TSTP Solution File: SWW218+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW218+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n026.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 May 19 12:25:47 EDT 2023
% Result : Theorem 135.51s 130.27s
% Output : Proof 135.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW218+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : nanocop.sh %s %d
% 0.13/0.35 % Computer : n026.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
% 0.19/0.35 % DateTime : Thu May 18 22:34:50 EDT 2023
% 0.19/0.35 % CPUTime :
% 135.51/130.27
% 135.51/130.27 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 135.51/130.27 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 135.51/130.27 %-----------------------------------------------------
% 135.51/130.27 ncf(matrix, plain, [(12806 ^ _206868) ^ [] : [v_thesis____], (820 ^ _206868) ^ [_232385, _232387, _232389, _232391, _232393, _232395, _232397, _232399] : [-(c_If(_232399, _232395, _232391, _232387) = c_If(_232397, _232393, _232389, _232385)), _232399 = _232397, _232395 = _232393, _232391 = _232389, _232387 = _232385], (838 ^ _206868) ^ [_233102, _233104, _233106, _233108, _233110, _233112, _233114, _233116, _233118, _233120] : [-(c_Polynomial_Opoly__rec(_233120, _233116, _233112, _233108, _233104) = c_Polynomial_Opoly__rec(_233118, _233114, _233110, _233106, _233102)), _233120 = _233118, _233116 = _233114, _233112 = _233110, _233108 = _233106, _233104 = _233102], (860 ^ _206868) ^ [_233924, _233926, _233928, _233930, _233932, _233934] : [-(c_Polynomial_Oorder(_233934, _233930, _233926) = c_Polynomial_Oorder(_233932, _233928, _233924)), _233934 = _233932, _233930 = _233928, _233926 = _233924], (874 ^ _206868) ^ [_234412, _234414, _234416, _234418] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_234418, _234414) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_234416, _234412)), _234418 = _234416, _234414 = _234412], (884 ^ _206868) ^ [_234799, _234801, _234803, _234805, _234807, _234809] : [-(c_Nat_Onat_Onat__case(_234809, _234805, _234801) = c_Nat_Onat_Onat__case(_234807, _234803, _234799)), _234809 = _234807, _234805 = _234803, _234801 = _234799], (898 ^ _206868) ^ [_235287, _235289, _235291, _235293] : [-(c_Polynomial_OAbs__poly(_235293, _235289) = c_Polynomial_OAbs__poly(_235291, _235287)), _235293 = _235291, _235289 = _235287], (908 ^ _206868) ^ [_235674, _235676, _235678, _235680, _235682, _235684] : [-(c_Polynomial_Opoly__gcd(_235684, _235680, _235676) = c_Polynomial_Opoly__gcd(_235682, _235678, _235674)), _235684 = _235682, _235680 = _235678, _235676 = _235674], (922 ^ _206868) ^ [_236190, _236192, _236194, _236196, _236198, _236200] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_236200, _236196, _236192) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_236198, _236194, _236190)), _236200 = _236198, _236196 = _236194, _236192 = _236190], (936 ^ _206868) ^ [_236650, _236652] : [_236652 = _236650, -(c_RComplete_Onatceiling(_236652) = c_RComplete_Onatceiling(_236650))], (942 ^ _206868) ^ [_236924, _236926, _236928, _236930, _236932, _236934] : [-(c_Polynomial_Osynthetic__div(_236934, _236930, _236926) = c_Polynomial_Osynthetic__div(_236932, _236928, _236924)), _236934 = _236932, _236930 = _236928, _236926 = _236924], (956 ^ _206868) ^ [_237412, _237414, _237416, _237418] : [-(c_Polynomial_Ocoeff(_237418, _237414) = c_Polynomial_Ocoeff(_237416, _237412)), _237418 = _237416, _237414 = _237412], (966 ^ _206868) ^ [_237771, _237773, _237775, _237777] : [-(c_Groups_Osgn__class_Osgn(_237777, _237773) = c_Groups_Osgn__class_Osgn(_237775, _237771)), _237777 = _237775, _237773 = _237771], (976 ^ _206868) ^ [_238158, _238160, _238162, _238164, _238166, _238168] : [-(c_Polynomial_OpCons(_238168, _238164, _238160) = c_Polynomial_OpCons(_238166, _238162, _238158)), _238168 = _238166, _238164 = _238162, _238160 = _238158], (990 ^ _206868) ^ [_238674, _238676, _238678, _238680, _238682, _238684] : [-(c_Polynomial_Opcompose(_238684, _238680, _238676) = c_Polynomial_Opcompose(_238682, _238678, _238674)), _238684 = _238682, _238680 = _238678, _238676 = _238674], (1004 ^ _206868) ^ [_239162, _239164, _239166, _239168] : [-(c_NthRoot_Oroot(_239168, _239164) = c_NthRoot_Oroot(_239166, _239162)), _239168 = _239166, _239164 = _239162], (1014 ^ _206868) ^ [_239493, _239495] : [_239495 = _239493, -(c_RComplete_Onatfloor(_239495) = c_RComplete_Onatfloor(_239493))], (1020 ^ _206868) ^ [_239767, _239769, _239771, _239773, _239775, _239777] : [-(c_Power_Opower_Opower(_239777, _239773, _239769) = c_Power_Opower_Opower(_239775, _239771, _239767)), _239777 = _239775, _239773 = _239771, _239769 = _239767], (1034 ^ _206868) ^ [_240255, _240257, _240259, _240261] : [-(c_Polynomial_Odegree(_240261, _240257) = c_Polynomial_Odegree(_240259, _240255)), _240261 = _240259, _240257 = _240255], (1044 ^ _206868) ^ [_240614, _240616, _240618, _240620] : [-(c_Complex_Orcis(_240620, _240616) = c_Complex_Orcis(_240618, _240614)), _240620 = _240618, _240616 = _240614], (1054 ^ _206868) ^ [_240945, _240947] : [_240947 = _240945, -(c_Complex_Ocis(_240947) = c_Complex_Ocis(_240945))], (1060 ^ _206868) ^ [_241163, _241165] : [_241165 = _241163, -(c_Complex_Oexpi(_241165) = c_Complex_Oexpi(_241163))], (1066 ^ _206868) ^ [_241409, _241411, _241413, _241415] : [-(c_RealDef_Oreal(_241415, _241411) = c_RealDef_Oreal(_241413, _241409)), _241415 = _241413, _241411 = _241409], (1076 ^ _206868) ^ [_241740, _241742] : [_241742 = _241740, -(c_Transcendental_Oln(_241742) = c_Transcendental_Oln(_241740))], (1082 ^ _206868) ^ [_241958, _241960] : [_241960 = _241958, -(c_Power_Opower__class_Opower(_241960) = c_Power_Opower__class_Opower(_241958))], (1088 ^ _206868) ^ [_242176, _242178] : [_242178 = _242176, -(c_Groups_Oone__class_Oone(_242178) = c_Groups_Oone__class_Oone(_242176))], (1094 ^ _206868) ^ [_242394, _242396] : [_242396 = _242394, -(c_Rings_Odvd__class_Odvd(_242396) = c_Rings_Odvd__class_Odvd(_242394))], (1100 ^ _206868) ^ [_242612, _242614] : [_242614 = _242612, -(c_Groups_Otimes__class_Otimes(_242614) = c_Groups_Otimes__class_Otimes(_242612))], (1106 ^ _206868) ^ [_242830, _242832] : [_242832 = _242830, -(c_Groups_Ozero__class_Ozero(_242832) = c_Groups_Ozero__class_Ozero(_242830))], (1112 ^ _206868) ^ [_243104, _243106, _243108, _243110, _243112, _243114] : [-(c_Groups_Ominus__class_Ominus(_243114, _243110, _243106) = c_Groups_Ominus__class_Ominus(_243112, _243108, _243104)), _243114 = _243112, _243110 = _243108, _243106 = _243104], (1126 ^ _206868) ^ [_243620, _243622, _243624, _243626, _243628, _243630] : [-(c_Groups_Oplus__class_Oplus(_243630, _243626, _243622) = c_Groups_Oplus__class_Oplus(_243628, _243624, _243620)), _243630 = _243628, _243626 = _243624, _243622 = _243620], (1140 ^ _206868) ^ [_244080, _244082] : [_244082 = _244080, -(c_Nat_OSuc(_244082) = c_Nat_OSuc(_244080))], (1146 ^ _206868) ^ [_244326, _244328, _244330, _244332] : [-(tc_fun(_244332, _244328) = tc_fun(_244330, _244326)), _244332 = _244330, _244328 = _244326], (1156 ^ _206868) ^ [_244657, _244659] : [_244659 = _244657, -(tc_Polynomial_Opoly(_244659) = tc_Polynomial_Opoly(_244657))], (1162 ^ _206868) ^ [_244903, _244905, _244907, _244909] : [-(c_fequal(_244909, _244905) = c_fequal(_244907, _244903)), _244909 = _244907, _244905 = _244903], (1172 ^ _206868) ^ [_245262, _245264, _245266, _245268] : [-(c_RealVector_Onorm__class_Onorm(_245268, _245264) = c_RealVector_Onorm__class_Onorm(_245266, _245262)), _245268 = _245266, _245264 = _245262], (1182 ^ _206868) ^ [_245621, _245623, _245625, _245627] : [-(hAPP(_245627, _245623) = hAPP(_245625, _245621)), _245627 = _245625, _245623 = _245621], (1192 ^ _206868) ^ [_245980, _245982, _245984, _245986] : [-(c_Polynomial_Opoly(_245986, _245982) = c_Polynomial_Opoly(_245984, _245980)), _245986 = _245984, _245982 = _245980], (1202 ^ _206868) ^ [_246319, _246321, _246323, _246325] : [-(c_Groups_Ouminus__class_Ouminus(_246325, _246321) = c_Groups_Ouminus__class_Ouminus(_246323, _246319)), _246325 = _246323, _246321 = _246319], (2 ^ _206868) ^ [_207012] : [-(_207012 = _207012)], (4 ^ _206868) ^ [_207119, _207121] : [_207121 = _207119, -(_207119 = _207121)], (10 ^ _206868) ^ [_207323, _207325, _207327] : [-(_207327 = _207323), _207327 = _207325, _207325 = _207323], (20 ^ _206868) ^ [_207664, _207666, _207668, _207670] : [-(c_SEQ_Odecseq(_207668, _207664)), c_SEQ_Odecseq(_207670, _207666), _207670 = _207668, _207666 = _207664], (34 ^ _206868) ^ [_208164, _208166, _208168, _208170, _208172, _208174, _208176, _208178] : [-(c_Orderings_Oorder_Omono(_208176, _208172, _208168, _208164)), c_Orderings_Oorder_Omono(_208178, _208174, _208170, _208166), _208178 = _208176, _208174 = _208172, _208170 = _208168, _208166 = _208164], (56 ^ _206868) ^ [_208898, _208900, _208902, _208904] : [-(c_SEQ_Oincseq(_208902, _208898)), c_SEQ_Oincseq(_208904, _208900), _208904 = _208902, _208900 = _208898], (70 ^ _206868) ^ [_209342, _209344, _209346, _209348] : [-(c_SEQ_OBseq(_209346, _209342)), c_SEQ_OBseq(_209348, _209344), _209348 = _209346, _209344 = _209342], (84 ^ _206868) ^ [_209786, _209788, _209790, _209792] : [-(c_Polynomial_Opos__poly(_209790, _209786)), c_Polynomial_Opos__poly(_209792, _209788), _209792 = _209790, _209788 = _209786], (98 ^ _206868) ^ [_210202, _210204] : [-(c_RealDef_Opositive(_210202)), _210204 = _210202, c_RealDef_Opositive(_210204)], (108 ^ _206868) ^ [_210497, _210499] : [-(class_Lattices_Oab__semigroup__idem__mult(_210497)), _210499 = _210497, class_Lattices_Oab__semigroup__idem__mult(_210499)], (118 ^ _206868) ^ [_210904, _210906, _210908, _210910, _210912, _210914, _210916, _210918, _210920, _210922] : [-(c_Polynomial_Opdivmod__rel(_210920, _210916, _210912, _210908, _210904)), c_Polynomial_Opdivmod__rel(_210922, _210918, _210914, _210910, _210906), _210922 = _210920, _210918 = _210916, _210914 = _210912, _210910 = _210908, _210906 = _210904], (144 ^ _206868) ^ [_211779, _211781] : [-(class_Lattices_Oboolean__algebra(_211779)), _211781 = _211779, class_Lattices_Oboolean__algebra(_211781)], (154 ^ _206868) ^ [_212074, _212076] : [-(class_RealVector_Oreal__normed__div__algebra(_212074)), _212076 = _212074, class_RealVector_Oreal__normed__div__algebra(_212076)], (164 ^ _206868) ^ [_212369, _212371] : [-(class_RealVector_Oreal__normed__algebra__1(_212369)), _212371 = _212369, class_RealVector_Oreal__normed__algebra__1(_212371)], (174 ^ _206868) ^ [_212664, _212666] : [-(class_RealVector_Oreal__normed__algebra(_212664)), _212666 = _212664, class_RealVector_Oreal__normed__algebra(_212666)], (184 ^ _206868) ^ [_212959, _212961] : [-(class_RealVector_Oreal__normed__vector(_212959)), _212961 = _212959, class_RealVector_Oreal__normed__vector(_212961)], (194 ^ _206868) ^ [_213254, _213256] : [-(class_Fields_Ofield(_213254)), _213256 = _213254, class_Fields_Ofield(_213256)], (204 ^ _206868) ^ [_213549, _213551] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_213549)), _213551 = _213549, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_213551)], (214 ^ _206868) ^ [_213844, _213846] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_213844)), _213846 = _213844, class_Groups_Oordered__cancel__ab__semigroup__add(_213846)], (224 ^ _206868) ^ [_214139, _214141] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_214139)), _214141 = _214139, class_Groups_Oordered__ab__semigroup__add__imp__le(_214141)], (234 ^ _206868) ^ [_214434, _214436] : [-(class_Rings_Olinordered__comm__semiring__strict(_214434)), _214436 = _214434, class_Rings_Olinordered__comm__semiring__strict(_214436)], (244 ^ _206868) ^ [_214729, _214731] : [-(class_Rings_Olinordered__semiring__1__strict(_214729)), _214731 = _214729, class_Rings_Olinordered__semiring__1__strict(_214731)], (254 ^ _206868) ^ [_215024, _215026] : [-(class_Rings_Olinordered__semiring__strict(_215024)), _215026 = _215024, class_Rings_Olinordered__semiring__strict(_215026)], (264 ^ _206868) ^ [_215319, _215321] : [-(class_Groups_Oordered__ab__semigroup__add(_215319)), _215321 = _215319, class_Groups_Oordered__ab__semigroup__add(_215321)], (274 ^ _206868) ^ [_215614, _215616] : [-(class_Groups_Oordered__comm__monoid__add(_215614)), _215616 = _215614, class_Groups_Oordered__comm__monoid__add(_215616)], (284 ^ _206868) ^ [_215909, _215911] : [-(class_Groups_Olinordered__ab__group__add(_215909)), _215911 = _215909, class_Groups_Olinordered__ab__group__add(_215911)], (294 ^ _206868) ^ [_216204, _216206] : [-(class_Groups_Ocancel__ab__semigroup__add(_216204)), _216206 = _216204, class_Groups_Ocancel__ab__semigroup__add(_216206)], (304 ^ _206868) ^ [_216499, _216501] : [-(class_Rings_Oring__1__no__zero__divisors(_216499)), _216501 = _216499, class_Rings_Oring__1__no__zero__divisors(_216501)], (314 ^ _206868) ^ [_216794, _216796] : [-(class_Rings_Oordered__cancel__semiring(_216794)), _216796 = _216794, class_Rings_Oordered__cancel__semiring(_216796)], (324 ^ _206868) ^ [_217089, _217091] : [-(class_Rings_Olinordered__ring__strict(_217089)), _217091 = _217089, class_Rings_Olinordered__ring__strict(_217091)], (334 ^ _206868) ^ [_217384, _217386] : [-(class_Rings_Oring__no__zero__divisors(_217384)), _217386 = _217384, class_Rings_Oring__no__zero__divisors(_217386)], (344 ^ _206868) ^ [_217679, _217681] : [-(class_Rings_Oordered__comm__semiring(_217679)), _217681 = _217679, class_Rings_Oordered__comm__semiring(_217681)], (354 ^ _206868) ^ [_217974, _217976] : [-(class_Rings_Olinordered__semiring__1(_217974)), _217976 = _217974, class_Rings_Olinordered__semiring__1(_217976)], (364 ^ _206868) ^ [_218269, _218271] : [-(class_Groups_Oordered__ab__group__add(_218269)), _218271 = _218269, class_Groups_Oordered__ab__group__add(_218271)], (374 ^ _206868) ^ [_218564, _218566] : [-(class_Groups_Ocancel__comm__monoid__add(_218564)), _218566 = _218564, class_Groups_Ocancel__comm__monoid__add(_218566)], (384 ^ _206868) ^ [_218859, _218861] : [-(class_Groups_Ocancel__semigroup__add(_218859)), _218861 = _218859, class_Groups_Ocancel__semigroup__add(_218861)], (394 ^ _206868) ^ [_219154, _219156] : [-(class_Rings_Olinordered__semiring(_219154)), _219156 = _219154, class_Rings_Olinordered__semiring(_219156)], (404 ^ _206868) ^ [_219449, _219451] : [-(class_Rings_Olinordered__semidom(_219449)), _219451 = _219449, class_Rings_Olinordered__semidom(_219451)], (414 ^ _206868) ^ [_219744, _219746] : [-(class_Groups_Oab__semigroup__mult(_219744)), _219746 = _219744, class_Groups_Oab__semigroup__mult(_219746)], (424 ^ _206868) ^ [_220039, _220041] : [-(class_Groups_Ocomm__monoid__mult(_220039)), _220041 = _220039, class_Groups_Ocomm__monoid__mult(_220041)], (434 ^ _206868) ^ [_220334, _220336] : [-(class_Groups_Oab__semigroup__add(_220334)), _220336 = _220334, class_Groups_Oab__semigroup__add(_220336)], (444 ^ _206868) ^ [_220629, _220631] : [-(class_Rings_Oordered__semiring(_220629)), _220631 = _220629, class_Rings_Oordered__semiring(_220631)], (454 ^ _206868) ^ [_220924, _220926] : [-(class_Rings_Ono__zero__divisors(_220924)), _220926 = _220924, class_Rings_Ono__zero__divisors(_220926)], (464 ^ _206868) ^ [_221219, _221221] : [-(class_Rings_Olinordered__ring(_221219)), _221221 = _221219, class_Rings_Olinordered__ring(_221221)], (474 ^ _206868) ^ [_221514, _221516] : [-(class_Rings_Ocomm__semiring(_221514)), _221516 = _221514, class_Rings_Ocomm__semiring(_221516)], (484 ^ _206868) ^ [_221809, _221811] : [-(class_Rings_Ozero__neq__one(_221809)), _221811 = _221809, class_Rings_Ozero__neq__one(_221811)], (494 ^ _206868) ^ [_222104, _222106] : [-(class_Rings_Oordered__ring(_222104)), _222106 = _222104, class_Rings_Oordered__ring(_222106)], (504 ^ _206868) ^ [_222399, _222401] : [-(class_Orderings_Opreorder(_222399)), _222401 = _222399, class_Orderings_Opreorder(_222401)], (514 ^ _206868) ^ [_222694, _222696] : [-(class_Orderings_Olinorder(_222694)), _222696 = _222694, class_Orderings_Olinorder(_222696)], (524 ^ _206868) ^ [_222989, _222991] : [-(class_Groups_Omonoid__mult(_222989)), _222991 = _222989, class_Groups_Omonoid__mult(_222991)], (534 ^ _206868) ^ [_223284, _223286] : [-(class_Groups_Ocomm__monoid__add(_223284)), _223286 = _223284, class_Groups_Ocomm__monoid__add(_223286)], (544 ^ _206868) ^ [_223579, _223581] : [-(class_Groups_Omonoid__add(_223579)), _223581 = _223579, class_Groups_Omonoid__add(_223581)], (554 ^ _206868) ^ [_223874, _223876] : [-(class_Rings_Osemiring__0(_223874)), _223876 = _223874, class_Rings_Osemiring__0(_223876)], (564 ^ _206868) ^ [_224169, _224171] : [-(class_Groups_Ogroup__add(_224169)), _224171 = _224169, class_Groups_Ogroup__add(_224171)], (574 ^ _206868) ^ [_224464, _224466] : [-(class_Rings_Omult__zero(_224464)), _224466 = _224464, class_Rings_Omult__zero(_224466)], (584 ^ _206868) ^ [_224759, _224761] : [-(class_Orderings_Oorder(_224759)), _224761 = _224759, class_Orderings_Oorder(_224761)], (594 ^ _206868) ^ [_225054, _225056] : [-(class_Int_Oring__char__0(_225054)), _225056 = _225054, class_Int_Oring__char__0(_225056)], (604 ^ _206868) ^ [_225349, _225351] : [-(class_Rings_Ocomm__semiring__0(_225349)), _225351 = _225349, class_Rings_Ocomm__semiring__0(_225351)], (614 ^ _206868) ^ [_225644, _225646] : [-(class_Rings_Osemiring(_225644)), _225646 = _225644, class_Rings_Osemiring(_225646)], (624 ^ _206868) ^ [_225939, _225941] : [-(class_Orderings_Oord(_225939)), _225941 = _225939, class_Orderings_Oord(_225941)], (634 ^ _206868) ^ [_226234, _226236] : [-(class_Groups_Oab__group__add(_226234)), _226236 = _226234, class_Groups_Oab__group__add(_226236)], (644 ^ _206868) ^ [_226529, _226531] : [-(class_Groups_Ouminus(_226529)), _226531 = _226529, class_Groups_Ouminus(_226531)], (654 ^ _206868) ^ [_226824, _226826] : [-(class_Rings_Olinordered__idom(_226824)), _226826 = _226824, class_Rings_Olinordered__idom(_226826)], (664 ^ _206868) ^ [_227119, _227121] : [-(class_Groups_Osgn__if(_227119)), _227121 = _227119, class_Groups_Osgn__if(_227121)], (674 ^ _206868) ^ [_227414, _227416] : [-(class_Rings_Ocomm__ring__1(_227414)), _227416 = _227414, class_Rings_Ocomm__ring__1(_227416)], (684 ^ _206868) ^ [_227709, _227711] : [-(class_Rings_Oring__1(_227709)), _227711 = _227709, class_Rings_Oring__1(_227711)], (694 ^ _206868) ^ [_228004, _228006] : [-(class_Power_Opower(_228004)), _228006 = _228004, class_Power_Opower(_228006)], (704 ^ _206868) ^ [_228299, _228301] : [-(class_Groups_Ozero(_228299)), _228301 = _228299, class_Groups_Ozero(_228301)], (714 ^ _206868) ^ [_228594, _228596] : [-(class_Rings_Ocomm__ring(_228594)), _228596 = _228594, class_Rings_Ocomm__ring(_228596)], (724 ^ _206868) ^ [_228889, _228891] : [-(class_Rings_Oring(_228889)), _228891 = _228889, class_Rings_Oring(_228891)], (734 ^ _206868) ^ [_229184, _229186] : [-(class_Rings_Oidom(_229184)), _229186 = _229184, class_Rings_Oidom(_229186)], (744 ^ _206868) ^ [_229479, _229481] : [-(class_Groups_Oone(_229479)), _229481 = _229479, class_Groups_Oone(_229481)], (754 ^ _206868) ^ [_229774, _229776] : [-(class_Rings_Ocomm__semiring__1(_229774)), _229776 = _229774, class_Rings_Ocomm__semiring__1(_229776)], (764 ^ _206868) ^ [_230069, _230071] : [-(class_Rings_Odvd(_230069)), _230071 = _230069, class_Rings_Odvd(_230071)], (774 ^ _206868) ^ [_230364, _230366] : [-(hBOOL(_230364)), _230366 = _230364, hBOOL(_230366)], (784 ^ _206868) ^ [_230715, _230717, _230719, _230721, _230723, _230725] : [-(c_Orderings_Oord__class_Oless__eq(_230723, _230719, _230715)), c_Orderings_Oord__class_Oless__eq(_230725, _230721, _230717), _230725 = _230723, _230721 = _230719, _230717 = _230715], (802 ^ _206868) ^ [_231304, _231306, _231308, _231310, _231312, _231314] : [-(c_Orderings_Oord__class_Oless(_231312, _231308, _231304)), c_Orderings_Oord__class_Oless(_231314, _231310, _231306), _231314 = _231312, _231310 = _231308, _231306 = _231304], (1212 ^ _206868) ^ [_246896, _246898] : [hAPP(_246896, 1213 ^ [_246896, _246898]) = hAPP(_246898, 1213 ^ [_246896, _246898]), -(_246896 = _246898)], (1219 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_r))], (1236 ^ _206868) ^ [_247863] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _247863, 1220 ^ []), 1241 ^ _206868 : [(1242 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 1240 ^ [_247863]), v_r))], (1244 ^ _206868) ^ [] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), 1240 ^ [_247863])) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, 1239 ^ [_247863]))], (1246 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _247863, 1239 ^ [_247863]))]]], (1222 ^ _206868) ^ [_247341] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _247341, 1220 ^ [])), 1223 ^ _206868 : [(1224 ^ _206868) ^ [_247457] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _247341, _247457), 1225 ^ _206868 : [(1226 ^ _206868) ^ [_247565] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _247565), v_r), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), _247565)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _247457)]]]]], (1249 ^ _206868) ^ [_248472] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _248472, 1247 ^ [])), 1250 ^ _206868 : [(1251 ^ _206868) ^ [_248576] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _248576), v_r), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), _248576)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _248472)]]], (1259 ^ _206868) ^ [_248863, _248865] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _248863), v_r), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), _248863)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _248865), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _248865, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1269 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_r))], (1271 ^ _206868) ^ [] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))))], (1273 ^ _206868) ^ [_249269] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _249269)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _249269)))], (1277 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 1275 ^ []), v_r))], (1279 ^ _206868) ^ [] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), 1275 ^ [])) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, 1274 ^ []))], (1281 ^ _206868) ^ [_249608, _249610] : [class_Orderings_Opreorder(_249608), -(c_Orderings_Oord__class_Oless__eq(_249608, _249610, _249610))], (1287 ^ _206868) ^ [_249832, _249834, _249836] : [class_Rings_Ocomm__ring(_249832), -(hAPP(c_Polynomial_Opoly(_249832, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_249832), _249834)), _249836) = c_Groups_Ouminus__class_Ouminus(_249832, hAPP(c_Polynomial_Opoly(_249832, _249834), _249836)))], (1293 ^ _206868) ^ [_250086, _250088] : [class_RealVector_Oreal__normed__vector(_250086), -(c_RealVector_Onorm__class_Onorm(_250086, c_Groups_Ouminus__class_Ouminus(_250086, _250088)) = c_RealVector_Onorm__class_Onorm(_250086, _250088))], (1299 ^ _206868) ^ [_250341, _250343] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _250341, _250343), 1302 ^ _206868 : [(1303 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _250341, _250343))], (1305 ^ _206868) ^ [] : [_250341 = _250343]]], (1307 ^ _206868) ^ [_250583, _250585] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _250583, _250585)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _250583, _250585), -(_250583 = _250585)], (1327 ^ _206868) ^ [_251176, _251178] : [1328 ^ _206868 : [(1329 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _251176, _251178)], (1331 ^ _206868) ^ [] : [_251176 = _251178]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _251176, _251178))], (1317 ^ _206868) ^ [_250920, _250922] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _250920, _250922), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _250920, _250922)), -(_250920 = _250922)], (1335 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_r)), 1339 ^ _206868 : [(1340 ^ _206868) ^ [_251580] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _251580), v_r), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), 1338 ^ [])), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), _251580))))]]], (1346 ^ _206868) ^ [_251825, _251827, _251829] : [class_Groups_Oordered__ab__group__add(_251825), 1349 ^ _206868 : [(1350 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_251825, _251827, c_Groups_Ouminus__class_Ouminus(_251825, _251829)), -(c_Orderings_Oord__class_Oless(_251825, _251829, c_Groups_Ouminus__class_Ouminus(_251825, _251827)))], (1356 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_251825, _251829, c_Groups_Ouminus__class_Ouminus(_251825, _251827)), -(c_Orderings_Oord__class_Oless(_251825, _251827, c_Groups_Ouminus__class_Ouminus(_251825, _251829)))]]], (1362 ^ _206868) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (1364 ^ _206868) ^ [_252361] : [class_RealVector_Oreal__normed__algebra__1(_252361), -(c_RealVector_Onorm__class_Onorm(_252361, c_Groups_Oone__class_Oone(_252361)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (1370 ^ _206868) ^ [_252559] : [class_RealVector_Oreal__normed__vector(_252559), -(c_RealVector_Onorm__class_Onorm(_252559, c_Groups_Ozero__class_Ozero(_252559)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1376 ^ _206868) ^ [_252771, _252773] : [class_Rings_Ocomm__semiring__1(_252771), -(hAPP(c_Polynomial_Opoly(_252771, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_252771))), _252773) = c_Groups_Oone__class_Oone(_252771))], (1382 ^ _206868) ^ [_253003, _253005] : [class_Rings_Ocomm__semiring__0(_253003), -(hAPP(c_Polynomial_Opoly(_253003, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_253003))), _253005) = c_Groups_Ozero__class_Ozero(_253003))], (1388 ^ _206868) ^ [_253235, _253237] : [class_Groups_Oone(_253235), 1391 ^ _206868 : [(1392 ^ _206868) ^ [] : [c_Groups_Oone__class_Oone(_253235) = _253237, -(_253237 = c_Groups_Oone__class_Oone(_253235))], (1398 ^ _206868) ^ [] : [_253237 = c_Groups_Oone__class_Oone(_253235), -(c_Groups_Oone__class_Oone(_253235) = _253237)]]], (1404 ^ _206868) ^ [_253705, _253707] : [class_Groups_Ozero(_253705), 1407 ^ _206868 : [(1408 ^ _206868) ^ [] : [c_Groups_Ozero__class_Ozero(_253705) = _253707, -(_253707 = c_Groups_Ozero__class_Ozero(_253705))], (1414 ^ _206868) ^ [] : [_253707 = c_Groups_Ozero__class_Ozero(_253705), -(c_Groups_Ozero__class_Ozero(_253705) = _253707)]]], (1420 ^ _206868) ^ [_254175, _254177] : [class_RealVector_Oreal__normed__vector(_254175), 1423 ^ _206868 : [(1424 ^ _206868) ^ [] : [c_RealVector_Onorm__class_Onorm(_254175, _254177) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_254177 = c_Groups_Ozero__class_Ozero(_254175))], (1430 ^ _206868) ^ [] : [_254177 = c_Groups_Ozero__class_Ozero(_254175), -(c_RealVector_Onorm__class_Onorm(_254175, _254177) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1436 ^ _206868) ^ [_254648, _254650] : [class_Groups_Olinordered__ab__group__add(_254648), 1439 ^ _206868 : [(1440 ^ _206868) ^ [] : [c_Groups_Ouminus__class_Ouminus(_254648, _254650) = _254650, -(_254650 = c_Groups_Ozero__class_Ozero(_254648))], (1446 ^ _206868) ^ [] : [_254650 = c_Groups_Ozero__class_Ozero(_254648), -(c_Groups_Ouminus__class_Ouminus(_254648, _254650) = _254650)]]], (1452 ^ _206868) ^ [_255121, _255123] : [class_Groups_Ogroup__add(_255121), 1455 ^ _206868 : [(1456 ^ _206868) ^ [] : [c_Groups_Ouminus__class_Ouminus(_255121, _255123) = c_Groups_Ozero__class_Ozero(_255121), -(_255123 = c_Groups_Ozero__class_Ozero(_255121))], (1462 ^ _206868) ^ [] : [_255123 = c_Groups_Ozero__class_Ozero(_255121), -(c_Groups_Ouminus__class_Ouminus(_255121, _255123) = c_Groups_Ozero__class_Ozero(_255121))]]], (1468 ^ _206868) ^ [_255600, _255602] : [class_Groups_Olinordered__ab__group__add(_255600), 1471 ^ _206868 : [(1472 ^ _206868) ^ [] : [_255602 = c_Groups_Ouminus__class_Ouminus(_255600, _255602), -(_255602 = c_Groups_Ozero__class_Ozero(_255600))], (1478 ^ _206868) ^ [] : [_255602 = c_Groups_Ozero__class_Ozero(_255600), -(_255602 = c_Groups_Ouminus__class_Ouminus(_255600, _255602))]]], (1484 ^ _206868) ^ [_256073, _256075] : [class_Groups_Ogroup__add(_256073), 1487 ^ _206868 : [(1488 ^ _206868) ^ [] : [c_Groups_Ozero__class_Ozero(_256073) = c_Groups_Ouminus__class_Ouminus(_256073, _256075), -(c_Groups_Ozero__class_Ozero(_256073) = _256075)], (1494 ^ _206868) ^ [] : [c_Groups_Ozero__class_Ozero(_256073) = _256075, -(c_Groups_Ozero__class_Ozero(_256073) = c_Groups_Ouminus__class_Ouminus(_256073, _256075))]]], (1500 ^ _206868) ^ [_256538] : [class_Groups_Ogroup__add(_256538), -(c_Groups_Ouminus__class_Ouminus(_256538, c_Groups_Ozero__class_Ozero(_256538)) = c_Groups_Ozero__class_Ozero(_256538))], (1506 ^ _206868) ^ [_256754, _256756] : [class_RealVector_Oreal__normed__vector(_256754), 1509 ^ _206868 : [(1510 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_256754, _256756), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_256756 = c_Groups_Ozero__class_Ozero(_256754))], (1516 ^ _206868) ^ [] : [_256756 = c_Groups_Ozero__class_Ozero(_256754), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_256754, _256756), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (1522 ^ _206868) ^ [_257230, _257232] : [class_RealVector_Oreal__normed__vector(_257230), 1525 ^ _206868 : [(1526 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_257230, _257232)), _257232 = c_Groups_Ozero__class_Ozero(_257230)], (1532 ^ _206868) ^ [] : [-(_257232 = c_Groups_Ozero__class_Ozero(_257230)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_257230, _257232)))]]], (1538 ^ _206868) ^ [_257708, _257710] : [class_Groups_Olinordered__ab__group__add(_257708), 1541 ^ _206868 : [(1542 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_257708, c_Groups_Ouminus__class_Ouminus(_257708, _257710), _257710), -(c_Orderings_Oord__class_Oless__eq(_257708, c_Groups_Ozero__class_Ozero(_257708), _257710))], (1548 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_257708, c_Groups_Ozero__class_Ozero(_257708), _257710), -(c_Orderings_Oord__class_Oless__eq(_257708, c_Groups_Ouminus__class_Ouminus(_257708, _257710), _257710))]]], (1554 ^ _206868) ^ [_258187, _258189] : [class_Groups_Oordered__ab__group__add(_258187), 1557 ^ _206868 : [(1558 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_258187, c_Groups_Ouminus__class_Ouminus(_258187, _258189), c_Groups_Ozero__class_Ozero(_258187)), -(c_Orderings_Oord__class_Oless__eq(_258187, c_Groups_Ozero__class_Ozero(_258187), _258189))], (1564 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_258187, c_Groups_Ozero__class_Ozero(_258187), _258189), -(c_Orderings_Oord__class_Oless__eq(_258187, c_Groups_Ouminus__class_Ouminus(_258187, _258189), c_Groups_Ozero__class_Ozero(_258187)))]]], (1570 ^ _206868) ^ [_258672, _258674] : [class_Groups_Olinordered__ab__group__add(_258672), 1573 ^ _206868 : [(1574 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_258672, _258674, c_Groups_Ouminus__class_Ouminus(_258672, _258674)), -(c_Orderings_Oord__class_Oless__eq(_258672, _258674, c_Groups_Ozero__class_Ozero(_258672)))], (1580 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_258672, _258674, c_Groups_Ozero__class_Ozero(_258672)), -(c_Orderings_Oord__class_Oless__eq(_258672, _258674, c_Groups_Ouminus__class_Ouminus(_258672, _258674)))]]], (1586 ^ _206868) ^ [_259151, _259153] : [class_Groups_Oordered__ab__group__add(_259151), 1589 ^ _206868 : [(1590 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_259151, c_Groups_Ozero__class_Ozero(_259151), c_Groups_Ouminus__class_Ouminus(_259151, _259153)), -(c_Orderings_Oord__class_Oless__eq(_259151, _259153, c_Groups_Ozero__class_Ozero(_259151)))], (1596 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_259151, _259153, c_Groups_Ozero__class_Ozero(_259151)), -(c_Orderings_Oord__class_Oless__eq(_259151, c_Groups_Ozero__class_Ozero(_259151), c_Groups_Ouminus__class_Ouminus(_259151, _259153)))]]], (1602 ^ _206868) ^ [_259636, _259638] : [class_Groups_Olinordered__ab__group__add(_259636), 1605 ^ _206868 : [(1606 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_259636, c_Groups_Ouminus__class_Ouminus(_259636, _259638), _259638), -(c_Orderings_Oord__class_Oless(_259636, c_Groups_Ozero__class_Ozero(_259636), _259638))], (1612 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_259636, c_Groups_Ozero__class_Ozero(_259636), _259638), -(c_Orderings_Oord__class_Oless(_259636, c_Groups_Ouminus__class_Ouminus(_259636, _259638), _259638))]]], (1618 ^ _206868) ^ [_260115, _260117] : [class_Groups_Oordered__ab__group__add(_260115), 1621 ^ _206868 : [(1622 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_260115, c_Groups_Ouminus__class_Ouminus(_260115, _260117), c_Groups_Ozero__class_Ozero(_260115)), -(c_Orderings_Oord__class_Oless(_260115, c_Groups_Ozero__class_Ozero(_260115), _260117))], (1628 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_260115, c_Groups_Ozero__class_Ozero(_260115), _260117), -(c_Orderings_Oord__class_Oless(_260115, c_Groups_Ouminus__class_Ouminus(_260115, _260117), c_Groups_Ozero__class_Ozero(_260115)))]]], (1634 ^ _206868) ^ [_260600, _260602] : [class_Groups_Oordered__ab__group__add(_260600), 1637 ^ _206868 : [(1638 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_260600, c_Groups_Ozero__class_Ozero(_260600), c_Groups_Ouminus__class_Ouminus(_260600, _260602)), -(c_Orderings_Oord__class_Oless(_260600, _260602, c_Groups_Ozero__class_Ozero(_260600)))], (1644 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_260600, _260602, c_Groups_Ozero__class_Ozero(_260600)), -(c_Orderings_Oord__class_Oless(_260600, c_Groups_Ozero__class_Ozero(_260600), c_Groups_Ouminus__class_Ouminus(_260600, _260602)))]]], (1650 ^ _206868) ^ [_261085, _261087] : [class_RealVector_Oreal__normed__vector(_261085), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_261085, _261087)))], (1656 ^ _206868) ^ [_261301, _261303] : [class_RealVector_Oreal__normed__vector(_261301), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_261301, _261303), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1662 ^ _206868) ^ [_261532, _261534, _261536] : [class_Orderings_Olinorder(_261532), -(c_Orderings_Oord__class_Oless__eq(_261532, _261534, _261536)), -(c_Orderings_Oord__class_Oless__eq(_261532, _261536, _261534))], (1672 ^ _206868) ^ [_261888, _261890, _261892, _261894, _261896] : [class_Orderings_Oord(_261888), c_Orderings_Oord__class_Oless__eq(tc_fun(_261890, _261888), _261892, _261894), -(c_Orderings_Oord__class_Oless__eq(_261888, hAPP(_261892, _261896), hAPP(_261894, _261896)))], (1682 ^ _206868) ^ [_262265, _262267, _262269, _262271] : [class_Orderings_Oorder(_262265), c_Orderings_Oord__class_Oless__eq(_262265, _262267, _262269), c_Orderings_Oord__class_Oless__eq(_262265, _262271, _262267), -(c_Orderings_Oord__class_Oless__eq(_262265, _262271, _262269))], (1696 ^ _206868) ^ [_262699, _262701, _262703] : [class_Orderings_Oorder(_262699), c_Orderings_Oord__class_Oless__eq(_262699, _262701, _262703), c_Orderings_Oord__class_Oless__eq(_262699, _262703, _262701), -(_262703 = _262701)], (1710 ^ _206868) ^ [_263131, _263133, _263135, _263137] : [class_Orderings_Opreorder(_263131), c_Orderings_Oord__class_Oless__eq(_263131, _263133, _263135), c_Orderings_Oord__class_Oless__eq(_263131, _263135, _263137), -(c_Orderings_Oord__class_Oless__eq(_263131, _263133, _263137))], (1724 ^ _206868) ^ [_263565, _263567, _263569] : [class_Orderings_Oorder(_263565), c_Orderings_Oord__class_Oless__eq(_263565, _263567, _263569), c_Orderings_Oord__class_Oless__eq(_263565, _263569, _263567), -(_263567 = _263569)], (1738 ^ _206868) ^ [_263997, _263999, _264001, _264003] : [class_Orderings_Oorder(_263997), c_Orderings_Oord__class_Oless__eq(_263997, _263999, _264001), _263999 = _264003, -(c_Orderings_Oord__class_Oless__eq(_263997, _264003, _264001))], (1752 ^ _206868) ^ [_264443, _264445, _264447, _264449] : [class_Orderings_Oord(_264443), c_Orderings_Oord__class_Oless__eq(_264443, _264445, _264447), _264447 = _264449, -(c_Orderings_Oord__class_Oless__eq(_264443, _264445, _264449))], (1766 ^ _206868) ^ [_264889, _264891, _264893, _264895] : [class_Orderings_Oorder(_264889), _264891 = _264893, c_Orderings_Oord__class_Oless__eq(_264889, _264895, _264893), -(c_Orderings_Oord__class_Oless__eq(_264889, _264895, _264891))], (1780 ^ _206868) ^ [_265335, _265337, _265339, _265341] : [class_Orderings_Oord(_265335), _265337 = _265339, c_Orderings_Oord__class_Oless__eq(_265335, _265339, _265341), -(c_Orderings_Oord__class_Oless__eq(_265335, _265337, _265341))], (1794 ^ _206868) ^ [_265767, _265769, _265771] : [class_Orderings_Oorder(_265767), c_Orderings_Oord__class_Oless__eq(_265767, _265769, _265771), 1801 ^ _206868 : [(1802 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_265767, _265771, _265769), -(_265771 = _265769)], (1808 ^ _206868) ^ [] : [_265771 = _265769, -(c_Orderings_Oord__class_Oless__eq(_265767, _265771, _265769))]]], (1814 ^ _206868) ^ [_266381, _266383, _266385, _266387, _266389] : [class_Orderings_Oord(_266381), c_Orderings_Oord__class_Oless__eq(tc_fun(_266383, _266381), _266385, _266387), -(c_Orderings_Oord__class_Oless__eq(_266381, hAPP(_266385, _266389), hAPP(_266387, _266389)))], (1824 ^ _206868) ^ [_266744, _266746, _266748] : [class_Orderings_Opreorder(_266744), _266746 = _266748, -(c_Orderings_Oord__class_Oless__eq(_266744, _266746, _266748))], (1834 ^ _206868) ^ [_267067, _267069, _267071] : [class_Orderings_Oorder(_267067), 1837 ^ _206868 : [(1838 ^ _206868) ^ [] : [_267069 = _267071, 1841 ^ _206868 : [(1842 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_267067, _267069, _267071))], (1844 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_267067, _267071, _267069))]]], (1846 ^ _206868) ^ [] : [-(_267069 = _267071), c_Orderings_Oord__class_Oless__eq(_267067, _267069, _267071), c_Orderings_Oord__class_Oless__eq(_267067, _267071, _267069)]]], (1856 ^ _206868) ^ [_267725, _267727, _267729] : [class_Orderings_Olinorder(_267725), -(c_Orderings_Oord__class_Oless__eq(_267725, _267727, _267729)), -(c_Orderings_Oord__class_Oless__eq(_267725, _267729, _267727))], (1866 ^ _206868) ^ [_268065, _268067, _268069, _268071] : [class_Orderings_Oord(_268065), 1869 ^ _206868 : [(1870 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_268067, _268065), _268069, _268071), 1873 ^ _206868 : [(1874 ^ _206868) ^ [_268324] : [-(c_Orderings_Oord__class_Oless__eq(_268065, hAPP(_268069, _268324), hAPP(_268071, _268324)))]]], (1876 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_268065, hAPP(_268069, 1877 ^ [_268065, _268067, _268069, _268071]), hAPP(_268071, 1877 ^ [_268065, _268067, _268069, _268071])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_268067, _268065), _268069, _268071))]]], (1883 ^ _206868) ^ [_268706, _268708, _268710] : [class_Orderings_Olinorder(_268706), -(c_Orderings_Oord__class_Oless(_268706, _268708, _268710)), -(_268708 = _268710), -(c_Orderings_Oord__class_Oless(_268706, _268710, _268708))], (1897 ^ _206868) ^ [_269130, _269132, _269134] : [class_Orderings_Opreorder(_269130), c_Orderings_Oord__class_Oless(_269130, _269132, _269134), c_Orderings_Oord__class_Oless(_269130, _269134, _269132)], (1907 ^ _206868) ^ [_269470, _269472, _269474, _269476] : [class_Orderings_Oorder(_269470), c_Orderings_Oord__class_Oless(_269470, _269472, _269474), c_Orderings_Oord__class_Oless(_269470, _269476, _269472), -(c_Orderings_Oord__class_Oless(_269470, _269476, _269474))], (1921 ^ _206868) ^ [_269918, _269920, _269922, _269924] : [class_Orderings_Opreorder(_269918), c_Orderings_Oord__class_Oless(_269918, _269920, _269922), c_Orderings_Oord__class_Oless(_269918, _269922, _269924), -(c_Orderings_Oord__class_Oless(_269918, _269920, _269924))], (1935 ^ _206868) ^ [_270366, _270368, _270370, _270372] : [class_Orderings_Oorder(_270366), c_Orderings_Oord__class_Oless(_270366, _270368, _270370), _270368 = _270372, -(c_Orderings_Oord__class_Oless(_270366, _270372, _270370))], (1949 ^ _206868) ^ [_270812, _270814, _270816, _270818] : [class_Orderings_Oord(_270812), c_Orderings_Oord__class_Oless(_270812, _270814, _270816), _270816 = _270818, -(c_Orderings_Oord__class_Oless(_270812, _270814, _270818))], (1963 ^ _206868) ^ [_271258, _271260, _271262, _271264] : [class_Orderings_Oorder(_271258), _271260 = _271262, c_Orderings_Oord__class_Oless(_271258, _271264, _271262), -(c_Orderings_Oord__class_Oless(_271258, _271264, _271260))], (1977 ^ _206868) ^ [_271704, _271706, _271708, _271710] : [class_Orderings_Oord(_271704), _271706 = _271708, c_Orderings_Oord__class_Oless(_271704, _271708, _271710), -(c_Orderings_Oord__class_Oless(_271704, _271706, _271710))], (1991 ^ _206868) ^ [_272136, _272138, _272140] : [class_Orderings_Oorder(_272136), c_Orderings_Oord__class_Oless(_272136, _272138, _272140), c_Orderings_Oord__class_Oless(_272136, _272140, _272138)], (2001 ^ _206868) ^ [_272462, _272464, _272466] : [class_Orderings_Opreorder(_272462), c_Orderings_Oord__class_Oless(_272462, _272464, _272466), c_Orderings_Oord__class_Oless(_272462, _272466, _272464)], (2011 ^ _206868) ^ [_272788, _272790, _272792] : [class_Orderings_Oorder(_272788), c_Orderings_Oord__class_Oless(_272788, _272790, _272792), _272792 = _272790], (2021 ^ _206868) ^ [_273112, _273114, _273116] : [class_Orderings_Oorder(_273112), c_Orderings_Oord__class_Oless(_273112, _273114, _273116), _273114 = _273116], (2031 ^ _206868) ^ [_273436, _273438, _273440] : [class_Orderings_Opreorder(_273436), c_Orderings_Oord__class_Oless(_273436, _273438, _273440), c_Orderings_Oord__class_Oless(_273436, _273440, _273438)], (2041 ^ _206868) ^ [_273762, _273764, _273766] : [class_Orderings_Opreorder(_273762), c_Orderings_Oord__class_Oless(_273762, _273764, _273766), c_Orderings_Oord__class_Oless(_273762, _273766, _273764)], (2051 ^ _206868) ^ [_274088, _274090, _274092] : [class_Orderings_Oorder(_274088), c_Orderings_Oord__class_Oless(_274088, _274090, _274092), _274090 = _274092], (2061 ^ _206868) ^ [_274412, _274414, _274416] : [class_Orderings_Olinorder(_274412), -(_274414 = _274416), -(c_Orderings_Oord__class_Oless(_274412, _274414, _274416)), -(c_Orderings_Oord__class_Oless(_274412, _274416, _274414))], (2075 ^ _206868) ^ [_274836, _274838, _274840] : [class_Orderings_Olinorder(_274836), -(c_Orderings_Oord__class_Oless(_274836, _274838, _274840)), 2082 ^ _206868 : [(2083 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_274836, _274840, _274838)), -(_274840 = _274838)], (2089 ^ _206868) ^ [] : [_274840 = _274838, c_Orderings_Oord__class_Oless(_274836, _274840, _274838)]]], (2095 ^ _206868) ^ [_275427, _275429, _275431] : [class_Orderings_Olinorder(_275427), -(c_Orderings_Oord__class_Oless(_275427, _275429, _275431)), -(_275429 = _275431), -(c_Orderings_Oord__class_Oless(_275427, _275431, _275429))], (2109 ^ _206868) ^ [_275847, _275849, _275851] : [class_Orderings_Olinorder(_275847), 2112 ^ _206868 : [(2123 ^ _206868) ^ [] : [2124 ^ _206868 : [(2125 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_275847, _275851, _275849)], (2127 ^ _206868) ^ [] : [_275849 = _275851]], c_Orderings_Oord__class_Oless(_275847, _275849, _275851)], (2113 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_275847, _275849, _275851)), -(c_Orderings_Oord__class_Oless(_275847, _275851, _275849)), -(_275849 = _275851)]]], (2131 ^ _206868) ^ [_276507, _276509, _276511] : [class_Orderings_Olinorder(_276507), 2134 ^ _206868 : [(2145 ^ _206868) ^ [] : [2146 ^ _206868 : [(2147 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_276507, _276509, _276511)], (2149 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_276507, _276511, _276509)]], _276509 = _276511], (2135 ^ _206868) ^ [] : [-(_276509 = _276511), -(c_Orderings_Oord__class_Oless(_276507, _276509, _276511)), -(c_Orderings_Oord__class_Oless(_276507, _276511, _276509))]]], (2153 ^ _206868) ^ [_277153, _277155] : [class_Orderings_Opreorder(_277153), c_Orderings_Oord__class_Oless(_277153, _277155, _277155)], (2159 ^ _206868) ^ [_277378, _277380, _277382] : [class_Groups_Ogroup__add(_277378), 2162 ^ _206868 : [(2163 ^ _206868) ^ [] : [c_Groups_Ouminus__class_Ouminus(_277378, _277380) = c_Groups_Ouminus__class_Ouminus(_277378, _277382), -(_277380 = _277382)], (2169 ^ _206868) ^ [] : [_277380 = _277382, -(c_Groups_Ouminus__class_Ouminus(_277378, _277380) = c_Groups_Ouminus__class_Ouminus(_277378, _277382))]]], (2175 ^ _206868) ^ [_277884, _277886, _277888] : [class_Groups_Ogroup__add(_277884), 2178 ^ _206868 : [(2179 ^ _206868) ^ [] : [c_Groups_Ouminus__class_Ouminus(_277884, _277886) = _277888, -(c_Groups_Ouminus__class_Ouminus(_277884, _277888) = _277886)], (2185 ^ _206868) ^ [] : [c_Groups_Ouminus__class_Ouminus(_277884, _277888) = _277886, -(c_Groups_Ouminus__class_Ouminus(_277884, _277886) = _277888)]]], (2191 ^ _206868) ^ [_278390, _278392, _278394] : [class_Groups_Ogroup__add(_278390), 2194 ^ _206868 : [(2195 ^ _206868) ^ [] : [_278392 = c_Groups_Ouminus__class_Ouminus(_278390, _278394), -(_278394 = c_Groups_Ouminus__class_Ouminus(_278390, _278392))], (2201 ^ _206868) ^ [] : [_278394 = c_Groups_Ouminus__class_Ouminus(_278390, _278392), -(_278392 = c_Groups_Ouminus__class_Ouminus(_278390, _278394))]]], (2207 ^ _206868) ^ [_278882, _278884] : [class_Groups_Ogroup__add(_278882), -(c_Groups_Ouminus__class_Ouminus(_278882, c_Groups_Ouminus__class_Ouminus(_278882, _278884)) = _278884)], (2213 ^ _206868) ^ [_279102, _279104] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _279102, _279104), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _279104, _279102), -(_279102 = _279104)], (2223 ^ _206868) ^ [_279419, _279421, _279423] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _279419, _279421), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _279421, _279423), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _279419, _279423))], (2233 ^ _206868) ^ [_279734, _279736] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _279734, _279736)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _279736, _279734))], (2239 ^ _206868) ^ [_279920] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _279920, _279920))], (2241 ^ _206868) ^ [_280042, _280044, _280046] : [class_Int_Oring__char__0(_280042), class_Rings_Oidom(_280042), 2248 ^ _206868 : [(2249 ^ _206868) ^ [] : [c_Polynomial_Opoly(_280042, _280044) = c_Polynomial_Opoly(_280042, _280046), -(_280044 = _280046)], (2255 ^ _206868) ^ [] : [_280044 = _280046, -(c_Polynomial_Opoly(_280042, _280044) = c_Polynomial_Opoly(_280042, _280046))]]], (2261 ^ _206868) ^ [_280655, _280657, _280659, _280661] : [class_Orderings_Oorder(_280655), c_Orderings_Oord__class_Oless__eq(_280655, _280657, _280659), c_Orderings_Oord__class_Oless(_280655, _280661, _280657), -(c_Orderings_Oord__class_Oless(_280655, _280661, _280659))], (2275 ^ _206868) ^ [_281103, _281105, _281107, _281109] : [class_Orderings_Opreorder(_281103), c_Orderings_Oord__class_Oless__eq(_281103, _281105, _281107), c_Orderings_Oord__class_Oless(_281103, _281107, _281109), -(c_Orderings_Oord__class_Oless(_281103, _281105, _281109))], (2289 ^ _206868) ^ [_281551, _281553, _281555, _281557] : [class_Orderings_Oorder(_281551), c_Orderings_Oord__class_Oless(_281551, _281553, _281555), c_Orderings_Oord__class_Oless__eq(_281551, _281557, _281553), -(c_Orderings_Oord__class_Oless(_281551, _281557, _281555))], (2303 ^ _206868) ^ [_281999, _282001, _282003, _282005] : [class_Orderings_Opreorder(_281999), c_Orderings_Oord__class_Oless(_281999, _282001, _282003), c_Orderings_Oord__class_Oless__eq(_281999, _282003, _282005), -(c_Orderings_Oord__class_Oless(_281999, _282001, _282005))], (2317 ^ _206868) ^ [_282433, _282435, _282437] : [class_Orderings_Oorder(_282433), c_Orderings_Oord__class_Oless__eq(_282433, _282435, _282437), -(_282437 = _282435), -(c_Orderings_Oord__class_Oless(_282433, _282435, _282437))], (2331 ^ _206868) ^ [_282854, _282856, _282858] : [class_Orderings_Oorder(_282854), c_Orderings_Oord__class_Oless__eq(_282854, _282856, _282858), -(_282856 = _282858), -(c_Orderings_Oord__class_Oless(_282854, _282856, _282858))], (2345 ^ _206868) ^ [_283275, _283277, _283279] : [class_Orderings_Oorder(_283275), c_Orderings_Oord__class_Oless__eq(_283275, _283277, _283279), -(c_Orderings_Oord__class_Oless(_283275, _283277, _283279)), -(_283277 = _283279)], (2359 ^ _206868) ^ [_283694, _283696, _283698] : [class_Orderings_Olinorder(_283694), c_Orderings_Oord__class_Oless__eq(_283694, _283696, _283698), 2366 ^ _206868 : [(2367 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_283694, _283696, _283698)), -(_283696 = _283698)], (2373 ^ _206868) ^ [] : [_283696 = _283698, c_Orderings_Oord__class_Oless(_283694, _283696, _283698)]]], (2379 ^ _206868) ^ [_284282, _284284, _284286] : [class_Orderings_Opreorder(_284282), c_Orderings_Oord__class_Oless(_284282, _284284, _284286), -(c_Orderings_Oord__class_Oless__eq(_284282, _284284, _284286))], (2389 ^ _206868) ^ [_284607, _284609, _284611] : [class_Orderings_Olinorder(_284607), c_Orderings_Oord__class_Oless__eq(_284607, _284609, _284611), c_Orderings_Oord__class_Oless(_284607, _284611, _284609)], (2399 ^ _206868) ^ [_284933, _284935, _284937] : [class_Orderings_Oorder(_284933), -(_284935 = _284937), c_Orderings_Oord__class_Oless__eq(_284933, _284937, _284935), -(c_Orderings_Oord__class_Oless(_284933, _284937, _284935))], (2413 ^ _206868) ^ [_285354, _285356, _285358] : [class_Orderings_Oorder(_285354), -(_285356 = _285358), c_Orderings_Oord__class_Oless__eq(_285354, _285356, _285358), -(c_Orderings_Oord__class_Oless(_285354, _285356, _285358))], (2427 ^ _206868) ^ [_285775, _285777, _285779] : [class_Orderings_Olinorder(_285775), -(c_Orderings_Oord__class_Oless(_285775, _285777, _285779)), 2434 ^ _206868 : [(2435 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_285775, _285777, _285779), -(_285777 = _285779)], (2441 ^ _206868) ^ [] : [_285777 = _285779, -(c_Orderings_Oord__class_Oless__eq(_285775, _285777, _285779))]]], (2447 ^ _206868) ^ [_286364, _286366, _286368] : [class_Orderings_Olinorder(_286364), -(c_Orderings_Oord__class_Oless__eq(_286364, _286366, _286368)), -(c_Orderings_Oord__class_Oless(_286364, _286368, _286366))], (2457 ^ _206868) ^ [_286692, _286694, _286696] : [class_Orderings_Olinorder(_286692), -(c_Orderings_Oord__class_Oless(_286692, _286694, _286696)), -(c_Orderings_Oord__class_Oless__eq(_286692, _286696, _286694))], (2467 ^ _206868) ^ [_287020, _287022, _287024] : [class_Orderings_Oorder(_287020), 2470 ^ _206868 : [(2481 ^ _206868) ^ [] : [2482 ^ _206868 : [(2483 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_287020, _287022, _287024)], (2485 ^ _206868) ^ [] : [_287022 = _287024]], -(c_Orderings_Oord__class_Oless__eq(_287020, _287022, _287024))], (2471 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_287020, _287022, _287024), -(c_Orderings_Oord__class_Oless(_287020, _287022, _287024)), -(_287022 = _287024)]]], (2489 ^ _206868) ^ [_287678, _287680, _287682] : [class_Orderings_Opreorder(_287678), 2492 ^ _206868 : [(2493 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_287678, _287680, _287682), 2496 ^ _206868 : [(2497 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_287678, _287680, _287682))], (2499 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_287678, _287682, _287680)]]], (2501 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_287678, _287680, _287682)), c_Orderings_Oord__class_Oless__eq(_287678, _287680, _287682), -(c_Orderings_Oord__class_Oless__eq(_287678, _287682, _287680))]]], (2511 ^ _206868) ^ [_288341, _288343, _288345] : [class_Orderings_Oorder(_288341), 2514 ^ _206868 : [(2515 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_288341, _288343, _288345), 2518 ^ _206868 : [(2519 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_288341, _288343, _288345))], (2521 ^ _206868) ^ [] : [_288343 = _288345]]], (2523 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_288341, _288343, _288345)), c_Orderings_Oord__class_Oless__eq(_288341, _288343, _288345), -(_288343 = _288345)]]], (2533 ^ _206868) ^ [_289001, _289003, _289005] : [class_Orderings_Olinorder(_289001), -(c_Orderings_Oord__class_Oless__eq(_289001, _289003, _289005)), -(c_Orderings_Oord__class_Oless(_289001, _289005, _289003))], (2543 ^ _206868) ^ [_289327, _289329, _289331] : [class_Orderings_Olinorder(_289327), 2546 ^ _206868 : [(2547 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_289327, _289329, _289331)), -(c_Orderings_Oord__class_Oless(_289327, _289331, _289329))], (2553 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_289327, _289331, _289329), c_Orderings_Oord__class_Oless__eq(_289327, _289329, _289331)]]], (2559 ^ _206868) ^ [_289823, _289825, _289827] : [class_Orderings_Olinorder(_289823), 2562 ^ _206868 : [(2563 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_289823, _289825, _289827)), -(c_Orderings_Oord__class_Oless__eq(_289823, _289827, _289825))], (2569 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289823, _289827, _289825), c_Orderings_Oord__class_Oless(_289823, _289825, _289827)]]], (2575 ^ _206868) ^ [_290319, _290321, _290323] : [class_Groups_Oordered__ab__group__add(_290319), c_Orderings_Oord__class_Oless__eq(_290319, _290321, _290323), -(c_Orderings_Oord__class_Oless__eq(_290319, c_Groups_Ouminus__class_Ouminus(_290319, _290323), c_Groups_Ouminus__class_Ouminus(_290319, _290321)))], (2585 ^ _206868) ^ [_290656, _290658, _290660] : [class_Groups_Oordered__ab__group__add(_290656), 2588 ^ _206868 : [(2589 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290656, c_Groups_Ouminus__class_Ouminus(_290656, _290658), c_Groups_Ouminus__class_Ouminus(_290656, _290660)), -(c_Orderings_Oord__class_Oless__eq(_290656, _290660, _290658))], (2595 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290656, _290660, _290658), -(c_Orderings_Oord__class_Oless__eq(_290656, c_Groups_Ouminus__class_Ouminus(_290656, _290658), c_Groups_Ouminus__class_Ouminus(_290656, _290660)))]]], (2601 ^ _206868) ^ [_291168, _291170, _291172] : [class_Groups_Oordered__ab__group__add(_291168), 2604 ^ _206868 : [(2605 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_291168, c_Groups_Ouminus__class_Ouminus(_291168, _291170), _291172), -(c_Orderings_Oord__class_Oless__eq(_291168, c_Groups_Ouminus__class_Ouminus(_291168, _291172), _291170))], (2611 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_291168, c_Groups_Ouminus__class_Ouminus(_291168, _291172), _291170), -(c_Orderings_Oord__class_Oless__eq(_291168, c_Groups_Ouminus__class_Ouminus(_291168, _291170), _291172))]]], (2617 ^ _206868) ^ [_291680, _291682, _291684] : [class_Groups_Oordered__ab__group__add(_291680), 2620 ^ _206868 : [(2621 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_291680, _291682, c_Groups_Ouminus__class_Ouminus(_291680, _291684)), -(c_Orderings_Oord__class_Oless__eq(_291680, _291684, c_Groups_Ouminus__class_Ouminus(_291680, _291682)))], (2627 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_291680, _291684, c_Groups_Ouminus__class_Ouminus(_291680, _291682)), -(c_Orderings_Oord__class_Oless__eq(_291680, _291682, c_Groups_Ouminus__class_Ouminus(_291680, _291684)))]]], (2633 ^ _206868) ^ [_292192, _292194, _292196] : [class_Groups_Oordered__ab__group__add(_292192), 2636 ^ _206868 : [(2637 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_292192, c_Groups_Ouminus__class_Ouminus(_292192, _292194), c_Groups_Ouminus__class_Ouminus(_292192, _292196)), -(c_Orderings_Oord__class_Oless(_292192, _292196, _292194))], (2643 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_292192, _292196, _292194), -(c_Orderings_Oord__class_Oless(_292192, c_Groups_Ouminus__class_Ouminus(_292192, _292194), c_Groups_Ouminus__class_Ouminus(_292192, _292196)))]]], (2649 ^ _206868) ^ [_292704, _292706, _292708] : [class_Groups_Oordered__ab__group__add(_292704), 2652 ^ _206868 : [(2653 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_292704, c_Groups_Ouminus__class_Ouminus(_292704, _292706), _292708), -(c_Orderings_Oord__class_Oless(_292704, c_Groups_Ouminus__class_Ouminus(_292704, _292708), _292706))], (2659 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_292704, c_Groups_Ouminus__class_Ouminus(_292704, _292708), _292706), -(c_Orderings_Oord__class_Oless(_292704, c_Groups_Ouminus__class_Ouminus(_292704, _292706), _292708))]]], (2665 ^ _206868) ^ [_293202, _293204] : [class_Rings_Olinordered__idom(_293202), 2668 ^ _206868 : [(2669 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_293202, _293204, c_Groups_Ouminus__class_Ouminus(_293202, _293204)), -(c_Orderings_Oord__class_Oless(_293202, _293204, c_Groups_Ozero__class_Ozero(_293202)))], (2675 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_293202, _293204, c_Groups_Ozero__class_Ozero(_293202)), -(c_Orderings_Oord__class_Oless(_293202, _293204, c_Groups_Ouminus__class_Ouminus(_293202, _293204)))]]], (2681 ^ _206868) ^ [_293667] : [class_Rings_Olinordered__semidom(_293667), c_Orderings_Oord__class_Oless(_293667, c_Groups_Oone__class_Oone(_293667), c_Groups_Ozero__class_Ozero(_293667))], (2687 ^ _206868) ^ [_293866] : [class_Rings_Olinordered__semidom(_293866), -(c_Orderings_Oord__class_Oless(_293866, c_Groups_Ozero__class_Ozero(_293866), c_Groups_Oone__class_Oone(_293866)))], (2693 ^ _206868) ^ [_294064] : [class_Rings_Olinordered__semidom(_294064), c_Orderings_Oord__class_Oless__eq(_294064, c_Groups_Oone__class_Oone(_294064), c_Groups_Ozero__class_Ozero(_294064))], (2699 ^ _206868) ^ [_294263] : [class_Rings_Olinordered__semidom(_294263), -(c_Orderings_Oord__class_Oless__eq(_294263, c_Groups_Ozero__class_Ozero(_294263), c_Groups_Oone__class_Oone(_294263)))], (2705 ^ _206868) ^ [_294489, _294491, _294493] : [class_Lattices_Oboolean__algebra(_294489), c_Orderings_Oord__class_Oless__eq(_294489, _294491, _294493), -(c_Orderings_Oord__class_Oless__eq(_294489, c_Groups_Ouminus__class_Ouminus(_294489, _294493), c_Groups_Ouminus__class_Ouminus(_294489, _294491)))], (2715 ^ _206868) ^ [_294826, _294828, _294830] : [class_Lattices_Oboolean__algebra(_294826), 2718 ^ _206868 : [(2719 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_294826, c_Groups_Ouminus__class_Ouminus(_294826, _294828), c_Groups_Ouminus__class_Ouminus(_294826, _294830)), -(c_Orderings_Oord__class_Oless__eq(_294826, _294830, _294828))], (2725 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_294826, _294830, _294828), -(c_Orderings_Oord__class_Oless__eq(_294826, c_Groups_Ouminus__class_Ouminus(_294826, _294828), c_Groups_Ouminus__class_Ouminus(_294826, _294830)))]]], (2732 ^ _206868) ^ [_295402, _295404] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 2730 ^ [_295402, _295404]))], (2734 ^ _206868) ^ [_295485, _295487, _295489] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _295485), _295487), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _295489), _295485)), 2730 ^ [_295487, _295489]))], (2740 ^ _206868) ^ [_295731] : [class_Rings_Ozero__neq__one(_295731), c_Groups_Oone__class_Oone(_295731) = c_Groups_Ozero__class_Ozero(_295731)], (2746 ^ _206868) ^ [_295928] : [class_Rings_Ozero__neq__one(_295928), c_Groups_Ozero__class_Ozero(_295928) = c_Groups_Oone__class_Oone(_295928)], (2752 ^ _206868) ^ [_296139, _296141] : [class_RealVector_Oreal__normed__vector(_296139), 2755 ^ _206868 : [(2756 ^ _206868) ^ [] : [_296141 = c_Groups_Ozero__class_Ozero(_296139), -(c_RealVector_Onorm__class_Onorm(_296139, c_Groups_Osgn__class_Osgn(_296139, _296141)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2762 ^ _206868) ^ [] : [-(_296141 = c_Groups_Ozero__class_Ozero(_296139)), -(c_RealVector_Onorm__class_Onorm(_296139, c_Groups_Osgn__class_Osgn(_296139, _296141)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (2768 ^ _206868) ^ [_296635, _296637] : [class_Groups_Osgn__if(_296635), 2771 ^ _206868 : [(2772 ^ _206868) ^ [] : [_296637 = c_Groups_Ozero__class_Ozero(_296635), -(c_Groups_Osgn__class_Osgn(_296635, _296637) = c_Groups_Ozero__class_Ozero(_296635))], (2778 ^ _206868) ^ [] : [-(_296637 = c_Groups_Ozero__class_Ozero(_296635)), 2781 ^ _206868 : [(2782 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_296635, c_Groups_Ozero__class_Ozero(_296635), _296637), -(c_Groups_Osgn__class_Osgn(_296635, _296637) = c_Groups_Oone__class_Oone(_296635))], (2788 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_296635, c_Groups_Ozero__class_Ozero(_296635), _296637)), -(c_Groups_Osgn__class_Osgn(_296635, _296637) = c_Groups_Ouminus__class_Ouminus(_296635, c_Groups_Oone__class_Oone(_296635)))]]]]], (2794 ^ _206868) ^ [_297411, _297413] : [class_Rings_Olinordered__idom(_297411), 2797 ^ _206868 : [(2798 ^ _206868) ^ [] : [_297413 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297411)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_297411), _297413) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297411)))], (2804 ^ _206868) ^ [] : [-(_297413 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297411))), 2807 ^ _206868 : [(2808 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_297411), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297411)), _297413), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_297411), _297413) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_297411)))], (2814 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_297411), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297411)), _297413)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_297411), _297413) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_297411), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_297411))))]]]]], (2820 ^ _206868) ^ [_298267, _298269, _298271, _298273] : [class_Orderings_Oord(_298267), 2823 ^ _206868 : [(2824 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_298269, _298267), _298271, _298273), 2827 ^ _206868 : [(2828 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_298269, _298267), _298271, _298273))], (2830 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_298269, _298267), _298273, _298271)]]], (2832 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_298269, _298267), _298271, _298273)), c_Orderings_Oord__class_Oless__eq(tc_fun(_298269, _298267), _298271, _298273), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_298269, _298267), _298273, _298271))]]], (2842 ^ _206868) ^ [_298965, _298967] : [class_Rings_Olinordered__idom(_298965), -(c_Groups_Osgn__class_Osgn(_298965, c_Groups_Osgn__class_Osgn(_298965, _298967)) = c_Groups_Osgn__class_Osgn(_298965, _298967))], (2848 ^ _206868) ^ [_299191, _299193] : [class_Rings_Olinordered__idom(_299191), 2851 ^ _206868 : [(2852 ^ _206868) ^ [] : [c_Groups_Osgn__class_Osgn(_299191, _299193) = c_Groups_Ozero__class_Ozero(_299191), -(_299193 = c_Groups_Ozero__class_Ozero(_299191))], (2858 ^ _206868) ^ [] : [_299193 = c_Groups_Ozero__class_Ozero(_299191), -(c_Groups_Osgn__class_Osgn(_299191, _299193) = c_Groups_Ozero__class_Ozero(_299191))]]], (2864 ^ _206868) ^ [_299670, _299672] : [class_RealVector_Oreal__normed__vector(_299670), 2867 ^ _206868 : [(2868 ^ _206868) ^ [] : [c_Groups_Osgn__class_Osgn(_299670, _299672) = c_Groups_Ozero__class_Ozero(_299670), -(_299672 = c_Groups_Ozero__class_Ozero(_299670))], (2874 ^ _206868) ^ [] : [_299672 = c_Groups_Ozero__class_Ozero(_299670), -(c_Groups_Osgn__class_Osgn(_299670, _299672) = c_Groups_Ozero__class_Ozero(_299670))]]], (2880 ^ _206868) ^ [_300135] : [class_RealVector_Oreal__normed__vector(_300135), -(c_Groups_Osgn__class_Osgn(_300135, c_Groups_Ozero__class_Ozero(_300135)) = c_Groups_Ozero__class_Ozero(_300135))], (2886 ^ _206868) ^ [_300337] : [class_Groups_Osgn__if(_300337), -(c_Groups_Osgn__class_Osgn(_300337, c_Groups_Ozero__class_Ozero(_300337)) = c_Groups_Ozero__class_Ozero(_300337))], (2892 ^ _206868) ^ [_300539] : [class_RealVector_Oreal__normed__algebra__1(_300539), -(c_Groups_Osgn__class_Osgn(_300539, c_Groups_Oone__class_Oone(_300539)) = c_Groups_Oone__class_Oone(_300539))], (2898 ^ _206868) ^ [_300755, _300757] : [class_Int_Oring__char__0(_300755), class_Rings_Oidom(_300755), 2905 ^ _206868 : [(2906 ^ _206868) ^ [] : [c_Polynomial_Opoly(_300755, _300757) = c_Polynomial_Opoly(_300755, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_300755))), -(_300757 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_300755)))], (2912 ^ _206868) ^ [] : [_300757 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_300755)), -(c_Polynomial_Opoly(_300755, _300757) = c_Polynomial_Opoly(_300755, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_300755))))]]], (2918 ^ _206868) ^ [_301344, _301346] : [class_RealVector_Oreal__normed__vector(_301344), -(c_Groups_Osgn__class_Osgn(_301344, c_Groups_Ouminus__class_Ouminus(_301344, _301346)) = c_Groups_Ouminus__class_Ouminus(_301344, c_Groups_Osgn__class_Osgn(_301344, _301346)))], (2924 ^ _206868) ^ [_301576, _301578] : [class_Rings_Olinordered__idom(_301576), 2927 ^ _206868 : [(2928 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_301576, c_Groups_Osgn__class_Osgn(_301576, _301578), c_Groups_Ozero__class_Ozero(_301576)), -(c_Orderings_Oord__class_Oless(_301576, _301578, c_Groups_Ozero__class_Ozero(_301576)))], (2934 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_301576, _301578, c_Groups_Ozero__class_Ozero(_301576)), -(c_Orderings_Oord__class_Oless(_301576, c_Groups_Osgn__class_Osgn(_301576, _301578), c_Groups_Ozero__class_Ozero(_301576)))]]], (2940 ^ _206868) ^ [_302061, _302063] : [class_Rings_Olinordered__idom(_302061), 2943 ^ _206868 : [(2944 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_302061, c_Groups_Ozero__class_Ozero(_302061), c_Groups_Osgn__class_Osgn(_302061, _302063)), -(c_Orderings_Oord__class_Oless(_302061, c_Groups_Ozero__class_Ozero(_302061), _302063))], (2950 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_302061, c_Groups_Ozero__class_Ozero(_302061), _302063), -(c_Orderings_Oord__class_Oless(_302061, c_Groups_Ozero__class_Ozero(_302061), c_Groups_Osgn__class_Osgn(_302061, _302063)))]]], (2956 ^ _206868) ^ [_302532] : [class_Groups_Oab__group__add(_302532), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_302532), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_302532))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_302532)))], (2962 ^ _206868) ^ [_302760, _302762] : [class_Rings_Olinordered__idom(_302760), c_Orderings_Oord__class_Oless(_302760, c_Groups_Ozero__class_Ozero(_302760), _302762), -(c_Groups_Osgn__class_Osgn(_302760, _302762) = c_Groups_Oone__class_Oone(_302760))], (2972 ^ _206868) ^ [_303073, _303075] : [class_Rings_Olinordered__idom(_303073), 2975 ^ _206868 : [(2976 ^ _206868) ^ [] : [c_Groups_Osgn__class_Osgn(_303073, _303075) = c_Groups_Oone__class_Oone(_303073), -(c_Orderings_Oord__class_Oless(_303073, c_Groups_Ozero__class_Ozero(_303073), _303075))], (2982 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_303073, c_Groups_Ozero__class_Ozero(_303073), _303075), -(c_Groups_Osgn__class_Osgn(_303073, _303075) = c_Groups_Oone__class_Oone(_303073))]]], (2988 ^ _206868) ^ [_303555, _303557] : [class_Rings_Olinordered__idom(_303555), 2991 ^ _206868 : [(2992 ^ _206868) ^ [] : [c_Groups_Osgn__class_Osgn(_303555, _303557) = c_Groups_Ouminus__class_Ouminus(_303555, c_Groups_Oone__class_Oone(_303555)), -(c_Orderings_Oord__class_Oless(_303555, _303557, c_Groups_Ozero__class_Ozero(_303555)))], (2998 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_303555, _303557, c_Groups_Ozero__class_Ozero(_303555)), -(c_Groups_Osgn__class_Osgn(_303555, _303557) = c_Groups_Ouminus__class_Ouminus(_303555, c_Groups_Oone__class_Oone(_303555)))]]], (3004 ^ _206868) ^ [_304046, _304048] : [class_Rings_Olinordered__idom(_304046), c_Orderings_Oord__class_Oless(_304046, _304048, c_Groups_Ozero__class_Ozero(_304046)), -(c_Groups_Osgn__class_Osgn(_304046, _304048) = c_Groups_Ouminus__class_Ouminus(_304046, c_Groups_Oone__class_Oone(_304046)))], (3014 ^ _206868) ^ [_304379, _304381, _304383] : [class_Rings_Olinordered__idom(_304379), -(_304381 = _304383), -(c_Orderings_Oord__class_Oless(_304379, _304381, _304383)), -(c_Orderings_Oord__class_Oless(_304379, _304383, _304381))], (3028 ^ _206868) ^ [_304789, _304791] : [class_Lattices_Oboolean__algebra(_304789), -(c_Groups_Ouminus__class_Ouminus(_304789, c_Groups_Ouminus__class_Ouminus(_304789, _304791)) = _304791)], (3034 ^ _206868) ^ [_305037, _305039, _305041, _305043] : [class_Groups_Ouminus(_305037), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_305039, _305037), _305041), _305043) = c_Groups_Ouminus__class_Ouminus(_305037, hAPP(_305041, _305043)))], (3040 ^ _206868) ^ [_305301, _305303, _305305] : [class_Lattices_Oboolean__algebra(_305301), 3043 ^ _206868 : [(3044 ^ _206868) ^ [] : [c_Groups_Ouminus__class_Ouminus(_305301, _305303) = c_Groups_Ouminus__class_Ouminus(_305301, _305305), -(_305303 = _305305)], (3050 ^ _206868) ^ [] : [_305303 = _305305, -(c_Groups_Ouminus__class_Ouminus(_305301, _305303) = c_Groups_Ouminus__class_Ouminus(_305301, _305305))]]], (3056 ^ _206868) ^ [_305779] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _305779), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _305779) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (3062 ^ _206868) ^ [_305997] : [_305997 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _305997) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3068 ^ _206868) ^ [_306159] : [-(_306159 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 3071 ^ _206868 : [(3072 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _306159), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _306159) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (3078 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _306159)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _306159) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]]], (3084 ^ _206868) ^ [_306636] : [_306636 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _306636) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3090 ^ _206868) ^ [_306798] : [-(_306798 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 3093 ^ _206868 : [(3094 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _306798), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _306798) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (3100 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _306798)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _306798) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]]], (3106 ^ _206868) ^ [_307283, _307285, _307287] : [class_Rings_Oidom(_307283), 3109 ^ _206868 : [(3120 ^ _206868) ^ [] : [3121 ^ _206868 : [(3122 ^ _206868) ^ [] : [_307285 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_307283))], (3124 ^ _206868) ^ [] : [-(c_Polynomial_Oorder(_307283, _307287, _307285) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_307283, _307285), _307287) = c_Groups_Ozero__class_Ozero(_307283))], (3110 ^ _206868) ^ [] : [hAPP(c_Polynomial_Opoly(_307283, _307285), _307287) = c_Groups_Ozero__class_Ozero(_307283), -(_307285 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_307283))), c_Polynomial_Oorder(_307283, _307287, _307285) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (3128 ^ _206868) ^ [_307971, _307973] : [class_Groups_Ozero(_307971), 3131 ^ _206868 : [(3132 ^ _206868) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_307971, _307973) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_307973 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_307971)))], (3138 ^ _206868) ^ [] : [_307973 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_307971)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_307971, _307973) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3144 ^ _206868) ^ [_308478, _308480, _308482, _308484] : [class_Groups_Ozero(_308478), hAPP(hAPP(hAPP(_308480, c_Groups_Ozero__class_Ozero(_308478)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_308478))), _308482) = _308482, -(c_Polynomial_Opoly__rec(_308484, _308478, _308482, _308480, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_308478))) = _308482)], (3154 ^ _206868) ^ [_308845, _308847] : [class_Rings_Olinordered__idom(_308845), -(_308847 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_308845))), -(c_Polynomial_Opos__poly(_308845, _308847)), -(c_Polynomial_Opos__poly(_308845, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_308845), _308847)))], (3168 ^ _206868) ^ [_309237] : [-(c_RealDef_Opositive(_309237)), -(_309237 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RealDef_Opositive(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _309237)))], (3178 ^ _206868) ^ [_309534, _309536] : [class_RealVector_Oreal__normed__vector(_309534), 3181 ^ _206868 : [(3182 ^ _206868) ^ [] : [c_SEQ_OBseq(_309534, _309536), 3186 ^ _206868 : [(3187 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3185 ^ [_309534, _309536]))], (3189 ^ _206868) ^ [_309919] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_309534, hAPP(_309536, _309919)), 3185 ^ [_309534, _309536]))]]], (3191 ^ _206868) ^ [] : [-(c_SEQ_OBseq(_309534, _309536)), 3192 ^ _206868 : [(3193 ^ _206868) ^ [_310051] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _310051), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_309534, hAPP(_309536, 3196 ^ [_309534, _309536, _310051])), _310051)]]]]], (3202 ^ _206868) ^ [_310385] : [-(c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _310385) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (3204 ^ _206868) ^ [_310495, _310497] : [class_Rings_Ocomm__semiring__1(_310495), 3207 ^ _206868 : [(3208 ^ _206868) ^ [] : [_310497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Polynomial_Ocoeff(_310495, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_310495))), _310497) = c_Groups_Oone__class_Oone(_310495))], (3214 ^ _206868) ^ [] : [-(_310497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_Polynomial_Ocoeff(_310495, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_310495))), _310497) = c_Groups_Ozero__class_Ozero(_310495))]]], (3220 ^ _206868) ^ [_310993] : [class_Rings_Ocomm__semiring__1(_310993), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_310993)) = c_Polynomial_OpCons(_310993, c_Groups_Oone__class_Oone(_310993), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_310993))))], (3226 ^ _206868) ^ [_311237, _311239, _311241] : [class_Groups_Ozero(_311237), -(hAPP(c_Polynomial_Ocoeff(_311237, c_Polynomial_OpCons(_311237, _311239, _311241)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _311239)], (3232 ^ _206868) ^ [_311513, _311515, _311517, _311519, _311521] : [class_Groups_Ozero(_311513), 3235 ^ _206868 : [(3236 ^ _206868) ^ [] : [c_Polynomial_OpCons(_311513, _311515, _311517) = c_Polynomial_OpCons(_311513, _311519, _311521), 3239 ^ _206868 : [(3240 ^ _206868) ^ [] : [-(_311515 = _311519)], (3242 ^ _206868) ^ [] : [-(_311517 = _311521)]]], (3244 ^ _206868) ^ [] : [-(c_Polynomial_OpCons(_311513, _311515, _311517) = c_Polynomial_OpCons(_311513, _311519, _311521)), _311515 = _311519, _311517 = _311521]]], (3254 ^ _206868) ^ [_312233, _312235, _312237] : [class_Groups_Ozero(_312233), 3257 ^ _206868 : [(3258 ^ _206868) ^ [] : [c_Polynomial_Ocoeff(_312233, _312235) = c_Polynomial_Ocoeff(_312233, _312237), -(_312235 = _312237)], (3264 ^ _206868) ^ [] : [_312235 = _312237, -(c_Polynomial_Ocoeff(_312233, _312235) = c_Polynomial_Ocoeff(_312233, _312237))]]], (3270 ^ _206868) ^ [_312739, _312741, _312743] : [class_Groups_Ozero(_312739), 3273 ^ _206868 : [(3274 ^ _206868) ^ [] : [_312741 = _312743, 3277 ^ _206868 : [(3278 ^ _206868) ^ [_312987] : [-(hAPP(c_Polynomial_Ocoeff(_312739, _312741), _312987) = hAPP(c_Polynomial_Ocoeff(_312739, _312743), _312987))]]], (3280 ^ _206868) ^ [] : [hAPP(c_Polynomial_Ocoeff(_312739, _312741), 3281 ^ [_312739, _312741, _312743]) = hAPP(c_Polynomial_Ocoeff(_312739, _312743), 3281 ^ [_312739, _312741, _312743]), -(_312741 = _312743)]]], (3287 ^ _206868) ^ [_313406, _313408, _313410, _313412, _313414, _313416] : [class_Groups_Ozero(_313406), -(c_Polynomial_Opoly__rec(_313408, _313406, _313410, _313412, c_Polynomial_OpCons(_313406, _313414, _313416)) = hAPP(hAPP(hAPP(_313412, _313414), _313416), c_If(_313408, c_fequal(_313416, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_313406))), _313410, c_Polynomial_Opoly__rec(_313408, _313406, _313410, _313412, _313416))))], (3293 ^ _206868) ^ [_313768, _313770, _313772, _313774, _313776, _313778] : [class_Groups_Ozero(_313768), hAPP(hAPP(hAPP(_313770, c_Groups_Ozero__class_Ozero(_313768)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_313768))), _313772) = _313772, -(c_Polynomial_Opoly__rec(_313774, _313768, _313772, _313770, c_Polynomial_OpCons(_313768, _313776, _313778)) = hAPP(hAPP(hAPP(_313770, _313776), _313778), c_Polynomial_Opoly__rec(_313774, _313768, _313772, _313770, _313778)))], (3303 ^ _206868) ^ [_314199, _314201, _314203] : [class_Rings_Olinordered__idom(_314199), 3306 ^ _206868 : [(3307 ^ _206868) ^ [] : [c_Polynomial_Opos__poly(_314199, c_Polynomial_OpCons(_314199, _314201, _314203)), -(c_Polynomial_Opos__poly(_314199, _314203)), 3314 ^ _206868 : [(3315 ^ _206868) ^ [] : [-(_314203 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_314199)))], (3317 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_314199, c_Groups_Ozero__class_Ozero(_314199), _314201))]]], (3319 ^ _206868) ^ [] : [-(c_Polynomial_Opos__poly(_314199, c_Polynomial_OpCons(_314199, _314201, _314203))), 3320 ^ _206868 : [(3321 ^ _206868) ^ [] : [c_Polynomial_Opos__poly(_314199, _314203)], (3323 ^ _206868) ^ [] : [_314203 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_314199)), c_Orderings_Oord__class_Oless(_314199, c_Groups_Ozero__class_Ozero(_314199), _314201)]]]]], (3331 ^ _206868) ^ [_315020] : [class_Groups_Ozero(_315020), -(c_Polynomial_OpCons(_315020, c_Groups_Ozero__class_Ozero(_315020), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_315020))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_315020)))], (3337 ^ _206868) ^ [_315264, _315266, _315268] : [class_Groups_Ozero(_315264), 3340 ^ _206868 : [(3341 ^ _206868) ^ [] : [c_Polynomial_OpCons(_315264, _315266, _315268) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_315264)), 3344 ^ _206868 : [(3345 ^ _206868) ^ [] : [-(_315266 = c_Groups_Ozero__class_Ozero(_315264))], (3347 ^ _206868) ^ [] : [-(_315268 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_315264)))]]], (3349 ^ _206868) ^ [] : [-(c_Polynomial_OpCons(_315264, _315266, _315268) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_315264))), _315266 = c_Groups_Ozero__class_Ozero(_315264), _315268 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_315264))]]], (3359 ^ _206868) ^ [_315930] : [class_Rings_Olinordered__idom(_315930), c_Polynomial_Opos__poly(_315930, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_315930)))], (3365 ^ _206868) ^ [] : [c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3367 ^ _206868) ^ [_316193, _316195] : [class_Groups_Ozero(_316193), -(hAPP(c_Polynomial_Ocoeff(_316193, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_316193))), _316195) = c_Groups_Ozero__class_Ozero(_316193))], (3373 ^ _206868) ^ [_316439, _316441, _316443] : [class_Groups_Oab__group__add(_316439), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_316439), c_Polynomial_OpCons(_316439, _316441, _316443)) = c_Polynomial_OpCons(_316439, c_Groups_Ouminus__class_Ouminus(_316439, _316441), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_316439), _316443)))], (3379 ^ _206868) ^ [_316709, _316711, _316713] : [class_Groups_Oab__group__add(_316709), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_316709), c_Polynomial_OpCons(_316709, _316711, _316713)) = c_Polynomial_OpCons(_316709, c_Groups_Ouminus__class_Ouminus(_316709, _316711), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_316709), _316713)))], (3385 ^ _206868) ^ [_316979, _316981, _316983] : [class_Groups_Oab__group__add(_316979), -(hAPP(c_Polynomial_Ocoeff(_316979, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_316979), _316981)), _316983) = c_Groups_Ouminus__class_Ouminus(_316979, hAPP(c_Polynomial_Ocoeff(_316979, _316981), _316983)))], (3391 ^ _206868) ^ [_317204] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _317204))], (3393 ^ _206868) ^ [_317282] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _317282, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3395 ^ _206868) ^ [_317404, _317406, _317408] : [class_RealVector_Oreal__normed__vector(_317404), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _317406), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_317404, hAPP(_317408, 3404 ^ [_317404, _317406, _317408])), _317406), -(c_SEQ_OBseq(_317404, _317408))], (3410 ^ _206868) ^ [_317890, _317892] : [class_RealVector_Oreal__normed__vector(_317890), c_SEQ_OBseq(_317890, _317892), 3418 ^ _206868 : [(3419 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3417 ^ [_317890, _317892]))], (3421 ^ _206868) ^ [_318246] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_317890, hAPP(_317892, _318246)), 3417 ^ [_317890, _317892]))]]], (3423 ^ _206868) ^ [_318396, _318398, _318400] : [class_Rings_Oidom(_318396), 3426 ^ _206868 : [(3427 ^ _206868) ^ [] : [hAPP(c_Polynomial_Opoly(_318396, _318398), _318400) = c_Groups_Ozero__class_Ozero(_318396), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_318396)), c_Polynomial_OpCons(_318396, c_Groups_Ouminus__class_Ouminus(_318396, _318400), c_Polynomial_OpCons(_318396, c_Groups_Oone__class_Oone(_318396), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_318396))))), _318398)))], (3433 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_318396)), c_Polynomial_OpCons(_318396, c_Groups_Ouminus__class_Ouminus(_318396, _318400), c_Polynomial_OpCons(_318396, c_Groups_Oone__class_Oone(_318396), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_318396))))), _318398)), -(hAPP(c_Polynomial_Opoly(_318396, _318398), _318400) = c_Groups_Ozero__class_Ozero(_318396))]]], (3439 ^ _206868) ^ [_318986, _318988, _318990] : [class_Rings_Oidom(_318986), 3442 ^ _206868 : [(3443 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_318986)), c_Polynomial_OpCons(_318986, _318988, c_Polynomial_OpCons(_318986, c_Groups_Oone__class_Oone(_318986), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_318986))))), _318990)), -(hAPP(c_Polynomial_Opoly(_318986, _318990), c_Groups_Ouminus__class_Ouminus(_318986, _318988)) = c_Groups_Ozero__class_Ozero(_318986))], (3449 ^ _206868) ^ [] : [hAPP(c_Polynomial_Opoly(_318986, _318990), c_Groups_Ouminus__class_Ouminus(_318986, _318988)) = c_Groups_Ozero__class_Ozero(_318986), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_318986)), c_Polynomial_OpCons(_318986, _318988, c_Polynomial_OpCons(_318986, c_Groups_Oone__class_Oone(_318986), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_318986))))), _318990)))]]], (3455 ^ _206868) ^ [_319576, _319578, _319580] : [class_Rings_Ocomm__semiring__0(_319576), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_319576, c_Polynomial_OpCons(_319576, _319578, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_319576))), _319580) = c_Polynomial_OpCons(_319576, _319578, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_319576))))], (3461 ^ _206868) ^ [_319858, _319860, _319862, _319864] : [class_Rings_Ocomm__semiring__0(_319858), -(c_Polynomial_Osynthetic__div(_319858, c_Polynomial_OpCons(_319858, _319860, _319862), _319864) = c_Polynomial_OpCons(_319858, hAPP(c_Polynomial_Opoly(_319858, _319862), _319864), c_Polynomial_Osynthetic__div(_319858, _319862, _319864)))], (3467 ^ _206868) ^ [_320122, _320124] : [class_Rings_Ocomm__semiring__1(_320122), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_320122), _320124), c_Groups_Ozero__class_Ozero(_320122))))], (3473 ^ _206868) ^ [_320377, _320379] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _320377, _320379), 3476 ^ _206868 : [(3477 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _320377, _320379))], (3479 ^ _206868) ^ [] : [_320377 = _320379]]], (3481 ^ _206868) ^ [_320619, _320621] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _320619, _320621)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _320619, _320621), -(_320619 = _320621)], (3501 ^ _206868) ^ [_321212, _321214] : [3502 ^ _206868 : [(3503 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321212, _321214)], (3505 ^ _206868) ^ [] : [_321212 = _321214]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _321212, _321214))], (3491 ^ _206868) ^ [_320956, _320958] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _320956, _320958), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _320956, _320958)), -(_320956 = _320958)], (3509 ^ _206868) ^ [_321502, _321504] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321502, _321504), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _321502, _321504))], (3515 ^ _206868) ^ [_321716, _321718] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _321716, _321718), -(_321716 = _321718), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321716, _321718))], (3525 ^ _206868) ^ [_322022, _322024] : [3526 ^ _206868 : [(3527 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _322022, _322024)], (3529 ^ _206868) ^ [] : [_322022 = _322024]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _322022, _322024))], (3533 ^ _206868) ^ [_322324, _322326, _322328] : [3534 ^ _206868 : [(3535 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _322324, _322326))], (3537 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(_322328, _322326), _322324))]], 3540 ^ _206868 : [(3541 ^ _206868) ^ [] : [-(_322324 = _322326)], (3543 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(_322328, _322326), _322324))]], 3546 ^ _206868 : [(3547 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _322326, _322324))], (3549 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(_322328, _322326), _322324))]], -(hBOOL(hAPP(hAPP(_322328, _322326), _322324)))], (3553 ^ _206868) ^ [_323001, _323003] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323001, _323003), _323001 = _323003], (3559 ^ _206868) ^ [_323214, _323216] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323214, _323216), _323216 = _323214], (3565 ^ _206868) ^ [_323397] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323397, _323397)], (3567 ^ _206868) ^ [_323505, _323507] : [-(_323505 = _323507), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323505, _323507)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323507, _323505))], (3587 ^ _206868) ^ [_324102, _324104] : [3588 ^ _206868 : [(3589 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324102, _324104)], (3591 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324104, _324102)]], _324102 = _324104], (3577 ^ _206868) ^ [_323843, _323845] : [-(_323843 = _323845), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323843, _323845)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323845, _323843))], (3595 ^ _206868) ^ [_324363] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324363, _324363)], (3597 ^ _206868) ^ [_324471, _324473] : [class_Rings_Ocomm__semiring__1(_324471), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_324471), _324473), _324473)))], (3603 ^ _206868) ^ [_324721, _324723, _324725, _324727] : [class_Rings_Ocomm__semiring__1(_324721), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_324721), _324723), _324725)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_324721), _324725), _324727)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_324721), _324723), _324727)))], (3617 ^ _206868) ^ [_325177, _325179] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325177, _325179), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325179, _325177), -(_325177 = _325179)], (3627 ^ _206868) ^ [_325494, _325496, _325498] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325494, _325496), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325496, _325498), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325494, _325498))], (3637 ^ _206868) ^ [_325809, _325811] : [_325809 = _325811, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325809, _325811))], (3643 ^ _206868) ^ [_326021, _326023] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _326021, _326023)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _326023, _326021))], (3649 ^ _206868) ^ [_326207] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _326207, _326207))], (3651 ^ _206868) ^ [_326315, _326317] : [class_Rings_Ocomm__semiring__1(_326315), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_326315), c_Groups_Ozero__class_Ozero(_326315)), _326317)), -(_326317 = c_Groups_Ozero__class_Ozero(_326315))], (3661 ^ _206868) ^ [_326634, _326636] : [class_Rings_Ocomm__semiring__1(_326634), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_326634), c_Groups_Oone__class_Oone(_326634)), _326636)))], (3667 ^ _206868) ^ [_326874, _326876, _326878] : [class_Rings_Ocomm__ring__1(_326874), 3670 ^ _206868 : [(3671 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_326874), _326876), c_Groups_Ouminus__class_Ouminus(_326874, _326878))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_326874), _326876), _326878)))], (3677 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_326874), _326876), _326878)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_326874), _326876), c_Groups_Ouminus__class_Ouminus(_326874, _326878))))]]], (3683 ^ _206868) ^ [_327413, _327415, _327417] : [class_Rings_Ocomm__ring__1(_327413), 3686 ^ _206868 : [(3687 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_327413), c_Groups_Ouminus__class_Ouminus(_327413, _327415)), _327417)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_327413), _327415), _327417)))], (3693 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_327413), _327415), _327417)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_327413), c_Groups_Ouminus__class_Ouminus(_327413, _327415)), _327417)))]]], (3699 ^ _206868) ^ [_327938, _327940] : [class_Rings_Ocomm__semiring__0(_327938), -(c_Polynomial_Osynthetic__div(_327938, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_327938)), _327940) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_327938)))], (3705 ^ _206868) ^ [_328170, _328172] : [class_Rings_Ocomm__semiring__0(_328170), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_328170, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_328170)), _328172) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_328170)))], (3711 ^ _206868) ^ [_328416, _328418, _328420] : [class_Rings_Ocomm__semiring__0(_328416), 3714 ^ _206868 : [(3715 ^ _206868) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_328416, _328418, _328420) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_328416)), -(_328418 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_328416)))], (3721 ^ _206868) ^ [] : [_328418 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_328416)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_328416, _328418, _328420) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_328416)))]]], (3727 ^ _206868) ^ [_328912] : [-(_328912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _328912))], (3733 ^ _206868) ^ [_329121, _329123] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329121, _329123), _329123 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3739 ^ _206868) ^ [_329349] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _329349, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_329349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3745 ^ _206868) ^ [_329507] : [_329507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _329507, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3751 ^ _206868) ^ [_329685] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329685, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3753 ^ _206868) ^ [_329764] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _329764))], (3755 ^ _206868) ^ [_329887] : [-(_329887 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _329887))], (3761 ^ _206868) ^ [_330048] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _330048), _330048 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3767 ^ _206868) ^ [_330227] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _330227, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3769 ^ _206868) ^ [_330335, _330337] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _330335, _330337), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _330335, _330337))], (3775 ^ _206868) ^ [_330549, _330551] : [class_Orderings_Oorder(_330549), 3778 ^ _206868 : [(3789 ^ _206868) ^ [] : [3792 ^ _206868 : [(3793 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 3790 ^ [_330549, _330551], 3791 ^ [_330549, _330551]))], (3795 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330549, hAPP(_330551, 3791 ^ [_330549, _330551]), hAPP(_330551, 3790 ^ [_330549, _330551]))]], -(c_SEQ_Odecseq(_330549, _330551))], (3779 ^ _206868) ^ [] : [c_SEQ_Odecseq(_330549, _330551), 3782 ^ _206868 : [(3783 ^ _206868) ^ [_330825, _330827] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _330827, _330825), -(c_Orderings_Oord__class_Oless__eq(_330549, hAPP(_330551, _330825), hAPP(_330551, _330827)))]]]]], (3799 ^ _206868) ^ [_331464, _331466, _331468] : [class_Rings_Oidom(_331464), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_331464)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_331464)), c_Polynomial_OpCons(_331464, c_Groups_Ouminus__class_Ouminus(_331464, _331466), c_Polynomial_OpCons(_331464, c_Groups_Oone__class_Oone(_331464), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_331464))))), c_Polynomial_Oorder(_331464, _331466, _331468))), _331468)))], (3805 ^ _206868) ^ [_331758, _331760] : [class_Orderings_Oorder(_331758), 3808 ^ _206868 : [(3819 ^ _206868) ^ [] : [3822 ^ _206868 : [(3823 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 3820 ^ [_331758, _331760], 3821 ^ [_331758, _331760]))], (3825 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_331758, hAPP(_331760, 3820 ^ [_331758, _331760]), hAPP(_331760, 3821 ^ [_331758, _331760]))]], -(c_SEQ_Oincseq(_331758, _331760))], (3809 ^ _206868) ^ [] : [c_SEQ_Oincseq(_331758, _331760), 3812 ^ _206868 : [(3813 ^ _206868) ^ [_332034, _332036] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _332036, _332034), -(c_Orderings_Oord__class_Oless__eq(_331758, hAPP(_331760, _332036), hAPP(_331760, _332034)))]]]]], (3829 ^ _206868) ^ [_332687, _332689, _332691, _332693] : [class_RealVector_Oreal__normed__vector(_332687), 3835 ^ _206868 : [(3836 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _332689, 3834 ^ [_332687, _332689, _332691, _332693]))], (3838 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_332687, hAPP(_332691, 3834 ^ [_332687, _332689, _332691, _332693])), _332693)]], -(c_SEQ_OBseq(_332687, _332691))], (3842 ^ _206868) ^ [_333207, _333209, _333211] : [class_Groups_Ozero(_333207), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_333207, _333209), _333211), hAPP(c_Polynomial_Ocoeff(_333207, _333209), _333211) = c_Groups_Ozero__class_Ozero(_333207), -(_333209 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_333207))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_333207, _333209), _333211))], (3860 ^ _206868) ^ [_333755, _333757, _333759] : [class_Rings_Ocomm__semiring__1(_333755), -(hAPP(c_Polynomial_Ocoeff(_333755, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_333755)), c_Polynomial_OpCons(_333755, _333757, c_Polynomial_OpCons(_333755, c_Groups_Oone__class_Oone(_333755), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_333755))))), _333759)), _333759) = c_Groups_Oone__class_Oone(_333755))], (3866 ^ _206868) ^ [_334047, _334049, _334051] : [class_Groups_Ozero(_334047), -(c_Polynomial_Ocoeff(_334047, c_Polynomial_OpCons(_334047, _334049, _334051)) = c_Nat_Onat_Onat__case(_334047, _334049, c_Polynomial_Ocoeff(_334047, _334051)))], (3872 ^ _206868) ^ [_334303, _334305, _334307] : [class_RealVector_Oreal__normed__div__algebra(_334303), -(c_RealVector_Onorm__class_Onorm(_334303, hAPP(hAPP(c_Power_Opower__class_Opower(_334303), _334305), _334307)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_334303, _334305)), _334307))], (3878 ^ _206868) ^ [_334585, _334587, _334589, _334591] : [class_Rings_Ocomm__semiring__1(_334585), -(hAPP(c_Polynomial_Opoly(_334585, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_334585)), _334587), _334589)), _334591) = hAPP(hAPP(c_Power_Opower__class_Opower(_334585), hAPP(c_Polynomial_Opoly(_334585, _334587), _334591)), _334589))], (3884 ^ _206868) ^ [_334879, _334881, _334883] : [class_RealVector_Oreal__normed__algebra__1(_334879), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_334879, hAPP(hAPP(c_Power_Opower__class_Opower(_334879), _334881), _334883)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_334879, _334881)), _334883)))], (3890 ^ _206868) ^ [_335135, _335137] : [class_Groups_Oab__group__add(_335135), -(c_Polynomial_Odegree(_335135, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_335135), _335137)) = c_Polynomial_Odegree(_335135, _335137))], (3896 ^ _206868) ^ [_335379, _335381, _335383] : [class_Rings_Ocomm__semiring__0(_335379), -(c_Polynomial_Odegree(_335379, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_335379, _335381, _335383)) = c_Polynomial_Odegree(_335379, _335381))], (3902 ^ _206868) ^ [_335627, _335629, _335631] : [class_Rings_Ocomm__semiring__1(_335627), -(c_Polynomial_Odegree(_335627, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_335627)), c_Polynomial_OpCons(_335627, _335629, c_Polynomial_OpCons(_335627, c_Groups_Oone__class_Oone(_335627), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_335627))))), _335631)) = _335631)], (3908 ^ _206868) ^ [_335881] : [class_Groups_Ozero(_335881), -(c_Polynomial_Odegree(_335881, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_335881))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3914 ^ _206868) ^ [_336097, _336099] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _336097), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _336097, _336099), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _336099), _336097))], (3924 ^ _206868) ^ [_336410, _336412, _336414] : [-(hAPP(c_Nat_Onat_Onat__case(_336410, _336412, _336414), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _336412)], (3926 ^ _206868) ^ [_336542, _336544, _336546] : [class_Rings_Oidom(_336542), hAPP(c_Polynomial_Ocoeff(_336542, _336544), c_Polynomial_Odegree(_336542, _336544)) = hAPP(c_Polynomial_Ocoeff(_336542, _336546), c_Polynomial_Odegree(_336542, _336546)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_336542)), _336544), _336546)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_336542)), _336546), _336544)), -(_336544 = _336546)], (3944 ^ _206868) ^ [_337093] : [class_Rings_Ocomm__semiring__1(_337093), -(c_Polynomial_Odegree(_337093, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_337093))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3950 ^ _206868) ^ [_337323, _337325, _337327] : [class_Groups_Ozero(_337323), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_337323, _337325), _337327), -(hAPP(c_Polynomial_Ocoeff(_337323, _337325), _337327) = c_Groups_Ozero__class_Ozero(_337323))], (3960 ^ _206868) ^ [_337668, _337670, _337672] : [class_Groups_Ozero(_337668), -(hAPP(c_Polynomial_Ocoeff(_337668, _337670), _337672) = c_Groups_Ozero__class_Ozero(_337668)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _337672, c_Polynomial_Odegree(_337668, _337670)))], (3970 ^ _206868) ^ [_338002, _338004] : [class_Groups_Ozero(_338002), 3973 ^ _206868 : [(3974 ^ _206868) ^ [] : [hAPP(c_Polynomial_Ocoeff(_338002, _338004), c_Polynomial_Odegree(_338002, _338004)) = c_Groups_Ozero__class_Ozero(_338002), -(_338004 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_338002)))], (3980 ^ _206868) ^ [] : [_338004 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_338002)), -(hAPP(c_Polynomial_Ocoeff(_338002, _338004), c_Polynomial_Odegree(_338002, _338004)) = c_Groups_Ozero__class_Ozero(_338002))]]], (3986 ^ _206868) ^ [_338505, _338507] : [class_Groups_Ozero(_338505), -(_338507 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_338505))), hAPP(c_Polynomial_Ocoeff(_338505, _338507), c_Polynomial_Odegree(_338505, _338507)) = c_Groups_Ozero__class_Ozero(_338505)], (3996 ^ _206868) ^ [_338836, _338838] : [class_Groups_Ozero(_338836), -(c_Polynomial_Odegree(_338836, c_Polynomial_OpCons(_338836, _338838, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_338836)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4002 ^ _206868) ^ [_339080, _339082, _339084] : [class_Rings_Oidom(_339080), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_339080)), _339082), _339084)), -(_339084 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_339080))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_339080, _339082), c_Polynomial_Odegree(_339080, _339084)))], (4016 ^ _206868) ^ [_339523, _339525] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _339523), _339525)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _339525), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _339523, _339525))], (4026 ^ _206868) ^ [_339850, _339852, _339854] : [class_Rings_Ocomm__semiring__0(_339850), 4029 ^ _206868 : [(4030 ^ _206868) ^ [] : [c_Polynomial_Osynthetic__div(_339850, _339852, _339854) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_339850)), -(c_Polynomial_Odegree(_339850, _339852) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4036 ^ _206868) ^ [] : [c_Polynomial_Odegree(_339850, _339852) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Osynthetic__div(_339850, _339852, _339854) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_339850)))]]], (4042 ^ _206868) ^ [_340371, _340373, _340375] : [class_Rings_Oidom(_340371), -(_340373 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_340371))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(_340371, _340375, _340373), c_Polynomial_Odegree(_340371, _340373)))], (4052 ^ _206868) ^ [_340705, _340707] : [class_Rings_Olinordered__idom(_340705), 4055 ^ _206868 : [(4056 ^ _206868) ^ [] : [c_Polynomial_Opos__poly(_340705, _340707), -(c_Orderings_Oord__class_Oless(_340705, c_Groups_Ozero__class_Ozero(_340705), hAPP(c_Polynomial_Ocoeff(_340705, _340707), c_Polynomial_Odegree(_340705, _340707))))], (4062 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_340705, c_Groups_Ozero__class_Ozero(_340705), hAPP(c_Polynomial_Ocoeff(_340705, _340707), c_Polynomial_Odegree(_340705, _340707))), -(c_Polynomial_Opos__poly(_340705, _340707))]]], (4068 ^ _206868) ^ [_341227, _341229, _341231, _341233] : [class_Rings_Olinordered__semidom(_341227), c_Orderings_Oord__class_Oless(_341227, _341229, _341231), c_Orderings_Oord__class_Oless__eq(_341227, c_Groups_Ozero__class_Ozero(_341227), _341229), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _341233), -(c_Orderings_Oord__class_Oless(_341227, hAPP(hAPP(c_Power_Opower__class_Opower(_341227), _341229), _341233), hAPP(hAPP(c_Power_Opower__class_Opower(_341227), _341231), _341233)))], (4086 ^ _206868) ^ [_341796, _341798, _341800] : [class_Rings_Ocomm__semiring__1(_341796), 4091 ^ _206868 : [(4092 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _341798)], (4094 ^ _206868) ^ [] : [_341800 = c_Groups_Oone__class_Oone(_341796)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_341796), _341800), hAPP(hAPP(c_Power_Opower__class_Opower(_341796), _341800), _341798))))], (4098 ^ _206868) ^ [_342229, _342231, _342233] : [class_Rings_Olinordered__semidom(_342229), c_Orderings_Oord__class_Oless(_342229, c_Groups_Oone__class_Oone(_342229), _342231), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _342233), -(c_Orderings_Oord__class_Oless(_342229, c_Groups_Oone__class_Oone(_342229), hAPP(hAPP(c_Power_Opower__class_Opower(_342229), _342231), _342233)))], (4112 ^ _206868) ^ [_342687, _342689, _342691, _342693] : [class_Rings_Olinordered__semidom(_342687), c_Orderings_Oord__class_Oless(_342687, c_Groups_Oone__class_Oone(_342687), _342689), c_Orderings_Oord__class_Oless__eq(_342687, hAPP(hAPP(c_Power_Opower__class_Opower(_342687), _342689), _342691), hAPP(hAPP(c_Power_Opower__class_Opower(_342687), _342689), _342693)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _342691, _342693))], (4126 ^ _206868) ^ [_343171, _343173, _343175, _343177] : [class_Rings_Olinordered__semidom(_343171), c_Orderings_Oord__class_Oless(_343171, c_Groups_Oone__class_Oone(_343171), _343173), 4133 ^ _206868 : [(4134 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343171, hAPP(hAPP(c_Power_Opower__class_Opower(_343171), _343173), _343175), hAPP(hAPP(c_Power_Opower__class_Opower(_343171), _343173), _343177)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _343175, _343177))], (4140 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _343175, _343177), -(c_Orderings_Oord__class_Oless__eq(_343171, hAPP(hAPP(c_Power_Opower__class_Opower(_343171), _343173), _343175), hAPP(hAPP(c_Power_Opower__class_Opower(_343171), _343173), _343177)))]]], (4146 ^ _206868) ^ [_343846, _343848, _343850, _343852] : [class_Rings_Olinordered__semidom(_343846), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _343848, _343850), c_Orderings_Oord__class_Oless__eq(_343846, c_Groups_Ozero__class_Ozero(_343846), _343852), c_Orderings_Oord__class_Oless__eq(_343846, _343852, c_Groups_Oone__class_Oone(_343846)), -(c_Orderings_Oord__class_Oless__eq(_343846, hAPP(hAPP(c_Power_Opower__class_Opower(_343846), _343852), _343850), hAPP(hAPP(c_Power_Opower__class_Opower(_343846), _343852), _343848)))], (4164 ^ _206868) ^ [_344433, _344435, _344437, _344439] : [class_Rings_Olinordered__semidom(_344433), hAPP(hAPP(c_Power_Opower__class_Opower(_344433), _344435), _344437) = hAPP(hAPP(c_Power_Opower__class_Opower(_344433), _344439), _344437), c_Orderings_Oord__class_Oless__eq(_344433, c_Groups_Ozero__class_Ozero(_344433), _344435), c_Orderings_Oord__class_Oless__eq(_344433, c_Groups_Ozero__class_Ozero(_344433), _344439), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _344437), -(_344435 = _344439)], (4186 ^ _206868) ^ [_345058] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345058), _345058)))], (4188 ^ _206868) ^ [_345170, _345172] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345170), _345172)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345172), _345170))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345172), _345170)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345170), _345172)))], (4202 ^ _206868) ^ [_345621, _345623, _345625] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345621), _345623)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345623), _345621))), 4217 ^ _206868 : [(4218 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345621), _345625)))], (4220 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345625), _345621))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345623), _345625)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _345625), _345623)))], (4222 ^ _206868) ^ [_346262, _346264] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346262), _346264)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346264), _346262))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346264), _346262)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346262), _346264)))], (4236 ^ _206868) ^ [_346713, _346715, _346717] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346713), _346715)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346715), _346713))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346715), _346717)), 4247 ^ _206868 : [(4248 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346713), _346717)))], (4250 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _346717), _346713))]]], (4252 ^ _206868) ^ [_347262, _347264, _347266] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _347262), _347264)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _347264), _347262))), _347264 = _347266, 4263 ^ _206868 : [(4264 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _347262), _347266)))], (4266 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _347266), _347262))]]], (4268 ^ _206868) ^ [_347787, _347789] : [_347789 = _347787, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _347787), _347789)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _347789), _347787)))], (4278 ^ _206868) ^ [_348110, _348112] : [_348110 = _348112, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348110), _348112)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348112), _348110)))], (4288 ^ _206868) ^ [_348433, _348435] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348433), _348435)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348435), _348433))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348435), _348433)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348433), _348435)))], (4302 ^ _206868) ^ [_348870, _348872] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348870), _348872))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348870), _348872)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _348872), _348870)))], (4312 ^ _206868) ^ [_349202, _349204] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349202), _349204)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349204), _349202))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349204), _349202)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349202), _349204)))], (4326 ^ _206868) ^ [_349639, _349641] : [_349639 = _349641, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349639), _349641)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349641), _349639)))], (4336 ^ _206868) ^ [_349976, _349978, _349980] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349976), _349978)), 4347 ^ _206868 : [(4348 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349976), _349980)))], (4350 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349980), _349976))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349978), _349980)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _349980), _349978)))], (4352 ^ _206868) ^ [_350523, _350525, _350527] : [_350523 = _350525, 4363 ^ _206868 : [(4364 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _350523), _350527)))], (4366 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _350527), _350523))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _350525), _350527)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _350527), _350525)))], (4368 ^ _206868) ^ [_351060, _351062, _351064] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _351060), _351062)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _351062), _351064)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _351060), _351064)))], (4378 ^ _206868) ^ [_351399, _351401] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _351399), _351401)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _351401), _351399)), -(_351399 = _351401)], (4388 ^ _206868) ^ [_351718, _351720] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _351718), _351720)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _351720), _351718)), -(_351718 = _351720)], (4398 ^ _206868) ^ [_352051, _352053, _352055] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _352051), _352053)), _352053 = _352055, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _352051), _352055)))], (4408 ^ _206868) ^ [_352394, _352396, _352398] : [_352394 = _352396, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _352396), _352398)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _352394), _352398)))], (4418 ^ _206868) ^ [_352723, _352725] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _352723), _352725)), -(_352723 = _352725), 4425 ^ _206868 : [(4426 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _352723), _352725)))], (4428 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _352725), _352723))]]], (4430 ^ _206868) ^ [_353131, _353133] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _353131), _353133)), 4435 ^ _206868 : [(4436 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _353131), _353133)))], (4438 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _353133), _353131))]], -(_353131 = _353133)], (4442 ^ _206868) ^ [_353537, _353539] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _353537), _353539)), 4445 ^ _206868 : [(4446 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _353539), _353537)), -(_353539 = _353537)], (4452 ^ _206868) ^ [] : [_353539 = _353537, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _353539), _353537)))]]], (4458 ^ _206868) ^ [_354022, _354024] : [_354022 = _354024, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _354022), _354024)))], (4464 ^ _206868) ^ [_354242, _354244] : [-(_354242 = _354244), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _354242), _354244)), 4471 ^ _206868 : [(4472 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _354242), _354244)))], (4474 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _354244), _354242))]]], (4476 ^ _206868) ^ [_354679, _354681] : [4483 ^ _206868 : [(4484 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _354679), _354681)))], (4486 ^ _206868) ^ [] : [_354679 = _354681]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _354679), _354681)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _354681), _354679)))], (4488 ^ _206868) ^ [_355039, _355041] : [4495 ^ _206868 : [(4496 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355039), _355041)))], (4498 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355041), _355039))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355039), _355041)), -(_355039 = _355041)], (4500 ^ _206868) ^ [_355478, _355480] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355478), _355480)), 4505 ^ _206868 : [(4506 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355478), _355480)))], (4508 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355480), _355478))]], -(_355478 = _355480)], (4512 ^ _206868) ^ [_355836, _355838] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355836), _355838))), 4513 ^ _206868 : [(4520 ^ _206868) ^ [] : [_355836 = _355838], (4514 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355836), _355838)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _355838), _355836)))]]], (4524 ^ _206868) ^ [_356273, _356275] : [_356273 = _356275, 4527 ^ _206868 : [(4528 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _356273), _356275)))], (4530 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _356275), _356273)))]]], (4532 ^ _206868) ^ [_356530, _356532] : [-(_356530 = _356532), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _356530), _356532)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _356532), _356530))], (4542 ^ _206868) ^ [_356866] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _356866), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_356866 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4548 ^ _206868) ^ [_357032] : [_357032 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _357032), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (4564 ^ _206868) ^ [_357545, _357547] : [4565 ^ _206868 : [(4566 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _357545)], (4568 ^ _206868) ^ [] : [_357547 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _357545), _357547)))], (4554 ^ _206868) ^ [_357277, _357279] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _357277), _357279)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _357277)), -(_357279 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4572 ^ _206868) ^ [_357861, _357863, _357865] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _357861), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _357861), _357863), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _357861), _357865)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _357863, _357865))], (4582 ^ _206868) ^ [_358214, _358216, _358218] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _358214), _358216)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _358214), _358218))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _358214), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _358216, _358218))], (4592 ^ _206868) ^ [_358561, _358563] : [class_Groups_Omonoid__mult(_358561), -(hAPP(hAPP(c_Power_Opower__class_Opower(_358561), _358563), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _358563)], (4598 ^ _206868) ^ [_358799, _358801, _358803] : [class_Rings_Oring__1__no__zero__divisors(_358799), -(_358801 = c_Groups_Ozero__class_Ozero(_358799)), hAPP(hAPP(c_Power_Opower__class_Opower(_358799), _358801), _358803) = c_Groups_Ozero__class_Ozero(_358799)], (4608 ^ _206868) ^ [_359134, _359136] : [class_Groups_Omonoid__mult(_359134), -(hAPP(hAPP(c_Power_Opower__class_Opower(_359134), c_Groups_Oone__class_Oone(_359134)), _359136) = c_Groups_Oone__class_Oone(_359134))], (4614 ^ _206868) ^ [_359394, _359396, _359398, _359400] : [class_Rings_Ocomm__semiring__1(_359394), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_359394), _359396), _359398)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_359394), hAPP(hAPP(c_Power_Opower__class_Opower(_359394), _359396), _359400)), hAPP(hAPP(c_Power_Opower__class_Opower(_359394), _359398), _359400))))], (4624 ^ _206868) ^ [_359799, _359801, _359803, _359805] : [class_Rings_Olinordered__semidom(_359799), c_Orderings_Oord__class_Oless__eq(_359799, _359801, _359803), c_Orderings_Oord__class_Oless__eq(_359799, c_Groups_Ozero__class_Ozero(_359799), _359801), -(c_Orderings_Oord__class_Oless__eq(_359799, hAPP(hAPP(c_Power_Opower__class_Opower(_359799), _359801), _359805), hAPP(hAPP(c_Power_Opower__class_Opower(_359799), _359803), _359805)))], (4638 ^ _206868) ^ [_360269, _360271, _360273] : [class_Rings_Olinordered__semidom(_360269), c_Orderings_Oord__class_Oless__eq(_360269, c_Groups_Ozero__class_Ozero(_360269), _360271), -(c_Orderings_Oord__class_Oless__eq(_360269, c_Groups_Ozero__class_Ozero(_360269), hAPP(hAPP(c_Power_Opower__class_Opower(_360269), _360271), _360273)))], (4648 ^ _206868) ^ [_360618, _360620, _360622] : [class_Rings_Olinordered__semidom(_360618), c_Orderings_Oord__class_Oless(_360618, c_Groups_Ozero__class_Ozero(_360618), _360620), -(c_Orderings_Oord__class_Oless(_360618, c_Groups_Ozero__class_Ozero(_360618), hAPP(hAPP(c_Power_Opower__class_Opower(_360618), _360620), _360622)))], (4658 ^ _206868) ^ [_360967, _360969, _360971] : [class_Rings_Olinordered__semidom(_360967), c_Orderings_Oord__class_Oless__eq(_360967, c_Groups_Oone__class_Oone(_360967), _360969), -(c_Orderings_Oord__class_Oless__eq(_360967, c_Groups_Oone__class_Oone(_360967), hAPP(hAPP(c_Power_Opower__class_Opower(_360967), _360969), _360971)))], (4668 ^ _206868) ^ [_361316, _361318, _361320] : [class_Power_Opower(_361316), class_Rings_Omult__zero(_361316), class_Rings_Ono__zero__divisors(_361316), class_Rings_Ozero__neq__one(_361316), 4683 ^ _206868 : [(4684 ^ _206868) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_361316), _361318), _361320) = c_Groups_Ozero__class_Ozero(_361316), 4687 ^ _206868 : [(4688 ^ _206868) ^ [] : [-(_361318 = c_Groups_Ozero__class_Ozero(_361316))], (4690 ^ _206868) ^ [] : [_361320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (4692 ^ _206868) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_361316), _361318), _361320) = c_Groups_Ozero__class_Ozero(_361316)), _361318 = c_Groups_Ozero__class_Ozero(_361316), -(_361320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4702 ^ _206868) ^ [_362299, _362301, _362303, _362305] : [class_Rings_Olinordered__semidom(_362299), c_Orderings_Oord__class_Oless(_362299, c_Groups_Oone__class_Oone(_362299), _362301), 4709 ^ _206868 : [(4710 ^ _206868) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_362299), _362301), _362303) = hAPP(hAPP(c_Power_Opower__class_Opower(_362299), _362301), _362305), -(_362303 = _362305)], (4716 ^ _206868) ^ [] : [_362303 = _362305, -(hAPP(hAPP(c_Power_Opower__class_Opower(_362299), _362301), _362303) = hAPP(hAPP(c_Power_Opower__class_Opower(_362299), _362301), _362305))]]], (4722 ^ _206868) ^ [_362940, _362942] : [class_Power_Opower(_362940), -(hAPP(hAPP(c_Power_Opower__class_Opower(_362940), _362942), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_362940))], (4728 ^ _206868) ^ [_363210, _363212, _363214, _363216, _363218] : [class_Rings_Ocomm__semiring__1(_363210), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_363210), hAPP(hAPP(c_Power_Opower__class_Opower(_363210), _363212), _363214)), _363216)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363218, _363214), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_363210), hAPP(hAPP(c_Power_Opower__class_Opower(_363210), _363212), _363218)), _363216)))], (4742 ^ _206868) ^ [_363742, _363744, _363746, _363748, _363750] : [class_Rings_Ocomm__semiring__1(_363742), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_363742), _363744), _363746)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363748, _363750), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_363742), hAPP(hAPP(c_Power_Opower__class_Opower(_363742), _363744), _363748)), hAPP(hAPP(c_Power_Opower__class_Opower(_363742), _363746), _363750))))], (4756 ^ _206868) ^ [_364260, _364262, _364264, _364266] : [class_Rings_Ocomm__semiring__1(_364260), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _364262, _364264), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_364260), hAPP(hAPP(c_Power_Opower__class_Opower(_364260), _364266), _364262)), hAPP(hAPP(c_Power_Opower__class_Opower(_364260), _364266), _364264))))], (4766 ^ _206868) ^ [_364653, _364655, _364657, _364659] : [class_Rings_Olinordered__semidom(_364653), c_Orderings_Oord__class_Oless(_364653, hAPP(hAPP(c_Power_Opower__class_Opower(_364653), _364655), _364657), hAPP(hAPP(c_Power_Opower__class_Opower(_364653), _364659), _364657)), c_Orderings_Oord__class_Oless__eq(_364653, c_Groups_Ozero__class_Ozero(_364653), _364659), -(c_Orderings_Oord__class_Oless(_364653, _364655, _364659))], (4780 ^ _206868) ^ [_365109, _365111] : [class_Power_Opower(_365109), class_Rings_Osemiring__0(_365109), 4787 ^ _206868 : [(4788 ^ _206868) ^ [] : [_365111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_365109), c_Groups_Ozero__class_Ozero(_365109)), _365111) = c_Groups_Oone__class_Oone(_365109))], (4794 ^ _206868) ^ [] : [-(_365111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_365109), c_Groups_Ozero__class_Ozero(_365109)), _365111) = c_Groups_Ozero__class_Ozero(_365109))]]], (4800 ^ _206868) ^ [_365738, _365740, _365742, _365744] : [class_Rings_Olinordered__semidom(_365738), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _365740, _365742), c_Orderings_Oord__class_Oless(_365738, c_Groups_Oone__class_Oone(_365738), _365744), -(c_Orderings_Oord__class_Oless(_365738, hAPP(hAPP(c_Power_Opower__class_Opower(_365738), _365744), _365740), hAPP(hAPP(c_Power_Opower__class_Opower(_365738), _365744), _365742)))], (4814 ^ _206868) ^ [_366222, _366224, _366226, _366228] : [class_Rings_Olinordered__semidom(_366222), c_Orderings_Oord__class_Oless(_366222, c_Groups_Oone__class_Oone(_366222), _366224), c_Orderings_Oord__class_Oless(_366222, hAPP(hAPP(c_Power_Opower__class_Opower(_366222), _366224), _366226), hAPP(hAPP(c_Power_Opower__class_Opower(_366222), _366224), _366228)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _366226, _366228))], (4828 ^ _206868) ^ [_366706, _366708, _366710, _366712] : [class_Rings_Olinordered__semidom(_366706), c_Orderings_Oord__class_Oless(_366706, c_Groups_Oone__class_Oone(_366706), _366708), 4835 ^ _206868 : [(4836 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_366706, hAPP(hAPP(c_Power_Opower__class_Opower(_366706), _366708), _366710), hAPP(hAPP(c_Power_Opower__class_Opower(_366706), _366708), _366712)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _366710, _366712))], (4842 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _366710, _366712), -(c_Orderings_Oord__class_Oless(_366706, hAPP(hAPP(c_Power_Opower__class_Opower(_366706), _366708), _366710), hAPP(hAPP(c_Power_Opower__class_Opower(_366706), _366708), _366712)))]]], (4848 ^ _206868) ^ [_367381, _367383, _367385, _367387] : [class_Rings_Olinordered__semidom(_367381), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _367383, _367385), c_Orderings_Oord__class_Oless__eq(_367381, c_Groups_Oone__class_Oone(_367381), _367387), -(c_Orderings_Oord__class_Oless__eq(_367381, hAPP(hAPP(c_Power_Opower__class_Opower(_367381), _367387), _367383), hAPP(hAPP(c_Power_Opower__class_Opower(_367381), _367387), _367385)))], (4862 ^ _206868) ^ [_367865, _367867, _367869, _367871] : [class_Rings_Olinordered__semidom(_367865), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _367867, _367869), c_Orderings_Oord__class_Oless(_367865, c_Groups_Ozero__class_Ozero(_367865), _367871), c_Orderings_Oord__class_Oless(_367865, _367871, c_Groups_Oone__class_Oone(_367865)), -(c_Orderings_Oord__class_Oless(_367865, hAPP(hAPP(c_Power_Opower__class_Opower(_367865), _367871), _367869), hAPP(hAPP(c_Power_Opower__class_Opower(_367865), _367871), _367867)))], (4880 ^ _206868) ^ [_368424, _368426] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _368424), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _368426), _368424)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _368426))], (4890 ^ _206868) ^ [_368737, _368739] : [class_Rings_Ocomm__semiring__1(_368737), -(hAPP(hAPP(c_Power_Opower__class_Opower(_368737), _368739), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_368737))], (4896 ^ _206868) ^ [_368979, _368981, _368983] : [class_Rings_Oidom(_368979), -(_368981 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_368979))), 4903 ^ _206868 : [(4904 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_368979)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_368979)), c_Polynomial_OpCons(_368979, c_Groups_Ouminus__class_Ouminus(_368979, _368983), c_Polynomial_OpCons(_368979, c_Groups_Oone__class_Oone(_368979), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_368979))))), c_Polynomial_Oorder(_368979, _368983, _368981))), _368981)))], (4906 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_368979)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_368979)), c_Polynomial_OpCons(_368979, c_Groups_Ouminus__class_Ouminus(_368979, _368983), c_Polynomial_OpCons(_368979, c_Groups_Oone__class_Oone(_368979), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_368979))))), c_Nat_OSuc(c_Polynomial_Oorder(_368979, _368983, _368981)))), _368981))]]], (4908 ^ _206868) ^ [_369553, _369555, _369557] : [class_Rings_Oidom(_369553), -(_369555 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_369553))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_369553)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_369553)), c_Polynomial_OpCons(_369553, c_Groups_Ouminus__class_Ouminus(_369553, _369557), c_Polynomial_OpCons(_369553, c_Groups_Oone__class_Oone(_369553), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_369553))))), c_Nat_OSuc(c_Polynomial_Oorder(_369553, _369557, _369555)))), _369555))], (4918 ^ _206868) ^ [_369970, _369972, _369974] : [-(_369970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 4921 ^ _206868 : [(4922 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _369972), _369970)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _369974), _369970))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _369972), _369974)))], (4928 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _369972), _369974)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _369972), _369970)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _369974), _369970))))]]], (4934 ^ _206868) ^ [_370529, _370531, _370533] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _370529), _370531)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _370533), _370531))), -(_370531 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _370529), _370533)))], (4944 ^ _206868) ^ [_370856] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _370856), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4946 ^ _206868) ^ [_370939] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _370939, c_Nat_OSuc(_370939)))], (4948 ^ _206868) ^ [_371049, _371051] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _371049, _371051), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_371049), c_Nat_OSuc(_371051)))], (4954 ^ _206868) ^ [_371242] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_371242)))], (4956 ^ _206868) ^ [_371323] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _371323)))], (4958 ^ _206868) ^ [_371432, _371434] : [c_Nat_OSuc(_371432) = c_Nat_OSuc(_371434), -(_371432 = _371434)], (4964 ^ _206868) ^ [_371679, _371681] : [c_Nat_OSuc(_371679) = c_Nat_OSuc(_371681), -(_371679 = _371681)], (4970 ^ _206868) ^ [_371849, _371851] : [_371849 = _371851, -(c_Nat_OSuc(_371849) = c_Nat_OSuc(_371851))], (4976 ^ _206868) ^ [_372039] : [c_Nat_OSuc(_372039) = _372039], (4978 ^ _206868) ^ [_372118] : [_372118 = c_Nat_OSuc(_372118)], (4980 ^ _206868) ^ [_372197] : [c_Nat_OSuc(_372197) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4982 ^ _206868) ^ [_372276] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_372276)], (4984 ^ _206868) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4986 ^ _206868) ^ [_372408] : [c_Nat_OSuc(_372408) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4988 ^ _206868) ^ [_372487] : [c_Nat_OSuc(_372487) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4990 ^ _206868) ^ [_372566] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_372566)], (4992 ^ _206868) ^ [_372645] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_372645)], (4994 ^ _206868) ^ [_372725] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _372725) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5006 ^ _206868) ^ [_373128, _373130] : [5007 ^ _206868 : [(5008 ^ _206868) ^ [] : [_373130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5010 ^ _206868) ^ [] : [_373128 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _373128), _373130) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4996 ^ _206868) ^ [_372864, _372866] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _372864), _372866) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_372866 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_372864 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5014 ^ _206868) ^ [_373455, _373457] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373455, _373457)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373457, c_Nat_OSuc(_373455)))], (5020 ^ _206868) ^ [_373628, _373630] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373630, c_Nat_OSuc(_373628)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373628, _373630)], (5036 ^ _206868) ^ [_374138, _374140] : [5037 ^ _206868 : [(5038 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374138, _374140)], (5040 ^ _206868) ^ [] : [_374138 = _374140]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374138, c_Nat_OSuc(_374140)))], (5026 ^ _206868) ^ [_373878, _373880] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373878, c_Nat_OSuc(_373880)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373878, _373880)), -(_373878 = _373880)], (5044 ^ _206868) ^ [_374461, _374463] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_374461), c_Nat_OSuc(_374463)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374461, _374463))], (5050 ^ _206868) ^ [_374635, _374637] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374635, _374637), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_374635), c_Nat_OSuc(_374637)))], (5056 ^ _206868) ^ [_374859, _374861] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374859, _374861)), 5059 ^ _206868 : [(5060 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374859, c_Nat_OSuc(_374861)), -(_374859 = _374861)], (5066 ^ _206868) ^ [] : [_374859 = _374861, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374859, c_Nat_OSuc(_374861)))]]], (5072 ^ _206868) ^ [_375333, _375335] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375333, _375335)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375333, c_Nat_OSuc(_375335)), -(_375335 = _375333)], (5082 ^ _206868) ^ [_375643, _375645] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375643, _375645), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375643, c_Nat_OSuc(_375645)))], (5088 ^ _206868) ^ [_375861, _375863] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375861, _375863), -(c_Nat_OSuc(_375861) = _375863), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_375861), _375863))], (5098 ^ _206868) ^ [_376189, _376191, _376193] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _376189, _376191), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _376191, _376193), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_376189), _376193))], (5108 ^ _206868) ^ [_376508, _376510] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _376508, c_Nat_OSuc(_376510)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _376508, _376510)), -(_376508 = _376510)], (5118 ^ _206868) ^ [_376818, _376820] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_376818), _376820), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _376818, _376820))], (5124 ^ _206868) ^ [_377036, _377038] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_377036), c_Nat_OSuc(_377038)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _377036, _377038))], (5130 ^ _206868) ^ [_377228] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_377228), _377228)], (5132 ^ _206868) ^ [_377367, _377369] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377367, _377369)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_377369), _377367))], (5138 ^ _206868) ^ [_377540, _377542] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_377542), _377540), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377540, _377542)], (5154 ^ _206868) ^ [_378054, _378056] : [5155 ^ _206868 : [(5156 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378054, _378056)], (5158 ^ _206868) ^ [] : [_378054 = c_Nat_OSuc(_378056)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378054, c_Nat_OSuc(_378056)))], (5144 ^ _206868) ^ [_377790, _377792] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377790, c_Nat_OSuc(_377792)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377790, _377792)), -(_377790 = c_Nat_OSuc(_377792))], (5162 ^ _206868) ^ [_378381, _378383] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_378381), c_Nat_OSuc(_378383)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378381, _378383))], (5168 ^ _206868) ^ [_378555, _378557] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378555, _378557), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_378555), c_Nat_OSuc(_378557)))], (5174 ^ _206868) ^ [_378779, _378781] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378779, _378781), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378779, c_Nat_OSuc(_378781)))], (5180 ^ _206868) ^ [_378997, _378999] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378997, c_Nat_OSuc(_378999)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378997, _378999)), -(_378997 = c_Nat_OSuc(_378999))], (5190 ^ _206868) ^ [_379311, _379313] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_379311), _379313), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _379311, _379313))], (5196 ^ _206868) ^ [_379542, _379544, _379546, _379548] : [-(hAPP(c_Nat_Onat_Onat__case(_379542, _379544, _379546), c_Nat_OSuc(_379548)) = hAPP(_379546, _379548))], (5198 ^ _206868) ^ [_379667, _379669] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_379667), c_Groups_Ozero__class_Ozero(_379667)), c_Nat_OSuc(_379669)) = c_Groups_Ozero__class_Ozero(_379667)), class_Power_Opower(_379667), class_Rings_Osemiring__0(_379667)], (5208 ^ _206868) ^ [_380019, _380021] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _380019, c_Nat_OSuc(_380021)), -(_380019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5216 ^ _206868 : [(5217 ^ _206868) ^ [] : [-(_380019 = c_Nat_OSuc(5215 ^ [_380019, _380021]))], (5219 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 5215 ^ [_380019, _380021], _380021))]]], (5221 ^ _206868) ^ [_380431, _380433] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _380431, c_Nat_OSuc(_380433))), 5222 ^ _206868 : [(5223 ^ _206868) ^ [] : [_380431 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5225 ^ _206868) ^ [_380600] : [_380431 = c_Nat_OSuc(_380600), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _380600, _380433)]]], (5233 ^ _206868) ^ [_380898] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _380898, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_380898 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5239 ^ _206868) ^ [_381056] : [_381056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _381056, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5245 ^ _206868) ^ [_381279] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _381279), -(_381279 = c_Nat_OSuc(5248 ^ [_381279]))], (5252 ^ _206868) ^ [_381494] : [5253 ^ _206868 : [(5254 ^ _206868) ^ [_381565] : [_381494 = c_Nat_OSuc(_381565)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _381494))], (5258 ^ _206868) ^ [_381743] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _381743), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_381743 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5264 ^ _206868) ^ [_381909] : [_381909 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _381909), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (5270 ^ _206868) ^ [_382125, _382127] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _382125), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _382125), _382127)))], (5276 ^ _206868) ^ [_382351, _382353] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_382351), _382353), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _382351, _382353))], (5282 ^ _206868) ^ [_382569, _382571] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _382569, _382571), 5285 ^ _206868 : [(5286 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _382571, c_Nat_OSuc(_382569)), -(_382571 = _382569)], (5292 ^ _206868) ^ [] : [_382571 = _382569, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _382571, c_Nat_OSuc(_382569)))]]], (5298 ^ _206868) ^ [_383040, _383042] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _383040, _383042), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_383040), _383042))], (5304 ^ _206868) ^ [_383258, _383260] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _383258, _383260), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _383258, c_Nat_OSuc(_383260)))], (5310 ^ _206868) ^ [_383505, _383507] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_383505), _383507), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _383505, _383507))], (5316 ^ _206868) ^ [_383675, _383677] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _383675, _383677), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_383675), _383677))], (5322 ^ _206868) ^ [_383924, _383926] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _383924, c_Nat_OSuc(_383926)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _383924, _383926))], (5328 ^ _206868) ^ [_384094, _384096] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _384094, _384096), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _384094, c_Nat_OSuc(_384096)))], (5334 ^ _206868) ^ [_384343, _384345] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _384343, _384345), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_384343), _384345))], (5340 ^ _206868) ^ [_384513, _384515] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_384513), _384515), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _384513, _384515))], (5346 ^ _206868) ^ [_384761, _384763, _384765, _384767] : [class_Groups_Ozero(_384761), -(hAPP(c_Polynomial_Ocoeff(_384761, c_Polynomial_OpCons(_384761, _384763, _384765)), c_Nat_OSuc(_384767)) = hAPP(c_Polynomial_Ocoeff(_384761, _384765), _384767))], (5352 ^ _206868) ^ [_385045, _385047, _385049, _385051] : [class_Rings_Olinordered__semidom(_385045), c_Orderings_Oord__class_Oless__eq(_385045, hAPP(hAPP(c_Power_Opower__class_Opower(_385045), _385047), c_Nat_OSuc(_385049)), hAPP(hAPP(c_Power_Opower__class_Opower(_385045), _385051), c_Nat_OSuc(_385049))), c_Orderings_Oord__class_Oless__eq(_385045, c_Groups_Ozero__class_Ozero(_385045), _385051), -(c_Orderings_Oord__class_Oless__eq(_385045, _385047, _385051))], (5366 ^ _206868) ^ [_385537, _385539, _385541, _385543] : [class_Rings_Olinordered__semidom(_385537), hAPP(hAPP(c_Power_Opower__class_Opower(_385537), _385539), c_Nat_OSuc(_385541)) = hAPP(hAPP(c_Power_Opower__class_Opower(_385537), _385543), c_Nat_OSuc(_385541)), c_Orderings_Oord__class_Oless__eq(_385537, c_Groups_Ozero__class_Ozero(_385537), _385539), c_Orderings_Oord__class_Oless__eq(_385537, c_Groups_Ozero__class_Ozero(_385537), _385543), -(_385539 = _385543)], (5384 ^ _206868) ^ [_386114, _386116, _386118] : [class_Rings_Olinordered__semidom(_386114), c_Orderings_Oord__class_Oless(_386114, c_Groups_Oone__class_Oone(_386114), _386116), -(c_Orderings_Oord__class_Oless(_386114, c_Groups_Oone__class_Oone(_386114), hAPP(hAPP(c_Power_Opower__class_Opower(_386114), _386116), c_Nat_OSuc(_386118))))], (5394 ^ _206868) ^ [_386467, _386469, _386471] : [class_Rings_Oidom(_386467), 5397 ^ _206868 : [(5408 ^ _206868) ^ [] : [5409 ^ _206868 : [(5410 ^ _206868) ^ [] : [_386469 = _386471], (5412 ^ _206868) ^ [] : [_386469 = c_Groups_Ouminus__class_Ouminus(_386467, _386471)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_386467), _386469), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_386467), _386471), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (5398 ^ _206868) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_386467), _386469), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_386467), _386471), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_386469 = _386471), -(_386469 = c_Groups_Ouminus__class_Ouminus(_386467, _386471))]]], (5416 ^ _206868) ^ [_387176, _387178, _387180] : [class_Groups_Ozero(_387176), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_387176, c_Polynomial_OpCons(_387176, _387178, _387180)), c_Nat_OSuc(c_Polynomial_Odegree(_387176, _387180))))], (5422 ^ _206868) ^ [_387430, _387432, _387434] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _387430), _387432)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _387434), _387432))), -(_387432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _387430), _387434)))], (5432 ^ _206868) ^ [_387800, _387802, _387804] : [-(_387800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5435 ^ _206868 : [(5436 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _387802), _387800)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _387804), _387800))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _387802), _387804)))], (5442 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _387802), _387804)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _387802), _387800)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _387804), _387800))))]]], (5448 ^ _206868) ^ [_388345, _388347] : [class_Rings_Ocomm__semiring__1(_388345), -(hAPP(hAPP(c_Power_Opower__class_Opower(_388345), _388347), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _388347)], (5454 ^ _206868) ^ [_388583, _388585, _388587] : [class_Groups_Ozero(_388583), -(_388585 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388583))), -(c_Polynomial_Odegree(_388583, c_Polynomial_OpCons(_388583, _388587, _388585)) = c_Nat_OSuc(c_Polynomial_Odegree(_388583, _388585)))], (5464 ^ _206868) ^ [_388896] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _388896)))], (5466 ^ _206868) ^ [_389019, _389021, _389023] : [class_Rings_Olinordered__semidom(_389019), c_Orderings_Oord__class_Oless__eq(_389019, c_Groups_Ozero__class_Ozero(_389019), _389021), c_Orderings_Oord__class_Oless__eq(_389019, _389021, c_Groups_Oone__class_Oone(_389019)), -(c_Orderings_Oord__class_Oless__eq(_389019, hAPP(hAPP(c_Power_Opower__class_Opower(_389019), _389021), c_Nat_OSuc(_389023)), _389021))], (5480 ^ _206868) ^ [_389467, _389469, _389471] : [class_Rings_Olinordered__semidom(_389467), c_Orderings_Oord__class_Oless(_389467, c_Groups_Ozero__class_Ozero(_389467), _389469), c_Orderings_Oord__class_Oless(_389467, _389469, c_Groups_Oone__class_Oone(_389467)), -(c_Orderings_Oord__class_Oless(_389467, hAPP(hAPP(c_Power_Opower__class_Opower(_389467), _389469), c_Nat_OSuc(_389471)), c_Groups_Oone__class_Oone(_389467)))], (5494 ^ _206868) ^ [_389919, _389921, _389923] : [class_Groups_Ozero(_389919), 5497 ^ _206868 : [(5498 ^ _206868) ^ [] : [_389921 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_389919)), -(c_Polynomial_Odegree(_389919, c_Polynomial_OpCons(_389919, _389923, _389921)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5504 ^ _206868) ^ [] : [-(_389921 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_389919))), -(c_Polynomial_Odegree(_389919, c_Polynomial_OpCons(_389919, _389923, _389921)) = c_Nat_OSuc(c_Polynomial_Odegree(_389919, _389921)))]]], (5510 ^ _206868) ^ [_390453, _390455] : [class_Groups_Ozero(_390453), 5513 ^ _206868 : [(5514 ^ _206868) ^ [] : [_390455 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_390453)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_390453, _390455) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5520 ^ _206868) ^ [] : [-(_390455 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_390453))), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_390453, _390455) = c_Nat_OSuc(c_Polynomial_Odegree(_390453, _390455)))]]], (5536 ^ _206868) ^ [_391252, _391254] : [5537 ^ _206868 : [(5538 ^ _206868) ^ [] : [_391254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5540 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _391252)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _391252), _391254)))], (5526 ^ _206868) ^ [_390984, _390986] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _390984), _390986)), -(_390986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _390984))], (5544 ^ _206868) ^ [_391540] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _391540, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_391540 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_391540 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5554 ^ _206868) ^ [_391846, _391848, _391850] : [class_Groups_Ozero(_391846), 5560 ^ _206868 : [(5561 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _391848, 5559 ^ [_391846, _391848, _391850]))], (5563 ^ _206868) ^ [] : [hAPP(c_Polynomial_Ocoeff(_391846, _391850), 5559 ^ [_391846, _391848, _391850]) = c_Groups_Ozero__class_Ozero(_391846)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_391846, _391850), _391848))], (5567 ^ _206868) ^ [_392357, _392359, _392361] : [class_Fields_Ofield(_392357), 5570 ^ _206868 : [(5581 ^ _206868) ^ [] : [5582 ^ _206868 : [(5583 ^ _206868) ^ [] : [-(_392359 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_392357)))], (5585 ^ _206868) ^ [] : [-(_392361 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_392357)))]], -(hAPP(c_Polynomial_Ocoeff(_392357, c_Polynomial_Opoly__gcd(_392357, _392359, _392361)), c_Polynomial_Odegree(_392357, c_Polynomial_Opoly__gcd(_392357, _392359, _392361))) = c_Groups_Oone__class_Oone(_392357))], (5571 ^ _206868) ^ [] : [-(hAPP(c_Polynomial_Ocoeff(_392357, c_Polynomial_Opoly__gcd(_392357, _392359, _392361)), c_Polynomial_Odegree(_392357, c_Polynomial_Opoly__gcd(_392357, _392359, _392361))) = c_Groups_Ozero__class_Ozero(_392357)), _392359 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_392357)), _392361 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_392357))]]], (5589 ^ _206868) ^ [_393129, _393131, _393133] : [class_Groups_Ozero(_393129), -(c_Polynomial_OpCons(_393129, _393131, _393133) = c_Polynomial_OAbs__poly(_393129, c_Nat_Onat_Onat__case(_393129, _393131, c_Polynomial_Ocoeff(_393129, _393133))))], (5595 ^ _206868) ^ [_393385, _393387, _393389] : [class_Fields_Ofield(_393385), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_393385)), c_Polynomial_Opoly__gcd(_393385, _393387, _393389)), _393387)))], (5601 ^ _206868) ^ [_393639, _393641, _393643] : [class_Fields_Ofield(_393639), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_393639)), c_Polynomial_Opoly__gcd(_393639, _393641, _393643)), _393643)))], (5607 ^ _206868) ^ [_393893, _393895, _393897] : [class_Fields_Ofield(_393893), -(c_Polynomial_Opoly__gcd(_393893, _393895, _393897) = c_Polynomial_Opoly__gcd(_393893, _393897, _393895))], (5613 ^ _206868) ^ [_394151, _394153, _394155, _394157] : [class_Fields_Ofield(_394151), -(c_Polynomial_Opoly__gcd(_394151, _394153, c_Polynomial_Opoly__gcd(_394151, _394155, _394157)) = c_Polynomial_Opoly__gcd(_394151, _394155, c_Polynomial_Opoly__gcd(_394151, _394153, _394157)))], (5619 ^ _206868) ^ [_394431, _394433, _394435, _394437] : [class_Fields_Ofield(_394431), -(c_Polynomial_Opoly__gcd(_394431, c_Polynomial_Opoly__gcd(_394431, _394433, _394435), _394437) = c_Polynomial_Opoly__gcd(_394431, _394433, c_Polynomial_Opoly__gcd(_394431, _394435, _394437)))], (5625 ^ _206868) ^ [_394669] : [class_Fields_Ofield(_394669), -(c_Polynomial_Opoly__gcd(_394669, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394669)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394669))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394669)))], (5631 ^ _206868) ^ [_394917, _394919, _394921] : [class_Fields_Ofield(_394917), 5634 ^ _206868 : [(5635 ^ _206868) ^ [] : [c_Polynomial_Opoly__gcd(_394917, _394919, _394921) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394917)), 5638 ^ _206868 : [(5639 ^ _206868) ^ [] : [-(_394919 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394917)))], (5641 ^ _206868) ^ [] : [-(_394921 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394917)))]]], (5643 ^ _206868) ^ [] : [-(c_Polynomial_Opoly__gcd(_394917, _394919, _394921) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394917))), _394919 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394917)), _394921 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394917))]]], (5653 ^ _206868) ^ [_395631, _395633, _395635, _395637] : [class_Fields_Ofield(_395631), 5656 ^ _206868 : [(5657 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_395631)), _395633), c_Polynomial_Opoly__gcd(_395631, _395635, _395637))), 5660 ^ _206868 : [(5661 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_395631)), _395633), _395635)))], (5663 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_395631)), _395633), _395637)))]]], (5665 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_395631)), _395633), c_Polynomial_Opoly__gcd(_395631, _395635, _395637)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_395631)), _395633), _395635)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_395631)), _395633), _395637))]]], (5675 ^ _206868) ^ [_396412, _396414, _396416, _396418] : [class_Fields_Ofield(_396412), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_396412)), _396414), _396416)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_396412)), _396414), _396418)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_396412)), _396414), c_Polynomial_Opoly__gcd(_396412, _396416, _396418))))], (5689 ^ _206868) ^ [_396902, _396904, _396906] : [class_Fields_Ofield(_396902), -(c_Polynomial_Opoly__gcd(_396902, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_396902), _396904), _396906) = c_Polynomial_Opoly__gcd(_396902, _396904, _396906))], (5695 ^ _206868) ^ [_397156, _397158, _397160] : [class_Fields_Ofield(_397156), -(c_Polynomial_Opoly__gcd(_397156, _397158, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_397156), _397160)) = c_Polynomial_Opoly__gcd(_397156, _397158, _397160))], (5701 ^ _206868) ^ [_397396, _397398] : [class_Fields_Ofield(_397396), -(c_Polynomial_Opoly__gcd(_397396, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_397396)), _397398) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_397396)))], (5707 ^ _206868) ^ [_397628, _397630] : [class_Fields_Ofield(_397628), -(c_Polynomial_Opoly__gcd(_397628, _397630, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_397628))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_397628)))], (5713 ^ _206868) ^ [_397860, _397862] : [class_Groups_Ozero(_397860), -(c_Polynomial_OAbs__poly(_397860, c_Polynomial_Ocoeff(_397860, _397862)) = _397862)], (5719 ^ _206868) ^ [_398108, _398110, _398112, _398114] : [class_Fields_Ofield(_398108), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_398108)), _398110), _398112)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_398108)), _398110), _398114)), 5733 ^ _206868 : [(5734 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_398108)), 5732 ^ [_398108, _398110, _398112, _398114]), _398112)))], (5736 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_398108)), 5732 ^ [_398108, _398110, _398112, _398114]), _398114)))], (5738 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_398108)), 5732 ^ [_398108, _398110, _398112, _398114]), _398110))]], -(c_Polynomial_Opoly__gcd(_398108, _398112, _398114) = _398110), 5743 ^ _206868 : [(5744 ^ _206868) ^ [] : [-(_398112 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398108)))], (5746 ^ _206868) ^ [] : [-(_398114 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398108)))], (5748 ^ _206868) ^ [] : [hAPP(c_Polynomial_Ocoeff(_398108, _398110), c_Polynomial_Odegree(_398108, _398110)) = c_Groups_Ozero__class_Ozero(_398108)]], 5749 ^ _206868 : [(5756 ^ _206868) ^ [] : [hAPP(c_Polynomial_Ocoeff(_398108, _398110), c_Polynomial_Odegree(_398108, _398110)) = c_Groups_Oone__class_Oone(_398108)], (5750 ^ _206868) ^ [] : [_398112 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398108)), _398114 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398108))]]], (5760 ^ _206868) ^ [_399624, _399626, _399628] : [class_Groups_Ozero(_399624), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _399626, c_Polynomial_Odegree(_399624, _399628)), 5768 ^ _206868 : [(5769 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _399626, 5767 ^ [_399624, _399626, _399628]))], (5771 ^ _206868) ^ [] : [hAPP(c_Polynomial_Ocoeff(_399624, _399628), 5767 ^ [_399624, _399626, _399628]) = c_Groups_Ozero__class_Ozero(_399624)]]], (5773 ^ _206868) ^ [_400152, _400154, _400156, _400158] : [class_Orderings_Oorder(_400152), c_Orderings_Oorder_Omono(tc_Nat_Onat, _400152, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _400154), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _400156), _400158)), -(c_Orderings_Oord__class_Oless__eq(_400152, hAPP(_400154, _400156), hAPP(_400154, _400158)))], (5787 ^ _206868) ^ [_400594, _400596] : [class_RealVector_Oreal__normed__vector(_400594), 5790 ^ _206868 : [(5803 ^ _206868) ^ [] : [5805 ^ _206868 : [(5806 ^ _206868) ^ [_401330] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_400594, hAPP(_400596, 5804 ^ [_400594, _400596, _401330])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_401330)))]], 5808 ^ _206868 : [(5809 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 5807 ^ [_400594, _400596]))], (5811 ^ _206868) ^ [_401551] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_400594, hAPP(_400596, _401551)), 5807 ^ [_400594, _400596]))]]], (5791 ^ _206868) ^ [] : [5800 ^ _206868 : [(5801 ^ _206868) ^ [_401151] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_400594, hAPP(_400596, _401151)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(5799 ^ [_400594, _400596]))))]], 5792 ^ _206868 : [(5793 ^ _206868) ^ [_400833] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _400833), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_400594, hAPP(_400596, 5796 ^ [_400594, _400596, _400833])), _400833)]]]]], (5813 ^ _206868) ^ [_401691, _401693] : [class_RealVector_Oreal__normed__vector(_401691), 5816 ^ _206868 : [(5829 ^ _206868) ^ [] : [5831 ^ _206868 : [(5832 ^ _206868) ^ [_402427] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_401691, hAPP(_401693, 5830 ^ [_401691, _401693, _402427])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_402427)))]], 5834 ^ _206868 : [(5835 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 5833 ^ [_401691, _401693]))], (5837 ^ _206868) ^ [_402648] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_401691, hAPP(_401693, _402648)), 5833 ^ [_401691, _401693]))]]], (5817 ^ _206868) ^ [] : [5826 ^ _206868 : [(5827 ^ _206868) ^ [_402248] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_401691, hAPP(_401693, _402248)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(5825 ^ [_401691, _401693]))))]], 5818 ^ _206868 : [(5819 ^ _206868) ^ [_401930] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _401930), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_401691, hAPP(_401693, 5822 ^ [_401691, _401693, _401930])), _401930)]]]]], (5839 ^ _206868) ^ [_402759] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _402759)))], (5841 ^ _206868) ^ [_402899, _402901] : [c_RealDef_Oreal(tc_Nat_Onat, _402899) = c_RealDef_Oreal(tc_Nat_Onat, _402901), -(_402899 = _402901)], (5847 ^ _206868) ^ [_403073, _403075] : [_403073 = _403075, -(c_RealDef_Oreal(tc_Nat_Onat, _403073) = c_RealDef_Oreal(tc_Nat_Onat, _403075))], (5853 ^ _206868) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5855 ^ _206868) ^ [_403365] : [c_RealDef_Oreal(tc_Nat_Onat, _403365) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_403365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5861 ^ _206868) ^ [_403527] : [_403527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _403527) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5867 ^ _206868) ^ [_403709] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _403709), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5869 ^ _206868) ^ [_403849, _403851] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _403849), c_RealDef_Oreal(tc_Nat_Onat, _403851)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _403849, _403851))], (5875 ^ _206868) ^ [_404027, _404029] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404027, _404029), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _404027), c_RealDef_Oreal(tc_Nat_Onat, _404029)))], (5881 ^ _206868) ^ [_404284, _404286] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _404284), c_RealDef_Oreal(tc_Nat_Onat, _404286)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _404284, _404286))], (5887 ^ _206868) ^ [_404462, _404464] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _404462, _404464), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _404462), c_RealDef_Oreal(tc_Nat_Onat, _404464)))], (5893 ^ _206868) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5895 ^ _206868) ^ [_404728, _404730] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _404728), _404730)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _404728)), _404730))], (5897 ^ _206868) ^ [_404840, _404842] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _404840)), _404842) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _404840), _404842)))], (5899 ^ _206868) ^ [_404982] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _404982), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_404982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5905 ^ _206868) ^ [_405146] : [_405146 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _405146), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (5911 ^ _206868) ^ [_405331] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_405331))))], (5913 ^ _206868) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5915 ^ _206868) ^ [_405512] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _405512)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _405512))], (5921 ^ _206868) ^ [_405678] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _405678), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _405678)))], (5927 ^ _206868) ^ [_405894, _405896] : [class_RealVector_Oreal__normed__vector(_405894), 5930 ^ _206868 : [(5931 ^ _206868) ^ [] : [c_SEQ_OBseq(_405894, _405896), 5935 ^ _206868 : [(5936 ^ _206868) ^ [_406201] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_405894, hAPP(_405896, _406201)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(5934 ^ [_405894, _405896]))))]]], (5938 ^ _206868) ^ [] : [5940 ^ _206868 : [(5941 ^ _206868) ^ [_406379] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_405894, hAPP(_405896, 5939 ^ [_405894, _405896, _406379])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_406379)))]], -(c_SEQ_OBseq(_405894, _405896))]]], (5945 ^ _206868) ^ [_406569, _406571] : [class_RealVector_Oreal__normed__vector(_406569), 5948 ^ _206868 : [(5949 ^ _206868) ^ [] : [c_SEQ_OBseq(_406569, _406571), 5953 ^ _206868 : [(5954 ^ _206868) ^ [_406876] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_406569, hAPP(_406571, _406876)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(5952 ^ [_406569, _406571]))))]]], (5956 ^ _206868) ^ [] : [5958 ^ _206868 : [(5959 ^ _206868) ^ [_407054] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_406569, hAPP(_406571, 5957 ^ [_406569, _406571, _407054])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_407054)))]], -(c_SEQ_OBseq(_406569, _406571))]]], (5963 ^ _206868) ^ [_407244, _407246] : [class_Orderings_Oorder(_407244), 5970 ^ _206868 : [(5971 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 5968 ^ [_407244, _407246]), 5969 ^ [_407244, _407246])))], (5973 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_407244, hAPP(_407246, 5968 ^ [_407244, _407246]), hAPP(_407246, 5969 ^ [_407244, _407246]))]], -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _407244, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _407246))], (5977 ^ _206868) ^ [_407827, _407829] : [class_Orderings_Oorder(_407827), c_Orderings_Oord__class_Oless__eq(_407827, hAPP(_407829, 5982 ^ [_407827, _407829]), hAPP(_407829, c_Nat_OSuc(5982 ^ [_407827, _407829]))), -(c_SEQ_Oincseq(_407827, _407829))], (5988 ^ _206868) ^ [_408201] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _408201), 5992 ^ _206868 : [(5993 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, 5991 ^ [_408201]), _408201))], (5995 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _408201, c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(5991 ^ [_408201]))))]]], (5997 ^ _206868) ^ [_408572, _408574] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _408572), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _408574), 6005 ^ _206868 : [(6006 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6004 ^ [_408572, _408574]))], (6008 ^ _206868) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 6004 ^ [_408572, _408574]), _408572) = _408574)]]], (6010 ^ _206868) ^ [_409041, _409043] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _409041), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _409043), 6018 ^ _206868 : [(6019 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6017 ^ [_409041, _409043]))], (6021 ^ _206868) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 6017 ^ [_409041, _409043]), _409041) = _409043)], (6023 ^ _206868) ^ [_409545] : [-(_409545 = 6017 ^ [_409041, _409043]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _409545), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _409545), _409041) = _409043]]], (6033 ^ _206868) ^ [_409899, _409901] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _409899), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _409899, c_RealDef_Oreal(tc_Nat_Onat, _409901)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_409899), _409901))], (6043 ^ _206868) ^ [_410229] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_410229), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410229, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (6049 ^ _206868) ^ [_410393] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410393, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_410393), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6055 ^ _206868) ^ [_410607, _410609] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _410607), 6058 ^ _206868 : [(6059 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_410607), _410609), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410607, c_RealDef_Oreal(tc_Nat_Onat, _410609)))], (6065 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410607, c_RealDef_Oreal(tc_Nat_Onat, _410609)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_410607), _410609))]]], (6071 ^ _206868) ^ [_411090, _411092] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _411090), 6075 ^ _206868 : [(6076 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6074 ^ [_411090, _411092]))], (6078 ^ _206868) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 6074 ^ [_411090, _411092]), c_Nat_OSuc(_411092)) = _411090)]]], (6080 ^ _206868) ^ [_411489] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_411489)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _411489))], (6086 ^ _206868) ^ [_411653] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _411653), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_411653)))], (6092 ^ _206868) ^ [_411838] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _411838)) = _411838)], (6094 ^ _206868) ^ [_411921] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _411921)) = _411921)], (6096 ^ _206868) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6098 ^ _206868) ^ [_412057] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_412057)))], (6100 ^ _206868) ^ [_412167, _412169] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _412167, _412169), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_412167), c_RComplete_Onatfloor(_412169)))], (6106 ^ _206868) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6108 ^ _206868) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6110 ^ _206868) ^ [_412466] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_412466)))], (6112 ^ _206868) ^ [_412576, _412578] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _412576, _412578), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_412576), c_RComplete_Onatceiling(_412578)))], (6118 ^ _206868) ^ [_412769] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _412769, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_412769))))], (6120 ^ _206868) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6122 ^ _206868) ^ [_412921] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _412921, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_412921) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6128 ^ _206868) ^ [_413117] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _413117), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_413117)), _413117))], (6134 ^ _206868) ^ [_413335, _413337] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _413335), _413337), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413335, c_RComplete_Onatfloor(_413337)))], (6140 ^ _206868) ^ [_413559, _413561] : [_413559 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_413559)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _413559), _413561)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_413559)), _413561))], (6146 ^ _206868) ^ [_413797] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _413797, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_413797) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6152 ^ _206868) ^ [_414007, _414009] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _414007, c_RealDef_Oreal(tc_Nat_Onat, _414009)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_414007), _414009))], (6158 ^ _206868) ^ [_414231, _414233] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _414231), 6161 ^ _206868 : [(6162 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _414233, c_RComplete_Onatfloor(_414231)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _414233), _414231))], (6168 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _414233), _414231), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _414233, c_RComplete_Onatfloor(_414231)))]]], (6174 ^ _206868) ^ [_414714, _414716] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_414714), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _414716), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _414714, c_RealDef_Oreal(tc_Nat_Onat, _414716)))], (6180 ^ _206868) ^ [_414946, _414948] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _414946), _414948), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _414948, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _414946), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_414948) = _414946)], (6190 ^ _206868) ^ [_415287, _415289, _415291] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _415287), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _415287, _415289), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _415291), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _415291, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_415287, _415291), c_NthRoot_Oroot(_415289, _415291)))], (6208 ^ _206868) ^ [_415818, _415820, _415822] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _415818), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _415818, _415820), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _415822), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _415822, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_415818, _415822), c_NthRoot_Oroot(_415820, _415822)))], (6226 ^ _206868) ^ [_416335, _416337] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _416335), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _416337), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_416335, _416337)), _416335) = _416337)], (6236 ^ _206868) ^ [_416641, _416643] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _416641, _416643)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _416641), c_RealDef_Oreal(tc_Nat_Onat, _416643)))], (6238 ^ _206868) ^ [_416767, _416769] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _416767, _416769) = _416767, -(_416769 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6244 ^ _206868) ^ [_417014, _417016] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417014, _417016) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 6247 ^ _206868 : [(6248 ^ _206868) ^ [] : [-(_417014 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6250 ^ _206868) ^ [] : [-(_417016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6252 ^ _206868) ^ [_417259, _417261] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417259, _417261) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _417259 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _417261 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6262 ^ _206868) ^ [_417539] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417539, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _417539)], (6264 ^ _206868) ^ [_417621] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _417621) = _417621)], (6266 ^ _206868) ^ [_417717, _417719] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_417717), _417719) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417717, c_Nat_OSuc(_417719)))], (6268 ^ _206868) ^ [_417823, _417825] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_417823), _417825) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417823, _417825)))], (6270 ^ _206868) ^ [_417929, _417931] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417929, c_Nat_OSuc(_417931)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417929, _417931)))], (6272 ^ _206868) ^ [_418064, _418066, _418068] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418064, _418066), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418064, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418068, _418066)))], (6278 ^ _206868) ^ [_418306, _418308, _418310] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418306, _418308), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418306, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418308, _418310)))], (6284 ^ _206868) ^ [_418518, _418520] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418518, _418520), _418518)], (6286 ^ _206868) ^ [_418616, _418618] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418616, _418618), _418618)], (6288 ^ _206868) ^ [_418773, _418775, _418777] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418773, _418775), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418773, _418777)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418775, _418777))], (6294 ^ _206868) ^ [_418961, _418963, _418965] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418963, _418965), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418961, _418963), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418961, _418965)))], (6300 ^ _206868) ^ [_419213, _419215, _419217] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419213, _419215), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419213, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _419215, _419217)))], (6306 ^ _206868) ^ [_419455, _419457, _419459] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419455, _419457), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419455, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _419459, _419457)))], (6312 ^ _206868) ^ [_419697, _419699, _419701] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419697, _419699), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _419697, _419701), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _419699, _419701)))], (6318 ^ _206868) ^ [_419961, _419963, _419965, _419967] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419961, _419963), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419965, _419967), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _419961, _419965), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _419963, _419967)))], (6328 ^ _206868) ^ [_420330, _420332, _420334, _420336] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _420330, _420332), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _420334, _420332) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _420330, _420336), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _420334, _420336))], (6338 ^ _206868) ^ [_420683, _420685, _420687] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _420683, _420685), _420687), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _420683, _420687))], (6344 ^ _206868) ^ [_420940, _420942] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _420940), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _420942, _420940))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _420940), _420942)))], (6350 ^ _206868) ^ [_421130, _421132] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _421130), _421132)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _421130), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _421132, _421130))))], (6356 ^ _206868) ^ [_421384, _421386, _421388] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _421384, _421386), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _421384, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _421388, _421386)))], (6362 ^ _206868) ^ [_421626, _421628, _421630] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _421626, _421628), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _421626, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _421628, _421630)))], (6368 ^ _206868) ^ [_421839, _421841] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _421839, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _421841, _421839)))], (6370 ^ _206868) ^ [_421938, _421940] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _421938, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _421938, _421940)))], (6372 ^ _206868) ^ [_422081, _422083] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _422081, _422083), -(_422083 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _422081, 6375 ^ [_422081, _422083]))], (6379 ^ _206868) ^ [_422314, _422316] : [6380 ^ _206868 : [(6381 ^ _206868) ^ [_422389] : [_422316 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _422314, _422389)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _422314, _422316))], (6385 ^ _206868) ^ [_422601, _422603, _422605] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _422601, _422603), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _422601, _422605)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _422603, _422605))], (6391 ^ _206868) ^ [_422789, _422791, _422793] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _422791, _422793), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _422789, _422791), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _422789, _422793)))], (6397 ^ _206868) ^ [_423041, _423043, _423045] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _423041, _423043), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _423041, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _423043, _423045)))], (6403 ^ _206868) ^ [_423283, _423285, _423287] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _423283, _423285), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _423283, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _423287, _423285)))], (6409 ^ _206868) ^ [_423525, _423527, _423529] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _423525, _423527), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _423525, _423529), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _423527, _423529)))], (6415 ^ _206868) ^ [_423789, _423791, _423793, _423795] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _423789, _423791), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _423793, _423795), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _423789, _423793), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _423791, _423795)))], (6425 ^ _206868) ^ [_424144, _424146, _424148] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _424144, _424146), _424148), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _424146, _424148))], (6431 ^ _206868) ^ [_424386, _424388, _424390] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _424386, _424388), _424390), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _424386, _424390))], (6437 ^ _206868) ^ [_424628, _424630, _424632] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _424628, _424630), _424632), 6440 ^ _206868 : [(6441 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _424628, _424632))], (6443 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _424630, _424632))]]], (6445 ^ _206868) ^ [_424953, _424955, _424957] : [class_Rings_Ocomm__semiring__1(_424953), -(c_Groups_Oplus__class_Oplus(_424953, _424955, _424957) = c_Groups_Oplus__class_Oplus(_424953, _424957, _424955))], (6451 ^ _206868) ^ [_425211, _425213, _425215, _425217] : [class_Rings_Ocomm__semiring__1(_425211), -(c_Groups_Oplus__class_Oplus(_425211, _425213, c_Groups_Oplus__class_Oplus(_425211, _425215, _425217)) = c_Groups_Oplus__class_Oplus(_425211, _425215, c_Groups_Oplus__class_Oplus(_425211, _425213, _425217)))], (6457 ^ _206868) ^ [_425491, _425493, _425495, _425497] : [class_Rings_Ocomm__semiring__1(_425491), -(c_Groups_Oplus__class_Oplus(_425491, _425493, c_Groups_Oplus__class_Oplus(_425491, _425495, _425497)) = c_Groups_Oplus__class_Oplus(_425491, c_Groups_Oplus__class_Oplus(_425491, _425493, _425495), _425497))], (6463 ^ _206868) ^ [_425771, _425773, _425775, _425777] : [class_Rings_Ocomm__semiring__1(_425771), -(c_Groups_Oplus__class_Oplus(_425771, c_Groups_Oplus__class_Oplus(_425771, _425773, _425775), _425777) = c_Groups_Oplus__class_Oplus(_425771, _425773, c_Groups_Oplus__class_Oplus(_425771, _425775, _425777)))], (6469 ^ _206868) ^ [_426051, _426053, _426055, _426057] : [class_Rings_Ocomm__semiring__1(_426051), -(c_Groups_Oplus__class_Oplus(_426051, c_Groups_Oplus__class_Oplus(_426051, _426053, _426055), _426057) = c_Groups_Oplus__class_Oplus(_426051, c_Groups_Oplus__class_Oplus(_426051, _426053, _426057), _426055))], (6475 ^ _206868) ^ [_426345, _426347, _426349, _426351, _426353] : [class_Rings_Ocomm__semiring__1(_426345), -(c_Groups_Oplus__class_Oplus(_426345, c_Groups_Oplus__class_Oplus(_426345, _426347, _426349), c_Groups_Oplus__class_Oplus(_426345, _426351, _426353)) = c_Groups_Oplus__class_Oplus(_426345, c_Groups_Oplus__class_Oplus(_426345, _426347, _426351), c_Groups_Oplus__class_Oplus(_426345, _426349, _426353)))], (6481 ^ _206868) ^ [_426633, _426635, _426637] : [class_RealVector_Oreal__normed__vector(_426633), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_426633, c_Groups_Oplus__class_Oplus(_426633, _426635, _426637)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_426633, _426635), c_RealVector_Onorm__class_Onorm(_426633, _426637))))], (6487 ^ _206868) ^ [_426925, _426927, _426929, _426931, _426933] : [class_RealVector_Oreal__normed__vector(_426925), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_426925, _426927), _426929), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_426925, _426931), _426933), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_426925, c_Groups_Oplus__class_Oplus(_426925, _426927, _426931)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _426929, _426933)))], (6501 ^ _206868) ^ [_427435, _427437, _427439, _427441, _427443] : [class_Groups_Ocomm__monoid__add(_427435), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_427435), c_Polynomial_OpCons(_427435, _427437, _427439), c_Polynomial_OpCons(_427435, _427441, _427443)) = c_Polynomial_OpCons(_427435, c_Groups_Oplus__class_Oplus(_427435, _427437, _427441), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_427435), _427439, _427443)))], (6507 ^ _206868) ^ [_427745, _427747, _427749, _427751] : [class_Groups_Ocomm__monoid__add(_427745), -(hAPP(c_Polynomial_Ocoeff(_427745, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_427745), _427747, _427749)), _427751) = c_Groups_Oplus__class_Oplus(_427745, hAPP(c_Polynomial_Ocoeff(_427745, _427747), _427751), hAPP(c_Polynomial_Ocoeff(_427745, _427749), _427751)))], (6513 ^ _206868) ^ [_428049, _428051, _428053, _428055] : [class_Groups_Oab__semigroup__add(_428049), -(c_Groups_Oplus__class_Oplus(_428049, c_Groups_Oplus__class_Oplus(_428049, _428051, _428053), _428055) = c_Groups_Oplus__class_Oplus(_428049, _428051, c_Groups_Oplus__class_Oplus(_428049, _428053, _428055)))], (6519 ^ _206868) ^ [_428329, _428331, _428333, _428335] : [class_Groups_Ocancel__semigroup__add(_428329), 6522 ^ _206868 : [(6523 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_428329, _428331, _428333) = c_Groups_Oplus__class_Oplus(_428329, _428331, _428335), -(_428333 = _428335)], (6529 ^ _206868) ^ [] : [_428333 = _428335, -(c_Groups_Oplus__class_Oplus(_428329, _428331, _428333) = c_Groups_Oplus__class_Oplus(_428329, _428331, _428335))]]], (6535 ^ _206868) ^ [_428871, _428873, _428875, _428877] : [class_Groups_Ocancel__semigroup__add(_428871), 6538 ^ _206868 : [(6539 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_428871, _428873, _428875) = c_Groups_Oplus__class_Oplus(_428871, _428877, _428875), -(_428873 = _428877)], (6545 ^ _206868) ^ [] : [_428873 = _428877, -(c_Groups_Oplus__class_Oplus(_428871, _428873, _428875) = c_Groups_Oplus__class_Oplus(_428871, _428877, _428875))]]], (6551 ^ _206868) ^ [_429413, _429415, _429417, _429419] : [class_Groups_Ocancel__semigroup__add(_429413), c_Groups_Oplus__class_Oplus(_429413, _429415, _429417) = c_Groups_Oplus__class_Oplus(_429413, _429415, _429419), -(_429417 = _429419)], (6561 ^ _206868) ^ [_429774, _429776, _429778, _429780] : [class_Groups_Ocancel__ab__semigroup__add(_429774), c_Groups_Oplus__class_Oplus(_429774, _429776, _429778) = c_Groups_Oplus__class_Oplus(_429774, _429776, _429780), -(_429778 = _429780)], (6571 ^ _206868) ^ [_430135, _430137, _430139, _430141] : [class_Groups_Ocancel__semigroup__add(_430135), c_Groups_Oplus__class_Oplus(_430135, _430137, _430139) = c_Groups_Oplus__class_Oplus(_430135, _430141, _430139), -(_430137 = _430141)], (6581 ^ _206868) ^ [_430496, _430498, _430500, _430502] : [class_Rings_Ocomm__semiring__0(_430496), -(hAPP(c_Polynomial_Opoly(_430496, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_430496), _430498, _430500)), _430502) = c_Groups_Oplus__class_Oplus(_430496, hAPP(c_Polynomial_Opoly(_430496, _430498), _430502), hAPP(c_Polynomial_Opoly(_430496, _430500), _430502)))], (6587 ^ _206868) ^ [_430757, _430759] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430757, _430759) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430759, _430757))], (6589 ^ _206868) ^ [_430873, _430875, _430877] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430873, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430875, _430877)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430875, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430873, _430877)))], (6591 ^ _206868) ^ [_430999, _431001, _431003] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430999, _431001), _431003) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430999, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431001, _431003)))], (6593 ^ _206868) ^ [_431169, _431171, _431173] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431169, _431171) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431169, _431173), -(_431171 = _431173)], (6599 ^ _206868) ^ [_431353, _431355, _431357] : [_431355 = _431357, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431353, _431355) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431353, _431357))], (6605 ^ _206868) ^ [_431630, _431632, _431634] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431630, _431632) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431634, _431632), -(_431630 = _431634)], (6611 ^ _206868) ^ [_431814, _431816, _431818] : [_431814 = _431818, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431814, _431816) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431818, _431816))], (6617 ^ _206868) ^ [_432062, _432064, _432066] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _432062, _432064), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432066, _432062), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432066, _432064)))], (6623 ^ _206868) ^ [_432326, _432328, _432330, _432332] : [class_Rings_Ocomm__semiring__1(_432326), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_432326), _432328), _432330)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_432326), _432328), _432332)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_432326), _432328), c_Groups_Oplus__class_Oplus(_432326, _432330, _432332))))], (6637 ^ _206868) ^ [_432804, _432806, _432808] : [class_Groups_Ogroup__add(_432804), -(c_Groups_Oplus__class_Oplus(_432804, c_Groups_Ouminus__class_Ouminus(_432804, _432806), c_Groups_Oplus__class_Oplus(_432804, _432806, _432808)) = _432808)], (6643 ^ _206868) ^ [_433054, _433056, _433058] : [class_Groups_Ogroup__add(_433054), -(c_Groups_Oplus__class_Oplus(_433054, _433056, c_Groups_Oplus__class_Oplus(_433054, c_Groups_Ouminus__class_Ouminus(_433054, _433056), _433058)) = _433058)], (6649 ^ _206868) ^ [_433304, _433306, _433308] : [class_Groups_Ogroup__add(_433304), -(c_Groups_Ouminus__class_Ouminus(_433304, c_Groups_Oplus__class_Oplus(_433304, _433306, _433308)) = c_Groups_Oplus__class_Oplus(_433304, c_Groups_Ouminus__class_Ouminus(_433304, _433308), c_Groups_Ouminus__class_Ouminus(_433304, _433306)))], (6655 ^ _206868) ^ [_433566, _433568, _433570] : [class_Groups_Oab__group__add(_433566), -(c_Groups_Ouminus__class_Ouminus(_433566, c_Groups_Oplus__class_Oplus(_433566, _433568, _433570)) = c_Groups_Oplus__class_Oplus(_433566, c_Groups_Ouminus__class_Ouminus(_433566, _433568), c_Groups_Ouminus__class_Ouminus(_433566, _433570)))], (6661 ^ _206868) ^ [_433842, _433844, _433846, _433848] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_433842), c_Orderings_Oord__class_Oless(_433842, c_Groups_Oplus__class_Oplus(_433842, _433844, _433846), c_Groups_Oplus__class_Oplus(_433842, _433844, _433848)), -(c_Orderings_Oord__class_Oless(_433842, _433846, _433848))], (6671 ^ _206868) ^ [_434207, _434209, _434211, _434213] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_434207), c_Orderings_Oord__class_Oless(_434207, c_Groups_Oplus__class_Oplus(_434207, _434209, _434211), c_Groups_Oplus__class_Oplus(_434207, _434213, _434211)), -(c_Orderings_Oord__class_Oless(_434207, _434209, _434213))], (6681 ^ _206868) ^ [_434586, _434588, _434590, _434592, _434594] : [class_Groups_Oordered__cancel__ab__semigroup__add(_434586), c_Orderings_Oord__class_Oless(_434586, _434588, _434590), c_Orderings_Oord__class_Oless(_434586, _434592, _434594), -(c_Orderings_Oord__class_Oless(_434586, c_Groups_Oplus__class_Oplus(_434586, _434588, _434592), c_Groups_Oplus__class_Oplus(_434586, _434590, _434594)))], (6695 ^ _206868) ^ [_435064, _435066, _435068, _435070] : [class_Groups_Oordered__cancel__ab__semigroup__add(_435064), c_Orderings_Oord__class_Oless(_435064, _435066, _435068), -(c_Orderings_Oord__class_Oless(_435064, c_Groups_Oplus__class_Oplus(_435064, _435070, _435066), c_Groups_Oplus__class_Oplus(_435064, _435070, _435068)))], (6705 ^ _206868) ^ [_435429, _435431, _435433, _435435] : [class_Groups_Oordered__cancel__ab__semigroup__add(_435429), c_Orderings_Oord__class_Oless(_435429, _435431, _435433), -(c_Orderings_Oord__class_Oless(_435429, c_Groups_Oplus__class_Oplus(_435429, _435431, _435435), c_Groups_Oplus__class_Oplus(_435429, _435433, _435435)))], (6715 ^ _206868) ^ [_435794, _435796, _435798, _435800] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_435794), 6718 ^ _206868 : [(6719 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_435794, c_Groups_Oplus__class_Oplus(_435794, _435796, _435798), c_Groups_Oplus__class_Oplus(_435794, _435796, _435800)), -(c_Orderings_Oord__class_Oless(_435794, _435798, _435800))], (6725 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_435794, _435798, _435800), -(c_Orderings_Oord__class_Oless(_435794, c_Groups_Oplus__class_Oplus(_435794, _435796, _435798), c_Groups_Oplus__class_Oplus(_435794, _435796, _435800)))]]], (6731 ^ _206868) ^ [_436342, _436344, _436346, _436348] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_436342), 6734 ^ _206868 : [(6735 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_436342, c_Groups_Oplus__class_Oplus(_436342, _436344, _436346), c_Groups_Oplus__class_Oplus(_436342, _436348, _436346)), -(c_Orderings_Oord__class_Oless(_436342, _436344, _436348))], (6741 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_436342, _436344, _436348), -(c_Orderings_Oord__class_Oless(_436342, c_Groups_Oplus__class_Oplus(_436342, _436344, _436346), c_Groups_Oplus__class_Oplus(_436342, _436348, _436346)))]]], (6747 ^ _206868) ^ [_436890, _436892, _436894, _436896] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_436890), c_Orderings_Oord__class_Oless__eq(_436890, c_Groups_Oplus__class_Oplus(_436890, _436892, _436894), c_Groups_Oplus__class_Oplus(_436890, _436892, _436896)), -(c_Orderings_Oord__class_Oless__eq(_436890, _436894, _436896))], (6757 ^ _206868) ^ [_437255, _437257, _437259, _437261] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_437255), c_Orderings_Oord__class_Oless__eq(_437255, c_Groups_Oplus__class_Oplus(_437255, _437257, _437259), c_Groups_Oplus__class_Oplus(_437255, _437261, _437259)), -(c_Orderings_Oord__class_Oless__eq(_437255, _437257, _437261))], (6767 ^ _206868) ^ [_437634, _437636, _437638, _437640, _437642] : [class_Groups_Oordered__ab__semigroup__add(_437634), c_Orderings_Oord__class_Oless__eq(_437634, _437636, _437638), c_Orderings_Oord__class_Oless__eq(_437634, _437640, _437642), -(c_Orderings_Oord__class_Oless__eq(_437634, c_Groups_Oplus__class_Oplus(_437634, _437636, _437640), c_Groups_Oplus__class_Oplus(_437634, _437638, _437642)))], (6781 ^ _206868) ^ [_438112, _438114, _438116, _438118] : [class_Groups_Oordered__ab__semigroup__add(_438112), c_Orderings_Oord__class_Oless__eq(_438112, _438114, _438116), -(c_Orderings_Oord__class_Oless__eq(_438112, c_Groups_Oplus__class_Oplus(_438112, _438118, _438114), c_Groups_Oplus__class_Oplus(_438112, _438118, _438116)))], (6791 ^ _206868) ^ [_438477, _438479, _438481, _438483] : [class_Groups_Oordered__ab__semigroup__add(_438477), c_Orderings_Oord__class_Oless__eq(_438477, _438479, _438481), -(c_Orderings_Oord__class_Oless__eq(_438477, c_Groups_Oplus__class_Oplus(_438477, _438479, _438483), c_Groups_Oplus__class_Oplus(_438477, _438481, _438483)))], (6801 ^ _206868) ^ [_438842, _438844, _438846, _438848] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_438842), 6804 ^ _206868 : [(6805 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_438842, c_Groups_Oplus__class_Oplus(_438842, _438844, _438846), c_Groups_Oplus__class_Oplus(_438842, _438844, _438848)), -(c_Orderings_Oord__class_Oless__eq(_438842, _438846, _438848))], (6811 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_438842, _438846, _438848), -(c_Orderings_Oord__class_Oless__eq(_438842, c_Groups_Oplus__class_Oplus(_438842, _438844, _438846), c_Groups_Oplus__class_Oplus(_438842, _438844, _438848)))]]], (6817 ^ _206868) ^ [_439390, _439392, _439394, _439396] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_439390), 6820 ^ _206868 : [(6821 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_439390, c_Groups_Oplus__class_Oplus(_439390, _439392, _439394), c_Groups_Oplus__class_Oplus(_439390, _439396, _439394)), -(c_Orderings_Oord__class_Oless__eq(_439390, _439392, _439396))], (6827 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_439390, _439392, _439396), -(c_Orderings_Oord__class_Oless__eq(_439390, c_Groups_Oplus__class_Oplus(_439390, _439392, _439394), c_Groups_Oplus__class_Oplus(_439390, _439396, _439394)))]]], (6833 ^ _206868) ^ [_439910, _439912] : [class_Rings_Ocomm__semiring__1(_439910), -(c_Groups_Oplus__class_Oplus(_439910, c_Groups_Ozero__class_Ozero(_439910), _439912) = _439912)], (6839 ^ _206868) ^ [_440130, _440132] : [class_Rings_Ocomm__semiring__1(_440130), -(c_Groups_Oplus__class_Oplus(_440130, _440132, c_Groups_Ozero__class_Ozero(_440130)) = _440132)], (6845 ^ _206868) ^ [_440364, _440366, _440368] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_440364), 6848 ^ _206868 : [(6849 ^ _206868) ^ [] : [_440366 = c_Groups_Oplus__class_Oplus(_440364, _440366, _440368), -(_440368 = c_Groups_Ozero__class_Ozero(_440364))], (6855 ^ _206868) ^ [] : [_440368 = c_Groups_Ozero__class_Ozero(_440364), -(_440366 = c_Groups_Oplus__class_Oplus(_440364, _440366, _440368))]]], (6861 ^ _206868) ^ [_440856, _440858] : [class_Groups_Omonoid__add(_440856), -(c_Groups_Oplus__class_Oplus(_440856, c_Groups_Ozero__class_Ozero(_440856), _440858) = _440858)], (6867 ^ _206868) ^ [_441076, _441078] : [class_Groups_Ocomm__monoid__add(_441076), -(c_Groups_Oplus__class_Oplus(_441076, c_Groups_Ozero__class_Ozero(_441076), _441078) = _441078)], (6873 ^ _206868) ^ [_441296, _441298] : [class_Groups_Olinordered__ab__group__add(_441296), 6876 ^ _206868 : [(6877 ^ _206868) ^ [] : [c_Groups_Ozero__class_Ozero(_441296) = c_Groups_Oplus__class_Oplus(_441296, _441298, _441298), -(_441298 = c_Groups_Ozero__class_Ozero(_441296))], (6883 ^ _206868) ^ [] : [_441298 = c_Groups_Ozero__class_Ozero(_441296), -(c_Groups_Ozero__class_Ozero(_441296) = c_Groups_Oplus__class_Oplus(_441296, _441298, _441298))]]], (6889 ^ _206868) ^ [_441778, _441780] : [class_Groups_Omonoid__add(_441778), -(c_Groups_Oplus__class_Oplus(_441778, _441780, c_Groups_Ozero__class_Ozero(_441778)) = _441780)], (6895 ^ _206868) ^ [_441998, _442000] : [class_Groups_Ocomm__monoid__add(_441998), -(c_Groups_Oplus__class_Oplus(_441998, _442000, c_Groups_Ozero__class_Ozero(_441998)) = _442000)], (6901 ^ _206868) ^ [_442189] : [-(c_NthRoot_Oroot(_442189, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6903 ^ _206868) ^ [_442299, _442301] : [c_RealDef_Opositive(_442299), c_RealDef_Opositive(_442301), -(c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _442299, _442301)))], (6913 ^ _206868) ^ [_442571] : [-(c_NthRoot_Oroot(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _442571) = _442571)], (6915 ^ _206868) ^ [_442695, _442697, _442699] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _442695), 6918 ^ _206868 : [(6919 ^ _206868) ^ [] : [c_NthRoot_Oroot(_442695, _442697) = c_NthRoot_Oroot(_442695, _442699), -(_442697 = _442699)], (6925 ^ _206868) ^ [] : [_442697 = _442699, -(c_NthRoot_Oroot(_442695, _442697) = c_NthRoot_Oroot(_442695, _442699))]]], (6931 ^ _206868) ^ [_443205, _443207, _443209] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _443205), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _443207), -(c_NthRoot_Oroot(_443205, c_NthRoot_Oroot(_443207, _443209)) = c_NthRoot_Oroot(_443207, c_NthRoot_Oroot(_443205, _443209)))], (6941 ^ _206868) ^ [_443556, _443558, _443560] : [class_Groups_Oordered__comm__monoid__add(_443556), c_Orderings_Oord__class_Oless__eq(_443556, _443558, c_Groups_Ozero__class_Ozero(_443556)), c_Orderings_Oord__class_Oless__eq(_443556, _443560, c_Groups_Ozero__class_Ozero(_443556)), -(c_Orderings_Oord__class_Oless__eq(_443556, c_Groups_Oplus__class_Oplus(_443556, _443558, _443560), c_Groups_Ozero__class_Ozero(_443556)))], (6955 ^ _206868) ^ [_444010, _444012, _444014, _444016] : [class_Groups_Oordered__comm__monoid__add(_444010), c_Orderings_Oord__class_Oless__eq(_444010, c_Groups_Ozero__class_Ozero(_444010), _444012), c_Orderings_Oord__class_Oless__eq(_444010, _444014, _444016), -(c_Orderings_Oord__class_Oless__eq(_444010, _444014, c_Groups_Oplus__class_Oplus(_444010, _444016, _444012)))], (6969 ^ _206868) ^ [_444470, _444472, _444474, _444476] : [class_Groups_Oordered__comm__monoid__add(_444470), c_Orderings_Oord__class_Oless__eq(_444470, c_Groups_Ozero__class_Ozero(_444470), _444472), c_Orderings_Oord__class_Oless__eq(_444470, _444474, _444476), -(c_Orderings_Oord__class_Oless__eq(_444470, _444474, c_Groups_Oplus__class_Oplus(_444470, _444472, _444476)))], (6983 ^ _206868) ^ [_444916, _444918, _444920] : [class_Groups_Oordered__comm__monoid__add(_444916), c_Orderings_Oord__class_Oless__eq(_444916, c_Groups_Ozero__class_Ozero(_444916), _444918), c_Orderings_Oord__class_Oless__eq(_444916, c_Groups_Ozero__class_Ozero(_444916), _444920), 6994 ^ _206868 : [(6995 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_444916, _444918, _444920) = c_Groups_Ozero__class_Ozero(_444916), 6998 ^ _206868 : [(6999 ^ _206868) ^ [] : [-(_444918 = c_Groups_Ozero__class_Ozero(_444916))], (7001 ^ _206868) ^ [] : [-(_444920 = c_Groups_Ozero__class_Ozero(_444916))]]], (7003 ^ _206868) ^ [] : [-(c_Groups_Oplus__class_Oplus(_444916, _444918, _444920) = c_Groups_Ozero__class_Ozero(_444916)), _444918 = c_Groups_Ozero__class_Ozero(_444916), _444920 = c_Groups_Ozero__class_Ozero(_444916)]]], (7013 ^ _206868) ^ [_445796, _445798, _445800] : [class_Groups_Oordered__comm__monoid__add(_445796), c_Orderings_Oord__class_Oless__eq(_445796, c_Groups_Ozero__class_Ozero(_445796), _445798), c_Orderings_Oord__class_Oless__eq(_445796, c_Groups_Ozero__class_Ozero(_445796), _445800), -(c_Orderings_Oord__class_Oless__eq(_445796, c_Groups_Ozero__class_Ozero(_445796), c_Groups_Oplus__class_Oplus(_445796, _445798, _445800)))], (7027 ^ _206868) ^ [_446222, _446224] : [class_Groups_Olinordered__ab__group__add(_446222), 7030 ^ _206868 : [(7031 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_446222, c_Groups_Oplus__class_Oplus(_446222, _446224, _446224), c_Groups_Ozero__class_Ozero(_446222)), -(c_Orderings_Oord__class_Oless__eq(_446222, _446224, c_Groups_Ozero__class_Ozero(_446222)))], (7037 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_446222, _446224, c_Groups_Ozero__class_Ozero(_446222)), -(c_Orderings_Oord__class_Oless__eq(_446222, c_Groups_Oplus__class_Oplus(_446222, _446224, _446224), c_Groups_Ozero__class_Ozero(_446222)))]]], (7043 ^ _206868) ^ [_446710, _446712] : [class_Groups_Olinordered__ab__group__add(_446710), 7046 ^ _206868 : [(7047 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_446710, c_Groups_Ozero__class_Ozero(_446710), c_Groups_Oplus__class_Oplus(_446710, _446712, _446712)), -(c_Orderings_Oord__class_Oless__eq(_446710, c_Groups_Ozero__class_Ozero(_446710), _446712))], (7053 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_446710, c_Groups_Ozero__class_Ozero(_446710), _446712), -(c_Orderings_Oord__class_Oless__eq(_446710, c_Groups_Ozero__class_Ozero(_446710), c_Groups_Oplus__class_Oplus(_446710, _446712, _446712)))]]], (7059 ^ _206868) ^ [_447226, _447228, _447230, _447232] : [class_Rings_Olinordered__semidom(_447226), c_Orderings_Oord__class_Oless(_447226, c_Groups_Ozero__class_Ozero(_447226), _447228), c_Orderings_Oord__class_Oless(_447226, _447230, _447232), -(c_Orderings_Oord__class_Oless(_447226, _447230, c_Groups_Oplus__class_Oplus(_447226, _447228, _447232)))], (7073 ^ _206868) ^ [_447672, _447674, _447676] : [class_Groups_Oordered__comm__monoid__add(_447672), c_Orderings_Oord__class_Oless(_447672, _447674, c_Groups_Ozero__class_Ozero(_447672)), c_Orderings_Oord__class_Oless(_447672, _447676, c_Groups_Ozero__class_Ozero(_447672)), -(c_Orderings_Oord__class_Oless(_447672, c_Groups_Oplus__class_Oplus(_447672, _447674, _447676), c_Groups_Ozero__class_Ozero(_447672)))], (7087 ^ _206868) ^ [_448112, _448114, _448116] : [class_Groups_Oordered__comm__monoid__add(_448112), c_Orderings_Oord__class_Oless(_448112, c_Groups_Ozero__class_Ozero(_448112), _448114), c_Orderings_Oord__class_Oless(_448112, c_Groups_Ozero__class_Ozero(_448112), _448116), -(c_Orderings_Oord__class_Oless(_448112, c_Groups_Ozero__class_Ozero(_448112), c_Groups_Oplus__class_Oplus(_448112, _448114, _448116)))], (7101 ^ _206868) ^ [_448538, _448540] : [class_Groups_Olinordered__ab__group__add(_448538), 7104 ^ _206868 : [(7105 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_448538, c_Groups_Oplus__class_Oplus(_448538, _448540, _448540), c_Groups_Ozero__class_Ozero(_448538)), -(c_Orderings_Oord__class_Oless(_448538, _448540, c_Groups_Ozero__class_Ozero(_448538)))], (7111 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_448538, _448540, c_Groups_Ozero__class_Ozero(_448538)), -(c_Orderings_Oord__class_Oless(_448538, c_Groups_Oplus__class_Oplus(_448538, _448540, _448540), c_Groups_Ozero__class_Ozero(_448538)))]]], (7117 ^ _206868) ^ [_449026, _449028] : [class_Groups_Olinordered__ab__group__add(_449026), 7120 ^ _206868 : [(7121 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_449026, c_Groups_Ozero__class_Ozero(_449026), c_Groups_Oplus__class_Oplus(_449026, _449028, _449028)), -(c_Orderings_Oord__class_Oless(_449026, c_Groups_Ozero__class_Ozero(_449026), _449028))], (7127 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_449026, c_Groups_Ozero__class_Ozero(_449026), _449028), -(c_Orderings_Oord__class_Oless(_449026, c_Groups_Ozero__class_Ozero(_449026), c_Groups_Oplus__class_Oplus(_449026, _449028, _449028)))]]], (7133 ^ _206868) ^ [_449556, _449558, _449560, _449562, _449564] : [class_Groups_Oordered__cancel__ab__semigroup__add(_449556), c_Orderings_Oord__class_Oless(_449556, _449558, _449560), c_Orderings_Oord__class_Oless__eq(_449556, _449562, _449564), -(c_Orderings_Oord__class_Oless(_449556, c_Groups_Oplus__class_Oplus(_449556, _449558, _449562), c_Groups_Oplus__class_Oplus(_449556, _449560, _449564)))], (7147 ^ _206868) ^ [_450048, _450050, _450052, _450054, _450056] : [class_Groups_Oordered__cancel__ab__semigroup__add(_450048), c_Orderings_Oord__class_Oless__eq(_450048, _450050, _450052), c_Orderings_Oord__class_Oless(_450048, _450054, _450056), -(c_Orderings_Oord__class_Oless(_450048, c_Groups_Oplus__class_Oplus(_450048, _450050, _450054), c_Groups_Oplus__class_Oplus(_450048, _450052, _450056)))], (7161 ^ _206868) ^ [_450498, _450500] : [class_Rings_Olinordered__semidom(_450498), -(c_Orderings_Oord__class_Oless(_450498, _450500, c_Groups_Oplus__class_Oplus(_450498, _450500, c_Groups_Oone__class_Oone(_450498))))], (7167 ^ _206868) ^ [_450734, _450736, _450738] : [class_Groups_Ogroup__add(_450734), c_Groups_Oplus__class_Oplus(_450734, _450736, _450738) = c_Groups_Ozero__class_Ozero(_450734), -(c_Groups_Ouminus__class_Ouminus(_450734, _450736) = _450738)], (7177 ^ _206868) ^ [_451073, _451075, _451077] : [class_Groups_Ogroup__add(_451073), 7180 ^ _206868 : [(7181 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_451073, _451075, _451077) = c_Groups_Ozero__class_Ozero(_451073), -(_451077 = c_Groups_Ouminus__class_Ouminus(_451073, _451075))], (7187 ^ _206868) ^ [] : [_451077 = c_Groups_Ouminus__class_Ouminus(_451073, _451075), -(c_Groups_Oplus__class_Oplus(_451073, _451075, _451077) = c_Groups_Ozero__class_Ozero(_451073))]]], (7193 ^ _206868) ^ [_451574, _451576] : [class_Groups_Oab__group__add(_451574), -(c_Groups_Oplus__class_Oplus(_451574, c_Groups_Ouminus__class_Ouminus(_451574, _451576), _451576) = c_Groups_Ozero__class_Ozero(_451574))], (7199 ^ _206868) ^ [_451800, _451802] : [class_Groups_Ogroup__add(_451800), -(c_Groups_Oplus__class_Oplus(_451800, c_Groups_Ouminus__class_Ouminus(_451800, _451802), _451802) = c_Groups_Ozero__class_Ozero(_451800))], (7205 ^ _206868) ^ [_452040, _452042, _452044] : [class_Groups_Ogroup__add(_452040), 7208 ^ _206868 : [(7209 ^ _206868) ^ [] : [_452042 = c_Groups_Ouminus__class_Ouminus(_452040, _452044), -(c_Groups_Oplus__class_Oplus(_452040, _452042, _452044) = c_Groups_Ozero__class_Ozero(_452040))], (7215 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_452040, _452042, _452044) = c_Groups_Ozero__class_Ozero(_452040), -(_452042 = c_Groups_Ouminus__class_Ouminus(_452040, _452044))]]], (7221 ^ _206868) ^ [_452541, _452543] : [class_Groups_Ogroup__add(_452541), -(c_Groups_Oplus__class_Oplus(_452541, _452543, c_Groups_Ouminus__class_Ouminus(_452541, _452543)) = c_Groups_Ozero__class_Ozero(_452541))], (7227 ^ _206868) ^ [_452767, _452769] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _452767), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _452767, c_RealDef_Oreal(tc_Nat_Onat, _452769))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_452767), _452769))], (7233 ^ _206868) ^ [_453009, _453011] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _453009), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _453009, c_RealDef_Oreal(tc_Nat_Onat, _453011))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_453009), _453011))], (7239 ^ _206868) ^ [_453280, _453282] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _453280, _453282) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7244 ^ _206868 : [(7245 ^ _206868) ^ [] : [-(_453280 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7247 ^ _206868) ^ [] : [-(_453282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7248 ^ _206868 : [(7249 ^ _206868) ^ [] : [-(_453280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7251 ^ _206868) ^ [] : [-(_453282 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7253 ^ _206868) ^ [_453690, _453692] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _453690, _453692) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7254 ^ _206868 : [(7255 ^ _206868) ^ [] : [_453690 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _453692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7261 ^ _206868) ^ [] : [_453690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _453692 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7269 ^ _206868) ^ [_454191, _454193] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _454191, _454193), 7274 ^ _206868 : [(7275 ^ _206868) ^ [] : [-(_454191 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7277 ^ _206868) ^ [] : [-(_454193 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7278 ^ _206868 : [(7279 ^ _206868) ^ [] : [-(_454191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7281 ^ _206868) ^ [] : [-(_454193 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7283 ^ _206868) ^ [_454601, _454603] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _454601, _454603)), 7284 ^ _206868 : [(7285 ^ _206868) ^ [] : [_454601 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _454603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7291 ^ _206868) ^ [] : [_454601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _454603 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7309 ^ _206868) ^ [_455368, _455370] : [7310 ^ _206868 : [(7311 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _455368)], (7313 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _455370)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _455368, _455370)))], (7299 ^ _206868) ^ [_455102, _455104] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _455102, _455104)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _455102)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _455104))], (7317 ^ _206868) ^ [_455653, _455655] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _455653, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _455653, _455655))))], (7319 ^ _206868) ^ [_455754, _455756] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _455754, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _455756, _455754))))], (7321 ^ _206868) ^ [_455899, _455901] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _455899, _455901), -(_455901 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _455899, 7324 ^ [_455899, _455901])))], (7328 ^ _206868) ^ [_456138, _456140] : [7329 ^ _206868 : [(7330 ^ _206868) ^ [_456215] : [_456140 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _456138, _456215))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _456138, _456140))], (7334 ^ _206868) ^ [_456357] : [-(c_Nat_OSuc(_456357) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _456357, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7336 ^ _206868) ^ [_456441] : [-(c_Nat_OSuc(_456441) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _456441))], (7338 ^ _206868) ^ [_456583, _456585] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _456583, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _456585)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_456583 = _456585)], (7344 ^ _206868) ^ [_456759, _456761] : [_456759 = _456761, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _456759, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _456761)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7350 ^ _206868) ^ [_457014, _457016] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _457014, _457016) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_457016 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _457014))], (7356 ^ _206868) ^ [_457190, _457192] : [_457192 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _457190), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _457190, _457192) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7362 ^ _206868) ^ [_457402] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _457402), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _457402, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_457402), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7368 ^ _206868) ^ [_457618] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _457618), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _457618, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_457618), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7374 ^ _206868) ^ [_457876, _457878, _457880, _457882] : [class_Rings_Ocomm__semiring__0(_457876), -(hAPP(c_Polynomial_Opoly(_457876, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_457876, _457878, _457880)), _457882) = hAPP(c_Polynomial_Opoly(_457876, _457878), c_Groups_Oplus__class_Oplus(_457876, _457880, _457882)))], (7380 ^ _206868) ^ [_458150, _458152, _458154] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _458150), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _458152, _458154), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_458150, _458152), c_NthRoot_Oroot(_458150, _458154)))], (7390 ^ _206868) ^ [_458491, _458493, _458495] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _458491), 7393 ^ _206868 : [(7394 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_458491, _458493), c_NthRoot_Oroot(_458491, _458495)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _458493, _458495))], (7400 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _458493, _458495), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_458491, _458493), c_NthRoot_Oroot(_458491, _458495)))]]], (7406 ^ _206868) ^ [_458993, _458995] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _458993), 7409 ^ _206868 : [(7410 ^ _206868) ^ [] : [c_NthRoot_Oroot(_458993, _458995) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_458995 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7416 ^ _206868) ^ [] : [_458995 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_NthRoot_Oroot(_458993, _458995) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (7422 ^ _206868) ^ [_459478, _459480, _459482] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _459478), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _459480, _459482), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_459478, _459480), c_NthRoot_Oroot(_459478, _459482)))], (7432 ^ _206868) ^ [_459819, _459821, _459823] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _459819), 7435 ^ _206868 : [(7436 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_459819, _459821), c_NthRoot_Oroot(_459819, _459823)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _459821, _459823))], (7442 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _459821, _459823), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_459819, _459821), c_NthRoot_Oroot(_459819, _459823)))]]], (7448 ^ _206868) ^ [_460335, _460337, _460339] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _460335), -(c_NthRoot_Oroot(_460335, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _460337), _460339)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_460335, _460337)), _460339))], (7454 ^ _206868) ^ [_460589, _460591] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _460589), 7457 ^ _206868 : [(7458 ^ _206868) ^ [] : [c_NthRoot_Oroot(_460589, _460591) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(_460591 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (7464 ^ _206868) ^ [] : [_460591 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_NthRoot_Oroot(_460589, _460591) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (7470 ^ _206868) ^ [_461046] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _461046), -(c_NthRoot_Oroot(_461046, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (7476 ^ _206868) ^ [_461272, _461274, _461276] : [class_Groups_Oordered__comm__monoid__add(_461272), c_Orderings_Oord__class_Oless(_461272, c_Groups_Ozero__class_Ozero(_461272), _461274), c_Orderings_Oord__class_Oless__eq(_461272, c_Groups_Ozero__class_Ozero(_461272), _461276), -(c_Orderings_Oord__class_Oless(_461272, c_Groups_Ozero__class_Ozero(_461272), c_Groups_Oplus__class_Oplus(_461272, _461274, _461276)))], (7490 ^ _206868) ^ [_461712, _461714, _461716] : [class_Groups_Oordered__comm__monoid__add(_461712), c_Orderings_Oord__class_Oless__eq(_461712, c_Groups_Ozero__class_Ozero(_461712), _461714), c_Orderings_Oord__class_Oless(_461712, c_Groups_Ozero__class_Ozero(_461712), _461716), -(c_Orderings_Oord__class_Oless(_461712, c_Groups_Ozero__class_Ozero(_461712), c_Groups_Oplus__class_Oplus(_461712, _461714, _461716)))], (7504 ^ _206868) ^ [_462166, _462168, _462170, _462172] : [class_Groups_Oordered__comm__monoid__add(_462166), c_Orderings_Oord__class_Oless(_462166, c_Groups_Ozero__class_Ozero(_462166), _462168), c_Orderings_Oord__class_Oless__eq(_462166, _462170, _462172), -(c_Orderings_Oord__class_Oless(_462166, _462170, c_Groups_Oplus__class_Oplus(_462166, _462168, _462172)))], (7518 ^ _206868) ^ [_462626, _462628, _462630, _462632] : [class_Groups_Oordered__comm__monoid__add(_462626), c_Orderings_Oord__class_Oless__eq(_462626, c_Groups_Ozero__class_Ozero(_462626), _462628), c_Orderings_Oord__class_Oless(_462626, _462630, _462632), -(c_Orderings_Oord__class_Oless(_462626, _462630, c_Groups_Oplus__class_Oplus(_462626, _462628, _462632)))], (7532 ^ _206868) ^ [_463072, _463074, _463076] : [class_Groups_Oordered__comm__monoid__add(_463072), c_Orderings_Oord__class_Oless(_463072, _463074, c_Groups_Ozero__class_Ozero(_463072)), c_Orderings_Oord__class_Oless__eq(_463072, _463076, c_Groups_Ozero__class_Ozero(_463072)), -(c_Orderings_Oord__class_Oless(_463072, c_Groups_Oplus__class_Oplus(_463072, _463074, _463076), c_Groups_Ozero__class_Ozero(_463072)))], (7546 ^ _206868) ^ [_463512, _463514, _463516] : [class_Groups_Oordered__comm__monoid__add(_463512), c_Orderings_Oord__class_Oless__eq(_463512, _463514, c_Groups_Ozero__class_Ozero(_463512)), c_Orderings_Oord__class_Oless(_463512, _463516, c_Groups_Ozero__class_Ozero(_463512)), -(c_Orderings_Oord__class_Oless(_463512, c_Groups_Oplus__class_Oplus(_463512, _463514, _463516), c_Groups_Ozero__class_Ozero(_463512)))], (7560 ^ _206868) ^ [_463938, _463940] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _463938), -(c_NthRoot_Oroot(_463938, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _463940)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_NthRoot_Oroot(_463938, _463940)))], (7566 ^ _206868) ^ [_464160] : [class_Rings_Olinordered__semidom(_464160), -(c_Orderings_Oord__class_Oless(_464160, c_Groups_Ozero__class_Ozero(_464160), c_Groups_Oplus__class_Oplus(_464160, c_Groups_Oone__class_Oone(_464160), c_Groups_Oone__class_Oone(_464160))))], (7572 ^ _206868) ^ [_464384, _464386] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _464384), _464386), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _464386, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _464384), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_464386) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _464384, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7582 ^ _206868) ^ [_464748, _464750] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _464748, _464750)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _464748), _464750))], (7588 ^ _206868) ^ [_464928, _464930] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _464928), _464930), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _464928, _464930)))], (7594 ^ _206868) ^ [_465187, _465189] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _465187, _465189), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _465189, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465187)))], (7600 ^ _206868) ^ [_465367, _465369] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _465369, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465367)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _465367, _465369), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7606 ^ _206868) ^ [_465626, _465628] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _465626, _465628)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465626), _465628))], (7612 ^ _206868) ^ [_465806, _465808] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465806), _465808), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _465806, _465808)))], (7618 ^ _206868) ^ [_466065, _466067] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _466065, _466067), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _466067, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _466065)))], (7624 ^ _206868) ^ [_466245, _466247] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _466247, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _466245)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _466245, _466247), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7630 ^ _206868) ^ [_466446] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_466446)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _466446), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7632 ^ _206868) ^ [_466565, _466567] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _466565), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _466567), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_466565, _466567)))], (7642 ^ _206868) ^ [_466876, _466878] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _466876), 7645 ^ _206868 : [(7646 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_466876, _466878), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _466878, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7652 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _466878, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_466876, _466878), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (7658 ^ _206868) ^ [_467353, _467355] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _467353), 7661 ^ _206868 : [(7662 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_467353, _467355)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _467355))], (7668 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _467355), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_467353, _467355)))]]], (7674 ^ _206868) ^ [_467830, _467832] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _467830), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _467832), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_467830, _467832)))], (7684 ^ _206868) ^ [_468141, _468143] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _468141), 7687 ^ _206868 : [(7688 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_468141, _468143), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _468143, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7694 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _468143, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_468141, _468143), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (7700 ^ _206868) ^ [_468618, _468620] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _468618), 7703 ^ _206868 : [(7704 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_468618, _468620)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _468620))], (7710 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _468620), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_468618, _468620)))]]], (7716 ^ _206868) ^ [_469109, _469111, _469113] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _469109), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _469109, _469111), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _469113), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_469111, _469113), c_NthRoot_Oroot(_469109, _469113)))], (7730 ^ _206868) ^ [_469531, _469533] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _469531), 7733 ^ _206868 : [(7734 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_469531, _469533), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _469533, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7740 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _469533, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_469531, _469533), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]]], (7746 ^ _206868) ^ [_470008, _470010] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _470008), 7749 ^ _206868 : [(7750 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_470008, _470010)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _470010))], (7756 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _470010), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_470008, _470010)))]]], (7762 ^ _206868) ^ [_470499, _470501, _470503] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _470499), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _470499, _470501), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _470503), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_470501, _470503), c_NthRoot_Oroot(_470499, _470503)))], (7776 ^ _206868) ^ [_470921, _470923] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _470921), 7779 ^ _206868 : [(7780 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_470921, _470923), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _470923, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7786 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _470923, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_470921, _470923), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]]], (7792 ^ _206868) ^ [_471398, _471400] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _471398), 7795 ^ _206868 : [(7796 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_471398, _471400)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _471400))], (7802 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _471400), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_471398, _471400)))]]], (7808 ^ _206868) ^ [_471875, _471877] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _471875), -(c_NthRoot_Oroot(c_Nat_OSuc(_471877), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _471875), c_Nat_OSuc(_471877))) = _471875)], (7814 ^ _206868) ^ [_472142, _472144] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _472142, _472144), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472142), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _472144)))], (7820 ^ _206868) ^ [_472328, _472330] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472328), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _472330)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _472328, _472330))], (7826 ^ _206868) ^ [_472593, _472595] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472593, _472595), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472593), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472595), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (7832 ^ _206868) ^ [_472779, _472781] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472779), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472781), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472779, _472781))], (7838 ^ _206868) ^ [_472986] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _472986, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_472986)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (7840 ^ _206868) ^ [_473117, _473119, _473121] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _473117), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _473119), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _473119, _473121), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_473117, _473119), c_NthRoot_Oroot(_473117, _473121)))], (7854 ^ _206868) ^ [_473539, _473541] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _473539), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _473541), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_473539, _473541)))], (7864 ^ _206868) ^ [_473864, _473866, _473868] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _473864), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _473866), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _473866), _473864) = _473868, -(c_NthRoot_Oroot(_473864, _473868) = _473866)], (7878 ^ _206868) ^ [_474288, _474290] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _474288), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _474290), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_474288, _474290)), _474288) = _474290)], (7888 ^ _206868) ^ [_474609, _474611] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _474609), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _474611), -(c_NthRoot_Oroot(_474609, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _474611), _474609)) = _474611)], (7898 ^ _206868) ^ [_474930, _474932] : [class_Rings_Olinordered__idom(_474930), 7901 ^ _206868 : [(7902 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_474930, c_Groups_Oplus__class_Oplus(_474930, _474932, _474932), c_Groups_Ozero__class_Ozero(_474930)), -(c_Orderings_Oord__class_Oless(_474930, _474932, c_Groups_Ozero__class_Ozero(_474930)))], (7908 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_474930, _474932, c_Groups_Ozero__class_Ozero(_474930)), -(c_Orderings_Oord__class_Oless(_474930, c_Groups_Oplus__class_Oplus(_474930, _474932, _474932), c_Groups_Ozero__class_Ozero(_474930)))]]], (7914 ^ _206868) ^ [_475418, _475420] : [class_RealVector_Oreal__normed__vector(_475418), 7917 ^ _206868 : [(7918 ^ _206868) ^ [] : [c_SEQ_OBseq(_475418, _475420), 7922 ^ _206868 : [(7923 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7921 ^ [_475418, _475420]))], (7926 ^ _206868) ^ [_475898] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_475418, c_Groups_Oplus__class_Oplus(_475418, hAPP(_475420, _475898), c_Groups_Ouminus__class_Ouminus(_475418, 7924 ^ [_475418, _475420]))), 7921 ^ [_475418, _475420]))]]], (7928 ^ _206868) ^ [] : [-(c_SEQ_OBseq(_475418, _475420)), 7929 ^ _206868 : [(7930 ^ _206868) ^ [_476044] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _476044), 7934 ^ _206868 : [(7935 ^ _206868) ^ [_476253] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_475418, c_Groups_Oplus__class_Oplus(_475418, hAPP(_475420, 7933 ^ [_475418, _475420, _476044, _476253]), c_Groups_Ouminus__class_Ouminus(_475418, _476253))), _476044)]]]]]]], (7939 ^ _206868) ^ [_476454, _476456] : [class_RealVector_Oreal__normed__vector(_476454), 7942 ^ _206868 : [(7943 ^ _206868) ^ [] : [c_SEQ_OBseq(_476454, _476456), 7947 ^ _206868 : [(7948 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7946 ^ [_476454, _476456]))], (7951 ^ _206868) ^ [_476943] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_476454, c_Groups_Oplus__class_Oplus(_476454, hAPP(_476456, _476943), c_Groups_Ouminus__class_Ouminus(_476454, hAPP(_476456, 7949 ^ [_476454, _476456])))), 7946 ^ [_476454, _476456]))]]], (7953 ^ _206868) ^ [] : [-(c_SEQ_OBseq(_476454, _476456)), 7954 ^ _206868 : [(7955 ^ _206868) ^ [_477092] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _477092), 7959 ^ _206868 : [(7960 ^ _206868) ^ [_477307] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_476454, c_Groups_Oplus__class_Oplus(_476454, hAPP(_476456, 7958 ^ [_476454, _476456, _477092, _477307]), c_Groups_Ouminus__class_Ouminus(_476454, hAPP(_476456, _477307)))), _477092)]]]]]]], (7964 ^ _206868) ^ [_477540, _477542] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _477540, _477542), -(_477542 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _477540, 7967 ^ [_477540, _477542]))], (7971 ^ _206868) ^ [_477773, _477775] : [7972 ^ _206868 : [(7973 ^ _206868) ^ [_477848] : [_477775 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _477773, _477848)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _477773, _477775))], (7977 ^ _206868) ^ [_478017, _478019] : [class_Groups_Ocomm__monoid__add(_478017), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478017), _478019, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_478017))) = _478019)], (7983 ^ _206868) ^ [_478245, _478247] : [class_Groups_Ocomm__monoid__add(_478245), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478245), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_478245)), _478247) = _478247)], (7989 ^ _206868) ^ [_478487, _478489, _478491] : [class_Rings_Olinordered__idom(_478487), c_Polynomial_Opos__poly(_478487, _478489), c_Polynomial_Opos__poly(_478487, _478491), -(c_Polynomial_Opos__poly(_478487, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478487), _478489, _478491)))], (8003 ^ _206868) ^ [_478913, _478915, _478917] : [class_Groups_Ocomm__monoid__add(_478913), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_478913, _478915), c_Polynomial_Odegree(_478913, _478917)), -(c_Polynomial_Odegree(_478913, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478913), _478917, _478915)) = c_Polynomial_Odegree(_478913, _478917))], (8013 ^ _206868) ^ [_479272, _479274, _479276] : [class_Groups_Ocomm__monoid__add(_479272), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_479272, _479274), c_Polynomial_Odegree(_479272, _479276)), -(c_Polynomial_Odegree(_479272, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_479272), _479274, _479276)) = c_Polynomial_Odegree(_479272, _479276))], (8023 ^ _206868) ^ [_479645, _479647, _479649, _479651] : [class_Groups_Ocomm__monoid__add(_479645), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_479645, _479647), _479649), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_479645, _479651), _479649), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_479645, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_479645), _479647, _479651)), _479649))], (8037 ^ _206868) ^ [_480123, _480125, _480127, _480129] : [class_Groups_Ocomm__monoid__add(_480123), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_480123, _480125), _480127), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_480123, _480129), _480127), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_480123, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_480123), _480125, _480129)), _480127))], (8051 ^ _206868) ^ [_480558, _480560] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _480558), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _480558, _480560)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _480560))))], (8053 ^ _206868) ^ [_480685, _480687] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _480685), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _480687), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _480685), _480687)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _480687), _480685)), -(_480685 = _480687)], (8071 ^ _206868) ^ [_481186, _481188] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _481186), c_Orderings_Oord__class_Oless(tc_Int_Oint, _481186, _481188), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _481188), _481186))], (8081 ^ _206868) ^ [_481500, _481502] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _481500), _481502)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _481502), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _481500, _481502))], (8091 ^ _206868) ^ [_481813, _481815] : [class_Groups_Olinordered__ab__group__add(_481813), 8094 ^ _206868 : [(8095 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_481813, _481815, _481815) = c_Groups_Ozero__class_Ozero(_481813), -(_481815 = c_Groups_Ozero__class_Ozero(_481813))], (8101 ^ _206868) ^ [] : [_481815 = c_Groups_Ozero__class_Ozero(_481813), -(c_Groups_Oplus__class_Oplus(_481813, _481815, _481815) = c_Groups_Ozero__class_Ozero(_481813))]]], (8107 ^ _206868) ^ [_482309, _482311, _482313] : [class_Rings_Ocomm__ring__1(_482309), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_482309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_482309)), c_Polynomial_OpCons(_482309, c_Groups_Ouminus__class_Ouminus(_482309, _482311), c_Polynomial_OpCons(_482309, c_Groups_Oone__class_Oone(_482309), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_482309))))), c_Polynomial_Osynthetic__div(_482309, _482313, _482311)), c_Polynomial_OpCons(_482309, hAPP(c_Polynomial_Opoly(_482309, _482313), _482311), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_482309)))) = _482313)], (8113 ^ _206868) ^ [_482625, _482627] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _482625), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _482627)), _482625), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _482625, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _482627)))], (8119 ^ _206868) ^ [_482885, _482887] : [-(hBOOL(hAPP(_482885, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_482885, _482887)), 8127 ^ _206868 : [(8128 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 8126 ^ [_482885, _482887], _482887))], (8136 ^ _206868) ^ [] : [-(hBOOL(hAPP(_482885, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 8126 ^ [_482885, _482887], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (8130 ^ _206868) ^ [_483321] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _483321, 8126 ^ [_482885, _482887]), hBOOL(hAPP(_482885, _483321))]]], (8138 ^ _206868) ^ [_483663, _483665] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _483663, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _483665, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _483663, _483665))], (8144 ^ _206868) ^ [_483837, _483839] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _483837, _483839), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _483837, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _483839, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8160 ^ _206868) ^ [_484354, _484356] : [8161 ^ _206868 : [(8162 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _484354, _484356)], (8164 ^ _206868) ^ [] : [_484354 = _484356]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _484354, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _484356, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8150 ^ _206868) ^ [_484090, _484092] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _484090, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _484092, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _484090, _484092)), -(_484090 = _484092)], (8168 ^ _206868) ^ [_484681, _484683] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _484681, c_Groups_Oone__class_Oone(tc_Int_Oint)), _484683), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _484681, _484683))], (8174 ^ _206868) ^ [_484855, _484857] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _484855, _484857), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _484855, c_Groups_Oone__class_Oone(tc_Int_Oint)), _484857))], (8180 ^ _206868) ^ [_485094] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _485094), _485094), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _485094, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8186 ^ _206868) ^ [_485270] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _485270, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _485270), _485270), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8192 ^ _206868) ^ [_485482] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _485482), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _485482)))], (8198 ^ _206868) ^ [_485698, _485700] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _485698, _485700), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _485698, c_Groups_Oone__class_Oone(tc_Int_Oint)), _485700))], (8204 ^ _206868) ^ [_485948, _485950, _485952, _485954] : [class_Rings_Ocomm__semiring__1(_485948), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485948), _485950), c_Groups_Oplus__class_Oplus(_485948, _485952, _485954)) = c_Groups_Oplus__class_Oplus(_485948, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485948), _485950), _485952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485948), _485950), _485954)))], (8210 ^ _206868) ^ [_486274, _486276, _486278, _486280, _486282] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_486274), 8213 ^ _206868 : [(8224 ^ _206868) ^ [] : [-(c_Groups_Oplus__class_Oplus(_486274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486274), _486276), _486280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486274), _486278), _486282)) = c_Groups_Oplus__class_Oplus(_486274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486274), _486276), _486282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486274), _486278), _486280))), 8227 ^ _206868 : [(8228 ^ _206868) ^ [] : [_486276 = _486278], (8230 ^ _206868) ^ [] : [_486280 = _486282]]], (8214 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_486274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486274), _486276), _486280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486274), _486278), _486282)) = c_Groups_Oplus__class_Oplus(_486274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486274), _486276), _486282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486274), _486278), _486280)), -(_486276 = _486278), -(_486280 = _486282)]]], (8232 ^ _206868) ^ [_487110, _487112, _487114, _487116] : [class_Rings_Ocomm__semiring__1(_487110), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487110), c_Groups_Oplus__class_Oplus(_487110, _487112, _487114)), _487116) = c_Groups_Oplus__class_Oplus(_487110, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487110), _487112), _487116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487110), _487114), _487116)))], (8238 ^ _206868) ^ [_487422, _487424, _487426, _487428] : [class_Rings_Ocomm__semiring__1(_487422), -(c_Groups_Oplus__class_Oplus(_487422, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487422), _487424), _487426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487422), _487428), _487426)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487422), c_Groups_Oplus__class_Oplus(_487422, _487424, _487428)), _487426))], (8244 ^ _206868) ^ [_487748, _487750, _487752, _487754, _487756] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_487748), 8247 ^ _206868 : [(8258 ^ _206868) ^ [] : [8259 ^ _206868 : [(8260 ^ _206868) ^ [] : [_487750 = _487754], (8262 ^ _206868) ^ [] : [_487752 = _487756]], -(c_Groups_Oplus__class_Oplus(_487748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487748), _487750), _487752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487748), _487754), _487756)) = c_Groups_Oplus__class_Oplus(_487748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487748), _487750), _487756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487748), _487754), _487752)))], (8248 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_487748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487748), _487750), _487752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487748), _487754), _487756)) = c_Groups_Oplus__class_Oplus(_487748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487748), _487750), _487756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487748), _487754), _487752)), -(_487750 = _487754), -(_487752 = _487756)]]], (8266 ^ _206868) ^ [_488520] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _488520), _488520) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (8268 ^ _206868) ^ [_488606] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _488606) = _488606)], (8270 ^ _206868) ^ [_488688] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _488688, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _488688)], (8272 ^ _206868) ^ [_488770] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _488770), _488770) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8274 ^ _206868) ^ [_488912, _488914, _488916, _488918] : [class_RealVector_Oreal__normed__algebra(_488912), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488912), _488914), c_Groups_Oplus__class_Oplus(_488912, _488916, _488918)) = c_Groups_Oplus__class_Oplus(_488912, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488912), _488914), _488916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488912), _488914), _488918)))], (8280 ^ _206868) ^ [_489224, _489226, _489228, _489230] : [class_RealVector_Oreal__normed__algebra(_489224), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489224), _489226), c_Groups_Oplus__class_Oplus(_489224, _489228, _489230)) = c_Groups_Oplus__class_Oplus(_489224, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489224), _489226), _489228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489224), _489226), _489230)))], (8286 ^ _206868) ^ [_489536, _489538, _489540, _489542] : [class_RealVector_Oreal__normed__algebra(_489536), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489536), c_Groups_Oplus__class_Oplus(_489536, _489538, _489540)), _489542) = c_Groups_Oplus__class_Oplus(_489536, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489536), _489538), _489542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489536), _489540), _489542)))], (8292 ^ _206868) ^ [_489848, _489850, _489852, _489854] : [class_Rings_Ocomm__semiring__0(_489848), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_489848)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_489848), _489850, _489852)), _489854) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_489848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_489848)), _489850), _489854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_489848)), _489852), _489854)))], (8298 ^ _206868) ^ [_490180, _490182, _490184, _490186] : [class_RealVector_Oreal__normed__algebra(_490180), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490180), c_Groups_Oplus__class_Oplus(_490180, _490182, _490184)), _490186) = c_Groups_Oplus__class_Oplus(_490180, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490180), _490182), _490186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490180), _490184), _490186)))], (8304 ^ _206868) ^ [_490463, _490465, _490467] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _490463, _490465)), _490467) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _490463), _490467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _490465), _490467)))], (8306 ^ _206868) ^ [_490628, _490630, _490632, _490634] : [class_Rings_Ocomm__semiring(_490628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490628), c_Groups_Oplus__class_Oplus(_490628, _490630, _490632)), _490634) = c_Groups_Oplus__class_Oplus(_490628, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490628), _490630), _490634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490628), _490632), _490634)))], (8312 ^ _206868) ^ [_490954, _490956, _490958, _490960, _490962] : [class_Rings_Osemiring(_490954), -(c_Groups_Oplus__class_Oplus(_490954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490954), _490956), _490958), c_Groups_Oplus__class_Oplus(_490954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490954), _490960), _490958), _490962)) = c_Groups_Oplus__class_Oplus(_490954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490954), c_Groups_Oplus__class_Oplus(_490954, _490956, _490960)), _490958), _490962))], (8318 ^ _206868) ^ [_491274, _491276, _491278] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _491274, _491276), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _491278, _491274), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _491278, _491276)))], (8324 ^ _206868) ^ [_491524, _491526, _491528] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _491524, _491526), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _491524, _491528), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _491526, _491528)))], (8330 ^ _206868) ^ [_491788, _491790, _491792, _491794] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _491788, _491790), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _491792, _491794), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _491788, _491792), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _491790, _491794)))], (8340 ^ _206868) ^ [_492158, _492160] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _492158, _492160), 8343 ^ _206868 : [(8344 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _492158, _492160))], (8346 ^ _206868) ^ [] : [_492158 = _492160]]], (8348 ^ _206868) ^ [_492400, _492402] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _492400, _492402)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _492400, _492402), -(_492400 = _492402)], (8358 ^ _206868) ^ [_492708, _492710] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _492708, _492710)), -(_492708 = _492710), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _492710, _492708))], (8368 ^ _206868) ^ [_493013, _493015] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _493013, _493015), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _493015, _493013), -(_493013 = _493015)], (8378 ^ _206868) ^ [_493330, _493332, _493334] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _493330, _493332), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _493332, _493334), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _493330, _493334))], (8388 ^ _206868) ^ [_493645, _493647] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _493645, _493647)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _493647, _493645))], (8394 ^ _206868) ^ [_493831] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _493831, _493831))], (8396 ^ _206868) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8398 ^ _206868) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (8400 ^ _206868) ^ [_494059] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _494059), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _494059))], (8406 ^ _206868) ^ [_494219] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _494219), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _494219))], (8412 ^ _206868) ^ [_494435] : [_494435 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _494435) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8418 ^ _206868) ^ [_494597] : [-(_494597 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 8421 ^ _206868 : [(8422 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _494597), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _494597) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8428 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _494597)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _494597) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (8434 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8436 ^ _206868) ^ [_495135, _495137, _495139] : [class_Rings_Olinordered__idom(_495135), c_Polynomial_Opos__poly(_495135, _495137), c_Polynomial_Opos__poly(_495135, _495139), -(c_Polynomial_Opos__poly(_495135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_495135)), _495137), _495139)))], (8450 ^ _206868) ^ [_495555, _495557] : [c_RealDef_Opositive(_495555), c_RealDef_Opositive(_495557), -(c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _495555), _495557)))], (8460 ^ _206868) ^ [_495874, _495876, _495878] : [class_Rings_Ocomm__semiring__0(_495874), -(hAPP(c_Polynomial_Ocoeff(_495874, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_495874)), _495876), _495878)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_495874, _495876), c_Polynomial_Odegree(_495874, _495878))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_495874), hAPP(c_Polynomial_Ocoeff(_495874, _495876), c_Polynomial_Odegree(_495874, _495876))), hAPP(c_Polynomial_Ocoeff(_495874, _495878), c_Polynomial_Odegree(_495874, _495878))))], (8466 ^ _206868) ^ [_496206, _496208, _496210] : [class_RealVector_Oreal__normed__algebra(_496206), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_496206), c_Groups_Ouminus__class_Ouminus(_496206, _496208)), _496210) = c_Groups_Ouminus__class_Ouminus(_496206, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_496206), _496208), _496210)))], (8472 ^ _206868) ^ [_496478, _496480, _496482] : [class_RealVector_Oreal__normed__algebra(_496478), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_496478), c_Groups_Ouminus__class_Ouminus(_496478, _496480)), _496482) = c_Groups_Ouminus__class_Ouminus(_496478, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_496478), _496480), _496482)))], (8478 ^ _206868) ^ [_496750, _496752, _496754] : [class_RealVector_Oreal__normed__algebra(_496750), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_496750), _496752), c_Groups_Ouminus__class_Ouminus(_496750, _496754)) = c_Groups_Ouminus__class_Ouminus(_496750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_496750), _496752), _496754)))], (8484 ^ _206868) ^ [_497022, _497024, _497026] : [class_RealVector_Oreal__normed__algebra(_497022), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497022), _497024), c_Groups_Ouminus__class_Ouminus(_497022, _497026)) = c_Groups_Ouminus__class_Ouminus(_497022, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497022), _497024), _497026)))], (8490 ^ _206868) ^ [_497294, _497296, _497298] : [class_Rings_Oidom(_497294), 8493 ^ _206868 : [(8504 ^ _206868) ^ [] : [8505 ^ _206868 : [(8506 ^ _206868) ^ [] : [_497296 = _497298], (8508 ^ _206868) ^ [] : [_497296 = c_Groups_Ouminus__class_Ouminus(_497294, _497298)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497294), _497296), _497296) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497294), _497298), _497298))], (8494 ^ _206868) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497294), _497296), _497296) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497294), _497298), _497298), -(_497296 = _497298), -(_497296 = c_Groups_Ouminus__class_Ouminus(_497294, _497298))]]], (8512 ^ _206868) ^ [_498003, _498005, _498007] : [class_Rings_Oring(_498003), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498003), c_Groups_Ouminus__class_Ouminus(_498003, _498005)), c_Groups_Ouminus__class_Ouminus(_498003, _498007)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498003), _498005), _498007))], (8518 ^ _206868) ^ [_498275, _498277, _498279] : [class_Rings_Oring(_498275), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498275), c_Groups_Ouminus__class_Ouminus(_498275, _498277)), _498279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498275), _498277), c_Groups_Ouminus__class_Ouminus(_498275, _498279)))], (8524 ^ _206868) ^ [_498547, _498549, _498551] : [class_Rings_Oring(_498547), -(c_Groups_Ouminus__class_Ouminus(_498547, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498547), _498549), _498551)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498547), c_Groups_Ouminus__class_Ouminus(_498547, _498549)), _498551))], (8530 ^ _206868) ^ [_498819, _498821, _498823] : [class_Rings_Oring(_498819), -(c_Groups_Ouminus__class_Ouminus(_498819, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498819), _498821), _498823)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498819), _498821), c_Groups_Ouminus__class_Ouminus(_498819, _498823)))], (8536 ^ _206868) ^ [_499105, _499107, _499109, _499111] : [class_Rings_Ocomm__semiring__1(_499105), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_499105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499105), _499107), _499109)), _499111)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_499105), _499109), _499111)))], (8546 ^ _206868) ^ [_499494, _499496, _499498, _499500] : [class_Rings_Ocomm__semiring__1(_499494), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_499494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499494), _499496), _499498)), _499500)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_499494), _499496), _499500)))], (8556 ^ _206868) ^ [_499883, _499885, _499887, _499889] : [class_Rings_Odvd(_499883), _499885 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499883), _499887), _499889), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_499883), _499887), _499885)))], (8566 ^ _206868) ^ [_500272, _500274, _500276, _500278, _500280] : [class_Rings_Ocomm__semiring__1(_500272), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_500272), _500274), _500276)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_500272), _500278), _500280)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_500272), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500272), _500274), _500278)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500272), _500276), _500280))))], (8580 ^ _206868) ^ [_500802, _500804, _500806, _500808] : [class_Rings_Ocomm__semiring__1(_500802), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_500802), _500804), _500806)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_500802), _500804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500802), _500808), _500806))))], (8590 ^ _206868) ^ [_501191, _501193, _501195, _501197] : [class_Rings_Ocomm__semiring__1(_501191), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_501191), _501193), _501195)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_501191), _501193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501191), _501195), _501197))))], (8600 ^ _206868) ^ [_501566, _501568, _501570] : [class_Rings_Ocomm__semiring__1(_501566), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_501566), _501568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501566), _501570), _501568))))], (8606 ^ _206868) ^ [_501824, _501826, _501828] : [class_Rings_Ocomm__semiring__1(_501824), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_501824), _501826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501824), _501826), _501828))))], (8612 ^ _206868) ^ [_502096, _502098, _502100, _502102] : [class_Rings_Ocomm__semiring__1(_502096), -(hAPP(hAPP(c_Power_Opower__class_Opower(_502096), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502096), _502098), _502100)), _502102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502096), hAPP(hAPP(c_Power_Opower__class_Opower(_502096), _502098), _502102)), hAPP(hAPP(c_Power_Opower__class_Opower(_502096), _502100), _502102)))], (8618 ^ _206868) ^ [_502424, _502426, _502428, _502430] : [class_Groups_Ocomm__monoid__mult(_502424), -(hAPP(hAPP(c_Power_Opower__class_Opower(_502424), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502424), _502426), _502428)), _502430) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502424), hAPP(hAPP(c_Power_Opower__class_Opower(_502424), _502426), _502430)), hAPP(hAPP(c_Power_Opower__class_Opower(_502424), _502428), _502430)))], (8624 ^ _206868) ^ [_502738, _502740, _502742] : [class_Groups_Omonoid__mult(_502738), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502738), hAPP(hAPP(c_Power_Opower__class_Opower(_502738), _502740), _502742)), _502740) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502738), _502740), hAPP(hAPP(c_Power_Opower__class_Opower(_502738), _502740), _502742)))], (8630 ^ _206868) ^ [_503030, _503032, _503034] : [-(_503030 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 8633 ^ _206868 : [(8634 ^ _206868) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _503032), _503030) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _503034), _503030), -(_503032 = _503034)], (8640 ^ _206868) ^ [] : [_503032 = _503034, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _503032), _503030) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _503034), _503030))]]], (8646 ^ _206868) ^ [_503559, _503561, _503563] : [-(_503559 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 8649 ^ _206868 : [(8650 ^ _206868) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _503559), _503561) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _503559), _503563), -(_503561 = _503563)], (8656 ^ _206868) ^ [] : [_503561 = _503563, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _503559), _503561) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _503559), _503563))]]], (8662 ^ _206868) ^ [_504088, _504090, _504092] : [class_Rings_Ocomm__semiring__1(_504088), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504088), _504090), _504092) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504088), _504092), _504090))], (8668 ^ _206868) ^ [_504362, _504364, _504366, _504368] : [class_Rings_Ocomm__semiring__1(_504362), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504362), _504364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504362), _504366), _504368)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504362), _504366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504362), _504364), _504368)))], (8674 ^ _206868) ^ [_504674, _504676, _504678, _504680] : [class_Rings_Ocomm__semiring__1(_504674), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504674), _504676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504674), _504678), _504680)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504674), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504674), _504676), _504678)), _504680))], (8680 ^ _206868) ^ [_504986, _504988, _504990, _504992] : [class_Rings_Ocomm__semiring__1(_504986), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504986), _504988), _504990)), _504992) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504986), _504988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504986), _504990), _504992)))], (8686 ^ _206868) ^ [_505298, _505300, _505302, _505304] : [class_Rings_Ocomm__semiring__1(_505298), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505298), _505300), _505302)), _505304) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505298), _505300), _505304)), _505302))], (8692 ^ _206868) ^ [_505624, _505626, _505628, _505630, _505632] : [class_Rings_Ocomm__semiring__1(_505624), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505624), _505626), _505628)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505624), _505630), _505632)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505624), _505626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505624), _505628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505624), _505630), _505632))))], (8698 ^ _206868) ^ [_505988, _505990, _505992, _505994, _505996] : [class_Rings_Ocomm__semiring__1(_505988), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505988), _505990), _505992)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505988), _505994), _505996)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505988), _505994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505988), _505990), _505992)), _505996)))], (8704 ^ _206868) ^ [_506352, _506354, _506356, _506358, _506360] : [class_Rings_Ocomm__semiring__1(_506352), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506352), _506354), _506356)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506352), _506358), _506360)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506352), _506354), _506358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506352), _506356), _506360)))], (8710 ^ _206868) ^ [_506659, _506661] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _506659), _506661) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _506661), _506659))], (8712 ^ _206868) ^ [_506808, _506810, _506812, _506814] : [class_Groups_Oab__semigroup__mult(_506808), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506808), _506810), _506812)), _506814) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506808), _506810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506808), _506812), _506814)))], (8718 ^ _206868) ^ [_507091, _507093, _507095] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _507091), _507093)), _507095) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _507091), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _507093), _507095)))], (8720 ^ _206868) ^ [_507254, _507256, _507258, _507260] : [class_Rings_Ocomm__semiring__0(_507254), -(hAPP(c_Polynomial_Opoly(_507254, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_507254)), _507256), _507258)), _507260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507254), hAPP(c_Polynomial_Opoly(_507254, _507256), _507260)), hAPP(c_Polynomial_Opoly(_507254, _507258), _507260)))], (8726 ^ _206868) ^ [_507560, _507562, _507564] : [class_RealVector_Oreal__normed__div__algebra(_507560), -(c_RealVector_Onorm__class_Onorm(_507560, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507560), _507562), _507564)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_507560, _507562)), c_RealVector_Onorm__class_Onorm(_507560, _507564)))], (8732 ^ _206868) ^ [_507820, _507822] : [class_Lattices_Oab__semigroup__idem__mult(_507820), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507820), _507822), _507822) = _507822)], (8738 ^ _206868) ^ [_508044, _508046] : [class_Lattices_Oab__semigroup__idem__mult(_508044), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508044), _508046), _508046) = _508046)], (8744 ^ _206868) ^ [_508282, _508284, _508286] : [class_Lattices_Oab__semigroup__idem__mult(_508282), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508282), _508284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508282), _508284), _508286)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508282), _508284), _508286))], (8750 ^ _206868) ^ [_508544, _508546] : [class_Rings_Ocomm__semiring__1(_508544), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508544), _508546), c_Groups_Oone__class_Oone(_508544)) = _508546)], (8756 ^ _206868) ^ [_508772, _508774] : [class_Rings_Ocomm__semiring__1(_508772), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508772), c_Groups_Oone__class_Oone(_508772)), _508774) = _508774)], (8762 ^ _206868) ^ [_509000, _509002] : [class_Groups_Omonoid__mult(_509000), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509000), c_Groups_Oone__class_Oone(_509000)), _509002) = _509002)], (8768 ^ _206868) ^ [_509228, _509230] : [class_Groups_Ocomm__monoid__mult(_509228), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509228), c_Groups_Oone__class_Oone(_509228)), _509230) = _509230)], (8774 ^ _206868) ^ [_509456, _509458] : [class_Groups_Omonoid__mult(_509456), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509456), _509458), c_Groups_Oone__class_Oone(_509456)) = _509458)], (8780 ^ _206868) ^ [_509684, _509686] : [class_Groups_Ocomm__monoid__mult(_509684), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509684), _509686), c_Groups_Oone__class_Oone(_509684)) = _509686)], (8786 ^ _206868) ^ [_509912, _509914] : [class_Rings_Ocomm__semiring__1(_509912), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509912), c_Groups_Ozero__class_Ozero(_509912)), _509914) = c_Groups_Ozero__class_Ozero(_509912))], (8792 ^ _206868) ^ [_510144, _510146] : [class_Rings_Ocomm__semiring__1(_510144), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510144), _510146), c_Groups_Ozero__class_Ozero(_510144)) = c_Groups_Ozero__class_Ozero(_510144))], (8798 ^ _206868) ^ [_510376, _510378] : [class_RealVector_Oreal__normed__algebra(_510376), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510376), c_Groups_Ozero__class_Ozero(_510376)), _510378) = c_Groups_Ozero__class_Ozero(_510376))], (8804 ^ _206868) ^ [_510608, _510610] : [class_RealVector_Oreal__normed__algebra(_510608), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510608), c_Groups_Ozero__class_Ozero(_510608)), _510610) = c_Groups_Ozero__class_Ozero(_510608))], (8810 ^ _206868) ^ [_510840, _510842] : [class_RealVector_Oreal__normed__algebra(_510840), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510840), _510842), c_Groups_Ozero__class_Ozero(_510840)) = c_Groups_Ozero__class_Ozero(_510840))], (8816 ^ _206868) ^ [_511072, _511074] : [class_RealVector_Oreal__normed__algebra(_511072), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511072), _511074), c_Groups_Ozero__class_Ozero(_511072)) = c_Groups_Ozero__class_Ozero(_511072))], (8822 ^ _206868) ^ [_511304, _511306] : [class_Rings_Omult__zero(_511304), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511304), c_Groups_Ozero__class_Ozero(_511304)), _511306) = c_Groups_Ozero__class_Ozero(_511304))], (8828 ^ _206868) ^ [_511536, _511538] : [class_Rings_Omult__zero(_511536), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511536), _511538), c_Groups_Ozero__class_Ozero(_511536)) = c_Groups_Ozero__class_Ozero(_511536))], (8834 ^ _206868) ^ [_511782, _511784, _511786] : [class_Rings_Oring__no__zero__divisors(_511782), 8837 ^ _206868 : [(8848 ^ _206868) ^ [] : [8849 ^ _206868 : [(8850 ^ _206868) ^ [] : [_511784 = c_Groups_Ozero__class_Ozero(_511782)], (8852 ^ _206868) ^ [] : [_511786 = c_Groups_Ozero__class_Ozero(_511782)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511782), _511784), _511786) = c_Groups_Ozero__class_Ozero(_511782))], (8838 ^ _206868) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511782), _511784), _511786) = c_Groups_Ozero__class_Ozero(_511782), -(_511784 = c_Groups_Ozero__class_Ozero(_511782)), -(_511786 = c_Groups_Ozero__class_Ozero(_511782))]]], (8856 ^ _206868) ^ [_512476, _512478, _512480] : [class_Rings_Ono__zero__divisors(_512476), -(_512478 = c_Groups_Ozero__class_Ozero(_512476)), -(_512480 = c_Groups_Ozero__class_Ozero(_512476)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512476), _512478), _512480) = c_Groups_Ozero__class_Ozero(_512476)], (8870 ^ _206868) ^ [_512925, _512927, _512929] : [class_Rings_Ono__zero__divisors(_512925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512925), _512927), _512929) = c_Groups_Ozero__class_Ozero(_512925), -(_512927 = c_Groups_Ozero__class_Ozero(_512925)), -(_512929 = c_Groups_Ozero__class_Ozero(_512925))], (8884 ^ _206868) ^ [_513396, _513398, _513400, _513402, _513404] : [class_RealVector_Oreal__normed__algebra(_513396), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_513396, _513398), _513400), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_513396, _513402), _513404), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_513396, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513396), _513398), _513402)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _513400), _513404)))], (8898 ^ _206868) ^ [_513890, _513892, _513894] : [class_RealVector_Oreal__normed__algebra(_513890), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_513890, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513890), _513892), _513894)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_513890, _513892)), c_RealVector_Onorm__class_Onorm(_513890, _513894))))], (8904 ^ _206868) ^ [_514152, _514154] : [class_Rings_Ocomm__semiring__0(_514152), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_514152)), _514154), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514152))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514152)))], (8910 ^ _206868) ^ [_514396, _514398] : [class_Rings_Ocomm__semiring__0(_514396), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_514396)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514396))), _514398) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514396)))], (8916 ^ _206868) ^ [_514611] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _514611) = _514611)], (8918 ^ _206868) ^ [_514735, _514737, _514739] : [class_Rings_Olinordered__idom(_514735), -(c_Groups_Osgn__class_Osgn(_514735, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514735), _514737), _514739)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514735), c_Groups_Osgn__class_Osgn(_514735, _514737)), c_Groups_Osgn__class_Osgn(_514735, _514739)))], (8924 ^ _206868) ^ [_515013, _515015, _515017] : [class_RealVector_Oreal__normed__div__algebra(_515013), -(c_Groups_Osgn__class_Osgn(_515013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515013), _515015), _515017)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515013), c_Groups_Osgn__class_Osgn(_515013, _515015)), c_Groups_Osgn__class_Osgn(_515013, _515017)))], (8930 ^ _206868) ^ [_515291, _515293, _515295] : [class_Rings_Oordered__cancel__semiring(_515291), -(c_Orderings_Oord__class_Oless__eq(_515291, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515291), _515293), _515295), c_Groups_Ozero__class_Ozero(_515291))), 8935 ^ _206868 : [(8936 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515291, c_Groups_Ozero__class_Ozero(_515291), _515293), c_Orderings_Oord__class_Oless__eq(_515291, _515295, c_Groups_Ozero__class_Ozero(_515291))], (8942 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515291, _515293, c_Groups_Ozero__class_Ozero(_515291)), c_Orderings_Oord__class_Oless__eq(_515291, c_Groups_Ozero__class_Ozero(_515291), _515295)]]], (8950 ^ _206868) ^ [_515920, _515922, _515924] : [class_Rings_Oordered__ring(_515920), -(c_Orderings_Oord__class_Oless__eq(_515920, c_Groups_Ozero__class_Ozero(_515920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515920), _515922), _515924))), 8955 ^ _206868 : [(8956 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515920, c_Groups_Ozero__class_Ozero(_515920), _515922), c_Orderings_Oord__class_Oless__eq(_515920, c_Groups_Ozero__class_Ozero(_515920), _515924)], (8962 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515920, _515922, c_Groups_Ozero__class_Ozero(_515920)), c_Orderings_Oord__class_Oless__eq(_515920, _515924, c_Groups_Ozero__class_Ozero(_515920))]]], (8970 ^ _206868) ^ [_516577, _516579, _516581, _516583, _516585] : [class_Rings_Oordered__semiring(_516577), c_Orderings_Oord__class_Oless__eq(_516577, _516579, _516581), c_Orderings_Oord__class_Oless__eq(_516577, _516583, _516585), c_Orderings_Oord__class_Oless__eq(_516577, c_Groups_Ozero__class_Ozero(_516577), _516581), c_Orderings_Oord__class_Oless__eq(_516577, c_Groups_Ozero__class_Ozero(_516577), _516583), -(c_Orderings_Oord__class_Oless__eq(_516577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516577), _516579), _516583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516577), _516581), _516585)))], (8992 ^ _206868) ^ [_517299, _517301, _517303, _517305, _517307] : [class_Rings_Oordered__semiring(_517299), c_Orderings_Oord__class_Oless__eq(_517299, _517301, _517303), c_Orderings_Oord__class_Oless__eq(_517299, _517305, _517307), c_Orderings_Oord__class_Oless__eq(_517299, c_Groups_Ozero__class_Ozero(_517299), _517301), c_Orderings_Oord__class_Oless__eq(_517299, c_Groups_Ozero__class_Ozero(_517299), _517305), -(c_Orderings_Oord__class_Oless__eq(_517299, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517299), _517301), _517305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517299), _517303), _517307)))], (9014 ^ _206868) ^ [_518007, _518009, _518011, _518013] : [class_Rings_Oordered__ring(_518007), c_Orderings_Oord__class_Oless__eq(_518007, _518009, _518011), c_Orderings_Oord__class_Oless__eq(_518007, _518013, c_Groups_Ozero__class_Ozero(_518007)), -(c_Orderings_Oord__class_Oless__eq(_518007, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518007), _518013), _518011), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518007), _518013), _518009)))], (9028 ^ _206868) ^ [_518491, _518493, _518495, _518497] : [class_Rings_Oordered__ring(_518491), c_Orderings_Oord__class_Oless__eq(_518491, _518493, _518495), c_Orderings_Oord__class_Oless__eq(_518491, _518497, c_Groups_Ozero__class_Ozero(_518491)), -(c_Orderings_Oord__class_Oless__eq(_518491, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518491), _518495), _518497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518491), _518493), _518497)))], (9042 ^ _206868) ^ [_518975, _518977, _518979, _518981] : [class_Rings_Oordered__comm__semiring(_518975), c_Orderings_Oord__class_Oless__eq(_518975, _518977, _518979), c_Orderings_Oord__class_Oless__eq(_518975, c_Groups_Ozero__class_Ozero(_518975), _518981), -(c_Orderings_Oord__class_Oless__eq(_518975, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518975), _518981), _518977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518975), _518981), _518979)))], (9056 ^ _206868) ^ [_519459, _519461, _519463, _519465] : [class_Rings_Oordered__semiring(_519459), c_Orderings_Oord__class_Oless__eq(_519459, _519461, _519463), c_Orderings_Oord__class_Oless__eq(_519459, c_Groups_Ozero__class_Ozero(_519459), _519465), -(c_Orderings_Oord__class_Oless__eq(_519459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519459), _519465), _519461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519459), _519465), _519463)))], (9070 ^ _206868) ^ [_519943, _519945, _519947, _519949] : [class_Rings_Oordered__semiring(_519943), c_Orderings_Oord__class_Oless__eq(_519943, _519945, _519947), c_Orderings_Oord__class_Oless__eq(_519943, c_Groups_Ozero__class_Ozero(_519943), _519949), -(c_Orderings_Oord__class_Oless__eq(_519943, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519943), _519945), _519949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519943), _519947), _519949)))], (9084 ^ _206868) ^ [_520413, _520415, _520417] : [class_Rings_Oordered__ring(_520413), c_Orderings_Oord__class_Oless__eq(_520413, _520415, c_Groups_Ozero__class_Ozero(_520413)), c_Orderings_Oord__class_Oless__eq(_520413, _520417, c_Groups_Ozero__class_Ozero(_520413)), -(c_Orderings_Oord__class_Oless__eq(_520413, c_Groups_Ozero__class_Ozero(_520413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520413), _520415), _520417)))], (9098 ^ _206868) ^ [_520861, _520863, _520865] : [class_Rings_Oordered__cancel__semiring(_520861), c_Orderings_Oord__class_Oless__eq(_520861, _520863, c_Groups_Ozero__class_Ozero(_520861)), c_Orderings_Oord__class_Oless__eq(_520861, c_Groups_Ozero__class_Ozero(_520861), _520865), -(c_Orderings_Oord__class_Oless__eq(_520861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520861), _520863), _520865), c_Groups_Ozero__class_Ozero(_520861)))], (9112 ^ _206868) ^ [_521309, _521311, _521313] : [class_Rings_Oordered__cancel__semiring(_521309), c_Orderings_Oord__class_Oless__eq(_521309, c_Groups_Ozero__class_Ozero(_521309), _521311), c_Orderings_Oord__class_Oless__eq(_521309, _521313, c_Groups_Ozero__class_Ozero(_521309)), -(c_Orderings_Oord__class_Oless__eq(_521309, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521309), _521313), _521311), c_Groups_Ozero__class_Ozero(_521309)))], (9126 ^ _206868) ^ [_521757, _521759, _521761] : [class_Rings_Oordered__cancel__semiring(_521757), c_Orderings_Oord__class_Oless__eq(_521757, c_Groups_Ozero__class_Ozero(_521757), _521759), c_Orderings_Oord__class_Oless__eq(_521757, _521761, c_Groups_Ozero__class_Ozero(_521757)), -(c_Orderings_Oord__class_Oless__eq(_521757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521757), _521759), _521761), c_Groups_Ozero__class_Ozero(_521757)))], (9140 ^ _206868) ^ [_522205, _522207, _522209] : [class_Rings_Oordered__cancel__semiring(_522205), c_Orderings_Oord__class_Oless__eq(_522205, c_Groups_Ozero__class_Ozero(_522205), _522207), c_Orderings_Oord__class_Oless__eq(_522205, c_Groups_Ozero__class_Ozero(_522205), _522209), -(c_Orderings_Oord__class_Oless__eq(_522205, c_Groups_Ozero__class_Ozero(_522205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522205), _522207), _522209)))], (9154 ^ _206868) ^ [_522653, _522655, _522657] : [class_Rings_Olinordered__ring__strict(_522653), 9157 ^ _206868 : [(9158 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522653), _522655), _522657), c_Groups_Ozero__class_Ozero(_522653)), 9163 ^ _206868 : [(9164 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_522653, c_Groups_Ozero__class_Ozero(_522653), _522655))], (9166 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_522653, _522657, c_Groups_Ozero__class_Ozero(_522653)))]], 9167 ^ _206868 : [(9168 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_522653, _522655, c_Groups_Ozero__class_Ozero(_522653)))], (9170 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_522653, c_Groups_Ozero__class_Ozero(_522653), _522657))]]], (9172 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_522653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522653), _522655), _522657), c_Groups_Ozero__class_Ozero(_522653))), 9173 ^ _206868 : [(9174 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522653, c_Groups_Ozero__class_Ozero(_522653), _522655), c_Orderings_Oord__class_Oless__eq(_522653, _522657, c_Groups_Ozero__class_Ozero(_522653))], (9180 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522653, _522655, c_Groups_Ozero__class_Ozero(_522653)), c_Orderings_Oord__class_Oless__eq(_522653, c_Groups_Ozero__class_Ozero(_522653), _522657)]]]]], (9188 ^ _206868) ^ [_523702, _523704, _523706] : [class_Rings_Olinordered__ring__strict(_523702), 9191 ^ _206868 : [(9192 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_523702, c_Groups_Ozero__class_Ozero(_523702), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523702), _523704), _523706)), 9197 ^ _206868 : [(9198 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_523702, c_Groups_Ozero__class_Ozero(_523702), _523704))], (9200 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_523702, c_Groups_Ozero__class_Ozero(_523702), _523706))]], 9201 ^ _206868 : [(9202 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_523702, _523704, c_Groups_Ozero__class_Ozero(_523702)))], (9204 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_523702, _523706, c_Groups_Ozero__class_Ozero(_523702)))]]], (9206 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_523702, c_Groups_Ozero__class_Ozero(_523702), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523702), _523704), _523706))), 9207 ^ _206868 : [(9208 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_523702, c_Groups_Ozero__class_Ozero(_523702), _523704), c_Orderings_Oord__class_Oless__eq(_523702, c_Groups_Ozero__class_Ozero(_523702), _523706)], (9214 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_523702, _523704, c_Groups_Ozero__class_Ozero(_523702)), c_Orderings_Oord__class_Oless__eq(_523702, _523706, c_Groups_Ozero__class_Ozero(_523702))]]]]], (9222 ^ _206868) ^ [_524737, _524739] : [class_Rings_Olinordered__ring(_524737), -(c_Orderings_Oord__class_Oless__eq(_524737, c_Groups_Ozero__class_Ozero(_524737), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524737), _524739), _524739)))], (9228 ^ _206868) ^ [_524995, _524997, _524999, _525001] : [class_Rings_Olinordered__ring__strict(_524995), c_Orderings_Oord__class_Oless(_524995, _524997, _524999), c_Orderings_Oord__class_Oless(_524995, _525001, c_Groups_Ozero__class_Ozero(_524995)), -(c_Orderings_Oord__class_Oless(_524995, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524995), _525001), _524999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524995), _525001), _524997)))], (9242 ^ _206868) ^ [_525479, _525481, _525483, _525485] : [class_Rings_Olinordered__ring__strict(_525479), c_Orderings_Oord__class_Oless(_525479, _525481, _525483), c_Orderings_Oord__class_Oless(_525479, _525485, c_Groups_Ozero__class_Ozero(_525479)), -(c_Orderings_Oord__class_Oless(_525479, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525479), _525483), _525485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525479), _525481), _525485)))], (9256 ^ _206868) ^ [_525963, _525965, _525967, _525969] : [class_Rings_Olinordered__comm__semiring__strict(_525963), c_Orderings_Oord__class_Oless(_525963, _525965, _525967), c_Orderings_Oord__class_Oless(_525963, c_Groups_Ozero__class_Ozero(_525963), _525969), -(c_Orderings_Oord__class_Oless(_525963, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525963), _525969), _525965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525963), _525969), _525967)))], (9270 ^ _206868) ^ [_526447, _526449, _526451, _526453] : [class_Rings_Olinordered__semiring__strict(_526447), c_Orderings_Oord__class_Oless(_526447, _526449, _526451), c_Orderings_Oord__class_Oless(_526447, c_Groups_Ozero__class_Ozero(_526447), _526453), -(c_Orderings_Oord__class_Oless(_526447, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526447), _526453), _526449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526447), _526453), _526451)))], (9284 ^ _206868) ^ [_526931, _526933, _526935, _526937] : [class_Rings_Olinordered__semiring__strict(_526931), c_Orderings_Oord__class_Oless(_526931, _526933, _526935), c_Orderings_Oord__class_Oless(_526931, c_Groups_Ozero__class_Ozero(_526931), _526937), -(c_Orderings_Oord__class_Oless(_526931, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526931), _526933), _526937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526931), _526935), _526937)))], (9298 ^ _206868) ^ [_527401, _527403, _527405] : [class_Rings_Olinordered__ring__strict(_527401), c_Orderings_Oord__class_Oless(_527401, _527403, c_Groups_Ozero__class_Ozero(_527401)), c_Orderings_Oord__class_Oless(_527401, _527405, c_Groups_Ozero__class_Ozero(_527401)), -(c_Orderings_Oord__class_Oless(_527401, c_Groups_Ozero__class_Ozero(_527401), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527401), _527403), _527405)))], (9312 ^ _206868) ^ [_527849, _527851, _527853] : [class_Rings_Olinordered__semiring__strict(_527849), c_Orderings_Oord__class_Oless(_527849, _527851, c_Groups_Ozero__class_Ozero(_527849)), c_Orderings_Oord__class_Oless(_527849, c_Groups_Ozero__class_Ozero(_527849), _527853), -(c_Orderings_Oord__class_Oless(_527849, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527849), _527851), _527853), c_Groups_Ozero__class_Ozero(_527849)))], (9326 ^ _206868) ^ [_528311, _528313, _528315, _528317] : [class_Rings_Olinordered__ring__strict(_528311), c_Orderings_Oord__class_Oless(_528311, _528313, c_Groups_Ozero__class_Ozero(_528311)), 9333 ^ _206868 : [(9334 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_528311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528311), _528313), _528315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528311), _528313), _528317)), -(c_Orderings_Oord__class_Oless(_528311, _528317, _528315))], (9340 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_528311, _528317, _528315), -(c_Orderings_Oord__class_Oless(_528311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528311), _528313), _528315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528311), _528313), _528317)))]]], (9346 ^ _206868) ^ [_528972, _528974, _528976] : [class_Rings_Olinordered__semiring__strict(_528972), c_Orderings_Oord__class_Oless(_528972, c_Groups_Ozero__class_Ozero(_528972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528972), _528974), _528976)), c_Orderings_Oord__class_Oless(_528972, c_Groups_Ozero__class_Ozero(_528972), _528976), -(c_Orderings_Oord__class_Oless(_528972, c_Groups_Ozero__class_Ozero(_528972), _528974))], (9360 ^ _206868) ^ [_529420, _529422, _529424] : [class_Rings_Olinordered__semiring__strict(_529420), c_Orderings_Oord__class_Oless(_529420, c_Groups_Ozero__class_Ozero(_529420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529420), _529422), _529424)), c_Orderings_Oord__class_Oless(_529420, c_Groups_Ozero__class_Ozero(_529420), _529422), -(c_Orderings_Oord__class_Oless(_529420, c_Groups_Ozero__class_Ozero(_529420), _529424))], (9374 ^ _206868) ^ [_529868, _529870, _529872] : [class_Rings_Olinordered__semiring__strict(_529868), c_Orderings_Oord__class_Oless(_529868, c_Groups_Ozero__class_Ozero(_529868), _529870), c_Orderings_Oord__class_Oless(_529868, _529872, c_Groups_Ozero__class_Ozero(_529868)), -(c_Orderings_Oord__class_Oless(_529868, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529868), _529872), _529870), c_Groups_Ozero__class_Ozero(_529868)))], (9388 ^ _206868) ^ [_530316, _530318, _530320] : [class_Rings_Olinordered__semiring__strict(_530316), c_Orderings_Oord__class_Oless(_530316, c_Groups_Ozero__class_Ozero(_530316), _530318), c_Orderings_Oord__class_Oless(_530316, _530320, c_Groups_Ozero__class_Ozero(_530316)), -(c_Orderings_Oord__class_Oless(_530316, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530316), _530318), _530320), c_Groups_Ozero__class_Ozero(_530316)))], (9402 ^ _206868) ^ [_530764, _530766, _530768] : [class_Rings_Olinordered__semiring__strict(_530764), c_Orderings_Oord__class_Oless(_530764, c_Groups_Ozero__class_Ozero(_530764), _530766), c_Orderings_Oord__class_Oless(_530764, c_Groups_Ozero__class_Ozero(_530764), _530768), -(c_Orderings_Oord__class_Oless(_530764, c_Groups_Ozero__class_Ozero(_530764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530764), _530766), _530768)))], (9416 ^ _206868) ^ [_531226, _531228, _531230, _531232] : [class_Rings_Olinordered__ring__strict(_531226), c_Orderings_Oord__class_Oless(_531226, c_Groups_Ozero__class_Ozero(_531226), _531228), 9423 ^ _206868 : [(9424 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_531226, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531226), _531228), _531230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531226), _531228), _531232)), -(c_Orderings_Oord__class_Oless(_531226, _531230, _531232))], (9430 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_531226, _531230, _531232), -(c_Orderings_Oord__class_Oless(_531226, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531226), _531228), _531230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531226), _531228), _531232)))]]], (9436 ^ _206868) ^ [_531901, _531903, _531905, _531907] : [class_Rings_Olinordered__ring__strict(_531901), 9439 ^ _206868 : [(9440 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_531901, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531901), _531903), _531905), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531901), _531903), _531907)), 9445 ^ _206868 : [(9446 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_531901, c_Groups_Ozero__class_Ozero(_531901), _531903))], (9448 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_531901, _531905, _531907))]], 9449 ^ _206868 : [(9450 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_531901, _531903, c_Groups_Ozero__class_Ozero(_531901)))], (9452 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_531901, _531907, _531905))]]], (9454 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_531901, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531901), _531903), _531905), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531901), _531903), _531907))), 9455 ^ _206868 : [(9456 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_531901, c_Groups_Ozero__class_Ozero(_531901), _531903), c_Orderings_Oord__class_Oless(_531901, _531905, _531907)], (9462 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_531901, _531903, c_Groups_Ozero__class_Ozero(_531901)), c_Orderings_Oord__class_Oless(_531901, _531907, _531905)]]]]], (9470 ^ _206868) ^ [_533004, _533006, _533008, _533010] : [class_Rings_Olinordered__ring__strict(_533004), 9473 ^ _206868 : [(9474 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_533004, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533004), _533006), _533008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533004), _533010), _533008)), 9479 ^ _206868 : [(9480 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_533004, c_Groups_Ozero__class_Ozero(_533004), _533008))], (9482 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_533004, _533006, _533010))]], 9483 ^ _206868 : [(9484 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_533004, _533008, c_Groups_Ozero__class_Ozero(_533004)))], (9486 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_533004, _533010, _533006))]]], (9488 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(_533004, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533004), _533006), _533008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533004), _533010), _533008))), 9489 ^ _206868 : [(9490 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_533004, c_Groups_Ozero__class_Ozero(_533004), _533008), c_Orderings_Oord__class_Oless(_533004, _533006, _533010)], (9496 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_533004, _533008, c_Groups_Ozero__class_Ozero(_533004)), c_Orderings_Oord__class_Oless(_533004, _533010, _533006)]]]]], (9504 ^ _206868) ^ [_534079, _534081] : [class_Rings_Olinordered__ring(_534079), c_Orderings_Oord__class_Oless(_534079, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534079), _534081), _534081), c_Groups_Ozero__class_Ozero(_534079))], (9510 ^ _206868) ^ [_534366, _534368, _534370, _534372, _534374, _534376] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_534366), -(_534368 = c_Groups_Ozero__class_Ozero(_534366)), c_Groups_Oplus__class_Oplus(_534366, _534370, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534366), _534368), _534374)) = c_Groups_Oplus__class_Oplus(_534366, _534372, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534366), _534368), _534376)), _534370 = _534372, -(_534374 = _534376)], (9528 ^ _206868) ^ [_534986, _534988, _534990] : [class_Rings_Olinordered__ring__strict(_534986), 9531 ^ _206868 : [(9532 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_534986, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534986), _534988), _534988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534986), _534990), _534990)) = c_Groups_Ozero__class_Ozero(_534986), 9535 ^ _206868 : [(9536 ^ _206868) ^ [] : [-(_534988 = c_Groups_Ozero__class_Ozero(_534986))], (9538 ^ _206868) ^ [] : [-(_534990 = c_Groups_Ozero__class_Ozero(_534986))]]], (9540 ^ _206868) ^ [] : [-(c_Groups_Oplus__class_Oplus(_534986, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534986), _534988), _534988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534986), _534990), _534990)) = c_Groups_Ozero__class_Ozero(_534986)), _534988 = c_Groups_Ozero__class_Ozero(_534986), _534990 = c_Groups_Ozero__class_Ozero(_534986)]]], (9550 ^ _206868) ^ [_535716, _535718, _535720] : [class_Rings_Olinordered__semidom(_535716), c_Orderings_Oord__class_Oless(_535716, c_Groups_Oone__class_Oone(_535716), _535718), c_Orderings_Oord__class_Oless(_535716, c_Groups_Oone__class_Oone(_535716), _535720), -(c_Orderings_Oord__class_Oless(_535716, c_Groups_Oone__class_Oone(_535716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535716), _535718), _535720)))], (9564 ^ _206868) ^ [_536178, _536180, _536182, _536184] : [class_Rings_Oidom(_536178), 9567 ^ _206868 : [(9578 ^ _206868) ^ [] : [9579 ^ _206868 : [(9580 ^ _206868) ^ [] : [_536182 = c_Groups_Ozero__class_Ozero(_536178)], (9582 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_536178), _536180), _536184))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_536178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536178), _536180), _536182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536178), _536184), _536182))))], (9568 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_536178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536178), _536180), _536182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536178), _536184), _536182))), -(_536182 = c_Groups_Ozero__class_Ozero(_536178)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_536178), _536180), _536184)))]]], (9586 ^ _206868) ^ [_536962, _536964, _536966, _536968] : [class_Rings_Oidom(_536962), 9589 ^ _206868 : [(9600 ^ _206868) ^ [] : [9601 ^ _206868 : [(9602 ^ _206868) ^ [] : [_536964 = c_Groups_Ozero__class_Ozero(_536962)], (9604 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_536962), _536966), _536968))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_536962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536962), _536964), _536966)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536962), _536964), _536968))))], (9590 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_536962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536962), _536964), _536966)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536962), _536964), _536968))), -(_536964 = c_Groups_Ozero__class_Ozero(_536962)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_536962), _536966), _536968)))]]], (9608 ^ _206868) ^ [_537718, _537720] : [class_Rings_Ocomm__semiring__1(_537718), -(c_Groups_Oplus__class_Oplus(_537718, _537720, _537720) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537718), c_Groups_Oplus__class_Oplus(_537718, c_Groups_Oone__class_Oone(_537718), c_Groups_Oone__class_Oone(_537718))), _537720))], (9614 ^ _206868) ^ [_537980, _537982, _537984] : [class_Rings_Ocomm__semiring__1(_537980), -(c_Groups_Oplus__class_Oplus(_537980, _537982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537980), _537984), _537982)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537980), c_Groups_Oplus__class_Oplus(_537980, _537984, c_Groups_Oone__class_Oone(_537980))), _537982))], (9620 ^ _206868) ^ [_538260, _538262, _538264] : [class_Rings_Ocomm__semiring__1(_538260), -(c_Groups_Oplus__class_Oplus(_538260, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538260), _538262), _538264), _538264) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538260), c_Groups_Oplus__class_Oplus(_538260, _538262, c_Groups_Oone__class_Oone(_538260))), _538264))], (9626 ^ _206868) ^ [_538526, _538528] : [class_Rings_Oring__1__no__zero__divisors(_538526), 9629 ^ _206868 : [(9640 ^ _206868) ^ [] : [9641 ^ _206868 : [(9642 ^ _206868) ^ [] : [_538528 = c_Groups_Oone__class_Oone(_538526)], (9644 ^ _206868) ^ [] : [_538528 = c_Groups_Ouminus__class_Ouminus(_538526, c_Groups_Oone__class_Oone(_538526))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538526), _538528), _538528) = c_Groups_Oone__class_Oone(_538526))], (9630 ^ _206868) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538526), _538528), _538528) = c_Groups_Oone__class_Oone(_538526), -(_538528 = c_Groups_Oone__class_Oone(_538526)), -(_538528 = c_Groups_Ouminus__class_Ouminus(_538526, c_Groups_Oone__class_Oone(_538526)))]]], (9648 ^ _206868) ^ [_539193, _539195] : [class_Rings_Ocomm__ring__1(_539193), -(c_Groups_Ouminus__class_Ouminus(_539193, _539195) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539193), c_Groups_Ouminus__class_Ouminus(_539193, c_Groups_Oone__class_Oone(_539193))), _539195))], (9654 ^ _206868) ^ [_539447, _539449, _539451] : [class_Rings_Ocomm__semiring__1(_539447), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539447), hAPP(hAPP(c_Power_Opower__class_Opower(_539447), _539449), _539451)), _539449) = hAPP(hAPP(c_Power_Opower__class_Opower(_539447), _539449), c_Nat_OSuc(_539451)))], (9660 ^ _206868) ^ [_539727, _539729, _539731] : [class_Rings_Ocomm__semiring__1(_539727), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539727), _539729), hAPP(hAPP(c_Power_Opower__class_Opower(_539727), _539729), _539731)) = hAPP(hAPP(c_Power_Opower__class_Opower(_539727), _539729), c_Nat_OSuc(_539731)))], (9666 ^ _206868) ^ [_540007, _540009, _540011] : [class_Groups_Omonoid__mult(_540007), -(hAPP(hAPP(c_Power_Opower__class_Opower(_540007), _540009), c_Nat_OSuc(_540011)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540007), hAPP(hAPP(c_Power_Opower__class_Opower(_540007), _540009), _540011)), _540009))], (9672 ^ _206868) ^ [_540287, _540289, _540291] : [class_Rings_Ocomm__semiring__1(_540287), -(hAPP(hAPP(c_Power_Opower__class_Opower(_540287), _540289), c_Nat_OSuc(_540291)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540287), _540289), hAPP(hAPP(c_Power_Opower__class_Opower(_540287), _540289), _540291)))], (9678 ^ _206868) ^ [_540567, _540569, _540571] : [class_Power_Opower(_540567), -(hAPP(hAPP(c_Power_Opower__class_Opower(_540567), _540569), c_Nat_OSuc(_540571)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540567), _540569), hAPP(hAPP(c_Power_Opower__class_Opower(_540567), _540569), _540571)))], (9684 ^ _206868) ^ [_540861, _540863, _540865, _540867] : [class_Rings_Ocomm__semiring__1(_540861), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540861), hAPP(hAPP(c_Power_Opower__class_Opower(_540861), _540863), _540865)), hAPP(hAPP(c_Power_Opower__class_Opower(_540861), _540863), _540867)) = hAPP(hAPP(c_Power_Opower__class_Opower(_540861), _540863), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _540865, _540867)))], (9690 ^ _206868) ^ [_541181, _541183, _541185, _541187] : [class_Groups_Omonoid__mult(_541181), -(hAPP(hAPP(c_Power_Opower__class_Opower(_541181), _541183), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _541185, _541187)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541181), hAPP(hAPP(c_Power_Opower__class_Opower(_541181), _541183), _541185)), hAPP(hAPP(c_Power_Opower__class_Opower(_541181), _541183), _541187)))], (9696 ^ _206868) ^ [_541488] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _541488), _541488))), -(_541488 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (9702 ^ _206868) ^ [_541661] : [_541661 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _541661), _541661))], (9708 ^ _206868) ^ [_541896, _541898, _541900] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _541896), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _541898, _541900), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _541896), _541898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _541896), _541900)))], (9718 ^ _206868) ^ [_542235, _542237] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _542235), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _542237), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _542235), _542237)))], (9728 ^ _206868) ^ [_542566, _542568, _542570] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _542566), 9731 ^ _206868 : [(9732 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _542568), _542566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _542570), _542566)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _542568, _542570))], (9738 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _542568, _542570), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _542568), _542566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _542570), _542566)))]]], (9744 ^ _206868) ^ [_543115, _543117] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _543115), _543115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _543117), _543117)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9747 ^ _206868 : [(9748 ^ _206868) ^ [] : [-(_543115 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (9750 ^ _206868) ^ [] : [-(_543117 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (9752 ^ _206868) ^ [_543384, _543386] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _543384), _543384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _543386), _543386)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _543384 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _543386 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (9762 ^ _206868) ^ [_543702, _543704] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _543702), _543702)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _543704), _543704)))], (9764 ^ _206868) ^ [_543855, _543857, _543859, _543861] : [class_Rings_Olinordered__ring__strict(_543855), c_Orderings_Oord__class_Oless(_543855, c_Groups_Ozero__class_Ozero(_543855), _543857), 9771 ^ _206868 : [(9772 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_543855, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_543855), _543857), _543859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_543855), _543857), _543861)), -(c_Orderings_Oord__class_Oless__eq(_543855, _543859, _543861))], (9778 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_543855, _543859, _543861), -(c_Orderings_Oord__class_Oless__eq(_543855, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_543855), _543857), _543859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_543855), _543857), _543861)))]]], (9784 ^ _206868) ^ [_544530, _544532, _544534, _544536] : [class_Rings_Olinordered__ring__strict(_544530), c_Orderings_Oord__class_Oless(_544530, _544532, c_Groups_Ozero__class_Ozero(_544530)), 9791 ^ _206868 : [(9792 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_544530, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544530), _544532), _544534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544530), _544532), _544536)), -(c_Orderings_Oord__class_Oless__eq(_544530, _544536, _544534))], (9798 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_544530, _544536, _544534), -(c_Orderings_Oord__class_Oless__eq(_544530, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544530), _544532), _544534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544530), _544532), _544536)))]]], (9804 ^ _206868) ^ [_545219, _545221, _545223, _545225, _545227] : [class_Rings_Olinordered__semiring__strict(_545219), c_Orderings_Oord__class_Oless(_545219, _545221, _545223), c_Orderings_Oord__class_Oless(_545219, _545225, _545227), c_Orderings_Oord__class_Oless(_545219, c_Groups_Ozero__class_Ozero(_545219), _545223), c_Orderings_Oord__class_Oless__eq(_545219, c_Groups_Ozero__class_Ozero(_545219), _545225), -(c_Orderings_Oord__class_Oless(_545219, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545219), _545221), _545225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545219), _545223), _545227)))], (9826 ^ _206868) ^ [_545941, _545943, _545945, _545947, _545949] : [class_Rings_Olinordered__semiring__strict(_545941), c_Orderings_Oord__class_Oless(_545941, _545943, _545945), c_Orderings_Oord__class_Oless(_545941, _545947, _545949), c_Orderings_Oord__class_Oless__eq(_545941, c_Groups_Ozero__class_Ozero(_545941), _545943), c_Orderings_Oord__class_Oless__eq(_545941, c_Groups_Ozero__class_Ozero(_545941), _545947), -(c_Orderings_Oord__class_Oless(_545941, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545941), _545943), _545947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545941), _545945), _545949)))], (9848 ^ _206868) ^ [_546663, _546665, _546667, _546669, _546671] : [class_Rings_Olinordered__semiring__strict(_546663), c_Orderings_Oord__class_Oless(_546663, _546665, _546667), c_Orderings_Oord__class_Oless__eq(_546663, _546669, _546671), c_Orderings_Oord__class_Oless__eq(_546663, c_Groups_Ozero__class_Ozero(_546663), _546665), c_Orderings_Oord__class_Oless(_546663, c_Groups_Ozero__class_Ozero(_546663), _546669), -(c_Orderings_Oord__class_Oless(_546663, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546663), _546665), _546669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546663), _546667), _546671)))], (9870 ^ _206868) ^ [_547385, _547387, _547389, _547391, _547393] : [class_Rings_Olinordered__semiring__strict(_547385), c_Orderings_Oord__class_Oless__eq(_547385, _547387, _547389), c_Orderings_Oord__class_Oless(_547385, _547391, _547393), c_Orderings_Oord__class_Oless(_547385, c_Groups_Ozero__class_Ozero(_547385), _547387), c_Orderings_Oord__class_Oless__eq(_547385, c_Groups_Ozero__class_Ozero(_547385), _547391), -(c_Orderings_Oord__class_Oless(_547385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547385), _547387), _547391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547385), _547389), _547393)))], (9892 ^ _206868) ^ [_548093, _548095, _548097, _548099] : [class_Rings_Olinordered__semiring(_548093), c_Orderings_Oord__class_Oless(_548093, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548093), _548095), _548097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548093), _548099), _548097)), c_Orderings_Oord__class_Oless__eq(_548093, c_Groups_Ozero__class_Ozero(_548093), _548097), -(c_Orderings_Oord__class_Oless(_548093, _548095, _548099))], (9906 ^ _206868) ^ [_548577, _548579, _548581, _548583] : [class_Rings_Olinordered__semiring__strict(_548577), c_Orderings_Oord__class_Oless(_548577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548577), _548579), _548581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548577), _548583), _548581)), c_Orderings_Oord__class_Oless__eq(_548577, c_Groups_Ozero__class_Ozero(_548577), _548581), -(c_Orderings_Oord__class_Oless(_548577, _548579, _548583))], (9920 ^ _206868) ^ [_549061, _549063, _549065, _549067] : [class_Rings_Olinordered__semiring(_549061), c_Orderings_Oord__class_Oless(_549061, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549061), _549063), _549065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549061), _549063), _549067)), c_Orderings_Oord__class_Oless__eq(_549061, c_Groups_Ozero__class_Ozero(_549061), _549063), -(c_Orderings_Oord__class_Oless(_549061, _549065, _549067))], (9934 ^ _206868) ^ [_549545, _549547, _549549, _549551] : [class_Rings_Olinordered__semiring__strict(_549545), c_Orderings_Oord__class_Oless(_549545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549545), _549547), _549549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549545), _549547), _549551)), c_Orderings_Oord__class_Oless__eq(_549545, c_Groups_Ozero__class_Ozero(_549545), _549547), -(c_Orderings_Oord__class_Oless(_549545, _549549, _549551))], (9948 ^ _206868) ^ [_550029, _550031, _550033, _550035] : [class_Rings_Olinordered__semiring__strict(_550029), c_Orderings_Oord__class_Oless__eq(_550029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550029), _550031), _550033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550029), _550035), _550033)), c_Orderings_Oord__class_Oless(_550029, c_Groups_Ozero__class_Ozero(_550029), _550033), -(c_Orderings_Oord__class_Oless__eq(_550029, _550031, _550035))], (9962 ^ _206868) ^ [_550513, _550515, _550517, _550519] : [class_Rings_Olinordered__semiring__strict(_550513), c_Orderings_Oord__class_Oless__eq(_550513, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550513), _550515), _550517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550513), _550515), _550519)), c_Orderings_Oord__class_Oless(_550513, c_Groups_Ozero__class_Ozero(_550513), _550515), -(c_Orderings_Oord__class_Oless__eq(_550513, _550517, _550519))], (9976 ^ _206868) ^ [_550983, _550985, _550987] : [class_Rings_Olinordered__ring(_550983), -(c_Orderings_Oord__class_Oless__eq(_550983, c_Groups_Ozero__class_Ozero(_550983), c_Groups_Oplus__class_Oplus(_550983, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550983), _550985), _550985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550983), _550987), _550987))))], (9982 ^ _206868) ^ [_551257, _551259, _551261] : [class_Rings_Olinordered__ring__strict(_551257), 9985 ^ _206868 : [(9986 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_551257, c_Groups_Oplus__class_Oplus(_551257, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551257), _551259), _551259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551257), _551261), _551261)), c_Groups_Ozero__class_Ozero(_551257)), 9989 ^ _206868 : [(9990 ^ _206868) ^ [] : [-(_551259 = c_Groups_Ozero__class_Ozero(_551257))], (9992 ^ _206868) ^ [] : [-(_551261 = c_Groups_Ozero__class_Ozero(_551257))]]], (9994 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_551257, c_Groups_Oplus__class_Oplus(_551257, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551257), _551259), _551259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551257), _551261), _551261)), c_Groups_Ozero__class_Ozero(_551257))), _551259 = c_Groups_Ozero__class_Ozero(_551257), _551261 = c_Groups_Ozero__class_Ozero(_551257)]]], (10004 ^ _206868) ^ [_551990, _551992, _551994] : [class_Rings_Olinordered__ring(_551990), c_Orderings_Oord__class_Oless(_551990, c_Groups_Oplus__class_Oplus(_551990, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551990), _551992), _551992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551990), _551994), _551994)), c_Groups_Ozero__class_Ozero(_551990))], (10010 ^ _206868) ^ [_552265, _552267, _552269] : [class_Rings_Olinordered__ring__strict(_552265), 10013 ^ _206868 : [(10024 ^ _206868) ^ [] : [10025 ^ _206868 : [(10026 ^ _206868) ^ [] : [-(_552267 = c_Groups_Ozero__class_Ozero(_552265))], (10028 ^ _206868) ^ [] : [-(_552269 = c_Groups_Ozero__class_Ozero(_552265))]], -(c_Orderings_Oord__class_Oless(_552265, c_Groups_Ozero__class_Ozero(_552265), c_Groups_Oplus__class_Oplus(_552265, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552265), _552267), _552267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552265), _552269), _552269))))], (10014 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_552265, c_Groups_Ozero__class_Ozero(_552265), c_Groups_Oplus__class_Oplus(_552265, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552265), _552267), _552267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552265), _552269), _552269))), _552267 = c_Groups_Ozero__class_Ozero(_552265), _552269 = c_Groups_Ozero__class_Ozero(_552265)]]], (10032 ^ _206868) ^ [_553002, _553004, _553006] : [class_Rings_Olinordered__idom(_553002), c_Orderings_Oord__class_Oless__eq(_553002, c_Groups_Ozero__class_Ozero(_553002), _553004), c_Orderings_Oord__class_Oless__eq(_553002, c_Groups_Ozero__class_Ozero(_553002), _553006), c_Orderings_Oord__class_Oless__eq(_553002, _553006, c_Groups_Oone__class_Oone(_553002)), -(c_Orderings_Oord__class_Oless__eq(_553002, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553002), _553006), _553004), _553004))], (10050 ^ _206868) ^ [_553545, _553547, _553549] : [class_Rings_Olinordered__idom(_553545), c_Orderings_Oord__class_Oless__eq(_553545, c_Groups_Ozero__class_Ozero(_553545), _553547), c_Orderings_Oord__class_Oless__eq(_553545, c_Groups_Ozero__class_Ozero(_553545), _553549), c_Orderings_Oord__class_Oless__eq(_553545, _553549, c_Groups_Oone__class_Oone(_553545)), -(c_Orderings_Oord__class_Oless__eq(_553545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553545), _553547), _553549), _553547))], (10068 ^ _206868) ^ [_554088, _554090, _554092] : [class_Rings_Olinordered__semidom(_554088), c_Orderings_Oord__class_Oless(_554088, c_Groups_Oone__class_Oone(_554088), _554090), -(c_Orderings_Oord__class_Oless(_554088, hAPP(hAPP(c_Power_Opower__class_Opower(_554088), _554090), _554092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554088), _554090), hAPP(hAPP(c_Power_Opower__class_Opower(_554088), _554090), _554092))))], (10078 ^ _206868) ^ [_554465, _554467, _554469] : [class_Rings_Olinordered__semidom(_554465), c_Orderings_Oord__class_Oless(_554465, c_Groups_Oone__class_Oone(_554465), _554467), -(c_Orderings_Oord__class_Oless(_554465, c_Groups_Oone__class_Oone(_554465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554465), _554467), hAPP(hAPP(c_Power_Opower__class_Opower(_554465), _554467), _554469))))], (10088 ^ _206868) ^ [_554830, _554832, _554834] : [class_Rings_Oring__1(_554830), -(hAPP(hAPP(c_Power_Opower__class_Opower(_554830), c_Groups_Ouminus__class_Ouminus(_554830, _554832)), _554834) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554830), hAPP(hAPP(c_Power_Opower__class_Opower(_554830), c_Groups_Ouminus__class_Ouminus(_554830, c_Groups_Oone__class_Oone(_554830))), _554834)), hAPP(hAPP(c_Power_Opower__class_Opower(_554830), _554832), _554834)))], (10094 ^ _206868) ^ [_555138, _555140, _555142] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _555138), 10097 ^ _206868 : [(10098 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555140), _555138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555142), _555138)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _555140, _555142))], (10104 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _555140, _555142), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555140), _555138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555142), _555138)))]]], (10110 ^ _206868) ^ [_555672, _555674, _555676] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _555672), 10113 ^ _206868 : [(10114 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555672), _555674), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555672), _555676)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _555674, _555676))], (10120 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _555674, _555676), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555672), _555674), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555672), _555676)))]]], (10126 ^ _206868) ^ [_556206, _556208, _556210] : [class_Rings_Ocomm__semiring__0(_556206), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_556206, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_556206)), _556208), _556210)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_556206, _556208), c_Polynomial_Odegree(_556206, _556210))))], (10132 ^ _206868) ^ [_556482, _556484, _556486] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _556482), -(c_NthRoot_Oroot(_556482, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556484), _556486)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_NthRoot_Oroot(_556482, _556484)), c_NthRoot_Oroot(_556482, _556486)))], (10138 ^ _206868) ^ [_556756, _556758, _556760] : [class_Rings_Oidom(_556756), -(_556758 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_556756))), -(_556760 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_556756))), -(c_Polynomial_Odegree(_556756, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_556756)), _556758), _556760)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_556756, _556758), c_Polynomial_Odegree(_556756, _556760)))], (10152 ^ _206868) ^ [_557252, _557254, _557256, _557258] : [class_Rings_Ocomm__semiring__0(_557252), -(hAPP(c_Polynomial_Opoly(_557252, c_Polynomial_OpCons(_557252, _557254, _557256)), _557258) = c_Groups_Oplus__class_Oplus(_557252, _557254, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557252), _557258), hAPP(c_Polynomial_Opoly(_557252, _557256), _557258))))], (10158 ^ _206868) ^ [_557527, _557529, _557531] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Orcis(_557527, _557529)), _557531) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _557527), _557531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _557531)), _557529)))], (10160 ^ _206868) ^ [_557721, _557723, _557725, _557727, _557729, _557731] : [class_Rings_Olinordered__semiring__1(_557721), c_Orderings_Oord__class_Oless__eq(_557721, _557723, _557725), c_Orderings_Oord__class_Oless__eq(_557721, _557727, _557725), c_Orderings_Oord__class_Oless__eq(_557721, c_Groups_Ozero__class_Ozero(_557721), _557729), c_Orderings_Oord__class_Oless__eq(_557721, c_Groups_Ozero__class_Ozero(_557721), _557731), c_Groups_Oplus__class_Oplus(_557721, _557729, _557731) = c_Groups_Oone__class_Oone(_557721), -(c_Orderings_Oord__class_Oless__eq(_557721, c_Groups_Oplus__class_Oplus(_557721, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557721), _557729), _557723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557721), _557731), _557727)), _557725))], (10186 ^ _206868) ^ [_558562, _558564, _558566] : [class_Rings_Olinordered__semidom(_558562), c_Orderings_Oord__class_Oless(_558562, c_Groups_Ozero__class_Ozero(_558562), _558564), c_Orderings_Oord__class_Oless(_558562, _558564, c_Groups_Oone__class_Oone(_558562)), -(c_Orderings_Oord__class_Oless(_558562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_558562), _558564), hAPP(hAPP(c_Power_Opower__class_Opower(_558562), _558564), _558566)), hAPP(hAPP(c_Power_Opower__class_Opower(_558562), _558564), _558566)))], (10200 ^ _206868) ^ [_559052, _559054, _559056, _559058] : [class_RealVector_Oreal__normed__vector(_559052), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _559054, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_559052, _559056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _559054), c_RealVector_Onorm__class_Onorm(_559052, _559058))), -(_559056 = c_Groups_Ozero__class_Ozero(_559052))], (10214 ^ _206868) ^ [_559554, _559556, _559558, _559560, _559562, _559564] : [class_Rings_Olinordered__semiring__1__strict(_559554), c_Orderings_Oord__class_Oless(_559554, _559556, _559558), c_Orderings_Oord__class_Oless(_559554, _559560, _559558), c_Orderings_Oord__class_Oless__eq(_559554, c_Groups_Ozero__class_Ozero(_559554), _559562), c_Orderings_Oord__class_Oless__eq(_559554, c_Groups_Ozero__class_Ozero(_559554), _559564), c_Groups_Oplus__class_Oplus(_559554, _559562, _559564) = c_Groups_Oone__class_Oone(_559554), -(c_Orderings_Oord__class_Oless(_559554, c_Groups_Oplus__class_Oplus(_559554, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_559554), _559562), _559556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_559554), _559564), _559560)), _559558))], (10240 ^ _206868) ^ [_560395, _560397, _560399] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _560395), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _560397), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _560399), -(c_NthRoot_Oroot(_560395, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _560397), _560399)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_NthRoot_Oroot(_560395, _560397)), c_NthRoot_Oroot(_560395, _560399)))], (10254 ^ _206868) ^ [_560859, _560861, _560863] : [class_Rings_Odvd(_560859), class_Rings_Osemiring__0(_560859), 10261 ^ _206868 : [(10262 ^ _206868) ^ [] : [10263 ^ _206868 : [(10264 ^ _206868) ^ [_561174] : [hBOOL(hAPP(_560861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_560859), _560863), _561174)))]], 10266 ^ _206868 : [(10267 ^ _206868) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_560859), _560863), c_Groups_Oplus__class_Oplus(_560859, 10265 ^ [_560859, _560861, _560863], c_Groups_Ozero__class_Ozero(_560859)))))], (10269 ^ _206868) ^ [] : [-(hBOOL(hAPP(_560861, 10265 ^ [_560859, _560861, _560863])))]]], (10271 ^ _206868) ^ [] : [-(hBOOL(hAPP(_560861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_560859), _560863), 10278 ^ [_560859, _560861, _560863])))), 10272 ^ _206868 : [(10273 ^ _206868) ^ [_561526] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_560859), _560863), c_Groups_Oplus__class_Oplus(_560859, _561526, c_Groups_Ozero__class_Ozero(_560859)))), hBOOL(hAPP(_560861, _561526))]]]]], (10282 ^ _206868) ^ [_561923, _561925] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _561923), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _561923), _561925)))], (10288 ^ _206868) ^ [_562177, _562179, _562181, _562183] : [class_Rings_Ocomm__semiring__0(_562177), -(c_Polynomial_Opcompose(_562177, c_Polynomial_OpCons(_562177, _562179, _562181), _562183) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_562177), c_Polynomial_OpCons(_562177, _562179, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_562177))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_562177)), _562183), c_Polynomial_Opcompose(_562177, _562181, _562183))))], (10294 ^ _206868) ^ [_562454, _562456] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562454, _562456)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _562454), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _562456)))], (10296 ^ _206868) ^ [_562579, _562581, _562583] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562579, _562581)), _562583) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562579), _562583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562581), _562583)))], (10298 ^ _206868) ^ [_562715, _562717, _562719] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562715, _562717), _562719) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562715, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562717, _562719)))], (10300 ^ _206868) ^ [_562841, _562843, _562845] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562841), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562843, _562845)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562841), _562843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562841), _562845)))], (10302 ^ _206868) ^ [_562977, _562979, _562981] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562977, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562979, _562981)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562979, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _562977, _562981)))], (10304 ^ _206868) ^ [_563089, _563091] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _563089, _563091) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _563091, _563089))], (10306 ^ _206868) ^ [_563205, _563207, _563209] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _563205), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _563207, _563209)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _563205), _563207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _563205), _563209)))], (10308 ^ _206868) ^ [_563341, _563343, _563345] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _563341, _563343)), _563345) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _563341), _563345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _563343), _563345)))], (10310 ^ _206868) ^ [_563520, _563522, _563524, _563526, _563528] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _563520), _563522)), 10313 ^ _206868 : [(10314 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _563520), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _563524, _563526))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _563520), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _563524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _563528), _563522)), _563526))))], (10320 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _563520), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _563524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _563528), _563522)), _563526))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _563520), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _563524, _563526))))]]], (10326 ^ _206868) ^ [_564165, _564167, _564169] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _564165), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _564167, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _564165), _564169)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _564165), _564167)))], (10332 ^ _206868) ^ [_564373, _564375, _564377] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _564373), _564375)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _564373), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _564375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _564373), _564377)))))], (10338 ^ _206868) ^ [_564630, _564632, _564634] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _564630), _564632)), _564634) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _564630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _564632), _564634)))], (10340 ^ _206868) ^ [_564750, _564752] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _564750)), _564752) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _564750), _564752)))], (10342 ^ _206868) ^ [_564848] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _564848), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _564848)], (10344 ^ _206868) ^ [_564932] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _564932) = _564932)], (10346 ^ _206868) ^ [_565056, _565058, _565060] : [class_Rings_Ocomm__semiring__0(_565056), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_565056, c_Polynomial_Opcompose(_565056, _565058, _565060)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_565056, _565058)), c_Polynomial_Odegree(_565056, _565060))))], (10362 ^ _206868) ^ [_565639, _565641, _565643] : [10363 ^ _206868 : [(10364 ^ _206868) ^ [] : [_565639 = _565643], (10366 ^ _206868) ^ [] : [_565641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565639), _565641) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565643), _565641))], (10352 ^ _206868) ^ [_565353, _565355, _565357] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565353), _565355) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565357), _565355), -(_565353 = _565357), -(_565355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10380 ^ _206868) ^ [_566286, _566288, _566290] : [10381 ^ _206868 : [(10382 ^ _206868) ^ [] : [_566288 = _566290], (10384 ^ _206868) ^ [] : [_566286 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566286), _566288) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566286), _566290))], (10370 ^ _206868) ^ [_566000, _566002, _566004] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566000), _566002) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566000), _566004), -(_566002 = _566004), -(_566000 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10398 ^ _206868) ^ [_566897, _566899] : [10399 ^ _206868 : [(10400 ^ _206868) ^ [] : [_566897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10402 ^ _206868) ^ [] : [_566899 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566897), _566899) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10388 ^ _206868) ^ [_566633, _566635] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566633), _566635) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_566633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_566635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10406 ^ _206868) ^ [_567166] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567166), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10408 ^ _206868) ^ [_567250] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _567250) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10410 ^ _206868) ^ [_567388, _567390, _567392, _567394] : [class_Rings_Ocomm__semiring__1(_567388), -(hAPP(hAPP(c_Power_Opower__class_Opower(_567388), hAPP(hAPP(c_Power_Opower__class_Opower(_567388), _567390), _567392)), _567394) = hAPP(hAPP(c_Power_Opower__class_Opower(_567388), _567390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567392), _567394)))], (10416 ^ _206868) ^ [_567696, _567698, _567700, _567702] : [class_Groups_Omonoid__mult(_567696), -(hAPP(hAPP(c_Power_Opower__class_Opower(_567696), _567698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567700), _567702)) = hAPP(hAPP(c_Power_Opower__class_Opower(_567696), hAPP(hAPP(c_Power_Opower__class_Opower(_567696), _567698), _567700)), _567702))], (10422 ^ _206868) ^ [_568019, _568021, _568023] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_568019)), _568021) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_568019)), _568023), -(_568021 = _568023)], (10428 ^ _206868) ^ [_568219, _568221, _568223] : [_568221 = _568223, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_568219)), _568221) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_568219)), _568223))], (10434 ^ _206868) ^ [_568440] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _568440, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568440), _568440)))], (10436 ^ _206868) ^ [_568525] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _568525, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568525), _568525))))], (10438 ^ _206868) ^ [_568659, _568661, _568663] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _568659, _568661), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568659), _568663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568661), _568663)))], (10444 ^ _206868) ^ [_568917, _568919, _568921] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _568917, _568919), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568921), _568917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568921), _568919)))], (10450 ^ _206868) ^ [_569189, _569191, _569193, _569195] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _569189, _569191), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _569193, _569195), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569189), _569193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569191), _569195)))], (10460 ^ _206868) ^ [_569538, _569540] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _569538), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _569540), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _569538), _569540)))], (10470 ^ _206868) ^ [_569869, _569871, _569873] : [-(_569869 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10473 ^ _206868 : [(10474 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _569871), _569873)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _569869), _569871)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _569869), _569873))))], (10480 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _569869), _569871)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _569869), _569873))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _569871), _569873)))]]], (10486 ^ _206868) ^ [_570443, _570445] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _570443), _570445) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 10489 ^ _206868 : [(10490 ^ _206868) ^ [] : [-(_570443 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10492 ^ _206868) ^ [] : [-(_570445 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (10494 ^ _206868) ^ [_570692, _570694] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _570692), _570694) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _570692 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _570694 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (10504 ^ _206868) ^ [_570976] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _570976), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _570976)], (10506 ^ _206868) ^ [_571118, _571120] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571118), _571120), 10509 ^ _206868 : [(10510 ^ _206868) ^ [] : [-(_571118 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10512 ^ _206868) ^ [] : [-(_571120 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (10514 ^ _206868) ^ [_571367, _571369] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571367), _571369)), _571367 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _571369 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (10524 ^ _206868) ^ [_571651] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _571651) = _571651)], (10526 ^ _206868) ^ [_571732] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _571732)) = _571732)], (10528 ^ _206868) ^ [_571874, _571876] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571874), _571876) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10531 ^ _206868 : [(10532 ^ _206868) ^ [] : [-(_571874 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10534 ^ _206868) ^ [] : [-(_571876 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10536 ^ _206868) ^ [_572123, _572125] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572123), _572125) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _572123 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _572125 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10546 ^ _206868) ^ [_572450, _572452, _572454] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572450, _572452), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _572454), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572454), _572450), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572454), _572452)))], (10556 ^ _206868) ^ [_572803, _572805, _572807] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572803, _572805), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _572807), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572803), _572807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572805), _572807)))], (10566 ^ _206868) ^ [_573185, _573187, _573189] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _573185), _573187), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _573189), _573187)), 10569 ^ _206868 : [(10570 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _573187))], (10572 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573185, _573189))]]], (10574 ^ _206868) ^ [_573460, _573462, _573464] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _573460), _573462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _573464), _573462))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _573462), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573460, _573464)], (10584 ^ _206868) ^ [_573844, _573846, _573848] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _573844), _573846), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _573844), _573848)), 10587 ^ _206868 : [(10588 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _573844))], (10590 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573846, _573848))]]], (10592 ^ _206868) ^ [_574119, _574121, _574123] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574119), _574121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574119), _574123))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _574119), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _574121, _574123)], (10602 ^ _206868) ^ [_574489, _574491] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574489), _574491)), 10605 ^ _206868 : [(10606 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _574489))], (10608 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _574491))]]], (10610 ^ _206868) ^ [_574744, _574746] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574744), _574746))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _574744), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _574746)], (10620 ^ _206868) ^ [_575106, _575108, _575110] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_575106)), _575108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_575106)), _575110)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575108, _575110))], (10626 ^ _206868) ^ [_575310, _575312, _575314] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575312, _575314), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_575310)), _575312), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_575310)), _575314)))], (10632 ^ _206868) ^ [_575549, _575551] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _575549), c_Nat_OSuc(_575551)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575549, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _575549), _575551)))], (10634 ^ _206868) ^ [_575661, _575663] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_575661)), _575663) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575663, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _575661), _575663)))], (10636 ^ _206868) ^ [_575788, _575790] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _575788), 10639 ^ _206868 : [(10640 ^ _206868) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _575788), _575790) = c_Groups_Oone__class_Oone(tc_Int_Oint), 10643 ^ _206868 : [(10644 ^ _206868) ^ [] : [-(_575788 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (10646 ^ _206868) ^ [] : [-(_575790 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (10648 ^ _206868) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _575788), _575790) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _575788 = c_Groups_Oone__class_Oone(tc_Int_Oint), _575790 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (10658 ^ _206868) ^ [_576440, _576442, _576444] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _576440, _576442), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _576444), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _576444), _576440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _576444), _576442)))], (10668 ^ _206868) ^ [_576822, _576824, _576826] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_576822)), _576824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_576822)), _576826)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _576824, _576826))], (10674 ^ _206868) ^ [_577026, _577028, _577030] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _577028, _577030), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_577026)), _577028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_577026)), _577030)))], (10680 ^ _206868) ^ [_577280, _577282] : [_577280 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _577280), _577282), -(_577282 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_577280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10690 ^ _206868) ^ [_577606, _577608, _577610] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _577606), _577608)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _577606), _577610))), -(_577606 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _577608), _577610)))], (10700 ^ _206868) ^ [_577947, _577949] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _577947), _577949)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _577947)), c_RealDef_Oreal(tc_Nat_Onat, _577949)))], (10702 ^ _206868) ^ [_578076, _578078, _578080] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _578076), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _578078, _578080)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _578076), _578078)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _578076), _578080)))], (10704 ^ _206868) ^ [_578215, _578217] : [class_Rings_Ocomm__semiring__0(_578215), -(c_Polynomial_Opcompose(_578215, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_578215)), _578217) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_578215)))], (10710 ^ _206868) ^ [_578475, _578477, _578479, _578481] : [class_Rings_Ocomm__semiring__0(_578475), -(hAPP(c_Polynomial_Opoly(_578475, c_Polynomial_Opcompose(_578475, _578477, _578479)), _578481) = hAPP(c_Polynomial_Opoly(_578475, _578477), hAPP(c_Polynomial_Opoly(_578475, _578479), _578481)))], (10716 ^ _206868) ^ [_578739, _578741] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _578739), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _578741), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _578741), _578739)))], (10726 ^ _206868) ^ [_579056, _579058] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579056), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579058), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _579056, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _579056), _579058)))], (10736 ^ _206868) ^ [_579373, _579375] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579373), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579375), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _579373, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _579375), _579373)))], (10746 ^ _206868) ^ [_579719, _579721] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _579719), _579721)), 10749 ^ _206868 : [(10750 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579719))], (10752 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579721))]]], (10754 ^ _206868) ^ [_579974, _579976] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _579974), _579976))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579974), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579976)], (10764 ^ _206868) ^ [_580307, _580309, _580311] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580307), _580309)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580307), _580311))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _580307), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _580309), _580311)))], (10784 ^ _206868) ^ [_580996, _580998, _581000] : [10785 ^ _206868 : [(10786 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _580998))], (10788 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580996, _581000)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580996), _580998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581000), _580998)))], (10774 ^ _206868) ^ [_580705, _580707, _580709] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580705), _580707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580709), _580707)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _580707), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580705, _580709))], (10802 ^ _206868) ^ [_581655, _581657, _581659] : [10803 ^ _206868 : [(10804 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _581655))], (10806 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581657, _581659)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581655), _581657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581655), _581659)))], (10792 ^ _206868) ^ [_581364, _581366, _581368] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581364), _581366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581364), _581368)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _581364), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581366, _581368))], (10810 ^ _206868) ^ [_581994, _581996, _581998] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _581994), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _581996), -(c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581994), _581996), _581998) = c_NthRoot_Oroot(_581994, c_NthRoot_Oroot(_581996, _581998)))], (10820 ^ _206868) ^ [_582350, _582352, _582354, _582356] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Orcis(_582350, _582352)), c_Complex_Orcis(_582354, _582356)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _582350), _582354), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _582352, _582356)))], (10822 ^ _206868) ^ [_582517, _582519] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _582517), _582519)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _582517)), _582519)))], (10828 ^ _206868) ^ [_582705, _582707] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _582705)), _582707)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _582705), _582707)))], (10834 ^ _206868) ^ [_582972, _582974] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _582972), _582974)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _582972), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _582974))))], (10840 ^ _206868) ^ [_583160, _583162] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _583160), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _583162))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _583160), _583162)))], (10846 ^ _206868) ^ [_583412, _583414, _583416] : [class_Rings_Ocomm__semiring__1(_583412), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_583412, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_583412)), _583414), _583416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_583412, _583414)), _583416)))], (10852 ^ _206868) ^ [_583672, _583674] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _583672), 10855 ^ _206868 : [(10856 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _583674), _583672)), _583672)), -(_583674 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10862 ^ _206868) ^ [] : [_583674 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _583674), _583672)), _583672)))]]], (10868 ^ _206868) ^ [_584167, _584169] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _584167), 10871 ^ _206868 : [(10872 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _584167), _584169)), _584167)), -(_584169 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10878 ^ _206868) ^ [] : [_584169 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _584167), _584169)), _584167)))]]], (10884 ^ _206868) ^ [_584676, _584678, _584680] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _584676), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _584678), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _584680), -(c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _584676), _584678), _584680) = c_NthRoot_Oroot(_584676, c_NthRoot_Oroot(_584678, _584680)))], (10898 ^ _206868) ^ [_585114, _585116] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585114), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585116), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_585114)), c_RComplete_Onatfloor(_585116)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _585114), _585116))))], (10908 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10910 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10912 ^ _206868) ^ [_585561, _585563] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _585561), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _585563), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _585561, _585563)))], (10922 ^ _206868) ^ [_585888, _585890, _585892] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _585888), _585888 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _585890, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _585888), _585892)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _585890, _585888), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _585892))], (10936 ^ _206868) ^ [_586330, _586332, _586334] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _586330), _586330 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _586332, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586330), _586334)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _586332), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _586334, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10950 ^ _206868) ^ [_586743, _586745] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586743), _586745) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586745), _586743))], (10952 ^ _206868) ^ [_586863, _586865, _586867] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586863), _586865)), _586867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586865), _586867)))], (10954 ^ _206868) ^ [_586983, _586985] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586983), _586985) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586985), _586983))], (10956 ^ _206868) ^ [_587103, _587105, _587107] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587103), _587105)), _587107) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587105), _587107)))], (10958 ^ _206868) ^ [_587294, _587296, _587298, _587300, _587302, _587304] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _587294), _587296), _587298) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _587300), _587302), _587304), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _587300), _587302), _587304), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _587298, _587294), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _587304), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _587300), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _587300, _587294), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _587302, _587296))], (10984 ^ _206868) ^ [_588167, _588169, _588171, _588173, _588175] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _588167), _588169), _588171), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _588167), _588173), _588175)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _588175, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _588167, _588175), c_Orderings_Oord__class_Oless(tc_Int_Oint, _588167, _588171), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _588173, _588169))], (11002 ^ _206868) ^ [_588804, _588806, _588808, _588810, _588812, _588814] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _588804), _588806), _588808) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _588810), _588812), _588814), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _588810), _588812), _588814)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _588814, _588810), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _588808), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _588810), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _588810, _588804), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _588806, _588812))], (11028 ^ _206868) ^ [_589677, _589679, _589681, _589683, _589685] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _589677), _589679), _589681), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _589677), _589683), _589685)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _589681), c_Orderings_Oord__class_Oless(tc_Int_Oint, _589681, _589677), c_Orderings_Oord__class_Oless(tc_Int_Oint, _589685, _589677), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _589679, _589683))], (11046 ^ _206868) ^ [_590272, _590274, _590276] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _590272), _590274), _590276), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _590276), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _590272), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _590274, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11060 ^ _206868) ^ [_590716, _590718, _590720] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _590716), _590718), _590720)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _590720, _590716), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _590716), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _590718))], (11074 ^ _206868) ^ [_591160, _591162, _591164] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _591160), 11077 ^ _206868 : [(11078 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591160), _591162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591160), _591164)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _591162, _591164))], (11084 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _591162, _591164), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591160), _591162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591160), _591164)))]]], (11090 ^ _206868) ^ [_591694, _591696, _591698] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _591694), 11093 ^ _206868 : [(11094 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591694), _591696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591694), _591698))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _591696), _591698)))], (11100 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _591696), _591698)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591694), _591696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591694), _591698))))]]], (11116 ^ _206868) ^ [_592567, _592569, _592571] : [11117 ^ _206868 : [(11118 ^ _206868) ^ [] : [_592567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11120 ^ _206868) ^ [] : [_592569 = _592571]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592567), _592569) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592567), _592571))], (11106 ^ _206868) ^ [_592281, _592283, _592285] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592281), _592283) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592281), _592285), -(_592281 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_592283 = _592285)], (11124 ^ _206868) ^ [_592898, _592900, _592902, _592904] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592898), _592900), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592902), _592900), _592904)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _592898, _592902)), _592900), _592904))], (11126 ^ _206868) ^ [_593059, _593061, _593063] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _593059), 11129 ^ _206868 : [(11130 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593059), _593061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593059), _593063)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _593061, _593063))], (11136 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _593061, _593063), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593059), _593061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593059), _593063)))]]], (11142 ^ _206868) ^ [_593593, _593595, _593597] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _593593), 11145 ^ _206868 : [(11146 ^ _206868) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593593), _593595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593593), _593597), -(_593595 = _593597)], (11152 ^ _206868) ^ [] : [_593595 = _593597, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593593), _593595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593593), _593597))]]], (11168 ^ _206868) ^ [_594456, _594458, _594460] : [11169 ^ _206868 : [(11170 ^ _206868) ^ [] : [_594456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11172 ^ _206868) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _594458), _594460))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _594456), _594458)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _594456), _594460))))], (11158 ^ _206868) ^ [_594150, _594152, _594154] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _594150), _594152)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _594150), _594154))), -(_594150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _594152), _594154)))], (11176 ^ _206868) ^ [_594794, _594796] : [-(_594794 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_594796 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _594794), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 11183 ^ [_594794, _594796]), _594796)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11187 ^ _206868) ^ [_595202] : [class_Power_Opower(_595202), -(c_Power_Opower__class_Opower(_595202) = c_Power_Opower_Opower(_595202, c_Groups_Oone__class_Oone(_595202), c_Groups_Otimes__class_Otimes(_595202)))], (11193 ^ _206868) ^ [_595437, _595439, _595441, _595443] : [-(hAPP(hAPP(c_Power_Opower_Opower(_595437, _595439, _595441), _595443), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _595439)], (11195 ^ _206868) ^ [_595587, _595589, _595591, _595593, _595595] : [-(hAPP(hAPP(c_Power_Opower_Opower(_595587, _595589, _595591), _595593), c_Nat_OSuc(_595595)) = hAPP(hAPP(_595591, _595593), hAPP(hAPP(c_Power_Opower_Opower(_595587, _595589, _595591), _595593), _595595)))], (11197 ^ _206868) ^ [_595730, _595732] : [class_RealVector_Oreal__normed__algebra(_595730), 11201 ^ _206868 : [(11202 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11200 ^ [_595730, _595732]))], (11204 ^ _206868) ^ [_596029] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_595730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_595730), _596029), _595732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_595730, _596029)), 11200 ^ [_595730, _595732])))]]], (11206 ^ _206868) ^ [_596175, _596177] : [class_RealVector_Oreal__normed__algebra(_596175), 11210 ^ _206868 : [(11211 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11209 ^ [_596175, _596177]))], (11213 ^ _206868) ^ [_596474] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_596175, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_596175), _596177), _596474)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_596175, _596474)), 11209 ^ [_596175, _596177])))]]], (11215 ^ _206868) ^ [_596606] : [class_RealVector_Oreal__normed__algebra(_596606), 11219 ^ _206868 : [(11220 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11218 ^ [_596606]))], (11222 ^ _206868) ^ [_596935, _596937] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_596606, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_596606), _596937), _596935)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_596606, _596937)), c_RealVector_Onorm__class_Onorm(_596606, _596935))), 11218 ^ [_596606])))]]], (11224 ^ _206868) ^ [_597130, _597132, _597134, _597136, _597138] : [class_Fields_Ofield(_597130), 11227 ^ _206868 : [(11250 ^ _206868) ^ [] : [-(c_Polynomial_Opdivmod__rel(_597130, _597132, _597134, _597136, _597138)), _597132 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_597130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_597130)), _597136), _597134), _597138), 11257 ^ _206868 : [(11258 ^ _206868) ^ [] : [-(_597134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597130)))], (11260 ^ _206868) ^ [] : [_597136 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597130))]], 11261 ^ _206868 : [(11262 ^ _206868) ^ [] : [_597134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597130))], (11264 ^ _206868) ^ [] : [_597138 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597130))], (11266 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_597130, _597138), c_Polynomial_Odegree(_597130, _597134))]]], (11228 ^ _206868) ^ [] : [c_Polynomial_Opdivmod__rel(_597130, _597132, _597134, _597136, _597138), 11231 ^ _206868 : [(11232 ^ _206868) ^ [] : [-(_597132 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_597130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_597130)), _597136), _597134), _597138))], (11234 ^ _206868) ^ [] : [_597134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597130)), -(_597136 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597130)))], (11240 ^ _206868) ^ [] : [-(_597134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597130))), -(_597138 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597130))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_597130, _597138), c_Polynomial_Odegree(_597130, _597134)))]]]]], (11270 ^ _206868) ^ [_598712, _598714, _598716, _598718, _598720, _598722, _598724] : [class_Fields_Ofield(_598712), c_Polynomial_Opdivmod__rel(_598712, _598714, _598716, _598718, _598720), c_Polynomial_Opdivmod__rel(_598712, _598714, _598716, _598722, _598724), -(_598718 = _598722)], (11284 ^ _206868) ^ [_599250, _599252, _599254, _599256, _599258, _599260, _599262] : [class_Fields_Ofield(_599250), c_Polynomial_Opdivmod__rel(_599250, _599252, _599254, _599256, _599258), c_Polynomial_Opdivmod__rel(_599250, _599252, _599254, _599260, _599262), -(_599258 = _599262)], (11298 ^ _206868) ^ [_599788, _599790, _599792, _599794, _599796, _599798, _599800] : [class_Fields_Ofield(_599788), c_Polynomial_Opdivmod__rel(_599788, _599790, _599792, _599794, _599796), c_Polynomial_Opdivmod__rel(_599788, _599790, _599792, _599798, _599800), 11309 ^ _206868 : [(11310 ^ _206868) ^ [] : [-(_599794 = _599798)], (11312 ^ _206868) ^ [] : [-(_599796 = _599800)]]], (11314 ^ _206868) ^ [_600369, _600371, _600373, _600375] : [class_Fields_Ofield(_600369), 11317 ^ _206868 : [(11318 ^ _206868) ^ [] : [c_Polynomial_Opdivmod__rel(_600369, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_600369)), _600371, _600373, _600375), 11321 ^ _206868 : [(11322 ^ _206868) ^ [] : [-(_600373 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_600369)))], (11324 ^ _206868) ^ [] : [-(_600375 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_600369)))]]], (11326 ^ _206868) ^ [] : [-(c_Polynomial_Opdivmod__rel(_600369, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_600369)), _600371, _600373, _600375)), _600373 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_600369)), _600375 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_600369))]]], (11336 ^ _206868) ^ [_601102, _601104, _601106, _601108] : [class_Fields_Ofield(_601102), 11339 ^ _206868 : [(11340 ^ _206868) ^ [] : [c_Polynomial_Opdivmod__rel(_601102, _601104, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_601102)), _601106, _601108), 11343 ^ _206868 : [(11344 ^ _206868) ^ [] : [-(_601106 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_601102)))], (11346 ^ _206868) ^ [] : [-(_601108 = _601104)]]], (11348 ^ _206868) ^ [] : [-(c_Polynomial_Opdivmod__rel(_601102, _601104, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_601102)), _601106, _601108)), _601106 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_601102)), _601108 = _601104]]], (11358 ^ _206868) ^ [_601795, _601797] : [class_Fields_Ofield(_601795), -(c_Polynomial_Opdivmod__rel(_601795, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_601795)), _601797, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_601795)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_601795))))], (11364 ^ _206868) ^ [_602033, _602035] : [class_Fields_Ofield(_602033), -(c_Polynomial_Opdivmod__rel(_602033, _602035, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_602033)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_602033)), _602035))], (11370 ^ _206868) ^ [_602347, _602349, _602351, _602353, _602355, _602357, _602359, _602361] : [class_Fields_Ofield(_602347), c_Polynomial_Opdivmod__rel(_602347, _602349, _602351, _602353, _602355), c_Polynomial_Opdivmod__rel(_602347, _602353, _602357, _602359, _602361), -(c_Polynomial_Opdivmod__rel(_602347, _602349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_602347)), _602351), _602357), _602359, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_602347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_602347)), _602351), _602361), _602355)))], (11384 ^ _206868) ^ [_602901, _602903, _602905] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _602901), 11390 ^ _206868 : [(11391 ^ _206868) ^ [] : [-(hBOOL(hAPP(_602903, 11389 ^ [_602901, _602903, _602905])))], (11393 ^ _206868) ^ [] : [hBOOL(hAPP(_602903, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 11389 ^ [_602901, _602903, _602905], _602901)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _602905), 11398 ^ _206868 : [(11399 ^ _206868) ^ [_603416] : [hBOOL(hAPP(_602903, _603416)), -(hBOOL(hAPP(_602903, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _603416, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _602905), _602901)))))]]], (11405 ^ _206868) ^ [_603672] : [class_RealVector_Oreal__normed__algebra(_603672), 11409 ^ _206868 : [(11410 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11408 ^ [_603672]))], (11412 ^ _206868) ^ [_604001, _604003] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_603672, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603672), _604003), _604001)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_603672, _604003)), c_RealVector_Onorm__class_Onorm(_603672, _604001))), 11408 ^ [_603672])))]]], (11414 ^ _206868) ^ [_604154, _604156] : [class_RealVector_Oreal__normed__algebra(_604154), 11418 ^ _206868 : [(11419 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11417 ^ [_604154, _604156]))], (11421 ^ _206868) ^ [_604453] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_604154, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604154), _604453), _604156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_604154, _604453)), 11417 ^ [_604154, _604156])))]]], (11423 ^ _206868) ^ [_604599, _604601] : [class_RealVector_Oreal__normed__algebra(_604599), 11427 ^ _206868 : [(11428 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11426 ^ [_604599, _604601]))], (11430 ^ _206868) ^ [_604898] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_604599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604599), _604601), _604898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_604599, _604898)), 11426 ^ [_604599, _604601])))]]], (11432 ^ _206868) ^ [_605029, _605031] : [-(c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_605029))), _605031)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocis(_605031)), c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _605029)), _605031))))], (11434 ^ _206868) ^ [] : [-(c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (11436 ^ _206868) ^ [_605208, _605210] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocis(_605208)), c_Complex_Ocis(_605210)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _605208, _605210)))], (11438 ^ _206868) ^ [] : [-(c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (11440 ^ _206868) ^ [_605357] : [-(c_Complex_Ocis(_605357) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _605357))], (11442 ^ _206868) ^ [_605454, _605456] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Ocis(_605454)), _605456) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _605456)), _605454)))], (11444 ^ _206868) ^ [_605567, _605569] : [-(c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _605567, _605569)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oexpi(_605567)), c_Complex_Oexpi(_605569)))], (11446 ^ _206868) ^ [_605692, _605694] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _605692), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _605694), 11454 ^ _206868 : [(11455 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 11453 ^ [_605692, _605694])), _605692), _605694))], (11457 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _605694, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(11453 ^ [_605692, _605694]))), _605692)))]]], (11459 ^ _206868) ^ [_606192] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _606192), 11463 ^ _206868 : [(11464 ^ _206868) ^ [_606374] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _606374, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 11462 ^ [_606192, _606374])), _606192)))]]], (11466 ^ _206868) ^ [_606505, _606507] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _606505), -(c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _606505), _606507)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _606507)), c_Transcendental_Oln(_606505)))], (11472 ^ _206868) ^ [_606755, _606757] : [class_RealVector_Oreal__normed__algebra(_606755), 11476 ^ _206868 : [(11477 ^ _206868) ^ [_606966] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_606755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_606755), _606966), _606757)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_606755, _606966)), 11475 ^ [_606755, _606757])))]]], (11479 ^ _206868) ^ [_607110, _607112] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _607110), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _607112), 11486 ^ _206868 : [(11487 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_607110), c_Transcendental_Oln(_607112)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _607110, _607112))], (11493 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _607110, _607112), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_607110), c_Transcendental_Oln(_607112)))]]], (11499 ^ _206868) ^ [_607681, _607683] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _607681), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _607683), 11506 ^ _206868 : [(11507 ^ _206868) ^ [] : [c_Transcendental_Oln(_607681) = c_Transcendental_Oln(_607683), -(_607681 = _607683)], (11513 ^ _206868) ^ [] : [_607681 = _607683, -(c_Transcendental_Oln(_607681) = c_Transcendental_Oln(_607683))]]], (11519 ^ _206868) ^ [_608232] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _608232), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_608232), _608232))], (11525 ^ _206868) ^ [] : [-(c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11527 ^ _206868) ^ [_608497, _608499] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _608497), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _608499), 11534 ^ _206868 : [(11535 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(_608497), c_Transcendental_Oln(_608499)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _608497, _608499))], (11541 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _608497, _608499), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(_608497), c_Transcendental_Oln(_608499)))]]], (11547 ^ _206868) ^ [_609054] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _609054), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_609054)))], (11553 ^ _206868) ^ [_609252] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _609252), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_609252)))], (11559 ^ _206868) ^ [_609450] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _609450), 11562 ^ _206868 : [(11563 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_609450)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _609450))], (11569 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _609450), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_609450)))]]], (11575 ^ _206868) ^ [_609894] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _609894), 11578 ^ _206868 : [(11579 ^ _206868) ^ [] : [c_Transcendental_Oln(_609894) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_609894 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (11585 ^ _206868) ^ [] : [_609894 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Transcendental_Oln(_609894) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (11591 ^ _206868) ^ [_610332] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _610332), 11594 ^ _206868 : [(11595 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_610332), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _610332, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11601 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _610332, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_610332), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (11607 ^ _206868) ^ [_610776] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _610776), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _610776, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_610776), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (11617 ^ _206868) ^ [_611061] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_611061)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _611061), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _611061))], (11627 ^ _206868) ^ [_611346] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _611346), 11630 ^ _206868 : [(11631 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_611346)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _611346))], (11637 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _611346), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_611346)))]]], (11643 ^ _206868) ^ [_611790] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_611790)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _611790), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _611790))], (11653 ^ _206868) ^ [_612089, _612091] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _612089), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _612091), -(c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _612089), _612091)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Transcendental_Oln(_612089), c_Transcendental_Oln(_612091)))], (11663 ^ _206868) ^ [_612410] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _612410), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _612410)), _612410))], (11669 ^ _206868) ^ [_612616] : [class_RealVector_Oreal__normed__algebra(_612616), 11673 ^ _206868 : [(11674 ^ _206868) ^ [_612861, _612863] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_612616, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_612616), _612863), _612861)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_612616, _612863)), c_RealVector_Onorm__class_Onorm(_612616, _612861))), 11672 ^ [_612616])))]]], (11676 ^ _206868) ^ [_613012, _613014] : [class_RealVector_Oreal__normed__algebra(_613012), 11680 ^ _206868 : [(11681 ^ _206868) ^ [_613223] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_613012, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613012), _613014), _613223)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_613012, _613223)), 11679 ^ [_613012, _613014])))]]], (11683 ^ _206868) ^ [_613381, _613383, _613385] : [class_Groups_Omonoid__mult(_613381), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _613383), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613381), hAPP(hAPP(c_Power_Opower__class_Opower(_613381), _613385), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613383, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _613385) = hAPP(hAPP(c_Power_Opower__class_Opower(_613381), _613385), _613383))], (11693 ^ _206868) ^ [_613760, _613762, _613764] : [class_Power_Opower(_613760), 11696 ^ _206868 : [(11697 ^ _206868) ^ [] : [_613762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_613760), _613764), _613762) = c_Groups_Oone__class_Oone(_613760))], (11703 ^ _206868) ^ [] : [-(_613762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_613760), _613764), _613762) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613760), _613764), hAPP(hAPP(c_Power_Opower__class_Opower(_613760), _613764), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613762, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (11709 ^ _206868) ^ [_614287] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_614287), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _614287)], (11711 ^ _206868) ^ [_614385, _614387] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614385, c_Nat_OSuc(_614387)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614385, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _614387))], (11713 ^ _206868) ^ [_614508, _614510] : [class_Rings_Oring__1(_614508), -(c_Groups_Ominus__class_Ominus(_614508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614508), _614510), _614510), c_Groups_Oone__class_Oone(_614508)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614508), c_Groups_Oplus__class_Oplus(_614508, _614510, c_Groups_Oone__class_Oone(_614508))), c_Groups_Ominus__class_Ominus(_614508, _614510, c_Groups_Oone__class_Oone(_614508))))], (11719 ^ _206868) ^ [_614812, _614814, _614816, _614818] : [class_RealVector_Oreal__normed__algebra(_614812), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614812), _614814), c_Groups_Ominus__class_Ominus(_614812, _614816, _614818)) = c_Groups_Ominus__class_Ominus(_614812, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614812), _614814), _614816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614812), _614814), _614818)))], (11725 ^ _206868) ^ [_615124, _615126, _615128, _615130] : [class_RealVector_Oreal__normed__algebra(_615124), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615124), _615126), c_Groups_Ominus__class_Ominus(_615124, _615128, _615130)) = c_Groups_Ominus__class_Ominus(_615124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615124), _615126), _615128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615124), _615126), _615130)))], (11731 ^ _206868) ^ [_615436, _615438, _615440, _615442] : [class_RealVector_Oreal__normed__algebra(_615436), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615436), c_Groups_Ominus__class_Ominus(_615436, _615438, _615440)), _615442) = c_Groups_Ominus__class_Ominus(_615436, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615436), _615438), _615442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615436), _615440), _615442)))], (11737 ^ _206868) ^ [_615748, _615750, _615752, _615754] : [class_RealVector_Oreal__normed__algebra(_615748), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615748), c_Groups_Ominus__class_Ominus(_615748, _615750, _615752)), _615754) = c_Groups_Ominus__class_Ominus(_615748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615748), _615750), _615754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615748), _615752), _615754)))], (11743 ^ _206868) ^ [_616031, _616033, _616035] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616031), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616033, _616035)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616031), _616033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616031), _616035)))], (11745 ^ _206868) ^ [_616167, _616169, _616171] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616167, _616169)), _616171) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616167), _616171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616169), _616171)))], (11747 ^ _206868) ^ [_616360, _616362, _616364, _616366, _616368, _616370] : [class_Rings_Oring(_616360), 11750 ^ _206868 : [(11751 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_616360, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_616360), _616362), _616364), _616366) = c_Groups_Oplus__class_Oplus(_616360, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_616360), _616368), _616364), _616370), -(c_Groups_Oplus__class_Oplus(_616360, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_616360), c_Groups_Ominus__class_Ominus(_616360, _616362, _616368)), _616364), _616366) = _616370)], (11757 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_616360, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_616360), c_Groups_Ominus__class_Ominus(_616360, _616362, _616368)), _616364), _616366) = _616370, -(c_Groups_Oplus__class_Oplus(_616360, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_616360), _616362), _616364), _616366) = c_Groups_Oplus__class_Oplus(_616360, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_616360), _616368), _616364), _616370))]]], (11763 ^ _206868) ^ [_617058, _617060, _617062, _617064, _617066, _617068] : [class_Rings_Oring(_617058), 11766 ^ _206868 : [(11767 ^ _206868) ^ [] : [c_Groups_Oplus__class_Oplus(_617058, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617058), _617060), _617062), _617064) = c_Groups_Oplus__class_Oplus(_617058, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617058), _617066), _617062), _617068), -(_617064 = c_Groups_Oplus__class_Oplus(_617058, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617058), c_Groups_Ominus__class_Ominus(_617058, _617066, _617060)), _617062), _617068))], (11773 ^ _206868) ^ [] : [_617064 = c_Groups_Oplus__class_Oplus(_617058, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617058), c_Groups_Ominus__class_Ominus(_617058, _617066, _617060)), _617062), _617068), -(c_Groups_Oplus__class_Oplus(_617058, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617058), _617060), _617062), _617064) = c_Groups_Oplus__class_Oplus(_617058, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617058), _617066), _617062), _617068))]]], (11779 ^ _206868) ^ [_617742, _617744, _617746, _617748, _617750] : [class_RealVector_Oreal__normed__algebra(_617742), -(c_Groups_Ominus__class_Ominus(_617742, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617742), _617744), _617746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617742), _617748), _617750)) = c_Groups_Oplus__class_Oplus(_617742, c_Groups_Oplus__class_Oplus(_617742, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617742), c_Groups_Ominus__class_Ominus(_617742, _617744, _617748)), c_Groups_Ominus__class_Ominus(_617742, _617746, _617750)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617742), c_Groups_Ominus__class_Ominus(_617742, _617744, _617748)), _617750)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617742), _617748), c_Groups_Ominus__class_Ominus(_617742, _617746, _617750))))], (11785 ^ _206868) ^ [_618146, _618148, _618150, _618152, _618154] : [class_Rings_Oring(_618146), -(c_Groups_Ominus__class_Ominus(_618146, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618146), _618148), _618150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618146), _618152), _618154)) = c_Groups_Oplus__class_Oplus(_618146, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618146), _618148), c_Groups_Ominus__class_Ominus(_618146, _618150, _618154)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618146), c_Groups_Ominus__class_Ominus(_618146, _618148, _618152)), _618154)))], (11791 ^ _206868) ^ [_618524, _618526, _618528, _618530, _618532, _618534] : [class_Rings_Oordered__ring(_618524), 11794 ^ _206868 : [(11795 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_618524, c_Groups_Oplus__class_Oplus(_618524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618524), _618526), _618528), _618530), c_Groups_Oplus__class_Oplus(_618524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618524), _618532), _618528), _618534)), -(c_Orderings_Oord__class_Oless__eq(_618524, _618530, c_Groups_Oplus__class_Oplus(_618524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618524), c_Groups_Ominus__class_Ominus(_618524, _618532, _618526)), _618528), _618534)))], (11801 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_618524, _618530, c_Groups_Oplus__class_Oplus(_618524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618524), c_Groups_Ominus__class_Ominus(_618524, _618532, _618526)), _618528), _618534)), -(c_Orderings_Oord__class_Oless__eq(_618524, c_Groups_Oplus__class_Oplus(_618524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618524), _618526), _618528), _618530), c_Groups_Oplus__class_Oplus(_618524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618524), _618532), _618528), _618534)))]]], (11807 ^ _206868) ^ [_619228, _619230, _619232, _619234, _619236, _619238] : [class_Rings_Oordered__ring(_619228), 11810 ^ _206868 : [(11811 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_619228, c_Groups_Oplus__class_Oplus(_619228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619228), _619230), _619232), _619234), c_Groups_Oplus__class_Oplus(_619228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619228), _619236), _619232), _619238)), -(c_Orderings_Oord__class_Oless__eq(_619228, c_Groups_Oplus__class_Oplus(_619228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619228), c_Groups_Ominus__class_Ominus(_619228, _619230, _619236)), _619232), _619234), _619238))], (11817 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless__eq(_619228, c_Groups_Oplus__class_Oplus(_619228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619228), c_Groups_Ominus__class_Ominus(_619228, _619230, _619236)), _619232), _619234), _619238), -(c_Orderings_Oord__class_Oless__eq(_619228, c_Groups_Oplus__class_Oplus(_619228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619228), _619230), _619232), _619234), c_Groups_Oplus__class_Oplus(_619228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619228), _619236), _619232), _619238)))]]], (11823 ^ _206868) ^ [_619932, _619934, _619936, _619938, _619940, _619942] : [class_Rings_Oordered__ring(_619932), 11826 ^ _206868 : [(11827 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_619932, c_Groups_Oplus__class_Oplus(_619932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619932), _619934), _619936), _619938), c_Groups_Oplus__class_Oplus(_619932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619932), _619940), _619936), _619942)), -(c_Orderings_Oord__class_Oless(_619932, c_Groups_Oplus__class_Oplus(_619932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619932), c_Groups_Ominus__class_Ominus(_619932, _619934, _619940)), _619936), _619938), _619942))], (11833 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_619932, c_Groups_Oplus__class_Oplus(_619932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619932), c_Groups_Ominus__class_Ominus(_619932, _619934, _619940)), _619936), _619938), _619942), -(c_Orderings_Oord__class_Oless(_619932, c_Groups_Oplus__class_Oplus(_619932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619932), _619934), _619936), _619938), c_Groups_Oplus__class_Oplus(_619932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619932), _619940), _619936), _619942)))]]], (11839 ^ _206868) ^ [_620636, _620638, _620640, _620642, _620644, _620646] : [class_Rings_Oordered__ring(_620636), 11842 ^ _206868 : [(11843 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_620636, c_Groups_Oplus__class_Oplus(_620636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_620636), _620638), _620640), _620642), c_Groups_Oplus__class_Oplus(_620636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_620636), _620644), _620640), _620646)), -(c_Orderings_Oord__class_Oless(_620636, _620642, c_Groups_Oplus__class_Oplus(_620636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_620636), c_Groups_Ominus__class_Ominus(_620636, _620644, _620638)), _620640), _620646)))], (11849 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(_620636, _620642, c_Groups_Oplus__class_Oplus(_620636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_620636), c_Groups_Ominus__class_Ominus(_620636, _620644, _620638)), _620640), _620646)), -(c_Orderings_Oord__class_Oless(_620636, c_Groups_Oplus__class_Oplus(_620636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_620636), _620638), _620640), _620642), c_Groups_Oplus__class_Oplus(_620636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_620636), _620644), _620640), _620646)))]]], (11855 ^ _206868) ^ [_621312, _621314, _621316, _621318] : [class_Rings_Ocomm__ring(_621312), class_Rings_Odvd(_621312), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_621312), _621314), _621316)), 11866 ^ _206868 : [(11867 ^ _206868) ^ [_621739, _621741] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_621312), _621314), c_Groups_Oplus__class_Oplus(_621312, _621741, _621318))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_621312), _621314), c_Groups_Oplus__class_Oplus(_621312, c_Groups_Ominus__class_Ominus(_621312, _621741, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_621312), _621739), _621316)), _621318))))], (11873 ^ _206868) ^ [_622001, _622003] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_621312), _621314), c_Groups_Oplus__class_Oplus(_621312, c_Groups_Ominus__class_Ominus(_621312, _622003, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_621312), _622001), _621316)), _621318))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_621312), _621314), c_Groups_Oplus__class_Oplus(_621312, _622003, _621318))))]]], (11879 ^ _206868) ^ [_622352, _622354, _622356, _622358] : [class_Rings_Ocomm__ring(_622352), class_Rings_Odvd(_622352), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_622352), _622354), _622356)), 11890 ^ _206868 : [(11891 ^ _206868) ^ [_622779, _622781] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_622352), _622354), c_Groups_Oplus__class_Oplus(_622352, _622781, _622358))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_622352), _622354), c_Groups_Oplus__class_Oplus(_622352, c_Groups_Ominus__class_Ominus(_622352, _622781, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_622352), _622779), _622356)), _622358))))], (11897 ^ _206868) ^ [_623041, _623043] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_622352), _622354), c_Groups_Oplus__class_Oplus(_622352, c_Groups_Ominus__class_Ominus(_622352, _623043, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_622352), _623041), _622356)), _622358))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_622352), _622354), c_Groups_Oplus__class_Oplus(_622352, _623043, _622358))))]]], (11903 ^ _206868) ^ [_623378, _623380, _623382] : [class_RealVector_Oreal__normed__vector(_623378), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_623378, c_Groups_Ominus__class_Ominus(_623378, _623380, _623382)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_623378, _623380), c_RealVector_Onorm__class_Onorm(_623378, _623382))))], (11909 ^ _206868) ^ [_623614] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _623614), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _623614, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _623614)], (11915 ^ _206868) ^ [_623832, _623834] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _623832), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _623832, c_Nat_OSuc(_623834)), _623832))], (11937 ^ _206868) ^ [_624632, _624634, _624636] : [-(hBOOL(hAPP(_624632, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _624634, _624636)))), 11940 ^ _206868 : [(11941 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624634, _624636))], (11943 ^ _206868) ^ [] : [hBOOL(hAPP(_624632, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11945 ^ _206868 : [(11946 ^ _206868) ^ [] : [-(_624634 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _624636, 11944 ^ [_624632, _624634, _624636]))], (11948 ^ _206868) ^ [] : [hBOOL(hAPP(_624632, 11944 ^ [_624632, _624634, _624636]))]]], (11921 ^ _206868) ^ [_624101, _624103, _624105] : [hBOOL(hAPP(_624101, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _624103, _624105))), 11924 ^ _206868 : [(11925 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624103, _624105), -(hBOOL(hAPP(_624101, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11931 ^ _206868) ^ [_624433] : [_624103 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _624105, _624433), -(hBOOL(hAPP(_624101, _624433)))]]], (11968 ^ _206868) ^ [_625793, _625795, _625797] : [-(hBOOL(hAPP(_625793, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _625795, _625797)))), 11971 ^ _206868 : [(11972 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _625795, _625797))], (11974 ^ _206868) ^ [] : [hBOOL(hAPP(_625793, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11976 ^ _206868 : [(11977 ^ _206868) ^ [] : [-(_625795 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _625797, 11975 ^ [_625793, _625795, _625797]))], (11979 ^ _206868) ^ [] : [hBOOL(hAPP(_625793, 11975 ^ [_625793, _625795, _625797]))]]], (11952 ^ _206868) ^ [_625254, _625256, _625258] : [hBOOL(hAPP(_625254, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _625256, _625258))), 11955 ^ _206868 : [(11956 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _625256, _625258), -(hBOOL(hAPP(_625254, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11962 ^ _206868) ^ [_625592] : [_625256 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _625258, _625592), -(hBOOL(hAPP(_625254, _625592)))]]], (11983 ^ _206868) ^ [_626394, _626396, _626398] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _626394, _626396), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _626396, _626394)), _626398) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_626396), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _626394, _626398)))], (11989 ^ _206868) ^ [_626666, _626668, _626670] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _626666, _626668), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _626670, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _626668, _626666))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _626670, _626666), c_Nat_OSuc(_626668)))], (11995 ^ _206868) ^ [_626910] : [class_Groups_Ocancel__comm__monoid__add(_626910), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_626910)))], (12001 ^ _206868) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (12003 ^ _206868) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (12005 ^ _206868) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (12007 ^ _206868) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (12009 ^ _206868) ^ [_627326, _627328] : [class_Lattices_Oboolean__algebra(_627326), -(class_Lattices_Oboolean__algebra(tc_fun(_627328, _627326)))], (12015 ^ _206868) ^ [_627538, _627540] : [class_Orderings_Opreorder(_627538), -(class_Orderings_Opreorder(tc_fun(_627540, _627538)))], (12021 ^ _206868) ^ [_627750, _627752] : [class_Orderings_Oorder(_627750), -(class_Orderings_Oorder(tc_fun(_627752, _627750)))], (12027 ^ _206868) ^ [_627962, _627964] : [class_Orderings_Oord(_627962), -(class_Orderings_Oord(tc_fun(_627964, _627962)))], (12033 ^ _206868) ^ [_628174, _628176] : [class_Groups_Ouminus(_628174), -(class_Groups_Ouminus(tc_fun(_628176, _628174)))], (12039 ^ _206868) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (12041 ^ _206868) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (12043 ^ _206868) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (12045 ^ _206868) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (12047 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (12049 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (12051 ^ _206868) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (12053 ^ _206868) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (12055 ^ _206868) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (12057 ^ _206868) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (12059 ^ _206868) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (12061 ^ _206868) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (12063 ^ _206868) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (12065 ^ _206868) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (12067 ^ _206868) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (12069 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (12071 ^ _206868) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (12073 ^ _206868) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (12075 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (12077 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (12079 ^ _206868) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (12081 ^ _206868) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (12083 ^ _206868) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (12085 ^ _206868) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (12087 ^ _206868) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (12089 ^ _206868) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (12091 ^ _206868) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (12093 ^ _206868) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (12095 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (12097 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (12099 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (12101 ^ _206868) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (12103 ^ _206868) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (12105 ^ _206868) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (12107 ^ _206868) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (12109 ^ _206868) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (12111 ^ _206868) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (12113 ^ _206868) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (12115 ^ _206868) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (12117 ^ _206868) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (12119 ^ _206868) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (12121 ^ _206868) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (12123 ^ _206868) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (12125 ^ _206868) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (12127 ^ _206868) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (12129 ^ _206868) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (12131 ^ _206868) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (12133 ^ _206868) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (12135 ^ _206868) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (12137 ^ _206868) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (12139 ^ _206868) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (12141 ^ _206868) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (12143 ^ _206868) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (12145 ^ _206868) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (12147 ^ _206868) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (12149 ^ _206868) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (12151 ^ _206868) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (12153 ^ _206868) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (12155 ^ _206868) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (12157 ^ _206868) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (12159 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (12161 ^ _206868) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (12163 ^ _206868) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (12165 ^ _206868) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (12167 ^ _206868) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (12169 ^ _206868) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (12171 ^ _206868) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (12173 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (12175 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (12177 ^ _206868) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (12179 ^ _206868) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (12181 ^ _206868) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (12183 ^ _206868) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (12185 ^ _206868) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (12187 ^ _206868) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (12189 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (12191 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (12193 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (12195 ^ _206868) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (12197 ^ _206868) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (12199 ^ _206868) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (12201 ^ _206868) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (12203 ^ _206868) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (12205 ^ _206868) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (12207 ^ _206868) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (12209 ^ _206868) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (12211 ^ _206868) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (12213 ^ _206868) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (12215 ^ _206868) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (12217 ^ _206868) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (12219 ^ _206868) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (12221 ^ _206868) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (12223 ^ _206868) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (12225 ^ _206868) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (12227 ^ _206868) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (12229 ^ _206868) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (12231 ^ _206868) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (12233 ^ _206868) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (12235 ^ _206868) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (12237 ^ _206868) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (12239 ^ _206868) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (12241 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (12243 ^ _206868) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (12245 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (12247 ^ _206868) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (12249 ^ _206868) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (12251 ^ _206868) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (12253 ^ _206868) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (12255 ^ _206868) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (12257 ^ _206868) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (12259 ^ _206868) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (12261 ^ _206868) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (12263 ^ _206868) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (12265 ^ _206868) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (12267 ^ _206868) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (12269 ^ _206868) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (12271 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (12273 ^ _206868) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (12275 ^ _206868) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (12277 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (12279 ^ _206868) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (12281 ^ _206868) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (12283 ^ _206868) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (12285 ^ _206868) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (12287 ^ _206868) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (12289 ^ _206868) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (12291 ^ _206868) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (12293 ^ _206868) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (12295 ^ _206868) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (12297 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (12299 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (12301 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (12303 ^ _206868) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (12305 ^ _206868) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (12307 ^ _206868) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (12309 ^ _206868) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (12311 ^ _206868) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (12313 ^ _206868) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (12315 ^ _206868) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (12317 ^ _206868) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (12319 ^ _206868) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (12321 ^ _206868) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (12323 ^ _206868) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (12325 ^ _206868) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (12327 ^ _206868) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (12329 ^ _206868) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (12331 ^ _206868) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (12333 ^ _206868) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (12335 ^ _206868) ^ [] : [-(class_Groups_Ouminus(tc_RealDef_Oreal))], (12337 ^ _206868) ^ [] : [-(class_Groups_Osgn__if(tc_RealDef_Oreal))], (12339 ^ _206868) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (12341 ^ _206868) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (12343 ^ _206868) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (12345 ^ _206868) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (12347 ^ _206868) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (12349 ^ _206868) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (12351 ^ _206868) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (12353 ^ _206868) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (12355 ^ _206868) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (12357 ^ _206868) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (12359 ^ _206868) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (12361 ^ _206868) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (12363 ^ _206868) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (12365 ^ _206868) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (12367 ^ _206868) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (12369 ^ _206868) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (12371 ^ _206868) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (12373 ^ _206868) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (12375 ^ _206868) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (12377 ^ _206868) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (12379 ^ _206868) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (12381 ^ _206868) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (12383 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (12385 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (12387 ^ _206868) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (12389 ^ _206868) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (12391 ^ _206868) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (12393 ^ _206868) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (12395 ^ _206868) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (12397 ^ _206868) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (12399 ^ _206868) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (12401 ^ _206868) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (12403 ^ _206868) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (12405 ^ _206868) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (12407 ^ _206868) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (12409 ^ _206868) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (12411 ^ _206868) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (12413 ^ _206868) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (12415 ^ _206868) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (12417 ^ _206868) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (12419 ^ _206868) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (12421 ^ _206868) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (12423 ^ _206868) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (12425 ^ _206868) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (12427 ^ _206868) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (12429 ^ _206868) ^ [_638707] : [class_Rings_Oidom(_638707), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_638707)))], (12435 ^ _206868) ^ [_638897] : [class_Rings_Olinordered__idom(_638897), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_638897)))], (12441 ^ _206868) ^ [_639087] : [class_Rings_Olinordered__idom(_639087), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_639087)))], (12447 ^ _206868) ^ [_639277] : [class_Rings_Olinordered__idom(_639277), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_639277)))], (12453 ^ _206868) ^ [_639467] : [class_Rings_Olinordered__idom(_639467), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_639467)))], (12459 ^ _206868) ^ [_639657] : [class_Rings_Olinordered__idom(_639657), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_639657)))], (12465 ^ _206868) ^ [_639847] : [class_Rings_Olinordered__idom(_639847), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_639847)))], (12471 ^ _206868) ^ [_640037] : [class_Rings_Olinordered__idom(_640037), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_640037)))], (12477 ^ _206868) ^ [_640227] : [class_Rings_Olinordered__idom(_640227), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_640227)))], (12483 ^ _206868) ^ [_640417] : [class_Groups_Ocancel__comm__monoid__add(_640417), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_640417)))], (12489 ^ _206868) ^ [_640607] : [class_Rings_Oidom(_640607), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_640607)))], (12495 ^ _206868) ^ [_640797] : [class_Rings_Olinordered__idom(_640797), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_640797)))], (12501 ^ _206868) ^ [_640987] : [class_Rings_Olinordered__idom(_640987), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_640987)))], (12507 ^ _206868) ^ [_641177] : [class_Rings_Oidom(_641177), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_641177)))], (12513 ^ _206868) ^ [_641367] : [class_Rings_Olinordered__idom(_641367), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_641367)))], (12519 ^ _206868) ^ [_641557] : [class_Rings_Olinordered__idom(_641557), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_641557)))], (12525 ^ _206868) ^ [_641747] : [class_Rings_Olinordered__idom(_641747), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_641747)))], (12531 ^ _206868) ^ [_641937] : [class_Groups_Ocancel__comm__monoid__add(_641937), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_641937)))], (12537 ^ _206868) ^ [_642127] : [class_Rings_Olinordered__idom(_642127), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_642127)))], (12543 ^ _206868) ^ [_642317] : [class_Rings_Olinordered__idom(_642317), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_642317)))], (12549 ^ _206868) ^ [_642507] : [class_Rings_Ocomm__semiring__0(_642507), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_642507)))], (12555 ^ _206868) ^ [_642697] : [class_Rings_Ocomm__semiring__1(_642697), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_642697)))], (12561 ^ _206868) ^ [_642887] : [class_Groups_Ocomm__monoid__add(_642887), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_642887)))], (12567 ^ _206868) ^ [_643077] : [class_Rings_Olinordered__idom(_643077), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_643077)))], (12573 ^ _206868) ^ [_643267] : [class_Rings_Oidom(_643267), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_643267)))], (12579 ^ _206868) ^ [_643457] : [class_Groups_Ocomm__monoid__add(_643457), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_643457)))], (12585 ^ _206868) ^ [_643647] : [class_Rings_Olinordered__idom(_643647), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_643647)))], (12591 ^ _206868) ^ [_643837] : [class_Rings_Olinordered__idom(_643837), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_643837)))], (12597 ^ _206868) ^ [_644027] : [class_Rings_Ocomm__semiring__1(_644027), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_644027)))], (12603 ^ _206868) ^ [_644217] : [class_Rings_Ocomm__semiring__0(_644217), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_644217)))], (12609 ^ _206868) ^ [_644407] : [class_Rings_Ocomm__semiring__0(_644407), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_644407)))], (12615 ^ _206868) ^ [_644597] : [class_Groups_Oab__group__add(_644597), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_644597)))], (12621 ^ _206868) ^ [_644787] : [class_Rings_Ocomm__semiring__1(_644787), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_644787)))], (12627 ^ _206868) ^ [_644977] : [class_Rings_Olinordered__idom(_644977), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_644977)))], (12633 ^ _206868) ^ [_645167] : [class_Rings_Olinordered__idom(_645167), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_645167)))], (12639 ^ _206868) ^ [_645357] : [class_Rings_Olinordered__idom(_645357), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_645357)))], (12645 ^ _206868) ^ [_645547] : [class_Rings_Ocomm__semiring__1(_645547), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_645547)))], (12651 ^ _206868) ^ [_645737] : [class_Rings_Ocomm__ring__1(_645737), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_645737)))], (12657 ^ _206868) ^ [_645927] : [class_Groups_Ocomm__monoid__add(_645927), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_645927)))], (12663 ^ _206868) ^ [_646117] : [class_Rings_Ocomm__semiring__0(_646117), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_646117)))], (12669 ^ _206868) ^ [_646307] : [class_Groups_Oab__group__add(_646307), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_646307)))], (12675 ^ _206868) ^ [_646497] : [class_Rings_Ocomm__semiring__0(_646497), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_646497)))], (12681 ^ _206868) ^ [_646687] : [class_Rings_Ocomm__ring(_646687), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_646687)))], (12687 ^ _206868) ^ [_646877] : [class_Rings_Olinordered__idom(_646877), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_646877)))], (12693 ^ _206868) ^ [_647067] : [class_Rings_Olinordered__idom(_647067), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_647067)))], (12699 ^ _206868) ^ [_647257] : [class_Rings_Ocomm__semiring__0(_647257), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_647257)))], (12705 ^ _206868) ^ [_647447] : [class_Rings_Olinordered__idom(_647447), -(class_Orderings_Oord(tc_Polynomial_Opoly(_647447)))], (12711 ^ _206868) ^ [_647637] : [class_Groups_Oab__group__add(_647637), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_647637)))], (12717 ^ _206868) ^ [_647827] : [class_Rings_Olinordered__idom(_647827), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_647827)))], (12723 ^ _206868) ^ [_648017] : [class_Rings_Ocomm__ring__1(_648017), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_648017)))], (12729 ^ _206868) ^ [_648207] : [class_Rings_Ocomm__semiring__1(_648207), -(class_Power_Opower(tc_Polynomial_Opoly(_648207)))], (12735 ^ _206868) ^ [_648397] : [class_Groups_Ozero(_648397), -(class_Groups_Ozero(tc_Polynomial_Opoly(_648397)))], (12741 ^ _206868) ^ [_648587] : [class_Rings_Ocomm__ring(_648587), -(class_Rings_Oring(tc_Polynomial_Opoly(_648587)))], (12747 ^ _206868) ^ [_648777] : [class_Rings_Oidom(_648777), -(class_Rings_Oidom(tc_Polynomial_Opoly(_648777)))], (12753 ^ _206868) ^ [_648967] : [class_Rings_Ocomm__semiring__1(_648967), -(class_Groups_Oone(tc_Polynomial_Opoly(_648967)))], (12759 ^ _206868) ^ [_649157] : [class_Rings_Ocomm__semiring__1(_649157), -(class_Rings_Odvd(tc_Polynomial_Opoly(_649157)))], (12765 ^ _206868) ^ [_649361, _649363] : [hBOOL(c_fequal(_649361, _649363)), -(_649361 = _649363)], (12771 ^ _206868) ^ [_649577, _649579] : [_649577 = _649579, -(hBOOL(c_fequal(_649577, _649579)))], (12777 ^ _206868) ^ [] : [-(v_thesis____), 12779 ^ _206868 : [(12780 ^ _206868) ^ [_649880] : [12783 ^ _206868 : [(12784 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12782 ^ [_649880]), v_r))], (12786 ^ _206868) ^ [] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), 12782 ^ [_649880])) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, 12781 ^ [_649880]))], (12788 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [_649880], 12781 ^ [_649880]))], (12790 ^ _206868) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [_649880], _649880)]], 12791 ^ _206868 : [(12792 ^ _206868) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [_649880], _649880))], (12794 ^ _206868) ^ [_650569] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [_649880], _650569), 12795 ^ _206868 : [(12796 ^ _206868) ^ [_650682] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _650682), v_r), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), _650682)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _650569)]]]]]]]], input).
% 135.51/130.27 ncf('1',plain,[v_thesis____],start(12806 ^ 0)).
% 135.51/130.27 ncf('1.1',plain,[-(v_thesis____), 12784 : -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12782 ^ [1220 ^ []]), v_r)), 12794 : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1239 ^ [12778 ^ [1220 ^ []]]), 12796 : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 1240 ^ [12778 ^ [1220 ^ []]]), v_r), 12796 : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), 1240 ^ [12778 ^ [1220 ^ []]])) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, 1239 ^ [12778 ^ [1220 ^ []]])],extension(12777 ^ 1,bind([[_649880, _650569, _650682], [1220 ^ [], 1239 ^ [12778 ^ [1220 ^ []]], 1240 ^ [12778 ^ [1220 ^ []]]]]))).
% 135.51/130.27 ncf('1.1.1',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12782 ^ [1220 ^ []]), v_r), 1226 : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), 12782 ^ [1220 ^ []])) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, 12781 ^ [1220 ^ []]), 1226 : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 12781 ^ [1220 ^ []]), 1224 : -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1220 ^ []))],extension(1222 ^ 6,bind([[_247341, _247457, _247565], [12778 ^ [1220 ^ []], 12781 ^ [1220 ^ []], 12782 ^ [1220 ^ []]]]))).
% 135.51/130.27 ncf('1.1.1.1',plain,[-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), 12782 ^ [1220 ^ []])) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, 12781 ^ [1220 ^ []]))],extension(12786 ^ 11)).
% 135.51/130.27 ncf('1.1.1.2',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 12781 ^ [1220 ^ []]))],extension(12788 ^ 9)).
% 135.51/130.27 ncf('1.1.1.3',plain,[c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1220 ^ [])],extension(12790 ^ 7)).
% 135.51/130.27 ncf('1.1.2',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1239 ^ [12778 ^ [1220 ^ []]])), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1220 ^ [])],extension(1236 ^ 6,bind([[_247863], [12778 ^ [1220 ^ []]]]))).
% 135.51/130.27 ncf('1.1.2.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1220 ^ []))],extension(12792 ^ 7)).
% 135.51/130.27 ncf('1.1.3',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 1240 ^ [12778 ^ [1220 ^ []]]), v_r)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1220 ^ [])],extension(1236 ^ 8,bind([[_247863], [12778 ^ [1220 ^ []]]]))).
% 135.51/130.27 ncf('1.1.3.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1220 ^ []))],extension(12792 ^ 9)).
% 135.51/130.27 ncf('1.1.4',plain,[-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), 1240 ^ [12778 ^ [1220 ^ []]])) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, 1239 ^ [12778 ^ [1220 ^ []]])), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1220 ^ [])],extension(1236 ^ 8,bind([[_247863], [12778 ^ [1220 ^ []]]]))).
% 135.51/130.27 ncf('1.1.4.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 12778 ^ [1220 ^ []], 1220 ^ []))],extension(12792 ^ 9)).
% 135.51/130.27 %-----------------------------------------------------
% 135.51/130.27 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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