%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW225+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 : n018.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 00:49:30 EDT 2023 % Result : Theorem 82.05s 11.70s % Output : Proof 229.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n018.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 19:16:46 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 17.50/3.14 Prover 4: Preprocessing ... % 19.11/3.32 Prover 6: Preprocessing ... % 19.11/3.47 Prover 2: Preprocessing ... % 19.11/3.48 Prover 5: Preprocessing ... % 19.11/3.51 Prover 3: Preprocessing ... % 21.56/3.66 Prover 1: Preprocessing ... % 22.36/3.78 Prover 0: Preprocessing ... % 56.00/8.19 Prover 3: Warning: ignoring some quantifiers % 56.81/8.41 Prover 3: Constructing countermodel ... % 57.77/8.45 Prover 1: Warning: ignoring some quantifiers % 58.06/8.53 Prover 6: Proving ... % 60.10/8.73 Prover 1: Constructing countermodel ... % 68.63/9.91 Prover 4: Warning: ignoring some quantifiers % 71.59/10.26 Prover 0: Proving ... % 71.59/10.35 Prover 4: Constructing countermodel ... % 75.13/10.76 Prover 5: Proving ... % 79.69/11.36 Prover 2: Proving ... % 82.05/11.69 Prover 3: proved (11027ms) % 82.05/11.70 % 82.05/11.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 82.05/11.70 % 82.05/11.71 Prover 6: stopped % 82.05/11.71 Prover 2: stopped % 82.05/11.75 Prover 0: stopped % 82.05/11.75 Prover 5: stopped % 82.05/11.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 82.05/11.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 82.05/11.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 82.05/11.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 82.05/11.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 92.06/12.99 Prover 8: Preprocessing ... % 92.06/13.00 Prover 11: Preprocessing ... % 92.71/13.04 Prover 7: Preprocessing ... % 92.71/13.08 Prover 10: Preprocessing ... % 93.21/13.23 Prover 13: Preprocessing ... % 107.93/15.04 Prover 8: Warning: ignoring some quantifiers % 108.58/15.21 Prover 8: Constructing countermodel ... % 108.58/15.21 Prover 7: Warning: ignoring some quantifiers % 108.58/15.22 Prover 10: Warning: ignoring some quantifiers % 109.25/15.41 Prover 10: Constructing countermodel ... % 111.06/15.47 Prover 7: Constructing countermodel ... % 114.26/16.04 Prover 1: stopped % 114.26/16.05 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 114.26/16.06 Prover 13: Warning: ignoring some quantifiers % 119.36/16.74 Prover 13: Constructing countermodel ... % 122.64/17.07 Prover 11: Warning: ignoring some quantifiers % 125.55/17.37 Prover 16: Preprocessing ... % 125.55/17.40 Prover 11: Constructing countermodel ... % 135.87/18.76 Prover 16: Warning: ignoring some quantifiers % 135.87/18.84 Prover 16: Constructing countermodel ... % 152.17/20.90 Prover 16: stopped % 152.17/20.91 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 157.54/21.75 Prover 19: Preprocessing ... % 161.97/22.27 Prover 13: stopped % 170.65/23.40 Prover 19: Warning: ignoring some quantifiers % 171.70/23.52 Prover 19: Constructing countermodel ... % 174.40/23.98 Prover 19: stopped % 202.00/28.00 Prover 4: stopped % 221.78/31.46 Prover 7: stopped % 227.94/32.82 Prover 10: Found proof (size 368) % 227.94/32.82 Prover 10: proved (21077ms) % 227.94/32.83 Prover 11: stopped % 228.23/32.83 Prover 8: stopped % 228.23/32.83 % 228.23/32.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 228.23/32.84 % 228.56/32.92 % SZS output start Proof for theBenchmark % 228.56/32.95 Assumptions after simplification: % 228.56/32.95 --------------------------------- % 228.56/32.95 % 228.56/32.95 (arity_RealDef__Oreal__Rings_Olinordered__semidom) % 228.56/32.96 $i(tc_RealDef_Oreal) & class_Rings_Olinordered__semidom(tc_RealDef_Oreal) % 228.56/32.96 % 228.56/32.96 (conj_0) % 228.56/32.98 $i(tc_RealDef_Oreal) & $i(v_N2____) & $i(v_N1____) & $i(tc_Nat_Onat) & % 228.56/32.98 $i(v_f____) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 228.56/32.98 $i] : ? [v5: $i] : ? [v6: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & % 228.56/32.98 c_Nat_OSuc(v4) = v5 & c_Nat_OSuc(v1) = v2 & % 228.56/32.98 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____) = v1 & hAPP(v0, % 228.56/32.98 v5) = v6 & hAPP(v0, v2) = v3 & hAPP(v_f____, v1) = v4 & $i(v6) & $i(v5) & % 228.56/32.98 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 228.56/32.98 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v6)) % 228.56/32.98 % 228.56/32.98 (fact_Bseq__iff) % 228.56/32.99 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/32.99 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ? [v1: $i] : ! [v2: $i] : ! % 228.56/32.99 [v3: $i] : ! [v4: $i] : ( ~ (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 228.56/32.99 ~ $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | % 228.56/32.99 c_SEQ_OBseq(v2, v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 228.56/32.99 $i] : (c_RealVector_Onorm__class_Onorm(v2, v7) = v8 & hAPP(v1, v6) = v7 % 228.56/32.99 & hAPP(v0, v4) = v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ~ % 228.56/32.99 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v5))) & ! [v1: % 228.56/32.99 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~ % 228.56/32.99 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? [v4: $i] : % 228.56/32.99 ? [v5: $i] : (c_Nat_OSuc(v3) = v4 & hAPP(v0, v4) = v5 & $i(v5) & $i(v4) & % 228.56/32.99 $i(v3) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 228.56/32.99 (c_RealVector_Onorm__class_Onorm(v2, v7) = v8) | ~ (hAPP(v1, v6) = % 228.56/32.99 v7) | ~ $i(v6) | % 228.56/32.99 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v5))))) % 228.56/32.99 % 228.56/32.99 (fact_Bseq__iff1a) % 228.56/32.99 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/32.99 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ? [v1: $i] : ! [v2: $i] : ! % 228.56/32.99 [v3: $i] : ! [v4: $i] : ( ~ (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 228.56/32.99 ~ $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | % 228.56/32.99 c_SEQ_OBseq(v2, v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 228.56/32.99 $i] : (c_RealVector_Onorm__class_Onorm(v2, v7) = v8 & hAPP(v1, v6) = v7 % 228.56/32.99 & hAPP(v0, v4) = v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ~ % 228.56/32.99 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v5))) & ! [v1: $i] % 228.56/32.99 : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~ % 228.56/32.99 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? [v4: $i] : % 228.56/32.99 ? [v5: $i] : (c_Nat_OSuc(v3) = v4 & hAPP(v0, v4) = v5 & $i(v5) & $i(v4) & % 228.56/32.99 $i(v3) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 228.56/32.99 (c_RealVector_Onorm__class_Onorm(v2, v7) = v8) | ~ (hAPP(v1, v6) = % 228.56/32.99 v7) | ~ $i(v6) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 228.56/32.99 v8, v5))))) % 228.56/32.99 % 228.56/32.99 (fact_DeMoivre) % 228.56/32.99 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] % 228.56/32.99 : ? [v1: $i] : ? [v2: $i] : % 228.56/32.99 (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v0 & % 228.56/32.99 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 228.56/32.99 c_RealDef_Oreal(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 228.56/32.99 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v6, v4) = % 228.56/32.99 v7) | ~ (hAPP(v2, v3) = v5) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ % 228.56/32.99 $i(v3) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : (c_Complex_Ocis(v7) = % 228.56/32.99 v10 & c_Complex_Ocis(v4) = v8 & hAPP(v9, v3) = v10 & hAPP(v0, v8) = v9 & % 228.56/32.99 $i(v10) & $i(v9) & $i(v8)))) % 228.56/32.99 % 228.56/32.99 (fact_DeMoivre2) % 228.56/33.00 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] % 228.56/33.00 : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 228.56/33.00 (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v0 & % 228.56/33.00 c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 & % 228.56/33.00 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & % 228.56/33.00 c_RealDef_Oreal(tc_Nat_Onat) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 228.56/33.00 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: % 228.56/33.00 $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 228.56/33.00 (c_Complex_Orcis(v8, v11) = v12) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v7, % 228.56/33.00 v4) = v8) | ~ (hAPP(v3, v4) = v9) | ~ (hAPP(v2, v9) = v10) | ~ % 228.56/33.00 (hAPP(v1, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v13: $i] : % 228.56/33.00 ? [v14: $i] : (c_Complex_Orcis(v6, v5) = v13 & hAPP(v14, v4) = v12 & % 228.56/33.00 hAPP(v0, v13) = v14 & $i(v14) & $i(v13) & $i(v12)))) % 228.56/33.00 % 228.56/33.00 (fact_LIMSEQ__inverse__realpow__zero__lemma) % 228.56/33.00 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.56/33.00 $i] : ? [v3: $i] : ? [v4: $i] : % 228.56/33.00 (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v4 & % 228.56/33.00 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 228.56/33.00 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.00 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v3 & % 228.56/33.00 c_RealDef_Oreal(tc_Nat_Onat) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 228.56/33.00 $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 228.56/33.00 : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v3) = v7) | ~ % 228.56/33.00 (hAPP(v8, v5) = v9) | ~ (hAPP(v4, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ~ % 228.56/33.00 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v6) | ? [v10: $i] % 228.56/33.00 : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 228.56/33.00 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v12, v3) = v13 & hAPP(v11, % 228.56/33.00 v6) = v12 & hAPP(v2, v5) = v10 & hAPP(v1, v10) = v11 & $i(v13) & % 228.56/33.00 $i(v12) & $i(v11) & $i(v10) & % 228.56/33.00 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, v9)))) % 228.56/33.00 % 228.56/33.00 (fact_Suc__le__mono) % 228.56/33.00 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 228.56/33.00 (c_Nat_OSuc(v1) = v2) | ~ (c_Nat_OSuc(v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 228.56/33.00 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v3) | % 228.56/33.00 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! % 228.56/33.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (c_Nat_OSuc(v1) = v2) | ~ % 228.56/33.00 (c_Nat_OSuc(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 228.56/33.00 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 228.56/33.00 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v3)) % 228.56/33.00 % 228.56/33.00 (fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) % 228.56/33.00 $i(v_N2____) & $i(v_N1____) & $i(tc_Nat_Onat) & $i(v_f____) & ? [v0: $i] : ? % 228.56/33.00 [v1: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____) = v0 % 228.56/33.00 & hAPP(v_f____, v0) = v1 & $i(v1) & $i(v0) & % 228.56/33.00 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1)) % 228.56/33.00 % 228.56/33.00 (fact_abs__real__of__nat__cancel) % 228.56/33.00 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.00 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 228.56/33.00 (hAPP(v0, v1) = v2) | ~ $i(v1) | % 228.56/33.00 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v2 & $i(v2)))) % 228.56/33.00 % 228.56/33.00 (fact_cis__real__of__nat__Suc__mult) % 228.56/33.01 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] % 228.56/33.01 : ? [v1: $i] : ? [v2: $i] : % 228.56/33.01 (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v2 & % 228.56/33.01 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 228.56/33.01 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 228.56/33.01 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! % 228.56/33.01 [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ (c_Complex_Ocis(v9) = v10) | ~ % 228.56/33.01 (c_Complex_Ocis(v3) = v5) | ~ (hAPP(v8, v3) = v9) | ~ (hAPP(v6, v10) = % 228.56/33.01 v11) | ~ (hAPP(v2, v5) = v6) | ~ (hAPP(v1, v4) = v7) | ~ (hAPP(v0, % 228.56/33.01 v7) = v8) | ~ $i(v4) | ~ $i(v3) | ? [v12: $i] : ? [v13: $i] : ? % 228.56/33.01 [v14: $i] : ? [v15: $i] : (c_Complex_Ocis(v15) = v11 & c_Nat_OSuc(v4) = % 228.56/33.01 v12 & hAPP(v14, v3) = v15 & hAPP(v1, v12) = v13 & hAPP(v0, v13) = v14 & % 228.56/33.01 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11)))) % 228.56/33.01 % 228.56/33.01 (fact_ge__natfloor__plus__one__imp__gt) % 228.56/33.01 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.01 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & c_RealDef_Oreal(tc_Nat_Onat) = % 228.56/33.01 v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 228.56/33.01 : ( ~ (c_RComplete_Onatfloor(v3) = v4) | ~ (hAPP(v1, v2) = v5) | ~ $i(v3) % 228.56/33.01 | ~ $i(v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5) | ? % 228.56/33.01 [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v0) = v6 & $i(v6) % 228.56/33.01 & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, v2)))) % 228.56/33.01 % 228.56/33.01 (fact_le__natfloor) % 228.56/33.01 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.01 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.56/33.01 [v3: $i] : ! [v4: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v4) | ~ (hAPP(v0, % 228.56/33.01 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 228.56/33.01 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | % 228.56/33.01 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v4))) % 228.56/33.01 % 228.56/33.01 (fact_le__natfloor__eq) % 228.56/33.01 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.01 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.01 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.01 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_RComplete_Onatfloor(v3) = v4) | % 228.56/33.01 ~ (hAPP(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.01 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v3) | ~ % 228.56/33.01 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 228.56/33.01 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v4)) & ! [v2: $i] : ! % 228.56/33.01 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_RComplete_Onatfloor(v3) = v4) % 228.56/33.01 | ~ (hAPP(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.01 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~ % 228.56/33.01 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v4) | % 228.56/33.01 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v3))) % 228.56/33.01 % 228.56/33.01 (fact_lemma__NBseq__def) % 228.56/33.02 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.02 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.02 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : ! [v3: % 228.56/33.02 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Nat_OSuc(v4) = v5) | ~ $i(v4) | % 228.56/33.02 ~ $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v3) | ? % 228.56/33.02 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 228.56/33.02 ($i(v8) & $i(v6) & ((c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & % 228.56/33.02 hAPP(v2, v8) = v9 & hAPP(v1, v5) = v7 & $i(v10) & $i(v9) & $i(v7) & % 228.56/33.02 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v7)) | % 228.56/33.02 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6) & ! [v11: % 228.56/33.02 $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 228.56/33.02 (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ (hAPP(v2, % 228.56/33.02 v11) = v12) | ~ $i(v11) | % 228.56/33.02 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, v6)))))) % 228.56/33.02 & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 228.56/33.02 $i(v2) | ~ class_RealVector_Oreal__normed__vector(v3) | ~ % 228.56/33.02 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v5: $i] : ? % 228.56/33.02 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 228.56/33.02 ($i(v8) & $i(v5) & ((c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & % 228.56/33.02 hAPP(v2, v8) = v9 & $i(v10) & $i(v9) & ~ % 228.56/33.02 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v4)) | % 228.56/33.02 (c_Nat_OSuc(v5) = v6 & hAPP(v1, v6) = v7 & $i(v7) & $i(v6) & ! [v11: % 228.56/33.02 $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 228.56/33.02 (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ (hAPP(v2, % 228.56/33.02 v11) = v12) | ~ $i(v11) | % 228.56/33.02 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, v7))))))) % 228.56/33.02 % 228.56/33.02 (fact_lemma__NBseq__def2) % 228.56/33.02 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.02 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.02 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : ! [v3: % 228.56/33.02 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Nat_OSuc(v4) = v5) | ~ $i(v4) | % 228.56/33.02 ~ $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v3) | ? % 228.56/33.02 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 228.56/33.02 ($i(v8) & $i(v6) & ((c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & % 228.56/33.02 hAPP(v2, v8) = v9 & hAPP(v1, v5) = v7 & $i(v10) & $i(v9) & $i(v7) & % 228.56/33.02 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10, v7)) | % 228.56/33.02 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6) & ! [v11: % 228.56/33.02 $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 228.56/33.02 (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ (hAPP(v2, % 228.56/33.02 v11) = v12) | ~ $i(v11) | % 228.56/33.02 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, v6)))))) % 228.56/33.02 & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 228.56/33.02 $i(v2) | ~ class_RealVector_Oreal__normed__vector(v3) | ~ % 228.56/33.02 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v5: $i] : ? % 228.56/33.02 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 228.56/33.02 ($i(v8) & $i(v5) & ((c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & % 228.56/33.02 hAPP(v2, v8) = v9 & $i(v10) & $i(v9) & ~ % 228.56/33.02 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v4)) | % 228.56/33.02 (c_Nat_OSuc(v5) = v6 & hAPP(v1, v6) = v7 & $i(v7) & $i(v6) & ! [v11: % 228.56/33.02 $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 228.56/33.02 (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ (hAPP(v2, % 228.56/33.02 v11) = v12) | ~ $i(v11) | % 228.56/33.02 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v7))))))) % 228.56/33.02 % 228.56/33.02 (fact_less__natfloor) % 228.56/33.02 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.02 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.02 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.02 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_RComplete_Onatfloor(v3) = v5) | % 228.56/33.02 ~ (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.02 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~ % 228.56/33.02 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 228.56/33.02 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v5, v2))) % 228.56/33.02 % 228.56/33.02 (fact_nat__add__commute) % 228.56/33.02 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 228.56/33.02 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) | ~ % 228.56/33.02 $i(v0) | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2 & $i(v2))) % 228.56/33.02 % 228.56/33.02 (fact_nat__le__real__less) % 228.56/33.03 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.03 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.56/33.03 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.03 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, % 228.56/33.03 v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.03 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | ? [v6: $i] : % 228.56/33.03 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v1) = v6 & $i(v6) & % 228.56/33.03 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6))) & ! [v2: $i] % 228.56/33.03 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v0, v3) = v4) | ~ % 228.56/33.03 (hAPP(v0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | % 228.56/33.03 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | ? [v6: $i] : % 228.56/33.03 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v1) = v6 & $i(v6) & ~ % 228.56/33.03 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6)))) % 228.56/33.03 % 228.56/33.03 (fact_nat__less__real__le) % 228.56/33.03 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.03 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.56/33.03 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.03 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, % 228.56/33.03 v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.03 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ? [v6: $i] : % 228.56/33.03 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v1) = v6 & $i(v6) & % 228.56/33.03 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v5))) & ! [v2: % 228.56/33.03 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v0, v3) = v4) | % 228.56/33.03 ~ (hAPP(v0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | % 228.56/33.03 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ? [v6: $i] : % 228.56/33.03 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v1) = v6 & $i(v6) & ~ % 228.56/33.03 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v5)))) % 228.56/33.03 % 228.56/33.03 (fact_natceiling__add) % 228.56/33.03 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.03 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.03 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.03 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.56/33.03 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 228.56/33.03 (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.03 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v6: $i] % 228.56/33.03 : ? [v7: $i] : (c_RComplete_Onatceiling(v5) = v6 & % 228.56/33.03 c_RComplete_Onatceiling(v3) = v7 & % 228.56/33.03 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, v2) = v6 & $i(v7) & % 228.56/33.03 $i(v6)))) % 228.56/33.03 % 228.56/33.03 (fact_natceiling__eq) % 228.56/33.03 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.56/33.03 $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.56/33.03 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & c_RealDef_Oreal(tc_Nat_Onat) = % 228.56/33.03 v0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 228.56/33.03 [v6: $i] : (v6 = v5 | ~ (c_RComplete_Onatceiling(v3) = v5) | ~ % 228.56/33.03 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = v6) | ~ $i(v4) | ~ % 228.56/33.03 $i(v3) | ? [v7: $i] : ? [v8: $i] : (hAPP(v0, v4) = v7 & $i(v7) & ( ~ % 228.56/33.03 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v3) | % 228.56/33.03 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, v1) = v8 & $i(v8) & % 228.56/33.03 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v8)))))) % 228.56/33.03 % 228.56/33.03 (fact_natceiling__le) % 228.56/33.03 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.03 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.56/33.03 [v3: $i] : ! [v4: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v4) | ~ % 228.56/33.03 (hAPP(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 228.56/33.03 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3) | % 228.56/33.03 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v1))) % 228.56/33.03 % 228.56/33.03 (fact_natceiling__le__eq) % 228.56/33.04 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.04 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.04 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.04 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_RComplete_Onatceiling(v3) = v4) | % 228.56/33.04 ~ (hAPP(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2: $i] : ! % 228.56/33.04 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_RComplete_Onatceiling(v3) = % 228.56/33.04 v4) | ~ (hAPP(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) | % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5))) % 228.56/33.04 % 228.56/33.04 (fact_natceiling__real__of__nat) % 228.56/33.04 $i(tc_Nat_Onat) & ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & % 228.56/33.04 ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v0, v1) = v2) | ~ $i(v1) | % 228.56/33.04 c_RComplete_Onatceiling(v2) = v1)) % 228.56/33.04 % 228.56/33.04 (fact_natceiling__subtract) % 228.56/33.04 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.04 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.56/33.04 [v3: $i] : ! [v4: $i] : ( ~ % 228.56/33.04 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v3) = v4) | ~ % 228.56/33.04 (hAPP(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? [v5: $i] % 228.56/33.04 : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 & % 228.56/33.04 c_RComplete_Onatceiling(v1) = v6 & % 228.56/33.04 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) & % 228.56/33.04 $i(v5)))) % 228.56/33.04 % 228.56/33.04 (fact_natfloor__add) % 228.56/33.04 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.04 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.04 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.04 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.56/33.04 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 228.56/33.04 (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v6: $i] % 228.56/33.04 : ? [v7: $i] : (c_RComplete_Onatfloor(v5) = v6 & % 228.56/33.04 c_RComplete_Onatfloor(v3) = v7 & % 228.56/33.04 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, v2) = v6 & $i(v7) & % 228.56/33.04 $i(v6)))) % 228.56/33.04 % 228.56/33.04 (fact_natfloor__div__nat) % 228.56/33.04 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.56/33.04 $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 228.56/33.04 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 228.56/33.04 c_RealDef_Oreal(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 228.56/33.04 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 228.56/33.04 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v4, v5) = v6) | ~ % 228.56/33.04 (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ? [v7: $i] % 228.56/33.04 : ? [v8: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v8, v3) = v7 & % 228.56/33.04 c_RComplete_Onatfloor(v6) = v7 & c_RComplete_Onatfloor(v4) = v8 & $i(v8) % 228.56/33.04 & $i(v7)))) % 228.56/33.04 % 228.56/33.04 (fact_natfloor__eq) % 228.56/33.04 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.04 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.56/33.04 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.04 $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ (c_RComplete_Onatfloor(v2) % 228.56/33.04 = v5) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.56/33.04 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ? [v6: $i] % 228.56/33.04 : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v1) = v6 & $i(v6) & % 228.56/33.04 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6)))) % 228.56/33.04 % 228.56/33.04 (fact_natfloor__power) % 228.56/33.05 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.56/33.05 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 & % 228.56/33.05 c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & % 228.56/33.05 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 228.56/33.05 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 228.56/33.05 (c_RComplete_Onatfloor(v4) = v5) | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v2, % 228.56/33.05 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ? [v8: $i] : ? [v9: $i] : ? % 228.56/33.05 [v10: $i] : ? [v11: $i] : ((v11 = v7 & c_RComplete_Onatfloor(v10) = v7 & % 228.56/33.05 hAPP(v9, v3) = v10 & hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & $i(v7)) | % 228.56/33.05 ( ~ (v8 = v4) & hAPP(v0, v5) = v8 & $i(v8))))) % 228.56/33.05 % 228.56/33.05 (fact_natfloor__real__of__nat) % 228.56/33.05 $i(tc_Nat_Onat) & ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & % 228.56/33.05 ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v0, v1) = v2) | ~ $i(v1) | % 228.56/33.05 c_RComplete_Onatfloor(v2) = v1)) % 228.56/33.05 % 228.56/33.05 (fact_natfloor__subtract) % 228.56/33.05 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.05 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.56/33.05 [v3: $i] : ! [v4: $i] : ( ~ % 228.56/33.05 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v3) = v4) | ~ % 228.56/33.05 (hAPP(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 228.56/33.05 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? [v5: $i] % 228.56/33.05 : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 & % 228.56/33.05 c_RComplete_Onatfloor(v1) = v6 & % 228.56/33.05 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) & % 228.56/33.05 $i(v5)))) % 228.56/33.05 % 228.56/33.05 (fact_not__real__of__nat__less__zero) % 228.56/33.05 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.05 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & % 228.56/33.05 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.05 $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ~ % 228.56/33.05 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1))) % 228.56/33.05 % 228.56/33.05 (fact_of__nat__le__iff) % 228.56/33.05 $i(tc_Nat_Onat) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 228.56/33.05 [v4: $i] : ! [v5: $i] : ( ~ (c_Nat_Osemiring__1__class_Oof__nat(v2) = v3) | % 228.56/33.05 ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 228.56/33.05 $i(v0) | ~ class_Rings_Olinordered__semidom(v2) | ~ % 228.56/33.05 c_Orderings_Oord__class_Oless__eq(v2, v4, v5) | % 228.56/33.05 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : ! % 228.56/33.05 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.56/33.05 (c_Nat_Osemiring__1__class_Oof__nat(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~ % 228.56/33.05 (hAPP(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 228.56/33.05 class_Rings_Olinordered__semidom(v2) | ~ % 228.56/33.05 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 228.56/33.05 c_Orderings_Oord__class_Oless__eq(v2, v4, v5)) % 228.56/33.05 % 228.56/33.05 (fact_power__real__of__nat) % 228.56/33.05 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.56/33.05 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v0 & % 228.56/33.05 c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & % 228.56/33.05 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 228.56/33.05 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v6, v3) = % 228.56/33.05 v7) | ~ (hAPP(v1, v4) = v5) | ~ (hAPP(v0, v5) = v6) | ~ $i(v4) | ~ % 228.56/33.05 $i(v3) | ? [v8: $i] : ? [v9: $i] : (hAPP(v8, v3) = v9 & hAPP(v2, v4) = % 228.56/33.05 v8 & hAPP(v1, v9) = v7 & $i(v9) & $i(v8) & $i(v7)))) % 228.56/33.05 % 228.56/33.05 (fact_real__eq__of__nat) % 228.56/33.06 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.06 (c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) = v0 & % 228.56/33.06 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0)) % 228.56/33.06 % 228.56/33.06 (fact_real__natceiling__ge) % 228.56/33.06 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.06 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 228.56/33.06 (c_RComplete_Onatceiling(v1) = v2) | ~ $i(v1) | ? [v3: $i] : (hAPP(v0, % 228.56/33.06 v2) = v3 & $i(v3) & % 228.56/33.06 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)))) % 228.56/33.06 % 228.56/33.06 (fact_real__natfloor__add__one__gt) % 228.56/33.06 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.06 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.56/33.06 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.06 $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? % 228.56/33.06 [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v1) = v5 & % 228.56/33.06 hAPP(v0, v3) = v4 & $i(v5) & $i(v4) & % 228.56/33.06 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v5)))) % 228.56/33.06 % 228.56/33.06 (fact_real__natfloor__gt__diff__one) % 228.56/33.06 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.06 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 228.56/33.06 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.06 $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v0) = v3) | % 228.56/33.06 ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatfloor(v2) = v4 & % 228.56/33.06 hAPP(v1, v4) = v5 & $i(v5) & $i(v4) & % 228.56/33.06 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5)))) % 228.56/33.06 % 228.56/33.06 (fact_real__natfloor__le) % 228.56/33.06 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.06 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.06 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.06 $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ % 228.56/33.06 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v4: $i] % 228.56/33.06 : (hAPP(v1, v3) = v4 & $i(v4) & % 228.56/33.06 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)))) % 228.56/33.06 % 228.56/33.06 (fact_real__of__nat__1) % 228.56/33.06 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.56/33.06 $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & % 228.56/33.06 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & c_RealDef_Oreal(tc_Nat_Onat) = % 228.56/33.06 v0 & hAPP(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 228.56/33.06 % 228.56/33.06 (fact_real__of__nat__Suc) % 228.56/33.07 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.07 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.56/33.07 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.07 $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 228.56/33.07 (c_Nat_OSuc(v2) = v4 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, % 228.56/33.07 v1) = v5 & hAPP(v0, v4) = v5 & $i(v5) & $i(v4)))) % 228.56/33.07 % 228.56/33.07 (fact_real__of__nat__Suc__gt__zero) % 228.56/33.07 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.07 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.07 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.07 $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ? [v4: $i] : (hAPP(v1, v3) % 228.56/33.07 = v4 & $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, % 228.56/33.07 v4)))) % 228.56/33.07 % 228.56/33.07 (fact_real__of__nat__add) % 228.56/33.07 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.07 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.56/33.07 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.56/33.07 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 228.56/33.07 (hAPP(v0, v2) = v3) | ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ? % 228.56/33.07 [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, v1) = v6 & % 228.56/33.07 hAPP(v0, v6) = v5 & $i(v6) & $i(v5)))) % 228.56/33.07 % 228.56/33.07 (fact_real__of__nat__def) % 228.56/33.07 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.07 (c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) = v0 & % 228.56/33.07 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0)) % 228.56/33.07 % 228.56/33.07 (fact_real__of__nat__diff) % 228.56/33.07 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.07 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.56/33.07 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.56/33.07 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 228.56/33.07 (hAPP(v0, v2) = v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 228.56/33.07 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v6: $i] : % 228.56/33.07 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, v2) = v6 & hAPP(v0, v6) = % 228.56/33.07 v5 & $i(v6) & $i(v5)))) % 228.56/33.07 % 228.56/33.07 (fact_real__of__nat__div4) % 228.56/33.07 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.56/33.07 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.56/33.07 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.56/33.07 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 228.56/33.07 (hAPP(v0, v2) = v3) | ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ? % 228.56/33.07 [v6: $i] : ? [v7: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) % 228.56/33.07 = v6 & hAPP(v0, v6) = v7 & $i(v7) & $i(v6) & % 228.56/33.07 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v5)))) % 228.56/33.07 % 228.56/33.07 (fact_real__of__nat__ge__zero) % 228.56/33.07 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.56/33.07 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.56/33.07 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.56/33.07 $i] : ( ~ (hAPP(v1, v2) = v3) | ~ $i(v2) | % 228.56/33.07 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3))) % 228.56/33.07 % 228.56/33.07 (fact_real__of__nat__gt__zero__cancel__iff) % 228.76/33.08 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.08 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.08 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & c_RealDef_Oreal(tc_Nat_Onat) % 228.76/33.08 = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v1, % 228.76/33.08 v3) = v4) | ~ $i(v3) | ~ % 228.76/33.08 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | % 228.76/33.08 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v3: $i] : ! % 228.76/33.08 [v4: $i] : ( ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 228.76/33.08 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | % 228.76/33.08 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))) % 228.76/33.08 % 228.76/33.08 (fact_real__of__nat__inject) % 228.76/33.08 $i(tc_Nat_Onat) & ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & % 228.76/33.08 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (hAPP(v0, v2) = v3) | % 228.76/33.08 ~ (hAPP(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1))) % 228.76/33.08 % 228.76/33.08 (fact_real__of__nat__le__iff) % 228.76/33.08 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.76/33.08 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.76/33.08 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ (hAPP(v0, v1) = v4) | % 228.76/33.08 ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.08 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) | % 228.76/33.08 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & ! [v1: $i] : ! % 228.76/33.08 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ % 228.76/33.08 (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.08 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | % 228.76/33.08 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4))) % 228.76/33.08 % 228.76/33.08 (fact_real__of__nat__le__zero__cancel__iff) % 228.76/33.08 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.08 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & % 228.76/33.08 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & c_RealDef_Oreal(tc_Nat_Onat) % 228.76/33.08 = v0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v3 = v2 | ~ % 228.76/33.08 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ % 228.76/33.08 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v1)) & ! [v3: $i] % 228.76/33.08 : ( ~ (hAPP(v0, v2) = v3) | % 228.76/33.08 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))) % 228.76/33.08 % 228.76/33.08 (fact_real__of__nat__less__iff) % 228.76/33.08 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : % 228.76/33.08 (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 228.76/33.08 [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ (hAPP(v0, v1) = v4) | % 228.76/33.08 ~ $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 228.76/33.08 v3, v4) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)) & ! [v1: % 228.76/33.08 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0, v2) = v3) | % 228.76/33.08 ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.08 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | % 228.76/33.08 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4))) % 228.76/33.08 % 228.76/33.08 (fact_real__of__nat__mult) % 228.76/33.08 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.08 $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & % 228.76/33.08 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 228.76/33.08 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 228.76/33.08 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 228.76/33.08 (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v5) = v6) | ~ (hAPP(v0, v4) = v5) | ~ % 228.76/33.08 (hAPP(v0, v3) = v7) | ~ $i(v4) | ~ $i(v3) | ? [v9: $i] : ? [v10: $i] : % 228.76/33.08 (hAPP(v9, v3) = v10 & hAPP(v1, v4) = v9 & hAPP(v0, v10) = v8 & $i(v10) & % 228.76/33.08 $i(v9) & $i(v8)))) % 228.76/33.08 % 228.76/33.08 (fact_real__of__nat__number__of) % 228.76/33.08 $i(tc_Int_Oint) & $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? % 228.76/33.08 [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & % 228.76/33.08 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 228.76/33.08 $i] : ( ~ (c_Int_Onumber__class_Onumber__of(tc_Int_Oint, v2) = v3) | ~ % 228.76/33.08 $i(v2) | ~ c_Nat__Numeral_Oneg(v3) | ? [v4: $i] : % 228.76/33.08 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v4 & hAPP(v0, v4) = % 228.76/33.08 v1 & $i(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 228.76/33.08 (c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2) % 228.76/33.08 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v3 & % 228.76/33.08 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v5 & hAPP(v0, v5) % 228.76/33.09 = v3 & $i(v5) & $i(v3)) | % 228.76/33.09 (c_Int_Onumber__class_Onumber__of(tc_Int_Oint, v2) = v4 & $i(v4) & % 228.76/33.09 c_Nat__Numeral_Oneg(v4))))) % 228.76/33.09 % 228.76/33.09 (fact_real__of__nat__one) % 228.76/33.09 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.09 $i] : ? [v3: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 228.76/33.09 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v3 & % 228.76/33.09 c_RealDef_Oreal(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v2 & hAPP(v0, v2) = v3 % 228.76/33.09 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 228.76/33.09 % 228.76/33.09 (fact_real__of__nat__power) % 228.76/33.09 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.09 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 & % 228.76/33.09 c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 228.76/33.09 c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 228.76/33.09 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v6, v3) = % 228.76/33.09 v7) | ~ (hAPP(v2, v5) = v6) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ % 228.76/33.09 $i(v3) | ? [v8: $i] : ? [v9: $i] : (hAPP(v8, v3) = v9 & hAPP(v1, v4) = % 228.76/33.09 v8 & hAPP(v0, v9) = v7 & $i(v9) & $i(v8) & $i(v7)))) % 228.76/33.09 % 228.76/33.09 (fact_real__of__nat__zero) % 228.76/33.09 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.09 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v2 & % 228.76/33.09 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & c_RealDef_Oreal(tc_Nat_Onat) % 228.76/33.09 = v0 & hAPP(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 228.76/33.09 % 228.76/33.09 (fact_real__of__nat__zero__iff) % 228.76/33.09 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.09 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & % 228.76/33.09 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & c_RealDef_Oreal(tc_Nat_Onat) % 228.76/33.09 = v0 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v2 | ~ (hAPP(v0, v3) % 228.76/33.09 = v1) | ~ $i(v3)) & ! [v3: $i] : (v3 = v1 | ~ (hAPP(v0, v2) = v3))) % 228.76/33.09 % 228.76/33.09 (fact_reals__Archimedean4) % 228.76/33.09 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.09 $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 228.76/33.09 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.09 c_RealDef_Oreal(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 228.76/33.09 ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 228.76/33.09 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 228.76/33.09 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5: $i] % 228.76/33.09 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 228.76/33.09 ? [v11: $i] : ? [v12: $i] : (c_Nat_OSuc(v5) = v9 & hAPP(v11, v4) = v12 & % 228.76/33.09 hAPP(v7, v4) = v8 & hAPP(v2, v9) = v10 & hAPP(v2, v5) = v6 & hAPP(v1, % 228.76/33.09 v10) = v11 & hAPP(v1, v6) = v7 & $i(v12) & $i(v11) & $i(v10) & $i(v9) % 228.76/33.09 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 228.76/33.09 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v12) & % 228.76/33.09 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v3)))) % 228.76/33.09 % 228.76/33.09 (fact_reals__Archimedean6) % 228.76/33.09 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 228.76/33.09 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.09 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & c_RealDef_Oreal(tc_Nat_Onat) = % 228.76/33.09 v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ( ~ $i(v3) | ~ % 228.76/33.09 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v4: $i] % 228.76/33.09 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 228.76/33.09 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5 & hAPP(v1, v5) = % 228.76/33.09 v6 & hAPP(v1, v4) = v7 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 228.76/33.09 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v7) & % 228.76/33.09 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3)))) % 228.76/33.09 % 228.76/33.09 (fact_reals__Archimedean6a) % 228.76/33.09 $i(tc_RealDef_Oreal) & $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : % 228.76/33.09 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.09 c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ % 228.76/33.09 $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | % 228.76/33.09 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (c_Nat_OSuc(v3) = % 228.76/33.09 v5 & hAPP(v1, v5) = v6 & hAPP(v1, v3) = v4 & $i(v6) & $i(v5) & $i(v4) & % 228.76/33.09 $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6) & % 228.76/33.09 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)))) % 228.76/33.09 % 228.76/33.09 (function-axioms) % 228.76/33.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 228.76/33.10 $i] : (v1 = v0 | ~ (c_Nat_Osemiring__1__class_Oof__nat__aux(v5, v4, v3, v2) % 228.76/33.10 = v1) | ~ (c_Nat_Osemiring__1__class_Oof__nat__aux(v5, v4, v3, v2) = v0)) % 228.76/33.10 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 228.76/33.10 v0 | ~ (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v1) | ~ % 228.76/33.10 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 228.76/33.10 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~ % 228.76/33.10 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 228.76/33.10 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ (c_Power_Opower_Opower(v4, v3, % 228.76/33.10 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 228.76/33.10 [v4: $i] : (v1 = v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 228.76/33.10 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 228.76/33.10 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~ % 228.76/33.10 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 228.76/33.10 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Complex_Orcis(v3, v2) = v1) | % 228.76/33.10 ~ (c_Complex_Orcis(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 228.76/33.10 : ! [v3: $i] : (v1 = v0 | ~ (c_Nat__Transfer_Otsub(v3, v2) = v1) | ~ % 228.76/33.10 (c_Nat__Transfer_Otsub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 228.76/33.10 $i] : ! [v3: $i] : (v1 = v0 | ~ (c_RealVector_Onorm__class_Onorm(v3, v2) = % 228.76/33.10 v1) | ~ (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) & ! [v0: $i] : % 228.76/33.10 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v1) | ~ % 228.76/33.10 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v0)) & ! [v0: % 228.76/33.10 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_Int_Onumber__class_Onumber__of(v3, v2) = v1) | ~ % 228.76/33.10 (c_Int_Onumber__class_Onumber__of(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 228.76/33.10 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Groups_Oabs__class_Oabs(v3, v2) % 228.76/33.10 = v1) | ~ (c_Groups_Oabs__class_Oabs(v3, v2) = v0)) & ! [v0: $i] : ! % 228.76/33.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | % 228.76/33.10 ~ (tc_fun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 228.76/33.10 $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) & ! [v0: % 228.76/33.10 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Complex_Ocis(v2) = v1) | % 228.76/33.10 ~ (c_Complex_Ocis(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 228.76/33.10 = v0 | ~ (c_Power_Opower__class_Opower(v2) = v1) | ~ % 228.76/33.10 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 228.76/33.10 [v2: $i] : (v1 = v0 | ~ (c_Nat_Osemiring__1__class_Oof__nat(v2) = v1) | ~ % 228.76/33.10 (c_Nat_Osemiring__1__class_Oof__nat(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 228.76/33.10 ! [v2: $i] : (v1 = v0 | ~ (c_Groups_Otimes__class_Otimes(v2) = v1) | ~ % 228.76/33.10 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 228.76/33.10 [v2: $i] : (v1 = v0 | ~ (c_Complex_Oexpi(v2) = v1) | ~ (c_Complex_Oexpi(v2) % 228.76/33.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_Int_Opred(v2) = v1) | ~ (c_Int_Opred(v2) = v0)) & ! [v0: $i] : ! [v1: % 228.76/33.10 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Int_Osucc(v2) = v1) | ~ % 228.76/33.10 (c_Int_Osucc(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 228.76/33.10 | ~ (v_g____(v2) = v1) | ~ (v_g____(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 228.76/33.10 : ! [v2: $i] : (v1 = v0 | ~ (c_RComplete_Onatfloor(v2) = v1) | ~ % 228.76/33.10 (c_RComplete_Onatfloor(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 228.76/33.10 : (v1 = v0 | ~ (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = % 228.76/33.10 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_RComplete_Onatceiling(v2) = v1) | ~ (c_RComplete_Onatceiling(v2) = v0)) % 228.76/33.10 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_Groups_Ozero__class_Ozero(v2) = v1) | ~ (c_Groups_Ozero__class_Ozero(v2) % 228.76/33.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_Groups_Oone__class_Oone(v2) = v1) | ~ (c_Groups_Oone__class_Oone(v2) = % 228.76/33.10 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 228.76/33.10 (c_RealDef_Oreal(v2) = v1) | ~ (c_RealDef_Oreal(v2) = v0)) & ! [v0: $i] : % 228.76/33.10 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Nat_OSuc(v2) = v1) | ~ % 228.76/33.10 (c_Nat_OSuc(v2) = v0)) % 228.76/33.10 % 228.76/33.10 Further assumptions not needed in the proof: % 228.76/33.10 -------------------------------------------- % 228.76/33.10 arity_Complex__Ocomplex__Fields_Ofield, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Oab__group__add, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Oab__semigroup__add, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Ogroup__add, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Omonoid__add, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Omonoid__mult, % 228.76/33.10 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ozero, % 228.76/33.10 arity_Complex__Ocomplex__Int_Onumber, % 228.76/33.10 arity_Complex__Ocomplex__Int_Onumber__ring, % 228.76/33.10 arity_Complex__Ocomplex__Int_Oring__char__0, % 228.76/33.10 arity_Complex__Ocomplex__Nat_Osemiring__char__0, % 228.76/33.10 arity_Complex__Ocomplex__Power_Opower, % 228.76/33.10 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, % 228.76/33.10 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, % 228.76/33.11 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, % 228.76/33.11 arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Ocomm__ring, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Ocomm__ring__1, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Ocomm__semiring, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Oidom, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Omult__zero, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Ono__zero__divisors, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Osemiring, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Osemiring__0, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Osemiring__1, % 228.76/33.11 arity_Complex__Ocomplex__Rings_Ozero__neq__one, % 228.76/33.11 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 228.76/33.11 arity_HOL__Obool__Orderings_Oord, arity_HOL__Obool__Orderings_Oorder, % 228.76/33.11 arity_HOL__Obool__Orderings_Opreorder, arity_Int__Oint__Divides_Osemiring__div, % 228.76/33.11 arity_Int__Oint__Groups_Oab__group__add, % 228.76/33.11 arity_Int__Oint__Groups_Oab__semigroup__add, % 228.76/33.11 arity_Int__Oint__Groups_Oab__semigroup__mult, % 228.76/33.11 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, % 228.76/33.11 arity_Int__Oint__Groups_Ocancel__comm__monoid__add, % 228.76/33.11 arity_Int__Oint__Groups_Ocancel__semigroup__add, % 228.76/33.11 arity_Int__Oint__Groups_Ocomm__monoid__add, % 228.76/33.11 arity_Int__Oint__Groups_Ocomm__monoid__mult, % 228.76/33.11 arity_Int__Oint__Groups_Ogroup__add, % 228.76/33.11 arity_Int__Oint__Groups_Olinordered__ab__group__add, % 228.76/33.11 arity_Int__Oint__Groups_Omonoid__add, arity_Int__Oint__Groups_Omonoid__mult, % 228.76/33.11 arity_Int__Oint__Groups_Oone, arity_Int__Oint__Groups_Oordered__ab__group__add, % 228.76/33.11 arity_Int__Oint__Groups_Oordered__ab__group__add__abs, % 228.76/33.11 arity_Int__Oint__Groups_Oordered__ab__semigroup__add, % 228.76/33.11 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, % 228.76/33.11 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, % 228.76/33.11 arity_Int__Oint__Groups_Oordered__comm__monoid__add, % 228.76/33.11 arity_Int__Oint__Groups_Ozero, arity_Int__Oint__Int_Onumber, % 228.76/33.11 arity_Int__Oint__Int_Onumber__ring, arity_Int__Oint__Int_Oring__char__0, % 228.76/33.11 arity_Int__Oint__Nat_Osemiring__char__0, arity_Int__Oint__Orderings_Olinorder, % 228.76/33.11 arity_Int__Oint__Orderings_Oord, arity_Int__Oint__Orderings_Oorder, % 228.76/33.11 arity_Int__Oint__Orderings_Opreorder, arity_Int__Oint__Power_Opower, % 228.76/33.11 arity_Int__Oint__Rings_Ocomm__ring, arity_Int__Oint__Rings_Ocomm__ring__1, % 228.76/33.11 arity_Int__Oint__Rings_Ocomm__semiring, % 228.76/33.11 arity_Int__Oint__Rings_Ocomm__semiring__0, % 228.76/33.11 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Oidom, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__idom, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__ring, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__ring__strict, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__semidom, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__semiring, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__semiring__1, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__semiring__1__strict, % 228.76/33.11 arity_Int__Oint__Rings_Olinordered__semiring__strict, % 228.76/33.11 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors, % 228.76/33.11 arity_Int__Oint__Rings_Oordered__cancel__semiring, % 228.76/33.11 arity_Int__Oint__Rings_Oordered__comm__semiring, % 228.76/33.11 arity_Int__Oint__Rings_Oordered__ring, % 228.76/33.11 arity_Int__Oint__Rings_Oordered__ring__abs, % 228.76/33.11 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring, % 228.76/33.11 arity_Int__Oint__Rings_Oring__1, % 228.76/33.11 arity_Int__Oint__Rings_Oring__1__no__zero__divisors, % 228.76/33.11 arity_Int__Oint__Rings_Oring__no__zero__divisors, % 228.76/33.11 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0, % 228.76/33.11 arity_Int__Oint__Rings_Osemiring__1, arity_Int__Oint__Rings_Ozero__neq__one, % 228.76/33.11 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 228.76/33.11 arity_Nat__Onat__Divides_Osemiring__div, % 228.76/33.11 arity_Nat__Onat__Groups_Oab__semigroup__add, % 228.76/33.11 arity_Nat__Onat__Groups_Oab__semigroup__mult, % 228.76/33.11 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, % 228.76/33.11 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, % 228.76/33.11 arity_Nat__Onat__Groups_Ocancel__semigroup__add, % 228.76/33.11 arity_Nat__Onat__Groups_Ocomm__monoid__add, % 228.76/33.11 arity_Nat__Onat__Groups_Ocomm__monoid__mult, % 228.76/33.11 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult, % 228.76/33.11 arity_Nat__Onat__Groups_Oone, % 228.76/33.11 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, % 228.76/33.11 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, % 228.76/33.11 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, % 228.76/33.11 arity_Nat__Onat__Groups_Oordered__comm__monoid__add, % 228.76/33.11 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Int_Onumber, % 228.76/33.11 arity_Nat__Onat__Nat_Osemiring__char__0, arity_Nat__Onat__Orderings_Olinorder, % 228.76/33.11 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder, % 228.76/33.11 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Power_Opower, % 228.76/33.11 arity_Nat__Onat__Rings_Ocomm__semiring, % 228.76/33.11 arity_Nat__Onat__Rings_Ocomm__semiring__0, % 228.76/33.11 arity_Nat__Onat__Rings_Ocomm__semiring__1, % 228.76/33.11 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, % 228.76/33.11 arity_Nat__Onat__Rings_Olinordered__semidom, % 228.76/33.11 arity_Nat__Onat__Rings_Olinordered__semiring, % 228.76/33.11 arity_Nat__Onat__Rings_Olinordered__semiring__strict, % 228.76/33.11 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors, % 228.76/33.11 arity_Nat__Onat__Rings_Oordered__cancel__semiring, % 228.76/33.11 arity_Nat__Onat__Rings_Oordered__comm__semiring, % 228.76/33.11 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring, % 228.76/33.11 arity_Nat__Onat__Rings_Osemiring__0, arity_Nat__Onat__Rings_Osemiring__1, % 228.76/33.11 arity_Nat__Onat__Rings_Ozero__neq__one, % 228.76/33.11 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 228.76/33.11 arity_Polynomial__Opoly__Divides_Osemiring__div, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oab__group__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oab__semigroup__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Ogroup__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Omonoid__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Omonoid__mult, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oone, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, % 228.76/33.11 arity_Polynomial__Opoly__Groups_Ozero, arity_Polynomial__Opoly__Int_Onumber, % 228.76/33.11 arity_Polynomial__Opoly__Int_Onumber__ring, % 228.76/33.11 arity_Polynomial__Opoly__Int_Oring__char__0, % 228.76/33.11 arity_Polynomial__Opoly__Nat_Osemiring__char__0, % 228.76/33.11 arity_Polynomial__Opoly__Orderings_Olinorder, % 228.76/33.11 arity_Polynomial__Opoly__Orderings_Oord, % 228.76/33.11 arity_Polynomial__Opoly__Orderings_Oorder, % 228.76/33.11 arity_Polynomial__Opoly__Orderings_Opreorder, % 228.76/33.11 arity_Polynomial__Opoly__Power_Opower, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Ocomm__ring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Ocomm__ring__1, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Ocomm__semiring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oidom, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__idom, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__ring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__semidom, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__semiring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Omult__zero, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Ono__zero__divisors, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oordered__ring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oordered__ring__abs, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oordered__semiring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Osemiring, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Osemiring__0, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Osemiring__1, % 228.76/33.11 arity_Polynomial__Opoly__Rings_Ozero__neq__one, % 228.76/33.11 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 228.76/33.11 arity_RealDef__Oreal__Fields_Ofield, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oab__group__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oab__semigroup__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oab__semigroup__mult, % 228.76/33.11 arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Ocomm__monoid__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, % 228.76/33.11 arity_RealDef__Oreal__Groups_Ogroup__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Omonoid__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Omonoid__mult, arity_RealDef__Oreal__Groups_Oone, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oordered__ab__group__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, % 228.76/33.11 arity_RealDef__Oreal__Groups_Ozero, arity_RealDef__Oreal__Int_Onumber, % 228.76/33.11 arity_RealDef__Oreal__Int_Onumber__ring, % 228.76/33.11 arity_RealDef__Oreal__Int_Oring__char__0, % 228.76/33.11 arity_RealDef__Oreal__Nat_Osemiring__char__0, % 228.76/33.11 arity_RealDef__Oreal__Orderings_Olinorder, arity_RealDef__Oreal__Orderings_Oord, % 228.76/33.11 arity_RealDef__Oreal__Orderings_Oorder, % 228.76/33.11 arity_RealDef__Oreal__Orderings_Opreorder, arity_RealDef__Oreal__Power_Opower, % 228.76/33.11 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, % 228.76/33.11 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, % 228.76/33.11 arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, % 228.76/33.11 arity_RealDef__Oreal__RealVector_Oreal__normed__vector, % 228.76/33.11 arity_RealDef__Oreal__Rings_Ocomm__ring, % 228.76/33.11 arity_RealDef__Oreal__Rings_Ocomm__ring__1, % 228.76/33.11 arity_RealDef__Oreal__Rings_Ocomm__semiring, % 228.76/33.11 arity_RealDef__Oreal__Rings_Ocomm__semiring__0, % 228.76/33.11 arity_RealDef__Oreal__Rings_Ocomm__semiring__1, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oidom, % 228.76/33.11 arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict, % 228.76/33.11 arity_RealDef__Oreal__Rings_Olinordered__idom, % 228.76/33.11 arity_RealDef__Oreal__Rings_Olinordered__ring, % 228.76/33.11 arity_RealDef__Oreal__Rings_Olinordered__ring__strict, % 228.76/33.11 arity_RealDef__Oreal__Rings_Olinordered__semiring, % 228.76/33.11 arity_RealDef__Oreal__Rings_Olinordered__semiring__1, % 228.76/33.11 arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, % 228.76/33.11 arity_RealDef__Oreal__Rings_Olinordered__semiring__strict, % 228.76/33.11 arity_RealDef__Oreal__Rings_Omult__zero, % 228.76/33.11 arity_RealDef__Oreal__Rings_Ono__zero__divisors, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oordered__cancel__semiring, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oordered__comm__semiring, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oordered__ring, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oordered__ring__abs, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oordered__semiring, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oring, arity_RealDef__Oreal__Rings_Oring__1, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, % 228.76/33.11 arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, % 228.76/33.11 arity_RealDef__Oreal__Rings_Osemiring, arity_RealDef__Oreal__Rings_Osemiring__0, % 228.76/33.11 arity_RealDef__Oreal__Rings_Osemiring__1, % 228.76/33.11 arity_RealDef__Oreal__Rings_Ozero__neq__one, % 228.76/33.11 arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, % 228.76/33.11 arity_fun__Orderings_Oord, arity_fun__Orderings_Oorder, % 228.76/33.11 arity_fun__Orderings_Opreorder, fact_BseqD, fact_BseqI, fact_Bseq__def, % 228.76/33.11 fact_Deriv_Oadd__diff__add, fact_Divides_Otransfer__int__nat__functions_I1_J, % 228.76/33.11 fact_Divides_Otransfer__nat__int__function__closures_I1_J, fact_N1, % 228.76/33.11 fact_Nat_Oadd__0__right, fact_Nat_Odiff__diff__eq, % 228.76/33.11 fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, % 228.76/33.11 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, % 228.76/33.11 fact_One__nat__def, fact_Pls__def, fact_Suc__diff__1, fact_Suc__diff__diff, % 228.76/33.11 fact_Suc__diff__le, fact_Suc__diff__number__of, fact_Suc__eq__plus1, % 228.76/33.11 fact_Suc__eq__plus1__left, fact_Suc__inject, fact_Suc__leD, fact_Suc__leI, % 228.76/33.11 fact_Suc__le__eq, fact_Suc__le__lessD, fact_Suc__lessD, fact_Suc__lessI, % 228.76/33.11 fact_Suc__less__SucD, fact_Suc__less__eq, fact_Suc__mono, % 228.76/33.11 fact_Suc__mult__cancel1, fact_Suc__mult__le__cancel1, % 228.76/33.11 fact_Suc__mult__less__cancel1, fact_Suc__n__not__le__n, fact_Suc__n__not__n, % 228.76/33.11 fact_Suc__nat__number__of, fact_Suc__nat__number__of__add, fact_Suc__neq__Zero, % 228.76/33.11 fact_Suc__not__Zero, fact_Suc__pred, fact_Suc__pred_H, fact_Zero__neq__Suc, % 228.76/33.11 fact_Zero__not__Suc, % 228.76/33.11 fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096, % 228.76/33.11 fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, % 228.76/33.11 fact_ab__semigroup__add__class_Oadd__ac_I1_J, % 228.76/33.11 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_abs__add__abs, % 228.76/33.11 fact_abs__add__one__gt__zero, fact_abs__add__one__not__less__self, % 228.76/33.11 fact_abs__diff__less__iff, fact_abs__diff__triangle__ineq, fact_abs__eq__0, % 228.76/33.11 fact_abs__eq__mult, fact_abs__ge__self, fact_abs__ge__zero, % 228.76/33.11 fact_abs__idempotent, fact_abs__int__eq, fact_abs__le__D1, % 228.76/33.11 fact_abs__le__zero__iff, fact_abs__minus__commute, fact_abs__mult, % 228.76/33.11 fact_abs__mult__less, fact_abs__mult__pos, fact_abs__mult__self, % 228.76/33.11 fact_abs__norm__cancel, fact_abs__not__less__zero, fact_abs__of__nat, % 228.76/33.11 fact_abs__of__nonneg, fact_abs__of__pos, fact_abs__one, % 228.76/33.11 fact_abs__triangle__ineq, fact_abs__triangle__ineq2, % 228.76/33.11 fact_abs__triangle__ineq2__sym, fact_abs__triangle__ineq3, % 228.76/33.11 fact_abs__triangle__ineq4, fact_abs__zero, fact_abs__zmult__eq__1, % 228.76/33.11 fact_add1__zle__eq, fact_add_Ocomm__neutral, fact_add__0, fact_add__0__iff, % 228.76/33.11 fact_add__0__left, fact_add__0__right, fact_add__Pls, fact_add__Pls__right, % 228.76/33.11 fact_add__Suc, fact_add__Suc__right, fact_add__Suc__shift, % 228.76/33.11 fact_add__diff__assoc, fact_add__diff__assoc2, fact_add__diff__cancel, % 228.76/33.11 fact_add__diff__inverse, fact_add__eq__if, fact_add__eq__self__zero, % 228.76/33.11 fact_add__gr__0, fact_add__imp__eq, fact_add__increasing, fact_add__increasing2, % 228.76/33.11 fact_add__is__0, fact_add__is__1, fact_add__leD1, fact_add__leD2, fact_add__leE, % 228.76/33.11 fact_add__le__cancel__left, fact_add__le__cancel__right, % 228.76/33.11 fact_add__le__imp__le__left, fact_add__le__imp__le__right, % 228.76/33.11 fact_add__le__less__mono, fact_add__le__mono, fact_add__le__mono1, % 228.76/33.11 fact_add__left__cancel, fact_add__left__imp__eq, fact_add__left__mono, % 228.76/33.11 fact_add__lessD1, fact_add__less__cancel__left, fact_add__less__cancel__right, % 228.76/33.11 fact_add__less__imp__less__left, fact_add__less__imp__less__right, % 228.76/33.11 fact_add__less__le__mono, fact_add__less__mono, fact_add__less__mono1, % 228.76/33.11 fact_add__mono, fact_add__mult__distrib, fact_add__mult__distrib2, % 228.76/33.11 fact_add__nat__number__of, fact_add__neg__neg, fact_add__neg__nonpos, % 228.76/33.11 fact_add__nonneg__eq__0__iff, fact_add__nonneg__nonneg, fact_add__nonneg__pos, % 228.76/33.11 fact_add__nonpos__neg, fact_add__nonpos__nonpos, fact_add__number__of__diff1, % 228.76/33.11 fact_add__number__of__eq, fact_add__number__of__left, fact_add__numeral__0, % 228.76/33.11 fact_add__numeral__0__right, fact_add__pos__nonneg, fact_add__pos__pos, % 228.76/33.11 fact_add__right__cancel, fact_add__right__imp__eq, fact_add__right__mono, % 228.76/33.11 fact_add__scale__eq__noteq, fact_add__strict__increasing, % 228.76/33.11 fact_add__strict__increasing2, fact_add__strict__left__mono, % 228.76/33.11 fact_add__strict__mono, fact_add__strict__right__mono, fact_arith__simps_I32_J, % 228.76/33.11 fact_ath, fact_bin__less__0__simps_I1_J, fact_cis__mult, fact_cis__rcis__eq, % 228.76/33.11 fact_cis__zero, fact_combine__common__factor, fact_comm__mult__left__mono, % 228.76/33.11 fact_comm__mult__strict__left__mono, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, % 228.76/33.11 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, % 228.76/33.11 fact_comm__semiring__class_Odistrib, fact_complex__i__not__number__of, % 228.76/33.11 fact_complex__i__not__one, fact_complex__i__not__zero, fact_complex__mod__rcis, % 228.76/33.11 fact_complex__mod__triangle__ineq2, fact_complex__mod__triangle__sub, % 228.76/33.11 fact_convex__bound__le, fact_convex__bound__lt, fact_crossproduct__eq, % 228.76/33.11 fact_crossproduct__noteq, fact_d_I1_J, fact_decr__lemma, fact_decr__mult__lemma, % 228.76/33.11 fact_decseq__def, fact_decseq__imp__monoseq, fact_diff__0__eq__0, % 228.76/33.11 fact_diff__0__right, fact_diff__Suc__1, fact_diff__Suc__Suc, % 228.76/33.11 fact_diff__Suc__diff__eq1, fact_diff__Suc__diff__eq2, % 228.76/33.11 fact_diff__Suc__eq__diff__pred, fact_diff__Suc__less, fact_diff__add__0, % 228.76/33.11 fact_diff__add__assoc, fact_diff__add__assoc2, fact_diff__add__cancel, % 228.76/33.11 fact_diff__add__inverse, fact_diff__add__inverse2, fact_diff__bin__simps_I1_J, % 228.76/33.11 fact_diff__cancel, fact_diff__cancel2, fact_diff__commute, % 228.76/33.11 fact_diff__diff__cancel, fact_diff__diff__left, fact_diff__diff__right, % 228.76/33.11 fact_diff__eq__diff__eq, fact_diff__eq__diff__less, % 228.76/33.11 fact_diff__eq__diff__less__eq, fact_diff__is__0__eq, fact_diff__is__0__eq_H, % 228.76/33.11 fact_diff__le__mono, fact_diff__le__mono2, fact_diff__le__self, fact_diff__less, % 228.76/33.11 fact_diff__less__Suc, fact_diff__less__mono, fact_diff__less__mono2, % 228.76/33.11 fact_diff__mult__distrib, fact_diff__mult__distrib2, fact_diff__self, % 228.76/33.11 fact_diff__self__eq__0, fact_diffs0__imp__equal, fact_div__0, fact_div__1, % 228.76/33.11 fact_div__add__self1, fact_div__add__self2, fact_div__by__0, fact_div__by__1, % 228.76/33.11 fact_div__geq, fact_div__if, fact_div__le__dividend, fact_div__le__mono, % 228.76/33.11 fact_div__le__mono2, fact_div__less, fact_div__less__dividend, % 228.76/33.11 fact_div__mult2__eq, fact_div__mult__mult1, fact_div__mult__mult1__if, % 228.76/33.11 fact_div__mult__mult2, fact_div__mult__self1, fact_div__mult__self1__is__id, % 228.76/33.11 fact_div__mult__self1__is__m, fact_div__mult__self2, % 228.76/33.11 fact_div__mult__self2__is__id, fact_div__mult__self__is__m, % 228.76/33.11 fact_div__neg__neg__trivial, fact_div__neg__pos__less0, % 228.76/33.11 fact_div__nonneg__neg__le0, fact_div__nonpos__pos__le0, % 228.76/33.11 fact_div__pos__pos__trivial, fact_div__self, fact_divisors__zero, % 228.76/33.11 fact_divmod__int__rel__div__eq, % 228.76/33.11 fact_double__add__le__zero__iff__single__add__le__zero, % 228.76/33.11 fact_double__add__less__zero__iff__single__add__less__zero, % 228.76/33.11 fact_double__eq__0__iff, fact_double__zero__sym, fact_eq__0__number__of, % 228.76/33.11 fact_eq__add__iff1, fact_eq__add__iff2, fact_eq__diff__iff, % 228.76/33.11 fact_eq__iff__diff__eq__0, fact_eq__imp__le, fact_eq__nat__number__of, % 228.76/33.11 fact_eq__number__of, fact_eq__number__of__0, fact_even__less__0__iff, % 228.76/33.11 fact_ex__least__nat__less, fact_expand__Suc, fact_expi__add, fact_expi__zero, % 228.76/33.11 fact_ext, fact_field__power__not__zero, fact_fz_I1_J, fact_fz_I2_J, fact_g_I1_J, % 228.76/33.11 fact_gr0I, fact_gr0__conv__Suc, fact_gr__implies__not0, fact_incr__lemma, % 228.76/33.11 fact_incr__mult__lemma, fact_incseq__SucI, fact_incseq__def, % 228.76/33.11 fact_incseq__imp__monoseq, fact_int__0, fact_int__0__less__1, % 228.76/33.11 fact_int__0__neq__1, fact_int__1, fact_int__Suc, fact_int__Suc0__eq__1, % 228.76/33.11 fact_int__div__less__self, fact_int__eq__0__conv, fact_int__int__eq, % 228.76/33.11 fact_int__le__0__conv, fact_int__less__0__conv, fact_int__mult, % 228.76/33.11 fact_int__nat__number__of, fact_int__one__le__iff__zero__less, fact_int__power, % 228.76/33.11 fact_int__power__div__base, fact_le0, fact_leD, fact_leI, fact_le__0__eq, % 228.76/33.11 fact_le__SucE, fact_le__SucI, fact_le__Suc__eq, fact_le__Suc__ex__iff, % 228.76/33.11 fact_le__add1, fact_le__add2, fact_le__add__diff, fact_le__add__diff__inverse, % 228.76/33.11 fact_le__add__diff__inverse2, fact_le__add__iff1, fact_le__add__iff2, % 228.76/33.11 fact_le__antisym, fact_le__cube, fact_le__diff__conv, fact_le__diff__conv2, % 228.76/33.11 fact_le__diff__iff, fact_le__div__geq, fact_le__eq__less__or__eq, fact_le__funD, % 228.76/33.11 fact_le__funE, fact_le__fun__def, fact_le__iff__add, fact_le__iff__diff__le__0, % 228.76/33.11 fact_le__iff__pred__less, fact_le__imp__0__less, fact_le__imp__diff__is__add, % 228.76/33.11 fact_le__imp__less__Suc, fact_le__less__Suc__eq, fact_le__mult__natfloor, % 228.76/33.11 fact_le__nat__number__of, fact_le__natfloor__eq__number__of, % 228.76/33.11 fact_le__natfloor__eq__one, fact_le__neq__implies__less, fact_le__number__of, % 228.76/33.11 fact_le__number__of__eq__not__less, fact_le__refl, fact_le__special_I1_J, % 228.76/33.11 fact_le__special_I3_J, fact_le__square, fact_le__trans, % 228.76/33.11 fact_left__add__mult__distrib, fact_left__diff__distrib__number__of, % 228.76/33.11 fact_left__distrib__number__of, fact_lemmaCauchy, fact_lemma__interval, % 228.76/33.11 fact_lemma__realpow__diff, fact_lessI, fact_less__0__number__of, % 228.76/33.11 fact_less__1__mult, fact_less__Suc0, fact_less__SucE, fact_less__SucI, % 228.76/33.11 fact_less__Suc__eq, fact_less__Suc__eq__0__disj, fact_less__Suc__eq__le, % 228.76/33.11 fact_less__add__Suc1, fact_less__add__Suc2, fact_less__add__eq__less, % 228.76/33.11 fact_less__add__iff1, fact_less__add__iff2, fact_less__add__one, % 228.76/33.11 fact_less__antisym, fact_less__bin__lemma, fact_less__diff__conv, % 228.76/33.11 fact_less__diff__iff, fact_less__eq__Suc__le, fact_less__eq__nat_Osimps_I1_J, % 228.76/33.11 fact_less__eq__number__of__int__code, fact_less__eq__real__def, % 228.76/33.11 fact_less__fun__def, fact_less__iff__Suc__add, fact_less__iff__diff__less__0, % 228.76/33.11 fact_less__imp__diff__less, fact_less__imp__le__nat, fact_less__imp__neq, % 228.76/33.11 fact_less__imp__of__nat__less, fact_less__irrefl__nat, fact_less__le__not__le, % 228.76/33.11 fact_less__nat__number__of, fact_less__nat__zero__code, fact_less__not__refl, % 228.76/33.11 fact_less__not__refl2, fact_less__not__refl3, fact_less__number__of, % 228.76/33.11 fact_less__number__of__int__code, fact_less__or__eq__imp__le, % 228.76/33.11 fact_less__special_I1_J, fact_less__special_I3_J, fact_less__trans__Suc, % 228.76/33.11 fact_less__zeroE, fact_lift__Suc__mono__le, fact_linorder__antisym__conv1, % 228.76/33.11 fact_linorder__antisym__conv2, fact_linorder__antisym__conv3, % 228.76/33.11 fact_linorder__cases, fact_linorder__le__cases, fact_linorder__le__less__linear, % 228.76/33.11 fact_linorder__less__linear, fact_linorder__linear, fact_linorder__neqE, % 228.76/33.11 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat, % 228.76/33.11 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less, % 228.76/33.11 fact_minus__nat_Odiff__0, fact_monoI1, fact_monoI2, fact_mono__SucI1, % 228.76/33.11 fact_mono__SucI2, fact_monoseq__Suc, fact_monoseq__def, fact_mult_Oadd__left, % 228.76/33.11 fact_mult_Oadd__right, fact_mult_Ocomm__neutral, fact_mult_Odiff__left, % 228.76/33.11 fact_mult_Odiff__right, fact_mult_Ononneg__bounded, fact_mult_Opos__bounded, % 228.76/33.11 fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, fact_mult_Ozero__right, % 228.76/33.11 fact_mult__0, fact_mult__0__right, fact_mult__1, fact_mult__1__left, % 228.76/33.11 fact_mult__1__right, fact_mult__Pls, fact_mult__Suc, fact_mult__Suc__right, % 228.76/33.11 fact_mult__cancel1, fact_mult__cancel2, fact_mult__diff__mult, % 228.76/33.11 fact_mult__eq__0__iff, fact_mult__eq__1__iff, fact_mult__eq__if, % 228.76/33.11 fact_mult__eq__self__implies__10, fact_mult__is__0, fact_mult__le__0__iff, % 228.76/33.11 fact_mult__le__cancel1, fact_mult__le__cancel2, % 228.76/33.11 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos, % 228.76/33.11 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1, % 228.76/33.11 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Odiff, % 228.76/33.11 fact_mult__left_Ononneg__bounded, fact_mult__left_Opos__bounded, % 228.76/33.11 fact_mult__left_Ozero, fact_mult__left__le__imp__le, % 228.76/33.11 fact_mult__left__le__one__le, fact_mult__left__less__imp__less, % 228.76/33.11 fact_mult__left__mono, fact_mult__left__mono__neg, fact_mult__less__cancel1, % 228.76/33.11 fact_mult__less__cancel2, fact_mult__less__cancel__left__disj, % 228.76/33.11 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos, % 228.76/33.11 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left, % 228.76/33.11 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less, % 228.76/33.11 fact_mult__less__mono1, fact_mult__less__mono2, fact_mult__mono, % 228.76/33.11 fact_mult__mono_H, fact_mult__nat__number__of, fact_mult__neg__neg, % 228.76/33.11 fact_mult__neg__pos, fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos, % 228.76/33.11 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg, % 228.76/33.11 fact_mult__nonpos__nonpos, fact_mult__number__of__left, fact_mult__pos__neg, % 228.76/33.11 fact_mult__pos__neg2, fact_mult__pos__pos, fact_mult__right_Oadd, % 228.76/33.11 fact_mult__right_Odiff, fact_mult__right_Ononneg__bounded, % 228.76/33.11 fact_mult__right_Opos__bounded, fact_mult__right_Ozero, % 228.76/33.11 fact_mult__right__le__imp__le, fact_mult__right__le__one__le, % 228.76/33.11 fact_mult__right__less__imp__less, fact_mult__right__mono, % 228.76/33.11 fact_mult__right__mono__neg, fact_mult__strict__left__mono, % 228.76/33.11 fact_mult__strict__left__mono__neg, fact_mult__strict__mono, % 228.76/33.11 fact_mult__strict__mono_H, fact_mult__strict__right__mono, % 228.76/33.11 fact_mult__strict__right__mono__neg, fact_mult__zero__left, % 228.76/33.11 fact_mult__zero__right, fact_n__less__m__mult__n, fact_n__less__n__mult__m, % 228.76/33.11 fact_n__not__Suc__n, fact_nat_Oinject, fact_nat_Osimps_I2_J, % 228.76/33.11 fact_nat_Osimps_I3_J, fact_nat__0__less__mult__iff, % 228.76/33.11 fact_nat__1__add__number__of, fact_nat__1__eq__mult__iff, fact_nat__add__assoc, % 228.76/33.11 fact_nat__add__left__cancel, fact_nat__add__left__cancel__le, % 228.76/33.11 fact_nat__add__left__cancel__less, fact_nat__add__left__commute, % 228.76/33.11 fact_nat__add__right__cancel, fact_nat__diff__add__eq1, % 228.76/33.11 fact_nat__diff__add__eq2, fact_nat__diff__split, fact_nat__diff__split__asm, % 228.76/33.11 fact_nat__eq__add__iff1, fact_nat__eq__add__iff2, fact_nat__le__add__iff1, % 228.76/33.11 fact_nat__le__add__iff2, fact_nat__le__linear, fact_nat__less__add__iff1, % 228.76/33.11 fact_nat__less__add__iff2, fact_nat__less__cases, fact_nat__less__le, % 228.76/33.11 fact_nat__lt__two__imp__zero__or__one, fact_nat__mult__1, % 228.76/33.11 fact_nat__mult__1__right, fact_nat__mult__assoc, fact_nat__mult__commute, % 228.76/33.11 fact_nat__mult__div__cancel1, fact_nat__mult__div__cancel__disj, % 228.76/33.11 fact_nat__mult__eq__1__iff, fact_nat__mult__eq__cancel1, % 228.76/33.11 fact_nat__mult__eq__cancel__disj, fact_nat__mult__le__cancel1, % 228.76/33.11 fact_nat__mult__less__cancel1, fact_nat__neq__iff, fact_nat__number__of__Pls, % 228.76/33.11 fact_nat__number__of__add__1, fact_nat__number__of__add__left, % 228.76/33.11 fact_nat__number__of__diff__1, fact_nat__number__of__mult__left, % 228.76/33.11 fact_nat__one__le__power, fact_nat__power__eq__Suc__0__iff, % 228.76/33.11 fact_nat__power__less__imp__less, fact_nat__zero__less__power__iff, % 228.76/33.11 fact_natceiling__add__number__of, fact_natceiling__add__one, % 228.76/33.11 fact_natceiling__le__eq__number__of, fact_natceiling__le__eq__one, % 228.76/33.11 fact_natceiling__mono, fact_natceiling__neg, fact_natceiling__number__of__eq, % 228.76/33.11 fact_natceiling__one, fact_natceiling__zero, fact_natfloor__add__number__of, % 228.76/33.11 fact_natfloor__add__one, fact_natfloor__mono, fact_natfloor__neg, % 228.76/33.11 fact_natfloor__number__of__eq, fact_natfloor__one, fact_natfloor__zero, % 228.76/33.11 fact_neg__def, fact_neg__imp__number__of__eq__0, fact_neg__imp__zdiv__neg__iff, % 228.76/33.11 fact_neg__imp__zdiv__nonneg__iff, fact_neg__number__of__pred__iff__0, % 228.76/33.11 fact_neq0__conv, fact_no__zero__divisors, fact_nonneg1__imp__zdiv__pos__iff, % 228.76/33.11 fact_nonzero__power__divide, fact_norm__add__less, fact_norm__diff__ineq, % 228.76/33.11 fact_norm__diff__triangle__ineq, fact_norm__eq__zero, fact_norm__ge__zero, % 228.76/33.11 fact_norm__le__zero__iff, fact_norm__minus__commute, fact_norm__mult, % 228.76/33.11 fact_norm__mult__ineq, fact_norm__mult__less, fact_norm__not__less__zero, % 228.76/33.11 fact_norm__number__of, fact_norm__of__nat, fact_norm__one, fact_norm__power, % 228.76/33.11 fact_norm__power__ineq, fact_norm__ratiotest__lemma, fact_norm__triangle__ineq, % 228.76/33.11 fact_norm__triangle__ineq2, fact_norm__triangle__ineq3, % 228.76/33.11 fact_norm__triangle__ineq4, fact_norm__zero, fact_not__add__less1, % 228.76/33.11 fact_not__add__less2, fact_not__leE, fact_not__less0, fact_not__less__eq, % 228.76/33.11 fact_not__less__eq__eq, fact_not__less__iff__gr__or__eq, % 228.76/33.11 fact_not__less__less__Suc__eq, fact_not__neg__0, fact_not__neg__1, % 228.76/33.11 fact_not__neg__eq__ge__0, fact_not__neg__int, fact_not__neg__number__of__Pls, % 228.76/33.11 fact_not__one__le__zero, fact_not__one__less__zero, % 228.76/33.11 fact_not__real__square__gt__zero, fact_not__square__less__zero, % 228.76/33.11 fact_not__sum__squares__lt__zero, fact_number__of2, fact_number__of__Pls, % 228.76/33.11 fact_number__of__add, fact_number__of__diff, fact_number__of__is__id, % 228.76/33.11 fact_number__of__mult, fact_number__of__reorient, fact_number__of__succ, % 228.76/33.11 fact_odd__less__0, fact_odd__nonzero, fact_of__nat__0, fact_of__nat__0__le__iff, % 228.76/33.11 fact_of__nat__0__less__iff, fact_of__nat__1, fact_of__nat__Suc, % 228.76/33.11 fact_of__nat__add, fact_of__nat__aux_Osimps_I1_J, fact_of__nat__aux_Osimps_I2_J, % 228.76/33.11 fact_of__nat__diff, fact_of__nat__eq__iff, fact_of__nat__less__0__iff, % 228.76/33.11 fact_of__nat__less__iff, fact_of__nat__less__imp__less, fact_of__nat__mult, % 228.76/33.11 fact_of__nat__number__of__eq, fact_of__nat__number__of__lemma, % 228.76/33.11 fact_of__nat__power, fact_one__is__add, fact_one__le__mult__iff, % 228.76/33.11 fact_one__le__power, fact_one__less__mult, fact_one__less__power, % 228.76/33.11 fact_one__neq__zero, fact_one__reorient, fact_ord__eq__le__trans, % 228.76/33.11 fact_ord__eq__less__trans, fact_ord__le__eq__trans, fact_ord__less__eq__trans, % 228.76/33.11 fact_order__antisym, fact_order__antisym__conv, fact_order__eq__iff, % 228.76/33.11 fact_order__eq__refl, fact_order__le__imp__less__or__eq, fact_order__le__less, % 228.76/33.11 fact_order__le__less__trans, fact_order__le__neq__trans, fact_order__less__asym, % 228.76/33.11 fact_order__less__asym_H, fact_order__less__imp__le, % 228.76/33.11 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2, % 228.76/33.11 fact_order__less__imp__not__less, fact_order__less__irrefl, % 228.76/33.11 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym, % 228.76/33.11 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl, % 228.76/33.11 fact_order__trans, fact_plus__nat_Oadd__0, fact_plus__numeral__code_I9_J, % 228.76/33.11 fact_pos__add__strict, fact_pos__imp__zdiv__neg__iff, % 228.76/33.11 fact_pos__imp__zdiv__nonneg__iff, fact_pos__imp__zdiv__pos__iff, % 228.76/33.11 fact_pos__zmult__eq__1__iff, fact_power_Opower_Opower__0, % 228.76/33.11 fact_power_Opower_Opower__Suc, fact_power__0, fact_power__0__Suc, % 228.76/33.11 fact_power__0__left, fact_power__0__left__number__of, fact_power__Suc, % 228.76/33.11 fact_power__Suc2, fact_power__Suc__0, fact_power__Suc__less, % 228.76/33.11 fact_power__Suc__less__one, fact_power__abs, fact_power__add, % 228.76/33.11 fact_power__commutes, fact_power__decreasing, fact_power__eq__0__iff, % 228.76/33.11 fact_power__eq__0__iff__number__of, fact_power__eq__if, % 228.76/33.11 fact_power__eq__imp__eq__base, fact_power__gt1, fact_power__gt1__lemma, % 228.76/33.11 fact_power__increasing, fact_power__increasing__iff, fact_power__inject__base, % 228.76/33.11 fact_power__inject__exp, fact_power__le__imp__le__base, % 228.76/33.11 fact_power__le__imp__le__exp, fact_power__less__imp__less__base, % 228.76/33.11 fact_power__less__imp__less__exp, fact_power__less__power__Suc, % 228.76/33.11 fact_power__mono, fact_power__mult, fact_power__mult__distrib, fact_power__one, % 228.76/33.11 fact_power__one__right, fact_power__power__power, % 228.76/33.11 fact_power__strict__decreasing, fact_power__strict__increasing, % 228.76/33.11 fact_power__strict__increasing__iff, fact_power__strict__mono, fact_pred__def, % 228.76/33.11 fact_psize__eq__0__iff, fact_q__neg__lemma, fact_q__pos__lemma, % 228.76/33.11 fact_rabs__ratiotest__lemma, fact_rcis__mult, fact_rcis__zero__mod, % 228.76/33.11 fact_real__add__left__mono, fact_real__add__mult__distrib, % 228.76/33.11 fact_real__le__antisym, fact_real__le__eq__diff, fact_real__le__linear, % 228.76/33.11 fact_real__le__refl, fact_real__le__trans, fact_real__less__def, % 228.76/33.11 fact_real__mult__1, fact_real__mult__assoc, fact_real__mult__commute, % 228.76/33.11 fact_real__mult__le__cancel__iff1, fact_real__mult__le__cancel__iff2, % 228.76/33.11 fact_real__mult__left__cancel, fact_real__mult__less__iff1, % 228.76/33.11 fact_real__mult__less__mono2, fact_real__mult__order, % 228.76/33.11 fact_real__mult__right__cancel, fact_real__norm__def, % 228.76/33.11 fact_real__squared__diff__one__factored, % 228.76/33.11 fact_real__two__squares__add__zero__iff, fact_real__zero__not__eq__one, % 228.76/33.11 fact_realpow__Suc__le__self, fact_realpow__minus__mult, % 228.76/33.11 fact_realpow__num__eq__if, fact_realpow__pos__nth, % 228.76/33.11 fact_realpow__pos__nth__unique, fact_realpow__two__diff, % 228.76/33.11 fact_reduce__poly__simple, fact_rel__simps_I19_J, fact_rel__simps_I2_J, % 228.76/33.11 fact_right__diff__distrib__number__of, fact_right__distrib__number__of, % 228.76/33.11 fact_right__minus__eq, fact_rp, fact_self__quotient__aux1, % 228.76/33.11 fact_self__quotient__aux2, fact_semiring__norm_I112_J, % 228.76/33.11 fact_semiring__norm_I113_J, fact_seq__suble, fact_split__div, fact_split__div_H, % 228.76/33.11 fact_split__div__lemma, fact_split__mult__neg__le, fact_split__mult__pos__le, % 228.76/33.11 fact_split__zdiv, fact_subseq__Suc__iff, fact_subseq__def, fact_succ__def, % 228.76/33.11 fact_succ__pred, fact_sum__squares__eq__zero__iff, fact_sum__squares__ge__zero, % 228.76/33.11 fact_sum__squares__gt__zero__iff, fact_sum__squares__le__zero__iff, % 228.76/33.11 fact_termination__basic__simps_I1_J, fact_termination__basic__simps_I2_J, % 228.76/33.11 fact_termination__basic__simps_I3_J, fact_termination__basic__simps_I4_J, % 228.76/33.11 fact_termination__basic__simps_I5_J, fact_times__numeral__code_I5_J, % 228.76/33.11 fact_trans__le__add1, fact_trans__le__add2, fact_trans__less__add1, % 228.76/33.11 fact_trans__less__add2, fact_transfer__int__nat__numerals_I1_J, % 228.76/33.11 fact_transfer__int__nat__numerals_I2_J, % 228.76/33.11 fact_transfer__int__nat__quantifiers_I1_J, % 228.76/33.11 fact_transfer__int__nat__quantifiers_I2_J, fact_tsub__def, fact_tsub__eq, % 228.76/33.11 fact_unimodular__reduce__norm, fact_unique__quotient__lemma, % 228.76/33.11 fact_unique__quotient__lemma__neg, fact_wr, fact_xt1_I10_J, fact_xt1_I11_J, % 228.76/33.11 fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J, % 228.76/33.11 fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J, % 228.76/33.11 fact_zabs__less__one__iff, fact_zadd__0, fact_zadd__0__right, fact_zadd__assoc, % 228.76/33.11 fact_zadd__commute, fact_zadd__int, fact_zadd__int__left, % 228.76/33.11 fact_zadd__left__commute, fact_zadd__left__mono, fact_zadd__strict__right__mono, % 228.76/33.11 fact_zadd__zless__mono, fact_zadd__zmult__distrib, fact_zadd__zmult__distrib2, % 228.76/33.11 fact_zdiff__int, fact_zdiff__int__split, fact_zdiff__zmult__distrib, % 228.76/33.11 fact_zdiff__zmult__distrib2, fact_zdiv__eq__0__iff, fact_zdiv__int, % 228.76/33.11 fact_zdiv__mono1, fact_zdiv__mono1__neg, fact_zdiv__mono2, % 228.76/33.11 fact_zdiv__mono2__lemma, fact_zdiv__mono2__neg, fact_zdiv__mono2__neg__lemma, % 228.76/33.11 fact_zdiv__self, fact_zdiv__zero, fact_zdiv__zmult2__eq, % 228.76/33.11 fact_zero__is__num__zero, % 228.76/33.11 fact_zero__le__double__add__iff__zero__le__single__add, % 228.76/33.11 fact_zero__le__imp__of__nat, fact_zero__le__mult__iff, % 228.76/33.11 fact_zero__le__natceiling, fact_zero__le__natfloor, fact_zero__le__one, % 228.76/33.11 fact_zero__le__power, fact_zero__le__power__abs, fact_zero__le__square, % 228.76/33.11 fact_zero__le__zpower__abs, fact_zero__less__Suc, fact_zero__less__abs__iff, % 228.76/33.11 fact_zero__less__diff, % 228.76/33.11 fact_zero__less__double__add__iff__zero__less__single__add, % 228.76/33.11 fact_zero__less__imp__eq__int, fact_zero__less__int__conv, % 228.76/33.11 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, % 228.76/33.11 fact_zero__less__norm__iff, fact_zero__less__one, fact_zero__less__power, % 228.76/33.11 fact_zero__less__power__nat__eq, fact_zero__less__power__nat__eq__number__of, % 228.76/33.11 fact_zero__less__two, fact_zero__less__zpower__abs__iff, fact_zero__neq__one, % 228.76/33.11 fact_zero__reorient, fact_zero__zle__int, fact_zle__add1__eq__le, % 228.76/33.11 fact_zle__antisym, fact_zle__diff1__eq, fact_zle__iff__zadd, fact_zle__int, % 228.76/33.11 fact_zle__linear, fact_zle__refl, fact_zle__trans, fact_zless__add1__eq, % 228.76/33.11 fact_zless__iff__Suc__zadd, fact_zless__imp__add1__zle, fact_zless__int, % 228.76/33.11 fact_zless__le, fact_zless__linear, fact_zmult__1, fact_zmult__1__right, % 228.76/33.11 fact_zmult__assoc, fact_zmult__commute, fact_zmult__int, % 228.76/33.11 fact_zmult__zless__mono2, fact_zmult__zless__mono2__lemma, fact_zpower__int, % 228.76/33.11 fact_zpower__zadd__distrib, fact_zpower__zpower % 228.76/33.11 % 228.76/33.11 Those formulas are unsatisfiable: % 228.76/33.11 --------------------------------- % 228.76/33.11 % 228.76/33.11 Begin of proof % 228.76/33.11 | % 228.76/33.11 | ALPHA: (fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) implies: % 228.76/33.12 | (1) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 228.76/33.12 | v_N1____, v_N2____) = v0 & hAPP(v_f____, v0) = v1 & $i(v1) & $i(v0) % 228.76/33.12 | & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v1)) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_Suc__le__mono) implies: % 228.76/33.12 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 228.76/33.12 | (c_Nat_OSuc(v1) = v2) | ~ (c_Nat_OSuc(v0) = v3) | ~ $i(v1) | ~ % 228.76/33.12 | $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 228.76/33.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v3)) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_nat__add__commute) implies: % 228.76/33.12 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 228.76/33.12 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1) | % 228.76/33.12 | ~ $i(v0) | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v2 & % 228.76/33.12 | $i(v2))) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_real__of__nat__le__iff) implies: % 228.76/33.12 | (4) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] % 228.76/33.12 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0, v2) = v3) | % 228.76/33.12 | ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.12 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) | % 228.76/33.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1)) & ! [v1: % 228.76/33.12 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0, v2) = % 228.76/33.12 | v3) | ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | % 228.76/33.12 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4))) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_real__of__nat__add) implies: % 228.76/33.12 | (5) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] % 228.76/33.12 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.76/33.12 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 228.76/33.12 | (hAPP(v0, v2) = v3) | ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ % 228.76/33.12 | $i(v1) | ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, % 228.76/33.12 | v2, v1) = v6 & hAPP(v0, v6) = v5 & $i(v6) & $i(v5)))) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_real__of__nat__inject) implies: % 228.76/33.12 | (6) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] % 228.76/33.12 | : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (hAPP(v0, v2) = v3) | ~ % 228.76/33.12 | (hAPP(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1))) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_real__of__nat__Suc) implies: % 228.76/33.12 | (7) ? [v0: $i] : ? [v1: $i] : % 228.76/33.12 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.76/33.12 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.12 | ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? % 228.76/33.12 | [v5: $i] : (c_Nat_OSuc(v2) = v4 & % 228.76/33.12 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v5 & % 228.76/33.12 | hAPP(v0, v4) = v5 & $i(v5) & $i(v4)))) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_nat__le__real__less) implies: % 228.76/33.12 | (8) ? [v0: $i] : ? [v1: $i] : % 228.76/33.12 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.76/33.12 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.12 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v0, v3) = v4) | ~ % 228.76/33.12 | (hAPP(v0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 228.76/33.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | ? [v6: % 228.76/33.12 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v1) = v6 % 228.76/33.12 | & $i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, % 228.76/33.12 | v6))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 228.76/33.12 | ( ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v5) | ~ $i(v3) | ~ % 228.76/33.12 | $i(v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2) | % 228.76/33.12 | ? [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v1) % 228.76/33.12 | = v6 & $i(v6) & ~ % 228.76/33.12 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6)))) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_nat__less__real__le) implies: % 228.76/33.12 | (9) ? [v0: $i] : ? [v1: $i] : % 228.76/33.12 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.76/33.12 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.12 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v0, v3) = v4) | ~ % 228.76/33.12 | (hAPP(v0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 228.76/33.12 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ? [v6: $i] : % 228.76/33.12 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v1) = v6 & % 228.76/33.12 | $i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, % 228.76/33.12 | v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 228.76/33.12 | ( ~ (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v5) | ~ $i(v3) | ~ % 228.76/33.12 | $i(v2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v2) | ? % 228.76/33.12 | [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v1) = % 228.76/33.12 | v6 & $i(v6) & ~ % 228.76/33.12 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v5)))) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_real__of__nat__one) implies: % 228.76/33.12 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 228.76/33.12 | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 228.76/33.12 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v3 & % 228.76/33.12 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & c_Nat_OSuc(v1) = v2 & hAPP(v0, % 228.76/33.12 | v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 228.76/33.12 | % 228.76/33.12 | ALPHA: (fact_real__of__nat__less__iff) implies: % 228.76/33.13 | (11) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.13 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0, v2) % 228.76/33.13 | = v3) | ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1)) & ! [v1: $i] % 228.76/33.13 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v0, v2) = v3) % 228.76/33.13 | | ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__of__nat__1) implies: % 228.76/33.13 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 228.76/33.13 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & % 228.76/33.13 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 & $i(v2) & % 228.76/33.13 | $i(v1) & $i(v0)) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__of__nat__ge__zero) implies: % 228.76/33.13 | (13) ? [v0: $i] : ? [v1: $i] : % 228.76/33.13 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.13 | ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~ $i(v2) | % 228.76/33.13 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__of__nat__zero) implies: % 228.76/33.13 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 228.76/33.13 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v2 & % 228.76/33.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & hAPP(v0, v1) = v2 & $i(v2) & % 228.76/33.13 | $i(v1) & $i(v0)) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__of__nat__zero__iff) implies: % 228.76/33.13 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 228.76/33.13 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & % 228.76/33.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! % 228.76/33.13 | [v3: $i] : (v3 = v2 | ~ (hAPP(v0, v3) = v1) | ~ $i(v3)) & ! [v3: % 228.76/33.13 | $i] : (v3 = v1 | ~ (hAPP(v0, v2) = v3))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_not__real__of__nat__less__zero) implies: % 228.76/33.13 | (16) ? [v0: $i] : ? [v1: $i] : % 228.76/33.13 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.13 | ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ~ % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__of__nat__diff) implies: % 228.76/33.13 | (17) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.13 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.76/33.13 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v3, v4) = v5) | % 228.76/33.13 | ~ (hAPP(v0, v2) = v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2) | ~ % 228.76/33.13 | $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) % 228.76/33.13 | | ? [v6: $i] : (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, % 228.76/33.13 | v2) = v6 & hAPP(v0, v6) = v5 & $i(v6) & $i(v5)))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__of__nat__le__zero__cancel__iff) implies: % 228.76/33.13 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 228.76/33.13 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & % 228.76/33.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! % 228.76/33.13 | [v3: $i] : ! [v4: $i] : (v3 = v2 | ~ (hAPP(v0, v3) = v4) | ~ % 228.76/33.13 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 228.76/33.13 | v4, v1)) & ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | % 228.76/33.13 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__of__nat__Suc__gt__zero) implies: % 228.76/33.13 | (19) ? [v0: $i] : ? [v1: $i] : % 228.76/33.13 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.13 | ! [v3: $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ? [v4: $i] : % 228.76/33.13 | (hAPP(v1, v3) = v4 & $i(v4) & % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__of__nat__gt__zero__cancel__iff) implies: % 228.76/33.13 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 228.76/33.13 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.13 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & ! % 228.76/33.13 | [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3)) & ! [v3: $i] % 228.76/33.13 | : ! [v4: $i] : ( ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v3) | % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_natceiling__eq) implies: % 228.76/33.13 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 228.76/33.13 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.76/33.13 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 228.76/33.13 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! % 228.76/33.13 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ % 228.76/33.13 | (c_RComplete_Onatceiling(v3) = v5) | ~ % 228.76/33.13 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v2) = v6) | ~ % 228.76/33.13 | $i(v4) | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : (hAPP(v0, v4) = % 228.76/33.13 | v7 & $i(v7) & ( ~ % 228.76/33.13 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v3) | % 228.76/33.13 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, v1) = v8 & % 228.76/33.13 | $i(v8) & ~ % 228.76/33.13 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, % 228.76/33.13 | v8)))))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_natceiling__real__of__nat) implies: % 228.76/33.13 | (22) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.13 | $i] : ! [v2: $i] : ( ~ (hAPP(v0, v1) = v2) | ~ $i(v1) | % 228.76/33.13 | c_RComplete_Onatceiling(v2) = v1)) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_abs__real__of__nat__cancel) implies: % 228.76/33.13 | (23) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.13 | $i] : ! [v2: $i] : ( ~ (hAPP(v0, v1) = v2) | ~ $i(v1) | % 228.76/33.13 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v2 & $i(v2)))) % 228.76/33.13 | % 228.76/33.13 | ALPHA: (fact_real__natceiling__ge) implies: % 228.76/33.13 | (24) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.13 | $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatceiling(v1) = v2) | ~ % 228.76/33.13 | $i(v1) | ? [v3: $i] : (hAPP(v0, v2) = v3 & $i(v3) & % 228.76/33.13 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_natceiling__le) implies: % 228.76/33.14 | (25) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.14 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 228.76/33.14 | (c_RComplete_Onatceiling(v2) = v4) | ~ (hAPP(v0, v1) = v3) | ~ % 228.76/33.14 | $i(v2) | ~ $i(v1) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3) | % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v1))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_natceiling__le__eq) implies: % 228.76/33.14 | (26) ? [v0: $i] : ? [v1: $i] : % 228.76/33.14 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.14 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.14 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.76/33.14 | (c_RComplete_Onatceiling(v3) = v4) | ~ (hAPP(v1, v2) = v5) | ~ % 228.76/33.14 | $i(v3) | ~ $i(v2) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2)) & ! [v2: % 228.76/33.14 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.76/33.14 | (c_RComplete_Onatceiling(v3) = v4) | ~ (hAPP(v1, v2) = v5) | ~ % 228.76/33.14 | $i(v3) | ~ $i(v2) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v4, v2) | % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_natceiling__subtract) implies: % 228.76/33.14 | (27) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.14 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 228.76/33.14 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v3) = v4) | % 228.76/33.14 | ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? % 228.76/33.14 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 & % 228.76/33.14 | c_RComplete_Onatceiling(v1) = v6 & % 228.76/33.14 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) % 228.76/33.14 | & $i(v5)))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_natceiling__add) implies: % 228.76/33.14 | (28) ? [v0: $i] : ? [v1: $i] : % 228.76/33.14 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.14 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.14 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.76/33.14 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 228.76/33.14 | (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? % 228.76/33.14 | [v6: $i] : ? [v7: $i] : (c_RComplete_Onatceiling(v5) = v6 & % 228.76/33.14 | c_RComplete_Onatceiling(v3) = v7 & % 228.76/33.14 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, v2) = v6 & $i(v7) & % 228.76/33.14 | $i(v6)))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_reals__Archimedean6) implies: % 228.76/33.14 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 228.76/33.14 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.14 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & % 228.76/33.14 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & ! % 228.76/33.14 | [v3: $i] : ( ~ $i(v3) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? % 228.76/33.14 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 228.76/33.14 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5 & % 228.76/33.14 | hAPP(v1, v5) = v6 & hAPP(v1, v4) = v7 & $i(v7) & $i(v6) & $i(v5) % 228.76/33.14 | & $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, % 228.76/33.14 | v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, % 228.76/33.14 | v3)))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_reals__Archimedean6a) implies: % 228.76/33.14 | (30) ? [v0: $i] : ? [v1: $i] : % 228.76/33.14 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.14 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.14 | ( ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 228.76/33.14 | v0, v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 228.76/33.14 | : (c_Nat_OSuc(v3) = v5 & hAPP(v1, v5) = v6 & hAPP(v1, v3) = v4 & % 228.76/33.14 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 228.76/33.14 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6) & % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_natfloor__real__of__nat) implies: % 228.76/33.14 | (31) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.14 | $i] : ! [v2: $i] : ( ~ (hAPP(v0, v1) = v2) | ~ $i(v1) | % 228.76/33.14 | c_RComplete_Onatfloor(v2) = v1)) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_real__natfloor__le) implies: % 228.76/33.14 | (32) ? [v0: $i] : ? [v1: $i] : % 228.76/33.14 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.14 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.14 | ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? % 228.76/33.14 | [v4: $i] : (hAPP(v1, v3) = v4 & $i(v4) & % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_le__natfloor) implies: % 228.76/33.14 | (33) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.14 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 228.76/33.14 | (c_RComplete_Onatfloor(v1) = v4) | ~ (hAPP(v0, v2) = v3) | ~ % 228.76/33.14 | $i(v2) | ~ $i(v1) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v4))) % 228.76/33.14 | % 228.76/33.14 | ALPHA: (fact_lemma__NBseq__def) implies: % 228.76/33.14 | (34) ? [v0: $i] : ? [v1: $i] : % 228.76/33.14 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.14 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : % 228.76/33.14 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Nat_OSuc(v4) = v5) | % 228.76/33.14 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.76/33.14 | class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ? [v7: % 228.76/33.14 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v8) & % 228.76/33.14 | $i(v6) & ((c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & % 228.76/33.14 | hAPP(v2, v8) = v9 & hAPP(v1, v5) = v7 & $i(v10) & $i(v9) & % 228.76/33.14 | $i(v7) & ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 228.76/33.14 | v7)) | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 228.76/33.14 | v0, v6) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 228.76/33.14 | (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ % 228.76/33.14 | (hAPP(v2, v11) = v12) | ~ $i(v11) | % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, % 228.76/33.14 | v6)))))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 228.76/33.14 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.76/33.14 | class_RealVector_Oreal__normed__vector(v3) | ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v5: % 228.76/33.14 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 228.76/33.14 | [v10: $i] : ($i(v8) & $i(v5) & % 228.76/33.14 | ((c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & hAPP(v2, v8) = % 228.76/33.14 | v9 & $i(v10) & $i(v9) & ~ % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 228.76/33.14 | v4)) | (c_Nat_OSuc(v5) = v6 & hAPP(v1, v6) = v7 & $i(v7) & % 228.76/33.14 | $i(v6) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 228.76/33.14 | (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ % 228.76/33.14 | (hAPP(v2, v11) = v12) | ~ $i(v11) | % 228.76/33.14 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, % 228.76/33.14 | v7))))))) % 228.76/33.15 | % 228.76/33.15 | ALPHA: (fact_lemma__NBseq__def2) implies: % 228.76/33.15 | (35) ? [v0: $i] : ? [v1: $i] : % 228.76/33.15 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.15 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : % 228.76/33.15 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_Nat_OSuc(v4) = v5) | % 228.76/33.15 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.76/33.15 | class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ? [v7: % 228.76/33.15 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v8) & % 228.76/33.15 | $i(v6) & ((c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & % 228.76/33.15 | hAPP(v2, v8) = v9 & hAPP(v1, v5) = v7 & $i(v10) & $i(v9) & % 228.76/33.15 | $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 228.76/33.15 | v10, v7)) | % 228.76/33.15 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6) & ! % 228.76/33.15 | [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 228.76/33.15 | (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ % 228.76/33.15 | (hAPP(v2, v11) = v12) | ~ $i(v11) | % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, % 228.76/33.15 | v6)))))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 228.76/33.15 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 228.76/33.15 | class_RealVector_Oreal__normed__vector(v3) | ~ % 228.76/33.15 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v5: % 228.76/33.15 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 228.76/33.15 | [v10: $i] : ($i(v8) & $i(v5) & % 228.76/33.15 | ((c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & hAPP(v2, v8) = % 228.76/33.15 | v9 & $i(v10) & $i(v9) & ~ % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, % 228.76/33.15 | v4)) | (c_Nat_OSuc(v5) = v6 & hAPP(v1, v6) = v7 & $i(v7) & % 228.76/33.15 | $i(v6) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ % 228.76/33.15 | (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~ % 228.76/33.15 | (hAPP(v2, v11) = v12) | ~ $i(v11) | % 228.76/33.15 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, % 228.76/33.15 | v7))))))) % 228.76/33.15 | % 228.76/33.15 | ALPHA: (fact_le__natfloor__eq) implies: % 228.76/33.15 | (36) ? [v0: $i] : ? [v1: $i] : % 228.76/33.15 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 228.76/33.15 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.15 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.76/33.15 | (c_RComplete_Onatfloor(v3) = v4) | ~ (hAPP(v1, v2) = v5) | ~ % 228.76/33.15 | $i(v3) | ~ $i(v2) | ~ % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v3) | ~ % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v4)) & ! [v2: % 228.76/33.15 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 228.76/33.15 | (c_RComplete_Onatfloor(v3) = v4) | ~ (hAPP(v1, v2) = v5) | ~ % 228.76/33.15 | $i(v3) | ~ $i(v2) | ~ % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~ % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v4) | % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v3))) % 228.76/33.15 | % 228.76/33.15 | ALPHA: (fact_real__natfloor__add__one__gt) implies: % 228.76/33.15 | (37) ? [v0: $i] : ? [v1: $i] : % 228.76/33.15 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 228.76/33.15 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.15 | ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ? % 228.76/33.15 | [v4: $i] : ? [v5: $i] : % 228.76/33.15 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v1) = v5 & % 228.76/33.15 | hAPP(v0, v3) = v4 & $i(v5) & $i(v4) & % 228.76/33.15 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v5)))) % 228.76/33.15 | % 228.76/33.15 | ALPHA: (fact_natfloor__subtract) implies: % 228.76/33.15 | (38) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 228.76/33.15 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 228.76/33.15 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v3) = v4) | % 228.76/33.15 | ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 228.76/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? % 228.76/33.15 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 & % 228.76/33.15 | c_RComplete_Onatfloor(v1) = v6 & % 228.76/33.15 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) % 228.76/33.15 | & $i(v5)))) % 228.76/33.15 | % 228.76/33.15 | ALPHA: (fact_real__natfloor__gt__diff__one) implies: % 228.76/33.15 | (39) ? [v0: $i] : ? [v1: $i] : % 228.76/33.15 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 228.76/33.15 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 228.76/33.15 | ! [v3: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, % 228.76/33.15 | v2, v0) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : % 229.54/33.15 | (c_RComplete_Onatfloor(v2) = v4 & hAPP(v1, v4) = v5 & $i(v5) & % 229.54/33.15 | $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, % 229.54/33.15 | v5)))) % 229.54/33.15 | % 229.54/33.15 | ALPHA: (fact_less__natfloor) implies: % 229.54/33.15 | (40) ? [v0: $i] : ? [v1: $i] : % 229.54/33.15 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 229.54/33.15 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 229.54/33.15 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 229.54/33.15 | (c_RComplete_Onatfloor(v3) = v5) | ~ (hAPP(v1, v2) = v4) | ~ % 229.54/33.15 | $i(v3) | ~ $i(v2) | ~ % 229.54/33.15 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~ % 229.54/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | % 229.54/33.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v5, v2))) % 229.54/33.15 | % 229.54/33.15 | ALPHA: (fact_natfloor__add) implies: % 229.54/33.15 | (41) ? [v0: $i] : ? [v1: $i] : % 229.54/33.15 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 229.54/33.15 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : % 229.54/33.15 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 229.54/33.15 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v4) = v5) | ~ % 229.54/33.15 | (hAPP(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 229.54/33.15 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? % 229.54/33.15 | [v6: $i] : ? [v7: $i] : (c_RComplete_Onatfloor(v5) = v6 & % 229.54/33.15 | c_RComplete_Onatfloor(v3) = v7 & % 229.54/33.15 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v7, v2) = v6 & $i(v7) & % 229.54/33.15 | $i(v6)))) % 229.54/33.15 | % 229.54/33.15 | ALPHA: (fact_ge__natfloor__plus__one__imp__gt) implies: % 229.54/33.15 | (42) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = % 229.54/33.15 | v0 & c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: % 229.54/33.15 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 229.54/33.15 | (c_RComplete_Onatfloor(v3) = v4) | ~ (hAPP(v1, v2) = v5) | ~ % 229.54/33.15 | $i(v3) | ~ $i(v2) | % 229.54/33.15 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5) | ? [v6: % 229.54/33.15 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, v0) = v6 & % 229.54/33.15 | $i(v6) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v6, % 229.54/33.15 | v2)))) % 229.54/33.15 | % 229.54/33.15 | ALPHA: (fact_natfloor__eq) implies: % 229.54/33.16 | (43) ? [v0: $i] : ? [v1: $i] : % 229.54/33.16 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & % 229.54/33.16 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : % 229.54/33.16 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 229.54/33.16 | (c_RComplete_Onatfloor(v2) = v5) | ~ (hAPP(v0, v3) = v4) | ~ % 229.54/33.16 | $i(v3) | ~ $i(v2) | ~ % 229.54/33.16 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ? % 229.54/33.16 | [v6: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v1) % 229.54/33.16 | = v6 & $i(v6) & ~ % 229.54/33.16 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6)))) % 229.54/33.16 | % 229.54/33.16 | ALPHA: (fact_real__of__nat__number__of) implies: % 229.54/33.16 | (44) ? [v0: $i] : ? [v1: $i] : % 229.54/33.16 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & % 229.54/33.16 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : % 229.54/33.16 | ! [v3: $i] : ( ~ (c_Int_Onumber__class_Onumber__of(tc_Int_Oint, v2) % 229.54/33.16 | = v3) | ~ $i(v2) | ~ c_Nat__Numeral_Oneg(v3) | ? [v4: $i] : % 229.54/33.16 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v4 & hAPP(v0, % 229.54/33.16 | v4) = v1 & $i(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 229.54/33.16 | (c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, v2) = v3) | ~ % 229.54/33.16 | $i(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v3 & % 229.54/33.16 | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v2) = v5 & % 229.54/33.16 | hAPP(v0, v5) = v3 & $i(v5) & $i(v3)) | % 229.54/33.16 | (c_Int_Onumber__class_Onumber__of(tc_Int_Oint, v2) = v4 & $i(v4) % 229.54/33.16 | & c_Nat__Numeral_Oneg(v4))))) % 229.54/33.16 | % 229.54/33.16 | ALPHA: (fact_Bseq__iff1a) implies: % 229.54/33.16 | (45) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ? [v1: % 229.54/33.16 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.54/33.16 | (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.54/33.16 | class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1) | % 229.54/33.16 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 229.54/33.16 | (c_RealVector_Onorm__class_Onorm(v2, v7) = v8 & hAPP(v1, v6) = v7 % 229.54/33.16 | & hAPP(v0, v4) = v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ~ % 229.54/33.16 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v5))) & ! % 229.54/33.16 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, % 229.54/33.16 | v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v3: % 229.54/33.16 | $i] : ? [v4: $i] : ? [v5: $i] : (c_Nat_OSuc(v3) = v4 & % 229.54/33.16 | hAPP(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & ! [v6: $i] : ! % 229.54/33.16 | [v7: $i] : ! [v8: $i] : ( ~ % 229.54/33.16 | (c_RealVector_Onorm__class_Onorm(v2, v7) = v8) | ~ (hAPP(v1, % 229.54/33.16 | v6) = v7) | ~ $i(v6) | % 229.54/33.16 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v5))))) % 229.54/33.16 | % 229.54/33.16 | ALPHA: (fact_Bseq__iff) implies: % 229.54/33.16 | (46) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ? [v1: % 229.54/33.16 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.54/33.16 | (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 229.54/33.16 | class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1) | % 229.54/33.16 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 229.54/33.16 | (c_RealVector_Onorm__class_Onorm(v2, v7) = v8 & hAPP(v1, v6) = v7 % 229.54/33.16 | & hAPP(v0, v4) = v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ~ % 229.54/33.16 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v5))) & % 229.54/33.16 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 229.54/33.16 | c_SEQ_OBseq(v2, v1) | ~ % 229.54/33.16 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? [v4: % 229.54/33.16 | $i] : ? [v5: $i] : (c_Nat_OSuc(v3) = v4 & hAPP(v0, v4) = v5 & % 229.54/33.16 | $i(v5) & $i(v4) & $i(v3) & ! [v6: $i] : ! [v7: $i] : ! [v8: % 229.54/33.16 | $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v7) = v8) | ~ % 229.54/33.16 | (hAPP(v1, v6) = v7) | ~ $i(v6) | % 229.54/33.16 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, % 229.54/33.16 | v5))))) % 229.54/33.16 | % 229.54/33.16 | ALPHA: (fact_real__of__nat__def) implies: % 229.54/33.16 | (47) ? [v0: $i] : (c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) = % 229.54/33.16 | v0 & c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0)) % 229.54/33.16 | % 229.54/33.16 | ALPHA: (fact_of__nat__le__iff) implies: % 229.54/33.16 | (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 229.54/33.16 | ! [v5: $i] : ( ~ (c_Nat_Osemiring__1__class_Oof__nat(v2) = v3) | ~ % 229.54/33.16 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) % 229.54/33.16 | | ~ $i(v0) | ~ class_Rings_Olinordered__semidom(v2) | ~ % 229.54/33.16 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 229.54/33.16 | c_Orderings_Oord__class_Oless__eq(v2, v4, v5)) % 229.54/33.16 | % 229.54/33.16 | ALPHA: (fact_real__of__nat__mult) implies: % 229.54/33.16 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.54/33.16 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & % 229.54/33.16 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 & % 229.54/33.16 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! % 229.54/33.16 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 229.54/33.16 | ! [v8: $i] : ( ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v2, v5) = v6) | ~ % 229.54/33.16 | (hAPP(v0, v4) = v5) | ~ (hAPP(v0, v3) = v7) | ~ $i(v4) | ~ % 229.54/33.16 | $i(v3) | ? [v9: $i] : ? [v10: $i] : (hAPP(v9, v3) = v10 & % 229.54/33.16 | hAPP(v1, v4) = v9 & hAPP(v0, v10) = v8 & $i(v10) & $i(v9) & % 229.54/33.16 | $i(v8)))) % 229.54/33.16 | % 229.54/33.16 | ALPHA: (fact_LIMSEQ__inverse__realpow__zero__lemma) implies: % 229.54/33.16 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 229.54/33.16 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v4 & % 229.54/33.16 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.54/33.16 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 229.54/33.16 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v3 & % 229.54/33.16 | c_RealDef_Oreal(tc_Nat_Onat) = v2 & $i(v4) & $i(v3) & $i(v2) & % 229.54/33.16 | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 229.54/33.16 | $i] : ! [v9: $i] : ( ~ % 229.54/33.16 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v3) = v7) | ~ % 229.54/33.16 | (hAPP(v8, v5) = v9) | ~ (hAPP(v4, v7) = v8) | ~ $i(v6) | ~ % 229.54/33.16 | $i(v5) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 229.54/33.16 | v0, v6) | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 229.54/33.16 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v12, v3) = % 229.54/33.16 | v13 & hAPP(v11, v6) = v12 & hAPP(v2, v5) = v10 & hAPP(v1, v10) = % 229.54/33.16 | v11 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 229.54/33.16 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13, v9)))) % 229.54/33.16 | % 229.54/33.16 | ALPHA: (fact_cis__real__of__nat__Suc__mult) implies: % 229.54/33.17 | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.54/33.17 | (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v2 & % 229.54/33.17 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & % 229.54/33.17 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & ! % 229.54/33.17 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 229.54/33.17 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 229.54/33.17 | (c_Complex_Ocis(v9) = v10) | ~ (c_Complex_Ocis(v3) = v5) | ~ % 229.54/33.17 | (hAPP(v8, v3) = v9) | ~ (hAPP(v6, v10) = v11) | ~ (hAPP(v2, v5) % 229.54/33.17 | = v6) | ~ (hAPP(v1, v4) = v7) | ~ (hAPP(v0, v7) = v8) | ~ % 229.54/33.17 | $i(v4) | ~ $i(v3) | ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 229.54/33.17 | ? [v15: $i] : (c_Complex_Ocis(v15) = v11 & c_Nat_OSuc(v4) = v12 & % 229.54/33.17 | hAPP(v14, v3) = v15 & hAPP(v1, v12) = v13 & hAPP(v0, v13) = v14 % 229.54/33.17 | & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11)))) % 229.54/33.17 | % 229.54/33.17 | ALPHA: (fact_power__real__of__nat) implies: % 229.54/33.17 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.54/33.17 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v0 & % 229.54/33.17 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & % 229.54/33.17 | c_RealDef_Oreal(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & ! % 229.54/33.17 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 229.54/33.17 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v4) = v5) | ~ (hAPP(v0, v5) % 229.54/33.17 | = v6) | ~ $i(v4) | ~ $i(v3) | ? [v8: $i] : ? [v9: $i] : % 229.54/33.17 | (hAPP(v8, v3) = v9 & hAPP(v2, v4) = v8 & hAPP(v1, v9) = v7 & % 229.54/33.17 | $i(v9) & $i(v8) & $i(v7)))) % 229.54/33.17 | % 229.54/33.17 | ALPHA: (fact_real__of__nat__power) implies: % 229.54/33.17 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.54/33.17 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 & % 229.54/33.17 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 & % 229.54/33.17 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! % 229.54/33.17 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 229.54/33.17 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v2, v5) = v6) | ~ (hAPP(v0, v4) % 229.54/33.17 | = v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: $i] : ? [v9: $i] : % 229.54/33.17 | (hAPP(v8, v3) = v9 & hAPP(v1, v4) = v8 & hAPP(v0, v9) = v7 & % 229.54/33.17 | $i(v9) & $i(v8) & $i(v7)))) % 229.54/33.17 | % 229.54/33.17 | ALPHA: (fact_natfloor__power) implies: % 229.54/33.17 | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.54/33.17 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 & % 229.54/33.17 | c_Power_Opower__class_Opower(tc_Nat_Onat) = v2 & % 229.54/33.17 | c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v2) & $i(v1) & $i(v0) & ! % 229.54/33.17 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 229.54/33.17 | ~ (c_RComplete_Onatfloor(v4) = v5) | ~ (hAPP(v6, v3) = v7) | ~ % 229.54/33.17 | (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ? [v8: $i] : ? % 229.54/33.17 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : ((v11 = v7 & % 229.54/33.17 | c_RComplete_Onatfloor(v10) = v7 & hAPP(v9, v3) = v10 & % 229.54/33.17 | hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & $i(v7)) | ( ~ (v8 = v4) % 229.54/33.17 | & hAPP(v0, v5) = v8 & $i(v8))))) % 229.54/33.17 | % 229.54/33.17 | ALPHA: (fact_DeMoivre) implies: % 229.54/33.17 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.54/33.17 | (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v0 & % 229.54/33.17 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.54/33.17 | c_RealDef_Oreal(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 229.54/33.17 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 229.54/33.17 | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v2, v3) = v5) | ~ (hAPP(v1, v5) % 229.54/33.17 | = v6) | ~ $i(v4) | ~ $i(v3) | ? [v8: $i] : ? [v9: $i] : ? % 229.54/33.17 | [v10: $i] : (c_Complex_Ocis(v7) = v10 & c_Complex_Ocis(v4) = v8 & % 229.54/33.17 | hAPP(v9, v3) = v10 & hAPP(v0, v8) = v9 & $i(v10) & $i(v9) & % 229.54/33.17 | $i(v8)))) % 229.54/33.17 | % 229.54/33.17 | ALPHA: (fact_reals__Archimedean4) implies: % 229.54/33.17 | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.54/33.17 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & % 229.54/33.17 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & % 229.54/33.17 | c_RealDef_Oreal(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 229.54/33.17 | [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ % 229.54/33.17 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~ % 229.54/33.17 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? % 229.54/33.17 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 229.54/33.17 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : (c_Nat_OSuc(v5) = v9 % 229.54/33.17 | & hAPP(v11, v4) = v12 & hAPP(v7, v4) = v8 & hAPP(v2, v9) = v10 & % 229.54/33.17 | hAPP(v2, v5) = v6 & hAPP(v1, v10) = v11 & hAPP(v1, v6) = v7 & % 229.54/33.17 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) % 229.54/33.17 | & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, % 229.54/33.17 | v12) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, % 229.54/33.17 | v3)))) % 229.54/33.17 | % 229.54/33.17 | ALPHA: (fact_DeMoivre2) implies: % 229.54/33.17 | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 229.54/33.17 | (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v0 & % 229.54/33.17 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 & % 229.54/33.17 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & % 229.54/33.17 | c_RealDef_Oreal(tc_Nat_Onat) = v3 & $i(v3) & $i(v2) & $i(v1) & % 229.54/33.17 | $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 229.54/33.17 | [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] % 229.54/33.17 | : ( ~ (c_Complex_Orcis(v8, v11) = v12) | ~ (hAPP(v10, v5) = v11) | % 229.54/33.17 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v4) = v9) | ~ (hAPP(v2, v9) % 229.54/33.17 | = v10) | ~ (hAPP(v1, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ % 229.54/33.17 | $i(v4) | ? [v13: $i] : ? [v14: $i] : (c_Complex_Orcis(v6, v5) = % 229.54/33.17 | v13 & hAPP(v14, v4) = v12 & hAPP(v0, v13) = v14 & $i(v14) & % 229.54/33.17 | $i(v13) & $i(v12)))) % 229.54/33.17 | % 229.54/33.17 | ALPHA: (fact_natfloor__div__nat) implies: % 229.54/33.17 | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 229.54/33.17 | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 & % 229.54/33.17 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & % 229.54/33.17 | c_RealDef_Oreal(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 229.54/33.17 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 229.54/33.17 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v4, v5) = v6) | % 229.54/33.17 | ~ (hAPP(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 229.54/33.17 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v3) | ~ % 229.54/33.17 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ? % 229.54/33.17 | [v7: $i] : ? [v8: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, % 229.54/33.17 | v8, v3) = v7 & c_RComplete_Onatfloor(v6) = v7 & % 229.54/33.17 | c_RComplete_Onatfloor(v4) = v8 & $i(v8) & $i(v7)))) % 229.54/33.17 | % 229.54/33.17 | ALPHA: (fact_real__of__nat__div4) implies: % 229.54/33.18 | (59) ? [v0: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: % 229.54/33.18 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 229.54/33.18 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) | % 229.54/33.18 | ~ (hAPP(v0, v2) = v3) | ~ (hAPP(v0, v1) = v4) | ~ $i(v2) | ~ % 229.54/33.18 | $i(v1) | ? [v6: $i] : ? [v7: $i] : % 229.54/33.18 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v6 & hAPP(v0, % 229.54/33.18 | v6) = v7 & $i(v7) & $i(v6) & % 229.54/33.18 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v5)))) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (arity_RealDef__Oreal__Rings_Olinordered__semidom) implies: % 229.54/33.18 | (60) class_Rings_Olinordered__semidom(tc_RealDef_Oreal) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (conj_0) implies: % 229.54/33.18 | (61) $i(v_N1____) % 229.54/33.18 | (62) $i(v_N2____) % 229.54/33.18 | (63) $i(tc_RealDef_Oreal) % 229.54/33.18 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 229.54/33.18 | ? [v5: $i] : ? [v6: $i] : (c_RealDef_Oreal(tc_Nat_Onat) = v0 & % 229.54/33.18 | c_Nat_OSuc(v4) = v5 & c_Nat_OSuc(v1) = v2 & % 229.54/33.18 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____) = v1 & % 229.54/33.18 | hAPP(v0, v5) = v6 & hAPP(v0, v2) = v3 & hAPP(v_f____, v1) = v4 & % 229.54/33.18 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 229.54/33.18 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v6)) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (function-axioms) implies: % 229.54/33.18 | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 229.54/33.18 | (c_RealDef_Oreal(v2) = v1) | ~ (c_RealDef_Oreal(v2) = v0)) % 229.54/33.18 | (66) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 229.54/33.18 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) % 229.54/33.18 | (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 229.54/33.18 | (v1 = v0 | ~ (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~ % 229.54/33.18 | (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) % 229.54/33.18 | % 229.54/33.18 | DELTA: instantiating (47) with fresh symbol all_618_0 gives: % 229.54/33.18 | (68) c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) = all_618_0 & % 229.54/33.18 | c_RealDef_Oreal(tc_Nat_Onat) = all_618_0 & $i(all_618_0) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (68) implies: % 229.54/33.18 | (69) c_RealDef_Oreal(tc_Nat_Onat) = all_618_0 % 229.54/33.18 | % 229.54/33.18 | DELTA: instantiating (47) with fresh symbol all_622_0 gives: % 229.54/33.18 | (70) c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) = all_622_0 & % 229.54/33.18 | c_RealDef_Oreal(tc_Nat_Onat) = all_622_0 & $i(all_622_0) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (70) implies: % 229.54/33.18 | (71) c_RealDef_Oreal(tc_Nat_Onat) = all_622_0 % 229.54/33.18 | (72) c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) = all_622_0 % 229.54/33.18 | % 229.54/33.18 | DELTA: instantiating (1) with fresh symbols all_678_0, all_678_1 gives: % 229.54/33.18 | (73) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____) = % 229.54/33.18 | all_678_1 & hAPP(v_f____, all_678_1) = all_678_0 & $i(all_678_0) & % 229.54/33.18 | $i(all_678_1) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 229.54/33.18 | all_678_1, all_678_0) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (73) implies: % 229.54/33.18 | (74) c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_678_1, all_678_0) % 229.54/33.18 | (75) hAPP(v_f____, all_678_1) = all_678_0 % 229.54/33.18 | (76) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____) = % 229.54/33.18 | all_678_1 % 229.54/33.18 | % 229.54/33.18 | DELTA: instantiating (22) with fresh symbol all_686_0 gives: % 229.54/33.18 | (77) c_RealDef_Oreal(tc_Nat_Onat) = all_686_0 & $i(all_686_0) & ! [v0: $i] % 229.54/33.18 | : ! [v1: $i] : ( ~ (hAPP(all_686_0, v0) = v1) | ~ $i(v0) | % 229.54/33.18 | c_RComplete_Onatceiling(v1) = v0) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (77) implies: % 229.54/33.18 | (78) c_RealDef_Oreal(tc_Nat_Onat) = all_686_0 % 229.54/33.18 | % 229.54/33.18 | DELTA: instantiating (31) with fresh symbol all_743_0 gives: % 229.54/33.18 | (79) c_RealDef_Oreal(tc_Nat_Onat) = all_743_0 & $i(all_743_0) & ! [v0: $i] % 229.54/33.18 | : ! [v1: $i] : ( ~ (hAPP(all_743_0, v0) = v1) | ~ $i(v0) | % 229.54/33.18 | c_RComplete_Onatfloor(v1) = v0) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (79) implies: % 229.54/33.18 | (80) c_RealDef_Oreal(tc_Nat_Onat) = all_743_0 % 229.54/33.18 | % 229.54/33.18 | DELTA: instantiating (23) with fresh symbol all_760_0 gives: % 229.54/33.18 | (81) c_RealDef_Oreal(tc_Nat_Onat) = all_760_0 & $i(all_760_0) & ! [v0: $i] % 229.54/33.18 | : ! [v1: $i] : ( ~ (hAPP(all_760_0, v0) = v1) | ~ $i(v0) | % 229.54/33.18 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v1 & $i(v1))) % 229.54/33.18 | % 229.54/33.18 | ALPHA: (81) implies: % 229.68/33.18 | (82) c_RealDef_Oreal(tc_Nat_Onat) = all_760_0 % 229.68/33.18 | % 229.68/33.18 | DELTA: instantiating (13) with fresh symbols all_815_0, all_815_1 gives: % 229.68/33.18 | (83) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_815_1 & % 229.68/33.18 | c_RealDef_Oreal(tc_Nat_Onat) = all_815_0 & $i(all_815_0) & % 229.68/33.18 | $i(all_815_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_815_0, v0) = % 229.68/33.18 | v1) | ~ $i(v0) | % 229.68/33.18 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_815_1, v1)) % 229.68/33.18 | % 229.68/33.18 | ALPHA: (83) implies: % 229.68/33.18 | (84) c_RealDef_Oreal(tc_Nat_Onat) = all_815_0 % 229.68/33.18 | % 229.68/33.18 | DELTA: instantiating (6) with fresh symbol all_863_0 gives: % 229.68/33.18 | (85) c_RealDef_Oreal(tc_Nat_Onat) = all_863_0 & $i(all_863_0) & ! [v0: $i] % 229.68/33.18 | : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (hAPP(all_863_0, v1) = v2) % 229.68/33.18 | | ~ (hAPP(all_863_0, v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 229.68/33.18 | % 229.68/33.18 | ALPHA: (85) implies: % 229.68/33.18 | (86) c_RealDef_Oreal(tc_Nat_Onat) = all_863_0 % 229.68/33.18 | % 229.68/33.18 | DELTA: instantiating (16) with fresh symbols all_869_0, all_869_1 gives: % 229.68/33.18 | (87) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_869_0 & % 229.68/33.18 | c_RealDef_Oreal(tc_Nat_Onat) = all_869_1 & $i(all_869_0) & % 229.68/33.18 | $i(all_869_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_869_1, v0) = % 229.68/33.18 | v1) | ~ $i(v0) | ~ % 229.68/33.18 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_869_0)) % 229.68/33.18 | % 229.68/33.18 | ALPHA: (87) implies: % 229.68/33.18 | (88) c_RealDef_Oreal(tc_Nat_Onat) = all_869_1 % 229.68/33.18 | % 229.68/33.18 | DELTA: instantiating (12) with fresh symbols all_872_0, all_872_1, all_872_2 % 229.68/33.18 | gives: % 229.68/33.18 | (89) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_872_0 & % 229.68/33.18 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_872_1 & % 229.68/33.18 | c_RealDef_Oreal(tc_Nat_Onat) = all_872_2 & hAPP(all_872_2, all_872_1) % 229.68/33.18 | = all_872_0 & $i(all_872_0) & $i(all_872_1) & $i(all_872_2) % 229.68/33.18 | % 229.68/33.18 | ALPHA: (89) implies: % 229.68/33.18 | (90) c_RealDef_Oreal(tc_Nat_Onat) = all_872_2 % 229.68/33.18 | % 229.68/33.18 | DELTA: instantiating (24) with fresh symbol all_874_0 gives: % 229.68/33.18 | (91) c_RealDef_Oreal(tc_Nat_Onat) = all_874_0 & $i(all_874_0) & ! [v0: $i] % 229.68/33.18 | : ! [v1: $i] : ( ~ (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | % 229.68/33.18 | ? [v2: $i] : (hAPP(all_874_0, v1) = v2 & $i(v2) & % 229.68/33.18 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2))) % 229.68/33.18 | % 229.68/33.18 | ALPHA: (91) implies: % 229.68/33.18 | (92) c_RealDef_Oreal(tc_Nat_Onat) = all_874_0 % 229.68/33.18 | % 229.68/33.18 | DELTA: instantiating (14) with fresh symbols all_883_0, all_883_1, all_883_2 % 229.68/33.18 | gives: % 229.68/33.18 | (93) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_883_0 & % 229.68/33.18 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_883_1 & % 229.68/33.18 | c_RealDef_Oreal(tc_Nat_Onat) = all_883_2 & hAPP(all_883_2, all_883_1) % 229.68/33.18 | = all_883_0 & $i(all_883_0) & $i(all_883_1) & $i(all_883_2) % 229.68/33.18 | % 229.68/33.18 | ALPHA: (93) implies: % 229.68/33.18 | (94) c_RealDef_Oreal(tc_Nat_Onat) = all_883_2 % 229.68/33.18 | % 229.68/33.18 | DELTA: instantiating (25) with fresh symbol all_953_0 gives: % 229.68/33.19 | (95) c_RealDef_Oreal(tc_Nat_Onat) = all_953_0 & $i(all_953_0) & ! [v0: $i] % 229.68/33.19 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.19 | (c_RComplete_Onatceiling(v1) = v3) | ~ (hAPP(all_953_0, v0) = v2) | % 229.68/33.19 | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) | % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0)) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (95) implies: % 229.68/33.19 | (96) c_RealDef_Oreal(tc_Nat_Onat) = all_953_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (33) with fresh symbol all_982_0 gives: % 229.68/33.19 | (97) c_RealDef_Oreal(tc_Nat_Onat) = all_982_0 & $i(all_982_0) & ! [v0: $i] % 229.68/33.19 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.19 | (c_RComplete_Onatfloor(v0) = v3) | ~ (hAPP(all_982_0, v1) = v2) | % 229.68/33.19 | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (97) implies: % 229.68/33.19 | (98) c_RealDef_Oreal(tc_Nat_Onat) = all_982_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (10) with fresh symbols all_991_0, all_991_1, all_991_2, % 229.68/33.19 | all_991_3 gives: % 229.68/33.19 | (99) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_991_2 & % 229.68/33.19 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_991_0 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_991_3 & c_Nat_OSuc(all_991_2) = % 229.68/33.19 | all_991_1 & hAPP(all_991_3, all_991_1) = all_991_0 & $i(all_991_0) & % 229.68/33.19 | $i(all_991_1) & $i(all_991_2) & $i(all_991_3) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (99) implies: % 229.68/33.19 | (100) c_RealDef_Oreal(tc_Nat_Onat) = all_991_3 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (19) with fresh symbols all_1007_0, all_1007_1 gives: % 229.68/33.19 | (101) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1007_1 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1007_0 & $i(all_1007_0) & % 229.68/33.19 | $i(all_1007_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_Nat_OSuc(v0) = % 229.68/33.19 | v1) | ~ $i(v0) | ? [v2: $i] : (hAPP(all_1007_0, v1) = v2 & % 229.68/33.19 | $i(v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 229.68/33.19 | all_1007_1, v2))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (101) implies: % 229.68/33.19 | (102) c_RealDef_Oreal(tc_Nat_Onat) = all_1007_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (32) with fresh symbols all_1059_0, all_1059_1 gives: % 229.68/33.19 | (103) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1059_1 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1059_0 & $i(all_1059_0) & % 229.68/33.19 | $i(all_1059_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 229.68/33.19 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1059_1, v0) % 229.68/33.19 | | ? [v2: $i] : (hAPP(all_1059_0, v1) = v2 & $i(v2) & % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (103) implies: % 229.68/33.19 | (104) c_RealDef_Oreal(tc_Nat_Onat) = all_1059_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (15) with fresh symbols all_1109_0, all_1109_1, % 229.68/33.19 | all_1109_2 gives: % 229.68/33.19 | (105) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1109_1 & % 229.68/33.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1109_0 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1109_2 & $i(all_1109_0) & % 229.68/33.19 | $i(all_1109_1) & $i(all_1109_2) & ! [v0: any] : (v0 = all_1109_0 | % 229.68/33.19 | ~ (hAPP(all_1109_2, v0) = all_1109_1) | ~ $i(v0)) & ! [v0: int] : % 229.68/33.19 | (v0 = all_1109_1 | ~ (hAPP(all_1109_2, all_1109_0) = v0)) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (105) implies: % 229.68/33.19 | (106) c_RealDef_Oreal(tc_Nat_Onat) = all_1109_2 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (7) with fresh symbols all_1142_0, all_1142_1 gives: % 229.68/33.19 | (107) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1142_0 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1142_1 & $i(all_1142_0) & % 229.68/33.19 | $i(all_1142_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1142_1, % 229.68/33.19 | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 229.68/33.19 | (c_Nat_OSuc(v0) = v2 & % 229.68/33.19 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1142_0) = % 229.68/33.19 | v3 & hAPP(all_1142_1, v2) = v3 & $i(v3) & $i(v2))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (107) implies: % 229.68/33.19 | (108) c_RealDef_Oreal(tc_Nat_Onat) = all_1142_1 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (5) with fresh symbol all_1163_0 gives: % 229.68/33.19 | (109) c_RealDef_Oreal(tc_Nat_Onat) = all_1163_0 & $i(all_1163_0) & ! [v0: % 229.68/33.19 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.68/33.19 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~ % 229.68/33.19 | (hAPP(all_1163_0, v1) = v2) | ~ (hAPP(all_1163_0, v0) = v3) | ~ % 229.68/33.19 | $i(v1) | ~ $i(v0) | ? [v5: $i] : % 229.68/33.19 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, v0) = v5 & % 229.68/33.19 | hAPP(all_1163_0, v5) = v4 & $i(v5) & $i(v4))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (109) implies: % 229.68/33.19 | (110) c_RealDef_Oreal(tc_Nat_Onat) = all_1163_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (37) with fresh symbols all_1169_0, all_1169_1 gives: % 229.68/33.19 | (111) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1169_0 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1169_1 & $i(all_1169_0) & % 229.68/33.19 | $i(all_1169_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 229.68/33.19 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 229.68/33.19 | [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 229.68/33.19 | all_1169_0) = v3 & hAPP(all_1169_1, v1) = v2 & $i(v3) & $i(v2) % 229.68/33.19 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (111) implies: % 229.68/33.19 | (112) c_RealDef_Oreal(tc_Nat_Onat) = all_1169_1 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (39) with fresh symbols all_1172_0, all_1172_1 gives: % 229.68/33.19 | (113) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1172_1 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1172_0 & $i(all_1172_0) & % 229.68/33.19 | $i(all_1172_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 229.68/33.19 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, all_1172_1) = % 229.68/33.19 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : % 229.68/33.19 | (c_RComplete_Onatfloor(v0) = v2 & hAPP(all_1172_0, v2) = v3 & % 229.68/33.19 | $i(v3) & $i(v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, % 229.68/33.19 | v1, v3))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (113) implies: % 229.68/33.19 | (114) c_RealDef_Oreal(tc_Nat_Onat) = all_1172_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (40) with fresh symbols all_1175_0, all_1175_1 gives: % 229.68/33.19 | (115) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1175_1 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1175_0 & $i(all_1175_0) & % 229.68/33.19 | $i(all_1175_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.19 | $i] : ( ~ (c_RComplete_Onatfloor(v1) = v3) | ~ (hAPP(all_1175_0, % 229.68/33.19 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1175_1, v1) % 229.68/33.19 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0)) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (115) implies: % 229.68/33.19 | (116) c_RealDef_Oreal(tc_Nat_Onat) = all_1175_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (17) with fresh symbol all_1181_0 gives: % 229.68/33.19 | (117) c_RealDef_Oreal(tc_Nat_Onat) = all_1181_0 & $i(all_1181_0) & ! [v0: % 229.68/33.19 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.68/33.19 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v3) = v4) | ~ % 229.68/33.19 | (hAPP(all_1181_0, v1) = v3) | ~ (hAPP(all_1181_0, v0) = v2) | ~ % 229.68/33.19 | $i(v1) | ~ $i(v0) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v5: % 229.68/33.19 | $i] : (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v0, v1) = v5 & % 229.68/33.19 | hAPP(all_1181_0, v5) = v4 & $i(v5) & $i(v4))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (117) implies: % 229.68/33.19 | (118) c_RealDef_Oreal(tc_Nat_Onat) = all_1181_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (59) with fresh symbol all_1235_0 gives: % 229.68/33.19 | (119) c_RealDef_Oreal(tc_Nat_Onat) = all_1235_0 & $i(all_1235_0) & ! [v0: % 229.68/33.19 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 229.68/33.19 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v3) = v4) | % 229.68/33.19 | ~ (hAPP(all_1235_0, v1) = v2) | ~ (hAPP(all_1235_0, v0) = v3) | ~ % 229.68/33.19 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 229.68/33.19 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v5 & % 229.68/33.19 | hAPP(all_1235_0, v5) = v6 & $i(v6) & $i(v5) & % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v4))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (119) implies: % 229.68/33.19 | (120) c_RealDef_Oreal(tc_Nat_Onat) = all_1235_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (18) with fresh symbols all_1238_0, all_1238_1, % 229.68/33.19 | all_1238_2 gives: % 229.68/33.19 | (121) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1238_1 & % 229.68/33.19 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1238_0 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1238_2 & $i(all_1238_0) & % 229.68/33.19 | $i(all_1238_1) & $i(all_1238_2) & ! [v0: any] : ! [v1: $i] : (v0 = % 229.68/33.19 | all_1238_0 | ~ (hAPP(all_1238_2, v0) = v1) | ~ $i(v0) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, % 229.68/33.19 | all_1238_1)) & ! [v0: $i] : ( ~ (hAPP(all_1238_2, all_1238_0) = % 229.68/33.19 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 229.68/33.19 | all_1238_1)) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (121) implies: % 229.68/33.19 | (122) c_RealDef_Oreal(tc_Nat_Onat) = all_1238_2 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (42) with fresh symbols all_1261_0, all_1261_1 gives: % 229.68/33.19 | (123) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1261_1 & % 229.68/33.19 | c_RealDef_Oreal(tc_Nat_Onat) = all_1261_0 & $i(all_1261_0) & % 229.68/33.19 | $i(all_1261_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.19 | $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ (hAPP(all_1261_0, % 229.68/33.19 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 229.68/33.19 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v4: % 229.68/33.19 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, all_1261_1) = % 229.68/33.19 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 229.68/33.19 | v4, v0))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (123) implies: % 229.68/33.19 | (124) c_RealDef_Oreal(tc_Nat_Onat) = all_1261_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (38) with fresh symbol all_1266_0 gives: % 229.68/33.19 | (125) c_RealDef_Oreal(tc_Nat_Onat) = all_1266_0 & $i(all_1266_0) & ! [v0: % 229.68/33.19 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.19 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, v2) = v3) | ~ % 229.68/33.19 | (hAPP(all_1266_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ? % 229.68/33.19 | [v4: $i] : ? [v5: $i] : (c_RComplete_Onatfloor(v3) = v4 & % 229.68/33.19 | c_RComplete_Onatfloor(v0) = v5 & % 229.68/33.19 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v1) = v4 & $i(v5) % 229.68/33.19 | & $i(v4))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (125) implies: % 229.68/33.19 | (126) c_RealDef_Oreal(tc_Nat_Onat) = all_1266_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (27) with fresh symbol all_1272_0 gives: % 229.68/33.19 | (127) c_RealDef_Oreal(tc_Nat_Onat) = all_1272_0 & $i(all_1272_0) & ! [v0: % 229.68/33.19 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.19 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, v2) = v3) | ~ % 229.68/33.19 | (hAPP(all_1272_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.19 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ? % 229.68/33.19 | [v4: $i] : ? [v5: $i] : (c_RComplete_Onatceiling(v3) = v4 & % 229.68/33.19 | c_RComplete_Onatceiling(v0) = v5 & % 229.68/33.19 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v1) = v4 & $i(v5) % 229.68/33.19 | & $i(v4))) % 229.68/33.19 | % 229.68/33.19 | ALPHA: (127) implies: % 229.68/33.19 | (128) c_RealDef_Oreal(tc_Nat_Onat) = all_1272_0 % 229.68/33.19 | % 229.68/33.19 | DELTA: instantiating (43) with fresh symbols all_1296_0, all_1296_1 gives: % 229.68/33.20 | (129) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1296_0 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1296_1 & $i(all_1296_0) & % 229.68/33.20 | $i(all_1296_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.20 | $i] : (v3 = v1 | ~ (c_RComplete_Onatfloor(v0) = v3) | ~ % 229.68/33.20 | (hAPP(all_1296_1, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ? % 229.68/33.20 | [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, % 229.68/33.20 | all_1296_0) = v4 & $i(v4) & ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (129) implies: % 229.68/33.20 | (130) c_RealDef_Oreal(tc_Nat_Onat) = all_1296_1 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (20) with fresh symbols all_1367_0, all_1367_1, % 229.68/33.20 | all_1367_2 gives: % 229.68/33.20 | (131) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1367_2 & % 229.68/33.20 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1367_0 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1367_1 & $i(all_1367_0) & % 229.68/33.20 | $i(all_1367_1) & $i(all_1367_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 229.68/33.20 | (hAPP(all_1367_1, v0) = v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1367_2, v1) | % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1367_0, v0)) & ! % 229.68/33.20 | [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1367_1, v0) = v1) | ~ $i(v0) % 229.68/33.20 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1367_0, v0) | % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1367_2, v1)) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (131) implies: % 229.68/33.20 | (132) c_RealDef_Oreal(tc_Nat_Onat) = all_1367_1 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (41) with fresh symbols all_1370_0, all_1370_1 gives: % 229.68/33.20 | (133) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1370_1 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1370_0 & $i(all_1370_0) & % 229.68/33.20 | $i(all_1370_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.20 | $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = % 229.68/33.20 | v3) | ~ (hAPP(all_1370_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1370_1, v1) % 229.68/33.20 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatfloor(v3) = v4 & % 229.68/33.20 | c_RComplete_Onatfloor(v1) = v5 & % 229.68/33.20 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) & % 229.68/33.20 | $i(v4))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (133) implies: % 229.68/33.20 | (134) c_RealDef_Oreal(tc_Nat_Onat) = all_1370_0 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (4) with fresh symbol all_1385_0 gives: % 229.68/33.20 | (135) c_RealDef_Oreal(tc_Nat_Onat) = all_1385_0 & $i(all_1385_0) & ! [v0: % 229.68/33.20 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.20 | (hAPP(all_1385_0, v1) = v2) | ~ (hAPP(all_1385_0, v0) = v3) | ~ % 229.68/33.20 | $i(v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3) | % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0)) & ! [v0: % 229.68/33.20 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.20 | (hAPP(all_1385_0, v1) = v2) | ~ (hAPP(all_1385_0, v0) = v3) | ~ % 229.68/33.20 | $i(v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3)) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (135) implies: % 229.68/33.20 | (136) c_RealDef_Oreal(tc_Nat_Onat) = all_1385_0 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (28) with fresh symbols all_1391_0, all_1391_1 gives: % 229.68/33.20 | (137) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1391_1 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1391_0 & $i(all_1391_0) & % 229.68/33.20 | $i(all_1391_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.20 | $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = % 229.68/33.20 | v3) | ~ (hAPP(all_1391_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1391_1, v1) % 229.68/33.20 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatceiling(v3) = v4 & % 229.68/33.20 | c_RComplete_Onatceiling(v1) = v5 & % 229.68/33.20 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) & % 229.68/33.20 | $i(v4))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (137) implies: % 229.68/33.20 | (138) c_RealDef_Oreal(tc_Nat_Onat) = all_1391_0 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (11) with fresh symbol all_1414_0 gives: % 229.68/33.20 | (139) c_RealDef_Oreal(tc_Nat_Onat) = all_1414_0 & $i(all_1414_0) & ! [v0: % 229.68/33.20 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.20 | (hAPP(all_1414_0, v1) = v2) | ~ (hAPP(all_1414_0, v0) = v3) | ~ % 229.68/33.20 | $i(v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0)) & ! [v0: $i] : % 229.68/33.20 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(all_1414_0, v1) = % 229.68/33.20 | v2) | ~ (hAPP(all_1414_0, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3)) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (139) implies: % 229.68/33.20 | (140) c_RealDef_Oreal(tc_Nat_Onat) = all_1414_0 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (30) with fresh symbols all_1441_0, all_1441_1 gives: % 229.68/33.20 | (141) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1441_1 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1441_0 & $i(all_1441_0) & % 229.68/33.20 | $i(all_1441_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1441_1, v0) % 229.68/33.20 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 229.68/33.20 | (c_Nat_OSuc(v1) = v3 & hAPP(all_1441_0, v3) = v4 & hAPP(all_1441_0, % 229.68/33.20 | v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (141) implies: % 229.68/33.20 | (142) c_RealDef_Oreal(tc_Nat_Onat) = all_1441_0 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (64) with fresh symbols all_1462_0, all_1462_1, % 229.68/33.20 | all_1462_2, all_1462_3, all_1462_4, all_1462_5, all_1462_6 gives: % 229.68/33.20 | (143) c_RealDef_Oreal(tc_Nat_Onat) = all_1462_6 & c_Nat_OSuc(all_1462_2) = % 229.68/33.20 | all_1462_1 & c_Nat_OSuc(all_1462_5) = all_1462_4 & % 229.68/33.20 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____) = % 229.68/33.20 | all_1462_5 & hAPP(all_1462_6, all_1462_1) = all_1462_0 & % 229.68/33.20 | hAPP(all_1462_6, all_1462_4) = all_1462_3 & hAPP(v_f____, all_1462_5) % 229.68/33.20 | = all_1462_2 & $i(all_1462_0) & $i(all_1462_1) & $i(all_1462_2) & % 229.68/33.20 | $i(all_1462_3) & $i(all_1462_4) & $i(all_1462_5) & $i(all_1462_6) & % 229.68/33.20 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1462_3, % 229.68/33.20 | all_1462_0) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (143) implies: % 229.68/33.20 | (144) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1462_3, % 229.68/33.20 | all_1462_0) % 229.68/33.20 | (145) $i(all_1462_4) % 229.68/33.20 | (146) $i(all_1462_2) % 229.68/33.20 | (147) $i(all_1462_1) % 229.68/33.20 | (148) hAPP(v_f____, all_1462_5) = all_1462_2 % 229.68/33.20 | (149) hAPP(all_1462_6, all_1462_4) = all_1462_3 % 229.68/33.20 | (150) hAPP(all_1462_6, all_1462_1) = all_1462_0 % 229.68/33.20 | (151) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____) = % 229.68/33.20 | all_1462_5 % 229.68/33.20 | (152) c_Nat_OSuc(all_1462_5) = all_1462_4 % 229.68/33.20 | (153) c_Nat_OSuc(all_1462_2) = all_1462_1 % 229.68/33.20 | (154) c_RealDef_Oreal(tc_Nat_Onat) = all_1462_6 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (52) with fresh symbols all_1503_0, all_1503_1, % 229.68/33.20 | all_1503_2 gives: % 229.68/33.20 | (155) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1503_2 & % 229.68/33.20 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1503_0 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1503_1 & $i(all_1503_0) & % 229.68/33.20 | $i(all_1503_1) & $i(all_1503_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 229.68/33.20 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ % 229.68/33.20 | (hAPP(all_1503_1, v1) = v2) | ~ (hAPP(all_1503_2, v2) = v3) | ~ % 229.68/33.20 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (hAPP(v5, v0) = v6 % 229.68/33.20 | & hAPP(all_1503_0, v1) = v5 & hAPP(all_1503_1, v6) = v4 & $i(v6) % 229.68/33.20 | & $i(v5) & $i(v4))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (155) implies: % 229.68/33.20 | (156) c_RealDef_Oreal(tc_Nat_Onat) = all_1503_1 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (29) with fresh symbols all_1521_0, all_1521_1, % 229.68/33.20 | all_1521_2 gives: % 229.68/33.20 | (157) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1521_2 & % 229.68/33.20 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1521_0 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1521_1 & $i(all_1521_0) & % 229.68/33.20 | $i(all_1521_1) & $i(all_1521_2) & ! [v0: $i] : ( ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1521_2, v0) % 229.68/33.20 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 229.68/33.20 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1521_0) = v2 & % 229.68/33.20 | hAPP(all_1521_1, v2) = v3 & hAPP(all_1521_1, v1) = v4 & $i(v4) & % 229.68/33.20 | $i(v3) & $i(v2) & $i(v1) & % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (157) implies: % 229.68/33.20 | (158) c_RealDef_Oreal(tc_Nat_Onat) = all_1521_1 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (58) with fresh symbols all_1530_0, all_1530_1, % 229.68/33.20 | all_1530_2 gives: % 229.68/33.20 | (159) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1530_1 & % 229.68/33.20 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1530_2 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1530_0 & $i(all_1530_0) & % 229.68/33.20 | $i(all_1530_1) & $i(all_1530_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 229.68/33.20 | $i] : ! [v3: $i] : ( ~ % 229.68/33.20 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v2) = v3) | % 229.68/33.20 | ~ (hAPP(all_1530_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1530_1, v0) | ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1530_2, v1) % 229.68/33.20 | | ? [v4: $i] : ? [v5: $i] : % 229.68/33.20 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v5, v0) = v4 & % 229.68/33.20 | c_RComplete_Onatfloor(v3) = v4 & c_RComplete_Onatfloor(v1) = v5 & % 229.68/33.20 | $i(v5) & $i(v4))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (159) implies: % 229.68/33.20 | (160) c_RealDef_Oreal(tc_Nat_Onat) = all_1530_0 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (53) with fresh symbols all_1533_0, all_1533_1, % 229.68/33.20 | all_1533_2 gives: % 229.68/33.20 | (161) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1533_0 & % 229.68/33.20 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1533_1 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1533_2 & $i(all_1533_0) & % 229.68/33.20 | $i(all_1533_1) & $i(all_1533_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 229.68/33.20 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v0) = v4) | ~ % 229.68/33.20 | (hAPP(all_1533_0, v2) = v3) | ~ (hAPP(all_1533_2, v1) = v2) | ~ % 229.68/33.20 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (hAPP(v5, v0) = v6 % 229.68/33.20 | & hAPP(all_1533_1, v1) = v5 & hAPP(all_1533_2, v6) = v4 & $i(v6) % 229.68/33.20 | & $i(v5) & $i(v4))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (161) implies: % 229.68/33.20 | (162) c_RealDef_Oreal(tc_Nat_Onat) = all_1533_2 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (21) with fresh symbols all_1542_0, all_1542_1, % 229.68/33.20 | all_1542_2 gives: % 229.68/33.20 | (163) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1542_1 & % 229.68/33.20 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1542_0 & % 229.68/33.20 | c_RealDef_Oreal(tc_Nat_Onat) = all_1542_2 & $i(all_1542_0) & % 229.68/33.20 | $i(all_1542_1) & $i(all_1542_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 229.68/33.20 | $i] : ! [v3: $i] : (v3 = v2 | ~ (c_RComplete_Onatceiling(v0) = % 229.68/33.20 | v2) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1, % 229.68/33.20 | all_1542_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? % 229.68/33.20 | [v5: $i] : (hAPP(all_1542_2, v1) = v4 & $i(v4) & ( ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0) | % 229.68/33.20 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, all_1542_1) % 229.68/33.20 | = v5 & $i(v5) & ~ % 229.68/33.20 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, % 229.68/33.20 | v5))))) % 229.68/33.20 | % 229.68/33.20 | ALPHA: (163) implies: % 229.68/33.20 | (164) c_RealDef_Oreal(tc_Nat_Onat) = all_1542_2 % 229.68/33.20 | % 229.68/33.20 | DELTA: instantiating (49) with fresh symbols all_1560_0, all_1560_1, % 229.68/33.20 | all_1560_2 gives: % 229.68/33.21 | (165) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1560_0 & % 229.68/33.21 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1560_1 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1560_2 & $i(all_1560_0) & % 229.68/33.21 | $i(all_1560_1) & $i(all_1560_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 229.68/33.21 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v4) = % 229.68/33.21 | v5) | ~ (hAPP(all_1560_0, v2) = v3) | ~ (hAPP(all_1560_2, v1) = % 229.68/33.21 | v2) | ~ (hAPP(all_1560_2, v0) = v4) | ~ $i(v1) | ~ $i(v0) | ? % 229.68/33.21 | [v6: $i] : ? [v7: $i] : (hAPP(v6, v0) = v7 & hAPP(all_1560_1, v1) % 229.68/33.21 | = v6 & hAPP(all_1560_2, v7) = v5 & $i(v7) & $i(v6) & $i(v5))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (165) implies: % 229.68/33.21 | (166) c_RealDef_Oreal(tc_Nat_Onat) = all_1560_2 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (36) with fresh symbols all_1569_0, all_1569_1 gives: % 229.68/33.21 | (167) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1569_1 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1569_0 & $i(all_1569_0) & % 229.68/33.21 | $i(all_1569_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.21 | $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ (hAPP(all_1569_0, % 229.68/33.21 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1569_1, v1) % 229.68/33.21 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2)) & ! [v0: % 229.68/33.21 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.21 | (c_RComplete_Onatfloor(v1) = v2) | ~ (hAPP(all_1569_0, v0) = v3) | % 229.68/33.21 | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1569_1, v1) % 229.68/33.21 | | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2) | % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (167) implies: % 229.68/33.21 | (168) c_RealDef_Oreal(tc_Nat_Onat) = all_1569_0 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (55) with fresh symbols all_1608_0, all_1608_1, % 229.68/33.21 | all_1608_2 gives: % 229.68/33.21 | (169) c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = all_1608_2 & % 229.68/33.21 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1608_1 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1608_0 & $i(all_1608_0) & % 229.68/33.21 | $i(all_1608_1) & $i(all_1608_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 229.68/33.21 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ % 229.68/33.21 | (hAPP(all_1608_0, v0) = v2) | ~ (hAPP(all_1608_1, v2) = v3) | ~ % 229.68/33.21 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 229.68/33.21 | (c_Complex_Ocis(v4) = v7 & c_Complex_Ocis(v1) = v5 & hAPP(v6, v0) = % 229.68/33.21 | v7 & hAPP(all_1608_2, v5) = v6 & $i(v7) & $i(v6) & $i(v5))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (169) implies: % 229.68/33.21 | (170) c_RealDef_Oreal(tc_Nat_Onat) = all_1608_0 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (26) with fresh symbols all_1623_0, all_1623_1 gives: % 229.68/33.21 | (171) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1623_1 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1623_0 & $i(all_1623_0) & % 229.68/33.21 | $i(all_1623_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.21 | $i] : ( ~ (c_RComplete_Onatceiling(v1) = v2) | ~ (hAPP(all_1623_0, % 229.68/33.21 | v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1623_1, v1) % 229.68/33.21 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0)) & ! [v0: % 229.68/33.21 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.21 | (c_RComplete_Onatceiling(v1) = v2) | ~ (hAPP(all_1623_0, v0) = v3) % 229.68/33.21 | | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1623_1, v1) % 229.68/33.21 | | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) | % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (171) implies: % 229.68/33.21 | (172) c_RealDef_Oreal(tc_Nat_Onat) = all_1623_0 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (44) with fresh symbols all_1656_0, all_1656_1 gives: % 229.68/33.21 | (173) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1656_0 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1656_1 & $i(all_1656_0) & % 229.68/33.21 | $i(all_1656_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 229.68/33.21 | (c_Int_Onumber__class_Onumber__of(tc_Int_Oint, v0) = v1) | ~ % 229.68/33.21 | $i(v0) | ~ c_Nat__Numeral_Oneg(v1) | ? [v2: $i] : % 229.68/33.21 | (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0) = v2 & % 229.68/33.21 | hAPP(all_1656_1, v2) = all_1656_0 & $i(v2))) & ! [v0: $i] : ! % 229.68/33.21 | [v1: $i] : ( ~ (c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, % 229.68/33.21 | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 229.68/33.21 | : ((v4 = v1 & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, v0) = % 229.68/33.21 | v3 & hAPP(all_1656_1, v3) = v1 & $i(v3) & $i(v1)) | % 229.68/33.21 | (c_Int_Onumber__class_Onumber__of(tc_Int_Oint, v0) = v2 & $i(v2) % 229.68/33.21 | & c_Nat__Numeral_Oneg(v2)))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (173) implies: % 229.68/33.21 | (174) c_RealDef_Oreal(tc_Nat_Onat) = all_1656_1 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (8) with fresh symbols all_1668_0, all_1668_1 gives: % 229.68/33.21 | (175) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1668_0 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1668_1 & $i(all_1668_0) & % 229.68/33.21 | $i(all_1668_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.21 | $i] : ( ~ (hAPP(all_1668_1, v1) = v2) | ~ (hAPP(all_1668_1, v0) = % 229.68/33.21 | v3) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4: % 229.68/33.21 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, % 229.68/33.21 | all_1668_0) = v4 & $i(v4) & % 229.68/33.21 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) & ! % 229.68/33.21 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 229.68/33.21 | (hAPP(all_1668_1, v1) = v2) | ~ (hAPP(all_1668_1, v0) = v3) | ~ % 229.68/33.21 | $i(v1) | ~ $i(v0) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, % 229.68/33.21 | v1, v0) | ? [v4: $i] : % 229.68/33.21 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, all_1668_0) = v4 % 229.68/33.21 | & $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, % 229.68/33.21 | v4))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (175) implies: % 229.68/33.21 | (176) c_RealDef_Oreal(tc_Nat_Onat) = all_1668_1 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (9) with fresh symbols all_1683_0, all_1683_1 gives: % 229.68/33.21 | (177) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1683_0 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1683_1 & $i(all_1683_0) & % 229.68/33.21 | $i(all_1683_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.21 | $i] : ( ~ (hAPP(all_1683_1, v1) = v2) | ~ (hAPP(all_1683_1, v0) = % 229.68/33.21 | v3) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] : % 229.68/33.21 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1683_0) = v4 % 229.68/33.21 | & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 229.68/33.21 | v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.21 | $i] : ( ~ (hAPP(all_1683_1, v1) = v2) | ~ (hAPP(all_1683_1, v0) = % 229.68/33.21 | v3) | ~ $i(v1) | ~ $i(v0) | % 229.68/33.21 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] : % 229.68/33.21 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1683_0) = v4 % 229.68/33.21 | & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, % 229.68/33.21 | v4, v3))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (177) implies: % 229.68/33.21 | (178) c_RealDef_Oreal(tc_Nat_Onat) = all_1683_1 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (54) with fresh symbols all_1723_0, all_1723_1, % 229.68/33.21 | all_1723_2 gives: % 229.68/33.21 | (179) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1723_1 & % 229.68/33.21 | c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1723_0 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1723_2 & $i(all_1723_0) & % 229.68/33.21 | $i(all_1723_1) & $i(all_1723_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 229.68/33.21 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RComplete_Onatfloor(v1) = % 229.68/33.21 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1723_0, v2) = v3) | % 229.68/33.21 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 229.68/33.21 | [v8: $i] : ((v8 = v4 & c_RComplete_Onatfloor(v7) = v4 & hAPP(v6, % 229.68/33.21 | v0) = v7 & hAPP(all_1723_1, v1) = v6 & $i(v7) & $i(v6) & % 229.68/33.21 | $i(v4)) | ( ~ (v5 = v1) & hAPP(all_1723_2, v2) = v5 & $i(v5)))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (179) implies: % 229.68/33.21 | (180) c_RealDef_Oreal(tc_Nat_Onat) = all_1723_2 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (57) with fresh symbols all_1759_0, all_1759_1, % 229.68/33.21 | all_1759_2, all_1759_3 gives: % 229.68/33.21 | (181) c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = all_1759_3 & % 229.68/33.21 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1759_2 & % 229.68/33.21 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1759_1 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1759_0 & $i(all_1759_0) & % 229.68/33.21 | $i(all_1759_1) & $i(all_1759_2) & $i(all_1759_3) & ! [v0: $i] : ! % 229.68/33.21 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 229.68/33.21 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Complex_Orcis(v4, v7) = % 229.68/33.21 | v8) | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v3, v0) = v4) | ~ % 229.68/33.21 | (hAPP(all_1759_0, v0) = v5) | ~ (hAPP(all_1759_1, v5) = v6) | ~ % 229.68/33.21 | (hAPP(all_1759_2, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 229.68/33.21 | ? [v9: $i] : ? [v10: $i] : (c_Complex_Orcis(v2, v1) = v9 & % 229.68/33.21 | hAPP(v10, v0) = v8 & hAPP(all_1759_3, v9) = v10 & $i(v10) & % 229.68/33.21 | $i(v9) & $i(v8))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (181) implies: % 229.68/33.21 | (182) c_RealDef_Oreal(tc_Nat_Onat) = all_1759_0 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (51) with fresh symbols all_1807_0, all_1807_1, % 229.68/33.21 | all_1807_2 gives: % 229.68/33.21 | (183) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1807_0 & % 229.68/33.21 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1807_2 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1807_1 & $i(all_1807_0) & % 229.68/33.21 | $i(all_1807_1) & $i(all_1807_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 229.68/33.21 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 229.68/33.21 | [v7: $i] : ! [v8: $i] : ( ~ (c_Complex_Ocis(v6) = v7) | ~ % 229.68/33.21 | (c_Complex_Ocis(v0) = v2) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v3, % 229.68/33.21 | v7) = v8) | ~ (hAPP(all_1807_0, v2) = v3) | ~ % 229.68/33.21 | (hAPP(all_1807_1, v1) = v4) | ~ (hAPP(all_1807_2, v4) = v5) | ~ % 229.68/33.21 | $i(v1) | ~ $i(v0) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 229.68/33.21 | [v12: $i] : (c_Complex_Ocis(v12) = v8 & c_Nat_OSuc(v1) = v9 & % 229.68/33.21 | hAPP(v11, v0) = v12 & hAPP(all_1807_1, v9) = v10 & % 229.68/33.21 | hAPP(all_1807_2, v10) = v11 & $i(v12) & $i(v11) & $i(v10) & % 229.68/33.21 | $i(v9) & $i(v8))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (183) implies: % 229.68/33.21 | (184) c_RealDef_Oreal(tc_Nat_Onat) = all_1807_1 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (50) with fresh symbols all_1813_0, all_1813_1, % 229.68/33.21 | all_1813_2, all_1813_3, all_1813_4 gives: % 229.68/33.21 | (185) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1813_0 & % 229.68/33.21 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1813_3 & % 229.68/33.21 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1813_4 & % 229.68/33.21 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1813_1 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1813_2 & $i(all_1813_0) & % 229.68/33.21 | $i(all_1813_1) & $i(all_1813_2) & $i(all_1813_3) & $i(all_1813_4) & % 229.68/33.21 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 229.68/33.21 | ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1813_1) = % 229.68/33.21 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1813_0, v2) = v3) | % 229.68/33.21 | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1813_4, v1) % 229.68/33.21 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 229.68/33.21 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, all_1813_1) = v8 % 229.68/33.21 | & hAPP(v6, v1) = v7 & hAPP(all_1813_2, v0) = v5 & % 229.68/33.21 | hAPP(all_1813_3, v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v4))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (185) implies: % 229.68/33.21 | (186) c_RealDef_Oreal(tc_Nat_Onat) = all_1813_2 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (56) with fresh symbols all_1837_0, all_1837_1, % 229.68/33.21 | all_1837_2 gives: % 229.68/33.21 | (187) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1837_1 & % 229.68/33.21 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1837_2 & % 229.68/33.21 | c_RealDef_Oreal(tc_Nat_Onat) = all_1837_0 & $i(all_1837_0) & % 229.68/33.21 | $i(all_1837_1) & $i(all_1837_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 229.68/33.21 | $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1837_2, v1) | % 229.68/33.21 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1837_2, % 229.68/33.21 | v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 229.68/33.21 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 229.68/33.21 | (c_Nat_OSuc(v2) = v6 & hAPP(v8, v1) = v9 & hAPP(v4, v1) = v5 & % 229.68/33.21 | hAPP(all_1837_0, v6) = v7 & hAPP(all_1837_0, v2) = v3 & % 229.68/33.21 | hAPP(all_1837_1, v7) = v8 & hAPP(all_1837_1, v3) = v4 & $i(v9) & % 229.68/33.21 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 229.68/33.21 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v9) & % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v0))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (187) implies: % 229.68/33.21 | (188) c_RealDef_Oreal(tc_Nat_Onat) = all_1837_0 % 229.68/33.21 | % 229.68/33.21 | DELTA: instantiating (46) with fresh symbol all_1855_0 gives: % 229.68/33.21 | (189) c_RealDef_Oreal(tc_Nat_Onat) = all_1855_0 & $i(all_1855_0) & ? [v0: % 229.68/33.21 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (c_Nat_OSuc(v2) % 229.68/33.21 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | class_RealVector_Oreal__normed__vector(v1) | c_SEQ_OBseq(v1, v0) | % 229.68/33.21 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 229.68/33.21 | (c_RealVector_Onorm__class_Onorm(v1, v6) = v7 & hAPP(v0, v5) = v6 & % 229.68/33.21 | hAPP(all_1855_0, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 229.68/33.21 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v4))) & % 229.68/33.21 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.21 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1) % 229.68/33.21 | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (c_Nat_OSuc(v2) = v3 & % 229.68/33.21 | hAPP(all_1855_0, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & ! [v5: % 229.68/33.21 | $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 229.68/33.21 | (c_RealVector_Onorm__class_Onorm(v1, v6) = v7) | ~ (hAPP(v0, % 229.68/33.21 | v5) = v6) | ~ $i(v5) | % 229.68/33.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v4)))) % 229.68/33.21 | % 229.68/33.21 | ALPHA: (189) implies: % 229.68/33.21 | (190) c_RealDef_Oreal(tc_Nat_Onat) = all_1855_0 % 229.68/33.22 | % 229.68/33.22 | DELTA: instantiating (45) with fresh symbol all_1858_0 gives: % 229.68/33.22 | (191) c_RealDef_Oreal(tc_Nat_Onat) = all_1858_0 & $i(all_1858_0) & ? [v0: % 229.68/33.22 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (c_Nat_OSuc(v2) % 229.68/33.22 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.22 | class_RealVector_Oreal__normed__vector(v1) | c_SEQ_OBseq(v1, v0) | % 229.68/33.22 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 229.68/33.22 | (c_RealVector_Onorm__class_Onorm(v1, v6) = v7 & hAPP(v0, v5) = v6 & % 229.68/33.22 | hAPP(all_1858_0, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 229.68/33.22 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v4))) & ! % 229.68/33.22 | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ c_SEQ_OBseq(v1, % 229.68/33.22 | v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v2: $i] % 229.68/33.22 | : ? [v3: $i] : ? [v4: $i] : (c_Nat_OSuc(v2) = v3 & % 229.68/33.22 | hAPP(all_1858_0, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & ! [v5: % 229.68/33.22 | $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 229.68/33.22 | (c_RealVector_Onorm__class_Onorm(v1, v6) = v7) | ~ (hAPP(v0, % 229.68/33.22 | v5) = v6) | ~ $i(v5) | % 229.68/33.22 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v4)))) % 229.68/33.22 | % 229.68/33.22 | ALPHA: (191) implies: % 229.68/33.22 | (192) c_RealDef_Oreal(tc_Nat_Onat) = all_1858_0 % 229.68/33.22 | % 229.68/33.22 | DELTA: instantiating (35) with fresh symbols all_1893_0, all_1893_1 gives: % 229.68/33.22 | (193) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1893_1 & % 229.68/33.22 | c_RealDef_Oreal(tc_Nat_Onat) = all_1893_0 & $i(all_1893_0) & % 229.68/33.22 | $i(all_1893_1) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.22 | $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 229.68/33.22 | | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ? % 229.68/33.22 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 229.68/33.22 | $i(v4) & ((c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & % 229.68/33.22 | hAPP(v0, v6) = v7 & hAPP(all_1893_0, v3) = v5 & $i(v8) & % 229.68/33.22 | $i(v7) & $i(v5) & ~ % 229.68/33.22 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v5)) | % 229.68/33.22 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1893_1, % 229.68/33.22 | v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 229.68/33.22 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~ % 229.68/33.22 | (hAPP(v0, v9) = v10) | ~ $i(v9) | % 229.68/33.22 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 229.68/33.22 | v4)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 229.68/33.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.22 | class_RealVector_Oreal__normed__vector(v1) | ~ % 229.68/33.22 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1893_1, v2) | % 229.68/33.22 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 229.68/33.22 | : ? [v8: $i] : ($i(v6) & $i(v3) & % 229.68/33.22 | ((c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6) = % 229.68/33.22 | v7 & $i(v8) & $i(v7) & ~ % 229.68/33.22 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v2)) % 229.68/33.22 | | (c_Nat_OSuc(v3) = v4 & hAPP(all_1893_0, v4) = v5 & $i(v5) & % 229.68/33.22 | $i(v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 229.68/33.22 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~ % 229.68/33.22 | (hAPP(v0, v9) = v10) | ~ $i(v9) | % 229.68/33.22 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, % 229.68/33.22 | v5)))))) % 229.68/33.22 | % 229.68/33.22 | ALPHA: (193) implies: % 229.68/33.22 | (194) c_RealDef_Oreal(tc_Nat_Onat) = all_1893_0 % 229.68/33.22 | % 229.68/33.22 | DELTA: instantiating (34) with fresh symbols all_1895_0, all_1895_1 gives: % 229.68/33.22 | (195) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1895_1 & % 229.68/33.22 | c_RealDef_Oreal(tc_Nat_Onat) = all_1895_0 & $i(all_1895_0) & % 229.68/33.22 | $i(all_1895_1) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 229.68/33.22 | $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 229.68/33.22 | | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ? % 229.68/33.22 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & % 229.68/33.22 | $i(v4) & ((c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & % 229.68/33.22 | hAPP(v0, v6) = v7 & hAPP(all_1895_0, v3) = v5 & $i(v8) & % 229.68/33.22 | $i(v7) & $i(v5) & ~ % 229.68/33.22 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v5)) % 229.68/33.22 | | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1895_1, % 229.68/33.22 | v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 229.68/33.22 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~ % 229.68/33.22 | (hAPP(v0, v9) = v10) | ~ $i(v9) | % 229.68/33.22 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 229.68/33.22 | v4)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 229.68/33.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 229.68/33.22 | class_RealVector_Oreal__normed__vector(v1) | ~ % 229.68/33.22 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1895_1, v2) | % 229.68/33.22 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 229.68/33.22 | : ? [v8: $i] : ($i(v6) & $i(v3) & % 229.68/33.22 | ((c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6) = % 229.68/33.22 | v7 & $i(v8) & $i(v7) & ~ % 229.68/33.22 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v2)) % 229.68/33.22 | | (c_Nat_OSuc(v3) = v4 & hAPP(all_1895_0, v4) = v5 & $i(v5) & % 229.68/33.22 | $i(v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 229.68/33.22 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~ % 229.68/33.22 | (hAPP(v0, v9) = v10) | ~ $i(v9) | % 229.68/33.22 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, % 229.68/33.22 | v5)))))) % 229.68/33.22 | % 229.68/33.22 | ALPHA: (195) implies: % 229.68/33.22 | (196) c_RealDef_Oreal(tc_Nat_Onat) = all_1895_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (67) with all_678_1, all_1462_5, v_N2____, % 229.68/33.22 | v_N1____, tc_Nat_Onat, simplifying with (76), (151) gives: % 229.68/33.22 | (197) all_1462_5 = all_678_1 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_622_0, all_686_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (71), (78) gives: % 229.68/33.22 | (198) all_686_0 = all_622_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_815_0, all_863_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (84), (86) gives: % 229.68/33.22 | (199) all_863_0 = all_815_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_863_0, all_869_1, tc_Nat_Onat, % 229.68/33.22 | simplifying with (86), (88) gives: % 229.68/33.22 | (200) all_869_1 = all_863_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_869_1, all_872_2, tc_Nat_Onat, % 229.68/33.22 | simplifying with (88), (90) gives: % 229.68/33.22 | (201) all_872_2 = all_869_1 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_883_2, all_953_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (94), (96) gives: % 229.68/33.22 | (202) all_953_0 = all_883_2 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_953_0, all_982_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (96), (98) gives: % 229.68/33.22 | (203) all_982_0 = all_953_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_982_0, all_991_3, tc_Nat_Onat, % 229.68/33.22 | simplifying with (98), (100) gives: % 229.68/33.22 | (204) all_991_3 = all_982_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_991_3, all_1007_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (100), (102) gives: % 229.68/33.22 | (205) all_1007_0 = all_991_3 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_883_2, all_1109_2, tc_Nat_Onat, % 229.68/33.22 | simplifying with (94), (106) gives: % 229.68/33.22 | (206) all_1109_2 = all_883_2 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_872_2, all_1109_2, tc_Nat_Onat, % 229.68/33.22 | simplifying with (90), (106) gives: % 229.68/33.22 | (207) all_1109_2 = all_872_2 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1142_1, all_1163_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (108), (110) gives: % 229.68/33.22 | (208) all_1163_0 = all_1142_1 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1163_0, all_1169_1, tc_Nat_Onat, % 229.68/33.22 | simplifying with (110), (112) gives: % 229.68/33.22 | (209) all_1169_1 = all_1163_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1169_1, all_1172_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (112), (114) gives: % 229.68/33.22 | (210) all_1172_0 = all_1169_1 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1172_0, all_1175_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (114), (116) gives: % 229.68/33.22 | (211) all_1175_0 = all_1172_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1109_2, all_1181_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (106), (118) gives: % 229.68/33.22 | (212) all_1181_0 = all_1109_2 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1175_0, all_1235_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (116), (120) gives: % 229.68/33.22 | (213) all_1235_0 = all_1175_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1235_0, all_1238_2, tc_Nat_Onat, % 229.68/33.22 | simplifying with (120), (122) gives: % 229.68/33.22 | (214) all_1238_2 = all_1235_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1238_2, all_1261_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (122), (124) gives: % 229.68/33.22 | (215) all_1261_0 = all_1238_2 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1261_0, all_1266_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (124), (126) gives: % 229.68/33.22 | (216) all_1266_0 = all_1261_0 % 229.68/33.22 | % 229.68/33.22 | GROUND_INST: instantiating (65) with all_1266_0, all_1272_0, tc_Nat_Onat, % 229.68/33.22 | simplifying with (126), (128) gives: % 229.68/33.22 | (217) all_1272_0 = all_1266_0 % 229.68/33.22 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1272_0, all_1367_1, tc_Nat_Onat, % 229.68/33.23 | simplifying with (128), (132) gives: % 229.68/33.23 | (218) all_1367_1 = all_1272_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1367_1, all_1370_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (132), (134) gives: % 229.68/33.23 | (219) all_1370_0 = all_1367_1 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1370_0, all_1385_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (134), (136) gives: % 229.68/33.23 | (220) all_1385_0 = all_1370_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1385_0, all_1391_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (136), (138) gives: % 229.68/33.23 | (221) all_1391_0 = all_1385_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1391_0, all_1414_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (138), (140) gives: % 229.68/33.23 | (222) all_1414_0 = all_1391_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1414_0, all_1441_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (140), (142) gives: % 229.68/33.23 | (223) all_1441_0 = all_1414_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1441_0, all_1503_1, tc_Nat_Onat, % 229.68/33.23 | simplifying with (142), (156) gives: % 229.68/33.23 | (224) all_1503_1 = all_1441_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1503_1, all_1521_1, tc_Nat_Onat, % 229.68/33.23 | simplifying with (156), (158) gives: % 229.68/33.23 | (225) all_1521_1 = all_1503_1 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1521_1, all_1530_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (158), (160) gives: % 229.68/33.23 | (226) all_1530_0 = all_1521_1 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1530_0, all_1533_2, tc_Nat_Onat, % 229.68/33.23 | simplifying with (160), (162) gives: % 229.68/33.23 | (227) all_1533_2 = all_1530_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1462_6, all_1542_2, tc_Nat_Onat, % 229.68/33.23 | simplifying with (154), (164) gives: % 229.68/33.23 | (228) all_1542_2 = all_1462_6 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1181_0, all_1542_2, tc_Nat_Onat, % 229.68/33.23 | simplifying with (118), (164) gives: % 229.68/33.23 | (229) all_1542_2 = all_1181_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1533_2, all_1560_2, tc_Nat_Onat, % 229.68/33.23 | simplifying with (162), (166) gives: % 229.68/33.23 | (230) all_1560_2 = all_1533_2 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_815_0, all_1569_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (84), (168) gives: % 229.68/33.23 | (231) all_1569_0 = all_815_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_686_0, all_1569_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (78), (168) gives: % 229.68/33.23 | (232) all_1569_0 = all_686_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1569_0, all_1608_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (168), (170) gives: % 229.68/33.23 | (233) all_1608_0 = all_1569_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1560_2, all_1623_0, tc_Nat_Onat, % 229.68/33.23 | simplifying with (166), (172) gives: % 229.68/33.23 | (234) all_1623_0 = all_1560_2 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1623_0, all_1656_1, tc_Nat_Onat, % 229.68/33.23 | simplifying with (172), (174) gives: % 229.68/33.23 | (235) all_1656_1 = all_1623_0 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1656_1, all_1668_1, tc_Nat_Onat, % 229.68/33.23 | simplifying with (174), (176) gives: % 229.68/33.23 | (236) all_1668_1 = all_1656_1 % 229.68/33.23 | % 229.68/33.23 | GROUND_INST: instantiating (65) with all_1462_6, all_1683_1, tc_Nat_Onat, % 229.68/33.23 | simplifying with (154), (178) gives: % 229.89/33.23 | (237) all_1683_1 = all_1462_6 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_874_0, all_1683_1, tc_Nat_Onat, % 229.89/33.23 | simplifying with (92), (178) gives: % 229.89/33.23 | (238) all_1683_1 = all_874_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1668_1, all_1723_2, tc_Nat_Onat, % 229.89/33.23 | simplifying with (176), (180) gives: % 229.89/33.23 | (239) all_1723_2 = all_1668_1 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1723_2, all_1759_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (180), (182) gives: % 229.89/33.23 | (240) all_1759_0 = all_1723_2 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1542_2, all_1807_1, tc_Nat_Onat, % 229.89/33.23 | simplifying with (164), (184) gives: % 229.89/33.23 | (241) all_1807_1 = all_1542_2 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1296_1, all_1807_1, tc_Nat_Onat, % 229.89/33.23 | simplifying with (130), (184) gives: % 229.89/33.23 | (242) all_1807_1 = all_1296_1 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1759_0, all_1813_2, tc_Nat_Onat, % 229.89/33.23 | simplifying with (182), (186) gives: % 229.89/33.23 | (243) all_1813_2 = all_1759_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1813_2, all_1837_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (186), (188) gives: % 229.89/33.23 | (244) all_1837_0 = all_1813_2 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_743_0, all_1837_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (80), (188) gives: % 229.89/33.23 | (245) all_1837_0 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1608_0, all_1858_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (170), (192) gives: % 229.89/33.23 | (246) all_1858_0 = all_1608_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_760_0, all_1858_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (82), (192) gives: % 229.89/33.23 | (247) all_1858_0 = all_760_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1855_0, all_1893_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (190), (194) gives: % 229.89/33.23 | (248) all_1893_0 = all_1855_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1142_1, all_1893_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (108), (194) gives: % 229.89/33.23 | (249) all_1893_0 = all_1142_1 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1059_0, all_1893_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (104), (194) gives: % 229.89/33.23 | (250) all_1893_0 = all_1059_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1007_0, all_1893_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (102), (194) gives: % 229.89/33.23 | (251) all_1893_0 = all_1007_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_1569_0, all_1895_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (168), (196) gives: % 229.89/33.23 | (252) all_1895_0 = all_1569_0 % 229.89/33.23 | % 229.89/33.23 | GROUND_INST: instantiating (65) with all_618_0, all_1895_0, tc_Nat_Onat, % 229.89/33.23 | simplifying with (69), (196) gives: % 229.89/33.23 | (253) all_1895_0 = all_618_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (252), (253) imply: % 229.89/33.23 | (254) all_1569_0 = all_618_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (254) implies: % 229.89/33.23 | (255) all_1569_0 = all_618_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (248), (251) imply: % 229.89/33.23 | (256) all_1855_0 = all_1007_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (248), (249) imply: % 229.89/33.23 | (257) all_1855_0 = all_1142_1 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (248), (250) imply: % 229.89/33.23 | (258) all_1855_0 = all_1059_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (246), (247) imply: % 229.89/33.23 | (259) all_1608_0 = all_760_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (259) implies: % 229.89/33.23 | (260) all_1608_0 = all_760_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (256), (258) imply: % 229.89/33.23 | (261) all_1059_0 = all_1007_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (257), (258) imply: % 229.89/33.23 | (262) all_1142_1 = all_1059_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (262) implies: % 229.89/33.23 | (263) all_1142_1 = all_1059_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (244), (245) imply: % 229.89/33.23 | (264) all_1813_2 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (264) implies: % 229.89/33.23 | (265) all_1813_2 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (243), (265) imply: % 229.89/33.23 | (266) all_1759_0 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (266) implies: % 229.89/33.23 | (267) all_1759_0 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (241), (242) imply: % 229.89/33.23 | (268) all_1542_2 = all_1296_1 % 229.89/33.23 | % 229.89/33.23 | SIMP: (268) implies: % 229.89/33.23 | (269) all_1542_2 = all_1296_1 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (240), (267) imply: % 229.89/33.23 | (270) all_1723_2 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (270) implies: % 229.89/33.23 | (271) all_1723_2 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (239), (271) imply: % 229.89/33.23 | (272) all_1668_1 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (272) implies: % 229.89/33.23 | (273) all_1668_1 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (237), (238) imply: % 229.89/33.23 | (274) all_1462_6 = all_874_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (274) implies: % 229.89/33.23 | (275) all_1462_6 = all_874_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (236), (273) imply: % 229.89/33.23 | (276) all_1656_1 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (276) implies: % 229.89/33.23 | (277) all_1656_1 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | COMBINE_EQS: (235), (277) imply: % 229.89/33.23 | (278) all_1623_0 = all_743_0 % 229.89/33.23 | % 229.89/33.23 | SIMP: (278) implies: % 229.89/33.23 | (279) all_1623_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (234), (279) imply: % 229.89/33.24 | (280) all_1560_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (280) implies: % 229.89/33.24 | (281) all_1560_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (233), (260) imply: % 229.89/33.24 | (282) all_1569_0 = all_760_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (282) implies: % 229.89/33.24 | (283) all_1569_0 = all_760_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (231), (283) imply: % 229.89/33.24 | (284) all_815_0 = all_760_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (284) implies: % 229.89/33.24 | (285) all_815_0 = all_760_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (232), (283) imply: % 229.89/33.24 | (286) all_760_0 = all_686_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (255), (283) imply: % 229.89/33.24 | (287) all_760_0 = all_618_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (230), (281) imply: % 229.89/33.24 | (288) all_1533_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (288) implies: % 229.89/33.24 | (289) all_1533_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (228), (269) imply: % 229.89/33.24 | (290) all_1462_6 = all_1296_1 % 229.89/33.24 | % 229.89/33.24 | SIMP: (290) implies: % 229.89/33.24 | (291) all_1462_6 = all_1296_1 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (229), (269) imply: % 229.89/33.24 | (292) all_1296_1 = all_1181_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (227), (289) imply: % 229.89/33.24 | (293) all_1530_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (293) implies: % 229.89/33.24 | (294) all_1530_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (226), (294) imply: % 229.89/33.24 | (295) all_1521_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (295) implies: % 229.89/33.24 | (296) all_1521_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (225), (296) imply: % 229.89/33.24 | (297) all_1503_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (297) implies: % 229.89/33.24 | (298) all_1503_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (224), (298) imply: % 229.89/33.24 | (299) all_1441_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (299) implies: % 229.89/33.24 | (300) all_1441_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (275), (291) imply: % 229.89/33.24 | (301) all_1296_1 = all_874_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (301) implies: % 229.89/33.24 | (302) all_1296_1 = all_874_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (223), (300) imply: % 229.89/33.24 | (303) all_1414_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (303) implies: % 229.89/33.24 | (304) all_1414_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (222), (304) imply: % 229.89/33.24 | (305) all_1391_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (305) implies: % 229.89/33.24 | (306) all_1391_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (221), (306) imply: % 229.89/33.24 | (307) all_1385_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (307) implies: % 229.89/33.24 | (308) all_1385_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (220), (308) imply: % 229.89/33.24 | (309) all_1370_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (309) implies: % 229.89/33.24 | (310) all_1370_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (219), (310) imply: % 229.89/33.24 | (311) all_1367_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (311) implies: % 229.89/33.24 | (312) all_1367_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (218), (312) imply: % 229.89/33.24 | (313) all_1272_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (313) implies: % 229.89/33.24 | (314) all_1272_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (292), (302) imply: % 229.89/33.24 | (315) all_1181_0 = all_874_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (315) implies: % 229.89/33.24 | (316) all_1181_0 = all_874_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (217), (314) imply: % 229.89/33.24 | (317) all_1266_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (317) implies: % 229.89/33.24 | (318) all_1266_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (216), (318) imply: % 229.89/33.24 | (319) all_1261_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (319) implies: % 229.89/33.24 | (320) all_1261_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (215), (320) imply: % 229.89/33.24 | (321) all_1238_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (321) implies: % 229.89/33.24 | (322) all_1238_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (214), (322) imply: % 229.89/33.24 | (323) all_1235_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (323) implies: % 229.89/33.24 | (324) all_1235_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (213), (324) imply: % 229.89/33.24 | (325) all_1175_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (325) implies: % 229.89/33.24 | (326) all_1175_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (212), (316) imply: % 229.89/33.24 | (327) all_1109_2 = all_874_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (327) implies: % 229.89/33.24 | (328) all_1109_2 = all_874_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (211), (326) imply: % 229.89/33.24 | (329) all_1172_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (329) implies: % 229.89/33.24 | (330) all_1172_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (210), (330) imply: % 229.89/33.24 | (331) all_1169_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (331) implies: % 229.89/33.24 | (332) all_1169_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (209), (332) imply: % 229.89/33.24 | (333) all_1163_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (333) implies: % 229.89/33.24 | (334) all_1163_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (208), (334) imply: % 229.89/33.24 | (335) all_1142_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (335) implies: % 229.89/33.24 | (336) all_1142_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (263), (336) imply: % 229.89/33.24 | (337) all_1059_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (337) implies: % 229.89/33.24 | (338) all_1059_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (206), (328) imply: % 229.89/33.24 | (339) all_883_2 = all_874_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (339) implies: % 229.89/33.24 | (340) all_883_2 = all_874_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (207), (328) imply: % 229.89/33.24 | (341) all_874_0 = all_872_2 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (261), (338) imply: % 229.89/33.24 | (342) all_1007_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (342) implies: % 229.89/33.24 | (343) all_1007_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (205), (343) imply: % 229.89/33.24 | (344) all_991_3 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (344) implies: % 229.89/33.24 | (345) all_991_3 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (204), (345) imply: % 229.89/33.24 | (346) all_982_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (346) implies: % 229.89/33.24 | (347) all_982_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (203), (347) imply: % 229.89/33.24 | (348) all_953_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (348) implies: % 229.89/33.24 | (349) all_953_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (202), (349) imply: % 229.89/33.24 | (350) all_883_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (350) implies: % 229.89/33.24 | (351) all_883_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (340), (351) imply: % 229.89/33.24 | (352) all_874_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (352) implies: % 229.89/33.24 | (353) all_874_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (341), (353) imply: % 229.89/33.24 | (354) all_872_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (354) implies: % 229.89/33.24 | (355) all_872_2 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (201), (355) imply: % 229.89/33.24 | (356) all_869_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (356) implies: % 229.89/33.24 | (357) all_869_1 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (200), (357) imply: % 229.89/33.24 | (358) all_863_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (358) implies: % 229.89/33.24 | (359) all_863_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (199), (359) imply: % 229.89/33.24 | (360) all_815_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (360) implies: % 229.89/33.24 | (361) all_815_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (285), (361) imply: % 229.89/33.24 | (362) all_760_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (362) implies: % 229.89/33.24 | (363) all_760_0 = all_743_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (286), (363) imply: % 229.89/33.24 | (364) all_743_0 = all_686_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (287), (363) imply: % 229.89/33.24 | (365) all_743_0 = all_618_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (364), (365) imply: % 229.89/33.24 | (366) all_686_0 = all_618_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (366) implies: % 229.89/33.24 | (367) all_686_0 = all_618_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (198), (367) imply: % 229.89/33.24 | (368) all_622_0 = all_618_0 % 229.89/33.24 | % 229.89/33.24 | SIMP: (368) implies: % 229.89/33.24 | (369) all_622_0 = all_618_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (353), (365) imply: % 229.89/33.24 | (370) all_874_0 = all_618_0 % 229.89/33.24 | % 229.89/33.24 | COMBINE_EQS: (275), (370) imply: % 229.89/33.24 | (371) all_1462_6 = all_618_0 % 229.89/33.24 | % 229.89/33.24 | REDUCE: (72), (369) imply: % 229.96/33.24 | (372) c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) = all_618_0 % 229.96/33.24 | % 229.96/33.24 | REDUCE: (152), (197) imply: % 229.96/33.24 | (373) c_Nat_OSuc(all_678_1) = all_1462_4 % 229.96/33.24 | % 229.96/33.24 | REDUCE: (150), (371) imply: % 229.96/33.24 | (374) hAPP(all_618_0, all_1462_1) = all_1462_0 % 229.96/33.24 | % 229.96/33.24 | REDUCE: (149), (371) imply: % 229.96/33.24 | (375) hAPP(all_618_0, all_1462_4) = all_1462_3 % 229.96/33.24 | % 229.96/33.24 | REDUCE: (148), (197) imply: % 229.96/33.24 | (376) hAPP(v_f____, all_678_1) = all_1462_2 % 229.96/33.24 | % 229.96/33.25 | GROUND_INST: instantiating (66) with all_678_0, all_1462_2, all_678_1, % 229.96/33.25 | v_f____, simplifying with (75), (376) gives: % 229.96/33.25 | (377) all_1462_2 = all_678_0 % 229.96/33.25 | % 229.96/33.25 | REDUCE: (153), (377) imply: % 229.96/33.25 | (378) c_Nat_OSuc(all_678_0) = all_1462_1 % 229.96/33.25 | % 229.96/33.25 | REDUCE: (146), (377) imply: % 229.96/33.25 | (379) $i(all_678_0) % 229.96/33.25 | % 229.96/33.25 | GROUND_INST: instantiating (3) with v_N1____, v_N2____, all_678_1, simplifying % 229.96/33.25 | with (61), (62), (76) gives: % 229.96/33.25 | (380) c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N2____, v_N1____) = % 229.96/33.25 | all_678_1 & $i(all_678_1) % 229.96/33.25 | % 229.96/33.25 | ALPHA: (380) implies: % 229.96/33.25 | (381) $i(all_678_1) % 229.96/33.25 | % 229.96/33.25 | GROUND_INST: instantiating (2) with all_678_0, all_678_1, all_1462_4, % 229.96/33.25 | all_1462_1, simplifying with (74), (373), (378), (379), (381) % 229.96/33.25 | gives: % 229.96/33.25 | (382) c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1462_4, % 229.96/33.25 | all_1462_1) % 229.96/33.25 | % 229.96/33.25 | GROUND_INST: instantiating (48) with all_1462_1, all_1462_4, tc_RealDef_Oreal, % 229.96/33.25 | all_618_0, all_1462_3, all_1462_0, simplifying with (60), (63), % 229.96/33.25 | (144), (145), (147), (372), (374), (375), (382) gives: % 229.96/33.25 | (383) $false % 229.96/33.25 | % 229.96/33.25 | CLOSE: (383) is inconsistent. % 229.96/33.25 | % 229.96/33.25 End of proof % 229.96/33.25 % SZS output end Proof for theBenchmark % 229.96/33.25 % 229.96/33.25 32602ms %------------------------------------------------------------------------------