.56 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = all_1018_0) | % 231.11/34.56 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ( ~ (v2 = all_1018_0) & % 231.11/34.56 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2 & % 231.11/34.56 | $i(v2))) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (433) implies: % 231.11/34.56 | (434) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1018_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (164) with fresh symbol all_1021_0 gives: % 231.11/34.56 | (435) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1021_0 & % 231.11/34.56 | $i(all_1021_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 231.11/34.56 | ~ (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) = % 231.11/34.56 | v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1021_0, v1) | % 231.11/34.56 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1021_0, v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (435) implies: % 231.11/34.56 | (436) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1021_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (155) with fresh symbol all_1024_0 gives: % 231.11/34.56 | (437) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1024_0 & % 231.11/34.56 | $i(all_1024_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.56 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Power_Opower_Opower(v3, % 231.11/34.56 | v2, v1) = v4) | ~ (hAPP(v4, v0) = v5) | ~ $i(v3) | ~ $i(v2) % 231.11/34.56 | | ~ $i(v1) | ~ $i(v0) | hAPP(v5, all_1024_0) = v2) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (437) implies: % 231.11/34.56 | (438) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1024_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (172) with fresh symbols all_1027_0, all_1027_1 gives: % 231.11/34.56 | (439) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1027_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1027_1 & % 231.11/34.56 | $i(all_1027_0) & $i(all_1027_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1027_0) | % 231.11/34.56 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1027_1, v0) | % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_1027_1)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (439) implies: % 231.11/34.56 | (440) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1027_1 % 231.11/34.56 | (441) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1027_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (204) with fresh symbol all_1030_0 gives: % 231.11/34.56 | (442) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1030_0 & % 231.11/34.56 | $i(all_1030_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 231.11/34.56 | ? [v3: $i] : (c_Nat_OSuc(v0) = v2 & c_RealDef_Oreal(tc_Nat_Onat, % 231.11/34.56 | v2) = v3 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, % 231.11/34.56 | all_1030_0) = v3 & $i(v3) & $i(v2))) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (442) implies: % 231.11/34.56 | (443) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1030_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (173) with fresh symbols all_1033_0, all_1033_1 gives: % 231.11/34.56 | (444) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1033_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1033_1 & % 231.11/34.56 | $i(all_1033_0) & $i(all_1033_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1033_1, v1) | % 231.11/34.56 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1033_1, v0) | % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1033_0, v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (444) implies: % 231.11/34.56 | (445) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1033_1 % 231.11/34.56 | (446) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1033_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (175) with fresh symbols all_1036_0, all_1036_1 gives: % 231.11/34.56 | (447) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1036_0 & % 231.11/34.56 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1036_1 & % 231.11/34.56 | $i(all_1036_0) & $i(all_1036_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.56 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.56 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1036_1, v0) | % 231.11/34.56 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1036_1, % 231.11/34.56 | v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.56 | all_1036_0, v0)) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (447) implies: % 231.11/34.56 | (448) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1036_1 % 231.11/34.56 | (449) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1036_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (17) with fresh symbol all_1039_0 gives: % 231.11/34.56 | (450) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1039_0 & % 231.11/34.56 | $i(all_1039_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.56 | $i] : ( ~ (hAPP(v2, v1) = v3) | ~ (hAPP(all_1039_0, v0) = v2) | ~ % 231.11/34.56 | $i(v1) | ~ $i(v0) | ? [v4: $i] : (hAPP(v4, v0) = v3 & % 231.11/34.56 | hAPP(all_1039_0, v1) = v4 & $i(v4) & $i(v3))) % 231.11/34.56 | % 231.11/34.56 | ALPHA: (450) implies: % 231.11/34.56 | (451) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1039_0 % 231.11/34.56 | % 231.11/34.56 | DELTA: instantiating (177) with fresh symbols all_1042_0, all_1042_1 gives: % 231.11/34.57 | (452) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1042_0 & % 231.11/34.57 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1042_1 & % 231.11/34.57 | $i(all_1042_0) & $i(all_1042_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.57 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1042_0, v0) = % 231.11/34.57 | v1) | ~ $i(v0) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1042_1, v0) % 231.11/34.57 | | ? [v2: $i] : (c_Transcendental_Oln(v1) = v2 & $i(v2) & % 231.11/34.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (452) implies: % 231.11/34.57 | (453) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1042_1 % 231.11/34.57 | (454) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1042_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (215) with fresh symbol all_1045_0 gives: % 231.11/34.57 | (455) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1045_0 & % 231.11/34.57 | $i(all_1045_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.57 | $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, % 231.11/34.57 | v0, v2) = v4) | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, % 231.11/34.57 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1045_0, v2) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | % 231.11/34.57 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v4)) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (455) implies: % 231.11/34.57 | (456) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1045_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (191) with fresh symbol all_1060_0 gives: % 231.11/34.57 | (457) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1060_0 & % 231.11/34.57 | $i(all_1060_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v1) = % 231.11/34.57 | v0) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1060_0, v0)) & ! % 231.11/34.57 | [v0: $i] : ( ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.57 | all_1060_0, v0) | ? [v1: $i] : (c_Nat_OSuc(v1) = v0 & $i(v1))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (457) implies: % 231.11/34.57 | (458) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1060_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (219) with fresh symbols all_1063_0, all_1063_1 gives: % 231.11/34.57 | (459) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1063_1 & % 231.11/34.57 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1063_0 & % 231.11/34.57 | $i(all_1063_0) & $i(all_1063_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.57 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v2) | % 231.11/34.57 | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1063_0, v0) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1063_1, v1) | % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0)) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (459) implies: % 231.11/34.57 | (460) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1063_0 % 231.11/34.57 | (461) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1063_1 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (182) with fresh symbols all_1084_0, all_1084_1, % 231.11/34.57 | all_1084_2 gives: % 231.11/34.57 | (462) c_Nat_OSuc(all_1084_1) = all_1084_0 & c_Nat_OSuc(all_1084_2) = % 231.11/34.57 | all_1084_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1084_2 & % 231.11/34.57 | $i(all_1084_0) & $i(all_1084_1) & $i(all_1084_2) & ! [v0: any] : (v0 % 231.11/34.57 | = all_1084_1 | v0 = all_1084_2 | ~ $i(v0) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, all_1084_0)) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (462) implies: % 231.11/34.57 | (463) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1084_2 % 231.11/34.57 | (464) c_Nat_OSuc(all_1084_2) = all_1084_1 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (129) with fresh symbol all_1093_0 gives: % 231.11/34.57 | (465) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1093_0 & $i(all_1093_0) % 231.11/34.57 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.57 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ % 231.11/34.57 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v4: % 231.11/34.57 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, all_1093_0) = % 231.11/34.57 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 231.11/34.57 | v4, v0))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (465) implies: % 231.11/34.57 | (466) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1093_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (118) with fresh symbols all_1096_0, all_1096_1 gives: % 231.11/34.57 | (467) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1096_0 & % 231.11/34.57 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1096_1 & % 231.11/34.57 | $i(all_1096_0) & $i(all_1096_1) & ! [v0: any] : ! [v1: $i] : (v0 = % 231.11/34.57 | all_1096_0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) % 231.11/34.57 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, % 231.11/34.57 | all_1096_1)) & ! [v0: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, % 231.11/34.57 | all_1096_0) = v0) | % 231.11/34.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.11/34.57 | all_1096_1)) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (467) implies: % 231.11/34.57 | (468) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1096_1 % 231.11/34.57 | (469) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1096_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (140) with fresh symbol all_1099_0 gives: % 231.11/34.57 | (470) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1099_0 & % 231.11/34.57 | $i(all_1099_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.57 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, % 231.11/34.57 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.57 | class_Rings_Ocomm__semiring__1(v1) | ? [v4: $i] : % 231.11/34.57 | (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, all_1099_0) = v4 & % 231.11/34.57 | $i(v4))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (470) implies: % 231.11/34.57 | (471) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1099_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (185) with fresh symbol all_1102_0 gives: % 231.11/34.57 | (472) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1102_0 & $i(all_1102_0) % 231.11/34.57 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.57 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v2, v0) = v3) | ~ % 231.11/34.57 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1102_0) = v2) | % 231.11/34.57 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (c_Nat_OSuc(v0) = v4 & % 231.11/34.57 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v4) = v3 & $i(v4) % 231.11/34.57 | & $i(v3))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (472) implies: % 231.11/34.57 | (473) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1102_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (150) with fresh symbol all_1105_0 gives: % 231.11/34.57 | (474) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1105_0 & % 231.11/34.57 | $i(all_1105_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.57 | $i] : ( ~ (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, % 231.11/34.57 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ class_Power_Opower(v1) | % 231.11/34.57 | ? [v4: $i] : (c_Groups_Oone__class_Oone(v1) = v4 & hAPP(v3, % 231.11/34.57 | all_1105_0) = v4 & $i(v4))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (474) implies: % 231.11/34.57 | (475) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1105_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (130) with fresh symbol all_1108_0 gives: % 231.11/34.57 | (476) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1108_0 & % 231.11/34.57 | $i(all_1108_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.57 | $i] : (v3 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 231.11/34.57 | (c_RComplete_Onatfloor(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ? % 231.11/34.57 | [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 231.11/34.57 | all_1108_0) = v4 & $i(v4) & ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (476) implies: % 231.11/34.57 | (477) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1108_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (218) with fresh symbols all_1111_0, all_1111_1 gives: % 231.11/34.57 | (478) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1111_0 & % 231.11/34.57 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1111_1 & % 231.11/34.57 | $i(all_1111_0) & $i(all_1111_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.57 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 231.11/34.57 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v1) = v4) | ~ % 231.11/34.57 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1111_0, v1) = v2) | ~ $i(v1) | % 231.11/34.57 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.57 | all_1111_1, v1)) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (478) implies: % 231.11/34.57 | (479) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1111_1 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (221) with fresh symbol all_1114_0 gives: % 231.11/34.57 | (480) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1114_0 & % 231.11/34.57 | $i(all_1114_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.57 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | % 231.11/34.57 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 231.11/34.57 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.57 | all_1114_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 231.11/34.57 | v1) | ? [v4: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, % 231.11/34.57 | v1) = v4 & c_Nat_OSuc(v3) = v4 & $i(v4))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (480) implies: % 231.11/34.57 | (481) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1114_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (58) with fresh symbol all_1117_0 gives: % 231.11/34.57 | (482) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1117_0 & % 231.11/34.57 | $i(all_1117_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.57 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v0) = v5) | ~ % 231.11/34.57 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1117_0, v1) = v2) | ~ % 231.11/34.57 | (hAPP(all_1117_0, v0) = v4) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 231.11/34.57 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v3) = v6 & % 231.11/34.57 | $i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, % 231.11/34.57 | v5))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (482) implies: % 231.11/34.57 | (483) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1117_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (66) with fresh symbol all_1120_0 gives: % 231.11/34.57 | (484) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1120_0 & % 231.11/34.57 | $i(all_1120_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 231.11/34.57 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 231.11/34.57 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1120_0)) % 231.11/34.57 | & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.57 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 231.11/34.57 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.11/34.57 | all_1120_0) | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, % 231.11/34.57 | v0) = v1 & $i(v1))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (484) implies: % 231.11/34.57 | (485) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1120_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (28) with fresh symbols all_1132_0, all_1132_1 gives: % 231.11/34.57 | (486) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1132_0 & % 231.11/34.57 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1132_1 & % 231.11/34.57 | $i(all_1132_0) & $i(all_1132_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.57 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1132_0, % 231.11/34.57 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1132_1, v1) | % 231.11/34.57 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1132_1, v0) | % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1132_1, v3)) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (486) implies: % 231.11/34.57 | (487) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1132_1 % 231.11/34.57 | (488) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1132_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (217) with fresh symbols all_1135_0, all_1135_1 gives: % 231.11/34.57 | (489) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1135_0 & % 231.11/34.57 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1135_1 & % 231.11/34.57 | $i(all_1135_0) & $i(all_1135_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.57 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 231.11/34.57 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v1) = v4) | ~ % 231.11/34.57 | (hAPP(v2, v1) = v3) | ~ (hAPP(all_1135_0, v0) = v2) | ~ $i(v1) | % 231.11/34.57 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.57 | all_1135_1, v1)) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (489) implies: % 231.11/34.57 | (490) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1135_1 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (66) with fresh symbol all_1138_0 gives: % 231.11/34.57 | (491) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1138_0 & % 231.11/34.57 | $i(all_1138_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 231.11/34.57 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 231.11/34.57 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1138_0)) % 231.11/34.57 | & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.57 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 231.11/34.57 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.11/34.57 | all_1138_0) | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, % 231.11/34.57 | v0) = v1 & $i(v1))) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (491) implies: % 231.11/34.57 | (492) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1138_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (170) with fresh symbols all_1141_0, all_1141_1 gives: % 231.11/34.57 | (493) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1141_0 & % 231.11/34.57 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1141_1 & % 231.11/34.57 | $i(all_1141_0) & $i(all_1141_1) & ! [v0: any] : (v0 = all_1141_0 | % 231.11/34.57 | ~ (c_Transcendental_Oln(v0) = all_1141_1) | ~ $i(v0) | ~ % 231.11/34.57 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1141_1, v0)) & % 231.11/34.57 | ! [v0: int] : (v0 = all_1141_1 | ~ (c_Transcendental_Oln(all_1141_0) % 231.11/34.57 | = v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.57 | all_1141_1, all_1141_0)) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (493) implies: % 231.11/34.57 | (494) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1141_1 % 231.11/34.57 | (495) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1141_0 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (2) with fresh symbols all_1147_0, all_1147_1, % 231.11/34.57 | all_1147_2, all_1147_3, all_1147_4 gives: % 231.11/34.57 | (496) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1147_3 & % 231.11/34.57 | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1147_1) = all_1147_0 % 231.11/34.57 | & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1147_4 & % 231.11/34.57 | hAPP(all_1147_2, v_m____) = all_1147_1 & hAPP(all_1147_3, v_r) = % 231.11/34.57 | all_1147_2 & $i(all_1147_0) & $i(all_1147_1) & $i(all_1147_2) & % 231.11/34.57 | $i(all_1147_3) & $i(all_1147_4) & % 231.11/34.57 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_4, % 231.11/34.57 | all_1147_0) % 231.11/34.57 | % 231.11/34.57 | ALPHA: (496) implies: % 231.11/34.57 | (497) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_4, % 231.11/34.57 | all_1147_0) % 231.11/34.57 | (498) hAPP(all_1147_3, v_r) = all_1147_2 % 231.11/34.57 | (499) hAPP(all_1147_2, v_m____) = all_1147_1 % 231.11/34.57 | (500) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1147_4 % 231.11/34.57 | (501) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1147_1) = all_1147_0 % 231.11/34.57 | (502) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1147_3 % 231.11/34.57 | % 231.11/34.57 | DELTA: instantiating (60) with fresh symbol all_1155_0 gives: % 231.11/34.58 | (503) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1155_0 & % 231.11/34.58 | $i(all_1155_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 231.11/34.58 | all_1155_0 | ~ (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, % 231.11/34.58 | v0) = v1) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, % 231.11/34.58 | v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 231.11/34.58 | [v2: $i] : (v1 = v0 | ~ % 231.11/34.58 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v0) = v2) | ~ % 231.11/34.58 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = % 231.11/34.58 | all_1155_0) | ~ $i(v1) | ~ $i(v0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (503) implies: % 231.11/34.58 | (504) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1155_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (55) with fresh symbol all_1163_0 gives: % 231.11/34.58 | (505) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1163_0 & % 231.11/34.58 | $i(all_1163_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 231.11/34.58 | all_1163_0 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) % 231.11/34.58 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: % 231.11/34.58 | $i] : ! [v1: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 231.11/34.58 | v1, v0) = all_1163_0) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (505) implies: % 231.11/34.58 | (506) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1163_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (193) with fresh symbols all_1166_0, all_1166_1, % 231.11/34.58 | all_1166_2, all_1166_3 gives: % 231.11/34.58 | (507) c_Nat_OSuc(all_1166_2) = all_1166_1 & % 231.11/34.58 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1166_3 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1166_2 & % 231.11/34.58 | hAPP(all_1166_3, all_1166_1) = all_1166_0 & $i(all_1166_0) & % 231.11/34.58 | $i(all_1166_1) & $i(all_1166_2) & $i(all_1166_3) & ! [v0: $i] : ! % 231.11/34.58 | [v1: int] : (v1 = all_1166_1 | ~ (hAPP(all_1166_0, v0) = v1) | ~ % 231.11/34.58 | $i(v0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (507) implies: % 231.11/34.58 | (508) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1166_2 % 231.11/34.58 | (509) c_Nat_OSuc(all_1166_2) = all_1166_1 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (18) with fresh symbols all_1169_0, all_1169_1 gives: % 231.11/34.58 | (510) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1169_0 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1169_1 & % 231.11/34.58 | $i(all_1169_0) & $i(all_1169_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.58 | any] : ! [v3: $i] : ! [v4: $i] : (v2 = all_1169_1 | v1 = v0 | ~ % 231.11/34.58 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1169_0, % 231.11/34.58 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (510) implies: % 231.11/34.58 | (511) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1169_1 % 231.11/34.58 | (512) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1169_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (205) with fresh symbols all_1186_0, all_1186_1, % 231.11/34.58 | all_1186_2 gives: % 231.11/34.58 | (513) c_Nat_OSuc(all_1186_2) = all_1186_1 & % 231.11/34.58 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1186_0 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_2 & % 231.11/34.58 | $i(all_1186_0) & $i(all_1186_1) & $i(all_1186_2) & ! [v0: $i] : ! % 231.11/34.58 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ % 231.11/34.58 | (hAPP(all_1186_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1186_1, v1) | % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1186_1, v3)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (513) implies: % 231.11/34.58 | (514) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1186_2 % 231.11/34.58 | (515) c_Nat_OSuc(all_1186_2) = all_1186_1 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (128) with fresh symbol all_1189_0 gives: % 231.11/34.58 | (516) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1189_0 & % 231.11/34.58 | $i(all_1189_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.58 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ % 231.11/34.58 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~ % 231.11/34.58 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1189_0, v1) % 231.11/34.58 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatfloor(v3) = v4 & % 231.11/34.58 | c_RComplete_Onatfloor(v1) = v5 & % 231.11/34.58 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) & % 231.11/34.58 | $i(v4))) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (516) implies: % 231.11/34.58 | (517) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1189_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (158) with fresh symbol all_1192_0 gives: % 231.11/34.58 | (518) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1192_0 & % 231.11/34.58 | $i(all_1192_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 231.11/34.58 | ~ c_SEQ_OBseq(v1, v0) | ~ % 231.11/34.58 | class_RealVector_Oreal__normed__vector(v1) | ? [v2: $i] : ($i(v2) % 231.11/34.58 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1192_0, v2) % 231.11/34.58 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.11/34.58 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v0, % 231.11/34.58 | v3) = v4) | ~ $i(v3) | % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2)))) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (518) implies: % 231.11/34.58 | (519) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1192_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (85) with fresh symbol all_1195_0 gives: % 231.11/34.58 | (520) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1195_0 & % 231.11/34.58 | $i(all_1195_0) & ! [v0: $i] : ! [v1: any] : (v1 = all_1195_0 | ~ % 231.11/34.58 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1195_0) | % 231.11/34.58 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 231.11/34.58 | all_1195_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = % 231.11/34.58 | all_1195_0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = % 231.11/34.58 | all_1195_0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 231.11/34.58 | all_1195_0, all_1195_0) = v0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (520) implies: % 231.11/34.58 | (521) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1195_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (107) with fresh symbols all_1198_0, all_1198_1 gives: % 231.11/34.58 | (522) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1198_1 & % 231.11/34.58 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1198_0 & % 231.11/34.58 | $i(all_1198_0) & $i(all_1198_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.58 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1198_1, v1) | % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1198_0, % 231.11/34.58 | v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0) % 231.11/34.58 | = v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1198_0, v0) % 231.11/34.58 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1198_1, v1)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (522) implies: % 231.11/34.58 | (523) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1198_0 % 231.11/34.58 | (524) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1198_1 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (120) with fresh symbols all_1204_0, all_1204_1 gives: % 231.11/34.58 | (525) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1204_0 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1204_1 & % 231.11/34.58 | $i(all_1204_0) & $i(all_1204_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.58 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1204_0, v0) | % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1204_1, v1)) & % 231.11/34.58 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = % 231.11/34.58 | v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1204_1, v1) | % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1204_0, v0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (525) implies: % 231.11/34.58 | (526) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1204_1 % 231.11/34.58 | (527) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1204_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (95) with fresh symbols all_1207_0, all_1207_1 gives: % 231.11/34.58 | (528) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1207_0 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1207_1 & % 231.11/34.58 | $i(all_1207_0) & $i(all_1207_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.58 | $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (hAPP(v3, v1) = v4) % 231.11/34.58 | | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1207_0, v2) = v3) | ~ % 231.11/34.58 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1207_1, v2)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (528) implies: % 231.11/34.58 | (529) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1207_1 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (131) with fresh symbol all_1212_0 gives: % 231.11/34.58 | (530) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1212_0 & % 231.11/34.58 | $i(all_1212_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.58 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ % 231.11/34.58 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~ % 231.11/34.58 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1212_0, v1) % 231.11/34.58 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatceiling(v3) = v4 & % 231.11/34.58 | c_RComplete_Onatceiling(v1) = v5 & % 231.11/34.58 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) & % 231.11/34.58 | $i(v4))) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (530) implies: % 231.11/34.58 | (531) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1212_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (57) with fresh symbol all_1215_0 gives: % 231.11/34.58 | (532) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1215_0 & % 231.11/34.58 | $i(all_1215_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.58 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.58 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1215_0) % 231.11/34.58 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & ! % 231.11/34.58 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.58 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.58 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 231.11/34.58 | all_1215_0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (532) implies: % 231.11/34.58 | (533) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1215_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (83) with fresh symbols all_1218_0, all_1218_1, % 231.11/34.58 | all_1218_2 gives: % 231.11/34.58 | (534) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1218_1 & % 231.11/34.58 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1218_2 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1218_0 & % 231.11/34.58 | $i(all_1218_0) & $i(all_1218_1) & $i(all_1218_2) & ! [v0: any] : ! % 231.11/34.58 | [v1: any] : ! [v2: $i] : (v1 = all_1218_0 | v0 = all_1218_1 | ~ % 231.11/34.58 | (hAPP(v2, v0) = v1) | ~ (hAPP(all_1218_2, v1) = v2) | ~ $i(v1) | % 231.11/34.58 | ~ $i(v0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (534) implies: % 231.11/34.58 | (535) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1218_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (49) with fresh symbol all_1221_0 gives: % 231.11/34.58 | (536) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1221_0 & % 231.11/34.58 | $i(all_1221_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.58 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 231.11/34.58 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.58 | v0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1221_0, % 231.11/34.58 | v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.58 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v2) | ~ % 231.11/34.58 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.58 | all_1221_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, % 231.11/34.58 | v1)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (536) implies: % 231.11/34.58 | (537) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1221_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (10) with fresh symbols all_1224_0, all_1224_1 gives: % 231.11/34.58 | (538) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1224_0 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1224_1 & % 231.11/34.58 | $i(all_1224_0) & $i(all_1224_1) & ! [v0: any] : ! [v1: $i] : ! % 231.11/34.58 | [v2: $i] : (v0 = all_1224_1 | ~ (hAPP(v1, v0) = v2) | ~ % 231.11/34.58 | (hAPP(all_1224_0, v0) = v1) | ~ $i(v0) | % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1224_1, v2)) & % 231.11/34.58 | ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(v0, all_1224_1) = v1) | ~ % 231.11/34.58 | (hAPP(all_1224_0, all_1224_1) = v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1224_1, v1)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (538) implies: % 231.11/34.58 | (539) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1224_1 % 231.11/34.58 | (540) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1224_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (108) with fresh symbols all_1227_0, all_1227_1 gives: % 231.11/34.58 | (541) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1227_1 & % 231.11/34.58 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1227_0 & % 231.11/34.58 | $i(all_1227_0) & $i(all_1227_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.58 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1227_1) | % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.11/34.58 | all_1227_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.58 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_1227_0) % 231.11/34.58 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1227_1)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (541) implies: % 231.11/34.58 | (542) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1227_0 % 231.11/34.58 | (543) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1227_1 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (19) with fresh symbols all_1230_0, all_1230_1 gives: % 231.11/34.58 | (544) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1230_0 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1230_1 & % 231.11/34.58 | $i(all_1230_0) & $i(all_1230_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.58 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1230_1 | % 231.11/34.58 | v1 = v0 | ~ (hAPP(v5, v2) = v4) | ~ (hAPP(v3, v2) = v4) | ~ % 231.11/34.58 | (hAPP(all_1230_0, v1) = v3) | ~ (hAPP(all_1230_0, v0) = v5) | ~ % 231.11/34.58 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (544) implies: % 231.11/34.58 | (545) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1230_1 % 231.11/34.58 | (546) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1230_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (72) with fresh symbols all_1233_0, all_1233_1 gives: % 231.11/34.58 | (547) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1233_0 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1233_1 & % 231.11/34.58 | $i(all_1233_0) & $i(all_1233_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.58 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v2) = % 231.11/34.58 | v4) | ~ (hAPP(v3, v1) = v5) | ~ (hAPP(all_1233_0, v0) = v3) | % 231.11/34.58 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1233_1, v0) | % 231.11/34.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (547) implies: % 231.11/34.58 | (548) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1233_1 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (24) with fresh symbol all_1236_0 gives: % 231.11/34.58 | (549) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1236_0 & % 231.11/34.58 | $i(all_1236_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.58 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ % 231.11/34.58 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3: % 231.11/34.58 | $i] : (( ~ (v2 = all_1236_0) | (v3 = v0 & % 231.11/34.58 | c_Groups_Ozero__class_Ozero(v1) = v0)) & (v2 = all_1236_0 | ( % 231.11/34.58 | ~ (v3 = v0) & c_Groups_Ozero__class_Ozero(v1) = v3 & % 231.11/34.58 | $i(v3))))) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (549) implies: % 231.11/34.58 | (550) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1236_0 % 231.11/34.58 | % 231.11/34.58 | DELTA: instantiating (211) with fresh symbol all_1242_0 gives: % 231.11/34.58 | (551) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1242_0 & % 231.11/34.58 | $i(all_1242_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 231.11/34.58 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1242_0, v0) % 231.11/34.58 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 231.11/34.58 | (c_Nat_OSuc(v1) = v3 & c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & % 231.11/34.58 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v4) & $i(v3) & $i(v2) % 231.11/34.58 | & $i(v1) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.11/34.58 | v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 231.11/34.58 | v0))) % 231.11/34.58 | % 231.11/34.58 | ALPHA: (551) implies: % 231.11/34.58 | (552) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1242_0 % 231.11/34.58 | % 231.11/34.59 | DELTA: instantiating (197) with fresh symbols all_1251_0, all_1251_1, % 231.11/34.59 | all_1251_2 gives: % 231.11/34.59 | (553) c_Nat_OSuc(all_1251_2) = all_1251_1 & % 231.11/34.59 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1251_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1251_2 & % 231.11/34.59 | $i(all_1251_0) & $i(all_1251_1) & $i(all_1251_2) & ! [v0: $i] : ! % 231.11/34.59 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ % 231.11/34.59 | (hAPP(all_1251_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1251_1, v1) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1251_1, v0) | % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (553) implies: % 231.11/34.59 | (554) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1251_2 % 231.11/34.59 | (555) c_Nat_OSuc(all_1251_2) = all_1251_1 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (59) with fresh symbol all_1260_0 gives: % 231.11/34.59 | (556) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1260_0 & % 231.11/34.59 | $i(all_1260_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 231.11/34.59 | all_1260_0 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, % 231.11/34.59 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v0) % 231.11/34.59 | & c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v3 & % 231.11/34.59 | $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.59 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = % 231.11/34.59 | all_1260_0) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.59 | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v0) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (556) implies: % 231.11/34.59 | (557) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1260_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (196) with fresh symbols all_1263_0, all_1263_1, % 231.11/34.59 | all_1263_2 gives: % 231.11/34.59 | (558) c_Nat_OSuc(all_1263_2) = all_1263_1 & % 231.11/34.59 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1263_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1263_2 & % 231.11/34.59 | $i(all_1263_0) & $i(all_1263_1) & $i(all_1263_2) & ! [v0: $i] : ! % 231.11/34.59 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~ % 231.11/34.59 | (hAPP(all_1263_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1263_1, v1) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1263_1, v0) | % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1263_1, v3)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (558) implies: % 231.11/34.59 | (559) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1263_2 % 231.11/34.59 | (560) c_Nat_OSuc(all_1263_2) = all_1263_1 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (198) with fresh symbols all_1266_0, all_1266_1, % 231.11/34.59 | all_1266_2 gives: % 231.11/34.59 | (561) c_Nat_OSuc(all_1266_2) = all_1266_1 & % 231.11/34.59 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1266_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1266_2 & % 231.11/34.59 | $i(all_1266_0) & $i(all_1266_1) & $i(all_1266_2) & ! [v0: $i] : ! % 231.11/34.59 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v1) = v3) | ~ % 231.11/34.59 | (hAPP(all_1266_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1266_1, v1) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1266_1, v0) | % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (561) implies: % 231.11/34.59 | (562) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1266_2 % 231.11/34.59 | (563) c_Nat_OSuc(all_1266_2) = all_1266_1 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (6) with fresh symbol all_1269_0 gives: % 231.11/34.59 | (564) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1269_0 & % 231.11/34.59 | $i(all_1269_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.59 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ % 231.11/34.59 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3: % 231.11/34.59 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.59 | all_1269_0, v2) | ( ~ (v3 = v0) & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3))) & % 231.11/34.59 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1269_0, v2) % 231.11/34.59 | | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1) = v0)))) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (564) implies: % 231.11/34.59 | (565) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1269_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (146) with fresh symbols all_1272_0, all_1272_1 gives: % 231.11/34.59 | (566) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1272_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1272_1 & % 231.11/34.59 | $i(all_1272_0) & $i(all_1272_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 231.11/34.59 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1272_0, v2) = v3) | % 231.11/34.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1272_1, v2) | % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (566) implies: % 231.11/34.59 | (567) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1272_1 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (12) with fresh symbol all_1275_0 gives: % 231.11/34.59 | (568) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1275_0 & % 231.11/34.59 | $i(all_1275_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.59 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ % 231.11/34.59 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3: % 231.11/34.59 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.59 | v2, all_1275_0) | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1) % 231.11/34.59 | = v0)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.59 | v2, all_1275_0) | ( ~ (v3 = v0) & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3))))) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (568) implies: % 231.11/34.59 | (569) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1275_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (27) with fresh symbols all_1286_0, all_1286_1 gives: % 231.11/34.59 | (570) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1286_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1286_1 & % 231.11/34.59 | $i(all_1286_0) & $i(all_1286_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 231.11/34.59 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1286_0, v2) = v3) | % 231.11/34.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1286_1, v2) | % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v5)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (570) implies: % 231.11/34.59 | (571) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1286_1 % 231.11/34.59 | (572) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1286_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (157) with fresh symbol all_1306_0 gives: % 231.11/34.59 | (573) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1306_0 & % 231.11/34.59 | $i(all_1306_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) % 231.11/34.59 | | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | class_RealVector_Oreal__normed__vector(v2) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1306_0, v1) | % 231.11/34.59 | c_SEQ_OBseq(v2, v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 231.11/34.59 | (c_RealVector_Onorm__class_Onorm(v2, v4) = v5 & hAPP(v0, v3) = v4 & % 231.11/34.59 | $i(v5) & $i(v4) & $i(v3) & ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1))) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (573) implies: % 231.11/34.59 | (574) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1306_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (145) with fresh symbol all_1311_0 gives: % 231.11/34.59 | (575) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1311_0 & % 231.11/34.59 | $i(all_1311_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.59 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.11/34.59 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) | % 231.11/34.59 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | class_Rings_Olinordered__semidom(v2) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1311_0, v0) | ? % 231.11/34.59 | [v6: $i] : (c_Groups_Oone__class_Oone(v2) = v6 & $i(v6) & ( ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(v2, v6, v1) | % 231.11/34.59 | c_Orderings_Oord__class_Oless(v2, v6, v5)))) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (575) implies: % 231.11/34.59 | (576) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1311_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (97) with fresh symbols all_1314_0, all_1314_1, % 231.11/34.59 | all_1314_2 gives: % 231.11/34.59 | (577) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1314_0 & % 231.11/34.59 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1314_1 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1314_2 & % 231.11/34.59 | $i(all_1314_0) & $i(all_1314_1) & $i(all_1314_2) & ! [v0: $i] : ! % 231.11/34.59 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, % 231.11/34.59 | all_1314_1) = v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1314_2, v0) % 231.11/34.59 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatceiling(v1) = v2 & % 231.11/34.59 | c_RComplete_Onatceiling(v0) = v3 & % 231.11/34.59 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1314_0) = v2 & % 231.11/34.59 | $i(v3) & $i(v2))) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (577) implies: % 231.11/34.59 | (578) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1314_2 % 231.11/34.59 | (579) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1314_1 % 231.11/34.59 | (580) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1314_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (31) with fresh symbols all_1317_0, all_1317_1 gives: % 231.11/34.59 | (581) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1317_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1317_1 & % 231.11/34.59 | $i(all_1317_0) & $i(all_1317_1) & ! [v0: $i] : ! [v1: any] : ! % 231.11/34.59 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 231.11/34.59 | (v1 = all_1317_1 | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, % 231.11/34.59 | v1) = v3) | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) % 231.11/34.59 | = v5) | ~ (hAPP(v4, v5) = v6) | ~ (hAPP(all_1317_0, v2) = v4) | % 231.11/34.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v6) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 231.11/34.59 | all_1317_1)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (581) implies: % 231.11/34.59 | (582) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1317_1 % 231.11/34.59 | (583) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1317_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (98) with fresh symbols all_1320_0, all_1320_1, % 231.11/34.59 | all_1320_2 gives: % 231.11/34.59 | (584) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1320_0 & % 231.11/34.59 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1320_1 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1320_2 & % 231.11/34.59 | $i(all_1320_0) & $i(all_1320_1) & $i(all_1320_2) & ! [v0: $i] : ! % 231.11/34.59 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, % 231.11/34.59 | all_1320_1) = v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1320_2, v0) % 231.11/34.59 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatfloor(v1) = v2 & % 231.11/34.59 | c_RComplete_Onatfloor(v0) = v3 & % 231.11/34.59 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1320_0) = v2 & % 231.11/34.59 | $i(v3) & $i(v2))) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (584) implies: % 231.11/34.59 | (585) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1320_2 % 231.11/34.59 | (586) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1320_1 % 231.11/34.59 | (587) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1320_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (73) with fresh symbols all_1328_0, all_1328_1 gives: % 231.11/34.59 | (588) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1328_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1328_1 & % 231.11/34.59 | $i(all_1328_0) & $i(all_1328_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.11/34.59 | (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1328_0, % 231.11/34.59 | v2) = v3) | ~ (hAPP(all_1328_0, v1) = v5) | ~ $i(v2) | ~ % 231.11/34.59 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.59 | v2, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.59 | all_1328_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, % 231.11/34.59 | v6)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (588) implies: % 231.11/34.59 | (589) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1328_1 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (174) with fresh symbols all_1337_0, all_1337_1 gives: % 231.11/34.59 | (590) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1337_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1337_1 & % 231.11/34.59 | $i(all_1337_0) & $i(all_1337_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.59 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1337_1, v0) | % 231.11/34.59 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1337_0, % 231.11/34.59 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.59 | all_1337_1, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.59 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1337_1, v0) | % 231.11/34.59 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1337_1, % 231.11/34.59 | v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.59 | all_1337_0, v0)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (590) implies: % 231.11/34.59 | (591) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1337_1 % 231.11/34.59 | (592) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1337_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (32) with fresh symbols all_1342_0, all_1342_1, % 231.11/34.59 | all_1342_2 gives: % 231.11/34.59 | (593) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1342_1 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1342_2 & % 231.11/34.59 | $i(all_1342_0) & $i(all_1342_1) & $i(all_1342_2) & % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1342_2, % 231.11/34.59 | all_1342_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1342_1, v0) % 231.11/34.59 | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 231.11/34.59 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 & % 231.11/34.59 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.59 | v3, all_1342_0)) | % 231.11/34.59 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 & % 231.11/34.59 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.59 | v2, v_r)))) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (593) implies: % 231.11/34.59 | (594) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1342_2 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (169) with fresh symbols all_1345_0, all_1345_1 gives: % 231.11/34.59 | (595) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1345_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1345_1 & % 231.11/34.59 | $i(all_1345_0) & $i(all_1345_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.59 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1345_0, v0) | % 231.11/34.59 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1345_1, v0) | % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1345_1, v1)) & % 231.11/34.59 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Transcendental_Oln(v0) = v1) | ~ % 231.11/34.59 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.59 | all_1345_1, v1) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1345_1, v0) | % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1345_0, v0)) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (595) implies: % 231.11/34.59 | (596) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1345_1 % 231.11/34.59 | (597) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1345_0 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (216) with fresh symbols all_1354_0, all_1354_1 gives: % 231.11/34.59 | (598) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1354_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1354_1 & % 231.11/34.59 | $i(all_1354_0) & $i(all_1354_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.59 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.11/34.59 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v4, v5) = v6) | ~ % 231.11/34.59 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1354_0, % 231.11/34.59 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.59 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1354_1, v2) | % 231.11/34.59 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v6 & $i(v6))) % 231.11/34.59 | % 231.11/34.59 | ALPHA: (598) implies: % 231.11/34.59 | (599) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1354_1 % 231.11/34.59 | % 231.11/34.59 | DELTA: instantiating (171) with fresh symbols all_1357_0, all_1357_1 gives: % 231.11/34.59 | (600) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1357_0 & % 231.11/34.59 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1357_1 & % 231.11/34.59 | $i(all_1357_0) & $i(all_1357_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.59 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_1357_1) | % 231.11/34.60 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1357_1, v0) | % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1357_0)) & % 231.11/34.60 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Transcendental_Oln(v0) = v1) | ~ % 231.11/34.60 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.11/34.60 | all_1357_0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.60 | all_1357_1, v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.60 | v1, all_1357_1)) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (600) implies: % 231.11/34.60 | (601) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1357_1 % 231.11/34.60 | (602) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1357_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (137) with fresh symbols all_1372_0, all_1372_1 gives: % 231.11/34.60 | (603) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1372_0 & % 231.11/34.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1372_1 & % 231.11/34.60 | $i(all_1372_0) & $i(all_1372_1) & ? [v0: $i] : ! [v1: $i] : ( ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1372_1, v1) | % 231.11/34.60 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 231.11/34.60 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & hAPP(v4, v1) = v5 & % 231.11/34.60 | hAPP(all_1372_0, v3) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (603) implies: % 231.11/34.60 | (604) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1372_1 % 231.11/34.60 | (605) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1372_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (110) with fresh symbols all_1374_0, all_1374_1 gives: % 231.11/34.60 | (606) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1374_0 & % 231.11/34.60 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1374_1 & % 231.11/34.60 | $i(all_1374_0) & $i(all_1374_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.60 | $i] : ! [v3: $i] : (v3 = v2 | ~ (c_RComplete_Onatceiling(v0) = % 231.11/34.60 | v2) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, % 231.11/34.60 | all_1374_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 231.11/34.60 | [v5: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 & $i(v4) & ( ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0) | % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, all_1374_1) % 231.11/34.60 | = v5 & $i(v5) & ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.11/34.60 | v5))))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (606) implies: % 231.11/34.60 | (607) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1374_1 % 231.11/34.60 | (608) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1374_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (207) with fresh symbols all_1379_0, all_1379_1 gives: % 231.11/34.60 | (609) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1379_0 & % 231.11/34.60 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1379_1 & % 231.11/34.60 | $i(all_1379_0) & $i(all_1379_1) & ! [v0: $i] : ! [v1: any] : ! % 231.11/34.60 | [v2: $i] : ! [v3: $i] : (v1 = all_1379_1 | ~ % 231.11/34.60 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1379_0) = v2) | % 231.11/34.60 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v0) = v3) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | ? [v4: $i] : (c_Nat_OSuc(v3) = v4 & % 231.11/34.60 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v4 & $i(v4))) % 231.11/34.60 | & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1379_1, v0) = v1) | % 231.11/34.60 | ~ $i(v0)) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (609) implies: % 231.11/34.60 | (610) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1379_1 % 231.11/34.60 | (611) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1379_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (220) with fresh symbol all_1382_0 gives: % 231.11/34.60 | (612) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1382_0 & % 231.11/34.60 | $i(all_1382_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.60 | $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v3) | % 231.11/34.60 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.60 | all_1382_0, v1) | ? [v4: any] : ? [v5: int] : (( ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v1) | (v4 = % 231.11/34.60 | all_1382_0 & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) % 231.11/34.60 | = all_1382_0)) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.60 | v0, v1) | (v5 = v4 & c_Divides_Odiv__class_Odiv(tc_Nat_Onat, % 231.11/34.60 | v0, v1) = v4 & c_Nat_OSuc(v3) = v4 & $i(v4))))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (612) implies: % 231.11/34.60 | (613) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1382_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (160) with fresh symbols all_1388_0, all_1388_1, % 231.11/34.60 | all_1388_2 gives: % 231.11/34.60 | (614) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1388_0 & % 231.11/34.60 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1388_2 & % 231.11/34.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1388_1 & % 231.11/34.60 | $i(all_1388_0) & $i(all_1388_1) & $i(all_1388_2) & ! [v0: $i] : ! % 231.11/34.60 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1388_2, v1) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1388_1, v0) | % 231.11/34.60 | ? [v2: $i] : ? [v3: $i] : (hAPP(v3, v1) = v0 & hAPP(all_1388_0, % 231.11/34.60 | v2) = v3 & $i(v3) & $i(v2) & % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1388_1, v2))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (614) implies: % 231.11/34.60 | (615) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1388_1 % 231.11/34.60 | (616) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1388_2 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (16) with fresh symbol all_1391_0 gives: % 231.11/34.60 | (617) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1391_0 & % 231.11/34.60 | $i(all_1391_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.60 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v0) = % 231.11/34.60 | v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1391_0, v4) = v5) | % 231.11/34.60 | ~ (hAPP(all_1391_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.60 | ? [v7: $i] : ? [v8: $i] : (hAPP(v7, v0) = v8 & hAPP(v3, v8) = v6 % 231.11/34.60 | & hAPP(all_1391_0, v1) = v7 & $i(v8) & $i(v7) & $i(v6))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (617) implies: % 231.11/34.60 | (618) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1391_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (132) with fresh symbols all_1394_0, all_1394_1 gives: % 231.11/34.60 | (619) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1394_0 & % 231.11/34.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1394_1 & % 231.11/34.60 | $i(all_1394_0) & $i(all_1394_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1394_1, v0) % 231.11/34.60 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 231.11/34.60 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & % 231.11/34.60 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 & % 231.11/34.60 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1394_0) = v2 & % 231.11/34.60 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (619) implies: % 231.11/34.60 | (620) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1394_1 % 231.11/34.60 | (621) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1394_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (115) with fresh symbols all_1408_0, all_1408_1 gives: % 231.11/34.60 | (622) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1408_1 & % 231.11/34.60 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1408_0 & % 231.11/34.60 | $i(all_1408_0) & $i(all_1408_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.60 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.11/34.60 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 231.11/34.60 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v4) | ~ (hAPP(v3, v4) = v5) | % 231.11/34.60 | ~ (hAPP(all_1408_0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 231.11/34.60 | : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v7) = v5 & hAPP(v6, % 231.11/34.60 | v0) = v7 & hAPP(all_1408_1, v1) = v6 & $i(v7) & $i(v6) & % 231.11/34.60 | $i(v5))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (622) implies: % 231.11/34.60 | (623) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1408_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (123) with fresh symbol all_1411_0 gives: % 231.11/34.60 | (624) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1411_0 & % 231.11/34.60 | $i(all_1411_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.60 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ % 231.11/34.60 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1411_0, v1) % 231.11/34.60 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)) & ! % 231.11/34.60 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.60 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ % 231.11/34.60 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1411_0, v1) % 231.11/34.60 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2)) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (624) implies: % 231.11/34.60 | (625) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1411_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (64) with fresh symbol all_1420_0 gives: % 231.11/34.60 | (626) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1420_0 & % 231.11/34.60 | $i(all_1420_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1420_0, v2) | % 231.11/34.60 | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) % 231.11/34.60 | = v3 & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.60 | v3, v0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1420_0, v2) | % 231.11/34.60 | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) % 231.11/34.60 | = v3 & $i(v3) & ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (626) implies: % 231.11/34.60 | (627) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1420_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (30) with fresh symbols all_1423_0, all_1423_1 gives: % 231.11/34.60 | (628) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1423_0 & % 231.11/34.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1423_1 & % 231.11/34.60 | $i(all_1423_0) & $i(all_1423_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.60 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 231.11/34.60 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v1) = v4) | ~ % 231.11/34.60 | (c_RealVector_Onorm__class_Onorm(v3, v0) = v6) | ~ (hAPP(v5, v6) = % 231.11/34.60 | v7) | ~ (hAPP(all_1423_0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v3) % 231.11/34.60 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v7) | % 231.11/34.60 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, % 231.11/34.60 | all_1423_1) | c_Groups_Ozero__class_Ozero(v3) = v1) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (628) implies: % 231.11/34.60 | (629) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1423_1 % 231.11/34.60 | (630) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1423_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (62) with fresh symbol all_1426_0 gives: % 231.11/34.60 | (631) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1426_0 & % 231.11/34.60 | $i(all_1426_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1426_0) % 231.11/34.60 | | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, % 231.11/34.60 | v1) = v3 & $i(v3) & % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3))) & % 231.11/34.60 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1426_0) % 231.11/34.60 | | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, % 231.11/34.60 | v1) = v3 & $i(v3) & ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (631) implies: % 231.11/34.60 | (632) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1426_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (43) with fresh symbols all_1432_0, all_1432_1 gives: % 231.11/34.60 | (633) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1432_0 & % 231.11/34.60 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1432_1 & % 231.11/34.60 | $i(all_1432_0) & $i(all_1432_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.60 | $i] : ! [v3: $i] : ( ~ (c_Groups_Osgn__class_Osgn(v1, v0) = v2) | % 231.11/34.60 | ~ (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~ % 231.11/34.60 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4: % 231.11/34.60 | $i] : ((v3 = all_1432_0 | (v4 = v0 & % 231.11/34.60 | c_Groups_Ozero__class_Ozero(v1) = v0)) & (v3 = all_1432_1 | ( % 231.11/34.60 | ~ (v4 = v0) & c_Groups_Ozero__class_Ozero(v1) = v4 & % 231.11/34.60 | $i(v4))))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (633) implies: % 231.11/34.60 | (634) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1432_1 % 231.11/34.60 | (635) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1432_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (124) with fresh symbol all_1435_0 gives: % 231.11/34.60 | (636) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1435_0 & % 231.11/34.60 | $i(all_1435_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.60 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ % 231.11/34.60 | (c_RComplete_Onatceiling(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1435_0, v1) % 231.11/34.60 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)) & ! % 231.11/34.60 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.60 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ % 231.11/34.60 | (c_RComplete_Onatceiling(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1435_0, v1) % 231.11/34.60 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0)) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (636) implies: % 231.11/34.60 | (637) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1435_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (22) with fresh symbol all_1441_0 gives: % 231.11/34.60 | (638) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1441_0 & % 231.11/34.60 | $i(all_1441_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.60 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v6) = v7) | ~ % 231.11/34.60 | (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1441_0, % 231.11/34.60 | v2) = v3) | ~ (hAPP(all_1441_0, v1) = v5) | ~ $i(v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v8 & % 231.11/34.60 | hAPP(v9, v0) = v7 & hAPP(all_1441_0, v8) = v9 & $i(v9) & $i(v8) & % 231.11/34.60 | $i(v7))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (638) implies: % 231.11/34.60 | (639) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1441_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (61) with fresh symbol all_1444_0 gives: % 231.11/34.60 | (640) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1444_0 & % 231.11/34.60 | $i(all_1444_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1444_0, v2) % 231.11/34.60 | | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, % 231.11/34.60 | v1) = v3 & $i(v3) & % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0))) & % 231.11/34.60 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.60 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.60 | $i(v1) | ~ $i(v0) | % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1444_0, v2) % 231.11/34.60 | | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, % 231.11/34.60 | v1) = v3 & $i(v3) & ~ % 231.11/34.60 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0))) % 231.11/34.60 | % 231.11/34.60 | ALPHA: (640) implies: % 231.11/34.60 | (641) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1444_0 % 231.11/34.60 | % 231.11/34.60 | DELTA: instantiating (65) with fresh symbol all_1453_0 gives: % 231.11/34.61 | (642) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1453_0 & % 231.11/34.61 | $i(all_1453_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.61 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.61 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, all_1453_0) | % 231.11/34.61 | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) % 231.11/34.61 | = v3 & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.61 | v0, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.61 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~ % 231.11/34.61 | $i(v1) | ~ $i(v0) | % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, all_1453_0) | % 231.11/34.61 | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) % 231.11/34.61 | = v3 & $i(v3) & ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (642) implies: % 231.11/34.61 | (643) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1453_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (42) with fresh symbol all_1456_0 gives: % 231.11/34.61 | (644) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1456_0 & % 231.11/34.61 | $i(all_1456_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.61 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ (hAPP(v2, % 231.11/34.61 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.61 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4) % 231.11/34.61 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 231.11/34.61 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7, % 231.11/34.61 | v4) = v8) | ~ (hAPP(all_1456_0, v6) = v7) | ~ $i(v5) | ? % 231.11/34.61 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1, % 231.11/34.61 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) & % 231.11/34.61 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 231.11/34.61 | v8))))) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (644) implies: % 231.11/34.61 | (645) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1456_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (176) with fresh symbols all_1459_0, all_1459_1 gives: % 231.11/34.61 | (646) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1459_0 & % 231.11/34.61 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1459_1 & % 231.11/34.61 | $i(all_1459_0) & $i(all_1459_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.61 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v1) = % 231.11/34.61 | v2) | ~ (c_Transcendental_Oln(v0) = v3) | ~ % 231.11/34.61 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~ % 231.11/34.61 | $i(v1) | ~ $i(v0) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1459_1, v1) | % 231.11/34.61 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1459_1, v0) | % 231.11/34.61 | ? [v5: $i] : ? [v6: $i] : (c_Transcendental_Oln(v6) = v4 & % 231.11/34.61 | hAPP(v5, v0) = v6 & hAPP(all_1459_0, v1) = v5 & $i(v6) & $i(v5) & % 231.11/34.61 | $i(v4))) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (646) implies: % 231.11/34.61 | (647) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1459_1 % 231.11/34.61 | (648) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1459_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (45) with fresh symbol all_1465_0 gives: % 231.11/34.61 | (649) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1465_0 & % 231.11/34.61 | $i(all_1465_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.61 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Polynomial_Ocoeff(v1, v3) % 231.11/34.61 | = v4) | ~ (tc_Polynomial_Opoly(v1) = v2) | ~ % 231.11/34.61 | (c_Groups_Oone__class_Oone(v2) = v3) | ~ (hAPP(v4, v0) = v5) | ~ % 231.11/34.61 | $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) | ? % 231.11/34.61 | [v6: $i] : ? [v7: $i] : (( ~ (v0 = all_1465_0) | (v6 = v5 & % 231.11/34.61 | c_Groups_Oone__class_Oone(v1) = v5 & $i(v5))) & (v0 = % 231.11/34.61 | all_1465_0 | (v7 = v5 & c_Groups_Ozero__class_Ozero(v1) = v5 & % 231.11/34.61 | $i(v5))))) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (649) implies: % 231.11/34.61 | (650) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1465_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (91) with fresh symbols all_1468_0, all_1468_1 gives: % 231.11/34.61 | (651) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1468_1 & % 231.11/34.61 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1468_0 & % 231.11/34.61 | $i(all_1468_0) & $i(all_1468_1) & ! [v0: $i] : ! [v1: any] : ! % 231.11/34.61 | [v2: $i] : (v1 = all_1468_1 | ~ (hAPP(v2, v0) = all_1468_1) | ~ % 231.11/34.61 | (hAPP(all_1468_0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] % 231.11/34.61 | : ! [v1: $i] : ! [v2: $i] : (v0 = all_1468_1 | ~ (hAPP(v2, v0) = % 231.11/34.61 | all_1468_1) | ~ (hAPP(all_1468_0, v1) = v2) | ~ $i(v1) | ~ % 231.11/34.61 | $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1468_1 | ~ % 231.11/34.61 | (hAPP(v0, all_1468_1) = v1) | ~ (hAPP(all_1468_0, all_1468_1) = % 231.11/34.61 | v0)) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (651) implies: % 231.11/34.61 | (652) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1468_1 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (93) with fresh symbols all_1480_0, all_1480_1 gives: % 231.11/34.61 | (653) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1480_0 & % 231.11/34.61 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1480_1 & % 231.11/34.61 | $i(all_1480_0) & $i(all_1480_1) & ! [v0: $i] : ! [v1: any] : ! % 231.11/34.61 | [v2: $i] : (v1 = all_1480_0 | ~ (hAPP(v2, v0) = all_1480_0) | ~ % 231.11/34.61 | (hAPP(all_1480_1, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] % 231.11/34.61 | : ! [v1: $i] : ! [v2: $i] : (v0 = all_1480_0 | ~ (hAPP(v2, v0) = % 231.11/34.61 | all_1480_0) | ~ (hAPP(all_1480_1, v1) = v2) | ~ $i(v1) | ~ % 231.11/34.61 | $i(v0)) & ! [v0: $i] : ! [v1: int] : (v1 = all_1480_0 | ~ % 231.11/34.61 | (hAPP(v0, all_1480_0) = v1) | ~ (hAPP(all_1480_1, all_1480_0) = % 231.11/34.61 | v0)) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (653) implies: % 231.11/34.61 | (654) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1480_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (63) with fresh symbols all_1483_0, all_1483_1, % 231.11/34.61 | all_1483_2 gives: % 231.11/34.61 | (655) c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, all_1483_1) = % 231.11/34.61 | all_1483_0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1483_1 % 231.11/34.61 | & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1483_2 & % 231.11/34.61 | $i(all_1483_0) & $i(all_1483_1) & $i(all_1483_2) & ! [v0: any] : ! % 231.11/34.61 | [v1: int] : (v1 = all_1483_0 | v0 = all_1483_2 | ~ % 231.11/34.61 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 231.11/34.61 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1483_2, v0)) % 231.11/34.61 | & ! [v0: any] : ! [v1: int] : (v1 = all_1483_1 | v0 = all_1483_2 | % 231.11/34.61 | ~ (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) = v1) | ~ % 231.11/34.61 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.61 | all_1483_2, v0)) & ! [v0: int] : (v0 = all_1483_2 | ~ % 231.11/34.61 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, all_1483_2) = v0)) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (655) implies: % 231.11/34.61 | (656) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1483_2 % 231.11/34.61 | (657) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1483_1 % 231.11/34.61 | (658) c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, all_1483_1) = % 231.11/34.61 | all_1483_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (152) with fresh symbol all_1486_0 gives: % 231.11/34.61 | (659) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1486_0 & % 231.11/34.61 | $i(all_1486_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.61 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v2 = % 231.11/34.61 | v0 | ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7, v1) % 231.11/34.61 | = v6) | ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v4, v2) = v5) | ~ % 231.11/34.61 | (hAPP(v4, v0) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 231.11/34.61 | | ~ class_Rings_Olinordered__semidom(v3) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1486_0, v1) | ? % 231.11/34.61 | [v8: $i] : (c_Groups_Ozero__class_Ozero(v3) = v8 & $i(v8) & ( ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless__eq(v3, v8, v2) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless__eq(v3, v8, v0)))) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (659) implies: % 231.11/34.61 | (660) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1486_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (144) with fresh symbol all_1489_0 gives: % 231.11/34.61 | (661) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1489_0 & % 231.11/34.61 | $i(all_1489_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.61 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 231.11/34.61 | [v8: $i] : ( ~ (c_Power_Opower__class_Opower(v3) = v4) | ~ (hAPP(v7, % 231.11/34.61 | v0) = v8) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v2) = v5) | % 231.11/34.61 | ~ (hAPP(v4, v1) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 231.11/34.61 | $i(v0) | ~ class_Rings_Olinordered__semidom(v3) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(v3, v2, v1) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1489_0, v0) | % 231.11/34.61 | c_Orderings_Oord__class_Oless(v3, v6, v8) | ? [v9: $i] : % 231.11/34.61 | (c_Groups_Ozero__class_Ozero(v3) = v9 & $i(v9) & ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless__eq(v3, v9, v2))) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (661) implies: % 231.11/34.61 | (662) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1489_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (63) with fresh symbols all_1497_0, all_1497_1, % 231.11/34.61 | all_1497_2 gives: % 231.11/34.61 | (663) c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, all_1497_1) = % 231.11/34.61 | all_1497_0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1497_1 % 231.11/34.61 | & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1497_2 & % 231.11/34.61 | $i(all_1497_0) & $i(all_1497_1) & $i(all_1497_2) & ! [v0: any] : ! % 231.11/34.61 | [v1: int] : (v1 = all_1497_0 | v0 = all_1497_2 | ~ % 231.11/34.61 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) % 231.11/34.61 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1497_2, v0)) % 231.11/34.61 | & ! [v0: any] : ! [v1: int] : (v1 = all_1497_1 | v0 = all_1497_2 | % 231.11/34.61 | ~ (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, v0) = v1) | ~ % 231.11/34.61 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.11/34.61 | all_1497_2, v0)) & ! [v0: int] : (v0 = all_1497_2 | ~ % 231.11/34.61 | (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, all_1497_2) = v0)) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (663) implies: % 231.11/34.61 | (664) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1497_2 % 231.11/34.61 | (665) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1497_1 % 231.11/34.61 | (666) c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, all_1497_1) = % 231.11/34.61 | all_1497_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (165) with fresh symbol all_1500_0 gives: % 231.11/34.61 | (667) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1500_0 & % 231.11/34.61 | $i(all_1500_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.61 | $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~ % 231.11/34.61 | (c_Transcendental_Oln(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1500_0, v1) | % 231.11/34.61 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1500_0, v0) | % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0: % 231.11/34.61 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.61 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) = % 231.11/34.61 | v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1500_0, v1) | % 231.11/34.61 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1500_0, v0) | % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3)) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (667) implies: % 231.11/34.61 | (668) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1500_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (142) with fresh symbols all_1503_0, all_1503_1 gives: % 231.11/34.61 | (669) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1503_0 & % 231.11/34.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1503_1 & % 231.11/34.61 | $i(all_1503_0) & $i(all_1503_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.61 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 231.11/34.61 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 231.11/34.61 | (c_Power_Opower__class_Opower(v2) = v4) | ~ % 231.11/34.61 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1503_0) = v6) | % 231.11/34.61 | ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~ (hAPP(v8, v0) = % 231.11/34.61 | v9) | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v4, v0) = v5) | ~ % 231.11/34.61 | (hAPP(v3, v7) = v8) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.61 | class_Groups_Omonoid__mult(v2) | ~ % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1503_1, v1) | % 231.11/34.61 | (hAPP(v5, v1) = v9 & $i(v9))) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (669) implies: % 231.11/34.61 | (670) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1503_1 % 231.11/34.61 | (671) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1503_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (77) with fresh symbols all_1506_0, all_1506_1 gives: % 231.11/34.61 | (672) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1506_1 & % 231.11/34.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1506_0 & % 231.11/34.61 | $i(all_1506_0) & $i(all_1506_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.61 | int] : (v2 = all_1506_0 | ~ (hAPP(v1, v0) = v2) | ~ % 231.11/34.61 | (hAPP(all_1506_1, all_1506_0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! % 231.11/34.61 | [v1: $i] : ! [v2: int] : (v2 = all_1506_0 | ~ (hAPP(v1, all_1506_0) % 231.11/34.61 | = v2) | ~ (hAPP(all_1506_1, v0) = v1) | ~ $i(v0)) & ! [v0: % 231.11/34.61 | any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1506_0 | v0 = % 231.11/34.61 | all_1506_0 | ~ (hAPP(v2, v0) = all_1506_0) | ~ (hAPP(all_1506_1, % 231.11/34.61 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (672) implies: % 231.11/34.61 | (673) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1506_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (121) with fresh symbol all_1509_0 gives: % 231.11/34.61 | (674) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1509_0 & % 231.11/34.61 | $i(all_1509_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.61 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 231.11/34.61 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.61 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] % 231.11/34.61 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1509_0) = % 231.11/34.61 | v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.61 | v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.61 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 231.11/34.61 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.61 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] : % 231.11/34.61 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1509_0) = v4 % 231.11/34.61 | & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.11/34.61 | v4, v3))) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (674) implies: % 231.11/34.61 | (675) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1509_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (87) with fresh symbol all_1515_0 gives: % 231.11/34.61 | (676) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1515_0 & % 231.11/34.61 | $i(all_1515_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.61 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 231.11/34.61 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.61 | all_1515_0, v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.61 | all_1515_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.61 | all_1515_0, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.61 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 231.11/34.61 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.61 | all_1515_0, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.61 | all_1515_0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.61 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2) | ~ $i(v1) % 231.11/34.61 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.61 | all_1515_0, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.61 | all_1515_0, v2)) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (676) implies: % 231.11/34.61 | (677) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1515_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (94) with fresh symbols all_1521_0, all_1521_1 gives: % 231.11/34.61 | (678) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1521_1 & % 231.11/34.61 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1521_0 & % 231.11/34.61 | $i(all_1521_0) & $i(all_1521_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.61 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3) % 231.11/34.61 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1521_1, all_1521_0) = v2) | % 231.11/34.61 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 231.11/34.61 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1521_0 | v1 = v0 | ~ (hAPP(v3, % 231.11/34.61 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1521_1, v2) = % 231.11/34.61 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 231.11/34.61 | % 231.11/34.61 | ALPHA: (678) implies: % 231.11/34.61 | (679) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1521_0 % 231.11/34.61 | % 231.11/34.61 | DELTA: instantiating (26) with fresh symbol all_1524_0 gives: % 231.11/34.61 | (680) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1524_0 & % 231.11/34.61 | $i(all_1524_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.61 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.11/34.61 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ % 231.11/34.61 | (c_RealVector_Onorm__class_Onorm(v2, v0) = v5) | ~ (hAPP(v4, v5) = % 231.11/34.61 | v6) | ~ (hAPP(all_1524_0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 231.11/34.61 | $i(v0) | ~ class_RealVector_Oreal__normed__div__algebra(v2) | ? % 231.11/34.61 | [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 231.11/34.61 | (c_Groups_Otimes__class_Otimes(v2) = v7 & % 231.11/34.61 | c_RealVector_Onorm__class_Onorm(v2, v9) = v6 & hAPP(v8, v0) = v9 % 231.11/34.61 | & hAPP(v7, v1) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6))) % 231.11/34.61 | % 231.11/34.62 | ALPHA: (680) implies: % 231.11/34.62 | (681) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1524_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (122) with fresh symbol all_1527_0 gives: % 231.11/34.62 | (682) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1527_0 & % 231.11/34.62 | $i(all_1527_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.62 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 231.11/34.62 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.62 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4: % 231.11/34.62 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, % 231.11/34.62 | all_1527_0) = v4 & $i(v4) & % 231.11/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) & ! % 231.11/34.62 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.62 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ % 231.11/34.62 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.62 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4: % 231.11/34.62 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, % 231.11/34.62 | all_1527_0) = v4 & $i(v4) & ~ % 231.11/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (682) implies: % 231.11/34.62 | (683) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1527_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (39) with fresh symbol all_1533_0 gives: % 231.11/34.62 | (684) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1533_0 & % 231.11/34.62 | $i(all_1533_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.11/34.62 | (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 231.11/34.62 | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3: $i] : % 231.11/34.62 | ($i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 231.11/34.62 | ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v6, % 231.11/34.62 | v3) = v7) | ~ (hAPP(all_1533_0, v5) = v6) | ~ $i(v4) | ? % 231.11/34.62 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 231.11/34.62 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) = % 231.11/34.62 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) & % 231.11/34.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 231.11/34.62 | v7))))) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (684) implies: % 231.11/34.62 | (685) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1533_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (94) with fresh symbols all_1535_0, all_1535_1 gives: % 231.11/34.62 | (686) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1535_1 & % 231.11/34.62 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1535_0 & % 231.11/34.62 | $i(all_1535_0) & $i(all_1535_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.11/34.62 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v1) = v3) % 231.11/34.62 | | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1535_1, all_1535_0) = v2) | % 231.11/34.62 | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 231.11/34.62 | ! [v3: $i] : ! [v4: $i] : (v2 = all_1535_0 | v1 = v0 | ~ (hAPP(v3, % 231.11/34.62 | v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1535_1, v2) = % 231.11/34.62 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (686) implies: % 231.11/34.62 | (687) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1535_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (166) with fresh symbol all_1538_0 gives: % 231.11/34.62 | (688) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1538_0 & % 231.11/34.62 | $i(all_1538_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.62 | $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~ % 231.11/34.62 | (c_Transcendental_Oln(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1538_0, v1) | % 231.11/34.62 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1538_0, v0) | % 231.11/34.62 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3) | % 231.11/34.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & ! % 231.11/34.62 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.11/34.62 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) = % 231.11/34.62 | v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1538_0, v1) | % 231.11/34.62 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1538_0, v0) | % 231.11/34.62 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | % 231.11/34.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3)) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (688) implies: % 231.11/34.62 | (689) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1538_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (13) with fresh symbol all_1541_0 gives: % 231.11/34.62 | (690) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1541_0 & % 231.11/34.62 | $i(all_1541_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.11/34.62 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.11/34.62 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ % 231.11/34.62 | (c_RealVector_Onorm__class_Onorm(v2, v0) = v5) | ~ (hAPP(v4, v5) = % 231.11/34.62 | v6) | ~ (hAPP(all_1541_0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 231.11/34.62 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v7: % 231.11/34.62 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 231.11/34.62 | (c_Groups_Otimes__class_Otimes(v2) = v7 & % 231.11/34.62 | c_RealVector_Onorm__class_Onorm(v2, v9) = v10 & hAPP(v8, v0) = v9 % 231.11/34.62 | & hAPP(v7, v1) = v8 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 231.11/34.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v6))) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (690) implies: % 231.11/34.62 | (691) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1541_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (210) with fresh symbols all_1547_0, all_1547_1, % 231.11/34.62 | all_1547_2, all_1547_3 gives: % 231.11/34.62 | (692) c_Nat_OSuc(all_1547_3) = all_1547_0 & % 231.11/34.62 | c_Power_Opower__class_Opower(tc_Int_Oint) = all_1547_1 & % 231.11/34.62 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1547_2 & % 231.11/34.62 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1547_3 & % 231.11/34.62 | $i(all_1547_0) & $i(all_1547_1) & $i(all_1547_2) & $i(all_1547_3) & % 231.11/34.62 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 231.11/34.62 | ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1547_0) = v3) % 231.11/34.62 | | ~ (hAPP(v2, v3) = v4) | ~ (hAPP(all_1547_1, v0) = v2) | ~ % 231.11/34.62 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, % 231.11/34.62 | all_1547_2, v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.11/34.62 | all_1547_3, v1) | ? [v5: $i] : % 231.11/34.62 | (c_Divides_Odiv__class_Odiv(tc_Int_Oint, v5, v0) = v4 & hAPP(v2, % 231.11/34.62 | v1) = v5 & $i(v5) & $i(v4))) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (692) implies: % 231.11/34.62 | (693) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1547_3 % 231.11/34.62 | (694) c_Nat_OSuc(all_1547_3) = all_1547_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (192) with fresh symbols all_1550_0, all_1550_1, % 231.11/34.62 | all_1550_2 gives: % 231.11/34.62 | (695) c_Nat_OSuc(all_1550_1) = all_1550_0 & % 231.11/34.62 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1550_2 & % 231.11/34.62 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1550_1 & % 231.11/34.62 | $i(all_1550_0) & $i(all_1550_1) & $i(all_1550_2) & ! [v0: $i] : ! % 231.11/34.62 | [v1: any] : ! [v2: $i] : (v1 = all_1550_0 | ~ (hAPP(v2, v0) = % 231.11/34.62 | all_1550_0) | ~ (hAPP(all_1550_2, v1) = v2) | ~ $i(v1) | ~ % 231.11/34.62 | $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 = % 231.11/34.62 | all_1550_0 | ~ (hAPP(v2, v0) = all_1550_0) | ~ (hAPP(all_1550_2, % 231.11/34.62 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int] % 231.11/34.62 | : (v1 = all_1550_0 | ~ (hAPP(v0, all_1550_0) = v1) | ~ % 231.11/34.62 | (hAPP(all_1550_2, all_1550_0) = v0)) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (695) implies: % 231.11/34.62 | (696) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1550_1 % 231.11/34.62 | (697) c_Nat_OSuc(all_1550_1) = all_1550_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (161) with fresh symbols all_1556_0, all_1556_1, % 231.11/34.62 | all_1556_2 gives: % 231.11/34.62 | (698) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1556_1 & % 231.11/34.62 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1556_0 & % 231.11/34.62 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1556_2 & % 231.11/34.62 | $i(all_1556_0) & $i(all_1556_1) & $i(all_1556_2) & ! [v0: $i] : ! % 231.11/34.62 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 231.11/34.62 | ~ (c_Transcendental_Oln(v1) = v4) | ~ % 231.11/34.62 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ (hAPP(v3, v4) = v5) | % 231.11/34.62 | ~ (hAPP(all_1556_0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.11/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1556_2, v1) | % 231.11/34.62 | ? [v6: $i] : ? [v7: $i] : (c_Transcendental_Oln(v7) = v5 & % 231.11/34.62 | hAPP(v6, v0) = v7 & hAPP(all_1556_1, v1) = v6 & $i(v7) & $i(v6) & % 231.11/34.62 | $i(v5))) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (698) implies: % 231.11/34.62 | (699) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1556_2 % 231.11/34.62 | (700) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1556_0 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (242) with fresh symbols all_1559_0, all_1559_1, % 231.11/34.62 | all_1559_2, all_1559_3, all_1559_4, all_1559_5, all_1559_6, all_1559_7, % 231.11/34.62 | all_1559_8 gives: % 231.11/34.62 | (701) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1559_7 & % 231.11/34.62 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1559_5, all_1559_1) % 231.11/34.62 | = all_1559_0 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, % 231.11/34.62 | all_1559_7, all_1559_6) = all_1559_5 & % 231.11/34.62 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1559_4 & % 231.11/34.62 | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1559_2) = all_1559_1 % 231.11/34.62 | & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1559_8 & % 231.11/34.62 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____) = % 231.11/34.62 | all_1559_6 & hAPP(all_1559_3, v_m____) = all_1559_2 & % 231.11/34.62 | hAPP(all_1559_4, v_r) = all_1559_3 & $i(all_1559_0) & $i(all_1559_1) % 231.11/34.62 | & $i(all_1559_2) & $i(all_1559_3) & $i(all_1559_4) & $i(all_1559_5) & % 231.11/34.62 | $i(all_1559_6) & $i(all_1559_7) & $i(all_1559_8) & ~ % 231.11/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1559_8, % 231.11/34.62 | all_1559_0) % 231.11/34.62 | % 231.11/34.62 | ALPHA: (701) implies: % 231.11/34.62 | (702) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1559_8, % 231.11/34.62 | all_1559_0) % 231.11/34.62 | (703) $i(all_1559_2) % 231.11/34.62 | (704) $i(all_1559_1) % 231.11/34.62 | (705) hAPP(all_1559_4, v_r) = all_1559_3 % 231.11/34.62 | (706) hAPP(all_1559_3, v_m____) = all_1559_2 % 231.11/34.62 | (707) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____) = % 231.11/34.62 | all_1559_6 % 231.11/34.62 | (708) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1559_8 % 231.11/34.62 | (709) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1559_2) = all_1559_1 % 231.11/34.62 | (710) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1559_4 % 231.11/34.62 | (711) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1559_7, all_1559_6) % 231.11/34.62 | = all_1559_5 % 231.11/34.62 | (712) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1559_5, all_1559_1) % 231.11/34.62 | = all_1559_0 % 231.11/34.62 | (713) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1559_7 % 231.11/34.62 | % 231.11/34.62 | DELTA: instantiating (159) with fresh symbols all_1573_0, all_1573_1, % 231.11/34.62 | all_1573_2 gives: % 231.47/34.62 | (714) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1573_0 & % 231.47/34.62 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1573_2 & % 231.47/34.62 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1573_1 & % 231.47/34.62 | $i(all_1573_0) & $i(all_1573_1) & $i(all_1573_2) & ! [v0: $i] : ! % 231.47/34.62 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1573_2, v1) | ~ % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1573_1, v0) | % 231.47/34.62 | ? [v2: $i] : ? [v3: $i] : (hAPP(v3, v1) = v0 & hAPP(all_1573_0, % 231.47/34.62 | v2) = v3 & $i(v3) & $i(v2) & % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1573_1, v2) & % 231.47/34.62 | ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v1) = v0) | % 231.47/34.62 | ~ (hAPP(all_1573_0, v4) = v5) | ~ $i(v4) | ~ % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1573_1, % 231.47/34.62 | v4)))) % 231.47/34.62 | % 231.47/34.62 | ALPHA: (714) implies: % 231.47/34.62 | (715) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1573_1 % 231.47/34.62 | (716) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1573_2 % 231.47/34.62 | % 231.47/34.62 | DELTA: instantiating (194) with fresh symbols all_1576_0, all_1576_1, % 231.47/34.62 | all_1576_2 gives: % 231.47/34.62 | (717) c_Nat_OSuc(all_1576_1) = all_1576_0 & % 231.47/34.62 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1576_2 & % 231.47/34.62 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1576_1 & % 231.47/34.62 | $i(all_1576_0) & $i(all_1576_1) & $i(all_1576_2) & ! [v0: $i] : ! % 231.47/34.62 | [v1: $i] : ! [v2: int] : (v2 = all_1576_0 | ~ (hAPP(v1, v0) = v2) | % 231.47/34.62 | ~ (hAPP(all_1576_2, all_1576_0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 231.47/34.62 | ! [v1: $i] : ! [v2: int] : (v2 = all_1576_0 | ~ (hAPP(v1, % 231.47/34.62 | all_1576_1) = v2) | ~ (hAPP(all_1576_2, v0) = v1) | ~ $i(v0)) % 231.47/34.62 | & ! [v0: any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1576_0 | v0 = % 231.47/34.62 | all_1576_1 | ~ (hAPP(v2, v0) = all_1576_0) | ~ (hAPP(all_1576_2, % 231.47/34.62 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 231.47/34.62 | % 231.47/34.62 | ALPHA: (717) implies: % 231.47/34.62 | (718) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1576_1 % 231.47/34.62 | (719) c_Nat_OSuc(all_1576_1) = all_1576_0 % 231.47/34.62 | % 231.47/34.62 | DELTA: instantiating (189) with fresh symbol all_1579_0 gives: % 231.47/34.62 | (720) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1579_0 & % 231.47/34.62 | $i(all_1579_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.62 | $i] : ( ~ (c_Nat_OSuc(v3) = v1) | ~ (c_Nat_OSuc(v0) = v2) | ~ % 231.47/34.62 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0) | % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)) & ! [v0: $i] : % 231.47/34.62 | ! [v1: any] : ! [v2: $i] : (v1 = all_1579_0 | ~ (c_Nat_OSuc(v0) = % 231.47/34.62 | v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v3: $i] : % 231.47/34.62 | (c_Nat_OSuc(v3) = v1 & $i(v3) & % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))) & ! [v0: % 231.47/34.62 | $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = v1) | ~ $i(v0) | % 231.47/34.62 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1579_0, v1)) % 231.47/34.62 | % 231.47/34.62 | ALPHA: (720) implies: % 231.47/34.62 | (721) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1579_0 % 231.47/34.62 | % 231.47/34.62 | DELTA: instantiating (34) with fresh symbols all_1582_0, all_1582_1 gives: % 231.47/34.62 | (722) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1582_0 & % 231.47/34.62 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1582_1 & % 231.47/34.62 | $i(all_1582_0) & $i(all_1582_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.62 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | % 231.47/34.62 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.62 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4) % 231.47/34.62 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1582_1, v4) % 231.47/34.62 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 231.47/34.62 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7, % 231.47/34.62 | v4) = v8) | ~ (hAPP(all_1582_0, v6) = v7) | ~ $i(v5) | ? % 231.47/34.62 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1, % 231.47/34.62 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) & % 231.47/34.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 231.47/34.62 | v8))))) % 231.47/34.62 | % 231.47/34.62 | ALPHA: (722) implies: % 231.47/34.62 | (723) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1582_1 % 231.47/34.62 | (724) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1582_0 % 231.47/34.62 | % 231.47/34.62 | DELTA: instantiating (37) with fresh symbols all_1585_0, all_1585_1 gives: % 231.47/34.62 | (725) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1585_0 & % 231.47/34.62 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1585_1 & % 231.47/34.62 | $i(all_1585_0) & $i(all_1585_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.62 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | % 231.47/34.62 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.62 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4) % 231.47/34.62 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1585_1, % 231.47/34.62 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( % 231.47/34.62 | ~ (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7, % 231.47/34.62 | v4) = v8) | ~ (hAPP(all_1585_0, v6) = v7) | ~ $i(v5) | ? % 231.47/34.62 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1, % 231.47/34.62 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) & % 231.47/34.62 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 231.47/34.62 | v8))))) % 231.47/34.62 | % 231.47/34.62 | ALPHA: (725) implies: % 231.47/34.62 | (726) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1585_1 % 231.47/34.62 | (727) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1585_0 % 231.47/34.62 | % 231.47/34.62 | DELTA: instantiating (149) with fresh symbol all_1588_0 gives: % 231.47/34.62 | (728) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1588_0 & % 231.47/34.62 | $i(all_1588_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.62 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.62 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v4, v0) = v5) | % 231.47/34.62 | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.62 | class_Power_Opower(v2) | ~ class_Rings_Ozero__neq__one(v2) | ~ % 231.47/34.62 | class_Rings_Omult__zero(v2) | ~ % 231.47/34.62 | class_Rings_Ono__zero__divisors(v2) | ? [v6: $i] : % 231.47/34.62 | (c_Groups_Ozero__class_Ozero(v2) = v6 & $i(v6) & ( ~ (v6 = v5) | % 231.47/34.62 | (v5 = v1 & ~ (v0 = all_1588_0))) & ( ~ (v6 = v1) | v5 = v1 | % 231.47/34.62 | v0 = all_1588_0))) % 231.47/34.62 | % 231.47/34.62 | ALPHA: (728) implies: % 231.47/34.62 | (729) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1588_0 % 231.47/34.62 | % 231.47/34.62 | DELTA: instantiating (74) with fresh symbols all_1591_0, all_1591_1 gives: % 231.47/34.62 | (730) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1591_1 & % 231.47/34.62 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1591_0 & % 231.47/34.62 | $i(all_1591_0) & $i(all_1591_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.62 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 231.47/34.62 | (hAPP(v4, all_1591_0) = v5) | ~ (hAPP(v2, all_1591_0) = v3) | ~ % 231.47/34.62 | (hAPP(all_1591_1, v1) = v2) | ~ (hAPP(all_1591_1, v0) = v4) | ~ % 231.47/34.62 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! % 231.47/34.62 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v0 | v1 = all_1591_0 | % 231.47/34.62 | ~ (hAPP(v5, v1) = v4) | ~ (hAPP(v3, v1) = v4) | ~ % 231.47/34.63 | (hAPP(all_1591_1, v2) = v3) | ~ (hAPP(all_1591_1, v0) = v5) | ~ % 231.47/34.63 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (730) implies: % 231.47/34.63 | (731) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1591_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (135) with fresh symbol all_1594_0 gives: % 231.47/34.63 | (732) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1594_0 & % 231.47/34.63 | $i(all_1594_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) % 231.47/34.63 | | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ? [v3: % 231.47/34.63 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.47/34.63 | all_1594_0, v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.63 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5) % 231.47/34.63 | | ~ $i(v4) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.47/34.63 | v4, v0) | ? [v6: $i] : % 231.47/34.63 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) = v6 & $i(v6) % 231.47/34.63 | & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, % 231.47/34.63 | v3))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.63 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5) % 231.47/34.63 | | ~ $i(v4) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.47/34.63 | v2, v4) | ? [v6: $i] : % 231.47/34.63 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) = v6 & $i(v6) % 231.47/34.63 | & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, % 231.47/34.63 | v3))))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (732) implies: % 231.47/34.63 | (733) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1594_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (151) with fresh symbol all_1597_0 gives: % 231.47/34.63 | (734) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1597_0 & % 231.47/34.63 | $i(all_1597_0) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.63 | $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | v0 = all_1597_0 | ~ % 231.47/34.63 | (c_Power_Opower__class_Opower(v1) = v2) | ~ % 231.47/34.63 | (c_Groups_Ozero__class_Ozero(v1) = v3) | ~ (hAPP(v4, v0) = v5) | % 231.47/34.63 | ~ (hAPP(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | class_Rings_Osemiring__0(v1) | ~ class_Power_Opower(v1)) & ! [v0: % 231.47/34.63 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.47/34.63 | (c_Power_Opower__class_Opower(v0) = v1) | ~ % 231.47/34.63 | (c_Groups_Ozero__class_Ozero(v0) = v2) | ~ (hAPP(v3, all_1597_0) = % 231.47/34.63 | v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v0) | ~ % 231.47/34.63 | class_Rings_Osemiring__0(v0) | ~ class_Power_Opower(v0) | % 231.47/34.63 | (c_Groups_Oone__class_Oone(v0) = v4 & $i(v4))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (734) implies: % 231.47/34.63 | (735) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1597_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (36) with fresh symbols all_1600_0, all_1600_1 gives: % 231.47/34.63 | (736) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1600_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1600_1 & % 231.47/34.63 | $i(all_1600_0) & $i(all_1600_1) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.63 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~ % 231.47/34.63 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3: % 231.47/34.63 | $i] : ($i(v3) & % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1600_1, % 231.47/34.63 | v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 231.47/34.63 | ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v6, % 231.47/34.63 | v3) = v7) | ~ (hAPP(all_1600_0, v5) = v6) | ~ $i(v4) | ? % 231.47/34.63 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 231.47/34.63 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) = % 231.47/34.63 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) & % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 231.47/34.63 | v7))))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (736) implies: % 231.47/34.63 | (737) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1600_1 % 231.47/34.63 | (738) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1600_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (133) with fresh symbol all_1602_0 gives: % 231.47/34.63 | (739) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1602_0 & % 231.47/34.63 | $i(all_1602_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) % 231.47/34.63 | | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ? [v3: % 231.47/34.63 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.47/34.63 | all_1602_0, v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.63 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5) % 231.47/34.63 | | ~ $i(v4) | % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) | % 231.47/34.63 | ? [v6: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) = % 231.47/34.63 | v6 & $i(v6) & ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v3))) & % 231.47/34.63 | ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.63 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5) % 231.47/34.63 | | ~ $i(v4) | % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) | % 231.47/34.63 | ? [v6: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) = % 231.47/34.63 | v6 & $i(v6) & ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v3))))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (739) implies: % 231.47/34.63 | (740) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1602_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (33) with fresh symbols all_1605_0, all_1605_1 gives: % 231.47/34.63 | (741) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1605_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1605_1 & % 231.47/34.63 | $i(all_1605_0) & $i(all_1605_1) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.63 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~ % 231.47/34.63 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3: % 231.47/34.63 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.47/34.63 | all_1605_1, v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 231.47/34.63 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | % 231.47/34.63 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(all_1605_0, v5) = v6) | ~ % 231.47/34.63 | $i(v4) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 231.47/34.63 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) = % 231.47/34.63 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) & % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 231.47/34.63 | v7))))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (741) implies: % 231.47/34.63 | (742) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1605_1 % 231.47/34.63 | (743) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1605_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (41) with fresh symbol all_1607_0 gives: % 231.47/34.63 | (744) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1607_0 & % 231.47/34.63 | $i(all_1607_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.47/34.63 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~ % 231.47/34.63 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2) % 231.47/34.63 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 231.47/34.63 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 231.47/34.63 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~ % 231.47/34.63 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9, % 231.47/34.63 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1607_0, % 231.47/34.63 | v8) = v9) | ~ (hAPP(all_1607_0, v5) = v6) | ~ $i(v4) | ~ % 231.47/34.63 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 231.47/34.63 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4) % 231.47/34.63 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) & % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, % 231.47/34.63 | v10))))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (744) implies: % 231.47/34.63 | (745) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1607_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (156) with fresh symbols all_1610_0, all_1610_1 gives: % 231.47/34.63 | (746) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1610_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1610_1 & % 231.47/34.63 | $i(all_1610_0) & $i(all_1610_1) & ! [v0: any] : ! [v1: $i] : ! % 231.47/34.63 | [v2: $i] : ! [v3: $i] : (v0 = all_1610_1 | ~ (hAPP(v2, v0) = v3) | % 231.47/34.63 | ~ (hAPP(all_1610_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1610_1, v3) | % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1610_1, v1)) & ! % 231.47/34.63 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 231.47/34.63 | v0) = v3) | ~ (hAPP(all_1610_0, v1) = v2) | ~ $i(v1) | ~ % 231.47/34.63 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1610_1, % 231.47/34.63 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1610_1, v3)) % 231.47/34.63 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1610_1) % 231.47/34.63 | = v2) | ~ (hAPP(all_1610_0, v0) = v1) | ~ $i(v0) | % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1610_1, v2)) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (746) implies: % 231.47/34.63 | (747) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1610_1 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (5) with fresh symbol all_1613_0 gives: % 231.47/34.63 | (748) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1613_0 & % 231.47/34.63 | $i(all_1613_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.63 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 231.47/34.63 | [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 231.47/34.63 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~ % 231.47/34.63 | (c_RealVector_Onorm__class_Onorm(v4, v7) = v8) | ~ (hAPP(v9, v0) = % 231.47/34.63 | v10) | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~ % 231.47/34.63 | (hAPP(all_1613_0, v2) = v9) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 231.47/34.63 | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | class_RealVector_Oreal__normed__algebra(v4) | % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v10) | ? [v11: % 231.47/34.63 | $i] : ? [v12: $i] : ((c_RealVector_Onorm__class_Onorm(v4, v3) = % 231.47/34.63 | v11 & $i(v11) & ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v2)) | % 231.47/34.63 | (c_RealVector_Onorm__class_Onorm(v4, v1) = v12 & $i(v12) & ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v0)))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (748) implies: % 231.47/34.63 | (749) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1613_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (109) with fresh symbols all_1619_0, all_1619_1, % 231.47/34.63 | all_1619_2 gives: % 231.47/34.63 | (750) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1619_1 & % 231.47/34.63 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1619_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1619_2 & % 231.47/34.63 | $i(all_1619_0) & $i(all_1619_1) & $i(all_1619_2) & ! [v0: $i] : ! % 231.47/34.63 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 231.47/34.63 | ~ (c_RComplete_Onatfloor(v1) = v2) | ~ (c_RComplete_Onatfloor(v0) % 231.47/34.63 | = v4) | ~ (hAPP(v3, v4) = v5) | ~ (hAPP(all_1619_1, v2) = v3) | % 231.47/34.63 | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1619_2, v1) % 231.47/34.63 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.47/34.63 | all_1619_2, v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 231.47/34.63 | (c_RComplete_Onatfloor(v7) = v8 & hAPP(v6, v0) = v7 & % 231.47/34.63 | hAPP(all_1619_0, v1) = v6 & $i(v8) & $i(v7) & $i(v6) & % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v8))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (750) implies: % 231.47/34.63 | (751) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1619_2 % 231.47/34.63 | (752) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1619_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (156) with fresh symbols all_1622_0, all_1622_1 gives: % 231.47/34.63 | (753) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1622_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1622_1 & % 231.47/34.63 | $i(all_1622_0) & $i(all_1622_1) & ! [v0: any] : ! [v1: $i] : ! % 231.47/34.63 | [v2: $i] : ! [v3: $i] : (v0 = all_1622_1 | ~ (hAPP(v2, v0) = v3) | % 231.47/34.63 | ~ (hAPP(all_1622_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1622_1, v3) | % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1622_1, v1)) & ! % 231.47/34.63 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 231.47/34.63 | v0) = v3) | ~ (hAPP(all_1622_0, v1) = v2) | ~ $i(v1) | ~ % 231.47/34.63 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1622_1, % 231.47/34.63 | v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1622_1, v3)) % 231.47/34.63 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1622_1) % 231.47/34.63 | = v2) | ~ (hAPP(all_1622_0, v0) = v1) | ~ $i(v0) | % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1622_1, v2)) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (753) implies: % 231.47/34.63 | (754) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1622_1 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (214) with fresh symbols all_1625_0, all_1625_1 gives: % 231.47/34.63 | (755) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1625_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1625_1 & % 231.47/34.63 | $i(all_1625_0) & $i(all_1625_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.63 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2 % 231.47/34.63 | = all_1625_1 | ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v4, v5) % 231.47/34.63 | = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 231.47/34.63 | (hAPP(all_1625_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.63 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v6 & $i(v6))) & % 231.47/34.63 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 231.47/34.63 | ! [v5: int] : (v5 = all_1625_1 | ~ % 231.47/34.63 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v3, v4) = v5) | ~ % 231.47/34.63 | (hAPP(v2, v1) = v3) | ~ (hAPP(v2, v0) = v4) | ~ (hAPP(all_1625_0, % 231.47/34.63 | all_1625_1) = v2) | ~ $i(v1) | ~ $i(v0)) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (755) implies: % 231.47/34.63 | (756) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1625_1 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (56) with fresh symbols all_1628_0, all_1628_1, % 231.47/34.63 | all_1628_2 gives: % 231.47/34.63 | (757) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1628_0 & % 231.47/34.63 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1628_1 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1628_2 & % 231.47/34.63 | $i(all_1628_0) & $i(all_1628_1) & $i(all_1628_2) & ! [v0: $i] : ! % 231.47/34.63 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 231.47/34.63 | (v1 = all_1628_2 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, % 231.47/34.63 | all_1628_0) = v2) | ~ % 231.47/34.63 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v4) = v5) | ~ % 231.47/34.63 | (hAPP(v3, v0) = v4) | ~ (hAPP(all_1628_1, v2) = v3) | ~ $i(v1) | % 231.47/34.63 | ~ $i(v0) | ? [v6: $i] : (hAPP(v6, v0) = v5 & hAPP(all_1628_1, v1) % 231.47/34.63 | = v6 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.63 | int] : (v2 = all_1628_2 | ~ (hAPP(v1, v0) = v2) | ~ % 231.47/34.63 | (hAPP(all_1628_1, all_1628_2) = v1) | ~ $i(v0)) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (757) implies: % 231.47/34.63 | (758) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1628_2 % 231.47/34.63 | (759) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1628_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (96) with fresh symbols all_1631_0, all_1631_1 gives: % 231.47/34.63 | (760) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1631_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1631_1 & % 231.47/34.63 | $i(all_1631_0) & $i(all_1631_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.63 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 231.47/34.63 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1631_0, v2) = v3) | % 231.47/34.63 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1631_1, v2) | % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : % 231.47/34.63 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 231.47/34.63 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 231.47/34.63 | (hAPP(all_1631_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.63 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1631_1, v2) | % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (760) implies: % 231.47/34.63 | (761) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1631_1 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (14) with fresh symbols all_1634_0, all_1634_1 gives: % 231.47/34.63 | (762) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1634_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1634_1 & % 231.47/34.63 | $i(all_1634_0) & $i(all_1634_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.63 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 231.47/34.63 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1634_0, v2) = v3) | % 231.47/34.63 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1634_1, v2) | % 231.47/34.63 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5) | % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & ! % 231.47/34.63 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.63 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 231.47/34.63 | (hAPP(all_1634_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.63 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1634_1, v2) | % 231.47/34.63 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5)) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (762) implies: % 231.47/34.63 | (763) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1634_1 % 231.47/34.63 | (764) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1634_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (134) with fresh symbols all_1637_0, all_1637_1 gives: % 231.47/34.63 | (765) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1637_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1637_1 & % 231.47/34.63 | $i(all_1637_0) & $i(all_1637_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.63 | $i] : ( ~ (hAPP(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | hBOOL(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 231.47/34.63 | ($i(v4) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, % 231.47/34.63 | all_1637_0) = v5 & hAPP(v1, v5) = v6 & $i(v6) & $i(v5) & % 231.47/34.63 | hBOOL(v6) & c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, % 231.47/34.63 | v0) & ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v1, v7) = v8) | % 231.47/34.63 | ~ $i(v7) | ~ hBOOL(v8) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v7, v4))) | % 231.47/34.63 | (hAPP(v1, all_1637_1) = v3 & $i(v3) & hBOOL(v3))))) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (765) implies: % 231.47/34.63 | (766) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1637_1 % 231.47/34.63 | (767) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1637_0 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (89) with fresh symbols all_1643_0, all_1643_1 gives: % 231.47/34.63 | (768) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1643_0 & % 231.47/34.63 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1643_1 & % 231.47/34.63 | $i(all_1643_0) & $i(all_1643_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.63 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 231.47/34.63 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1643_0, v2) = v3) | % 231.47/34.63 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1643_1, v2) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) | % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: % 231.47/34.63 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.63 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 231.47/34.63 | (hAPP(all_1643_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.63 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1643_1, v2) | ~ % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 231.47/34.63 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)) % 231.47/34.63 | % 231.47/34.63 | ALPHA: (768) implies: % 231.47/34.63 | (769) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1643_1 % 231.47/34.63 | % 231.47/34.63 | DELTA: instantiating (148) with fresh symbols all_1646_0, all_1646_1, % 231.47/34.63 | all_1646_2, all_1646_3 gives: % 231.47/34.64 | (770) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1646_2 & % 231.47/34.64 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1646_1 & % 231.47/34.64 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1646_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1646_3 & % 231.47/34.64 | $i(all_1646_0) & $i(all_1646_1) & $i(all_1646_2) & $i(all_1646_3) & % 231.47/34.64 | ! [v0: $i] : ! [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 231.47/34.64 | ! [v5: $i] : ! [v6: $i] : (v1 = all_1646_3 | ~ % 231.47/34.64 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1646_1) = v4) | % 231.47/34.64 | ~ (hAPP(v3, v5) = v6) | ~ (hAPP(v2, v4) = v5) | ~ % 231.47/34.64 | (hAPP(all_1646_0, v0) = v3) | ~ (hAPP(all_1646_2, v0) = v2) | ~ % 231.47/34.64 | $i(v1) | ~ $i(v0) | (hAPP(v2, v1) = v6 & $i(v6))) & ! [v0: $i] : % 231.47/34.64 | ! [v1: $i] : ! [v2: int] : (v2 = all_1646_1 | ~ (hAPP(v1, % 231.47/34.64 | all_1646_3) = v2) | ~ (hAPP(all_1646_2, v0) = v1) | ~ $i(v0)) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (770) implies: % 231.47/34.64 | (771) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1646_3 % 231.47/34.64 | (772) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1646_1 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (138) with fresh symbols all_1655_0, all_1655_1, % 231.47/34.64 | all_1655_2, all_1655_3 gives: % 231.47/34.64 | (773) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1655_0 & % 231.47/34.64 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1655_1 & % 231.47/34.64 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1655_2 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1655_3 & % 231.47/34.64 | $i(all_1655_0) & $i(all_1655_1) & $i(all_1655_2) & $i(all_1655_3) & % 231.47/34.64 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 231.47/34.64 | ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1655_1) = % 231.47/34.64 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1655_0, v2) = v3) | % 231.47/34.64 | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1655_3, v1) % 231.47/34.64 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 231.47/34.64 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v5 & % 231.47/34.64 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, all_1655_1) = % 231.47/34.64 | v8 & hAPP(v6, v1) = v7 & hAPP(all_1655_2, v5) = v6 & $i(v8) & % 231.47/34.64 | $i(v7) & $i(v6) & $i(v5) & % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v4))) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (773) implies: % 231.47/34.64 | (774) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1655_3 % 231.47/34.64 | (775) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1655_2 % 231.47/34.64 | (776) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1655_1 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (79) with fresh symbols all_1658_0, all_1658_1 gives: % 231.47/34.64 | (777) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1658_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1658_1 & % 231.47/34.64 | $i(all_1658_0) & $i(all_1658_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.64 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1658_0, % 231.47/34.64 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1658_1, v3) | % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1658_1, v1)) & ! % 231.47/34.64 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 231.47/34.64 | v0) = v3) | ~ (hAPP(all_1658_0, v1) = v2) | ~ $i(v1) | ~ % 231.47/34.64 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1658_1, % 231.47/34.64 | v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1658_1, v0)) % 231.47/34.64 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.47/34.64 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1658_0, v1) = v2) | ~ $i(v1) | % 231.47/34.64 | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.47/34.64 | all_1658_1, v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.47/34.64 | all_1658_1, v0) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.47/34.64 | all_1658_1, v3)) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (777) implies: % 231.47/34.64 | (778) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1658_1 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (139) with fresh symbol all_1661_0 gives: % 231.47/34.64 | (779) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1661_0 & % 231.47/34.64 | $i(all_1661_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) % 231.47/34.64 | | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | class_RealVector_Oreal__normed__vector(v1) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1661_0, v2) | % 231.47/34.64 | c_SEQ_OBseq(v1, v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5 & hAPP(v0, v3) = v4 & % 231.47/34.64 | $i(v5) & $i(v4) & $i(v3) & ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))) & % 231.47/34.64 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1) % 231.47/34.64 | | ? [v2: $i] : ($i(v2) & % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1661_0, v2) & % 231.47/34.64 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v0, % 231.47/34.64 | v3) = v4) | ~ $i(v3) | % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2)))) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (779) implies: % 231.47/34.64 | (780) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1661_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (7) with fresh symbols all_1664_0, all_1664_1 gives: % 231.47/34.64 | (781) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1664_1 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1664_0 & % 231.47/34.64 | $i(all_1664_0) & $i(all_1664_1) & ! [v0: $i] : ! [v1: any] : ! % 231.47/34.64 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = all_1664_0 % 231.47/34.64 | | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) = % 231.47/34.64 | all_1664_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) | % 231.47/34.64 | ~ (hAPP(all_1664_1, v1) = v2) | ~ (hAPP(all_1664_1, v0) = v4) | ~ % 231.47/34.64 | $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! % 231.47/34.64 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v0 = all_1664_0 | ~ % 231.47/34.64 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) = % 231.47/34.64 | all_1664_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) | % 231.47/34.64 | ~ (hAPP(all_1664_1, v1) = v2) | ~ (hAPP(all_1664_1, v0) = v4) | ~ % 231.47/34.64 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 231.47/34.64 | (v2 = all_1664_0 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, % 231.47/34.64 | v1, v1) = v2) | ~ (hAPP(v0, all_1664_0) = v1) | ~ % 231.47/34.64 | (hAPP(all_1664_1, all_1664_0) = v0)) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (781) implies: % 231.47/34.64 | (782) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1664_0 % 231.47/34.64 | (783) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1664_1 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (38) with fresh symbols all_1667_0, all_1667_1 gives: % 231.47/34.64 | (784) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1667_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1667_1 & % 231.47/34.64 | $i(all_1667_0) & $i(all_1667_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.47/34.64 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~ % 231.47/34.64 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2) % 231.47/34.64 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1667_1, % 231.47/34.64 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 231.47/34.64 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~ % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9, % 231.47/34.64 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1667_0, % 231.47/34.64 | v8) = v9) | ~ (hAPP(all_1667_0, v5) = v6) | ~ $i(v4) | ~ % 231.47/34.64 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4) % 231.47/34.64 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) & % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, % 231.47/34.64 | v10))))) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (784) implies: % 231.47/34.64 | (785) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1667_1 % 231.47/34.64 | (786) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1667_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (29) with fresh symbols all_1670_0, all_1670_1 gives: % 231.47/34.64 | (787) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1670_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1670_1 & % 231.47/34.64 | $i(all_1670_0) & $i(all_1670_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.64 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.47/34.64 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1670_0, % 231.47/34.64 | v1) = v3) | ~ (hAPP(all_1670_0, v0) = v5) | ~ $i(v2) | ~ % 231.47/34.64 | $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1670_1, v2) | % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0: % 231.47/34.64 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.64 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = % 231.47/34.64 | v4) | ~ (hAPP(all_1670_0, v1) = v3) | ~ (hAPP(all_1670_0, v0) = % 231.47/34.64 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1670_1, v2) | % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6)) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (787) implies: % 231.47/34.64 | (788) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1670_1 % 231.47/34.64 | (789) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1670_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (147) with fresh symbols all_1673_0, all_1673_1, % 231.47/34.64 | all_1673_2 gives: % 231.47/34.64 | (790) c_Power_Opower__class_Opower(tc_Int_Oint) = all_1673_1 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = all_1673_2 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1673_0 & % 231.47/34.64 | $i(all_1673_0) & $i(all_1673_1) & $i(all_1673_2) & ! [v0: $i] : ! % 231.47/34.64 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 231.47/34.64 | all_1673_2 | ~ (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v1) = v2) | % 231.47/34.64 | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1673_1, v2) = v3) | ~ $i(v1) % 231.47/34.64 | | ~ $i(v0) | c_Orderings_Oord__class_Oless(tc_Int_Oint, % 231.47/34.64 | all_1673_2, v4)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : ! % 231.47/34.64 | [v3: $i] : (v0 = all_1673_0 | ~ % 231.47/34.64 | (c_Groups_Oabs__class_Oabs(tc_Int_Oint, all_1673_2) = v1) | ~ % 231.47/34.64 | (hAPP(v2, v0) = v3) | ~ (hAPP(all_1673_1, v1) = v2) | ~ $i(v0) | % 231.47/34.64 | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1673_2, v3)) & ! % 231.47/34.64 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.47/34.64 | (c_Groups_Oabs__class_Oabs(tc_Int_Oint, v0) = v1) | ~ (hAPP(v2, % 231.47/34.64 | all_1673_0) = v3) | ~ (hAPP(all_1673_1, v1) = v2) | ~ $i(v0) % 231.47/34.64 | | c_Orderings_Oord__class_Oless(tc_Int_Oint, all_1673_2, v3)) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (790) implies: % 231.47/34.64 | (791) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1673_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (35) with fresh symbols all_1676_0, all_1676_1 gives: % 231.47/34.64 | (792) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1676_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1676_1 & % 231.47/34.64 | $i(all_1676_0) & $i(all_1676_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.47/34.64 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~ % 231.47/34.64 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2) % 231.47/34.64 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1676_1, v2) % 231.47/34.64 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 231.47/34.64 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~ % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9, % 231.47/34.64 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1676_0, % 231.47/34.64 | v8) = v9) | ~ (hAPP(all_1676_0, v5) = v6) | ~ $i(v4) | ~ % 231.47/34.64 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4) % 231.47/34.64 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) & % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, % 231.47/34.64 | v10))))) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (792) implies: % 231.47/34.64 | (793) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1676_1 % 231.47/34.64 | (794) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1676_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (15) with fresh symbols all_1679_0, all_1679_1 gives: % 231.47/34.64 | (795) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1679_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1679_1 & % 231.47/34.64 | $i(all_1679_0) & $i(all_1679_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.64 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.47/34.64 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1679_0, % 231.47/34.64 | v1) = v3) | ~ (hAPP(all_1679_0, v0) = v5) | ~ $i(v2) | ~ % 231.47/34.64 | $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1679_1, v2) | % 231.47/34.64 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6) | % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & ! % 231.47/34.64 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.64 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = % 231.47/34.64 | v4) | ~ (hAPP(all_1679_0, v1) = v3) | ~ (hAPP(all_1679_0, v0) = % 231.47/34.64 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1679_1, v2) | % 231.47/34.64 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6)) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (795) implies: % 231.47/34.64 | (796) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1679_1 % 231.47/34.64 | (797) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1679_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (143) with fresh symbols all_1682_0, all_1682_1 gives: % 231.47/34.64 | (798) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1682_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1682_1 & % 231.47/34.64 | $i(all_1682_0) & $i(all_1682_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.64 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 231.47/34.64 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 231.47/34.64 | (c_Power_Opower__class_Opower(v2) = v3) | ~ % 231.47/34.64 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1682_0) = v7) | % 231.47/34.64 | ~ (c_Groups_Otimes__class_Otimes(v2) = v5) | ~ (hAPP(v6, v8) = % 231.47/34.64 | v9) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v7) = v8) | ~ % 231.47/34.64 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | class_Power_Opower(v2) | ? [v10: $i] : ? [v11: $i] : (( ~ (v1 = % 231.47/34.64 | all_1682_1) | (v11 = v10 & c_Groups_Oone__class_Oone(v2) = % 231.47/34.64 | v10 & hAPP(v4, all_1682_1) = v10 & $i(v10))) & (v1 = % 231.47/34.64 | all_1682_1 | (v10 = v9 & hAPP(v4, v1) = v9 & $i(v9))))) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (798) implies: % 231.47/34.64 | (799) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1682_1 % 231.47/34.64 | (800) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1682_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (209) with fresh symbols all_1685_0, all_1685_1 gives: % 231.47/34.64 | (801) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1685_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1685_1 & % 231.47/34.64 | $i(all_1685_0) & $i(all_1685_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 231.47/34.64 | $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1685_1, v1) | % 231.47/34.64 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1685_1, % 231.47/34.64 | v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 231.47/34.64 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 231.47/34.64 | (c_Nat_OSuc(v2) = v6 & c_RealDef_Oreal(tc_Nat_Onat, v6) = v7 & % 231.47/34.64 | c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & hAPP(v8, v1) = v9 & % 231.47/34.64 | hAPP(v4, v1) = v5 & hAPP(all_1685_0, v7) = v8 & hAPP(all_1685_0, % 231.47/34.64 | v3) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) % 231.47/34.64 | & $i(v3) & $i(v2) & % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v9) & % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v0))) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (801) implies: % 231.47/34.64 | (802) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1685_1 % 231.47/34.64 | (803) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1685_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (201) with fresh symbols all_1694_0, all_1694_1, % 231.47/34.64 | all_1694_2 gives: % 231.47/34.64 | (804) c_Nat_OSuc(all_1694_2) = all_1694_1 & % 231.47/34.64 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1694_0 & % 231.47/34.64 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1694_2 & % 231.47/34.64 | $i(all_1694_0) & $i(all_1694_1) & $i(all_1694_2) & ! [v0: $i] : ! % 231.47/34.64 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ % 231.47/34.64 | (hAPP(all_1694_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1694_1, v3) | % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1694_1, v1)) & % 231.47/34.64 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v2, % 231.47/34.64 | v0) = v3) | ~ (hAPP(all_1694_0, v1) = v2) | ~ $i(v1) | ~ % 231.47/34.64 | $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 231.47/34.64 | all_1694_1, v3) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 231.47/34.64 | all_1694_1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 231.47/34.64 | [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1694_0, v1) = v2) | % 231.47/34.64 | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1694_1, v1) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1694_1, v0) | % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1694_1, v3)) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (804) implies: % 231.47/34.64 | (805) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1694_2 % 231.47/34.64 | (806) c_Nat_OSuc(all_1694_2) = all_1694_1 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (208) with fresh symbols all_1697_0, all_1697_1, % 231.47/34.64 | all_1697_2 gives: % 231.47/34.64 | (807) c_Nat_OSuc(all_1697_1) = all_1697_0 & c_Nat_OSuc(all_1697_2) = % 231.47/34.64 | all_1697_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1697_2 & % 231.47/34.64 | $i(all_1697_0) & $i(all_1697_1) & $i(all_1697_2) & ! [v0: $i] : ! % 231.47/34.64 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 231.47/34.64 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 231.47/34.64 | (c_Power_Opower__class_Opower(v2) = v3) | ~ % 231.47/34.64 | (c_Groups_Ominus__class_Ominus(v2, v5, v7) = v8) | ~ (hAPP(v6, % 231.47/34.64 | all_1697_0) = v7) | ~ (hAPP(v4, all_1697_0) = v5) | ~ % 231.47/34.64 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v6) | ~ $i(v2) | ~ % 231.47/34.64 | $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__ring__1(v2) | ? [v9: % 231.47/34.64 | $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : % 231.47/34.64 | (c_Groups_Ominus__class_Ominus(v2, v1, v0) = v10 & % 231.47/34.64 | c_Groups_Oplus__class_Oplus(v2, v1, v0) = v12 & % 231.47/34.64 | c_Groups_Otimes__class_Otimes(v2) = v9 & hAPP(v11, v12) = v8 & % 231.47/34.64 | hAPP(v9, v10) = v11 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & % 231.47/34.64 | $i(v8))) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (807) implies: % 231.47/34.64 | (808) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1697_2 % 231.47/34.64 | (809) c_Nat_OSuc(all_1697_2) = all_1697_1 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (136) with fresh symbol all_1700_0 gives: % 231.47/34.64 | (810) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1700_0 & % 231.47/34.64 | $i(all_1700_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.64 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.64 | (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ (hAPP(v0, v1) = % 231.47/34.64 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.64 | class_Orderings_Oord(v2) | ~ % 231.47/34.64 | class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ? [v7: % 231.47/34.64 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v7) & % 231.47/34.64 | ((c_Groups_Ominus__class_Ominus(v3, v4, v8) = v9 & % 231.47/34.64 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & hAPP(v0, v7) % 231.47/34.64 | = v8 & $i(v10) & $i(v9) & $i(v8) & % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(v2, v1, v7) & ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10, % 231.47/34.64 | all_1700_0)) | % 231.47/34.64 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1700_0, v5) % 231.47/34.64 | = v6 & $i(v6) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : % 231.47/34.64 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ % 231.47/34.64 | (hAPP(v0, v11) = v12) | ~ $i(v11) | ~ % 231.47/34.64 | c_Orderings_Oord__class_Oless__eq(v2, v1, v11) | % 231.47/34.64 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, % 231.47/34.64 | v6)))))) % 231.47/34.64 | % 231.47/34.64 | ALPHA: (810) implies: % 231.47/34.64 | (811) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1700_0 % 231.47/34.64 | % 231.47/34.64 | DELTA: instantiating (184) with fresh symbols all_1709_0, all_1709_1 gives: % 231.47/34.65 | (812) c_Nat_OSuc(all_1709_1) = all_1709_0 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1709_1 & % 231.47/34.65 | $i(all_1709_0) & $i(all_1709_1) & ! [v0: $i] : ! [v1: any] : (v1 = % 231.47/34.65 | all_1709_0 | v1 = all_1709_1 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1709_0) | % 231.47/34.65 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 231.47/34.65 | all_1709_0 | v0 = all_1709_0 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1709_0) | % 231.47/34.65 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 231.47/34.65 | all_1709_1 | v0 = all_1709_1 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1709_0) | % 231.47/34.65 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 231.47/34.65 | all_1709_0 | v0 = all_1709_1 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1709_0) | % 231.47/34.65 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1709_0 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1709_0, all_1709_1) = % 231.47/34.65 | v0)) & ! [v0: int] : (v0 = all_1709_0 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1709_1, all_1709_0) = % 231.47/34.65 | v0)) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (812) implies: % 231.47/34.65 | (813) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1709_1 % 231.47/34.65 | (814) c_Nat_OSuc(all_1709_1) = all_1709_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (184) with fresh symbols all_1712_0, all_1712_1 gives: % 231.47/34.65 | (815) c_Nat_OSuc(all_1712_1) = all_1712_0 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1712_1 & % 231.47/34.65 | $i(all_1712_0) & $i(all_1712_1) & ! [v0: $i] : ! [v1: any] : (v1 = % 231.47/34.65 | all_1712_0 | v1 = all_1712_1 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1712_0) | % 231.47/34.65 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 231.47/34.65 | all_1712_0 | v0 = all_1712_0 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1712_0) | % 231.47/34.65 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: any] : (v1 = % 231.47/34.65 | all_1712_1 | v0 = all_1712_1 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1712_0) | % 231.47/34.65 | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 = % 231.47/34.65 | all_1712_0 | v0 = all_1712_1 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = all_1712_0) | % 231.47/34.65 | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1712_0 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1712_0, all_1712_1) = % 231.47/34.65 | v0)) & ! [v0: int] : (v0 = all_1712_0 | ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, all_1712_1, all_1712_0) = % 231.47/34.65 | v0)) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (815) implies: % 231.47/34.65 | (816) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1712_1 % 231.47/34.65 | (817) c_Nat_OSuc(all_1712_1) = all_1712_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (40) with fresh symbol all_1715_0 gives: % 231.47/34.65 | (818) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1715_0 & % 231.47/34.65 | $i(all_1715_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.65 | $i] : ! [v4: $i] : ( ~ (c_Polynomial_Opoly(v2, v1) = v3) | ~ % 231.47/34.65 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | class_Rings_Oidom(v2) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 231.47/34.65 | ? [v8: any] : (((v8 = all_1715_0 & ~ (v7 = v1) & % 231.47/34.65 | c_Polynomial_Oorder(v2, v0, v1) = all_1715_0 & % 231.47/34.65 | tc_Polynomial_Opoly(v2) = v6 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(v6) = v7 & $i(v7) & $i(v6)) | (v5 % 231.47/34.65 | = v4 & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) & ((v7 % 231.47/34.65 | = v1 & tc_Polynomial_Opoly(v2) = v6 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(v6) = v1 & $i(v6)) | ( ~ (v8 = % 231.47/34.65 | all_1715_0) & c_Polynomial_Oorder(v2, v0, v1) = v8 & % 231.47/34.65 | $i(v8)) | ( ~ (v5 = v4) & c_Groups_Ozero__class_Ozero(v2) = % 231.47/34.65 | v5 & $i(v5))))) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (818) implies: % 231.47/34.65 | (819) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1715_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (76) with fresh symbols all_1718_0, all_1718_1 gives: % 231.47/34.65 | (820) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1718_1 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1718_0 & % 231.47/34.65 | $i(all_1718_0) & $i(all_1718_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.65 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 231.47/34.65 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1718_1, v2) = v3) | % 231.47/34.65 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : % 231.47/34.65 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 231.47/34.65 | ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 231.47/34.65 | (hAPP(all_1718_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.65 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5) | % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1718_0, v2)) & ! % 231.47/34.65 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.65 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 231.47/34.65 | (hAPP(all_1718_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.65 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1718_0, v2) | % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v5)) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (820) implies: % 231.47/34.65 | (821) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1718_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (69) with fresh symbols all_1721_0, all_1721_1 gives: % 231.47/34.65 | (822) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1721_1 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1721_0 & % 231.47/34.65 | $i(all_1721_0) & $i(all_1721_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.65 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = % 231.47/34.65 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1721_1, v2) = v3) | % 231.47/34.65 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1721_0, v2) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: % 231.47/34.65 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.65 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 231.47/34.65 | (hAPP(all_1721_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.65 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)) & ! [v0: % 231.47/34.65 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.65 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ % 231.47/34.65 | (hAPP(all_1721_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1721_0, v2) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v5)) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (822) implies: % 231.47/34.65 | (823) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1721_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (195) with fresh symbols all_1724_0, all_1724_1, % 231.47/34.65 | all_1724_2 gives: % 231.47/34.65 | (824) c_Nat_OSuc(all_1724_1) = all_1724_0 & c_Nat_OSuc(all_1724_2) = % 231.47/34.65 | all_1724_1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1724_2 & % 231.47/34.65 | $i(all_1724_0) & $i(all_1724_1) & $i(all_1724_2) & ! [v0: $i] : ! % 231.47/34.65 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 231.47/34.65 | ~ (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) % 231.47/34.65 | | ~ (hAPP(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | class_Rings_Oidom(v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 231.47/34.65 | ((v1 = v0 | (v8 = v1 & c_Groups_Ouminus__class_Ouminus(v2, v0) = % 231.47/34.65 | v1) | ( ~ (v7 = v6) & hAPP(v5, all_1724_0) = v7 & hAPP(v4, % 231.47/34.65 | all_1724_0) = v6 & $i(v7) & $i(v6))) & ((v7 = v6 & hAPP(v5, % 231.47/34.65 | all_1724_0) = v6 & hAPP(v4, all_1724_0) = v6 & $i(v6)) | ( % 231.47/34.65 | ~ (v8 = v1) & ~ (v1 = v0) & % 231.47/34.65 | c_Groups_Ouminus__class_Ouminus(v2, v0) = v8 & $i(v8))))) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (824) implies: % 231.47/34.65 | (825) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1724_2 % 231.47/34.65 | (826) c_Nat_OSuc(all_1724_2) = all_1724_1 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (178) with fresh symbols all_1727_0, all_1727_1, % 231.47/34.65 | all_1727_2 gives: % 231.47/34.65 | (827) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1727_1 & % 231.47/34.65 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1727_2 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1727_0 & % 231.47/34.65 | $i(all_1727_0) & $i(all_1727_1) & $i(all_1727_2) & ! [v0: $i] : ! % 231.47/34.65 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~ % 231.47/34.65 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) | ? [v4: % 231.47/34.65 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 231.47/34.65 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ($i(v7) & % 231.47/34.65 | $i(v5) & ((v6 = v0 & hAPP(v1, v5) = v0 & % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v2)) | % 231.47/34.65 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v9, v10) = v11 & % 231.47/34.65 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, all_1727_2) = v8 % 231.47/34.65 | & c_Groups_Oabs__class_Oabs(tc_Int_Oint, v11) = v12 & % 231.47/34.65 | hAPP(v1, v8) = v9 & hAPP(v1, v7) = v10 & $i(v12) & $i(v11) & % 231.47/34.65 | $i(v10) & $i(v9) & $i(v8) & % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v7, v2) & ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v12, % 231.47/34.65 | all_1727_1)) | (hAPP(v1, all_1727_0) = v4 & $i(v4) & ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v0))))) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (827) implies: % 231.47/34.65 | (828) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1727_0 % 231.47/34.65 | (829) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1727_2 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (178) with fresh symbols all_1733_0, all_1733_1, % 231.47/34.65 | all_1733_2 gives: % 231.47/34.65 | (830) c_Groups_Oone__class_Oone(tc_Int_Oint) = all_1733_1 & % 231.47/34.65 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1733_2 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1733_0 & % 231.47/34.65 | $i(all_1733_0) & $i(all_1733_1) & $i(all_1733_2) & ! [v0: $i] : ! % 231.47/34.65 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~ % 231.47/34.65 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v0, v3) | ? [v4: % 231.47/34.65 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 231.47/34.65 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ($i(v7) & % 231.47/34.65 | $i(v5) & ((v6 = v0 & hAPP(v1, v5) = v0 & % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v2)) | % 231.47/34.65 | (c_Groups_Ominus__class_Ominus(tc_Int_Oint, v9, v10) = v11 & % 231.47/34.65 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, all_1733_2) = v8 % 231.47/34.65 | & c_Groups_Oabs__class_Oabs(tc_Int_Oint, v11) = v12 & % 231.47/34.65 | hAPP(v1, v8) = v9 & hAPP(v1, v7) = v10 & $i(v12) & $i(v11) & % 231.47/34.65 | $i(v10) & $i(v9) & $i(v8) & % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v7, v2) & ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v12, % 231.47/34.65 | all_1733_1)) | (hAPP(v1, all_1733_0) = v4 & $i(v4) & ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, v4, v0))))) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (830) implies: % 231.47/34.65 | (831) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1733_0 % 231.47/34.65 | (832) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1733_2 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (153) with fresh symbol all_1751_0 gives: % 231.47/34.65 | (833) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1751_0 & % 231.47/34.65 | $i(all_1751_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.65 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ouminus__class_Ouminus(v1, v3) = % 231.47/34.65 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | class_RealVector_Oreal__normed__vector(v1) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1751_0, v2) | % 231.47/34.65 | c_SEQ_OBseq(v1, v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 231.47/34.65 | [v8: $i] : (c_Groups_Oplus__class_Oplus(v1, v6, v4) = v7 & % 231.47/34.65 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v5) = v6 % 231.47/34.65 | & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v2))) & % 231.47/34.65 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1) % 231.47/34.65 | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 231.47/34.65 | (c_Groups_Ouminus__class_Ouminus(v1, v3) = v4 & $i(v4) & $i(v3) & % 231.47/34.65 | $i(v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.47/34.65 | all_1751_0, v2) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 231.47/34.65 | [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(v1, v6, v4) = v7) | % 231.47/34.65 | ~ (c_RealVector_Onorm__class_Onorm(v1, v7) = v8) | ~ (hAPP(v0, % 231.47/34.65 | v5) = v6) | ~ $i(v5) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v2)))) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (833) implies: % 231.47/34.65 | (834) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1751_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (70) with fresh symbols all_1754_0, all_1754_1 gives: % 231.47/34.65 | (835) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1754_1 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1754_0 & % 231.47/34.65 | $i(all_1754_0) & $i(all_1754_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.65 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.47/34.65 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1754_1, % 231.47/34.65 | v2) = v3) | ~ (hAPP(all_1754_1, v0) = v5) | ~ $i(v2) | ~ % 231.47/34.65 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.47/34.65 | all_1754_0, v1) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0)) & ! [v0: % 231.47/34.65 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.65 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = % 231.47/34.65 | v4) | ~ (hAPP(all_1754_1, v2) = v3) | ~ (hAPP(all_1754_1, v0) = % 231.47/34.65 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6)) & ! [v0: % 231.47/34.65 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.65 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = % 231.47/34.65 | v4) | ~ (hAPP(all_1754_1, v2) = v3) | ~ (hAPP(all_1754_1, v0) = % 231.47/34.65 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1754_0, v1) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v6)) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (835) implies: % 231.47/34.65 | (836) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1754_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (75) with fresh symbols all_1757_0, all_1757_1 gives: % 231.47/34.65 | (837) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1757_1 & % 231.47/34.65 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1757_0 & % 231.47/34.65 | $i(all_1757_0) & $i(all_1757_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.65 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 231.47/34.65 | (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1757_1, % 231.47/34.65 | v2) = v3) | ~ (hAPP(all_1757_1, v0) = v5) | ~ $i(v2) | ~ % 231.47/34.65 | $i(v1) | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, % 231.47/34.65 | v4, v6) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0)) & % 231.47/34.65 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 231.47/34.65 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) % 231.47/34.65 | = v4) | ~ (hAPP(all_1757_1, v2) = v3) | ~ (hAPP(all_1757_1, v0) % 231.47/34.65 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6) | % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1757_0, v1)) & ! % 231.47/34.65 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 231.47/34.65 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v1) = v6) | ~ (hAPP(v3, v1) = % 231.47/34.65 | v4) | ~ (hAPP(all_1757_1, v2) = v3) | ~ (hAPP(all_1757_1, v0) = % 231.47/34.65 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v0) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1757_0, v1) | % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v6)) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (837) implies: % 231.47/34.65 | (838) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1757_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (154) with fresh symbol all_1760_0 gives: % 231.47/34.65 | (839) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1760_0 & % 231.47/34.65 | $i(all_1760_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.65 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.65 | (c_Groups_Ouminus__class_Ouminus(v1, v4) = v5) | ~ (hAPP(v0, v3) = % 231.47/34.65 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | class_RealVector_Oreal__normed__vector(v1) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1760_0, v2) | % 231.47/34.65 | c_SEQ_OBseq(v1, v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 231.47/34.65 | [v9: $i] : (c_Groups_Oplus__class_Oplus(v1, v7, v5) = v8 & % 231.47/34.65 | c_RealVector_Onorm__class_Onorm(v1, v8) = v9 & hAPP(v0, v6) = v7 % 231.47/34.65 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v2))) & % 231.47/34.65 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1) % 231.47/34.65 | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 231.47/34.65 | (c_Groups_Ouminus__class_Ouminus(v1, v4) = v5 & hAPP(v0, v3) = v4 & % 231.47/34.65 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1760_0, v2) & % 231.47/34.65 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ % 231.47/34.65 | (c_Groups_Oplus__class_Oplus(v1, v7, v5) = v8) | ~ % 231.47/34.65 | (c_RealVector_Onorm__class_Onorm(v1, v8) = v9) | ~ (hAPP(v0, % 231.47/34.65 | v6) = v7) | ~ $i(v6) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v2)))) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (839) implies: % 231.47/34.65 | (840) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1760_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (179) with fresh symbol all_1763_0 gives: % 231.47/34.65 | (841) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1763_0 & % 231.47/34.65 | $i(all_1763_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.65 | $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 231.47/34.65 | | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ? % 231.47/34.65 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 231.47/34.65 | $i(v4) & ((c_RealDef_Oreal(tc_Nat_Onat, v3) = v5 & % 231.47/34.65 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6) = % 231.47/34.65 | v7 & $i(v8) & $i(v7) & $i(v5) & ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v5)) % 231.47/34.65 | | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1763_0, % 231.47/34.65 | v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 231.47/34.65 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~ % 231.47/34.65 | (hAPP(v0, v9) = v10) | ~ $i(v9) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 231.47/34.65 | v4)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.47/34.65 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.65 | class_RealVector_Oreal__normed__vector(v1) | ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1763_0, v2) | % 231.47/34.65 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 231.47/34.65 | : ? [v8: $i] : ($i(v6) & $i(v3) & ((c_Nat_OSuc(v3) = v4 & % 231.47/34.65 | c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & $i(v5) & $i(v4) & ! % 231.47/34.65 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 231.47/34.65 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~ % 231.47/34.65 | (hAPP(v0, v9) = v10) | ~ $i(v9) | % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 231.47/34.65 | v5))) | (c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & % 231.47/34.65 | hAPP(v0, v6) = v7 & $i(v8) & $i(v7) & ~ % 231.47/34.65 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, % 231.47/34.65 | v2))))) % 231.47/34.65 | % 231.47/34.65 | ALPHA: (841) implies: % 231.47/34.65 | (842) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1763_0 % 231.47/34.65 | % 231.47/34.65 | DELTA: instantiating (180) with fresh symbol all_1768_0 gives: % 231.47/34.65 | (843) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1768_0 & % 231.47/34.65 | $i(all_1768_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.66 | $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 231.47/34.66 | | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ? % 231.47/34.66 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 231.47/34.66 | $i(v4) & ((c_RealDef_Oreal(tc_Nat_Onat, v3) = v5 & % 231.47/34.66 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6) = % 231.47/34.66 | v7 & $i(v8) & $i(v7) & $i(v5) & ~ % 231.47/34.66 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v5)) | % 231.47/34.66 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1768_0, % 231.47/34.66 | v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 231.47/34.66 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~ % 231.47/34.66 | (hAPP(v0, v9) = v10) | ~ $i(v9) | % 231.47/34.66 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 231.47/34.66 | v4)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.47/34.66 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.66 | class_RealVector_Oreal__normed__vector(v1) | ~ % 231.47/34.66 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1768_0, v2) | % 231.47/34.66 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 231.47/34.66 | : ? [v8: $i] : ($i(v6) & $i(v3) & ((c_Nat_OSuc(v3) = v4 & % 231.47/34.66 | c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & $i(v5) & $i(v4) & ! % 231.47/34.66 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 231.47/34.66 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~ % 231.47/34.66 | (hAPP(v0, v9) = v10) | ~ $i(v9) | % 231.47/34.66 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v5))) % 231.47/34.66 | | (c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6) % 231.47/34.66 | = v7 & $i(v8) & $i(v7) & ~ % 231.47/34.66 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, % 231.47/34.66 | v2))))) % 231.47/34.66 | % 231.47/34.66 | ALPHA: (843) implies: % 231.47/34.66 | (844) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1768_0 % 231.47/34.66 | % 231.47/34.66 | DELTA: instantiating (222) with fresh symbols all_1773_0, all_1773_1 gives: % 231.47/34.66 | (845) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1773_0 & % 231.47/34.66 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1773_1 & % 231.47/34.66 | $i(all_1773_0) & $i(all_1773_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.66 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.47/34.66 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v3) | ~ % 231.47/34.66 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.47/34.66 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : (( ~ (v0 = all_1773_1) | % 231.47/34.66 | (hAPP(v2, all_1773_1) = v5 & $i(v5) & hBOOL(v5))) & (v0 = % 231.47/34.66 | all_1773_1 | (hAPP(all_1773_0, v0) = v6 & $i(v6) & ! [v7: $i] % 231.47/34.66 | : ! [v8: $i] : ! [v9: $i] : ( ~ % 231.47/34.66 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v9, v8) = v1) | % 231.47/34.66 | ~ (hAPP(v6, v7) = v9) | ~ $i(v8) | ~ $i(v7) | ~ % 231.47/34.66 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v8, v0) | ? % 231.47/34.66 | [v10: $i] : (hAPP(v2, v7) = v10 & $i(v10) & % 231.47/34.66 | hBOOL(v10))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.47/34.66 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.47/34.66 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v3) | ~ % 231.47/34.66 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4) % 231.47/34.66 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 231.47/34.66 | $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & $i(v7) & ((v10 = v1 % 231.47/34.66 | & ~ (v0 = all_1773_1) & % 231.47/34.66 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v9, v8) = v1 & % 231.47/34.66 | hAPP(v6, v7) = v9 & hAPP(v2, v7) = v11 & hAPP(all_1773_0, v0) % 231.47/34.66 | = v6 & $i(v11) & $i(v9) & $i(v6) & % 231.47/34.66 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v8, v0) & ~ % 231.47/34.66 | hBOOL(v11)) | (v0 = all_1773_1 & hAPP(v2, all_1773_1) = v5 & % 231.47/34.66 | $i(v5) & ~ hBOOL(v5))))) % 231.47/34.66 | % 231.47/34.66 | ALPHA: (845) implies: % 231.47/34.66 | (846) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1773_1 % 231.47/34.66 | % 231.47/34.66 | DELTA: instantiating (46) with fresh symbol all_1776_0 gives: % 231.47/34.66 | (847) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1776_0 & % 231.47/34.66 | $i(all_1776_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.66 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.66 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 231.47/34.66 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1) | ~ % 231.47/34.66 | (hAPP(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 231.47/34.66 | | ~ hBOOL(v4) | ? [v6: $i] : (hAPP(v2, v5) = v6 & $i(v6) & % 231.47/34.66 | hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.66 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 231.47/34.66 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 231.47/34.66 | | ~ $i(v0) | ~ hBOOL(v4) | ~ % 231.47/34.66 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i] : % 231.47/34.66 | (hAPP(v2, all_1776_0) = v5 & $i(v5) & hBOOL(v5))) & ! [v0: $i] : % 231.47/34.66 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.47/34.66 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 231.47/34.66 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4) % 231.47/34.66 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i] % 231.47/34.66 | : ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = % 231.47/34.66 | v1 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) & ~ hBOOL(v6))) & ! % 231.47/34.66 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 231.47/34.66 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 231.47/34.66 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4) % 231.47/34.66 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 231.47/34.66 | ((v7 = v1 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v6) = v1 % 231.47/34.66 | & hAPP(v2, v6) = v8 & $i(v8) & ~ hBOOL(v8)) | (hAPP(v2, % 231.47/34.66 | all_1776_0) = v5 & $i(v5) & ~ hBOOL(v5))))) % 231.47/34.66 | % 231.47/34.66 | ALPHA: (847) implies: % 231.47/34.66 | (848) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1776_0 % 231.47/34.66 | % 231.47/34.66 | DELTA: instantiating (46) with fresh symbol all_1779_0 gives: % 231.47/34.66 | (849) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1779_0 & % 231.47/34.66 | $i(all_1779_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.66 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 231.47/34.66 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 231.47/34.66 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = v1) | ~ % 231.47/34.66 | (hAPP(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 231.47/34.66 | | ~ hBOOL(v4) | ? [v6: $i] : (hAPP(v2, v5) = v6 & $i(v6) & % 231.47/34.66 | hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 231.47/34.66 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, % 231.47/34.66 | v1, v0) = v3) | ~ (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 231.47/34.66 | | ~ $i(v0) | ~ hBOOL(v4) | ~ % 231.47/34.66 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i] : % 231.47/34.66 | (hAPP(v2, all_1779_0) = v5 & $i(v5) & hBOOL(v5))) & ! [v0: $i] : % 231.47/34.66 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 231.47/34.66 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 231.47/34.66 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4) % 231.47/34.66 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v5: $i] % 231.47/34.66 | : ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v5) = % 231.47/34.66 | v1 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) & ~ hBOOL(v6))) & ! % 231.47/34.66 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 231.47/34.66 | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v0) = v3) | ~ % 231.47/34.66 | (hAPP(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v4) % 231.47/34.66 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 231.47/34.66 | ((v7 = v1 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v6) = v1 % 231.47/34.66 | & hAPP(v2, v6) = v8 & $i(v8) & ~ hBOOL(v8)) | (hAPP(v2, % 231.47/34.66 | all_1779_0) = v5 & $i(v5) & ~ hBOOL(v5))))) % 231.47/34.66 | % 231.47/34.66 | ALPHA: (849) implies: % 231.47/34.66 | (850) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1779_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (248) with all_797_0, all_1559_6, v_c____, % 231.47/34.66 | tc_Complex_Ocomplex, simplifying with (322), (707) gives: % 231.47/34.66 | (851) all_1559_6 = all_797_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_772_1, all_783_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (306), (312) gives: % 231.47/34.66 | (852) all_783_1 = all_772_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_783_1, all_797_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (312), (323) gives: % 231.47/34.66 | (853) all_797_1 = all_783_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_797_1, all_800_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (323), (325) gives: % 231.47/34.66 | (854) all_800_0 = all_797_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_890_0, all_902_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (365), (373) gives: % 231.47/34.66 | (855) all_902_0 = all_890_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_800_0, all_905_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (325), (375) gives: % 231.47/34.66 | (856) all_905_0 = all_800_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_890_0, all_911_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (365), (377) gives: % 231.47/34.66 | (857) all_911_0 = all_890_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_902_0, all_922_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (373), (382) gives: % 231.47/34.66 | (858) all_922_1 = all_902_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_911_0, all_940_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (377), (390) gives: % 231.47/34.66 | (859) all_940_0 = all_911_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_940_0, all_946_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (390), (396) gives: % 231.47/34.66 | (860) all_946_1 = all_940_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_905_0, all_978_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (375), (409) gives: % 231.47/34.66 | (861) all_978_0 = all_905_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_890_0, all_978_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (365), (409) gives: % 231.47/34.66 | (862) all_978_0 = all_890_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_809_1, all_978_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (329), (409) gives: % 231.47/34.66 | (863) all_978_0 = all_809_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_946_1, all_997_0, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (396), (418) gives: % 231.47/34.66 | (864) all_997_0 = all_946_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_922_1, all_1000_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (382), (420) gives: % 231.47/34.66 | (865) all_1000_1 = all_922_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_781_0, all_1000_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (309), (420) gives: % 231.47/34.66 | (866) all_1000_1 = all_781_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_997_0, all_1015_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (418), (431) gives: % 231.47/34.66 | (867) all_1015_1 = all_997_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1000_1, all_1021_0, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (420), (436) gives: % 231.47/34.66 | (868) all_1021_0 = all_1000_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_905_0, all_1036_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (375), (448) gives: % 231.47/34.66 | (869) all_1036_1 = all_905_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1033_1, all_1042_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (445), (453) gives: % 231.47/34.66 | (870) all_1042_1 = all_1033_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1021_0, all_1042_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (436), (453) gives: % 231.47/34.66 | (871) all_1042_1 = all_1021_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1033_1, all_1096_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (445), (468) gives: % 231.47/34.66 | (872) all_1096_1 = all_1033_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1096_1, all_1120_0, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (468), (485) gives: % 231.47/34.66 | (873) all_1120_0 = all_1096_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1120_0, all_1132_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (485), (487) gives: % 231.47/34.66 | (874) all_1132_1 = all_1120_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1042_1, all_1141_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (453), (494) gives: % 231.47/34.66 | (875) all_1141_1 = all_1042_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1132_1, all_1155_0, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (487), (504) gives: % 231.47/34.66 | (876) all_1155_0 = all_1132_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_783_1, all_1169_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (312), (511) gives: % 231.47/34.66 | (877) all_1169_1 = all_783_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1155_0, all_1204_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (504), (526) gives: % 231.47/34.66 | (878) all_1204_1 = all_1155_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1204_1, all_1212_0, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (526), (531) gives: % 231.47/34.66 | (879) all_1212_0 = all_1204_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1036_1, all_1224_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (448), (539) gives: % 231.47/34.66 | (880) all_1224_1 = all_1036_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_949_1, all_1224_1, tc_RealDef_Oreal, % 231.47/34.66 | simplifying with (399), (539) gives: % 231.47/34.66 | (881) all_1224_1 = all_949_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1215_0, all_1230_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (533), (545) gives: % 231.47/34.66 | (882) all_1230_1 = all_1215_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1212_0, all_1236_0, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (531), (550) gives: % 231.47/34.66 | (883) all_1236_0 = all_1212_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1036_1, all_1242_0, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (448), (552) gives: % 231.47/34.66 | (884) all_1242_0 = all_1036_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1269_0, all_1275_0, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (565), (569) gives: % 231.47/34.66 | (885) all_1275_0 = all_1269_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1275_0, all_1286_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (569), (571) gives: % 231.47/34.66 | (886) all_1286_1 = all_1275_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1286_1, all_1306_0, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (571), (574) gives: % 231.47/34.66 | (887) all_1306_0 = all_1286_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1306_0, all_1317_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (574), (582) gives: % 231.47/34.66 | (888) all_1317_1 = all_1306_0 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1317_1, all_1337_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (582), (591) gives: % 231.47/34.66 | (889) all_1337_1 = all_1317_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1337_1, all_1342_2, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (591), (594) gives: % 231.47/34.66 | (890) all_1342_2 = all_1337_1 % 231.47/34.66 | % 231.47/34.66 | GROUND_INST: instantiating (243) with all_1342_2, all_1345_1, % 231.47/34.66 | tc_RealDef_Oreal, simplifying with (594), (596) gives: % 231.47/34.66 | (891) all_1345_1 = all_1342_2 % 231.47/34.66 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1236_0, all_1372_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (550), (604) gives: % 231.47/34.67 | (892) all_1372_1 = all_1236_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1372_1, all_1388_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (604), (615) gives: % 231.47/34.67 | (893) all_1388_1 = all_1372_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1372_1, all_1394_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (604), (620) gives: % 231.47/34.67 | (894) all_1394_1 = all_1372_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1169_1, all_1411_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (511), (625) gives: % 231.47/34.67 | (895) all_1411_0 = all_1169_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1345_1, all_1420_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (596), (627) gives: % 231.47/34.67 | (896) all_1420_0 = all_1345_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1027_1, all_1420_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (440), (627) gives: % 231.47/34.67 | (897) all_1420_0 = all_1027_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1411_0, all_1423_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (625), (629) gives: % 231.47/34.67 | (898) all_1423_1 = all_1411_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_757_0, all_1423_1, tc_RealDef_Oreal, % 231.47/34.67 | simplifying with (290), (629) gives: % 231.47/34.67 | (899) all_1423_1 = all_757_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1269_0, all_1426_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (565), (632) gives: % 231.47/34.67 | (900) all_1426_0 = all_1269_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1260_0, all_1426_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (557), (632) gives: % 231.47/34.67 | (901) all_1426_0 = all_1260_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1230_1, all_1426_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (545), (632) gives: % 231.47/34.67 | (902) all_1426_0 = all_1230_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1394_1, all_1432_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (620), (634) gives: % 231.47/34.67 | (903) all_1432_1 = all_1394_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1432_1, all_1435_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (634), (637) gives: % 231.47/34.67 | (904) all_1435_0 = all_1432_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1435_0, all_1444_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (637), (641) gives: % 231.47/34.67 | (905) all_1444_0 = all_1435_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1444_0, all_1453_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (641), (643) gives: % 231.47/34.67 | (906) all_1453_0 = all_1444_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1453_0, all_1483_2, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (643), (656) gives: % 231.47/34.67 | (907) all_1483_2 = all_1453_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1459_1, all_1497_2, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (647), (664) gives: % 231.47/34.67 | (908) all_1497_2 = all_1459_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1459_1, all_1500_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (647), (668) gives: % 231.47/34.67 | (909) all_1500_0 = all_1459_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1015_1, all_1500_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (431), (668) gives: % 231.47/34.67 | (910) all_1500_0 = all_1015_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1242_0, all_1538_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (552), (689) gives: % 231.47/34.67 | (911) all_1538_0 = all_1242_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1388_1, all_1556_2, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (615), (699) gives: % 231.47/34.67 | (912) all_1556_2 = all_1388_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1556_2, all_1559_8, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (699), (708) gives: % 231.47/34.67 | (913) all_1559_8 = all_1556_2 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1314_2, all_1582_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (578), (723) gives: % 231.47/34.67 | (914) all_1582_1 = all_1314_2 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1215_0, all_1582_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (533), (723) gives: % 231.47/34.67 | (915) all_1582_1 = all_1215_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1538_0, all_1594_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (689), (733) gives: % 231.47/34.67 | (916) all_1594_0 = all_1538_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1585_1, all_1600_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (726), (737) gives: % 231.47/34.67 | (917) all_1600_1 = all_1585_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1573_1, all_1600_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (715), (737) gives: % 231.47/34.67 | (918) all_1600_1 = all_1573_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1497_2, all_1600_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (664), (737) gives: % 231.47/34.67 | (919) all_1600_1 = all_1497_2 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1594_0, all_1602_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (733), (740) gives: % 231.47/34.67 | (920) all_1602_0 = all_1594_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1585_1, all_1605_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (726), (742) gives: % 231.47/34.67 | (921) all_1605_1 = all_1585_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_830_0, all_1605_1, tc_RealDef_Oreal, % 231.47/34.67 | simplifying with (338), (742) gives: % 231.47/34.67 | (922) all_1605_1 = all_830_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1602_0, all_1634_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (740), (763) gives: % 231.47/34.67 | (923) all_1634_1 = all_1602_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1420_0, all_1655_3, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (627), (774) gives: % 231.47/34.67 | (924) all_1655_3 = all_1420_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1314_2, all_1661_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (578), (780) gives: % 231.47/34.67 | (925) all_1661_0 = all_1314_2 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1147_4, all_1661_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (500), (780) gives: % 231.47/34.67 | (926) all_1661_0 = all_1147_4 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1141_1, all_1661_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (494), (780) gives: % 231.47/34.67 | (927) all_1661_0 = all_1141_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1634_1, all_1664_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (763), (782) gives: % 231.47/34.67 | (928) all_1664_0 = all_1634_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1500_0, all_1667_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (668), (785) gives: % 231.47/34.67 | (929) all_1667_1 = all_1500_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1138_0, all_1667_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (492), (785) gives: % 231.47/34.67 | (930) all_1667_1 = all_1138_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1582_1, all_1670_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (723), (788) gives: % 231.47/34.67 | (931) all_1670_1 = all_1582_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1192_0, all_1670_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (519), (788) gives: % 231.47/34.67 | (932) all_1670_1 = all_1192_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1483_2, all_1676_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (656), (793) gives: % 231.47/34.67 | (933) all_1676_1 = all_1483_2 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1320_2, all_1676_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (585), (793) gives: % 231.47/34.67 | (934) all_1676_1 = all_1320_2 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1664_0, all_1679_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (782), (796) gives: % 231.47/34.67 | (935) all_1679_1 = all_1664_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1655_3, all_1685_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (774), (802) gives: % 231.47/34.67 | (936) all_1685_1 = all_1655_3 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1357_1, all_1685_1, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (601), (802) gives: % 231.47/34.67 | (937) all_1685_1 = all_1357_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1619_2, all_1751_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (751), (834) gives: % 231.47/34.67 | (938) all_1751_0 = all_1619_2 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1559_8, all_1751_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (708), (834) gives: % 231.47/34.67 | (939) all_1751_0 = all_1559_8 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_987_0, all_1751_0, tc_RealDef_Oreal, % 231.47/34.67 | simplifying with (411), (834) gives: % 231.47/34.67 | (940) all_1751_0 = all_987_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1679_1, all_1760_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (796), (840) gives: % 231.47/34.67 | (941) all_1760_0 = all_1679_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1314_2, all_1763_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (578), (842) gives: % 231.47/34.67 | (942) all_1763_0 = all_1314_2 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1189_0, all_1763_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (517), (842) gives: % 231.47/34.67 | (943) all_1763_0 = all_1189_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1760_0, all_1768_0, % 231.47/34.67 | tc_RealDef_Oreal, simplifying with (840), (844) gives: % 231.47/34.67 | (944) all_1768_0 = all_1760_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_803_0, all_1768_0, tc_RealDef_Oreal, % 231.47/34.67 | simplifying with (327), (844) gives: % 231.47/34.67 | (945) all_1768_0 = all_803_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_710_0, all_724_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (264), (270) gives: % 231.47/34.67 | (946) all_724_0 = all_710_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_707_0, all_724_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (262), (270) gives: % 231.47/34.67 | (947) all_724_0 = all_707_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_724_0, all_727_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (270), (272) gives: % 231.47/34.67 | (948) all_727_0 = all_724_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_715_0, all_745_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (266), (282) gives: % 231.47/34.67 | (949) all_745_0 = all_715_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_710_0, all_745_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (264), (282) gives: % 231.47/34.67 | (950) all_745_0 = all_710_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_691_0, all_745_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (253), (282) gives: % 231.47/34.67 | (951) all_745_0 = all_691_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_730_0, all_752_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (274), (288) gives: % 231.47/34.67 | (952) all_752_0 = all_730_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_727_0, all_752_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (272), (288) gives: % 231.47/34.67 | (953) all_752_0 = all_727_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_739_0, all_757_1, tc_Nat_Onat, % 231.47/34.67 | simplifying with (278), (291) gives: % 231.47/34.67 | (954) all_757_1 = all_739_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_757_1, all_762_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (291), (293) gives: % 231.47/34.67 | (955) all_762_0 = all_757_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_767_0, all_783_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (298), (313) gives: % 231.47/34.67 | (956) all_783_0 = all_767_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_762_0, all_783_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (293), (313) gives: % 231.47/34.67 | (957) all_783_0 = all_762_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_710_0, all_809_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (264), (330) gives: % 231.47/34.67 | (958) all_809_0 = all_710_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_694_0, all_809_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (256), (330) gives: % 231.47/34.67 | (959) all_809_0 = all_694_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_809_0, all_856_2, tc_Nat_Onat, % 231.47/34.67 | simplifying with (330), (348) gives: % 231.47/34.67 | (960) all_856_2 = all_809_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_794_0, all_868_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (319), (357) gives: % 231.47/34.67 | (961) all_868_0 = all_794_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_752_0, all_868_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (288), (357) gives: % 231.47/34.67 | (962) all_868_0 = all_752_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_742_0, all_868_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (280), (357) gives: % 231.47/34.67 | (963) all_868_0 = all_742_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_739_0, all_868_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (278), (357) gives: % 231.47/34.67 | (964) all_868_0 = all_739_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_879_0, all_884_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (361), (363) gives: % 231.47/34.67 | (965) all_884_0 = all_879_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_794_0, all_893_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (319), (368) gives: % 231.47/34.67 | (966) all_893_0 = all_794_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_884_0, all_896_1, tc_Nat_Onat, % 231.47/34.67 | simplifying with (363), (370) gives: % 231.47/34.67 | (967) all_896_1 = all_884_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_931_1, all_937_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (385), (388) gives: % 231.47/34.67 | (968) all_937_0 = all_931_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_893_0, all_937_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (368), (388) gives: % 231.47/34.67 | (969) all_937_0 = all_893_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_946_0, all_961_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (397), (402) gives: % 231.47/34.67 | (970) all_961_0 = all_946_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_937_0, all_967_1, tc_Nat_Onat, % 231.47/34.67 | simplifying with (388), (404) gives: % 231.47/34.67 | (971) all_967_1 = all_937_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_961_0, all_994_1, tc_Nat_Onat, % 231.47/34.67 | simplifying with (402), (416) gives: % 231.47/34.67 | (972) all_994_1 = all_961_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_994_1, all_1000_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (416), (421) gives: % 231.47/34.67 | (973) all_1000_0 = all_994_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1000_0, all_1018_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (421), (434) gives: % 231.47/34.67 | (974) all_1018_0 = all_1000_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1018_0, all_1024_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (434), (438) gives: % 231.47/34.67 | (975) all_1024_0 = all_1018_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1024_0, all_1045_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (438), (456) gives: % 231.47/34.67 | (976) all_1045_0 = all_1024_0 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_967_1, all_1060_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (404), (458) gives: % 231.47/34.67 | (977) all_1060_0 = all_967_1 % 231.47/34.67 | % 231.47/34.67 | GROUND_INST: instantiating (243) with all_1045_0, all_1063_0, tc_Nat_Onat, % 231.47/34.67 | simplifying with (456), (460) gives: % 231.47/34.67 | (978) all_1063_0 = all_1045_0 % 231.47/34.67 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1063_0, all_1084_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (460), (463) gives: % 231.47/34.68 | (979) all_1084_2 = all_1063_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1084_2, all_1096_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (463), (469) gives: % 231.47/34.68 | (980) all_1096_0 = all_1084_2 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1096_0, all_1099_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (469), (471) gives: % 231.47/34.68 | (981) all_1099_0 = all_1096_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1099_0, all_1105_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (471), (475) gives: % 231.47/34.68 | (982) all_1105_0 = all_1099_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1114_0, all_1166_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (481), (508) gives: % 231.47/34.68 | (983) all_1166_2 = all_1114_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1105_0, all_1166_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (475), (508) gives: % 231.47/34.68 | (984) all_1166_2 = all_1105_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1163_0, all_1186_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (506), (514) gives: % 231.47/34.68 | (985) all_1186_2 = all_1163_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1186_2, all_1195_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (514), (521) gives: % 231.47/34.68 | (986) all_1195_0 = all_1186_2 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_946_0, all_1204_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (397), (527) gives: % 231.47/34.68 | (987) all_1204_0 = all_946_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_922_0, all_1204_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (383), (527) gives: % 231.47/34.68 | (988) all_1204_0 = all_922_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_856_2, all_1207_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (348), (529) gives: % 231.47/34.68 | (989) all_1207_1 = all_856_2 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1195_0, all_1218_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (521), (535) gives: % 231.47/34.68 | (990) all_1218_0 = all_1195_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1218_0, all_1221_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (535), (537) gives: % 231.47/34.68 | (991) all_1221_0 = all_1218_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1221_0, all_1233_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (537), (548) gives: % 231.47/34.68 | (992) all_1233_1 = all_1221_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1233_1, all_1251_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (548), (554) gives: % 231.47/34.68 | (993) all_1251_2 = all_1233_1 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1266_2, all_1272_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (562), (567) gives: % 231.47/34.68 | (994) all_1272_1 = all_1266_2 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1272_1, all_1311_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (567), (576) gives: % 231.47/34.68 | (995) all_1311_0 = all_1272_1 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1354_1, all_1379_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (599), (610) gives: % 231.47/34.68 | (996) all_1379_1 = all_1354_1 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1060_0, all_1382_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (458), (613) gives: % 231.47/34.68 | (997) all_1382_0 = all_1060_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_833_0, all_1465_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (340), (650) gives: % 231.47/34.68 | (998) all_1465_0 = all_833_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_718_0, all_1465_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (268), (650) gives: % 231.47/34.68 | (999) all_1465_0 = all_718_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_879_0, all_1486_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (361), (660) gives: % 231.47/34.68 | (1000) all_1486_0 = all_879_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_833_0, all_1486_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (340), (660) gives: % 231.47/34.68 | (1001) all_1486_0 = all_833_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1266_2, all_1489_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (562), (662) gives: % 231.47/34.68 | (1002) all_1489_0 = all_1266_2 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1251_2, all_1489_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (554), (662) gives: % 231.47/34.68 | (1003) all_1489_0 = all_1251_2 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1382_0, all_1503_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (613), (670) gives: % 231.47/34.68 | (1004) all_1503_1 = all_1382_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1465_0, all_1506_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (650), (673) gives: % 231.47/34.68 | (1005) all_1506_0 = all_1465_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_833_0, all_1515_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (340), (677) gives: % 231.47/34.68 | (1006) all_1515_0 = all_833_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1489_0, all_1521_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (662), (679) gives: % 231.47/34.68 | (1007) all_1521_0 = all_1489_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1503_1, all_1535_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (670), (687) gives: % 231.47/34.68 | (1008) all_1535_0 = all_1503_1 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1486_0, all_1547_3, tc_Nat_Onat, % 231.47/34.68 | simplifying with (660), (693) gives: % 231.47/34.68 | (1009) all_1547_3 = all_1486_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1515_0, all_1550_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (677), (696) gives: % 231.47/34.68 | (1010) all_1550_1 = all_1515_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_809_0, all_1573_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (330), (716) gives: % 231.47/34.68 | (1011) all_1573_2 = all_809_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1547_3, all_1579_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (693), (721) gives: % 231.47/34.68 | (1012) all_1579_0 = all_1547_3 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1579_0, all_1588_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (721), (729) gives: % 231.47/34.68 | (1013) all_1588_0 = all_1579_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1588_0, all_1591_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (729), (731) gives: % 231.47/34.68 | (1014) all_1591_0 = all_1588_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1379_1, all_1597_0, tc_Nat_Onat, % 231.47/34.68 | simplifying with (610), (735) gives: % 231.47/34.68 | (1015) all_1597_0 = all_1379_1 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1535_0, all_1610_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (687), (747) gives: % 231.47/34.68 | (1016) all_1610_1 = all_1535_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1573_2, all_1622_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (716), (754) gives: % 231.47/34.68 | (1017) all_1622_1 = all_1573_2 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1163_0, all_1628_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (506), (758) gives: % 231.47/34.68 | (1018) all_1628_2 = all_1163_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1135_1, all_1628_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (490), (758) gives: % 231.47/34.68 | (1019) all_1628_2 = all_1135_1 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1114_0, all_1628_2, tc_Nat_Onat, % 231.47/34.68 | simplifying with (481), (758) gives: % 231.47/34.68 | (1020) all_1628_2 = all_1114_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1591_0, all_1631_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (731), (761) gives: % 231.47/34.68 | (1021) all_1631_1 = all_1591_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1204_0, all_1637_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (527), (766) gives: % 231.47/34.68 | (1022) all_1637_1 = all_1204_0 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_919_1, all_1637_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (379), (766) gives: % 231.47/34.68 | (1023) all_1637_1 = all_919_1 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_896_1, all_1637_1, tc_Nat_Onat, % 231.47/34.68 | simplifying with (370), (766) gives: % 231.47/34.68 | (1024) all_1637_1 = all_896_1 % 231.47/34.68 | % 231.47/34.68 | GROUND_INST: instantiating (243) with all_1622_1, all_1643_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (754), (769) gives: % 231.72/34.68 | (1025) all_1643_1 = all_1622_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_705_0, all_1643_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (260), (769) gives: % 231.72/34.68 | (1026) all_1643_1 = all_705_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1506_0, all_1646_3, tc_Nat_Onat, % 231.72/34.68 | simplifying with (673), (771) gives: % 231.72/34.68 | (1027) all_1646_3 = all_1506_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1597_0, all_1658_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (735), (778) gives: % 231.72/34.68 | (1028) all_1658_1 = all_1597_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1631_1, all_1673_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (761), (791) gives: % 231.72/34.68 | (1029) all_1673_0 = all_1631_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1354_1, all_1694_2, tc_Nat_Onat, % 231.72/34.68 | simplifying with (599), (805) gives: % 231.72/34.68 | (1030) all_1694_2 = all_1354_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1328_1, all_1694_2, tc_Nat_Onat, % 231.72/34.68 | simplifying with (589), (805) gives: % 231.72/34.68 | (1031) all_1694_2 = all_1328_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1311_0, all_1694_2, tc_Nat_Onat, % 231.72/34.68 | simplifying with (576), (805) gives: % 231.72/34.68 | (1032) all_1694_2 = all_1311_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1550_1, all_1697_2, tc_Nat_Onat, % 231.72/34.68 | simplifying with (696), (808) gives: % 231.72/34.68 | (1033) all_1697_2 = all_1550_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_813_0, all_1697_2, tc_Nat_Onat, % 231.72/34.68 | simplifying with (332), (808) gives: % 231.72/34.68 | (1034) all_1697_2 = all_813_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1521_0, all_1709_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (679), (813) gives: % 231.72/34.68 | (1035) all_1709_1 = all_1521_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1207_1, all_1712_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (529), (816) gives: % 231.72/34.68 | (1036) all_1712_1 = all_1207_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_791_0, all_1712_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (317), (816) gives: % 231.72/34.68 | (1037) all_1712_1 = all_791_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1658_1, all_1715_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (778), (819) gives: % 231.72/34.68 | (1038) all_1715_0 = all_1658_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1625_1, all_1715_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (756), (819) gives: % 231.72/34.68 | (1039) all_1715_0 = all_1625_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1673_0, all_1718_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (791), (821) gives: % 231.72/34.68 | (1040) all_1718_0 = all_1673_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_809_0, all_1721_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (330), (823) gives: % 231.72/34.68 | (1041) all_1721_0 = all_809_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_697_0, all_1721_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (258), (823) gives: % 231.72/34.68 | (1042) all_1721_0 = all_697_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1166_2, all_1724_2, tc_Nat_Onat, % 231.72/34.68 | simplifying with (508), (825) gives: % 231.72/34.68 | (1043) all_1724_2 = all_1166_2 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1111_1, all_1724_2, tc_Nat_Onat, % 231.72/34.68 | simplifying with (479), (825) gives: % 231.72/34.68 | (1044) all_1724_2 = all_1111_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1610_1, all_1727_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (747), (828) gives: % 231.72/34.68 | (1045) all_1727_0 = all_1610_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_733_0, all_1727_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (276), (828) gives: % 231.72/34.68 | (1046) all_1727_0 = all_733_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1597_0, all_1733_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (735), (831) gives: % 231.72/34.68 | (1047) all_1733_0 = all_1597_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1576_1, all_1733_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (718), (831) gives: % 231.72/34.68 | (1048) all_1733_0 = all_1576_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_822_0, all_1733_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (336), (831) gives: % 231.72/34.68 | (1049) all_1733_0 = all_822_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1718_0, all_1754_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (821), (836) gives: % 231.72/34.68 | (1050) all_1754_0 = all_1718_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_849_0, all_1754_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (346), (836) gives: % 231.72/34.68 | (1051) all_1754_0 = all_849_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1709_1, all_1757_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (813), (838) gives: % 231.72/34.68 | (1052) all_1757_0 = all_1709_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1263_2, all_1757_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (559), (838) gives: % 231.72/34.68 | (1053) all_1757_0 = all_1263_2 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1682_1, all_1773_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (799), (846) gives: % 231.72/34.68 | (1054) all_1773_1 = all_1682_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1515_0, all_1773_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (677), (846) gives: % 231.72/34.68 | (1055) all_1773_1 = all_1515_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_788_0, all_1773_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (315), (846) gives: % 231.72/34.68 | (1056) all_1773_1 = all_788_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_783_0, all_1773_1, tc_Nat_Onat, % 231.72/34.68 | simplifying with (313), (846) gives: % 231.72/34.68 | (1057) all_1773_1 = all_783_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1646_3, all_1776_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (771), (848) gives: % 231.72/34.68 | (1058) all_1776_0 = all_1646_3 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_943_1, all_1776_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (393), (848) gives: % 231.72/34.68 | (1059) all_1776_0 = all_943_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1658_1, all_1779_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (778), (850) gives: % 231.72/34.68 | (1060) all_1779_0 = all_1658_1 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (243) with all_1388_2, all_1779_0, tc_Nat_Onat, % 231.72/34.68 | simplifying with (616), (850) gives: % 231.72/34.68 | (1061) all_1779_0 = all_1388_2 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1039_0, all_1117_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (451), (483) gives: % 231.72/34.68 | (1062) all_1117_0 = all_1039_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1147_3, all_1169_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (502), (512) gives: % 231.72/34.68 | (1063) all_1169_0 = all_1147_3 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1147_3, all_1224_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (502), (540) gives: % 231.72/34.68 | (1064) all_1224_0 = all_1147_3 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1117_0, all_1224_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (483), (540) gives: % 231.72/34.68 | (1065) all_1224_0 = all_1117_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1169_0, all_1230_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (512), (546) gives: % 231.72/34.68 | (1066) all_1230_0 = all_1169_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1230_0, all_1286_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (546), (572) gives: % 231.72/34.68 | (1067) all_1286_0 = all_1230_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1286_0, all_1317_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (572), (583) gives: % 231.72/34.68 | (1068) all_1317_0 = all_1286_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1317_0, all_1372_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (583), (605) gives: % 231.72/34.68 | (1069) all_1372_0 = all_1317_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1423_0, all_1441_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (630), (639) gives: % 231.72/34.68 | (1070) all_1441_0 = all_1423_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1441_0, all_1456_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (639), (645) gives: % 231.72/34.68 | (1071) all_1456_0 = all_1441_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1456_0, all_1459_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (645), (648) gives: % 231.72/34.68 | (1072) all_1459_0 = all_1456_0 % 231.72/34.68 | % 231.72/34.68 | GROUND_INST: instantiating (244) with all_1459_0, all_1524_0, % 231.72/34.68 | tc_RealDef_Oreal, simplifying with (648), (681) gives: % 231.72/34.69 | (1073) all_1524_0 = all_1459_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1524_0, all_1533_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (681), (685) gives: % 231.72/34.69 | (1074) all_1533_0 = all_1524_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1391_0, all_1541_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (618), (691) gives: % 231.72/34.69 | (1075) all_1541_0 = all_1391_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1372_0, all_1541_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (605), (691) gives: % 231.72/34.69 | (1076) all_1541_0 = all_1372_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1533_0, all_1556_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (685), (700) gives: % 231.72/34.69 | (1077) all_1556_0 = all_1533_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1556_0, all_1559_4, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (700), (710) gives: % 231.72/34.69 | (1078) all_1559_4 = all_1556_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1541_0, all_1582_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (691), (724) gives: % 231.72/34.69 | (1079) all_1582_0 = all_1541_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1423_0, all_1582_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (630), (724) gives: % 231.72/34.69 | (1080) all_1582_0 = all_1423_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1408_0, all_1582_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (623), (724) gives: % 231.72/34.69 | (1081) all_1582_0 = all_1408_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1559_4, all_1585_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (710), (727) gives: % 231.72/34.69 | (1082) all_1585_0 = all_1559_4 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1585_0, all_1600_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (727), (738) gives: % 231.72/34.69 | (1083) all_1600_0 = all_1585_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1607_0, all_1613_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (745), (749) gives: % 231.72/34.69 | (1084) all_1613_0 = all_1607_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1613_0, all_1619_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (749), (752) gives: % 231.72/34.69 | (1085) all_1619_0 = all_1613_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1619_0, all_1634_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (752), (764) gives: % 231.72/34.69 | (1086) all_1634_0 = all_1619_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1634_0, all_1664_1, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (764), (783) gives: % 231.72/34.69 | (1087) all_1664_1 = all_1634_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1664_1, all_1667_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (783), (786) gives: % 231.72/34.69 | (1088) all_1667_0 = all_1664_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1667_0, all_1670_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (786), (789) gives: % 231.72/34.69 | (1089) all_1670_0 = all_1667_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1670_0, all_1676_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (789), (794) gives: % 231.72/34.69 | (1090) all_1676_0 = all_1670_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1006_2, all_1676_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (425), (794) gives: % 231.72/34.69 | (1091) all_1676_0 = all_1006_2 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1607_0, all_1679_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (745), (797) gives: % 231.72/34.69 | (1092) all_1679_0 = all_1607_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1605_0, all_1679_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (743), (797) gives: % 231.72/34.69 | (1093) all_1679_0 = all_1605_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1600_0, all_1679_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (738), (797) gives: % 231.72/34.69 | (1094) all_1679_0 = all_1600_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1655_2, all_1685_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (775), (803) gives: % 231.72/34.69 | (1095) all_1685_0 = all_1655_2 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1224_0, all_1685_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (540), (803) gives: % 231.72/34.69 | (1096) all_1685_0 = all_1224_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (244) with all_1132_0, all_1685_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (488), (803) gives: % 231.72/34.69 | (1097) all_1685_0 = all_1132_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_772_0, all_856_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (307), (349) gives: % 231.72/34.69 | (1098) all_856_0 = all_772_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_770_1, all_856_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (300), (349) gives: % 231.72/34.69 | (1099) all_856_0 = all_770_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_765_0, all_856_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (296), (349) gives: % 231.72/34.69 | (1100) all_856_0 = all_765_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_748_1, all_856_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (284), (349) gives: % 231.72/34.69 | (1101) all_856_0 = all_748_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_856_0, all_858_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (349), (353) gives: % 231.72/34.69 | (1102) all_858_0 = all_856_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_858_0, all_865_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (353), (355) gives: % 231.72/34.69 | (1103) all_865_0 = all_858_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_865_0, all_949_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (355), (400) gives: % 231.72/34.69 | (1104) all_949_0 = all_865_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_949_0, all_987_1, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (400), (412) gives: % 231.72/34.69 | (1105) all_987_1 = all_949_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_987_1, all_991_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (412), (414) gives: % 231.72/34.69 | (1106) all_991_0 = all_987_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_991_0, all_1006_1, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (414), (426) gives: % 231.72/34.69 | (1107) all_1006_1 = all_991_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1006_1, all_1009_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (426), (428) gives: % 231.72/34.69 | (1108) all_1009_0 = all_1006_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1009_0, all_1015_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (428), (432) gives: % 231.72/34.69 | (1109) all_1015_0 = all_1009_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1015_0, all_1027_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (432), (441) gives: % 231.72/34.69 | (1110) all_1027_0 = all_1015_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1027_0, all_1030_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (441), (443) gives: % 231.72/34.69 | (1111) all_1030_0 = all_1027_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1030_0, all_1033_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (443), (446) gives: % 231.72/34.69 | (1112) all_1033_0 = all_1030_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1033_0, all_1036_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (446), (449) gives: % 231.72/34.69 | (1113) all_1036_0 = all_1033_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1108_0, all_1141_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (477), (495) gives: % 231.72/34.69 | (1114) all_1141_0 = all_1108_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1141_0, all_1198_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (495), (523) gives: % 231.72/34.69 | (1115) all_1198_0 = all_1141_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1198_0, all_1227_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (523), (542) gives: % 231.72/34.69 | (1116) all_1227_0 = all_1198_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1227_0, all_1314_1, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (542), (579) gives: % 231.72/34.69 | (1117) all_1314_1 = all_1227_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1314_1, all_1320_1, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (579), (586) gives: % 231.72/34.69 | (1118) all_1320_1 = all_1314_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1320_1, all_1337_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (586), (592) gives: % 231.72/34.69 | (1119) all_1337_0 = all_1320_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1337_0, all_1345_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (592), (597) gives: % 231.72/34.69 | (1120) all_1345_0 = all_1337_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1345_0, all_1357_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (597), (602) gives: % 231.72/34.69 | (1121) all_1357_0 = all_1345_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_940_1, all_1357_0, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (391), (602) gives: % 231.72/34.69 | (1122) all_1357_0 = all_940_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1108_0, all_1374_1, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (477), (607) gives: % 231.72/34.69 | (1123) all_1374_1 = all_1108_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1036_0, all_1374_1, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (449), (607) gives: % 231.72/34.69 | (1124) all_1374_1 = all_1036_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1374_1, all_1432_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (607), (635) gives: % 231.72/34.69 | (1125) all_1432_0 = all_1374_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1432_0, all_1483_1, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (635), (657) gives: % 231.72/34.69 | (1126) all_1483_1 = all_1432_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1483_1, all_1497_1, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (657), (665) gives: % 231.72/34.69 | (1127) all_1497_1 = all_1483_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1497_1, all_1509_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (665), (675) gives: % 231.72/34.69 | (1128) all_1509_0 = all_1497_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1509_0, all_1527_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (675), (683) gives: % 231.72/34.69 | (1129) all_1527_0 = all_1509_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1559_7, all_1655_1, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (713), (776) gives: % 231.72/34.69 | (1130) all_1655_1 = all_1559_7 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_949_0, all_1655_1, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (400), (776) gives: % 231.72/34.69 | (1131) all_1655_1 = all_949_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_781_1, all_1655_1, tc_RealDef_Oreal, % 231.72/34.69 | simplifying with (310), (776) gives: % 231.72/34.69 | (1132) all_1655_1 = all_781_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1527_0, all_1700_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (683), (811) gives: % 231.72/34.69 | (1133) all_1700_0 = all_1527_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1042_0, all_1700_0, % 231.72/34.69 | tc_RealDef_Oreal, simplifying with (454), (811) gives: % 231.72/34.69 | (1134) all_1700_0 = all_1042_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_770_0, all_813_1, tc_Nat_Onat, % 231.72/34.69 | simplifying with (301), (333) gives: % 231.72/34.69 | (1135) all_813_1 = all_770_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_813_1, all_842_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (333), (344) gives: % 231.72/34.69 | (1136) all_842_0 = all_813_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_748_0, all_943_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (285), (394) gives: % 231.72/34.69 | (1137) all_943_0 = all_748_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_943_0, all_967_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (394), (405) gives: % 231.72/34.69 | (1138) all_967_0 = all_943_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_871_0, all_967_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (359), (405) gives: % 231.72/34.69 | (1139) all_967_0 = all_871_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_842_0, all_967_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (344), (405) gives: % 231.72/34.69 | (1140) all_967_0 = all_842_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_842_0, all_1003_1, tc_Nat_Onat, % 231.72/34.69 | simplifying with (344), (423) gives: % 231.72/34.69 | (1141) all_1003_1 = all_842_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_839_0, all_1003_1, tc_Nat_Onat, % 231.72/34.69 | simplifying with (342), (423) gives: % 231.72/34.69 | (1142) all_1003_1 = all_839_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1003_1, all_1063_1, tc_Nat_Onat, % 231.72/34.69 | simplifying with (423), (461) gives: % 231.72/34.69 | (1143) all_1063_1 = all_1003_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1063_1, all_1093_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (461), (466) gives: % 231.72/34.69 | (1144) all_1093_0 = all_1063_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1093_0, all_1102_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (466), (473) gives: % 231.72/34.69 | (1145) all_1102_0 = all_1093_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1102_0, all_1198_1, tc_Nat_Onat, % 231.72/34.69 | simplifying with (473), (524) gives: % 231.72/34.69 | (1146) all_1198_1 = all_1102_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1198_1, all_1227_1, tc_Nat_Onat, % 231.72/34.69 | simplifying with (524), (543) gives: % 231.72/34.69 | (1147) all_1227_1 = all_1198_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1227_1, all_1314_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (543), (580) gives: % 231.72/34.69 | (1148) all_1314_0 = all_1227_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1314_0, all_1320_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (580), (587) gives: % 231.72/34.69 | (1149) all_1320_0 = all_1314_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1320_0, all_1374_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (587), (608) gives: % 231.72/34.69 | (1150) all_1374_0 = all_1320_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1468_1, all_1480_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (652), (654) gives: % 231.72/34.69 | (1151) all_1480_0 = all_1468_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1480_0, all_1503_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (654), (671) gives: % 231.72/34.69 | (1152) all_1503_0 = all_1480_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1503_0, all_1628_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (671), (759) gives: % 231.72/34.69 | (1153) all_1628_0 = all_1503_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1628_0, all_1637_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (759), (767) gives: % 231.72/34.69 | (1154) all_1637_0 = all_1628_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1637_0, all_1646_1, tc_Nat_Onat, % 231.72/34.69 | simplifying with (767), (772) gives: % 231.72/34.69 | (1155) all_1646_1 = all_1637_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1468_1, all_1682_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (652), (800) gives: % 231.72/34.69 | (1156) all_1682_0 = all_1468_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1394_0, all_1682_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (621), (800) gives: % 231.72/34.69 | (1157) all_1682_0 = all_1394_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1374_0, all_1682_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (608), (800) gives: % 231.72/34.69 | (1158) all_1682_0 = all_1374_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_975_0, all_1682_0, tc_Nat_Onat, % 231.72/34.69 | simplifying with (407), (800) gives: % 231.72/34.69 | (1159) all_1682_0 = all_975_0 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1646_1, all_1727_2, tc_Nat_Onat, % 231.72/34.69 | simplifying with (772), (829) gives: % 231.72/34.69 | (1160) all_1727_2 = all_1646_1 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1727_2, all_1733_2, tc_Nat_Onat, % 231.72/34.69 | simplifying with (829), (832) gives: % 231.72/34.69 | (1161) all_1733_2 = all_1727_2 % 231.72/34.69 | % 231.72/34.69 | GROUND_INST: instantiating (245) with all_1379_0, all_1733_2, tc_Nat_Onat, % 231.72/34.69 | simplifying with (611), (832) gives: % 231.72/34.69 | (1162) all_1733_2 = all_1379_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1060), (1061) imply: % 231.72/34.69 | (1163) all_1658_1 = all_1388_2 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1163) implies: % 231.72/34.69 | (1164) all_1658_1 = all_1388_2 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1058), (1059) imply: % 231.72/34.69 | (1165) all_1646_3 = all_943_1 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1165) implies: % 231.72/34.69 | (1166) all_1646_3 = all_943_1 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1054), (1057) imply: % 231.72/34.69 | (1167) all_1682_1 = all_783_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1054), (1056) imply: % 231.72/34.69 | (1168) all_1682_1 = all_788_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1054), (1055) imply: % 231.72/34.69 | (1169) all_1682_1 = all_1515_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (944), (945) imply: % 231.72/34.69 | (1170) all_1760_0 = all_803_0 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1170) implies: % 231.72/34.69 | (1171) all_1760_0 = all_803_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (942), (943) imply: % 231.72/34.69 | (1172) all_1314_2 = all_1189_0 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1172) implies: % 231.72/34.69 | (1173) all_1314_2 = all_1189_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (941), (1171) imply: % 231.72/34.69 | (1174) all_1679_1 = all_803_0 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1174) implies: % 231.72/34.69 | (1175) all_1679_1 = all_803_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1052), (1053) imply: % 231.72/34.69 | (1176) all_1709_1 = all_1263_2 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1176) implies: % 231.72/34.69 | (1177) all_1709_1 = all_1263_2 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1050), (1051) imply: % 231.72/34.69 | (1178) all_1718_0 = all_849_0 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1178) implies: % 231.72/34.69 | (1179) all_1718_0 = all_849_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (938), (940) imply: % 231.72/34.69 | (1180) all_1619_2 = all_987_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (938), (939) imply: % 231.72/34.69 | (1181) all_1619_2 = all_1559_8 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1047), (1048) imply: % 231.72/34.69 | (1182) all_1597_0 = all_1576_1 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1182) implies: % 231.72/34.69 | (1183) all_1597_0 = all_1576_1 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1048), (1049) imply: % 231.72/34.69 | (1184) all_1576_1 = all_822_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1161), (1162) imply: % 231.72/34.69 | (1185) all_1727_2 = all_1379_0 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1185) implies: % 231.72/34.69 | (1186) all_1727_2 = all_1379_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1045), (1046) imply: % 231.72/34.69 | (1187) all_1610_1 = all_733_0 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1187) implies: % 231.72/34.69 | (1188) all_1610_1 = all_733_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1160), (1186) imply: % 231.72/34.69 | (1189) all_1646_1 = all_1379_0 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1189) implies: % 231.72/34.69 | (1190) all_1646_1 = all_1379_0 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1043), (1044) imply: % 231.72/34.69 | (1191) all_1166_2 = all_1111_1 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1191) implies: % 231.72/34.69 | (1192) all_1166_2 = all_1111_1 % 231.72/34.69 | % 231.72/34.69 | COMBINE_EQS: (1041), (1042) imply: % 231.72/34.69 | (1193) all_809_0 = all_697_0 % 231.72/34.69 | % 231.72/34.69 | SIMP: (1193) implies: % 231.72/34.70 | (1194) all_809_0 = all_697_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1040), (1179) imply: % 231.72/34.70 | (1195) all_1673_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1195) implies: % 231.72/34.70 | (1196) all_1673_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1038), (1039) imply: % 231.72/34.70 | (1197) all_1658_1 = all_1625_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1197) implies: % 231.72/34.70 | (1198) all_1658_1 = all_1625_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1036), (1037) imply: % 231.72/34.70 | (1199) all_1207_1 = all_791_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1199) implies: % 231.72/34.70 | (1200) all_1207_1 = all_791_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1035), (1177) imply: % 231.72/34.70 | (1201) all_1521_0 = all_1263_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1201) implies: % 231.72/34.70 | (1202) all_1521_0 = all_1263_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1133), (1134) imply: % 231.72/34.70 | (1203) all_1527_0 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1203) implies: % 231.72/34.70 | (1204) all_1527_0 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1033), (1034) imply: % 231.72/34.70 | (1205) all_1550_1 = all_813_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1205) implies: % 231.72/34.70 | (1206) all_1550_1 = all_813_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1030), (1031) imply: % 231.72/34.70 | (1207) all_1354_1 = all_1328_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1207) implies: % 231.72/34.70 | (1208) all_1354_1 = all_1328_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1031), (1032) imply: % 231.72/34.70 | (1209) all_1328_1 = all_1311_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1095), (1097) imply: % 231.72/34.70 | (1210) all_1655_2 = all_1132_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1095), (1096) imply: % 231.72/34.70 | (1211) all_1655_2 = all_1224_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (936), (937) imply: % 231.72/34.70 | (1212) all_1655_3 = all_1357_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1212) implies: % 231.72/34.70 | (1213) all_1655_3 = all_1357_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1156), (1157) imply: % 231.72/34.70 | (1214) all_1468_1 = all_1394_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1214) implies: % 231.72/34.70 | (1215) all_1468_1 = all_1394_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1157), (1158) imply: % 231.72/34.70 | (1216) all_1394_0 = all_1374_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1157), (1159) imply: % 231.72/34.70 | (1217) all_1394_0 = all_975_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1168), (1169) imply: % 231.72/34.70 | (1218) all_1515_0 = all_788_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1218) implies: % 231.72/34.70 | (1219) all_1515_0 = all_788_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1167), (1168) imply: % 231.72/34.70 | (1220) all_788_0 = all_783_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1092), (1093) imply: % 231.72/34.70 | (1221) all_1607_0 = all_1605_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1221) implies: % 231.72/34.70 | (1222) all_1607_0 = all_1605_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1093), (1094) imply: % 231.72/34.70 | (1223) all_1605_0 = all_1600_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (935), (1175) imply: % 231.72/34.70 | (1224) all_1664_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1224) implies: % 231.72/34.70 | (1225) all_1664_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1090), (1091) imply: % 231.72/34.70 | (1226) all_1670_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1226) implies: % 231.72/34.70 | (1227) all_1670_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (933), (934) imply: % 231.72/34.70 | (1228) all_1483_2 = all_1320_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1228) implies: % 231.72/34.70 | (1229) all_1483_2 = all_1320_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1029), (1196) imply: % 231.72/34.70 | (1230) all_1631_1 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1230) implies: % 231.72/34.70 | (1231) all_1631_1 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1089), (1227) imply: % 231.72/34.70 | (1232) all_1667_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1232) implies: % 231.72/34.70 | (1233) all_1667_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (931), (932) imply: % 231.72/34.70 | (1234) all_1582_1 = all_1192_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1234) implies: % 231.72/34.70 | (1235) all_1582_1 = all_1192_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1088), (1233) imply: % 231.72/34.70 | (1236) all_1664_1 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1236) implies: % 231.72/34.70 | (1237) all_1664_1 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (929), (930) imply: % 231.72/34.70 | (1238) all_1500_0 = all_1138_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1238) implies: % 231.72/34.70 | (1239) all_1500_0 = all_1138_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (928), (1225) imply: % 231.72/34.70 | (1240) all_1634_1 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1240) implies: % 231.72/34.70 | (1241) all_1634_1 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1087), (1237) imply: % 231.72/34.70 | (1242) all_1634_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1242) implies: % 231.72/34.70 | (1243) all_1634_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (925), (926) imply: % 231.72/34.70 | (1244) all_1314_2 = all_1147_4 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1244) implies: % 231.72/34.70 | (1245) all_1314_2 = all_1147_4 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (926), (927) imply: % 231.72/34.70 | (1246) all_1147_4 = all_1141_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1028), (1198) imply: % 231.72/34.70 | (1247) all_1625_1 = all_1597_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1164), (1198) imply: % 231.72/34.70 | (1248) all_1625_1 = all_1388_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1130), (1132) imply: % 231.72/34.70 | (1249) all_1559_7 = all_781_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1130), (1131) imply: % 231.72/34.70 | (1250) all_1559_7 = all_949_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1210), (1211) imply: % 231.72/34.70 | (1251) all_1224_0 = all_1132_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1251) implies: % 231.72/34.70 | (1252) all_1224_0 = all_1132_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (924), (1213) imply: % 231.72/34.70 | (1253) all_1420_0 = all_1357_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1253) implies: % 231.72/34.70 | (1254) all_1420_0 = all_1357_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1155), (1190) imply: % 231.72/34.70 | (1255) all_1637_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1255) implies: % 231.72/34.70 | (1256) all_1637_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1027), (1166) imply: % 231.72/34.70 | (1257) all_1506_0 = all_943_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1257) implies: % 231.72/34.70 | (1258) all_1506_0 = all_943_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1025), (1026) imply: % 231.72/34.70 | (1259) all_1622_1 = all_705_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1259) implies: % 231.72/34.70 | (1260) all_1622_1 = all_705_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1154), (1256) imply: % 231.72/34.70 | (1261) all_1628_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1261) implies: % 231.72/34.70 | (1262) all_1628_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1022), (1023) imply: % 231.72/34.70 | (1263) all_1204_0 = all_919_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1263) implies: % 231.72/34.70 | (1264) all_1204_0 = all_919_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1023), (1024) imply: % 231.72/34.70 | (1265) all_919_1 = all_896_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1086), (1243) imply: % 231.72/34.70 | (1266) all_1619_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1266) implies: % 231.72/34.70 | (1267) all_1619_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (923), (1241) imply: % 231.72/34.70 | (1268) all_1602_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1268) implies: % 231.72/34.70 | (1269) all_1602_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1021), (1231) imply: % 231.72/34.70 | (1270) all_1591_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1270) implies: % 231.72/34.70 | (1271) all_1591_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1153), (1262) imply: % 231.72/34.70 | (1272) all_1503_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1272) implies: % 231.72/34.70 | (1273) all_1503_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1018), (1019) imply: % 231.72/34.70 | (1274) all_1163_0 = all_1135_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1274) implies: % 231.72/34.70 | (1275) all_1163_0 = all_1135_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1019), (1020) imply: % 231.72/34.70 | (1276) all_1135_1 = all_1114_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1247), (1248) imply: % 231.72/34.70 | (1277) all_1597_0 = all_1388_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1277) implies: % 231.72/34.70 | (1278) all_1597_0 = all_1388_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1017), (1260) imply: % 231.72/34.70 | (1279) all_1573_2 = all_705_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1279) implies: % 231.72/34.70 | (1280) all_1573_2 = all_705_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1085), (1267) imply: % 231.72/34.70 | (1281) all_1613_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1281) implies: % 231.72/34.70 | (1282) all_1613_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1180), (1181) imply: % 231.72/34.70 | (1283) all_1559_8 = all_987_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1283) implies: % 231.72/34.70 | (1284) all_1559_8 = all_987_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1084), (1282) imply: % 231.72/34.70 | (1285) all_1607_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1285) implies: % 231.72/34.70 | (1286) all_1607_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1016), (1188) imply: % 231.72/34.70 | (1287) all_1535_0 = all_733_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1287) implies: % 231.72/34.70 | (1288) all_1535_0 = all_733_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1222), (1286) imply: % 231.72/34.70 | (1289) all_1605_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1289) implies: % 231.72/34.70 | (1290) all_1605_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1223), (1290) imply: % 231.72/34.70 | (1291) all_1600_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1291) implies: % 231.72/34.70 | (1292) all_1600_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (921), (922) imply: % 231.72/34.70 | (1293) all_1585_1 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1293) implies: % 231.72/34.70 | (1294) all_1585_1 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (920), (1269) imply: % 231.72/34.70 | (1295) all_1594_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1295) implies: % 231.72/34.70 | (1296) all_1594_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1083), (1292) imply: % 231.72/34.70 | (1297) all_1585_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1297) implies: % 231.72/34.70 | (1298) all_1585_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (917), (918) imply: % 231.72/34.70 | (1299) all_1585_1 = all_1573_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1299) implies: % 231.72/34.70 | (1300) all_1585_1 = all_1573_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (918), (919) imply: % 231.72/34.70 | (1301) all_1573_1 = all_1497_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1183), (1278) imply: % 231.72/34.70 | (1302) all_1576_1 = all_1388_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1302) implies: % 231.72/34.70 | (1303) all_1576_1 = all_1388_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1015), (1278) imply: % 231.72/34.70 | (1304) all_1388_2 = all_1379_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (916), (1296) imply: % 231.72/34.70 | (1305) all_1538_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1305) implies: % 231.72/34.70 | (1306) all_1538_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1014), (1271) imply: % 231.72/34.70 | (1307) all_1588_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1307) implies: % 231.72/34.70 | (1308) all_1588_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1013), (1308) imply: % 231.72/34.70 | (1309) all_1579_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1309) implies: % 231.72/34.70 | (1310) all_1579_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1082), (1298) imply: % 231.72/34.70 | (1311) all_1559_4 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1311) implies: % 231.72/34.70 | (1312) all_1559_4 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1294), (1300) imply: % 231.72/34.70 | (1313) all_1573_1 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1313) implies: % 231.72/34.70 | (1314) all_1573_1 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1080), (1081) imply: % 231.72/34.70 | (1315) all_1423_0 = all_1408_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1315) implies: % 231.72/34.70 | (1316) all_1423_0 = all_1408_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1079), (1081) imply: % 231.72/34.70 | (1317) all_1541_0 = all_1408_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1317) implies: % 231.72/34.70 | (1318) all_1541_0 = all_1408_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (915), (1235) imply: % 231.72/34.70 | (1319) all_1215_0 = all_1192_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1319) implies: % 231.72/34.70 | (1320) all_1215_0 = all_1192_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (914), (1235) imply: % 231.72/34.70 | (1321) all_1314_2 = all_1192_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1321) implies: % 231.72/34.70 | (1322) all_1314_2 = all_1192_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1012), (1310) imply: % 231.72/34.70 | (1323) all_1547_3 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1323) implies: % 231.72/34.70 | (1324) all_1547_3 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1184), (1303) imply: % 231.72/34.70 | (1325) all_1388_2 = all_822_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1325) implies: % 231.72/34.70 | (1326) all_1388_2 = all_822_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1301), (1314) imply: % 231.72/34.70 | (1327) all_1497_2 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1327) implies: % 231.72/34.70 | (1328) all_1497_2 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1011), (1280) imply: % 231.72/34.70 | (1329) all_809_0 = all_705_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1329) implies: % 231.72/34.70 | (1330) all_809_0 = all_705_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1078), (1312) imply: % 231.72/34.70 | (1331) all_1556_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1331) implies: % 231.72/34.70 | (1332) all_1556_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1249), (1250) imply: % 231.72/34.70 | (1333) all_949_0 = all_781_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1333) implies: % 231.72/34.70 | (1334) all_949_0 = all_781_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (913), (1284) imply: % 231.72/34.70 | (1335) all_1556_2 = all_987_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1335) implies: % 231.72/34.70 | (1336) all_1556_2 = all_987_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1077), (1332) imply: % 231.72/34.70 | (1337) all_1533_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1337) implies: % 231.72/34.70 | (1338) all_1533_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (912), (1336) imply: % 231.72/34.70 | (1339) all_1388_1 = all_987_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1339) implies: % 231.72/34.70 | (1340) all_1388_1 = all_987_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1010), (1206) imply: % 231.72/34.70 | (1341) all_1515_0 = all_813_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1341) implies: % 231.72/34.70 | (1342) all_1515_0 = all_813_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1009), (1324) imply: % 231.72/34.70 | (1343) all_1486_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1343) implies: % 231.72/34.70 | (1344) all_1486_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1075), (1318) imply: % 231.72/34.70 | (1345) all_1408_0 = all_1391_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1345) implies: % 231.72/34.70 | (1346) all_1408_0 = all_1391_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1075), (1076) imply: % 231.72/34.70 | (1347) all_1391_0 = all_1372_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (911), (1306) imply: % 231.72/34.70 | (1348) all_1242_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1348) implies: % 231.72/34.70 | (1349) all_1242_0 = all_803_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1008), (1288) imply: % 231.72/34.70 | (1350) all_1503_1 = all_733_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1350) implies: % 231.72/34.70 | (1351) all_1503_1 = all_733_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1074), (1338) imply: % 231.72/34.70 | (1352) all_1524_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1352) implies: % 231.72/34.70 | (1353) all_1524_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1129), (1204) imply: % 231.72/34.70 | (1354) all_1509_0 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1354) implies: % 231.72/34.70 | (1355) all_1509_0 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1073), (1353) imply: % 231.72/34.70 | (1356) all_1459_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1356) implies: % 231.72/34.70 | (1357) all_1459_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1007), (1202) imply: % 231.72/34.70 | (1358) all_1489_0 = all_1263_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1358) implies: % 231.72/34.70 | (1359) all_1489_0 = all_1263_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1006), (1342) imply: % 231.72/34.70 | (1360) all_833_0 = all_813_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1360) implies: % 231.72/34.70 | (1361) all_833_0 = all_813_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1219), (1342) imply: % 231.72/34.70 | (1362) all_813_0 = all_788_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1128), (1355) imply: % 231.72/34.70 | (1363) all_1497_1 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1363) implies: % 231.72/34.70 | (1364) all_1497_1 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1005), (1258) imply: % 231.72/34.70 | (1365) all_1465_0 = all_943_1 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1365) implies: % 231.72/34.70 | (1366) all_1465_0 = all_943_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1152), (1273) imply: % 231.72/34.70 | (1367) all_1480_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1367) implies: % 231.72/34.70 | (1368) all_1480_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1004), (1351) imply: % 231.72/34.70 | (1369) all_1382_0 = all_733_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1369) implies: % 231.72/34.70 | (1370) all_1382_0 = all_733_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (910), (1239) imply: % 231.72/34.70 | (1371) all_1138_0 = all_1015_1 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (909), (1239) imply: % 231.72/34.70 | (1372) all_1459_1 = all_1138_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1372) implies: % 231.72/34.70 | (1373) all_1459_1 = all_1138_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1127), (1364) imply: % 231.72/34.70 | (1374) all_1483_1 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1374) implies: % 231.72/34.70 | (1375) all_1483_1 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (908), (1328) imply: % 231.72/34.70 | (1376) all_1459_1 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1376) implies: % 231.72/34.70 | (1377) all_1459_1 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1003), (1359) imply: % 231.72/34.70 | (1378) all_1263_2 = all_1251_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1002), (1359) imply: % 231.72/34.70 | (1379) all_1266_2 = all_1263_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1379) implies: % 231.72/34.70 | (1380) all_1266_2 = all_1263_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1001), (1344) imply: % 231.72/34.70 | (1381) all_849_0 = all_833_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1000), (1344) imply: % 231.72/34.70 | (1382) all_879_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1382) implies: % 231.72/34.70 | (1383) all_879_0 = all_849_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1126), (1375) imply: % 231.72/34.70 | (1384) all_1432_0 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1384) implies: % 231.72/34.70 | (1385) all_1432_0 = all_1042_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (907), (1229) imply: % 231.72/34.70 | (1386) all_1453_0 = all_1320_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1386) implies: % 231.72/34.70 | (1387) all_1453_0 = all_1320_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1151), (1368) imply: % 231.72/34.70 | (1388) all_1468_1 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1388) implies: % 231.72/34.70 | (1389) all_1468_1 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1215), (1389) imply: % 231.72/34.70 | (1390) all_1394_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1390) implies: % 231.72/34.70 | (1391) all_1394_0 = all_1379_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (999), (1366) imply: % 231.72/34.70 | (1392) all_943_1 = all_718_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (998), (1366) imply: % 231.72/34.70 | (1393) all_943_1 = all_833_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1072), (1357) imply: % 231.72/34.70 | (1394) all_1456_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1394) implies: % 231.72/34.70 | (1395) all_1456_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1373), (1377) imply: % 231.72/34.70 | (1396) all_1138_0 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1396) implies: % 231.72/34.70 | (1397) all_1138_0 = all_830_0 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1071), (1395) imply: % 231.72/34.70 | (1398) all_1441_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1398) implies: % 231.72/34.70 | (1399) all_1441_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (906), (1387) imply: % 231.72/34.70 | (1400) all_1444_0 = all_1320_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1400) implies: % 231.72/34.70 | (1401) all_1444_0 = all_1320_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (905), (1401) imply: % 231.72/34.70 | (1402) all_1435_0 = all_1320_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1402) implies: % 231.72/34.70 | (1403) all_1435_0 = all_1320_2 % 231.72/34.70 | % 231.72/34.70 | COMBINE_EQS: (1070), (1399) imply: % 231.72/34.70 | (1404) all_1423_0 = all_1006_2 % 231.72/34.70 | % 231.72/34.70 | SIMP: (1404) implies: % 231.72/34.71 | (1405) all_1423_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (904), (1403) imply: % 231.72/34.71 | (1406) all_1432_1 = all_1320_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1406) implies: % 231.72/34.71 | (1407) all_1432_1 = all_1320_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1125), (1385) imply: % 231.72/34.71 | (1408) all_1374_1 = all_1042_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1408) implies: % 231.72/34.71 | (1409) all_1374_1 = all_1042_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (903), (1407) imply: % 231.72/34.71 | (1410) all_1394_1 = all_1320_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1410) implies: % 231.72/34.71 | (1411) all_1394_1 = all_1320_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (900), (901) imply: % 231.72/34.71 | (1412) all_1269_0 = all_1260_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1412) implies: % 231.72/34.71 | (1413) all_1269_0 = all_1260_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (901), (902) imply: % 231.72/34.71 | (1414) all_1260_0 = all_1230_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1316), (1405) imply: % 231.72/34.71 | (1415) all_1408_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1415) implies: % 231.72/34.71 | (1416) all_1408_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (898), (899) imply: % 231.72/34.71 | (1417) all_1411_0 = all_757_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1417) implies: % 231.72/34.71 | (1418) all_1411_0 = all_757_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (897), (1254) imply: % 231.72/34.71 | (1419) all_1357_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (896), (1254) imply: % 231.72/34.71 | (1420) all_1357_1 = all_1345_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (895), (1418) imply: % 231.72/34.71 | (1421) all_1169_1 = all_757_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1421) implies: % 231.72/34.71 | (1422) all_1169_1 = all_757_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1346), (1416) imply: % 231.72/34.71 | (1423) all_1391_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1423) implies: % 231.72/34.71 | (1424) all_1391_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1216), (1391) imply: % 231.72/34.71 | (1425) all_1379_0 = all_1374_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1217), (1391) imply: % 231.72/34.71 | (1426) all_1379_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (894), (1411) imply: % 231.72/34.71 | (1427) all_1372_1 = all_1320_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1427) implies: % 231.72/34.71 | (1428) all_1372_1 = all_1320_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1347), (1424) imply: % 231.72/34.71 | (1429) all_1372_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1429) implies: % 231.72/34.71 | (1430) all_1372_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (893), (1340) imply: % 231.72/34.71 | (1431) all_1372_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1431) implies: % 231.72/34.71 | (1432) all_1372_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1304), (1326) imply: % 231.72/34.71 | (1433) all_1379_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1433) implies: % 231.72/34.71 | (1434) all_1379_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (997), (1370) imply: % 231.72/34.71 | (1435) all_1060_0 = all_733_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1435) implies: % 231.72/34.71 | (1436) all_1060_0 = all_733_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1425), (1426) imply: % 231.72/34.71 | (1437) all_1374_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1437) implies: % 231.72/34.71 | (1438) all_1374_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (996), (1434) imply: % 231.72/34.71 | (1439) all_1354_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1439) implies: % 231.72/34.71 | (1440) all_1354_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1150), (1438) imply: % 231.72/34.71 | (1441) all_1320_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1441) implies: % 231.72/34.71 | (1442) all_1320_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1124), (1409) imply: % 231.72/34.71 | (1443) all_1042_0 = all_1036_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1123), (1409) imply: % 231.72/34.71 | (1444) all_1108_0 = all_1042_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1444) implies: % 231.72/34.71 | (1445) all_1108_0 = all_1042_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1069), (1430) imply: % 231.72/34.71 | (1446) all_1317_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1446) implies: % 231.72/34.71 | (1447) all_1317_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (892), (1428) imply: % 231.72/34.71 | (1448) all_1320_2 = all_1236_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1428), (1432) imply: % 231.72/34.71 | (1449) all_1320_2 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1121), (1122) imply: % 231.72/34.71 | (1450) all_1345_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1450) implies: % 231.72/34.71 | (1451) all_1345_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1419), (1420) imply: % 231.72/34.71 | (1452) all_1345_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1452) implies: % 231.72/34.71 | (1453) all_1345_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1208), (1440) imply: % 231.72/34.71 | (1454) all_1328_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1454) implies: % 231.72/34.71 | (1455) all_1328_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1120), (1451) imply: % 231.72/34.71 | (1456) all_1337_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1456) implies: % 231.72/34.71 | (1457) all_1337_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (891), (1453) imply: % 231.72/34.71 | (1458) all_1342_2 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1458) implies: % 231.72/34.71 | (1459) all_1342_2 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (890), (1459) imply: % 231.72/34.71 | (1460) all_1337_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1460) implies: % 231.72/34.71 | (1461) all_1337_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1119), (1457) imply: % 231.72/34.71 | (1462) all_1320_1 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1462) implies: % 231.72/34.71 | (1463) all_1320_1 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (889), (1461) imply: % 231.72/34.71 | (1464) all_1317_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1464) implies: % 231.72/34.71 | (1465) all_1317_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1209), (1455) imply: % 231.72/34.71 | (1466) all_1311_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1466) implies: % 231.72/34.71 | (1467) all_1311_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1149), (1442) imply: % 231.72/34.71 | (1468) all_1314_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1468) implies: % 231.72/34.71 | (1469) all_1314_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1118), (1463) imply: % 231.72/34.71 | (1470) all_1314_1 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1470) implies: % 231.72/34.71 | (1471) all_1314_1 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1448), (1449) imply: % 231.72/34.71 | (1472) all_1236_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1472) implies: % 231.72/34.71 | (1473) all_1236_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1068), (1447) imply: % 231.72/34.71 | (1474) all_1286_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1474) implies: % 231.72/34.71 | (1475) all_1286_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (888), (1465) imply: % 231.72/34.71 | (1476) all_1306_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1476) implies: % 231.72/34.71 | (1477) all_1306_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1148), (1469) imply: % 231.72/34.71 | (1478) all_1227_1 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1478) implies: % 231.72/34.71 | (1479) all_1227_1 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1117), (1471) imply: % 231.72/34.71 | (1480) all_1227_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1480) implies: % 231.72/34.71 | (1481) all_1227_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1173), (1245) imply: % 231.72/34.71 | (1482) all_1189_0 = all_1147_4 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1173), (1322) imply: % 231.72/34.71 | (1483) all_1192_0 = all_1189_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1483) implies: % 231.72/34.71 | (1484) all_1192_0 = all_1189_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (995), (1467) imply: % 231.72/34.71 | (1485) all_1272_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1485) implies: % 231.72/34.71 | (1486) all_1272_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (887), (1477) imply: % 231.72/34.71 | (1487) all_1286_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1487) implies: % 231.72/34.71 | (1488) all_1286_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1067), (1475) imply: % 231.72/34.71 | (1489) all_1230_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1489) implies: % 231.72/34.71 | (1490) all_1230_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (886), (1488) imply: % 231.72/34.71 | (1491) all_1275_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1491) implies: % 231.72/34.71 | (1492) all_1275_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (885), (1492) imply: % 231.72/34.71 | (1493) all_1269_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1493) implies: % 231.72/34.71 | (1494) all_1269_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (994), (1486) imply: % 231.72/34.71 | (1495) all_1266_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1495) implies: % 231.72/34.71 | (1496) all_1266_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1413), (1494) imply: % 231.72/34.71 | (1497) all_1260_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1497) implies: % 231.72/34.71 | (1498) all_1260_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1380), (1496) imply: % 231.72/34.71 | (1499) all_1263_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1499) implies: % 231.72/34.71 | (1500) all_1263_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1378), (1500) imply: % 231.72/34.71 | (1501) all_1251_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1501) implies: % 231.72/34.71 | (1502) all_1251_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1414), (1498) imply: % 231.72/34.71 | (1503) all_1230_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1503) implies: % 231.72/34.71 | (1504) all_1230_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (993), (1502) imply: % 231.72/34.71 | (1505) all_1233_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1505) implies: % 231.72/34.71 | (1506) all_1233_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (884), (1349) imply: % 231.72/34.71 | (1507) all_1036_1 = all_803_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1507) implies: % 231.72/34.71 | (1508) all_1036_1 = all_803_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (883), (1473) imply: % 231.72/34.71 | (1509) all_1212_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1509) implies: % 231.72/34.71 | (1510) all_1212_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (992), (1506) imply: % 231.72/34.71 | (1511) all_1221_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1511) implies: % 231.72/34.71 | (1512) all_1221_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1066), (1490) imply: % 231.72/34.71 | (1513) all_1169_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1513) implies: % 231.72/34.71 | (1514) all_1169_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (882), (1504) imply: % 231.72/34.71 | (1515) all_1215_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1515) implies: % 231.72/34.71 | (1516) all_1215_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1116), (1481) imply: % 231.72/34.71 | (1517) all_1198_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1517) implies: % 231.72/34.71 | (1518) all_1198_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1147), (1479) imply: % 231.72/34.71 | (1519) all_1198_1 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1519) implies: % 231.72/34.71 | (1520) all_1198_1 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1064), (1252) imply: % 231.72/34.71 | (1521) all_1147_3 = all_1132_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1521) implies: % 231.72/34.71 | (1522) all_1147_3 = all_1132_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1065), (1252) imply: % 231.72/34.71 | (1523) all_1132_0 = all_1117_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (880), (881) imply: % 231.72/34.71 | (1524) all_1036_1 = all_949_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1524) implies: % 231.72/34.71 | (1525) all_1036_1 = all_949_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (991), (1512) imply: % 231.72/34.71 | (1526) all_1218_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1526) implies: % 231.72/34.71 | (1527) all_1218_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (990), (1527) imply: % 231.72/34.71 | (1528) all_1195_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1528) implies: % 231.72/34.71 | (1529) all_1195_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1320), (1516) imply: % 231.72/34.71 | (1530) all_1192_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1530) implies: % 231.72/34.71 | (1531) all_1192_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (879), (1510) imply: % 231.72/34.71 | (1532) all_1204_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1532) implies: % 231.72/34.71 | (1533) all_1204_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (989), (1200) imply: % 231.72/34.71 | (1534) all_856_2 = all_791_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1534) implies: % 231.72/34.71 | (1535) all_856_2 = all_791_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (987), (988) imply: % 231.72/34.71 | (1536) all_946_0 = all_922_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1536) implies: % 231.72/34.71 | (1537) all_946_0 = all_922_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (988), (1264) imply: % 231.72/34.71 | (1538) all_922_0 = all_919_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (878), (1533) imply: % 231.72/34.71 | (1539) all_1155_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1539) implies: % 231.72/34.71 | (1540) all_1155_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1115), (1518) imply: % 231.72/34.71 | (1541) all_1141_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1541) implies: % 231.72/34.71 | (1542) all_1141_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1146), (1520) imply: % 231.72/34.71 | (1543) all_1102_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1543) implies: % 231.72/34.71 | (1544) all_1102_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (986), (1529) imply: % 231.72/34.71 | (1545) all_1186_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1545) implies: % 231.72/34.71 | (1546) all_1186_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1484), (1531) imply: % 231.72/34.71 | (1547) all_1189_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1547) implies: % 231.72/34.71 | (1548) all_1189_0 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1482), (1548) imply: % 231.72/34.71 | (1549) all_1147_4 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1549) implies: % 231.72/34.71 | (1550) all_1147_4 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (985), (1546) imply: % 231.72/34.71 | (1551) all_1163_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1551) implies: % 231.72/34.71 | (1552) all_1163_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1063), (1514) imply: % 231.72/34.71 | (1553) all_1147_3 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1553) implies: % 231.72/34.71 | (1554) all_1147_3 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (877), (1422) imply: % 231.72/34.71 | (1555) all_783_1 = all_757_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1555) implies: % 231.72/34.71 | (1556) all_783_1 = all_757_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (983), (1192) imply: % 231.72/34.71 | (1557) all_1114_0 = all_1111_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1557) implies: % 231.72/34.71 | (1558) all_1114_0 = all_1111_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (984), (1192) imply: % 231.72/34.71 | (1559) all_1111_1 = all_1105_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1275), (1552) imply: % 231.72/34.71 | (1560) all_1135_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1560) implies: % 231.72/34.71 | (1561) all_1135_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (876), (1540) imply: % 231.72/34.71 | (1562) all_1132_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1562) implies: % 231.72/34.71 | (1563) all_1132_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1522), (1554) imply: % 231.72/34.71 | (1564) all_1132_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1564) implies: % 231.72/34.71 | (1565) all_1132_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1246), (1550) imply: % 231.72/34.71 | (1566) all_1141_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1566) implies: % 231.72/34.71 | (1567) all_1141_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1114), (1542) imply: % 231.72/34.71 | (1568) all_1108_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1568) implies: % 231.72/34.71 | (1569) all_1108_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (875), (1567) imply: % 231.72/34.71 | (1570) all_1042_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1570) implies: % 231.72/34.71 | (1571) all_1042_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1371), (1397) imply: % 231.72/34.71 | (1572) all_1015_1 = all_830_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1572) implies: % 231.72/34.71 | (1573) all_1015_1 = all_830_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1276), (1561) imply: % 231.72/34.71 | (1574) all_1114_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1574) implies: % 231.72/34.71 | (1575) all_1114_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1523), (1565) imply: % 231.72/34.71 | (1576) all_1117_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1576) implies: % 231.72/34.71 | (1577) all_1117_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (874), (1563) imply: % 231.72/34.71 | (1578) all_1120_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1578) implies: % 231.72/34.71 | (1579) all_1120_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (873), (1579) imply: % 231.72/34.71 | (1580) all_1096_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1580) implies: % 231.72/34.71 | (1581) all_1096_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1062), (1577) imply: % 231.72/34.71 | (1582) all_1039_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1582) implies: % 231.72/34.71 | (1583) all_1039_0 = all_1006_2 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1558), (1575) imply: % 231.72/34.71 | (1584) all_1111_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1584) implies: % 231.72/34.71 | (1585) all_1111_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1559), (1585) imply: % 231.72/34.71 | (1586) all_1105_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1586) implies: % 231.72/34.71 | (1587) all_1105_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1445), (1569) imply: % 231.72/34.71 | (1588) all_1042_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1588) implies: % 231.72/34.71 | (1589) all_1042_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (982), (1587) imply: % 231.72/34.71 | (1590) all_1099_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1590) implies: % 231.72/34.71 | (1591) all_1099_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1145), (1544) imply: % 231.72/34.71 | (1592) all_1093_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1592) implies: % 231.72/34.71 | (1593) all_1093_0 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (981), (1591) imply: % 231.72/34.71 | (1594) all_1096_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1594) implies: % 231.72/34.71 | (1595) all_1096_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (980), (1595) imply: % 231.72/34.71 | (1596) all_1084_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1596) implies: % 231.72/34.71 | (1597) all_1084_2 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (872), (1581) imply: % 231.72/34.71 | (1598) all_1033_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1598) implies: % 231.72/34.71 | (1599) all_1033_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1144), (1593) imply: % 231.72/34.71 | (1600) all_1063_1 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1600) implies: % 231.72/34.71 | (1601) all_1063_1 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (979), (1597) imply: % 231.72/34.71 | (1602) all_1063_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1602) implies: % 231.72/34.71 | (1603) all_1063_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (978), (1603) imply: % 231.72/34.71 | (1604) all_1045_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1604) implies: % 231.72/34.71 | (1605) all_1045_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1143), (1601) imply: % 231.72/34.71 | (1606) all_1003_1 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1606) implies: % 231.72/34.71 | (1607) all_1003_1 = all_975_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (977), (1436) imply: % 231.72/34.71 | (1608) all_967_1 = all_733_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1608) implies: % 231.72/34.71 | (1609) all_967_1 = all_733_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (976), (1605) imply: % 231.72/34.71 | (1610) all_1024_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1610) implies: % 231.72/34.71 | (1611) all_1024_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1443), (1589) imply: % 231.72/34.71 | (1612) all_1036_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1612) implies: % 231.72/34.71 | (1613) all_1036_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (871), (1571) imply: % 231.72/34.71 | (1614) all_1027_1 = all_1021_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (870), (1571) imply: % 231.72/34.71 | (1615) all_1033_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1615) implies: % 231.72/34.71 | (1616) all_1033_1 = all_1027_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1113), (1613) imply: % 231.72/34.71 | (1617) all_1033_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1617) implies: % 231.72/34.71 | (1618) all_1033_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (869), (1525) imply: % 231.72/34.71 | (1619) all_949_1 = all_905_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1508), (1525) imply: % 231.72/34.71 | (1620) all_949_1 = all_803_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1112), (1618) imply: % 231.72/34.71 | (1621) all_1030_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1621) implies: % 231.72/34.71 | (1622) all_1030_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1599), (1616) imply: % 231.72/34.71 | (1623) all_1027_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1623) implies: % 231.72/34.71 | (1624) all_1027_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1111), (1622) imply: % 231.72/34.71 | (1625) all_1027_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1625) implies: % 231.72/34.71 | (1626) all_1027_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1110), (1626) imply: % 231.72/34.71 | (1627) all_1015_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1627) implies: % 231.72/34.71 | (1628) all_1015_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1614), (1624) imply: % 231.72/34.71 | (1629) all_1021_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1629) implies: % 231.72/34.71 | (1630) all_1021_0 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (975), (1611) imply: % 231.72/34.71 | (1631) all_1018_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1631) implies: % 231.72/34.71 | (1632) all_1018_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (868), (1630) imply: % 231.72/34.71 | (1633) all_1000_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1633) implies: % 231.72/34.71 | (1634) all_1000_1 = all_987_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (974), (1632) imply: % 231.72/34.71 | (1635) all_1000_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1635) implies: % 231.72/34.71 | (1636) all_1000_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1109), (1628) imply: % 231.72/34.71 | (1637) all_1009_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1637) implies: % 231.72/34.71 | (1638) all_1009_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (867), (1573) imply: % 231.72/34.71 | (1639) all_997_0 = all_830_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1639) implies: % 231.72/34.71 | (1640) all_997_0 = all_830_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1108), (1638) imply: % 231.72/34.71 | (1641) all_1006_1 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1641) implies: % 231.72/34.71 | (1642) all_1006_1 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1107), (1642) imply: % 231.72/34.71 | (1643) all_991_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1643) implies: % 231.72/34.71 | (1644) all_991_0 = all_940_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1142), (1607) imply: % 231.72/34.71 | (1645) all_975_0 = all_839_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1141), (1607) imply: % 231.72/34.71 | (1646) all_975_0 = all_842_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (973), (1636) imply: % 231.72/34.71 | (1647) all_994_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1647) implies: % 231.72/34.71 | (1648) all_994_1 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (865), (1634) imply: % 231.72/34.71 | (1649) all_987_0 = all_922_1 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (866), (1634) imply: % 231.72/34.71 | (1650) all_987_0 = all_781_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (864), (1640) imply: % 231.72/34.71 | (1651) all_946_1 = all_830_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1651) implies: % 231.72/34.71 | (1652) all_946_1 = all_830_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (972), (1648) imply: % 231.72/34.71 | (1653) all_961_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | SIMP: (1653) implies: % 231.72/34.71 | (1654) all_961_0 = all_822_0 % 231.72/34.71 | % 231.72/34.71 | COMBINE_EQS: (1106), (1644) imply: % 231.72/34.72 | (1655) all_987_1 = all_940_1 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1655) implies: % 231.72/34.72 | (1656) all_987_1 = all_940_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1649), (1650) imply: % 231.72/34.72 | (1657) all_922_1 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1657) implies: % 231.72/34.72 | (1658) all_922_1 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1105), (1656) imply: % 231.72/34.72 | (1659) all_949_0 = all_940_1 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1659) implies: % 231.72/34.72 | (1660) all_949_0 = all_940_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (861), (863) imply: % 231.72/34.72 | (1661) all_905_0 = all_809_1 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1661) implies: % 231.72/34.72 | (1662) all_905_0 = all_809_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (862), (863) imply: % 231.72/34.72 | (1663) all_890_0 = all_809_1 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1663) implies: % 231.72/34.72 | (1664) all_890_0 = all_809_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1645), (1646) imply: % 231.72/34.72 | (1665) all_842_0 = all_839_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1665) implies: % 231.72/34.72 | (1666) all_842_0 = all_839_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1139), (1140) imply: % 231.72/34.72 | (1667) all_871_0 = all_842_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1138), (1139) imply: % 231.72/34.72 | (1668) all_943_0 = all_871_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1668) implies: % 231.72/34.72 | (1669) all_943_0 = all_871_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (971), (1609) imply: % 231.72/34.72 | (1670) all_937_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1670) implies: % 231.72/34.72 | (1671) all_937_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (970), (1654) imply: % 231.72/34.72 | (1672) all_946_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1672) implies: % 231.72/34.72 | (1673) all_946_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1334), (1660) imply: % 231.72/34.72 | (1674) all_940_1 = all_781_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1104), (1660) imply: % 231.72/34.72 | (1675) all_940_1 = all_865_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1619), (1620) imply: % 231.72/34.72 | (1676) all_905_0 = all_803_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1676) implies: % 231.72/34.72 | (1677) all_905_0 = all_803_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1537), (1673) imply: % 231.72/34.72 | (1678) all_922_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1678) implies: % 231.72/34.72 | (1679) all_922_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (860), (1652) imply: % 231.72/34.72 | (1680) all_940_0 = all_830_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1680) implies: % 231.72/34.72 | (1681) all_940_0 = all_830_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1137), (1669) imply: % 231.72/34.72 | (1682) all_871_0 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1682) implies: % 231.72/34.72 | (1683) all_871_0 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1392), (1393) imply: % 231.72/34.72 | (1684) all_833_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1684) implies: % 231.72/34.72 | (1685) all_833_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (859), (1681) imply: % 231.72/34.72 | (1686) all_911_0 = all_830_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1686) implies: % 231.72/34.72 | (1687) all_911_0 = all_830_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1674), (1675) imply: % 231.72/34.72 | (1688) all_865_0 = all_781_1 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1688) implies: % 231.72/34.72 | (1689) all_865_0 = all_781_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (968), (969) imply: % 231.72/34.72 | (1690) all_931_1 = all_893_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (968), (1671) imply: % 231.72/34.72 | (1691) all_931_1 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1690), (1691) imply: % 231.72/34.72 | (1692) all_893_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1692) implies: % 231.72/34.72 | (1693) all_893_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1538), (1679) imply: % 231.72/34.72 | (1694) all_919_1 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1694) implies: % 231.72/34.72 | (1695) all_919_1 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (858), (1658) imply: % 231.72/34.72 | (1696) all_902_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1696) implies: % 231.72/34.72 | (1697) all_902_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1265), (1695) imply: % 231.72/34.72 | (1698) all_896_1 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1698) implies: % 231.72/34.72 | (1699) all_896_1 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (857), (1687) imply: % 231.72/34.72 | (1700) all_890_0 = all_830_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1700) implies: % 231.72/34.72 | (1701) all_890_0 = all_830_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (856), (1677) imply: % 231.72/34.72 | (1702) all_803_0 = all_800_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1662), (1677) imply: % 231.72/34.72 | (1703) all_809_1 = all_803_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1703) implies: % 231.72/34.72 | (1704) all_809_1 = all_803_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (855), (1697) imply: % 231.72/34.72 | (1705) all_890_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1705) implies: % 231.72/34.72 | (1706) all_890_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (967), (1699) imply: % 231.72/34.72 | (1707) all_884_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1707) implies: % 231.72/34.72 | (1708) all_884_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (966), (1693) imply: % 231.72/34.72 | (1709) all_794_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1709) implies: % 231.72/34.72 | (1710) all_794_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1664), (1701) imply: % 231.72/34.72 | (1711) all_830_0 = all_809_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1701), (1706) imply: % 231.72/34.72 | (1712) all_830_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (965), (1708) imply: % 231.72/34.72 | (1713) all_879_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1713) implies: % 231.72/34.72 | (1714) all_879_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1383), (1714) imply: % 231.72/34.72 | (1715) all_849_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1715) implies: % 231.72/34.72 | (1716) all_849_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1667), (1683) imply: % 231.72/34.72 | (1717) all_842_0 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1717) implies: % 231.72/34.72 | (1718) all_842_0 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (963), (964) imply: % 231.72/34.72 | (1719) all_742_0 = all_739_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (961), (963) imply: % 231.72/34.72 | (1720) all_794_0 = all_742_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1720) implies: % 231.72/34.72 | (1721) all_794_0 = all_742_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (962), (963) imply: % 231.72/34.72 | (1722) all_752_0 = all_742_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1722) implies: % 231.72/34.72 | (1723) all_752_0 = all_742_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1103), (1689) imply: % 231.72/34.72 | (1724) all_858_0 = all_781_1 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1724) implies: % 231.72/34.72 | (1725) all_858_0 = all_781_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1102), (1725) imply: % 231.72/34.72 | (1726) all_856_0 = all_781_1 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1726) implies: % 231.72/34.72 | (1727) all_856_0 = all_781_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1099), (1727) imply: % 231.72/34.72 | (1728) all_781_1 = all_770_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1098), (1727) imply: % 231.72/34.72 | (1729) all_781_1 = all_772_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1101), (1727) imply: % 231.72/34.72 | (1730) all_781_1 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1100), (1727) imply: % 231.72/34.72 | (1731) all_781_1 = all_765_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (960), (1535) imply: % 231.72/34.72 | (1732) all_809_0 = all_791_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1732) implies: % 231.72/34.72 | (1733) all_809_0 = all_791_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1381), (1716) imply: % 231.72/34.72 | (1734) all_833_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1734) implies: % 231.72/34.72 | (1735) all_833_0 = all_822_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1136), (1666) imply: % 231.72/34.72 | (1736) all_839_0 = all_813_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1666), (1718) imply: % 231.72/34.72 | (1737) all_839_0 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1736), (1737) imply: % 231.72/34.72 | (1738) all_813_1 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1738) implies: % 231.72/34.72 | (1739) all_813_1 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1685), (1735) imply: % 231.72/34.72 | (1740) all_822_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1361), (1735) imply: % 231.72/34.72 | (1741) all_822_0 = all_813_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1711), (1712) imply: % 231.72/34.72 | (1742) all_809_1 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1742) implies: % 231.72/34.72 | (1743) all_809_1 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1740), (1741) imply: % 231.72/34.72 | (1744) all_813_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1744) implies: % 231.72/34.72 | (1745) all_813_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1362), (1745) imply: % 231.72/34.72 | (1746) all_788_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1746) implies: % 231.72/34.72 | (1747) all_788_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1135), (1739) imply: % 231.72/34.72 | (1748) all_770_0 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1748) implies: % 231.72/34.72 | (1749) all_770_0 = all_748_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (958), (1733) imply: % 231.72/34.72 | (1750) all_791_0 = all_710_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (959), (1733) imply: % 231.72/34.72 | (1751) all_791_0 = all_694_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1194), (1733) imply: % 231.72/34.72 | (1752) all_791_0 = all_697_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1330), (1733) imply: % 231.72/34.72 | (1753) all_791_0 = all_705_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1704), (1743) imply: % 231.72/34.72 | (1754) all_803_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1754) implies: % 231.72/34.72 | (1755) all_803_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1702), (1755) imply: % 231.72/34.72 | (1756) all_800_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1756) implies: % 231.72/34.72 | (1757) all_800_0 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (854), (1757) imply: % 231.72/34.72 | (1758) all_797_1 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1758) implies: % 231.72/34.72 | (1759) all_797_1 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (853), (1759) imply: % 231.72/34.72 | (1760) all_783_1 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1760) implies: % 231.72/34.72 | (1761) all_783_1 = all_781_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1710), (1721) imply: % 231.72/34.72 | (1762) all_742_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1762) implies: % 231.72/34.72 | (1763) all_742_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1752), (1753) imply: % 231.72/34.72 | (1764) all_705_0 = all_697_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1750), (1753) imply: % 231.72/34.72 | (1765) all_710_0 = all_705_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1765) implies: % 231.72/34.72 | (1766) all_710_0 = all_705_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1751), (1753) imply: % 231.72/34.72 | (1767) all_705_0 = all_694_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1220), (1747) imply: % 231.72/34.72 | (1768) all_783_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1768) implies: % 231.72/34.72 | (1769) all_783_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (956), (957) imply: % 231.72/34.72 | (1770) all_767_0 = all_762_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (956), (1769) imply: % 231.72/34.72 | (1771) all_767_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (852), (1761) imply: % 231.72/34.72 | (1772) all_781_0 = all_772_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1556), (1761) imply: % 231.72/34.72 | (1773) all_781_0 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1772), (1773) imply: % 231.72/34.72 | (1774) all_772_1 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1729), (1731) imply: % 231.72/34.72 | (1775) all_772_0 = all_765_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1729), (1730) imply: % 231.72/34.72 | (1776) all_772_0 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1728), (1729) imply: % 231.72/34.72 | (1777) all_772_0 = all_770_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1776), (1777) imply: % 231.72/34.72 | (1778) all_770_1 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1775), (1777) imply: % 231.72/34.72 | (1779) all_770_1 = all_765_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1778), (1779) imply: % 231.72/34.72 | (1780) all_765_0 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1780) implies: % 231.72/34.72 | (1781) all_765_0 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1770), (1771) imply: % 231.72/34.72 | (1782) all_762_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1782) implies: % 231.72/34.72 | (1783) all_762_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (955), (1783) imply: % 231.72/34.72 | (1784) all_757_1 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1784) implies: % 231.72/34.72 | (1785) all_757_1 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (954), (1785) imply: % 231.72/34.72 | (1786) all_739_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1786) implies: % 231.72/34.72 | (1787) all_739_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (952), (953) imply: % 231.72/34.72 | (1788) all_730_0 = all_727_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (952), (1723) imply: % 231.72/34.72 | (1789) all_742_0 = all_730_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1789) implies: % 231.72/34.72 | (1790) all_742_0 = all_730_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (949), (950) imply: % 231.72/34.72 | (1791) all_715_0 = all_710_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (949), (951) imply: % 231.72/34.72 | (1792) all_715_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1719), (1763) imply: % 231.72/34.72 | (1793) all_739_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1793) implies: % 231.72/34.72 | (1794) all_739_0 = all_733_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1763), (1790) imply: % 231.72/34.72 | (1795) all_733_0 = all_730_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1787), (1794) imply: % 231.72/34.72 | (1796) all_733_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1796) implies: % 231.72/34.72 | (1797) all_733_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1795), (1797) imply: % 231.72/34.72 | (1798) all_730_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1798) implies: % 231.72/34.72 | (1799) all_730_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1788), (1799) imply: % 231.72/34.72 | (1800) all_727_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1800) implies: % 231.72/34.72 | (1801) all_727_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (948), (1801) imply: % 231.72/34.72 | (1802) all_724_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1802) implies: % 231.72/34.72 | (1803) all_724_0 = all_718_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (946), (1803) imply: % 231.72/34.72 | (1804) all_718_0 = all_710_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (947), (1803) imply: % 231.72/34.72 | (1805) all_718_0 = all_707_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1804), (1805) imply: % 231.72/34.72 | (1806) all_710_0 = all_707_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1806) implies: % 231.72/34.72 | (1807) all_710_0 = all_707_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1791), (1792) imply: % 231.72/34.72 | (1808) all_710_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1808) implies: % 231.72/34.72 | (1809) all_710_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1807), (1809) imply: % 231.72/34.72 | (1810) all_707_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1766), (1807) imply: % 231.72/34.72 | (1811) all_707_0 = all_705_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1810), (1811) imply: % 231.72/34.72 | (1812) all_705_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1812) implies: % 231.72/34.72 | (1813) all_705_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1764), (1767) imply: % 231.72/34.72 | (1814) all_697_0 = all_694_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1764), (1813) imply: % 231.72/34.72 | (1815) all_697_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1814), (1815) imply: % 231.72/34.72 | (1816) all_694_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | SIMP: (1816) implies: % 231.72/34.72 | (1817) all_694_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1805), (1810) imply: % 231.72/34.72 | (1818) all_718_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1797), (1818) imply: % 231.72/34.72 | (1819) all_733_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1753), (1813) imply: % 231.72/34.72 | (1820) all_791_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1759), (1773) imply: % 231.72/34.72 | (1821) all_797_1 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1745), (1818) imply: % 231.72/34.72 | (1822) all_813_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1740), (1818) imply: % 231.72/34.72 | (1823) all_822_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1712), (1773) imply: % 231.72/34.72 | (1824) all_830_0 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1716), (1823) imply: % 231.72/34.72 | (1825) all_849_0 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1535), (1820) imply: % 231.72/34.72 | (1826) all_856_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1701), (1824) imply: % 231.72/34.72 | (1827) all_890_0 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1699), (1823) imply: % 231.72/34.72 | (1828) all_896_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1695), (1823) imply: % 231.72/34.72 | (1829) all_919_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1691), (1819) imply: % 231.72/34.72 | (1830) all_931_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1674), (1730) imply: % 231.72/34.72 | (1831) all_940_1 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1650), (1773) imply: % 231.72/34.72 | (1832) all_987_0 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1624), (1832) imply: % 231.72/34.72 | (1833) all_1027_1 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1589), (1831) imply: % 231.72/34.72 | (1834) all_1042_0 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1597), (1823) imply: % 231.72/34.72 | (1835) all_1084_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1585), (1823) imply: % 231.72/34.72 | (1836) all_1111_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1550), (1833) imply: % 231.72/34.72 | (1837) all_1147_4 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1192), (1836) imply: % 231.72/34.72 | (1838) all_1166_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1546), (1823) imply: % 231.72/34.72 | (1839) all_1186_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1502), (1823) imply: % 231.72/34.72 | (1840) all_1251_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1500), (1823) imply: % 231.72/34.72 | (1841) all_1263_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1496), (1823) imply: % 231.72/34.72 | (1842) all_1266_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1455), (1823) imply: % 231.72/34.72 | (1843) all_1328_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1375), (1834) imply: % 231.72/34.72 | (1844) all_1483_1 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1364), (1834) imply: % 231.72/34.72 | (1845) all_1497_1 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1324), (1825) imply: % 231.72/34.72 | (1846) all_1547_3 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1206), (1822) imply: % 231.72/34.72 | (1847) all_1550_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1284), (1832) imply: % 231.72/34.72 | (1848) all_1559_8 = all_757_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1249), (1730) imply: % 231.72/34.72 | (1849) all_1559_7 = all_748_1 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1184), (1823) imply: % 231.72/34.72 | (1850) all_1576_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1031), (1843) imply: % 231.72/34.72 | (1851) all_1694_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1034), (1822) imply: % 231.72/34.72 | (1852) all_1697_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1177), (1841) imply: % 231.72/34.72 | (1853) all_1709_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1037), (1820) imply: % 231.72/34.72 | (1854) all_1712_1 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | COMBINE_EQS: (1044), (1836) imply: % 231.72/34.72 | (1855) all_1724_2 = all_691_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (304), (1774), (1776) imply: % 231.72/34.72 | (1856) ~ (all_757_0 = all_748_1) % 231.72/34.72 | % 231.72/34.72 | SIMP: (1856) implies: % 231.72/34.72 | (1857) ~ (all_757_0 = all_748_1) % 231.72/34.72 | % 231.72/34.72 | REDUCE: (826), (1855) imply: % 231.72/34.72 | (1858) c_Nat_OSuc(all_691_0) = all_1724_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (817), (1854) imply: % 231.72/34.72 | (1859) c_Nat_OSuc(all_691_0) = all_1712_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (814), (1853) imply: % 231.72/34.72 | (1860) c_Nat_OSuc(all_691_0) = all_1709_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (809), (1852) imply: % 231.72/34.72 | (1861) c_Nat_OSuc(all_691_0) = all_1697_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (806), (1851) imply: % 231.72/34.72 | (1862) c_Nat_OSuc(all_691_0) = all_1694_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (719), (1850) imply: % 231.72/34.72 | (1863) c_Nat_OSuc(all_691_0) = all_1576_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (697), (1847) imply: % 231.72/34.72 | (1864) c_Nat_OSuc(all_691_0) = all_1550_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (694), (1846) imply: % 231.72/34.72 | (1865) c_Nat_OSuc(all_691_0) = all_1547_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (563), (1842) imply: % 231.72/34.72 | (1866) c_Nat_OSuc(all_691_0) = all_1266_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (560), (1841) imply: % 231.72/34.72 | (1867) c_Nat_OSuc(all_691_0) = all_1263_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (555), (1840) imply: % 231.72/34.72 | (1868) c_Nat_OSuc(all_691_0) = all_1251_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (515), (1839) imply: % 231.72/34.72 | (1869) c_Nat_OSuc(all_691_0) = all_1186_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (509), (1838) imply: % 231.72/34.72 | (1870) c_Nat_OSuc(all_691_0) = all_1166_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (464), (1835) imply: % 231.72/34.72 | (1871) c_Nat_OSuc(all_691_0) = all_1084_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (386), (1830) imply: % 231.72/34.72 | (1872) c_Nat_OSuc(all_691_0) = all_931_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (380), (1829) imply: % 231.72/34.72 | (1873) c_Nat_OSuc(all_691_0) = all_919_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (371), (1828) imply: % 231.72/34.72 | (1874) c_Nat_OSuc(all_691_0) = all_896_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (351), (1826) imply: % 231.72/34.72 | (1875) c_Nat_OSuc(all_691_0) = all_856_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (334), (1739), (1822) imply: % 231.72/34.72 | (1876) c_Nat_OSuc(all_691_0) = all_748_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (350), (1101) imply: % 231.72/34.72 | (1877) c_RealDef_Oreal(tc_Nat_Onat, all_856_1) = all_748_1 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (302), (1749), (1778) imply: % 231.72/34.72 | (1878) c_RComplete_Onatceiling(all_748_1) = all_748_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (666), (1845) imply: % 231.72/34.72 | (1879) c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, all_748_1) = % 231.72/34.72 | all_1497_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (658), (1844) imply: % 231.72/34.72 | (1880) c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, all_748_1) = % 231.72/34.72 | all_1483_0 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (711), (851), (1849) imply: % 231.72/34.72 | (1881) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_748_1, all_797_0) % 231.72/34.72 | = all_1559_5 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (705), (1312) imply: % 231.72/34.72 | (1882) hAPP(all_1006_2, v_r) = all_1559_3 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (498), (1554) imply: % 231.72/34.72 | (1883) hAPP(all_1006_2, v_r) = all_1147_2 % 231.72/34.72 | % 231.72/34.72 | REDUCE: (305), (1774) imply: % 231.72/34.72 | (1884) $i(all_757_0) % 231.72/34.72 | % 231.72/34.72 | REDUCE: (295), (1781) imply: % 231.72/34.72 | (1885) $i(all_748_1) % 231.72/34.72 | % 231.72/34.72 | REDUCE: (255), (1817) imply: % 231.72/34.72 | (1886) $i(all_691_0) % 231.72/34.72 | % 231.72/34.72 | REDUCE: (497), (1837) imply: % 231.72/34.72 | (1887) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_757_0, % 231.72/34.72 | all_1147_0) % 231.72/34.73 | % 231.72/34.73 | REDUCE: (321), (1821) imply: % 231.72/34.73 | (1888) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_757_0, % 231.72/34.73 | all_797_0) % 231.72/34.73 | % 231.72/34.73 | REDUCE: (702), (1848) imply: % 231.72/34.73 | (1889) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_757_0, % 231.72/34.73 | all_1559_0) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (247) with all_1147_2, all_1559_3, v_r, all_1006_2, % 231.72/34.73 | simplifying with (1882), (1883) gives: % 231.72/34.73 | (1890) all_1559_3 = all_1147_2 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (250) with all_1483_0, all_1497_0, all_748_1, % 231.72/34.73 | tc_RealDef_Oreal, simplifying with (1879), (1880) gives: % 231.72/34.73 | (1891) all_1497_0 = all_1483_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_896_0, all_931_0, all_691_0, % 231.72/34.73 | simplifying with (1872), (1874) gives: % 231.72/34.73 | (1892) all_931_0 = all_896_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_931_0, all_1084_1, all_691_0, % 231.72/34.73 | simplifying with (1871), (1872) gives: % 231.72/34.73 | (1893) all_1084_1 = all_931_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1084_1, all_1166_1, all_691_0, % 231.72/34.73 | simplifying with (1870), (1871) gives: % 231.72/34.73 | (1894) all_1166_1 = all_1084_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1166_1, all_1186_1, all_691_0, % 231.72/34.73 | simplifying with (1869), (1870) gives: % 231.72/34.73 | (1895) all_1186_1 = all_1166_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1186_1, all_1251_1, all_691_0, % 231.72/34.73 | simplifying with (1868), (1869) gives: % 231.72/34.73 | (1896) all_1251_1 = all_1186_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1266_1, all_1547_0, all_691_0, % 231.72/34.73 | simplifying with (1865), (1866) gives: % 231.72/34.73 | (1897) all_1547_0 = all_1266_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1547_0, all_1550_0, all_691_0, % 231.72/34.73 | simplifying with (1864), (1865) gives: % 231.72/34.73 | (1898) all_1550_0 = all_1547_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1550_0, all_1576_0, all_691_0, % 231.72/34.73 | simplifying with (1863), (1864) gives: % 231.72/34.73 | (1899) all_1576_0 = all_1550_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1266_1, all_1694_1, all_691_0, % 231.72/34.73 | simplifying with (1862), (1866) gives: % 231.72/34.73 | (1900) all_1694_1 = all_1266_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1263_1, all_1694_1, all_691_0, % 231.72/34.73 | simplifying with (1862), (1867) gives: % 231.72/34.73 | (1901) all_1694_1 = all_1263_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1251_1, all_1694_1, all_691_0, % 231.72/34.73 | simplifying with (1862), (1868) gives: % 231.72/34.73 | (1902) all_1694_1 = all_1251_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1576_0, all_1697_1, all_691_0, % 231.72/34.73 | simplifying with (1861), (1863) gives: % 231.72/34.73 | (1903) all_1697_1 = all_1576_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1697_1, all_1709_0, all_691_0, % 231.72/34.73 | simplifying with (1860), (1861) gives: % 231.72/34.73 | (1904) all_1709_0 = all_1697_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_919_0, all_1712_0, all_691_0, % 231.72/34.73 | simplifying with (1859), (1873) gives: % 231.72/34.73 | (1905) all_1712_0 = all_919_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_896_0, all_1712_0, all_691_0, % 231.72/34.73 | simplifying with (1859), (1874) gives: % 231.72/34.73 | (1906) all_1712_0 = all_896_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_856_1, all_1712_0, all_691_0, % 231.72/34.73 | simplifying with (1859), (1875) gives: % 231.72/34.73 | (1907) all_1712_0 = all_856_1 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_1709_0, all_1724_1, all_691_0, % 231.72/34.73 | simplifying with (1858), (1860) gives: % 231.72/34.73 | (1908) all_1724_1 = all_1709_0 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (246) with all_748_0, all_1724_1, all_691_0, % 231.72/34.73 | simplifying with (1858), (1876) gives: % 231.72/34.73 | (1909) all_1724_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1908), (1909) imply: % 231.72/34.73 | (1910) all_1709_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1910) implies: % 231.72/34.73 | (1911) all_1709_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1905), (1907) imply: % 231.72/34.73 | (1912) all_919_0 = all_856_1 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1905), (1906) imply: % 231.72/34.73 | (1913) all_919_0 = all_896_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1904), (1911) imply: % 231.72/34.73 | (1914) all_1697_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1914) implies: % 231.72/34.73 | (1915) all_1697_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1903), (1915) imply: % 231.72/34.73 | (1916) all_1576_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1916) implies: % 231.72/34.73 | (1917) all_1576_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1900), (1901) imply: % 231.72/34.73 | (1918) all_1266_1 = all_1263_1 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1918) implies: % 231.72/34.73 | (1919) all_1266_1 = all_1263_1 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1901), (1902) imply: % 231.72/34.73 | (1920) all_1263_1 = all_1251_1 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1899), (1917) imply: % 231.72/34.73 | (1921) all_1550_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1921) implies: % 231.72/34.73 | (1922) all_1550_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1898), (1922) imply: % 231.72/34.73 | (1923) all_1547_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1923) implies: % 231.72/34.73 | (1924) all_1547_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1897), (1924) imply: % 231.72/34.73 | (1925) all_1266_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1925) implies: % 231.72/34.73 | (1926) all_1266_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1919), (1926) imply: % 231.72/34.73 | (1927) all_1263_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1927) implies: % 231.72/34.73 | (1928) all_1263_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1920), (1928) imply: % 231.72/34.73 | (1929) all_1251_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1929) implies: % 231.72/34.73 | (1930) all_1251_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1896), (1930) imply: % 231.72/34.73 | (1931) all_1186_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1931) implies: % 231.72/34.73 | (1932) all_1186_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1895), (1932) imply: % 231.72/34.73 | (1933) all_1166_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1933) implies: % 231.72/34.73 | (1934) all_1166_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1894), (1934) imply: % 231.72/34.73 | (1935) all_1084_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1935) implies: % 231.72/34.73 | (1936) all_1084_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1893), (1936) imply: % 231.72/34.73 | (1937) all_931_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1937) implies: % 231.72/34.73 | (1938) all_931_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1892), (1938) imply: % 231.72/34.73 | (1939) all_896_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1939) implies: % 231.72/34.73 | (1940) all_896_0 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1912), (1913) imply: % 231.72/34.73 | (1941) all_896_0 = all_856_1 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1941) implies: % 231.72/34.73 | (1942) all_896_0 = all_856_1 % 231.72/34.73 | % 231.72/34.73 | COMBINE_EQS: (1940), (1942) imply: % 231.72/34.73 | (1943) all_856_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | SIMP: (1943) implies: % 231.72/34.73 | (1944) all_856_1 = all_748_0 % 231.72/34.73 | % 231.72/34.73 | REDUCE: (1877), (1944) imply: % 231.72/34.73 | (1945) c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = all_748_1 % 231.72/34.73 | % 231.72/34.73 | REDUCE: (706), (1890) imply: % 231.72/34.73 | (1946) hAPP(all_1147_2, v_m____) = all_1559_2 % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (247) with all_1147_1, all_1559_2, v_m____, % 231.72/34.73 | all_1147_2, simplifying with (499), (1946) gives: % 231.72/34.73 | (1947) all_1559_2 = all_1147_1 % 231.72/34.73 | % 231.72/34.73 | REDUCE: (709), (1947) imply: % 231.72/34.73 | (1948) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1147_1) = all_1559_1 % 231.72/34.73 | % 231.72/34.73 | REDUCE: (703), (1947) imply: % 231.72/34.73 | (1949) $i(all_1147_1) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (249) with all_1147_0, all_1559_1, all_1147_1, % 231.72/34.73 | tc_RealDef_Oreal, simplifying with (501), (1948) gives: % 231.72/34.73 | (1950) all_1559_1 = all_1147_0 % 231.72/34.73 | % 231.72/34.73 | REDUCE: (712), (1950) imply: % 231.72/34.73 | (1951) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1559_5, % 231.72/34.73 | all_1147_0) = all_1559_0 % 231.72/34.73 | % 231.72/34.73 | REDUCE: (704), (1950) imply: % 231.72/34.73 | (1952) $i(all_1147_0) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (23) with v_c____, tc_Complex_Ocomplex, all_797_0, % 231.72/34.73 | simplifying with (236), (238), (239), (322) gives: % 231.72/34.73 | (1953) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_797_0) = all_797_0 & % 231.72/34.73 | $i(all_797_0) % 231.72/34.73 | % 231.72/34.73 | ALPHA: (1953) implies: % 231.72/34.73 | (1954) $i(all_797_0) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_abs__not__less__zero) with all_1147_1, % 231.72/34.73 | tc_RealDef_Oreal, all_1147_0, simplifying with (224), (237), % 231.72/34.73 | (501), (1949) gives: % 231.72/34.73 | (1955) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.73 | all_1147_0, v0)) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_abs__eq__0) with all_1147_1, % 231.72/34.73 | tc_RealDef_Oreal, all_1147_0, simplifying with (224), (237), % 231.72/34.73 | (501), (1949) gives: % 231.72/34.73 | (1956) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ (v0 = all_1147_0) | all_1147_0 = all_1147_1) & ( ~ % 231.72/34.73 | (v0 = all_1147_1) | all_1147_0 = all_1147_1)) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_zero__less__abs__iff) with all_1147_1, % 231.72/34.73 | tc_RealDef_Oreal, all_1147_0, simplifying with (224), (237), % 231.72/34.73 | (501), (1949) gives: % 231.72/34.73 | (1957) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ (v0 = all_1147_1) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1147_1, % 231.72/34.73 | all_1147_0)) & (v0 = all_1147_1 | % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_0))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_abs__le__zero__iff) with all_1147_1, % 231.72/34.73 | tc_RealDef_Oreal, all_1147_0, simplifying with (224), (237), % 231.72/34.73 | (501), (1949) gives: % 231.72/34.73 | (1958) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ (v0 = all_1147_1) | % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_0, % 231.72/34.73 | all_1147_1)) & (v0 = all_1147_1 | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_0, % 231.72/34.73 | v0))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__pos__neg2) with v_r, v_m____, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (223), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1959) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_m____) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.73 | v_r, v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.73 | all_1147_1, v0))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_zero__less__mult__pos) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (223), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1960) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_1) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v_r) | % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v_m____))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_zero__less__mult__pos2) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (223), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1961) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_1) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v_m____) | % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v_r))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__pos__pos) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (223), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1962) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_m____) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.73 | v0, v_r) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_1))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__pos__neg) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (223), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1963) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_r) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.73 | v_m____, v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.73 | all_1147_1, v0))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__nonneg__nonpos2) with v_r, v_m____, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (227), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1964) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | v0, v_m____) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, v0) | % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_1, % 231.72/34.73 | v0))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__nonneg__nonneg) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (227), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1965) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | v0, v_m____) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v_r) | % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_1))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__nonneg__nonpos) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (227), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1966) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | v0, v_r) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, v0) % 231.72/34.73 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | all_1147_1, v0))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_split__mult__neg__le) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (227), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1967) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | all_1147_1, v0) | (( ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_m____) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.73 | v0)) & ( ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v_r) % 231.72/34.73 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | v_m____, v0))))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__eq__0__iff) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (229), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1968) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ (v0 = all_1147_1) | all_1147_1 = v_m____ | all_1147_1 % 231.72/34.73 | = v_r) & (v0 = all_1147_1 | ( ~ (v0 = v_m____) & ~ (v0 = % 231.72/34.73 | v_r)))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_no__zero__divisors) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (232), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1969) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ (v0 = all_1147_1) | all_1147_1 = v_m____ | all_1147_1 % 231.72/34.73 | = v_r)) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__nonpos__nonpos) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (234), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1970) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | v_m____, v0) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, v0) | % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_1))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_split__mult__pos__le) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (234), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1971) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_1) | (( ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_m____) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_r)) & ( ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.73 | v0) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.73 | v0))))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__neg__neg) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (228), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1972) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.73 | v_m____, v0) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_r, v0) | % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_1))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_zero__le__mult__iff) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (228), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1973) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | v0, all_1147_1) | % 231.72/34.73 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_m____) & % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v_r)) % 231.72/34.73 | | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.73 | v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | v_r, v0))) & % 231.72/34.73 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1147_1) | (( ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_m____) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_r)) & ( ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.73 | v0) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.73 | v0))))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_mult__le__0__iff) with v_m____, v_r, % 231.72/34.73 | tc_RealDef_Oreal, all_1006_2, all_1147_2, all_1147_1, simplifying % 231.72/34.73 | with (228), (237), (240), (241), (425), (499), (1883) gives: % 231.72/34.73 | (1974) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | all_1147_1, v0) | % 231.72/34.73 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_m____) & % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, v0)) % 231.72/34.73 | | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v_r) % 231.72/34.73 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.73 | v0))) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | all_1147_1, v0) | (( ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.73 | v_m____) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.73 | v0)) & ( ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v_r) % 231.72/34.73 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.73 | v_m____, v0))))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_add__pos__pos) with all_797_0, all_748_1, % 231.72/34.73 | tc_RealDef_Oreal, all_1559_5, simplifying with (225), (237), % 231.72/34.73 | (1881), (1885), (1954) gives: % 231.72/34.73 | (1975) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_797_0) | ~ % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_748_1) | % 231.72/34.73 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.73 | all_1559_5))) % 231.72/34.73 | % 231.72/34.73 | GROUND_INST: instantiating (fact_add__pos__nonneg) with all_797_0, all_748_1, % 231.72/34.73 | tc_RealDef_Oreal, all_1559_5, simplifying with (225), (237), % 231.72/34.73 | (1881), (1885), (1954) gives: % 231.72/34.73 | (1976) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.73 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_797_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_1559_5))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonneg__pos) with all_797_0, all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1559_5, simplifying with (225), (237), % 231.72/34.74 | (1881), (1885), (1954) gives: % 231.72/34.74 | (1977) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_797_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_1559_5))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__neg__neg) with all_797_0, all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1559_5, simplifying with (225), (237), % 231.72/34.74 | (1881), (1885), (1954) gives: % 231.72/34.74 | (1978) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_797_0, v0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_748_1, v0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1559_5, % 231.72/34.74 | v0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__neg__nonpos) with all_797_0, all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1559_5, simplifying with (225), (237), % 231.72/34.74 | (1881), (1885), (1954) gives: % 231.72/34.74 | (1979) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, v0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_797_0, % 231.72/34.74 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_5, v0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonpos__neg) with all_797_0, all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1559_5, simplifying with (225), (237), % 231.72/34.74 | (1881), (1885), (1954) gives: % 231.72/34.74 | (1980) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_797_0, v0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.74 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_5, v0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonneg__nonneg) with all_797_0, % 231.72/34.74 | all_748_1, tc_RealDef_Oreal, all_1559_5, simplifying with (225), % 231.72/34.74 | (237), (1881), (1885), (1954) gives: % 231.72/34.74 | (1981) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_797_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1) | % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1559_5))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonneg__eq__0__iff) with all_797_0, % 231.72/34.74 | all_748_1, tc_RealDef_Oreal, all_1559_5, simplifying with (225), % 231.72/34.74 | (237), (1881), (1885), (1954) gives: % 231.72/34.74 | (1982) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_797_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1) | (( ~ (v0 = all_1559_5) | (all_1559_5 = all_748_1 % 231.72/34.74 | & all_797_0 = all_748_1)) & ( ~ (v0 = all_748_1) | ~ % 231.72/34.74 | (all_797_0 = all_748_1) | all_1559_5 = all_748_1)))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonpos__nonpos) with all_797_0, % 231.72/34.74 | all_748_1, tc_RealDef_Oreal, all_1559_5, simplifying with (225), % 231.72/34.74 | (237), (1881), (1885), (1954) gives: % 231.72/34.74 | (1983) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_797_0, v0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.74 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_5, v0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating % 231.72/34.74 | (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) % 231.72/34.74 | with all_748_1, all_797_0, tc_RealDef_Oreal, all_1559_5, % 231.72/34.74 | simplifying with (233), (237), (1881), (1885), (1954) gives: % 231.72/34.74 | (1984) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_797_0, all_748_1) % 231.72/34.74 | = all_1559_5 & $i(all_1559_5) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (1984) implies: % 231.72/34.74 | (1985) $i(all_1559_5) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__strict__increasing) with all_1147_0, % 231.72/34.74 | all_757_0, all_1559_5, tc_RealDef_Oreal, all_1559_0, simplifying % 231.72/34.74 | with (225), (237), (1884), (1887), (1889), (1951), (1952), (1985) % 231.72/34.74 | gives: % 231.72/34.74 | (1986) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1559_5)) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__pos__pos) with all_1147_0, all_1559_5, % 231.72/34.74 | tc_RealDef_Oreal, all_1559_0, simplifying with (225), (237), % 231.72/34.74 | (1951), (1952), (1985) gives: % 231.72/34.74 | (1987) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1559_5) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1147_0) % 231.72/34.74 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1559_0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__pos__nonneg) with all_1147_0, % 231.72/34.74 | all_1559_5, tc_RealDef_Oreal, all_1559_0, simplifying with (225), % 231.72/34.74 | (237), (1951), (1952), (1985) gives: % 231.72/34.74 | (1988) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1559_5) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1147_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_1559_0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonneg__pos) with all_1147_0, % 231.72/34.74 | all_1559_5, tc_RealDef_Oreal, all_1559_0, simplifying with (225), % 231.72/34.74 | (237), (1951), (1952), (1985) gives: % 231.72/34.74 | (1989) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1147_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1559_5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_1559_0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__neg__neg) with all_1147_0, all_1559_5, % 231.72/34.74 | tc_RealDef_Oreal, all_1559_0, simplifying with (225), (237), % 231.72/34.74 | (1951), (1952), (1985) gives: % 231.72/34.74 | (1990) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_5, v0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1147_0, v0) % 231.72/34.74 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1559_0, % 231.72/34.74 | v0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__neg__nonpos) with all_1147_0, % 231.72/34.74 | all_1559_5, tc_RealDef_Oreal, all_1559_0, simplifying with (225), % 231.72/34.74 | (237), (1951), (1952), (1985) gives: % 231.72/34.74 | (1991) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_5, v0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_0, % 231.72/34.74 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_0, v0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonpos__neg) with all_1147_0, % 231.72/34.74 | all_1559_5, tc_RealDef_Oreal, all_1559_0, simplifying with (225), % 231.72/34.74 | (237), (1951), (1952), (1985) gives: % 231.72/34.74 | (1992) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1147_0, v0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1559_5, % 231.72/34.74 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_0, v0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonneg__nonneg) with all_1147_0, % 231.72/34.74 | all_1559_5, tc_RealDef_Oreal, all_1559_0, simplifying with (225), % 231.72/34.74 | (237), (1951), (1952), (1985) gives: % 231.72/34.74 | (1993) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_1559_5) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1147_0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1559_0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonneg__eq__0__iff) with all_1147_0, % 231.72/34.74 | all_1559_5, tc_RealDef_Oreal, all_1559_0, simplifying with (225), % 231.72/34.74 | (237), (1951), (1952), (1985) gives: % 231.72/34.74 | (1994) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_1559_5) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1147_0) | (( ~ (v0 = all_1559_0) | (all_1559_0 = % 231.72/34.74 | all_1147_0 & all_1559_5 = all_1147_0)) & ( ~ (v0 = % 231.72/34.74 | all_1147_0) | ~ (all_1559_5 = all_1147_0) | all_1559_0 = % 231.72/34.74 | all_1147_0)))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_add__nonpos__nonpos) with all_1147_0, % 231.72/34.74 | all_1559_5, tc_RealDef_Oreal, all_1559_0, simplifying with (225), % 231.72/34.74 | (237), (1951), (1952), (1985) gives: % 231.72/34.74 | (1995) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_5, v0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_0, % 231.72/34.74 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_0, v0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_zero__less__one) with tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, simplifying with (231), (237), (284) gives: % 231.72/34.74 | (1996) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1)) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_zero__le__one) with tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, simplifying with (231), (237), (284) gives: % 231.72/34.74 | (1997) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1)) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, simplifying with (231), (237), (284) gives: % 231.72/34.74 | (1998) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, v0)) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_not__one__le__zero) with tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, simplifying with (231), (237), (284) gives: % 231.72/34.74 | (1999) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, v0)) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_neg__0__less__iff__less) with all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1483_0, simplifying with (230), (237), % 231.72/34.74 | (1880), (1885) gives: % 231.72/34.74 | (2000) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1483_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, v0)) & ( ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_748_1, v0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1483_0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_neg__less__0__iff__less) with all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1483_0, simplifying with (230), (237), % 231.72/34.74 | (1880), (1885) gives: % 231.72/34.74 | (2001) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1483_0, v0)) & ( ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1483_0, v0) % 231.72/34.74 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_neg__0__le__iff__le) with all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1483_0, simplifying with (230), (237), % 231.72/34.74 | (1880), (1885) gives: % 231.72/34.74 | (2002) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_1483_0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.74 | v0)) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, v0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1483_0))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_neg__le__0__iff__le) with all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1483_0, simplifying with (230), (237), % 231.72/34.74 | (1880), (1885) gives: % 231.72/34.74 | (2003) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | v0, all_748_1) | % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1483_0, % 231.72/34.74 | v0)) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_1483_0, v0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_748_1))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_neg__equal__0__iff__equal) with all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1483_0, simplifying with (235), (237), % 231.72/34.74 | (1880), (1885) gives: % 231.72/34.74 | (2004) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 231.72/34.74 | $i(v0) & ( ~ (v0 = all_1483_0) | all_1483_0 = all_748_1) & ( ~ (v0 % 231.72/34.74 | = all_748_1) | all_1483_0 = all_748_1)) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (fact_neg__equal__zero) with all_748_1, % 231.72/34.74 | tc_RealDef_Oreal, all_1483_0, simplifying with (226), (237), % 231.72/34.74 | (1880), (1885) gives: % 231.72/34.74 | (2005) ? [v0: any] : (( ~ (all_1483_0 = all_748_1) | (v0 = all_748_1 & % 231.72/34.74 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_748_1)) & % 231.72/34.74 | (all_1483_0 = all_748_1 | ( ~ (v0 = all_748_1) & % 231.72/34.74 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0)))) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (117) with all_748_1, all_748_0, simplifying with % 231.72/34.74 | (1878), (1885) gives: % 231.72/34.74 | (2006) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = v0 & $i(v0) % 231.72/34.74 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.74 | v0)) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (429) with all_748_1, all_748_0, simplifying with % 231.72/34.74 | (286), (1885) gives: % 231.72/34.74 | (2007) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_748_0) % 231.72/34.74 | = v0 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, % 231.72/34.74 | all_1009_0) = v1 & $i(v1) & $i(v0) & % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_748_1, v1)) % 231.72/34.74 | % 231.72/34.74 | GROUND_INST: instantiating (366) with all_691_0, all_748_0, simplifying with % 231.72/34.74 | (1876), (1886) gives: % 231.72/34.74 | (2008) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = v0 & $i(v0) % 231.72/34.74 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_890_0, v0)) % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (2008) with fresh symbol all_1835_0 gives: % 231.72/34.74 | (2009) c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = all_1835_0 & % 231.72/34.74 | $i(all_1835_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_890_0, all_1835_0) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2009) implies: % 231.72/34.74 | (2010) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_890_0, % 231.72/34.74 | all_1835_0) % 231.72/34.74 | (2011) c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = all_1835_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1955) with fresh symbol all_1847_0 gives: % 231.72/34.74 | (2012) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1847_0 & % 231.72/34.74 | $i(all_1847_0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1147_0, all_1847_0) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2012) implies: % 231.72/34.74 | (2013) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1847_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (2006) with fresh symbol all_1853_0 gives: % 231.72/34.74 | (2014) c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = all_1853_0 & % 231.72/34.74 | $i(all_1853_0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, all_1853_0) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2014) implies: % 231.72/34.74 | (2015) c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = all_1853_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1996) with fresh symbol all_1865_0 gives: % 231.72/34.74 | (2016) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1865_0 & % 231.72/34.74 | $i(all_1865_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1865_0, all_748_1) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2016) implies: % 231.72/34.74 | (2017) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1865_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1999) with fresh symbol all_1871_0 gives: % 231.72/34.74 | (2018) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1871_0 & % 231.72/34.74 | $i(all_1871_0) & ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.74 | all_1871_0) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2018) implies: % 231.72/34.74 | (2019) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1871_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1998) with fresh symbol all_1873_0 gives: % 231.72/34.74 | (2020) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1873_0 & % 231.72/34.74 | $i(all_1873_0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_748_1, all_1873_0) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2020) implies: % 231.72/34.74 | (2021) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1873_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1997) with fresh symbol all_1875_0 gives: % 231.72/34.74 | (2022) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1875_0 & % 231.72/34.74 | $i(all_1875_0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.74 | all_1875_0, all_748_1) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2022) implies: % 231.72/34.74 | (2023) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1875_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1986) with fresh symbol all_1883_0 gives: % 231.72/34.74 | (2024) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1883_0 & % 231.72/34.74 | $i(all_1883_0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1883_0, all_1559_5) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2024) implies: % 231.72/34.74 | (2025) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1883_0, % 231.72/34.74 | all_1559_5) % 231.72/34.74 | (2026) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1883_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1978) with fresh symbol all_1895_0 gives: % 231.72/34.74 | (2027) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1895_0 & % 231.72/34.74 | $i(all_1895_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_797_0, all_1895_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_748_1, % 231.72/34.74 | all_1895_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_5, all_1895_0)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2027) implies: % 231.72/34.74 | (2028) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1895_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1977) with fresh symbol all_1897_0 gives: % 231.72/34.74 | (2029) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1897_0 & % 231.72/34.74 | $i(all_1897_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1897_0, all_797_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1897_0, % 231.72/34.74 | all_748_1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1897_0, all_1559_5)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2029) implies: % 231.72/34.74 | (2030) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1897_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1972) with fresh symbol all_1903_0 gives: % 231.72/34.74 | (2031) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1903_0 & % 231.72/34.74 | $i(all_1903_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | v_m____, all_1903_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_r, all_1903_0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1903_0, % 231.72/34.74 | all_1147_1)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2031) implies: % 231.72/34.74 | (2032) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1903_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1970) with fresh symbol all_1905_0 gives: % 231.72/34.74 | (2033) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1905_0 & % 231.72/34.74 | $i(all_1905_0) & ( ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.74 | all_1905_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.74 | all_1905_0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1905_0, % 231.72/34.74 | all_1147_1)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2033) implies: % 231.72/34.74 | (2034) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1905_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1991) with fresh symbol all_1909_0 gives: % 231.72/34.74 | (2035) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1909_0 & % 231.72/34.74 | $i(all_1909_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_5, all_1909_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_0, % 231.72/34.74 | all_1909_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1559_0, all_1909_0)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2035) implies: % 231.72/34.74 | (2036) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1909_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1989) with fresh symbol all_1911_0 gives: % 231.72/34.74 | (2037) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1911_0 & % 231.72/34.74 | $i(all_1911_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1911_0, all_1147_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1911_0, % 231.72/34.74 | all_1559_5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1911_0, all_1559_0)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2037) implies: % 231.72/34.74 | (2038) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1911_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1988) with fresh symbol all_1913_0 gives: % 231.72/34.74 | (2039) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1913_0 & % 231.72/34.74 | $i(all_1913_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1913_0, all_1559_5) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1913_0, % 231.72/34.74 | all_1147_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1913_0, all_1559_0)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2039) implies: % 231.72/34.74 | (2040) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1913_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1976) with fresh symbol all_1915_0 gives: % 231.72/34.74 | (2041) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1915_0 & % 231.72/34.74 | $i(all_1915_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1915_0, all_748_1) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1915_0, % 231.72/34.74 | all_797_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1915_0, all_1559_5)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2041) implies: % 231.72/34.74 | (2042) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1915_0 % 231.72/34.74 | (2043) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1915_0, % 231.72/34.74 | all_748_1) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1915_0, % 231.72/34.74 | all_797_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1915_0, all_1559_5) % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1975) with fresh symbol all_1917_0 gives: % 231.72/34.74 | (2044) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1917_0 & % 231.72/34.74 | $i(all_1917_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1917_0, all_797_0) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1917_0, % 231.72/34.74 | all_748_1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1917_0, all_1559_5)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2044) implies: % 231.72/34.74 | (2045) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1917_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1961) with fresh symbol all_1919_0 gives: % 231.72/34.74 | (2046) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1919_0 & % 231.72/34.74 | $i(all_1919_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1919_0, all_1147_1) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1919_0, % 231.72/34.74 | v_m____) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1919_0, v_r)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2046) implies: % 231.72/34.74 | (2047) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1919_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (1959) with fresh symbol all_1921_0 gives: % 231.72/34.74 | (2048) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1921_0 & % 231.72/34.74 | $i(all_1921_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.74 | all_1921_0, v_m____) | ~ % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_r, all_1921_0) | % 231.72/34.74 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1147_1, % 231.72/34.74 | all_1921_0)) % 231.72/34.74 | % 231.72/34.74 | ALPHA: (2048) implies: % 231.72/34.74 | (2049) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1921_0 % 231.72/34.74 | % 231.72/34.74 | DELTA: instantiating (2007) with fresh symbols all_1923_0, all_1923_1 gives: % 231.72/34.74 | (2050) c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = all_1923_1 & % 231.72/34.75 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1923_1, % 231.72/34.75 | all_1009_0) = all_1923_0 & $i(all_1923_0) & $i(all_1923_1) & % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_748_1, % 231.72/34.75 | all_1923_0) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2050) implies: % 231.72/34.75 | (2051) c_RealDef_Oreal(tc_Nat_Onat, all_748_0) = all_1923_1 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1990) with fresh symbol all_1925_0 gives: % 231.72/34.75 | (2052) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1925_0 & % 231.72/34.75 | $i(all_1925_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1559_5, all_1925_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1147_0, % 231.72/34.75 | all_1925_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1559_0, all_1925_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2052) implies: % 231.72/34.75 | (2053) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1925_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1969) with fresh symbol all_1927_0 gives: % 231.72/34.75 | (2054) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1927_0 & % 231.72/34.75 | $i(all_1927_0) & ( ~ (all_1927_0 = all_1147_1) | all_1147_1 = % 231.72/34.75 | v_m____ | all_1147_1 = v_r) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2054) implies: % 231.72/34.75 | (2055) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1927_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1966) with fresh symbol all_1929_0 gives: % 231.72/34.75 | (2056) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1929_0 & % 231.72/34.75 | $i(all_1929_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1929_0, % 231.72/34.75 | v_r) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | v_m____, all_1929_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_1, % 231.72/34.75 | all_1929_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2056) implies: % 231.72/34.75 | (2057) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1929_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1995) with fresh symbol all_1932_0 gives: % 231.72/34.75 | (2058) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1932_0 & % 231.72/34.75 | $i(all_1932_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1559_5, % 231.72/34.75 | all_1932_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_0, % 231.72/34.75 | all_1932_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1559_0, % 231.72/34.75 | all_1932_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2058) implies: % 231.72/34.75 | (2059) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1932_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1993) with fresh symbol all_1934_0 gives: % 231.72/34.75 | (2060) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1934_0 & % 231.72/34.75 | $i(all_1934_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1934_0, % 231.72/34.75 | all_1559_5) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1934_0, % 231.72/34.75 | all_1147_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1934_0, % 231.72/34.75 | all_1559_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2060) implies: % 231.72/34.75 | (2061) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1934_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1987) with fresh symbol all_1936_0 gives: % 231.72/34.75 | (2062) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1936_0 & % 231.72/34.75 | $i(all_1936_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1936_0, all_1559_5) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1936_0, % 231.72/34.75 | all_1147_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1936_0, all_1559_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2062) implies: % 231.72/34.75 | (2063) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1936_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1992) with fresh symbol all_1938_0 gives: % 231.72/34.75 | (2064) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1938_0 & % 231.72/34.75 | $i(all_1938_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1147_0, all_1938_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1559_5, % 231.72/34.75 | all_1938_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1559_0, all_1938_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2064) implies: % 231.72/34.75 | (2065) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1938_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1960) with fresh symbol all_1940_0 gives: % 231.72/34.75 | (2066) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1940_0 & % 231.72/34.75 | $i(all_1940_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1940_0, all_1147_1) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1940_0, v_r) | % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1940_0, % 231.72/34.75 | v_m____)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2066) implies: % 231.72/34.75 | (2067) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1940_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1983) with fresh symbol all_1943_0 gives: % 231.72/34.75 | (2068) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1943_0 & % 231.72/34.75 | $i(all_1943_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_797_0, % 231.72/34.75 | all_1943_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.75 | all_1943_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1559_5, % 231.72/34.75 | all_1943_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2068) implies: % 231.72/34.75 | (2069) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1943_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1965) with fresh symbol all_1945_0 gives: % 231.72/34.75 | (2070) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1945_0 & % 231.72/34.75 | $i(all_1945_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1945_0, % 231.72/34.75 | v_m____) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1945_0, % 231.72/34.75 | v_r) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_1945_0, all_1147_1)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2070) implies: % 231.72/34.75 | (2071) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1945_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1964) with fresh symbol all_1947_0 gives: % 231.72/34.75 | (2072) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1947_0 & % 231.72/34.75 | $i(all_1947_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1947_0, % 231.72/34.75 | v_m____) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.75 | all_1947_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_1, % 231.72/34.75 | all_1947_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2072) implies: % 231.72/34.75 | (2073) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1947_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1963) with fresh symbol all_1949_0 gives: % 231.72/34.75 | (2074) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1949_0 & % 231.72/34.75 | $i(all_1949_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1949_0, v_r) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_m____, % 231.72/34.75 | all_1949_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1147_1, all_1949_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2074) implies: % 231.72/34.75 | (2075) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1949_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1962) with fresh symbol all_1951_0 gives: % 231.72/34.75 | (2076) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1951_0 & % 231.72/34.75 | $i(all_1951_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1951_0, v_m____) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1951_0, v_r) | % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1951_0, % 231.72/34.75 | all_1147_1)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2076) implies: % 231.72/34.75 | (2077) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1951_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1981) with fresh symbol all_1953_0 gives: % 231.72/34.75 | (2078) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1953_0 & % 231.72/34.75 | $i(all_1953_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1953_0, % 231.72/34.75 | all_797_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1953_0, % 231.72/34.75 | all_748_1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_1953_0, all_1559_5)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2078) implies: % 231.72/34.75 | (2079) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1953_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1980) with fresh symbol all_1955_0 gives: % 231.72/34.75 | (2080) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1955_0 & % 231.72/34.75 | $i(all_1955_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_797_0, all_1955_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.75 | all_1955_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1559_5, all_1955_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2080) implies: % 231.72/34.75 | (2081) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1955_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1979) with fresh symbol all_1957_0 gives: % 231.72/34.75 | (2082) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1957_0 & % 231.72/34.75 | $i(all_1957_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_748_1, all_1957_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_797_0, % 231.72/34.75 | all_1957_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1559_5, all_1957_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2082) implies: % 231.72/34.75 | (2083) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1957_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (2004) with fresh symbol all_1959_0 gives: % 231.72/34.75 | (2084) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1959_0 & % 231.72/34.75 | $i(all_1959_0) & ( ~ (all_1959_0 = all_1483_0) | all_1483_0 = % 231.72/34.75 | all_748_1) & ( ~ (all_1959_0 = all_748_1) | all_1483_0 = % 231.72/34.75 | all_748_1) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2084) implies: % 231.72/34.75 | (2085) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1959_0 % 231.72/34.75 | (2086) ~ (all_1959_0 = all_1483_0) | all_1483_0 = all_748_1 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1957) with fresh symbol all_1961_0 gives: % 231.72/34.75 | (2087) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1961_0 & % 231.72/34.75 | $i(all_1961_0) & ( ~ (all_1961_0 = all_1147_1) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1147_1, % 231.72/34.75 | all_1147_0)) & (all_1961_0 = all_1147_1 | % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1961_0, % 231.72/34.75 | all_1147_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2087) implies: % 231.72/34.75 | (2088) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1961_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (2003) with fresh symbol all_1963_0 gives: % 231.72/34.75 | (2089) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1963_0 & % 231.72/34.75 | $i(all_1963_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1963_0, % 231.72/34.75 | all_748_1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_1483_0, all_1963_0)) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1483_0, % 231.72/34.75 | all_1963_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1963_0, % 231.72/34.75 | all_748_1)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2089) implies: % 231.72/34.75 | (2090) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1963_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (2002) with fresh symbol all_1965_0 gives: % 231.72/34.75 | (2091) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1965_0 & % 231.72/34.75 | $i(all_1965_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1965_0, % 231.72/34.75 | all_1483_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.75 | all_1965_0)) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_748_1, % 231.72/34.75 | all_1965_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1965_0, % 231.72/34.75 | all_1483_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2091) implies: % 231.72/34.75 | (2092) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1965_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (2001) with fresh symbol all_1969_0 gives: % 231.72/34.75 | (2093) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1969_0 & % 231.72/34.75 | $i(all_1969_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1969_0, all_748_1) | % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1483_0, % 231.72/34.75 | all_1969_0)) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1483_0, % 231.72/34.75 | all_1969_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1969_0, all_748_1)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2093) implies: % 231.72/34.75 | (2094) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1969_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (2000) with fresh symbol all_1971_0 gives: % 231.72/34.75 | (2095) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1971_0 & % 231.72/34.75 | $i(all_1971_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1971_0, all_1483_0) | % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_748_1, % 231.72/34.75 | all_1971_0)) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_748_1, % 231.72/34.75 | all_1971_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 231.72/34.75 | all_1971_0, all_1483_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2095) implies: % 231.72/34.75 | (2096) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1971_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1956) with fresh symbol all_1977_0 gives: % 231.72/34.75 | (2097) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1977_0 & % 231.72/34.75 | $i(all_1977_0) & ( ~ (all_1977_0 = all_1147_0) | all_1147_0 = % 231.72/34.75 | all_1147_1) & ( ~ (all_1977_0 = all_1147_1) | all_1147_0 = % 231.72/34.75 | all_1147_1) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2097) implies: % 231.72/34.75 | (2098) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1977_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1958) with fresh symbol all_1979_0 gives: % 231.72/34.75 | (2099) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1979_0 & % 231.72/34.75 | $i(all_1979_0) & ( ~ (all_1979_0 = all_1147_1) | % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_0, % 231.72/34.75 | all_1147_1)) & (all_1979_0 = all_1147_1 | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_0, % 231.72/34.75 | all_1979_0)) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2099) implies: % 231.72/34.75 | (2100) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1979_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1971) with fresh symbol all_1987_0 gives: % 231.72/34.75 | (2101) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1987_0 & % 231.72/34.75 | $i(all_1987_0) & % 231.72/34.75 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1987_0, % 231.72/34.75 | all_1147_1) | (( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_1987_0, v_m____) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_1987_0, v_r)) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.75 | all_1987_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.75 | all_1987_0)))) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2101) implies: % 231.72/34.75 | (2102) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1987_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (2005) with fresh symbol all_1990_0 gives: % 231.72/34.75 | (2103) ( ~ (all_1483_0 = all_748_1) | (all_1990_0 = all_748_1 & % 231.72/34.75 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_748_1)) & % 231.72/34.75 | (all_1483_0 = all_748_1 | ( ~ (all_1990_0 = all_748_1) & % 231.72/34.75 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1990_0 & % 231.72/34.75 | $i(all_1990_0))) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2103) implies: % 231.72/34.75 | (2104) all_1483_0 = all_748_1 | ( ~ (all_1990_0 = all_748_1) & % 231.72/34.75 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1990_0 & % 231.72/34.75 | $i(all_1990_0)) % 231.72/34.75 | (2105) ~ (all_1483_0 = all_748_1) | (all_1990_0 = all_748_1 & % 231.72/34.75 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_748_1) % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1967) with fresh symbol all_1992_0 gives: % 231.72/34.75 | (2106) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1992_0 & % 231.72/34.75 | $i(all_1992_0) & % 231.72/34.75 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_1, % 231.72/34.75 | all_1992_0) | (( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_1992_0, v_m____) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.75 | all_1992_0)) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_1992_0, v_r) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.75 | all_1992_0)))) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2106) implies: % 231.72/34.75 | (2107) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1992_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1968) with fresh symbol all_1998_0 gives: % 231.72/34.75 | (2108) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1998_0 & % 231.72/34.75 | $i(all_1998_0) & ( ~ (all_1998_0 = all_1147_1) | all_1147_1 = % 231.72/34.75 | v_m____ | all_1147_1 = v_r) & (all_1998_0 = all_1147_1 | ( ~ % 231.72/34.75 | (all_1998_0 = v_m____) & ~ (all_1998_0 = v_r))) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2108) implies: % 231.72/34.75 | (2109) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1998_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1994) with fresh symbol all_2011_0 gives: % 231.72/34.75 | (2110) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2011_0 & % 231.72/34.75 | $i(all_2011_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2011_0, % 231.72/34.75 | all_1559_5) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2011_0, % 231.72/34.75 | all_1147_0) | (( ~ (all_2011_0 = all_1559_0) | (all_1559_0 = % 231.72/34.75 | all_1147_0 & all_1559_5 = all_1147_0)) & ( ~ (all_2011_0 = % 231.72/34.75 | all_1147_0) | ~ (all_1559_5 = all_1147_0) | all_1559_0 = % 231.72/34.75 | all_1147_0))) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2110) implies: % 231.72/34.75 | (2111) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2011_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1982) with fresh symbol all_2014_0 gives: % 231.72/34.75 | (2112) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2014_0 & % 231.72/34.75 | $i(all_2014_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2014_0, % 231.72/34.75 | all_797_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2014_0, % 231.72/34.75 | all_748_1) | (( ~ (all_2014_0 = all_1559_5) | (all_1559_5 = % 231.72/34.75 | all_748_1 & all_797_0 = all_748_1)) & ( ~ (all_2014_0 = % 231.72/34.75 | all_748_1) | ~ (all_797_0 = all_748_1) | all_1559_5 = % 231.72/34.75 | all_748_1))) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2112) implies: % 231.72/34.75 | (2113) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2014_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1974) with fresh symbol all_2040_0 gives: % 231.72/34.75 | (2114) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2040_0 & % 231.72/34.75 | $i(all_2040_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_1, % 231.72/34.75 | all_2040_0) | % 231.72/34.75 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2040_0, % 231.72/34.75 | v_m____) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | v_r, all_2040_0)) | % 231.72/34.75 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2040_0, % 231.72/34.75 | v_r) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | v_m____, all_2040_0))) & % 231.72/34.75 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1147_1, % 231.72/34.75 | all_2040_0) | (( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_2040_0, v_m____) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.75 | all_2040_0)) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_2040_0, v_r) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.75 | all_2040_0)))) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2114) implies: % 231.72/34.75 | (2115) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2040_0 % 231.72/34.75 | % 231.72/34.75 | DELTA: instantiating (1973) with fresh symbol all_2042_0 gives: % 231.72/34.75 | (2116) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2042_0 & % 231.72/34.75 | $i(all_2042_0) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2042_0, % 231.72/34.75 | all_1147_1) | % 231.72/34.75 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2042_0, % 231.72/34.75 | v_m____) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_2042_0, v_r)) | % 231.72/34.75 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.75 | all_2042_0) & % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.75 | all_2042_0))) & % 231.72/34.75 | (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_2042_0, % 231.72/34.75 | all_1147_1) | (( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_2042_0, v_m____) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 231.72/34.75 | all_2042_0, v_r)) & ( ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_m____, % 231.72/34.75 | all_2042_0) | ~ % 231.72/34.75 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_r, % 231.72/34.75 | all_2042_0)))) % 231.72/34.75 | % 231.72/34.75 | ALPHA: (2116) implies: % 231.72/34.75 | (2117) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_2042_0 % 231.72/34.75 | % 231.72/34.75 | REDUCE: (1827), (2010) imply: % 231.72/34.75 | (2118) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_757_0, % 231.72/34.75 | all_1835_0) % 231.72/34.75 | % 231.72/34.75 | BETA: splitting (2105) gives: % 231.72/34.75 | % 231.72/34.75 | Case 1: % 231.72/34.75 | | % 231.72/34.75 | | (2119) ~ (all_1483_0 = all_748_1) % 231.72/34.75 | | % 231.72/34.75 | | BETA: splitting (2104) gives: % 231.72/34.75 | | % 231.72/34.75 | | Case 1: % 231.72/34.75 | | | % 231.72/34.75 | | | (2120) all_1483_0 = all_748_1 % 231.72/34.75 | | | % 231.72/34.75 | | | REDUCE: (2119), (2120) imply: % 231.72/34.75 | | | (2121) $false % 231.72/34.75 | | | % 231.72/34.75 | | | CLOSE: (2121) is inconsistent. % 231.72/34.75 | | | % 231.72/34.75 | | Case 2: % 231.72/34.75 | | | % 231.72/34.75 | | | (2122) ~ (all_1990_0 = all_748_1) & % 231.72/34.75 | | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1990_0 & % 231.72/34.75 | | | $i(all_1990_0) % 231.72/34.75 | | | % 231.72/34.75 | | | ALPHA: (2122) implies: % 231.72/34.75 | | | (2123) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1990_0 % 231.72/34.75 | | | % 231.72/34.75 | | | BETA: splitting (2086) gives: % 231.72/34.75 | | | % 231.72/34.75 | | | Case 1: % 231.72/34.75 | | | | % 231.72/34.75 | | | | % 231.72/34.75 | | | | GROUND_INST: instantiating (243) with all_1883_0, all_1895_0, % 231.72/34.75 | | | | tc_RealDef_Oreal, simplifying with (2026), (2028) gives: % 231.72/34.75 | | | | (2124) all_1895_0 = all_1883_0 % 231.72/34.75 | | | | % 231.72/34.75 | | | | GROUND_INST: instantiating (243) with all_1873_0, all_1897_0, % 231.72/34.75 | | | | tc_RealDef_Oreal, simplifying with (2021), (2030) gives: % 231.72/34.75 | | | | (2125) all_1897_0 = all_1873_0 % 231.72/34.75 | | | | % 231.72/34.75 | | | | GROUND_INST: instantiating (243) with all_1895_0, all_1903_0, % 231.72/34.75 | | | | tc_RealDef_Oreal, simplifying with (2028), (2032) gives: % 231.72/34.75 | | | | (2126) all_1903_0 = all_1895_0 % 231.72/34.75 | | | | % 231.72/34.76 | | | | GROUND_INST: instantiating (243) with all_1873_0, all_1915_0, % 231.72/34.76 | | | | tc_RealDef_Oreal, simplifying with (2021), (2042) gives: % 231.72/34.76 | | | | (2127) all_1915_0 = all_1873_0 % 231.72/34.76 | | | | % 231.72/34.76 | | | | GROUND_INST: instantiating (243) with all_1897_0, all_1919_0, % 231.72/34.76 | | | | tc_RealDef_Oreal, simplifying with (2030), (2047) gives: % 231.72/34.76 | | | | (2128) all_1919_0 = all_1897_0 % 231.72/34.76 | | | | % 231.72/34.76 | | | | GROUND_INST: instantiating (243) with all_1917_0, all_1921_0, % 231.72/34.76 | | | | tc_RealDef_Oreal, simplifying with (2045), (2049) gives: % 231.72/34.76 | | | | (2129) all_1921_0 = all_1917_0 % 231.72/34.76 | | | | % 231.72/34.76 | | | | GROUND_INST: instantiating (243) with all_1925_0, all_1927_0, % 231.72/34.76 | | | | tc_RealDef_Oreal, simplifying with (2053), (2055) gives: % 231.72/34.76 | | | | (2130) all_1927_0 = all_1925_0 % 231.72/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1927_0, all_1929_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2055), (2057) gives: % 232.02/34.76 | | | | (2131) all_1929_0 = all_1927_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1921_0, all_1932_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2049), (2059) gives: % 232.02/34.76 | | | | (2132) all_1932_0 = all_1921_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1929_0, all_1934_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2057), (2061) gives: % 232.02/34.76 | | | | (2133) all_1934_0 = all_1929_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1915_0, all_1936_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2042), (2063) gives: % 232.02/34.76 | | | | (2134) all_1936_0 = all_1915_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1940_0, all_1943_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2067), (2069) gives: % 232.02/34.76 | | | | (2135) all_1943_0 = all_1940_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1919_0, all_1943_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2047), (2069) gives: % 232.02/34.76 | | | | (2136) all_1943_0 = all_1919_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1871_0, all_1943_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2019), (2069) gives: % 232.02/34.76 | | | | (2137) all_1943_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1951_0, all_1955_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2077), (2081) gives: % 232.02/34.76 | | | | (2138) all_1955_0 = all_1951_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1945_0, all_1955_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2071), (2081) gives: % 232.02/34.76 | | | | (2139) all_1955_0 = all_1945_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1932_0, all_1957_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2059), (2083) gives: % 232.02/34.76 | | | | (2140) all_1957_0 = all_1932_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1953_0, all_1959_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2079), (2085) gives: % 232.02/34.76 | | | | (2141) all_1959_0 = all_1953_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1957_0, all_1961_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2083), (2088) gives: % 232.02/34.76 | | | | (2142) all_1961_0 = all_1957_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1955_0, all_1963_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2081), (2090) gives: % 232.02/34.76 | | | | (2143) all_1963_0 = all_1955_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1938_0, all_1963_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2065), (2090) gives: % 232.02/34.76 | | | | (2144) all_1963_0 = all_1938_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1936_0, all_1963_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2063), (2090) gives: % 232.02/34.76 | | | | (2145) all_1963_0 = all_1936_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1961_0, all_1965_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2088), (2092) gives: % 232.02/34.76 | | | | (2146) all_1965_0 = all_1961_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1917_0, all_1969_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2045), (2094) gives: % 232.02/34.76 | | | | (2147) all_1969_0 = all_1917_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1911_0, all_1969_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2038), (2094) gives: % 232.02/34.76 | | | | (2148) all_1969_0 = all_1911_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1959_0, all_1971_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2085), (2096) gives: % 232.02/34.76 | | | | (2149) all_1971_0 = all_1959_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1934_0, all_1977_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2061), (2098) gives: % 232.02/34.76 | | | | (2150) all_1977_0 = all_1934_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1951_0, all_1979_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2077), (2100) gives: % 232.02/34.76 | | | | (2151) all_1979_0 = all_1951_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1847_0, all_1979_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2013), (2100) gives: % 232.02/34.76 | | | | (2152) all_1979_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1971_0, all_1987_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2096), (2102) gives: % 232.02/34.76 | | | | (2153) all_1987_0 = all_1971_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_757_0, all_1990_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (290), (2123) gives: % 232.02/34.76 | | | | (2154) all_1990_0 = all_757_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1897_0, all_1990_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2030), (2123) gives: % 232.02/34.76 | | | | (2155) all_1990_0 = all_1897_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1883_0, all_1990_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2026), (2123) gives: % 232.02/34.76 | | | | (2156) all_1990_0 = all_1883_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1875_0, all_1990_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2023), (2123) gives: % 232.02/34.76 | | | | (2157) all_1990_0 = all_1875_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1977_0, all_1992_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2098), (2107) gives: % 232.02/34.76 | | | | (2158) all_1992_0 = all_1977_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1865_0, all_1992_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2017), (2107) gives: % 232.02/34.76 | | | | (2159) all_1992_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1969_0, all_1998_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2094), (2109) gives: % 232.02/34.76 | | | | (2160) all_1998_0 = all_1969_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1927_0, all_1998_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2055), (2109) gives: % 232.02/34.76 | | | | (2161) all_1998_0 = all_1927_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1913_0, all_1998_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2040), (2109) gives: % 232.02/34.76 | | | | (2162) all_1998_0 = all_1913_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1953_0, all_2011_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2079), (2111) gives: % 232.02/34.76 | | | | (2163) all_2011_0 = all_1953_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1947_0, all_2011_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2073), (2111) gives: % 232.02/34.76 | | | | (2164) all_2011_0 = all_1947_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1917_0, all_2011_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2045), (2111) gives: % 232.02/34.76 | | | | (2165) all_2011_0 = all_1917_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1903_0, all_2011_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2032), (2111) gives: % 232.02/34.76 | | | | (2166) all_2011_0 = all_1903_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1987_0, all_2014_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2102), (2113) gives: % 232.02/34.76 | | | | (2167) all_2014_0 = all_1987_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1905_0, all_2014_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2034), (2113) gives: % 232.02/34.76 | | | | (2168) all_2014_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1969_0, all_2040_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2094), (2115) gives: % 232.02/34.76 | | | | (2169) all_2040_0 = all_1969_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1949_0, all_2040_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2075), (2115) gives: % 232.02/34.76 | | | | (2170) all_2040_0 = all_1949_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1965_0, all_2042_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2092), (2117) gives: % 232.02/34.76 | | | | (2171) all_2042_0 = all_1965_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (243) with all_1909_0, all_2042_0, % 232.02/34.76 | | | | tc_RealDef_Oreal, simplifying with (2036), (2117) gives: % 232.02/34.76 | | | | (2172) all_2042_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (251) with all_1835_0, all_1853_0, all_748_0, % 232.02/34.76 | | | | tc_Nat_Onat, simplifying with (2011), (2015) gives: % 232.02/34.76 | | | | (2173) all_1853_0 = all_1835_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (251) with all_748_1, all_1923_1, all_748_0, % 232.02/34.76 | | | | tc_Nat_Onat, simplifying with (1945), (2051) gives: % 232.02/34.76 | | | | (2174) all_1923_1 = all_748_1 % 232.02/34.76 | | | | % 232.02/34.76 | | | | GROUND_INST: instantiating (251) with all_1853_0, all_1923_1, all_748_0, % 232.02/34.76 | | | | tc_Nat_Onat, simplifying with (2015), (2051) gives: % 232.02/34.76 | | | | (2175) all_1923_1 = all_1853_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2171), (2172) imply: % 232.02/34.76 | | | | (2176) all_1965_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2176) implies: % 232.02/34.76 | | | | (2177) all_1965_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2169), (2170) imply: % 232.02/34.76 | | | | (2178) all_1969_0 = all_1949_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2178) implies: % 232.02/34.76 | | | | (2179) all_1969_0 = all_1949_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2167), (2168) imply: % 232.02/34.76 | | | | (2180) all_1987_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2180) implies: % 232.02/34.76 | | | | (2181) all_1987_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2163), (2164) imply: % 232.02/34.76 | | | | (2182) all_1953_0 = all_1947_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2182) implies: % 232.02/34.76 | | | | (2183) all_1953_0 = all_1947_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2164), (2166) imply: % 232.02/34.76 | | | | (2184) all_1947_0 = all_1903_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2164), (2165) imply: % 232.02/34.76 | | | | (2185) all_1947_0 = all_1917_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2160), (2162) imply: % 232.02/34.76 | | | | (2186) all_1969_0 = all_1913_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2186) implies: % 232.02/34.76 | | | | (2187) all_1969_0 = all_1913_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2161), (2162) imply: % 232.02/34.76 | | | | (2188) all_1927_0 = all_1913_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2188) implies: % 232.02/34.76 | | | | (2189) all_1927_0 = all_1913_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2158), (2159) imply: % 232.02/34.76 | | | | (2190) all_1977_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2190) implies: % 232.02/34.76 | | | | (2191) all_1977_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2155), (2157) imply: % 232.02/34.76 | | | | (2192) all_1897_0 = all_1875_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2192) implies: % 232.02/34.76 | | | | (2193) all_1897_0 = all_1875_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2156), (2157) imply: % 232.02/34.76 | | | | (2194) all_1883_0 = all_1875_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2194) implies: % 232.02/34.76 | | | | (2195) all_1883_0 = all_1875_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2154), (2157) imply: % 232.02/34.76 | | | | (2196) all_1875_0 = all_757_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2153), (2181) imply: % 232.02/34.76 | | | | (2197) all_1971_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2197) implies: % 232.02/34.76 | | | | (2198) all_1971_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2151), (2152) imply: % 232.02/34.76 | | | | (2199) all_1951_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2199) implies: % 232.02/34.76 | | | | (2200) all_1951_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2150), (2191) imply: % 232.02/34.76 | | | | (2201) all_1934_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2201) implies: % 232.02/34.76 | | | | (2202) all_1934_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2149), (2198) imply: % 232.02/34.76 | | | | (2203) all_1959_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2203) implies: % 232.02/34.76 | | | | (2204) all_1959_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2148), (2179) imply: % 232.02/34.76 | | | | (2205) all_1949_0 = all_1911_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2147), (2179) imply: % 232.02/34.76 | | | | (2206) all_1949_0 = all_1917_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2179), (2187) imply: % 232.02/34.76 | | | | (2207) all_1949_0 = all_1913_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2146), (2177) imply: % 232.02/34.76 | | | | (2208) all_1961_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2208) implies: % 232.02/34.76 | | | | (2209) all_1961_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2144), (2145) imply: % 232.02/34.76 | | | | (2210) all_1938_0 = all_1936_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2143), (2144) imply: % 232.02/34.76 | | | | (2211) all_1955_0 = all_1938_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2211) implies: % 232.02/34.76 | | | | (2212) all_1955_0 = all_1938_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2142), (2209) imply: % 232.02/34.76 | | | | (2213) all_1957_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2213) implies: % 232.02/34.76 | | | | (2214) all_1957_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2141), (2204) imply: % 232.02/34.76 | | | | (2215) all_1953_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2215) implies: % 232.02/34.76 | | | | (2216) all_1953_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2140), (2214) imply: % 232.02/34.76 | | | | (2217) all_1932_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2217) implies: % 232.02/34.76 | | | | (2218) all_1932_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2138), (2139) imply: % 232.02/34.76 | | | | (2219) all_1951_0 = all_1945_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2219) implies: % 232.02/34.76 | | | | (2220) all_1951_0 = all_1945_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2139), (2212) imply: % 232.02/34.76 | | | | (2221) all_1945_0 = all_1938_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2183), (2216) imply: % 232.02/34.76 | | | | (2222) all_1947_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2222) implies: % 232.02/34.76 | | | | (2223) all_1947_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2200), (2220) imply: % 232.02/34.76 | | | | (2224) all_1945_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2224) implies: % 232.02/34.76 | | | | (2225) all_1945_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2205), (2207) imply: % 232.02/34.76 | | | | (2226) all_1913_0 = all_1911_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2226) implies: % 232.02/34.76 | | | | (2227) all_1913_0 = all_1911_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2205), (2206) imply: % 232.02/34.76 | | | | (2228) all_1917_0 = all_1911_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2228) implies: % 232.02/34.76 | | | | (2229) all_1917_0 = all_1911_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2184), (2223) imply: % 232.02/34.76 | | | | (2230) all_1905_0 = all_1903_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2185), (2223) imply: % 232.02/34.76 | | | | (2231) all_1917_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2231) implies: % 232.02/34.76 | | | | (2232) all_1917_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2221), (2225) imply: % 232.02/34.76 | | | | (2233) all_1938_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2233) implies: % 232.02/34.76 | | | | (2234) all_1938_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2135), (2137) imply: % 232.02/34.76 | | | | (2235) all_1940_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2135), (2136) imply: % 232.02/34.76 | | | | (2236) all_1940_0 = all_1919_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2235), (2236) imply: % 232.02/34.76 | | | | (2237) all_1919_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2237) implies: % 232.02/34.76 | | | | (2238) all_1919_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2210), (2234) imply: % 232.02/34.76 | | | | (2239) all_1936_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2239) implies: % 232.02/34.76 | | | | (2240) all_1936_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2134), (2240) imply: % 232.02/34.76 | | | | (2241) all_1915_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2241) implies: % 232.02/34.76 | | | | (2242) all_1915_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2133), (2202) imply: % 232.02/34.76 | | | | (2243) all_1929_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2243) implies: % 232.02/34.76 | | | | (2244) all_1929_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2132), (2218) imply: % 232.02/34.76 | | | | (2245) all_1921_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2245) implies: % 232.02/34.76 | | | | (2246) all_1921_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2131), (2244) imply: % 232.02/34.76 | | | | (2247) all_1927_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2247) implies: % 232.02/34.76 | | | | (2248) all_1927_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2130), (2248) imply: % 232.02/34.76 | | | | (2249) all_1925_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2130), (2189) imply: % 232.02/34.76 | | | | (2250) all_1925_0 = all_1913_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2249), (2250) imply: % 232.02/34.76 | | | | (2251) all_1913_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2251) implies: % 232.02/34.76 | | | | (2252) all_1913_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2174), (2175) imply: % 232.02/34.76 | | | | (2253) all_1853_0 = all_748_1 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2253) implies: % 232.02/34.76 | | | | (2254) all_1853_0 = all_748_1 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2129), (2246) imply: % 232.02/34.76 | | | | (2255) all_1917_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2255) implies: % 232.02/34.76 | | | | (2256) all_1917_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2128), (2238) imply: % 232.02/34.76 | | | | (2257) all_1897_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2257) implies: % 232.02/34.76 | | | | (2258) all_1897_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2229), (2256) imply: % 232.02/34.76 | | | | (2259) all_1911_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2259) implies: % 232.02/34.76 | | | | (2260) all_1911_0 = all_1909_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2232), (2256) imply: % 232.02/34.76 | | | | (2261) all_1909_0 = all_1905_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2127), (2242) imply: % 232.02/34.76 | | | | (2262) all_1873_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2262) implies: % 232.02/34.76 | | | | (2263) all_1873_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2227), (2252) imply: % 232.02/34.76 | | | | (2264) all_1911_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2264) implies: % 232.02/34.76 | | | | (2265) all_1911_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2260), (2265) imply: % 232.02/34.76 | | | | (2266) all_1909_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2266) implies: % 232.02/34.76 | | | | (2267) all_1909_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2261), (2267) imply: % 232.02/34.76 | | | | (2268) all_1905_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2268) implies: % 232.02/34.76 | | | | (2269) all_1905_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2230), (2269) imply: % 232.02/34.76 | | | | (2270) all_1903_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2270) implies: % 232.02/34.76 | | | | (2271) all_1903_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2126), (2271) imply: % 232.02/34.76 | | | | (2272) all_1895_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2272) implies: % 232.02/34.76 | | | | (2273) all_1895_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2125), (2258) imply: % 232.02/34.76 | | | | (2274) all_1873_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2274) implies: % 232.02/34.76 | | | | (2275) all_1873_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2193), (2258) imply: % 232.02/34.76 | | | | (2276) all_1875_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2276) implies: % 232.02/34.76 | | | | (2277) all_1875_0 = all_1871_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2124), (2273) imply: % 232.02/34.76 | | | | (2278) all_1883_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2278) implies: % 232.02/34.76 | | | | (2279) all_1883_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2195), (2279) imply: % 232.02/34.76 | | | | (2280) all_1875_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2280) implies: % 232.02/34.76 | | | | (2281) all_1875_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2196), (2281) imply: % 232.02/34.76 | | | | (2282) all_1865_0 = all_757_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2277), (2281) imply: % 232.02/34.76 | | | | (2283) all_1871_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2283) implies: % 232.02/34.76 | | | | (2284) all_1871_0 = all_1865_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2263), (2275) imply: % 232.02/34.76 | | | | (2285) all_1871_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2285) implies: % 232.02/34.76 | | | | (2286) all_1871_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2284), (2286) imply: % 232.02/34.76 | | | | (2287) all_1865_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | SIMP: (2287) implies: % 232.02/34.76 | | | | (2288) all_1865_0 = all_1847_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2282), (2288) imply: % 232.02/34.76 | | | | (2289) all_1847_0 = all_757_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2173), (2254) imply: % 232.02/34.76 | | | | (2290) all_1835_0 = all_748_1 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2279), (2282) imply: % 232.02/34.76 | | | | (2291) all_1883_0 = all_757_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | COMBINE_EQS: (2242), (2289) imply: % 232.02/34.76 | | | | (2292) all_1915_0 = all_757_0 % 232.02/34.76 | | | | % 232.02/34.76 | | | | REDUCE: (2118), (2290) imply: % 232.02/34.76 | | | | (2293) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_757_0, % 232.02/34.76 | | | | all_748_1) % 232.02/34.76 | | | | % 232.02/34.76 | | | | REDUCE: (2025), (2291) imply: % 232.02/34.76 | | | | (2294) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_757_0, % 232.02/34.76 | | | | all_1559_5) % 232.02/34.76 | | | | % 232.02/34.76 | | | | BETA: splitting (2043) gives: % 232.02/34.76 | | | | % 232.02/34.76 | | | | Case 1: % 232.02/34.76 | | | | | % 232.02/34.76 | | | | | (2295) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 232.02/34.76 | | | | | all_1915_0, all_748_1) % 232.02/34.76 | | | | | % 232.02/34.76 | | | | | REDUCE: (2292), (2295) imply: % 232.02/34.77 | | | | | (2296) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 232.02/34.77 | | | | | all_757_0, all_748_1) % 232.02/34.77 | | | | | % 232.02/34.77 | | | | | PRED_UNIFY: (2293), (2296) imply: % 232.02/34.77 | | | | | (2297) $false % 232.02/34.77 | | | | | % 232.02/34.77 | | | | | CLOSE: (2297) is inconsistent. % 232.02/34.77 | | | | | % 232.02/34.77 | | | | Case 2: % 232.02/34.77 | | | | | % 232.02/34.77 | | | | | (2298) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 232.02/34.77 | | | | | all_1915_0, all_797_0) | % 232.02/34.77 | | | | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1915_0, % 232.02/34.77 | | | | | all_1559_5) % 232.02/34.77 | | | | | % 232.02/34.77 | | | | | BETA: splitting (2298) gives: % 232.02/34.77 | | | | | % 232.02/34.77 | | | | | Case 1: % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | | (2299) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 232.02/34.77 | | | | | | all_1915_0, all_797_0) % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | | REDUCE: (2292), (2299) imply: % 232.02/34.77 | | | | | | (2300) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 232.02/34.77 | | | | | | all_757_0, all_797_0) % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | | PRED_UNIFY: (1888), (2300) imply: % 232.02/34.77 | | | | | | (2301) $false % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | | CLOSE: (2301) is inconsistent. % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | Case 2: % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | | (2302) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 232.02/34.77 | | | | | | all_1915_0, all_1559_5) % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | | REDUCE: (2292), (2302) imply: % 232.02/34.77 | | | | | | (2303) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_757_0, % 232.02/34.77 | | | | | | all_1559_5) % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | | PRED_UNIFY: (2294), (2303) imply: % 232.02/34.77 | | | | | | (2304) $false % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | | CLOSE: (2304) is inconsistent. % 232.02/34.77 | | | | | | % 232.02/34.77 | | | | | End of split % 232.02/34.77 | | | | | % 232.02/34.77 | | | | End of split % 232.02/34.77 | | | | % 232.12/34.78 | | | Case 2: % 232.12/34.78 | | | | % 232.12/34.78 | | | | (2305) all_1483_0 = all_748_1 % 232.12/34.78 | | | | % 232.12/34.78 | | | | REDUCE: (2119), (2305) imply: % 232.12/34.78 | | | | (2306) $false % 232.12/34.78 | | | | % 232.12/34.78 | | | | CLOSE: (2306) is inconsistent. % 232.12/34.78 | | | | % 232.12/34.78 | | | End of split % 232.12/34.78 | | | % 232.12/34.78 | | End of split % 232.12/34.78 | | % 232.12/34.78 | Case 2: % 232.12/34.78 | | % 232.12/34.78 | | (2307) all_1990_0 = all_748_1 & % 232.12/34.78 | | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_748_1 % 232.12/34.78 | | % 232.12/34.78 | | ALPHA: (2307) implies: % 232.12/34.78 | | (2308) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_748_1 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1883_0, all_1909_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2026), (2036) gives: % 232.12/34.78 | | (2309) all_1909_0 = all_1883_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1875_0, all_1913_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2023), (2040) gives: % 232.12/34.78 | | (2310) all_1913_0 = all_1875_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1873_0, all_1915_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2021), (2042) gives: % 232.12/34.78 | | (2311) all_1915_0 = all_1873_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_757_0, all_1917_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (290), (2045) gives: % 232.12/34.78 | | (2312) all_1917_0 = all_757_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1875_0, all_1917_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2023), (2045) gives: % 232.12/34.78 | | (2313) all_1917_0 = all_1875_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1909_0, all_1919_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2036), (2047) gives: % 232.12/34.78 | | (2314) all_1919_0 = all_1909_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1919_0, all_1921_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2047), (2049) gives: % 232.12/34.78 | | (2315) all_1921_0 = all_1919_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1921_0, all_1925_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2049), (2053) gives: % 232.12/34.78 | | (2316) all_1925_0 = all_1921_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1917_0, all_1927_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2045), (2055) gives: % 232.12/34.78 | | (2317) all_1927_0 = all_1917_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1929_0, all_1932_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2057), (2059) gives: % 232.12/34.78 | | (2318) all_1932_0 = all_1929_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1929_0, all_1934_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2057), (2061) gives: % 232.12/34.78 | | (2319) all_1934_0 = all_1929_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1909_0, all_1934_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2036), (2061) gives: % 232.12/34.78 | | (2320) all_1934_0 = all_1909_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1875_0, all_1936_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2023), (2063) gives: % 232.12/34.78 | | (2321) all_1936_0 = all_1875_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1934_0, all_1938_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2061), (2065) gives: % 232.12/34.78 | | (2322) all_1938_0 = all_1934_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1925_0, all_1940_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2053), (2067) gives: % 232.12/34.78 | | (2323) all_1940_0 = all_1925_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1927_0, all_1947_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2055), (2073) gives: % 232.12/34.78 | | (2324) all_1947_0 = all_1927_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1940_0, all_1953_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2067), (2079) gives: % 232.12/34.78 | | (2325) all_1953_0 = all_1940_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1953_0, all_1955_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2079), (2081) gives: % 232.12/34.78 | | (2326) all_1955_0 = all_1953_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1951_0, all_1957_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2077), (2083) gives: % 232.12/34.78 | | (2327) all_1957_0 = all_1951_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1957_0, all_1959_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2083), (2085) gives: % 232.12/34.78 | | (2328) all_1959_0 = all_1957_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1959_0, all_1961_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2085), (2088) gives: % 232.12/34.78 | | (2329) all_1961_0 = all_1959_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1934_0, all_1963_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2061), (2090) gives: % 232.12/34.78 | | (2330) all_1963_0 = all_1934_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1917_0, all_1963_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2045), (2090) gives: % 232.12/34.78 | | (2331) all_1963_0 = all_1917_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1915_0, all_1963_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2042), (2090) gives: % 232.12/34.78 | | (2332) all_1963_0 = all_1915_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1895_0, all_1963_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2028), (2090) gives: % 232.12/34.78 | | (2333) all_1963_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1953_0, all_1965_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2079), (2092) gives: % 232.12/34.78 | | (2334) all_1965_0 = all_1953_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1951_0, all_1965_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2077), (2092) gives: % 232.12/34.78 | | (2335) all_1965_0 = all_1951_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1949_0, all_1965_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2075), (2092) gives: % 232.12/34.78 | | (2336) all_1965_0 = all_1949_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1932_0, all_1969_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2059), (2094) gives: % 232.12/34.78 | | (2337) all_1969_0 = all_1932_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1913_0, all_1971_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2040), (2096) gives: % 232.12/34.78 | | (2338) all_1971_0 = all_1913_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1847_0, all_1971_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2013), (2096) gives: % 232.12/34.78 | | (2339) all_1971_0 = all_1847_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1936_0, all_1977_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2063), (2098) gives: % 232.12/34.78 | | (2340) all_1977_0 = all_1936_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_748_1, all_1977_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2098), (2308) gives: % 232.12/34.78 | | (2341) all_1977_0 = all_748_1 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1929_0, all_1979_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2057), (2100) gives: % 232.12/34.78 | | (2342) all_1979_0 = all_1929_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1897_0, all_1979_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2030), (2100) gives: % 232.12/34.78 | | (2343) all_1979_0 = all_1897_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1947_0, all_1987_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2073), (2102) gives: % 232.12/34.78 | | (2344) all_1987_0 = all_1947_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1871_0, all_1987_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2019), (2102) gives: % 232.12/34.78 | | (2345) all_1987_0 = all_1871_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1955_0, all_1992_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2081), (2107) gives: % 232.12/34.78 | | (2346) all_1992_0 = all_1955_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1969_0, all_1998_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2094), (2109) gives: % 232.12/34.78 | | (2347) all_1998_0 = all_1969_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1911_0, all_1998_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2038), (2109) gives: % 232.12/34.78 | | (2348) all_1998_0 = all_1911_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1963_0, all_2011_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2090), (2111) gives: % 232.12/34.78 | | (2349) all_2011_0 = all_1963_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1943_0, all_2011_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2069), (2111) gives: % 232.12/34.78 | | (2350) all_2011_0 = all_1943_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1865_0, all_2011_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2017), (2111) gives: % 232.12/34.78 | | (2351) all_2011_0 = all_1865_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1938_0, all_2014_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2065), (2113) gives: % 232.12/34.78 | | (2352) all_2014_0 = all_1938_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1903_0, all_2014_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2032), (2113) gives: % 232.12/34.78 | | (2353) all_2014_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1992_0, all_2040_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2107), (2115) gives: % 232.12/34.78 | | (2354) all_2040_0 = all_1992_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1945_0, all_2040_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2071), (2115) gives: % 232.12/34.78 | | (2355) all_2040_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1961_0, all_2042_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2088), (2117) gives: % 232.12/34.78 | | (2356) all_2042_0 = all_1961_0 % 232.12/34.78 | | % 232.12/34.78 | | GROUND_INST: instantiating (243) with all_1905_0, all_2042_0, % 232.12/34.78 | | tc_RealDef_Oreal, simplifying with (2034), (2117) gives: % 232.12/34.78 | | (2357) all_2042_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2356), (2357) imply: % 232.12/34.78 | | (2358) all_1961_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2358) implies: % 232.12/34.78 | | (2359) all_1961_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2354), (2355) imply: % 232.12/34.78 | | (2360) all_1992_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2360) implies: % 232.12/34.78 | | (2361) all_1992_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2352), (2353) imply: % 232.12/34.78 | | (2362) all_1938_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2362) implies: % 232.12/34.78 | | (2363) all_1938_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2349), (2350) imply: % 232.12/34.78 | | (2364) all_1963_0 = all_1943_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2364) implies: % 232.12/34.78 | | (2365) all_1963_0 = all_1943_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2350), (2351) imply: % 232.12/34.78 | | (2366) all_1943_0 = all_1865_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2347), (2348) imply: % 232.12/34.78 | | (2367) all_1969_0 = all_1911_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2367) implies: % 232.12/34.78 | | (2368) all_1969_0 = all_1911_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2346), (2361) imply: % 232.12/34.78 | | (2369) all_1955_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2369) implies: % 232.12/34.78 | | (2370) all_1955_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2344), (2345) imply: % 232.12/34.78 | | (2371) all_1947_0 = all_1871_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2371) implies: % 232.12/34.78 | | (2372) all_1947_0 = all_1871_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2342), (2343) imply: % 232.12/34.78 | | (2373) all_1929_0 = all_1897_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2373) implies: % 232.12/34.78 | | (2374) all_1929_0 = all_1897_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2340), (2341) imply: % 232.12/34.78 | | (2375) all_1936_0 = all_748_1 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2375) implies: % 232.12/34.78 | | (2376) all_1936_0 = all_748_1 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2338), (2339) imply: % 232.12/34.78 | | (2377) all_1913_0 = all_1847_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2377) implies: % 232.12/34.78 | | (2378) all_1913_0 = all_1847_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2337), (2368) imply: % 232.12/34.78 | | (2379) all_1932_0 = all_1911_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2379) implies: % 232.12/34.78 | | (2380) all_1932_0 = all_1911_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2335), (2336) imply: % 232.12/34.78 | | (2381) all_1951_0 = all_1949_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2381) implies: % 232.12/34.78 | | (2382) all_1951_0 = all_1949_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2334), (2336) imply: % 232.12/34.78 | | (2383) all_1953_0 = all_1949_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2383) implies: % 232.12/34.78 | | (2384) all_1953_0 = all_1949_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2332), (2333) imply: % 232.12/34.78 | | (2385) all_1915_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2385) implies: % 232.12/34.78 | | (2386) all_1915_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2330), (2333) imply: % 232.12/34.78 | | (2387) all_1934_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2387) implies: % 232.12/34.78 | | (2388) all_1934_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2333), (2365) imply: % 232.12/34.78 | | (2389) all_1943_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2389) implies: % 232.12/34.78 | | (2390) all_1943_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2331), (2333) imply: % 232.12/34.78 | | (2391) all_1917_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2391) implies: % 232.12/34.78 | | (2392) all_1917_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2329), (2359) imply: % 232.12/34.78 | | (2393) all_1959_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2393) implies: % 232.12/34.78 | | (2394) all_1959_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2328), (2394) imply: % 232.12/34.78 | | (2395) all_1957_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2395) implies: % 232.12/34.78 | | (2396) all_1957_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2327), (2396) imply: % 232.12/34.78 | | (2397) all_1951_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2397) implies: % 232.12/34.78 | | (2398) all_1951_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2326), (2370) imply: % 232.12/34.78 | | (2399) all_1953_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2399) implies: % 232.12/34.78 | | (2400) all_1953_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2384), (2400) imply: % 232.12/34.78 | | (2401) all_1949_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2401) implies: % 232.12/34.78 | | (2402) all_1949_0 = all_1945_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2325), (2400) imply: % 232.12/34.78 | | (2403) all_1945_0 = all_1940_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2382), (2398) imply: % 232.12/34.78 | | (2404) all_1949_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2404) implies: % 232.12/34.78 | | (2405) all_1949_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2402), (2405) imply: % 232.12/34.78 | | (2406) all_1945_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2406) implies: % 232.12/34.78 | | (2407) all_1945_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2324), (2372) imply: % 232.12/34.78 | | (2408) all_1927_0 = all_1871_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2408) implies: % 232.12/34.78 | | (2409) all_1927_0 = all_1871_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2403), (2407) imply: % 232.12/34.78 | | (2410) all_1940_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2410) implies: % 232.12/34.78 | | (2411) all_1940_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2366), (2390) imply: % 232.12/34.78 | | (2412) all_1895_0 = all_1865_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2412) implies: % 232.12/34.78 | | (2413) all_1895_0 = all_1865_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2323), (2411) imply: % 232.12/34.78 | | (2414) all_1925_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2414) implies: % 232.12/34.78 | | (2415) all_1925_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2322), (2363) imply: % 232.12/34.78 | | (2416) all_1934_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2416) implies: % 232.12/34.78 | | (2417) all_1934_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2321), (2376) imply: % 232.12/34.78 | | (2418) all_1875_0 = all_748_1 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2418) implies: % 232.12/34.78 | | (2419) all_1875_0 = all_748_1 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2319), (2417) imply: % 232.12/34.78 | | (2420) all_1929_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2420) implies: % 232.12/34.78 | | (2421) all_1929_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2320), (2417) imply: % 232.12/34.78 | | (2422) all_1909_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2422) implies: % 232.12/34.78 | | (2423) all_1909_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2388), (2417) imply: % 232.12/34.78 | | (2424) all_1903_0 = all_1895_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2318), (2380) imply: % 232.12/34.78 | | (2425) all_1929_0 = all_1911_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2425) implies: % 232.12/34.78 | | (2426) all_1929_0 = all_1911_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2421), (2426) imply: % 232.12/34.78 | | (2427) all_1911_0 = all_1903_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2374), (2426) imply: % 232.12/34.78 | | (2428) all_1911_0 = all_1897_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2317), (2409) imply: % 232.12/34.78 | | (2429) all_1917_0 = all_1871_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2429) implies: % 232.12/34.78 | | (2430) all_1917_0 = all_1871_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2316), (2415) imply: % 232.12/34.78 | | (2431) all_1921_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2431) implies: % 232.12/34.78 | | (2432) all_1921_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2315), (2432) imply: % 232.12/34.78 | | (2433) all_1919_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2433) implies: % 232.12/34.78 | | (2434) all_1919_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2314), (2434) imply: % 232.12/34.78 | | (2435) all_1909_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | SIMP: (2435) implies: % 232.12/34.78 | | (2436) all_1909_0 = all_1905_0 % 232.12/34.78 | | % 232.12/34.78 | | COMBINE_EQS: (2313), (2430) imply: % 232.12/34.78 | | (2437) all_1875_0 = all_1871_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2437) implies: % 232.12/34.79 | | (2438) all_1875_0 = all_1871_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2392), (2430) imply: % 232.12/34.79 | | (2439) all_1895_0 = all_1871_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2439) implies: % 232.12/34.79 | | (2440) all_1895_0 = all_1871_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2312), (2430) imply: % 232.12/34.79 | | (2441) all_1871_0 = all_757_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2311), (2386) imply: % 232.12/34.79 | | (2442) all_1895_0 = all_1873_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2442) implies: % 232.12/34.79 | | (2443) all_1895_0 = all_1873_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2310), (2378) imply: % 232.12/34.79 | | (2444) all_1875_0 = all_1847_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2444) implies: % 232.12/34.79 | | (2445) all_1875_0 = all_1847_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2427), (2428) imply: % 232.12/34.79 | | (2446) all_1903_0 = all_1897_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2446) implies: % 232.12/34.79 | | (2447) all_1903_0 = all_1897_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2423), (2436) imply: % 232.12/34.79 | | (2448) all_1905_0 = all_1903_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2309), (2436) imply: % 232.12/34.79 | | (2449) all_1905_0 = all_1883_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2448), (2449) imply: % 232.12/34.79 | | (2450) all_1903_0 = all_1883_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2450) implies: % 232.12/34.79 | | (2451) all_1903_0 = all_1883_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2424), (2447) imply: % 232.12/34.79 | | (2452) all_1897_0 = all_1895_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2447), (2451) imply: % 232.12/34.79 | | (2453) all_1897_0 = all_1883_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2452), (2453) imply: % 232.12/34.79 | | (2454) all_1895_0 = all_1883_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2454) implies: % 232.12/34.79 | | (2455) all_1895_0 = all_1883_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2440), (2455) imply: % 232.12/34.79 | | (2456) all_1883_0 = all_1871_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2443), (2455) imply: % 232.12/34.79 | | (2457) all_1883_0 = all_1873_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2413), (2455) imply: % 232.12/34.79 | | (2458) all_1883_0 = all_1865_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2457), (2458) imply: % 232.12/34.79 | | (2459) all_1873_0 = all_1865_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2456), (2457) imply: % 232.12/34.79 | | (2460) all_1873_0 = all_1871_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2438), (2445) imply: % 232.12/34.79 | | (2461) all_1871_0 = all_1847_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2461) implies: % 232.12/34.79 | | (2462) all_1871_0 = all_1847_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2419), (2445) imply: % 232.12/34.79 | | (2463) all_1847_0 = all_748_1 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2459), (2460) imply: % 232.12/34.79 | | (2464) all_1871_0 = all_1865_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2464) implies: % 232.12/34.79 | | (2465) all_1871_0 = all_1865_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2441), (2465) imply: % 232.12/34.79 | | (2466) all_1865_0 = all_757_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2462), (2465) imply: % 232.12/34.79 | | (2467) all_1865_0 = all_1847_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2466), (2467) imply: % 232.12/34.79 | | (2468) all_1847_0 = all_757_0 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2468) implies: % 232.12/34.79 | | (2469) all_1847_0 = all_757_0 % 232.12/34.79 | | % 232.12/34.79 | | COMBINE_EQS: (2463), (2469) imply: % 232.12/34.79 | | (2470) all_757_0 = all_748_1 % 232.12/34.79 | | % 232.12/34.79 | | SIMP: (2470) implies: % 232.12/34.79 | | (2471) all_757_0 = all_748_1 % 232.12/34.79 | | % 232.12/34.79 | | REDUCE: (1857), (2471) imply: % 232.12/34.79 | | (2472) $false % 232.12/34.79 | | % 232.12/34.79 | | CLOSE: (2472) is inconsistent. % 232.12/34.79 | | % 232.12/34.79 | End of split % 232.12/34.79 | % 232.12/34.79 End of proof % 232.12/34.79 % SZS output end Proof for theBenchmark % 232.12/34.79 % 232.12/34.79 34192ms %------------------------------------------------------------------------------