TSTP Solution File: SWW262+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW262+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n032.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 12:25:50 EDT 2023

% Result   : Theorem 0.42s 1.32s
% Output   : Proof 0.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SWW262+1 : TPTP v8.1.2. Released v5.2.0.
% 0.05/0.09  % Command  : nanocop.sh %s %d
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Thu May 18 22:28:19 EDT 2023
% 0.09/0.28  % CPUTime  : 
% 0.42/1.32  
% 0.42/1.32  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.42/1.32  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/1.32  %-----------------------------------------------------
% 0.42/1.32  ncf(matrix, plain, [(11980 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (880 ^ _166148) ^ [_193196, _193198, _193200, _193202, _193204, _193206] : [-(c_Polynomial_Omonom(_193206, _193202, _193198) = c_Polynomial_Omonom(_193204, _193200, _193196)), _193206 = _193204, _193202 = _193200, _193198 = _193196], (894 ^ _166148) ^ [_193712, _193714, _193716, _193718, _193720, _193722] : [-(c_Polynomial_Opcompose(_193722, _193718, _193714) = c_Polynomial_Opcompose(_193720, _193716, _193712)), _193722 = _193720, _193718 = _193716, _193714 = _193712], (908 ^ _166148) ^ [_194228, _194230, _194232, _194234, _194236, _194238] : [-(c_Polynomial_Osynthetic__div(_194238, _194234, _194230) = c_Polynomial_Osynthetic__div(_194236, _194232, _194228)), _194238 = _194236, _194234 = _194232, _194230 = _194228], (922 ^ _166148) ^ [_194716, _194718, _194720, _194722] : [-(c_Rings_Oinverse__class_Oinverse(_194722, _194718) = c_Rings_Oinverse__class_Oinverse(_194720, _194716)), _194722 = _194720, _194718 = _194716], (932 ^ _166148) ^ [_195103, _195105, _195107, _195109, _195111, _195113] : [-(c_Power_Opower_Opower(_195113, _195109, _195105) = c_Power_Opower_Opower(_195111, _195107, _195103)), _195113 = _195111, _195109 = _195107, _195105 = _195103], (946 ^ _166148) ^ [_195591, _195593, _195595, _195597] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_195597, _195593) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_195595, _195591)), _195597 = _195595, _195593 = _195591], (956 ^ _166148) ^ [_195950, _195952, _195954, _195956] : [-(c_Nat__Transfer_Otsub(_195956, _195952) = c_Nat__Transfer_Otsub(_195954, _195950)), _195956 = _195954, _195952 = _195950], (966 ^ _166148) ^ [_196281, _196283] : [_196283 = _196281, -(c_RComplete_Onatfloor(_196283) = c_RComplete_Onatfloor(_196281))], (972 ^ _166148) ^ [_196499, _196501] : [_196501 = _196499, -(c_RComplete_Onatceiling(_196501) = c_RComplete_Onatceiling(_196499))], (978 ^ _166148) ^ [_196745, _196747, _196749, _196751] : [-(c_RealDef_Oreal(_196751, _196747) = c_RealDef_Oreal(_196749, _196745)), _196751 = _196749, _196747 = _196745], (988 ^ _166148) ^ [_197104, _197106, _197108, _197110] : [-(c_Polynomial_Opoly(_197110, _197106) = c_Polynomial_Opoly(_197108, _197104)), _197110 = _197108, _197106 = _197104], (998 ^ _166148) ^ [_197463, _197465, _197467, _197469] : [-(c_Groups_Oabs__class_Oabs(_197469, _197465) = c_Groups_Oabs__class_Oabs(_197467, _197463)), _197469 = _197467, _197465 = _197463], (1008 ^ _166148) ^ [_197822, _197824, _197826, _197828] : [-(c_RealVector_Oof__real(_197828, _197824) = c_RealVector_Oof__real(_197826, _197822)), _197828 = _197826, _197824 = _197822], (1018 ^ _166148) ^ [_198181, _198183, _198185, _198187] : [-(c_Groups_Osgn__class_Osgn(_198187, _198183) = c_Groups_Osgn__class_Osgn(_198185, _198181)), _198187 = _198185, _198183 = _198181], (1028 ^ _166148) ^ [_198568, _198570, _198572, _198574, _198576, _198578] : [-(c_Polynomial_Oorder(_198578, _198574, _198570) = c_Polynomial_Oorder(_198576, _198572, _198568)), _198578 = _198576, _198574 = _198572, _198570 = _198568], (1042 ^ _166148) ^ [_199084, _199086, _199088, _199090, _199092, _199094] : [-(c_Polynomial_OpCons(_199094, _199090, _199086) = c_Polynomial_OpCons(_199092, _199088, _199084)), _199094 = _199092, _199090 = _199088, _199086 = _199084], (1056 ^ _166148) ^ [_199600, _199602, _199604, _199606, _199608, _199610] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_199610, _199606, _199602) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_199608, _199604, _199600)), _199610 = _199608, _199606 = _199604, _199602 = _199600], (1070 ^ _166148) ^ [_200088, _200090, _200092, _200094] : [-(c_Groups_Ouminus__class_Ouminus(_200094, _200090) = c_Groups_Ouminus__class_Ouminus(_200092, _200088)), _200094 = _200092, _200090 = _200088], (1080 ^ _166148) ^ [_200475, _200477, _200479, _200481, _200483, _200485] : [-(c_Groups_Ominus__class_Ominus(_200485, _200481, _200477) = c_Groups_Ominus__class_Ominus(_200483, _200479, _200475)), _200485 = _200483, _200481 = _200479, _200477 = _200475], (1094 ^ _166148) ^ [_200991, _200993, _200995, _200997, _200999, _201001] : [-(c_Polynomial_Osmult(_201001, _200997, _200993) = c_Polynomial_Osmult(_200999, _200995, _200991)), _201001 = _200999, _200997 = _200995, _200993 = _200991], (1108 ^ _166148) ^ [_201451, _201453] : [_201453 = _201451, -(c_Groups_Ozero__class_Ozero(_201453) = c_Groups_Ozero__class_Ozero(_201451))], (1114 ^ _166148) ^ [_201697, _201699, _201701, _201703] : [-(tc_fun(_201703, _201699) = tc_fun(_201701, _201697)), _201703 = _201701, _201699 = _201697], (1124 ^ _166148) ^ [_202028, _202030] : [_202030 = _202028, -(tc_Polynomial_Opoly(_202030) = tc_Polynomial_Opoly(_202028))], (1130 ^ _166148) ^ [_202274, _202276, _202278, _202280] : [-(c_RealVector_Onorm__class_Onorm(_202280, _202276) = c_RealVector_Onorm__class_Onorm(_202278, _202274)), _202280 = _202278, _202276 = _202274], (1140 ^ _166148) ^ [_202661, _202663, _202665, _202667, _202669, _202671] : [-(c_Groups_Oplus__class_Oplus(_202671, _202667, _202663) = c_Groups_Oplus__class_Oplus(_202669, _202665, _202661)), _202671 = _202669, _202667 = _202665, _202663 = _202661], (1154 ^ _166148) ^ [_203121, _203123] : [_203123 = _203121, -(c_Groups_Otimes__class_Otimes(_203123) = c_Groups_Otimes__class_Otimes(_203121))], (1160 ^ _166148) ^ [_203367, _203369, _203371, _203373] : [-(hAPP(_203373, _203369) = hAPP(_203371, _203367)), _203373 = _203371, _203369 = _203367], (1170 ^ _166148) ^ [_203698, _203700] : [_203700 = _203698, -(c_Power_Opower__class_Opower(_203700) = c_Power_Opower__class_Opower(_203698))], (1176 ^ _166148) ^ [_203896, _203898] : [_203898 = _203896, -(c_Groups_Oone__class_Oone(_203898) = c_Groups_Oone__class_Oone(_203896))], (2 ^ _166148) ^ [_166292] : [-(_166292 = _166292)], (4 ^ _166148) ^ [_166399, _166401] : [_166401 = _166399, -(_166399 = _166401)], (10 ^ _166148) ^ [_166603, _166605, _166607] : [-(_166607 = _166603), _166607 = _166605, _166605 = _166603], (20 ^ _166148) ^ [_166972, _166974, _166976, _166978, _166980, _166982] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_166980, _166976, _166972)), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_166982, _166978, _166974), _166982 = _166980, _166978 = _166976, _166974 = _166972], (38 ^ _166148) ^ [_167553, _167555, _167557, _167559] : [-(c_Polynomial_Opos__poly(_167557, _167553)), c_Polynomial_Opos__poly(_167559, _167555), _167559 = _167557, _167555 = _167553], (52 ^ _166148) ^ [_167997, _167999, _168001, _168003] : [-(c_SEQ_Odecseq(_168001, _167997)), c_SEQ_Odecseq(_168003, _167999), _168003 = _168001, _167999 = _167997], (66 ^ _166148) ^ [_168413, _168415] : [-(class_Lattices_Oab__semigroup__idem__mult(_168413)), _168415 = _168413, class_Lattices_Oab__semigroup__idem__mult(_168415)], (76 ^ _166148) ^ [_168764, _168766, _168768, _168770, _168772, _168774] : [-(c_Orderings_Oord__class_Oless__eq(_168772, _168768, _168764)), c_Orderings_Oord__class_Oless__eq(_168774, _168770, _168766), _168774 = _168772, _168770 = _168768, _168766 = _168764], (94 ^ _166148) ^ [_169317, _169319] : [-(hBOOL(_169317)), _169319 = _169317, hBOOL(_169319)], (104 ^ _166148) ^ [_169668, _169670, _169672, _169674, _169676, _169678] : [-(c_Rings_Odvd__class_Odvd(_169676, _169672, _169668)), c_Rings_Odvd__class_Odvd(_169678, _169674, _169670), _169678 = _169676, _169674 = _169672, _169670 = _169668], (122 ^ _166148) ^ [_170221, _170223] : [-(class_Lattices_Oboolean__algebra(_170221)), _170223 = _170221, class_Lattices_Oboolean__algebra(_170223)], (132 ^ _166148) ^ [_170516, _170518] : [-(class_Fields_Olinordered__field__inverse__zero(_170516)), _170518 = _170516, class_Fields_Olinordered__field__inverse__zero(_170518)], (142 ^ _166148) ^ [_170811, _170813] : [-(class_Fields_Olinordered__field(_170811)), _170813 = _170811, class_Fields_Olinordered__field(_170813)], (152 ^ _166148) ^ [_171106, _171108] : [-(class_RealVector_Oreal__normed__div__algebra(_171106)), _171108 = _171106, class_RealVector_Oreal__normed__div__algebra(_171108)], (162 ^ _166148) ^ [_171401, _171403] : [-(class_Rings_Odivision__ring__inverse__zero(_171401)), _171403 = _171401, class_Rings_Odivision__ring__inverse__zero(_171403)], (172 ^ _166148) ^ [_171696, _171698] : [-(class_RealVector_Oreal__normed__algebra__1(_171696)), _171698 = _171696, class_RealVector_Oreal__normed__algebra__1(_171698)], (182 ^ _166148) ^ [_171991, _171993] : [-(class_RealVector_Oreal__normed__algebra(_171991)), _171993 = _171991, class_RealVector_Oreal__normed__algebra(_171993)], (192 ^ _166148) ^ [_172286, _172288] : [-(class_RealVector_Oreal__normed__vector(_172286)), _172288 = _172286, class_RealVector_Oreal__normed__vector(_172288)], (202 ^ _166148) ^ [_172581, _172583] : [-(class_RealVector_Oreal__div__algebra(_172581)), _172583 = _172581, class_RealVector_Oreal__div__algebra(_172583)], (212 ^ _166148) ^ [_172876, _172878] : [-(class_RealVector_Oreal__algebra__1(_172876)), _172878 = _172876, class_RealVector_Oreal__algebra__1(_172878)], (222 ^ _166148) ^ [_173171, _173173] : [-(class_Fields_Ofield__inverse__zero(_173171)), _173173 = _173171, class_Fields_Ofield__inverse__zero(_173173)], (232 ^ _166148) ^ [_173466, _173468] : [-(class_Rings_Odivision__ring(_173466)), _173468 = _173466, class_Rings_Odivision__ring(_173468)], (242 ^ _166148) ^ [_173761, _173763] : [-(class_Fields_Ofield(_173761)), _173763 = _173761, class_Fields_Ofield(_173763)], (252 ^ _166148) ^ [_174056, _174058] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_174056)), _174058 = _174056, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_174058)], (262 ^ _166148) ^ [_174351, _174353] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_174351)), _174353 = _174351, class_Groups_Oordered__cancel__ab__semigroup__add(_174353)], (272 ^ _166148) ^ [_174646, _174648] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_174646)), _174648 = _174646, class_Groups_Oordered__ab__semigroup__add__imp__le(_174648)], (282 ^ _166148) ^ [_174941, _174943] : [-(class_Rings_Olinordered__comm__semiring__strict(_174941)), _174943 = _174941, class_Rings_Olinordered__comm__semiring__strict(_174943)], (292 ^ _166148) ^ [_175236, _175238] : [-(class_Rings_Olinordered__semiring__1__strict(_175236)), _175238 = _175236, class_Rings_Olinordered__semiring__1__strict(_175238)], (302 ^ _166148) ^ [_175531, _175533] : [-(class_Rings_Olinordered__semiring__strict(_175531)), _175533 = _175531, class_Rings_Olinordered__semiring__strict(_175533)], (312 ^ _166148) ^ [_175826, _175828] : [-(class_Groups_Oordered__ab__semigroup__add(_175826)), _175828 = _175826, class_Groups_Oordered__ab__semigroup__add(_175828)], (322 ^ _166148) ^ [_176121, _176123] : [-(class_Groups_Oordered__ab__group__add__abs(_176121)), _176123 = _176121, class_Groups_Oordered__ab__group__add__abs(_176123)], (332 ^ _166148) ^ [_176416, _176418] : [-(class_Groups_Oordered__comm__monoid__add(_176416)), _176418 = _176416, class_Groups_Oordered__comm__monoid__add(_176418)], (342 ^ _166148) ^ [_176711, _176713] : [-(class_Groups_Olinordered__ab__group__add(_176711)), _176713 = _176711, class_Groups_Olinordered__ab__group__add(_176713)], (352 ^ _166148) ^ [_177006, _177008] : [-(class_Groups_Ocancel__ab__semigroup__add(_177006)), _177008 = _177006, class_Groups_Ocancel__ab__semigroup__add(_177008)], (362 ^ _166148) ^ [_177301, _177303] : [-(class_Rings_Oring__1__no__zero__divisors(_177301)), _177303 = _177301, class_Rings_Oring__1__no__zero__divisors(_177303)], (372 ^ _166148) ^ [_177596, _177598] : [-(class_Rings_Oordered__cancel__semiring(_177596)), _177598 = _177596, class_Rings_Oordered__cancel__semiring(_177598)], (382 ^ _166148) ^ [_177891, _177893] : [-(class_Rings_Olinordered__ring__strict(_177891)), _177893 = _177891, class_Rings_Olinordered__ring__strict(_177893)], (392 ^ _166148) ^ [_178186, _178188] : [-(class_Rings_Oring__no__zero__divisors(_178186)), _178188 = _178186, class_Rings_Oring__no__zero__divisors(_178188)], (402 ^ _166148) ^ [_178481, _178483] : [-(class_Rings_Oordered__comm__semiring(_178481)), _178483 = _178481, class_Rings_Oordered__comm__semiring(_178483)], (412 ^ _166148) ^ [_178776, _178778] : [-(class_Rings_Olinordered__semiring__1(_178776)), _178778 = _178776, class_Rings_Olinordered__semiring__1(_178778)], (422 ^ _166148) ^ [_179071, _179073] : [-(class_Groups_Oordered__ab__group__add(_179071)), _179073 = _179071, class_Groups_Oordered__ab__group__add(_179073)], (432 ^ _166148) ^ [_179366, _179368] : [-(class_Groups_Ocancel__comm__monoid__add(_179366)), _179368 = _179366, class_Groups_Ocancel__comm__monoid__add(_179368)], (442 ^ _166148) ^ [_179661, _179663] : [-(class_Groups_Ocancel__semigroup__add(_179661)), _179663 = _179661, class_Groups_Ocancel__semigroup__add(_179663)], (452 ^ _166148) ^ [_179956, _179958] : [-(class_Rings_Olinordered__semiring(_179956)), _179958 = _179956, class_Rings_Olinordered__semiring(_179958)], (462 ^ _166148) ^ [_180251, _180253] : [-(class_Rings_Olinordered__semidom(_180251)), _180253 = _180251, class_Rings_Olinordered__semidom(_180253)], (472 ^ _166148) ^ [_180546, _180548] : [-(class_Groups_Oab__semigroup__mult(_180546)), _180548 = _180546, class_Groups_Oab__semigroup__mult(_180548)], (482 ^ _166148) ^ [_180841, _180843] : [-(class_Groups_Ocomm__monoid__mult(_180841)), _180843 = _180841, class_Groups_Ocomm__monoid__mult(_180843)], (492 ^ _166148) ^ [_181136, _181138] : [-(class_Groups_Oab__semigroup__add(_181136)), _181138 = _181136, class_Groups_Oab__semigroup__add(_181138)], (502 ^ _166148) ^ [_181431, _181433] : [-(class_Rings_Oordered__semiring(_181431)), _181433 = _181431, class_Rings_Oordered__semiring(_181433)], (512 ^ _166148) ^ [_181726, _181728] : [-(class_Rings_Oordered__ring__abs(_181726)), _181728 = _181726, class_Rings_Oordered__ring__abs(_181728)], (522 ^ _166148) ^ [_182021, _182023] : [-(class_Rings_Ono__zero__divisors(_182021)), _182023 = _182021, class_Rings_Ono__zero__divisors(_182023)], (532 ^ _166148) ^ [_182316, _182318] : [-(class_Rings_Olinordered__ring(_182316)), _182318 = _182316, class_Rings_Olinordered__ring(_182318)], (542 ^ _166148) ^ [_182611, _182613] : [-(class_Rings_Ocomm__semiring(_182611)), _182613 = _182611, class_Rings_Ocomm__semiring(_182613)], (552 ^ _166148) ^ [_182906, _182908] : [-(class_Rings_Ozero__neq__one(_182906)), _182908 = _182906, class_Rings_Ozero__neq__one(_182908)], (562 ^ _166148) ^ [_183201, _183203] : [-(class_Rings_Oordered__ring(_183201)), _183203 = _183201, class_Rings_Oordered__ring(_183203)], (572 ^ _166148) ^ [_183496, _183498] : [-(class_Orderings_Opreorder(_183496)), _183498 = _183496, class_Orderings_Opreorder(_183498)], (582 ^ _166148) ^ [_183791, _183793] : [-(class_Orderings_Olinorder(_183791)), _183793 = _183791, class_Orderings_Olinorder(_183793)], (592 ^ _166148) ^ [_184086, _184088] : [-(class_Groups_Omonoid__mult(_184086)), _184088 = _184086, class_Groups_Omonoid__mult(_184088)], (602 ^ _166148) ^ [_184381, _184383] : [-(class_Groups_Ocomm__monoid__add(_184381)), _184383 = _184381, class_Groups_Ocomm__monoid__add(_184383)], (612 ^ _166148) ^ [_184676, _184678] : [-(class_Groups_Omonoid__add(_184676)), _184678 = _184676, class_Groups_Omonoid__add(_184678)], (622 ^ _166148) ^ [_184971, _184973] : [-(class_Rings_Osemiring__0(_184971)), _184973 = _184971, class_Rings_Osemiring__0(_184973)], (632 ^ _166148) ^ [_185266, _185268] : [-(class_Groups_Ogroup__add(_185266)), _185268 = _185266, class_Groups_Ogroup__add(_185268)], (642 ^ _166148) ^ [_185561, _185563] : [-(class_Rings_Omult__zero(_185561)), _185563 = _185561, class_Rings_Omult__zero(_185563)], (652 ^ _166148) ^ [_185856, _185858] : [-(class_Orderings_Oorder(_185856)), _185858 = _185856, class_Orderings_Oorder(_185858)], (662 ^ _166148) ^ [_186151, _186153] : [-(class_Int_Oring__char__0(_186151)), _186153 = _186151, class_Int_Oring__char__0(_186153)], (672 ^ _166148) ^ [_186446, _186448] : [-(class_Rings_Ocomm__semiring__0(_186446)), _186448 = _186446, class_Rings_Ocomm__semiring__0(_186448)], (682 ^ _166148) ^ [_186741, _186743] : [-(class_Rings_Osemiring(_186741)), _186743 = _186741, class_Rings_Osemiring(_186743)], (692 ^ _166148) ^ [_187036, _187038] : [-(class_Orderings_Oord(_187036)), _187038 = _187036, class_Orderings_Oord(_187038)], (702 ^ _166148) ^ [_187331, _187333] : [-(class_Groups_Ouminus(_187331)), _187333 = _187331, class_Groups_Ouminus(_187333)], (712 ^ _166148) ^ [_187626, _187628] : [-(class_Groups_Osgn__if(_187626)), _187628 = _187626, class_Groups_Osgn__if(_187628)], (722 ^ _166148) ^ [_187921, _187923] : [-(class_Rings_Olinordered__idom(_187921)), _187923 = _187921, class_Rings_Olinordered__idom(_187923)], (732 ^ _166148) ^ [_188216, _188218] : [-(class_Groups_Oabs__if(_188216)), _188218 = _188216, class_Groups_Oabs__if(_188218)], (742 ^ _166148) ^ [_188511, _188513] : [-(class_Rings_Ocomm__ring__1(_188511)), _188513 = _188511, class_Rings_Ocomm__ring__1(_188513)], (752 ^ _166148) ^ [_188806, _188808] : [-(class_Rings_Oring__1(_188806)), _188808 = _188806, class_Rings_Oring__1(_188808)], (762 ^ _166148) ^ [_189101, _189103] : [-(class_Groups_Oab__group__add(_189101)), _189103 = _189101, class_Groups_Oab__group__add(_189103)], (772 ^ _166148) ^ [_189396, _189398] : [-(class_Groups_Ominus(_189396)), _189398 = _189396, class_Groups_Ominus(_189398)], (782 ^ _166148) ^ [_189691, _189693] : [-(class_Power_Opower(_189691)), _189693 = _189691, class_Power_Opower(_189693)], (792 ^ _166148) ^ [_189986, _189988] : [-(class_Groups_Ozero(_189986)), _189988 = _189986, class_Groups_Ozero(_189988)], (802 ^ _166148) ^ [_190281, _190283] : [-(class_Rings_Ocomm__ring(_190281)), _190283 = _190281, class_Rings_Ocomm__ring(_190283)], (812 ^ _166148) ^ [_190576, _190578] : [-(class_Rings_Oring(_190576)), _190578 = _190576, class_Rings_Oring(_190578)], (822 ^ _166148) ^ [_190871, _190873] : [-(class_Rings_Oidom(_190871)), _190873 = _190871, class_Rings_Oidom(_190873)], (832 ^ _166148) ^ [_191166, _191168] : [-(class_Groups_Oone(_191166)), _191168 = _191166, class_Groups_Oone(_191168)], (842 ^ _166148) ^ [_191461, _191463] : [-(class_Rings_Ocomm__semiring__1(_191461)), _191463 = _191461, class_Rings_Ocomm__semiring__1(_191463)], (852 ^ _166148) ^ [_191756, _191758] : [-(class_Rings_Odvd(_191756)), _191758 = _191756, class_Rings_Odvd(_191758)], (862 ^ _166148) ^ [_192087, _192089, _192091, _192093, _192095, _192097] : [-(c_Orderings_Oord__class_Oless(_192095, _192091, _192087)), c_Orderings_Oord__class_Oless(_192097, _192093, _192089), _192097 = _192095, _192093 = _192091, _192089 = _192087], (1182 ^ _166148) ^ [_204300, _204302] : [hAPP(_204300, 1183 ^ [_204300, _204302]) = hAPP(_204302, 1183 ^ [_204300, _204302]), -(_204300 = _204302)], (1189 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_t____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1191 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))], (1193 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1195 ^ _166148) ^ [] : [v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1197 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_t____))], (1199 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_m____))], (1201 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_t____, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (1203 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____))))], (1205 ^ _166148) ^ [_205057, _205059, _205061, _205063, _205065] : [class_RealVector_Oreal__normed__algebra(_205057), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_205057, _205059), _205061), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_205057, _205063), _205065), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_205057, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_205057), _205059), _205063)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _205061), _205065)))], (1219 ^ _166148) ^ [_205551, _205553, _205555] : [class_Rings_Olinordered__semidom(_205551), c_Orderings_Oord__class_Oless(_205551, c_Groups_Oone__class_Oone(_205551), _205553), -(c_Orderings_Oord__class_Oless(_205551, c_Groups_Oone__class_Oone(_205551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_205551), _205553), hAPP(hAPP(c_Power_Opower__class_Opower(_205551), _205553), _205555))))], (1229 ^ _166148) ^ [_205916, _205918, _205920] : [class_Rings_Olinordered__semidom(_205916), c_Orderings_Oord__class_Oless(_205916, c_Groups_Oone__class_Oone(_205916), _205918), -(c_Orderings_Oord__class_Oless(_205916, hAPP(hAPP(c_Power_Opower__class_Opower(_205916), _205918), _205920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_205916), _205918), hAPP(hAPP(c_Power_Opower__class_Opower(_205916), _205918), _205920))))], (1239 ^ _166148) ^ [_206293, _206295, _206297] : [class_RealVector_Oreal__normed__div__algebra(_206293), -(c_RealVector_Onorm__class_Onorm(_206293, hAPP(hAPP(c_Power_Opower__class_Opower(_206293), _206295), _206297)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_206293, _206295)), _206297))], (1245 ^ _166148) ^ [_206533] : [class_RealVector_Oreal__normed__algebra__1(_206533), -(c_RealVector_Onorm__class_Onorm(_206533, c_Groups_Oone__class_Oone(_206533)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (1251 ^ _166148) ^ [_206759, _206761, _206763] : [class_RealVector_Oreal__normed__div__algebra(_206759), -(c_RealVector_Onorm__class_Onorm(_206759, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_206759), _206761), _206763)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_206759, _206761)), c_RealVector_Onorm__class_Onorm(_206759, _206763)))], (1257 ^ _166148) ^ [_207061, _207063, _207065, _207067, _207069] : [class_RealVector_Oreal__normed__vector(_207061), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_207061, _207063), _207065), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_207061, _207067), _207069), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_207061, c_Groups_Oplus__class_Oplus(_207061, _207063, _207067)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _207065, _207069)))], (1271 ^ _166148) ^ [_207557, _207559, _207561, _207563] : [class_Groups_Omonoid__mult(_207557), -(hAPP(hAPP(c_Power_Opower__class_Opower(_207557), _207559), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _207561, _207563)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207557), hAPP(hAPP(c_Power_Opower__class_Opower(_207557), _207559), _207561)), hAPP(hAPP(c_Power_Opower__class_Opower(_207557), _207559), _207563)))], (1277 ^ _166148) ^ [_207877, _207879, _207881, _207883] : [class_Rings_Ocomm__semiring__1(_207877), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207877), hAPP(hAPP(c_Power_Opower__class_Opower(_207877), _207879), _207881)), hAPP(hAPP(c_Power_Opower__class_Opower(_207877), _207879), _207883)) = hAPP(hAPP(c_Power_Opower__class_Opower(_207877), _207879), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _207881, _207883)))], (1283 ^ _166148) ^ [_208197, _208199, _208201, _208203] : [class_Rings_Olinordered__semidom(_208197), c_Orderings_Oord__class_Oless(_208197, c_Groups_Oone__class_Oone(_208197), _208199), 1290 ^ _166148 : [(1291 ^ _166148) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_208197), _208199), _208201) = hAPP(hAPP(c_Power_Opower__class_Opower(_208197), _208199), _208203), -(_208201 = _208203)], (1297 ^ _166148) ^ [] : [_208201 = _208203, -(hAPP(hAPP(c_Power_Opower__class_Opower(_208197), _208199), _208201) = hAPP(hAPP(c_Power_Opower__class_Opower(_208197), _208199), _208203))]]], (1303 ^ _166148) ^ [_208866, _208868, _208870, _208872] : [class_Rings_Olinordered__semidom(_208866), c_Orderings_Oord__class_Oless(_208866, c_Groups_Oone__class_Oone(_208866), _208868), 1310 ^ _166148 : [(1311 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_208866, hAPP(hAPP(c_Power_Opower__class_Opower(_208866), _208868), _208870), hAPP(hAPP(c_Power_Opower__class_Opower(_208866), _208868), _208872)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _208870, _208872))], (1317 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _208870, _208872), -(c_Orderings_Oord__class_Oless(_208866, hAPP(hAPP(c_Power_Opower__class_Opower(_208866), _208868), _208870), hAPP(hAPP(c_Power_Opower__class_Opower(_208866), _208868), _208872)))]]], (1323 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (1325 ^ _166148) ^ [_209566, _209568] : [class_RealVector_Oreal__normed__vector(_209566), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_209566, _209568)))], (1331 ^ _166148) ^ [_209768] : [class_RealVector_Oreal__normed__vector(_209768), -(c_RealVector_Onorm__class_Onorm(_209768, c_Groups_Ozero__class_Ozero(_209768)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1337 ^ _166148) ^ [_209965, _209967] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _209965), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _209965, _209967)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _209967))))], (1339 ^ _166148) ^ [_210092, _210094] : [-(c_RealVector_Onorm__class_Onorm(_210092, c_Rings_Oinverse__class_Oinverse(_210092, _210094)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_210092, _210094))), class_RealVector_Oreal__normed__div__algebra(_210092), class_Rings_Odivision__ring__inverse__zero(_210092)], (1359 ^ _166148) ^ [_210708, _210710] : [1360 ^ _166148 : [(1361 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _210708)], (1363 ^ _166148) ^ [] : [_210710 = 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), _210708), _210710)))], (1349 ^ _166148) ^ [_210440, _210442] : [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), _210440), _210442)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _210440)), -(_210442 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1367 ^ _166148) ^ [_211010, _211012] : [class_RealVector_Oreal__normed__vector(_211010), 1370 ^ _166148 : [(1371 ^ _166148) ^ [] : [c_RealVector_Onorm__class_Onorm(_211010, _211012) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_211012 = c_Groups_Ozero__class_Ozero(_211010))], (1377 ^ _166148) ^ [] : [_211012 = c_Groups_Ozero__class_Ozero(_211010), -(c_RealVector_Onorm__class_Onorm(_211010, _211012) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1383 ^ _166148) ^ [_211483, _211485] : [class_RealVector_Oreal__normed__vector(_211483), 1386 ^ _166148 : [(1387 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_211483, _211485), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_211485 = c_Groups_Ozero__class_Ozero(_211483))], (1393 ^ _166148) ^ [] : [_211485 = c_Groups_Ozero__class_Ozero(_211483), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_211483, _211485), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (1399 ^ _166148) ^ [_211973, _211975, _211977] : [class_Power_Opower(_211973), class_Rings_Omult__zero(_211973), class_Rings_Ono__zero__divisors(_211973), class_Rings_Ozero__neq__one(_211973), 1414 ^ _166148 : [(1415 ^ _166148) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_211973), _211975), _211977) = c_Groups_Ozero__class_Ozero(_211973), 1418 ^ _166148 : [(1419 ^ _166148) ^ [] : [-(_211975 = c_Groups_Ozero__class_Ozero(_211973))], (1421 ^ _166148) ^ [] : [_211977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (1423 ^ _166148) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_211973), _211975), _211977) = c_Groups_Ozero__class_Ozero(_211973)), _211975 = c_Groups_Ozero__class_Ozero(_211973), -(_211977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (1433 ^ _166148) ^ [_212928, _212930] : [class_RealVector_Oreal__normed__div__algebra(_212928), -(_212930 = c_Groups_Ozero__class_Ozero(_212928)), -(c_RealVector_Onorm__class_Onorm(_212928, c_Rings_Oinverse__class_Oinverse(_212928, _212930)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_212928, _212930)))], (1443 ^ _166148) ^ [_213270, _213272, _213274] : [class_Rings_Odivision__ring(_213270), -(_213272 = c_Groups_Ozero__class_Ozero(_213270)), -(c_Rings_Oinverse__class_Oinverse(_213270, hAPP(hAPP(c_Power_Opower__class_Opower(_213270), _213272), _213274)) = hAPP(hAPP(c_Power_Opower__class_Opower(_213270), c_Rings_Oinverse__class_Oinverse(_213270, _213272)), _213274))], (1453 ^ _166148) ^ [_213642, _213644, _213646] : [class_Rings_Olinordered__semidom(_213642), c_Orderings_Oord__class_Oless__eq(_213642, c_Groups_Ozero__class_Ozero(_213642), _213644), -(c_Orderings_Oord__class_Oless__eq(_213642, c_Groups_Ozero__class_Ozero(_213642), hAPP(hAPP(c_Power_Opower__class_Opower(_213642), _213644), _213646)))], (1463 ^ _166148) ^ [_213991, _213993, _213995] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _213991), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _213991), _213993), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _213991), _213995)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _213993, _213995))], (1473 ^ _166148) ^ [_214358, _214360, _214362, _214364] : [class_Rings_Olinordered__semidom(_214358), c_Orderings_Oord__class_Oless__eq(_214358, _214360, _214362), c_Orderings_Oord__class_Oless__eq(_214358, c_Groups_Ozero__class_Ozero(_214358), _214360), -(c_Orderings_Oord__class_Oless__eq(_214358, hAPP(hAPP(c_Power_Opower__class_Opower(_214358), _214360), _214364), hAPP(hAPP(c_Power_Opower__class_Opower(_214358), _214362), _214364)))], (1487 ^ _166148) ^ [_214842, _214844, _214846, _214848] : [class_Rings_Olinordered__semidom(_214842), hAPP(hAPP(c_Power_Opower__class_Opower(_214842), _214844), _214846) = hAPP(hAPP(c_Power_Opower__class_Opower(_214842), _214848), _214846), c_Orderings_Oord__class_Oless__eq(_214842, c_Groups_Ozero__class_Ozero(_214842), _214844), c_Orderings_Oord__class_Oless__eq(_214842, c_Groups_Ozero__class_Ozero(_214842), _214848), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _214846), -(_214844 = _214848)], (1509 ^ _166148) ^ [_215524, _215526, _215528, _215530] : [class_Rings_Olinordered__semidom(_215524), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _215526, _215528), c_Orderings_Oord__class_Oless__eq(_215524, c_Groups_Ozero__class_Ozero(_215524), _215530), c_Orderings_Oord__class_Oless__eq(_215524, _215530, c_Groups_Oone__class_Oone(_215524)), -(c_Orderings_Oord__class_Oless__eq(_215524, hAPP(hAPP(c_Power_Opower__class_Opower(_215524), _215530), _215528), hAPP(hAPP(c_Power_Opower__class_Opower(_215524), _215530), _215526)))], (1527 ^ _166148) ^ [_216111, _216113, _216115, _216117] : [class_Rings_Olinordered__semidom(_216111), c_Orderings_Oord__class_Oless(_216111, _216113, _216115), c_Orderings_Oord__class_Oless__eq(_216111, c_Groups_Ozero__class_Ozero(_216111), _216113), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _216117), -(c_Orderings_Oord__class_Oless(_216111, hAPP(hAPP(c_Power_Opower__class_Opower(_216111), _216113), _216117), hAPP(hAPP(c_Power_Opower__class_Opower(_216111), _216115), _216117)))], (1545 ^ _166148) ^ [_216680, _216682, _216684] : [class_Rings_Odivision__ring__inverse__zero(_216680), -(c_Rings_Oinverse__class_Oinverse(_216680, hAPP(hAPP(c_Power_Opower__class_Opower(_216680), _216682), _216684)) = hAPP(hAPP(c_Power_Opower__class_Opower(_216680), c_Rings_Oinverse__class_Oinverse(_216680, _216682)), _216684))], (1551 ^ _166148) ^ [_216966, _216968, _216970, _216972] : [class_Rings_Ocomm__semiring__1(_216966), -(hAPP(hAPP(c_Power_Opower__class_Opower(_216966), hAPP(hAPP(c_Power_Opower__class_Opower(_216966), _216968), _216970)), _216972) = hAPP(hAPP(c_Power_Opower__class_Opower(_216966), _216968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _216970), _216972)))], (1557 ^ _166148) ^ [_217274, _217276, _217278, _217280] : [class_Groups_Omonoid__mult(_217274), -(hAPP(hAPP(c_Power_Opower__class_Opower(_217274), _217276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _217278), _217280)) = hAPP(hAPP(c_Power_Opower__class_Opower(_217274), hAPP(hAPP(c_Power_Opower__class_Opower(_217274), _217276), _217278)), _217280))], (1563 ^ _166148) ^ [_217554, _217556] : [class_RealVector_Oreal__normed__algebra(_217554), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_217554), _217556), c_Groups_Ozero__class_Ozero(_217554)) = c_Groups_Ozero__class_Ozero(_217554))], (1569 ^ _166148) ^ [_217786, _217788] : [class_RealVector_Oreal__normed__algebra(_217786), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_217786), _217788), c_Groups_Ozero__class_Ozero(_217786)) = c_Groups_Ozero__class_Ozero(_217786))], (1575 ^ _166148) ^ [_218018, _218020] : [class_Rings_Ocomm__semiring__1(_218018), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_218018), _218020), c_Groups_Ozero__class_Ozero(_218018)) = c_Groups_Ozero__class_Ozero(_218018))], (1581 ^ _166148) ^ [_218250, _218252] : [class_RealVector_Oreal__normed__algebra(_218250), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_218250), c_Groups_Ozero__class_Ozero(_218250)), _218252) = c_Groups_Ozero__class_Ozero(_218250))], (1587 ^ _166148) ^ [_218482, _218484] : [class_RealVector_Oreal__normed__algebra(_218482), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_218482), c_Groups_Ozero__class_Ozero(_218482)), _218484) = c_Groups_Ozero__class_Ozero(_218482))], (1593 ^ _166148) ^ [_218714, _218716] : [class_Rings_Ocomm__semiring__1(_218714), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_218714), c_Groups_Ozero__class_Ozero(_218714)), _218716) = c_Groups_Ozero__class_Ozero(_218714))], (1599 ^ _166148) ^ [_218960, _218962, _218964] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_218960), 1602 ^ _166148 : [(1603 ^ _166148) ^ [] : [_218962 = c_Groups_Oplus__class_Oplus(_218960, _218962, _218964), -(_218964 = c_Groups_Ozero__class_Ozero(_218960))], (1609 ^ _166148) ^ [] : [_218964 = c_Groups_Ozero__class_Ozero(_218960), -(_218962 = c_Groups_Oplus__class_Oplus(_218960, _218962, _218964))]]], (1615 ^ _166148) ^ [_219452, _219454] : [class_Rings_Ocomm__semiring__1(_219452), -(c_Groups_Oplus__class_Oplus(_219452, _219454, c_Groups_Ozero__class_Ozero(_219452)) = _219454)], (1621 ^ _166148) ^ [_219672, _219674] : [class_Rings_Ocomm__semiring__1(_219672), -(c_Groups_Oplus__class_Oplus(_219672, c_Groups_Ozero__class_Ozero(_219672), _219674) = _219674)], (1627 ^ _166148) ^ [_219906, _219908, _219910] : [class_Rings_Oring__1__no__zero__divisors(_219906), -(_219908 = c_Groups_Ozero__class_Ozero(_219906)), hAPP(hAPP(c_Power_Opower__class_Opower(_219906), _219908), _219910) = c_Groups_Ozero__class_Ozero(_219906)], (1637 ^ _166148) ^ [_220269, _220271, _220273, _220275] : [class_Rings_Olinordered__semidom(_220269), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _220271, _220273), c_Orderings_Oord__class_Oless__eq(_220269, c_Groups_Oone__class_Oone(_220269), _220275), -(c_Orderings_Oord__class_Oless__eq(_220269, hAPP(hAPP(c_Power_Opower__class_Opower(_220269), _220275), _220271), hAPP(hAPP(c_Power_Opower__class_Opower(_220269), _220275), _220273)))], (1651 ^ _166148) ^ [_220753, _220755, _220757, _220759] : [class_Rings_Olinordered__semidom(_220753), c_Orderings_Oord__class_Oless(_220753, hAPP(hAPP(c_Power_Opower__class_Opower(_220753), _220755), _220757), hAPP(hAPP(c_Power_Opower__class_Opower(_220753), _220759), _220757)), c_Orderings_Oord__class_Oless__eq(_220753, c_Groups_Ozero__class_Ozero(_220753), _220759), -(c_Orderings_Oord__class_Oless(_220753, _220755, _220759))], (1665 ^ _166148) ^ [_221209, _221211] : [class_Power_Opower(_221209), class_Rings_Osemiring__0(_221209), 1672 ^ _166148 : [(1673 ^ _166148) ^ [] : [_221211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_221209), c_Groups_Ozero__class_Ozero(_221209)), _221211) = c_Groups_Oone__class_Oone(_221209))], (1679 ^ _166148) ^ [] : [-(_221211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_221209), c_Groups_Ozero__class_Ozero(_221209)), _221211) = c_Groups_Ozero__class_Ozero(_221209))]]], (1685 ^ _166148) ^ [_221810, _221812] : [class_RealVector_Oreal__normed__vector(_221810), 1688 ^ _166148 : [(1689 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_221810, _221812)), _221812 = c_Groups_Ozero__class_Ozero(_221810)], (1695 ^ _166148) ^ [] : [-(_221812 = c_Groups_Ozero__class_Ozero(_221810)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_221810, _221812)))]]], (1701 ^ _166148) ^ [_222316, _222318, _222320, _222322] : [class_Rings_Olinordered__semidom(_222316), c_Orderings_Oord__class_Oless(_222316, c_Groups_Oone__class_Oone(_222316), _222318), c_Orderings_Oord__class_Oless__eq(_222316, hAPP(hAPP(c_Power_Opower__class_Opower(_222316), _222318), _222320), hAPP(hAPP(c_Power_Opower__class_Opower(_222316), _222318), _222322)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _222320, _222322))], (1715 ^ _166148) ^ [_222800, _222802, _222804, _222806] : [class_Rings_Olinordered__semidom(_222800), c_Orderings_Oord__class_Oless(_222800, c_Groups_Oone__class_Oone(_222800), _222802), 1722 ^ _166148 : [(1723 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_222800, hAPP(hAPP(c_Power_Opower__class_Opower(_222800), _222802), _222804), hAPP(hAPP(c_Power_Opower__class_Opower(_222800), _222802), _222806)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _222804, _222806))], (1729 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _222804, _222806), -(c_Orderings_Oord__class_Oless__eq(_222800, hAPP(hAPP(c_Power_Opower__class_Opower(_222800), _222802), _222804), hAPP(hAPP(c_Power_Opower__class_Opower(_222800), _222802), _222806)))]]], (1735 ^ _166148) ^ [_223461, _223463, _223465] : [class_Rings_Olinordered__semidom(_223461), c_Orderings_Oord__class_Oless__eq(_223461, c_Groups_Oone__class_Oone(_223461), _223463), -(c_Orderings_Oord__class_Oless__eq(_223461, c_Groups_Oone__class_Oone(_223461), hAPP(hAPP(c_Power_Opower__class_Opower(_223461), _223463), _223465)))], (1745 ^ _166148) ^ [_223852, _223854, _223856, _223858, _223860, _223862] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_223852), -(_223854 = c_Groups_Ozero__class_Ozero(_223852)), c_Groups_Oplus__class_Oplus(_223852, _223856, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223852), _223854), _223860)) = c_Groups_Oplus__class_Oplus(_223852, _223858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223852), _223854), _223862)), _223856 = _223858, -(_223860 = _223862)], (1763 ^ _166148) ^ [_224472, _224474, _224476] : [class_RealVector_Oreal__normed__vector(_224472), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_224472, c_Groups_Oplus__class_Oplus(_224472, _224474, _224476)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_224472, _224474), c_RealVector_Onorm__class_Onorm(_224472, _224476))))], (1769 ^ _166148) ^ [_224736, _224738, _224740] : [class_Rings_Olinordered__semidom(_224736), c_Orderings_Oord__class_Oless(_224736, c_Groups_Ozero__class_Ozero(_224736), _224738), -(c_Orderings_Oord__class_Oless(_224736, c_Groups_Ozero__class_Ozero(_224736), hAPP(hAPP(c_Power_Opower__class_Opower(_224736), _224738), _224740)))], (1779 ^ _166148) ^ [_225071, _225073] : [class_Rings_Ocomm__semiring__1(_225071), -(hAPP(hAPP(c_Power_Opower__class_Opower(_225071), _225073), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_225071))], (1785 ^ _166148) ^ [_225299, _225301] : [class_Power_Opower(_225299), -(hAPP(hAPP(c_Power_Opower__class_Opower(_225299), _225301), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_225299))], (1791 ^ _166148) ^ [_225527, _225529] : [class_RealVector_Oreal__normed__vector(_225527), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_225527, _225529), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1797 ^ _166148) ^ [_225772, _225774, _225776, _225778] : [class_Rings_Olinordered__semidom(_225772), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _225774, _225776), c_Orderings_Oord__class_Oless(_225772, c_Groups_Ozero__class_Ozero(_225772), _225778), c_Orderings_Oord__class_Oless(_225772, _225778, c_Groups_Oone__class_Oone(_225772)), -(c_Orderings_Oord__class_Oless(_225772, hAPP(hAPP(c_Power_Opower__class_Opower(_225772), _225778), _225776), hAPP(hAPP(c_Power_Opower__class_Opower(_225772), _225778), _225774)))], (1815 ^ _166148) ^ [_226345, _226347, _226349] : [class_RealVector_Oreal__normed__algebra(_226345), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_226345, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226345), _226347), _226349)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_226345, _226347)), c_RealVector_Onorm__class_Onorm(_226345, _226349))))], (1821 ^ _166148) ^ [_226621, _226623, _226625] : [class_Rings_Olinordered__semidom(_226621), c_Orderings_Oord__class_Oless(_226621, c_Groups_Oone__class_Oone(_226621), _226623), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _226625), -(c_Orderings_Oord__class_Oless(_226621, c_Groups_Oone__class_Oone(_226621), hAPP(hAPP(c_Power_Opower__class_Opower(_226621), _226623), _226625)))], (1835 ^ _166148) ^ [_227065, _227067, _227069] : [class_RealVector_Oreal__normed__algebra__1(_227065), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_227065, hAPP(hAPP(c_Power_Opower__class_Opower(_227065), _227067), _227069)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_227065, _227067)), _227069)))], (1841 ^ _166148) ^ [_227335, _227337, _227339] : [class_Rings_Olinordered__semidom(_227335), c_Orderings_Oord__class_Oless(_227335, c_Groups_Ozero__class_Ozero(_227335), _227337), c_Orderings_Oord__class_Oless(_227335, _227337, c_Groups_Oone__class_Oone(_227335)), -(c_Orderings_Oord__class_Oless(_227335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227335), _227337), hAPP(hAPP(c_Power_Opower__class_Opower(_227335), _227337), _227339)), hAPP(hAPP(c_Power_Opower__class_Opower(_227335), _227337), _227339)))], (1855 ^ _166148) ^ [_227839, _227841, _227843, _227845, _227847] : [class_Rings_Ocomm__semiring__1(_227839), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227839), _227841), _227843)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227839), _227845), _227847)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227839), _227841), _227845)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227839), _227843), _227847)))], (1861 ^ _166148) ^ [_228203, _228205, _228207, _228209, _228211] : [class_Rings_Ocomm__semiring__1(_228203), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228203), _228205), _228207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228203), _228209), _228211)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228203), _228209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228203), _228205), _228207)), _228211)))], (1867 ^ _166148) ^ [_228567, _228569, _228571, _228573, _228575] : [class_Rings_Ocomm__semiring__1(_228567), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228567), _228569), _228571)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228567), _228573), _228575)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228567), _228569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228567), _228571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228567), _228573), _228575))))], (1873 ^ _166148) ^ [_228917, _228919, _228921, _228923] : [class_Rings_Ocomm__semiring__1(_228917), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228917), _228919), _228921)), _228923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228917), _228919), _228923)), _228921))], (1879 ^ _166148) ^ [_229229, _229231, _229233, _229235] : [class_Rings_Ocomm__semiring__1(_229229), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229229), _229231), _229233)), _229235) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229229), _229231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229229), _229233), _229235)))], (1885 ^ _166148) ^ [_229541, _229543, _229545, _229547] : [class_Rings_Ocomm__semiring__1(_229541), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229541), _229543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229541), _229545), _229547)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229541), _229543), _229545)), _229547))], (1891 ^ _166148) ^ [_229853, _229855, _229857, _229859] : [class_Rings_Ocomm__semiring__1(_229853), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229853), _229855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229853), _229857), _229859)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229853), _229857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229853), _229855), _229859)))], (1897 ^ _166148) ^ [_230151, _230153, _230155] : [class_Rings_Ocomm__semiring__1(_230151), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_230151), _230153), _230155) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_230151), _230155), _230153))], (1903 ^ _166148) ^ [_230439, _230441, _230443, _230445, _230447] : [class_Rings_Ocomm__semiring__1(_230439), -(c_Groups_Oplus__class_Oplus(_230439, c_Groups_Oplus__class_Oplus(_230439, _230441, _230443), c_Groups_Oplus__class_Oplus(_230439, _230445, _230447)) = c_Groups_Oplus__class_Oplus(_230439, c_Groups_Oplus__class_Oplus(_230439, _230441, _230445), c_Groups_Oplus__class_Oplus(_230439, _230443, _230447)))], (1909 ^ _166148) ^ [_230741, _230743, _230745, _230747] : [class_Rings_Ocomm__semiring__1(_230741), -(c_Groups_Oplus__class_Oplus(_230741, c_Groups_Oplus__class_Oplus(_230741, _230743, _230745), _230747) = c_Groups_Oplus__class_Oplus(_230741, c_Groups_Oplus__class_Oplus(_230741, _230743, _230747), _230745))], (1915 ^ _166148) ^ [_231021, _231023, _231025, _231027] : [class_Rings_Ocomm__semiring__1(_231021), -(c_Groups_Oplus__class_Oplus(_231021, c_Groups_Oplus__class_Oplus(_231021, _231023, _231025), _231027) = c_Groups_Oplus__class_Oplus(_231021, _231023, c_Groups_Oplus__class_Oplus(_231021, _231025, _231027)))], (1921 ^ _166148) ^ [_231301, _231303, _231305, _231307] : [class_Rings_Ocomm__semiring__1(_231301), -(c_Groups_Oplus__class_Oplus(_231301, _231303, c_Groups_Oplus__class_Oplus(_231301, _231305, _231307)) = c_Groups_Oplus__class_Oplus(_231301, c_Groups_Oplus__class_Oplus(_231301, _231303, _231305), _231307))], (1927 ^ _166148) ^ [_231581, _231583, _231585, _231587] : [class_Rings_Ocomm__semiring__1(_231581), -(c_Groups_Oplus__class_Oplus(_231581, _231583, c_Groups_Oplus__class_Oplus(_231581, _231585, _231587)) = c_Groups_Oplus__class_Oplus(_231581, _231585, c_Groups_Oplus__class_Oplus(_231581, _231583, _231587)))], (1933 ^ _166148) ^ [_231847, _231849, _231851] : [class_Rings_Ocomm__semiring__1(_231847), -(c_Groups_Oplus__class_Oplus(_231847, _231849, _231851) = c_Groups_Oplus__class_Oplus(_231847, _231851, _231849))], (1939 ^ _166148) ^ [_232119, _232121, _232123, _232125, _232127] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_232119), 1942 ^ _166148 : [(1953 ^ _166148) ^ [] : [1954 ^ _166148 : [(1955 ^ _166148) ^ [] : [_232121 = _232125], (1957 ^ _166148) ^ [] : [_232123 = _232127]], -(c_Groups_Oplus__class_Oplus(_232119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232119), _232121), _232123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232119), _232125), _232127)) = c_Groups_Oplus__class_Oplus(_232119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232119), _232121), _232127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232119), _232125), _232123)))], (1943 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_232119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232119), _232121), _232123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232119), _232125), _232127)) = c_Groups_Oplus__class_Oplus(_232119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232119), _232121), _232127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232119), _232125), _232123)), -(_232121 = _232125), -(_232123 = _232127)]]], (1961 ^ _166148) ^ [_232949, _232951, _232953, _232955] : [class_Rings_Ocomm__semiring__1(_232949), -(c_Groups_Oplus__class_Oplus(_232949, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232949), _232951), _232953), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232949), _232955), _232953)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232949), c_Groups_Oplus__class_Oplus(_232949, _232951, _232955)), _232953))], (1967 ^ _166148) ^ [_233261, _233263, _233265, _233267] : [class_RealVector_Oreal__normed__algebra(_233261), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233261), c_Groups_Oplus__class_Oplus(_233261, _233263, _233265)), _233267) = c_Groups_Oplus__class_Oplus(_233261, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233261), _233263), _233267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233261), _233265), _233267)))], (1973 ^ _166148) ^ [_233573, _233575, _233577, _233579] : [class_RealVector_Oreal__normed__algebra(_233573), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233573), c_Groups_Oplus__class_Oplus(_233573, _233575, _233577)), _233579) = c_Groups_Oplus__class_Oplus(_233573, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233573), _233575), _233579), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233573), _233577), _233579)))], (1979 ^ _166148) ^ [_233885, _233887, _233889, _233891] : [class_Rings_Ocomm__semiring__1(_233885), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233885), c_Groups_Oplus__class_Oplus(_233885, _233887, _233889)), _233891) = c_Groups_Oplus__class_Oplus(_233885, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233885), _233887), _233891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233885), _233889), _233891)))], (1985 ^ _166148) ^ [_234211, _234213, _234215, _234217, _234219] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_234211), 1988 ^ _166148 : [(1999 ^ _166148) ^ [] : [-(c_Groups_Oplus__class_Oplus(_234211, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234211), _234213), _234217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234211), _234215), _234219)) = c_Groups_Oplus__class_Oplus(_234211, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234211), _234213), _234219), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234211), _234215), _234217))), 2002 ^ _166148 : [(2003 ^ _166148) ^ [] : [_234213 = _234215], (2005 ^ _166148) ^ [] : [_234217 = _234219]]], (1989 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_234211, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234211), _234213), _234217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234211), _234215), _234219)) = c_Groups_Oplus__class_Oplus(_234211, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234211), _234213), _234219), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234211), _234215), _234217)), -(_234213 = _234215), -(_234217 = _234219)]]], (2007 ^ _166148) ^ [_235047, _235049, _235051, _235053] : [class_RealVector_Oreal__normed__algebra(_235047), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235047), _235049), c_Groups_Oplus__class_Oplus(_235047, _235051, _235053)) = c_Groups_Oplus__class_Oplus(_235047, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235047), _235049), _235051), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235047), _235049), _235053)))], (2013 ^ _166148) ^ [_235359, _235361, _235363, _235365] : [class_Rings_Ocomm__semiring__1(_235359), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235359), _235361), c_Groups_Oplus__class_Oplus(_235359, _235363, _235365)) = c_Groups_Oplus__class_Oplus(_235359, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235359), _235361), _235363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235359), _235361), _235365)))], (2019 ^ _166148) ^ [_235671, _235673, _235675, _235677] : [class_RealVector_Oreal__normed__algebra(_235671), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235671), _235673), c_Groups_Oplus__class_Oplus(_235671, _235675, _235677)) = c_Groups_Oplus__class_Oplus(_235671, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235671), _235673), _235675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235671), _235673), _235677)))], (2025 ^ _166148) ^ [_235955, _235957] : [class_Rings_Ocomm__semiring__1(_235955), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235955), _235957), c_Groups_Oone__class_Oone(_235955)) = _235957)], (2031 ^ _166148) ^ [_236183, _236185] : [class_Rings_Ocomm__semiring__1(_236183), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236183), c_Groups_Oone__class_Oone(_236183)), _236185) = _236185)], (2037 ^ _166148) ^ [_236439, _236441, _236443, _236445] : [class_Rings_Ocomm__semiring__1(_236439), -(hAPP(hAPP(c_Power_Opower__class_Opower(_236439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236439), _236441), _236443)), _236445) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236439), hAPP(hAPP(c_Power_Opower__class_Opower(_236439), _236441), _236445)), hAPP(hAPP(c_Power_Opower__class_Opower(_236439), _236443), _236445)))], (2043 ^ _166148) ^ [_236767, _236769, _236771, _236773] : [class_Groups_Ocomm__monoid__mult(_236767), -(hAPP(hAPP(c_Power_Opower__class_Opower(_236767), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236767), _236769), _236771)), _236773) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236767), hAPP(hAPP(c_Power_Opower__class_Opower(_236767), _236769), _236773)), hAPP(hAPP(c_Power_Opower__class_Opower(_236767), _236771), _236773)))], (2049 ^ _166148) ^ [_237081, _237083, _237085] : [class_Groups_Omonoid__mult(_237081), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_237081), hAPP(hAPP(c_Power_Opower__class_Opower(_237081), _237083), _237085)), _237083) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_237081), _237083), hAPP(hAPP(c_Power_Opower__class_Opower(_237081), _237083), _237085)))], (2055 ^ _166148) ^ [_237359, _237361] : [class_Groups_Omonoid__mult(_237359), -(hAPP(hAPP(c_Power_Opower__class_Opower(_237359), c_Groups_Oone__class_Oone(_237359)), _237361) = c_Groups_Oone__class_Oone(_237359))], (2061 ^ _166148) ^ [_237591, _237593] : [class_Rings_Ocomm__semiring__1(_237591), -(hAPP(hAPP(c_Power_Opower__class_Opower(_237591), _237593), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _237593)], (2067 ^ _166148) ^ [_237815, _237817] : [class_Groups_Omonoid__mult(_237815), -(hAPP(hAPP(c_Power_Opower__class_Opower(_237815), _237817), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _237817)], (2073 ^ _166148) ^ [_238053, _238055, _238057] : [class_Rings_Ocomm__semiring__1(_238053), -(c_Groups_Oplus__class_Oplus(_238053, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238053), _238055), _238057), _238057) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238053), c_Groups_Oplus__class_Oplus(_238053, _238055, c_Groups_Oone__class_Oone(_238053))), _238057))], (2079 ^ _166148) ^ [_238333, _238335, _238337] : [class_Rings_Ocomm__semiring__1(_238333), -(c_Groups_Oplus__class_Oplus(_238333, _238335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238333), _238337), _238335)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238333), c_Groups_Oplus__class_Oplus(_238333, _238337, c_Groups_Oone__class_Oone(_238333))), _238335))], (2085 ^ _166148) ^ [_238599, _238601] : [class_Rings_Ocomm__semiring__1(_238599), -(c_Groups_Oplus__class_Oplus(_238599, _238601, _238601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238599), c_Groups_Oplus__class_Oplus(_238599, c_Groups_Oone__class_Oone(_238599), c_Groups_Oone__class_Oone(_238599))), _238601))], (2091 ^ _166148) ^ [_238875, _238877, _238879, _238881] : [class_Rings_Olinordered__semidom(_238875), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _238877, _238879), c_Orderings_Oord__class_Oless(_238875, c_Groups_Oone__class_Oone(_238875), _238881), -(c_Orderings_Oord__class_Oless(_238875, hAPP(hAPP(c_Power_Opower__class_Opower(_238875), _238881), _238877), hAPP(hAPP(c_Power_Opower__class_Opower(_238875), _238881), _238879)))], (2105 ^ _166148) ^ [_239359, _239361, _239363, _239365] : [class_Rings_Olinordered__semidom(_239359), c_Orderings_Oord__class_Oless(_239359, c_Groups_Oone__class_Oone(_239359), _239361), c_Orderings_Oord__class_Oless(_239359, hAPP(hAPP(c_Power_Opower__class_Opower(_239359), _239361), _239363), hAPP(hAPP(c_Power_Opower__class_Opower(_239359), _239361), _239365)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _239363, _239365))], (2120 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 2118 ^ []))], (2122 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 2118 ^ [], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (2124 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 2118 ^ [], c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (2126 ^ _166148) ^ [_240046, _240048, _240050] : [class_RealVector_Oreal__normed__div__algebra(_240046), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _240048, c_RealVector_Onorm__class_Onorm(_240046, _240050)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _240048), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_240046, c_Rings_Oinverse__class_Oinverse(_240046, _240050)), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _240048)))], (2140 ^ _166148) ^ [_240532, _240534, _240536, _240538, _240540, _240542] : [class_Rings_Olinordered__semiring__1__strict(_240532), c_Orderings_Oord__class_Oless(_240532, _240534, _240536), c_Orderings_Oord__class_Oless(_240532, _240538, _240536), c_Orderings_Oord__class_Oless__eq(_240532, c_Groups_Ozero__class_Ozero(_240532), _240540), c_Orderings_Oord__class_Oless__eq(_240532, c_Groups_Ozero__class_Ozero(_240532), _240542), c_Groups_Oplus__class_Oplus(_240532, _240540, _240542) = c_Groups_Oone__class_Oone(_240532), -(c_Orderings_Oord__class_Oless(_240532, c_Groups_Oplus__class_Oplus(_240532, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240532), _240540), _240534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240532), _240542), _240538)), _240536))], (2166 ^ _166148) ^ [_241387, _241389, _241391, _241393] : [class_RealVector_Oreal__normed__vector(_241387), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _241389, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_241387, _241391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _241389), c_RealVector_Onorm__class_Onorm(_241387, _241393))), -(_241391 = c_Groups_Ozero__class_Ozero(_241387))], (2180 ^ _166148) ^ [_241803] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _241803, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2182 ^ _166148) ^ [_241911, _241913] : [class_Fields_Olinordered__field(_241911), c_Orderings_Oord__class_Oless(_241911, c_Groups_Ozero__class_Ozero(_241911), _241913), c_Orderings_Oord__class_Oless__eq(_241911, _241913, c_Groups_Oone__class_Oone(_241911)), -(c_Orderings_Oord__class_Oless__eq(_241911, c_Groups_Oone__class_Oone(_241911), c_Rings_Oinverse__class_Oinverse(_241911, _241913)))], (2196 ^ _166148) ^ [_242321, _242323] : [class_Fields_Olinordered__field__inverse__zero(_242321), 2199 ^ _166148 : [(2210 ^ _166148) ^ [] : [2211 ^ _166148 : [(2212 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_242321, _242323, c_Groups_Ozero__class_Ozero(_242321))], (2214 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_242321, c_Groups_Oone__class_Oone(_242321), _242323)]], -(c_Orderings_Oord__class_Oless(_242321, c_Rings_Oinverse__class_Oinverse(_242321, _242323), c_Groups_Oone__class_Oone(_242321)))], (2200 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_242321, c_Rings_Oinverse__class_Oinverse(_242321, _242323), c_Groups_Oone__class_Oone(_242321)), -(c_Orderings_Oord__class_Oless__eq(_242321, _242323, c_Groups_Ozero__class_Ozero(_242321))), -(c_Orderings_Oord__class_Oless(_242321, c_Groups_Oone__class_Oone(_242321), _242323))]]], (2218 ^ _166148) ^ [_242973, _242975] : [class_Fields_Olinordered__field__inverse__zero(_242973), 2221 ^ _166148 : [(2222 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_242973, c_Groups_Oone__class_Oone(_242973), c_Rings_Oinverse__class_Oinverse(_242973, _242975)), 2225 ^ _166148 : [(2226 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_242973, c_Groups_Ozero__class_Ozero(_242973), _242975))], (2228 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_242973, _242975, c_Groups_Oone__class_Oone(_242973)))]]], (2230 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_242973, c_Groups_Oone__class_Oone(_242973), c_Rings_Oinverse__class_Oinverse(_242973, _242975))), c_Orderings_Oord__class_Oless(_242973, c_Groups_Ozero__class_Ozero(_242973), _242975), c_Orderings_Oord__class_Oless__eq(_242973, _242975, c_Groups_Oone__class_Oone(_242973))]]], (2240 ^ _166148) ^ [_243681, _243683, _243685, _243687, _243689, _243691] : [class_Rings_Olinordered__semiring__1(_243681), c_Orderings_Oord__class_Oless__eq(_243681, _243683, _243685), c_Orderings_Oord__class_Oless__eq(_243681, _243687, _243685), c_Orderings_Oord__class_Oless__eq(_243681, c_Groups_Ozero__class_Ozero(_243681), _243689), c_Orderings_Oord__class_Oless__eq(_243681, c_Groups_Ozero__class_Ozero(_243681), _243691), c_Groups_Oplus__class_Oplus(_243681, _243689, _243691) = c_Groups_Oone__class_Oone(_243681), -(c_Orderings_Oord__class_Oless__eq(_243681, c_Groups_Oplus__class_Oplus(_243681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_243681), _243689), _243683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_243681), _243691), _243687)), _243685))], (2266 ^ _166148) ^ [_244494] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _244494), 2270 ^ _166148 : [(2271 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 2269 ^ [_244494]))], (2273 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 2269 ^ [_244494], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (2275 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 2269 ^ [_244494], _244494))]]], (2277 ^ _166148) ^ [_244913] : [-(_244913 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _244913)), _244913) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (2283 ^ _166148) ^ [] : [v_a____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (2285 ^ _166148) ^ [] : [v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (2287 ^ _166148) ^ [_245213] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _245213))], (2289 ^ _166148) ^ [] : [-(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (2291 ^ _166148) ^ [_245345] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _245345, _245345))], (2293 ^ _166148) ^ [_245424] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _245424, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245424), _245424)))], (2295 ^ _166148) ^ [_245509] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _245509, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245509), _245509))))], (2297 ^ _166148) ^ [_245614, _245616] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245614), _245616) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245616), _245614))], (2299 ^ _166148) ^ [_245735, _245737] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _245735, _245737)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _245737, _245735))], (2305 ^ _166148) ^ [_245949, _245951, _245953] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245949), _245951)), _245953) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245951), _245953)))], (2307 ^ _166148) ^ [_246084, _246086] : [_246084 = _246086, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _246084, _246086))], (2313 ^ _166148) ^ [_246310, _246312, _246314] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _246310, _246312), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246310), _246314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246312), _246314)))], (2319 ^ _166148) ^ [_246568, _246570, _246572] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _246568, _246570), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246572), _246568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246572), _246570)))], (2325 ^ _166148) ^ [_246826, _246828, _246830] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _246826, _246828), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _246828, _246830), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _246826, _246830))], (2335 ^ _166148) ^ [_247141, _247143] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _247141, _247143), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _247143, _247141), -(_247141 = _247143)], (2345 ^ _166148) ^ [_247472, _247474, _247476, _247478] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _247472, _247474), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _247476, _247478), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _247472), _247476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _247474), _247478)))], (2355 ^ _166148) ^ [_247836] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _247836, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_247836 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2361 ^ _166148) ^ [_247994] : [_247994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _247994, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2367 ^ _166148) ^ [_248173] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _248173))], (2369 ^ _166148) ^ [_248281, _248283] : [2370 ^ _166148 : [(2371 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _248281, _248283)], (2373 ^ _166148) ^ [] : [_248281 = _248283]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _248281, _248283))], (2377 ^ _166148) ^ [_248569, _248571] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _248569, _248571), -(_248569 = _248571), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _248569, _248571))], (2387 ^ _166148) ^ [_248875, _248877] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _248875, _248877), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _248875, _248877))], (2403 ^ _166148) ^ [_249374, _249376] : [2404 ^ _166148 : [(2405 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _249374, _249376)], (2407 ^ _166148) ^ [] : [_249374 = _249376]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _249374, _249376))], (2393 ^ _166148) ^ [_249118, _249120] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _249118, _249120), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _249118, _249120)), -(_249118 = _249120)], (2411 ^ _166148) ^ [_249693, _249695] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _249693, _249695), 2414 ^ _166148 : [(2415 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _249693, _249695))], (2417 ^ _166148) ^ [] : [_249693 = _249695]]], (2419 ^ _166148) ^ [_249935, _249937] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _249935, _249937)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _249935, _249937), -(_249935 = _249937)], (2429 ^ _166148) ^ [_250228, _250230] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _250228, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250230, _250228)))], (2431 ^ _166148) ^ [_250327, _250329] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _250327, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250327, _250329)))], (2433 ^ _166148) ^ [_250470, _250472] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _250470, _250472), -(_250472 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250470, 2436 ^ [_250470, _250472]))], (2440 ^ _166148) ^ [_250703, _250705] : [2441 ^ _166148 : [(2442 ^ _166148) ^ [_250778] : [_250705 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250703, _250778)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _250703, _250705))], (2446 ^ _166148) ^ [_250976, _250978] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _250976, _250978), -(_250978 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250976, 2449 ^ [_250976, _250978]))], (2453 ^ _166148) ^ [_251209, _251211] : [2454 ^ _166148 : [(2455 ^ _166148) ^ [_251284] : [_251211 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251209, _251284)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _251209, _251211))], (2459 ^ _166148) ^ [_251496, _251498, _251500] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251496, _251498), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251496, _251500)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _251498, _251500))], (2465 ^ _166148) ^ [_251684, _251686, _251688] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _251686, _251688), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251684, _251686), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251684, _251688)))], (2471 ^ _166148) ^ [_251936, _251938, _251940] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _251936, _251938), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _251936, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251938, _251940)))], (2477 ^ _166148) ^ [_252178, _252180, _252182] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _252178, _252180), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _252178, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252182, _252180)))], (2483 ^ _166148) ^ [_252420, _252422, _252424] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _252420, _252422), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252420, _252424), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252422, _252424)))], (2489 ^ _166148) ^ [_252684, _252686, _252688, _252690] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _252684, _252686), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _252688, _252690), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252684, _252688), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252686, _252690)))], (2499 ^ _166148) ^ [_253039, _253041, _253043] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _253039, _253041), _253043), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _253041, _253043))], (2505 ^ _166148) ^ [_253281, _253283, _253285] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _253281, _253283), _253285), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _253281, _253285))], (2511 ^ _166148) ^ [_253523, _253525, _253527] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _253523, _253525), _253527), 2514 ^ _166148 : [(2515 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _253523, _253527))], (2517 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _253525, _253527))]]], (2529 ^ _166148) ^ [_254168, _254170, _254172] : [2530 ^ _166148 : [(2531 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _254170))], (2533 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _254168, _254172)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _254168), _254170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _254172), _254170)))], (2519 ^ _166148) ^ [_253877, _253879, _253881] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _253877), _253879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _253881), _253879)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _253879), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _253877, _253881))], (2547 ^ _166148) ^ [_254827, _254829, _254831] : [2548 ^ _166148 : [(2549 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _254827))], (2551 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _254829, _254831)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _254827), _254829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _254827), _254831)))], (2537 ^ _166148) ^ [_254536, _254538, _254540] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _254536), _254538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _254536), _254540)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _254536), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _254538, _254540))], (2555 ^ _166148) ^ [_255166, _255168, _255170] : [class_Rings_Olinordered__idom(_255166), -(_255168 = _255170), -(c_Orderings_Oord__class_Oless(_255166, _255168, _255170)), -(c_Orderings_Oord__class_Oless(_255166, _255170, _255168))], (2579 ^ _166148) ^ [_255905, _255907, _255909] : [2580 ^ _166148 : [(2581 ^ _166148) ^ [] : [_255905 = _255909], (2583 ^ _166148) ^ [] : [_255907 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _255905), _255907) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _255909), _255907))], (2569 ^ _166148) ^ [_255619, _255621, _255623] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _255619), _255621) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _255623), _255621), -(_255619 = _255623), -(_255621 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2597 ^ _166148) ^ [_256552, _256554, _256556] : [2598 ^ _166148 : [(2599 ^ _166148) ^ [] : [_256554 = _256556], (2601 ^ _166148) ^ [] : [_256552 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256552), _256554) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256552), _256556))], (2587 ^ _166148) ^ [_256266, _256268, _256270] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256266), _256268) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256266), _256270), -(_256268 = _256270), -(_256266 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2615 ^ _166148) ^ [_257163, _257165] : [2616 ^ _166148 : [(2617 ^ _166148) ^ [] : [_257163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2619 ^ _166148) ^ [] : [_257165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _257163), _257165) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2605 ^ _166148) ^ [_256899, _256901] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256899), _256901) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_256899 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_256901 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2623 ^ _166148) ^ [_257432] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _257432), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2625 ^ _166148) ^ [_257516] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _257516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2627 ^ _166148) ^ [_257626, _257628] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _257626, _257628), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _257628, _257626), -(_257626 = _257628)], (2637 ^ _166148) ^ [_257943, _257945, _257947] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _257943, _257945), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _257945, _257947), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _257943, _257947))], (2647 ^ _166148) ^ [_258258, _258260] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _258258, _258260)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _258260, _258258))], (2653 ^ _166148) ^ [_258444] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _258444, _258444))], (2655 ^ _166148) ^ [_258566, _258568, _258570] : [2656 ^ _166148 : [(2657 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _258566, _258568))], (2659 ^ _166148) ^ [] : [hBOOL(hAPP(hAPP(_258570, _258568), _258566))]], 2662 ^ _166148 : [(2663 ^ _166148) ^ [] : [-(_258566 = _258568)], (2665 ^ _166148) ^ [] : [hBOOL(hAPP(hAPP(_258570, _258568), _258566))]], 2668 ^ _166148 : [(2669 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _258568, _258566))], (2671 ^ _166148) ^ [] : [hBOOL(hAPP(hAPP(_258570, _258568), _258566))]], -(hBOOL(hAPP(hAPP(_258570, _258568), _258566)))], (2675 ^ _166148) ^ [_259243, _259245] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _259243, _259245), _259243 = _259245], (2681 ^ _166148) ^ [_259456, _259458] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _259456, _259458), _259458 = _259456], (2687 ^ _166148) ^ [_259639] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _259639, _259639)], (2689 ^ _166148) ^ [_259747, _259749] : [-(_259747 = _259749), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _259747, _259749)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _259749, _259747))], (2709 ^ _166148) ^ [_260344, _260346] : [2710 ^ _166148 : [(2711 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _260344, _260346)], (2713 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _260346, _260344)]], _260344 = _260346], (2699 ^ _166148) ^ [_260085, _260087] : [-(_260085 = _260087), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _260085, _260087)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _260087, _260085))], (2717 ^ _166148) ^ [_260605] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _260605, _260605)], (2719 ^ _166148) ^ [_260698, _260700] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260698, _260700) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260700, _260698))], (2721 ^ _166148) ^ [_260814, _260816, _260818] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260814, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260816, _260818)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260816, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260814, _260818)))], (2723 ^ _166148) ^ [_260940, _260942, _260944] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260940, _260942), _260944) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260940, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260942, _260944)))], (2725 ^ _166148) ^ [_261110, _261112, _261114] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261110, _261112) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261110, _261114), -(_261112 = _261114)], (2731 ^ _166148) ^ [_261294, _261296, _261298] : [_261296 = _261298, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261294, _261296) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261294, _261298))], (2737 ^ _166148) ^ [_261571, _261573, _261575] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261571, _261573) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261575, _261573), -(_261571 = _261575)], (2743 ^ _166148) ^ [_261755, _261757, _261759] : [_261755 = _261759, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261755, _261757) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261759, _261757))], (2749 ^ _166148) ^ [_261988, _261990, _261992] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261988), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261990, _261992)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261988), _261990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261988), _261992)))], (2751 ^ _166148) ^ [_262124, _262126, _262128] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262124, _262126)), _262128) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262124), _262128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262126), _262128)))], (2753 ^ _166148) ^ [_262246, _262248] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _262246), _262248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _262248), _262246))], (2755 ^ _166148) ^ [_262366, _262368, _262370] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _262366), _262368)), _262370) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _262366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _262368), _262370)))], (2757 ^ _166148) ^ [_262515, _262517, _262519] : [class_Rings_Odivision__ring__inverse__zero(_262515), c_Rings_Oinverse__class_Oinverse(_262515, _262517) = c_Rings_Oinverse__class_Oinverse(_262515, _262519), -(_262517 = _262519)], (2767 ^ _166148) ^ [_262848, _262850, _262852] : [class_Rings_Odivision__ring__inverse__zero(_262848), 2770 ^ _166148 : [(2771 ^ _166148) ^ [] : [c_Rings_Oinverse__class_Oinverse(_262848, _262850) = c_Rings_Oinverse__class_Oinverse(_262848, _262852), -(_262850 = _262852)], (2777 ^ _166148) ^ [] : [_262850 = _262852, -(c_Rings_Oinverse__class_Oinverse(_262848, _262850) = c_Rings_Oinverse__class_Oinverse(_262848, _262852))]]], (2783 ^ _166148) ^ [_263340, _263342] : [class_Rings_Odivision__ring__inverse__zero(_263340), -(c_Rings_Oinverse__class_Oinverse(_263340, c_Rings_Oinverse__class_Oinverse(_263340, _263342)) = _263342)], (2789 ^ _166148) ^ [_263531] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _263531) = _263531)], (2791 ^ _166148) ^ [_263670, _263672] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _263670), _263672), 2794 ^ _166148 : [(2795 ^ _166148) ^ [] : [-(_263670 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (2797 ^ _166148) ^ [] : [-(_263672 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (2799 ^ _166148) ^ [_263919, _263921] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _263919), _263921)), _263919 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _263921 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (2809 ^ _166148) ^ [_264203] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264203), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _264203)], (2811 ^ _166148) ^ [_264345, _264347] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264345), _264347) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 2814 ^ _166148 : [(2815 ^ _166148) ^ [] : [-(_264345 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (2817 ^ _166148) ^ [] : [-(_264347 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (2819 ^ _166148) ^ [_264594, _264596] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264594), _264596) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _264594 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _264596 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (2829 ^ _166148) ^ [_264907, _264909] : [class_Rings_Omult__zero(_264907), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_264907), c_Groups_Ozero__class_Ozero(_264907)), _264909) = c_Groups_Ozero__class_Ozero(_264907))], (2835 ^ _166148) ^ [_265139, _265141] : [class_Rings_Omult__zero(_265139), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265139), _265141), c_Groups_Ozero__class_Ozero(_265139)) = c_Groups_Ozero__class_Ozero(_265139))], (2841 ^ _166148) ^ [_265385, _265387, _265389] : [class_Rings_Oring__no__zero__divisors(_265385), 2844 ^ _166148 : [(2855 ^ _166148) ^ [] : [2856 ^ _166148 : [(2857 ^ _166148) ^ [] : [_265387 = c_Groups_Ozero__class_Ozero(_265385)], (2859 ^ _166148) ^ [] : [_265389 = c_Groups_Ozero__class_Ozero(_265385)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265385), _265387), _265389) = c_Groups_Ozero__class_Ozero(_265385))], (2845 ^ _166148) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265385), _265387), _265389) = c_Groups_Ozero__class_Ozero(_265385), -(_265387 = c_Groups_Ozero__class_Ozero(_265385)), -(_265389 = c_Groups_Ozero__class_Ozero(_265385))]]], (2863 ^ _166148) ^ [_266079, _266081, _266083] : [class_Rings_Ono__zero__divisors(_266079), -(_266081 = c_Groups_Ozero__class_Ozero(_266079)), -(_266083 = c_Groups_Ozero__class_Ozero(_266079)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266079), _266081), _266083) = c_Groups_Ozero__class_Ozero(_266079)], (2877 ^ _166148) ^ [_266528, _266530, _266532] : [class_Rings_Ono__zero__divisors(_266528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266528), _266530), _266532) = c_Groups_Ozero__class_Ozero(_266528), -(_266530 = c_Groups_Ozero__class_Ozero(_266528)), -(_266532 = c_Groups_Ozero__class_Ozero(_266528))], (2891 ^ _166148) ^ [_266943] : [class_Rings_Ozero__neq__one(_266943), c_Groups_Oone__class_Oone(_266943) = c_Groups_Ozero__class_Ozero(_266943)], (2897 ^ _166148) ^ [_267140] : [class_Rings_Ozero__neq__one(_267140), c_Groups_Ozero__class_Ozero(_267140) = c_Groups_Oone__class_Oone(_267140)], (2903 ^ _166148) ^ [_267379, _267381, _267383, _267385] : [class_Rings_Ocomm__semiring(_267379), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267379), c_Groups_Oplus__class_Oplus(_267379, _267381, _267383)), _267385) = c_Groups_Oplus__class_Oplus(_267379, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267379), _267381), _267385), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267379), _267383), _267385)))], (2909 ^ _166148) ^ [_267705, _267707, _267709, _267711, _267713] : [class_Rings_Osemiring(_267705), -(c_Groups_Oplus__class_Oplus(_267705, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267705), _267707), _267709), c_Groups_Oplus__class_Oplus(_267705, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267705), _267711), _267709), _267713)) = c_Groups_Oplus__class_Oplus(_267705, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267705), c_Groups_Oplus__class_Oplus(_267705, _267707, _267711)), _267709), _267713))], (2915 ^ _166148) ^ [_268025, _268027, _268029] : [class_Rings_Odivision__ring(_268025), c_Rings_Oinverse__class_Oinverse(_268025, _268027) = c_Rings_Oinverse__class_Oinverse(_268025, _268029), -(_268027 = c_Groups_Ozero__class_Ozero(_268025)), -(_268029 = c_Groups_Ozero__class_Ozero(_268025)), -(_268027 = _268029)], (2933 ^ _166148) ^ [_268544, _268546] : [class_Rings_Odivision__ring(_268544), c_Rings_Oinverse__class_Oinverse(_268544, _268546) = c_Groups_Ozero__class_Ozero(_268544), -(_268546 = c_Groups_Ozero__class_Ozero(_268544))], (2943 ^ _166148) ^ [_268855, _268857] : [class_Rings_Odivision__ring(_268855), -(_268857 = c_Groups_Ozero__class_Ozero(_268855)), -(c_Rings_Oinverse__class_Oinverse(_268855, c_Rings_Oinverse__class_Oinverse(_268855, _268857)) = _268857)], (2953 ^ _166148) ^ [_269171, _269173] : [class_Rings_Odivision__ring(_269171), -(_269173 = c_Groups_Ozero__class_Ozero(_269171)), c_Rings_Oinverse__class_Oinverse(_269171, _269173) = c_Groups_Ozero__class_Ozero(_269171)], (2963 ^ _166148) ^ [_269486, _269488] : [class_Rings_Odivision__ring__inverse__zero(_269486), 2966 ^ _166148 : [(2967 ^ _166148) ^ [] : [c_Rings_Oinverse__class_Oinverse(_269486, _269488) = c_Groups_Ozero__class_Ozero(_269486), -(_269488 = c_Groups_Ozero__class_Ozero(_269486))], (2973 ^ _166148) ^ [] : [_269488 = c_Groups_Ozero__class_Ozero(_269486), -(c_Rings_Oinverse__class_Oinverse(_269486, _269488) = c_Groups_Ozero__class_Ozero(_269486))]]], (2979 ^ _166148) ^ [_269951] : [class_Rings_Odivision__ring__inverse__zero(_269951), -(c_Rings_Oinverse__class_Oinverse(_269951, c_Groups_Ozero__class_Ozero(_269951)) = c_Groups_Ozero__class_Ozero(_269951))], (2985 ^ _166148) ^ [_270153] : [class_Fields_Ofield__inverse__zero(_270153), -(c_Rings_Oinverse__class_Oinverse(_270153, c_Groups_Ozero__class_Ozero(_270153)) = c_Groups_Ozero__class_Ozero(_270153))], (2991 ^ _166148) ^ [_270355] : [-(_270355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _270355))], (2997 ^ _166148) ^ [_270578, _270580, _270582] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _270578, _270580), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _270582), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _270582), _270578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _270582), _270580)))], (3007 ^ _166148) ^ [_270931, _270933, _270935] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _270931, _270933), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _270935), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _270931), _270935), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _270933), _270935)))], (3017 ^ _166148) ^ [_271270, _271272] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _271270, _271272), _271272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3023 ^ _166148) ^ [_271526, _271528, _271530] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _271526), _271528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _271530), _271528)), 3026 ^ _166148 : [(3027 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _271528))], (3029 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _271526, _271530))]]], (3031 ^ _166148) ^ [_271801, _271803, _271805] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _271801), _271803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _271805), _271803))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _271803), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _271801, _271805)], (3041 ^ _166148) ^ [_272185, _272187, _272189] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _272185), _272187), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _272185), _272189)), 3044 ^ _166148 : [(3045 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _272185))], (3047 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _272187, _272189))]]], (3049 ^ _166148) ^ [_272460, _272462, _272464] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _272460), _272462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _272460), _272464))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _272460), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _272462, _272464)], (3059 ^ _166148) ^ [_272771] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _272771, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3061 ^ _166148) ^ [_272908, _272910] : [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), _272908), _272910)), 3064 ^ _166148 : [(3065 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _272908))], (3067 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _272910))]]], (3069 ^ _166148) ^ [_273163, _273165] : [-(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), _273163), _273165))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _273163), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _273165)], (3079 ^ _166148) ^ [_273497] : [-(_273497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _273497))], (3085 ^ _166148) ^ [_273658] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _273658), _273658 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3091 ^ _166148) ^ [_273837] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _273837, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3093 ^ _166148) ^ [_273974, _273976] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _273974, _273976), 3096 ^ _166148 : [(3097 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _273974, _273976))], (3099 ^ _166148) ^ [] : [_273974 = _273976]]], (3101 ^ _166148) ^ [_274216, _274218] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _274216, _274218)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _274216, _274218), -(_274216 = _274218)], (3121 ^ _166148) ^ [_274809, _274811] : [3122 ^ _166148 : [(3123 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _274809, _274811)], (3125 ^ _166148) ^ [] : [_274809 = _274811]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _274809, _274811))], (3111 ^ _166148) ^ [_274553, _274555] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _274553, _274555), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _274553, _274555)), -(_274553 = _274555)], (3129 ^ _166148) ^ [_275070] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _275070) = _275070)], (3131 ^ _166148) ^ [_275152] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _275152, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _275152)], (3133 ^ _166148) ^ [_275292, _275294] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _275292, _275294) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 3136 ^ _166148 : [(3137 ^ _166148) ^ [] : [-(_275292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3139 ^ _166148) ^ [] : [-(_275294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3141 ^ _166148) ^ [_275537, _275539] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _275537, _275539) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _275537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _275539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3151 ^ _166148) ^ [_275846, _275848] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _275846, _275848) = _275846, -(_275848 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3157 ^ _166148) ^ [_276078, _276080, _276082] : [class_Fields_Ofield__inverse__zero(_276078), -(c_Rings_Oinverse__class_Oinverse(_276078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276078), _276080), _276082)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276078), c_Rings_Oinverse__class_Oinverse(_276078, _276080)), c_Rings_Oinverse__class_Oinverse(_276078, _276082)))], (3163 ^ _166148) ^ [_276328] : [class_Rings_Odivision__ring(_276328), -(c_Rings_Oinverse__class_Oinverse(_276328, c_Groups_Oone__class_Oone(_276328)) = c_Groups_Oone__class_Oone(_276328))], (3169 ^ _166148) ^ [_276544, _276546] : [class_Fields_Ofield__inverse__zero(_276544), 3172 ^ _166148 : [(3173 ^ _166148) ^ [] : [c_Rings_Oinverse__class_Oinverse(_276544, _276546) = c_Groups_Oone__class_Oone(_276544), -(_276546 = c_Groups_Oone__class_Oone(_276544))], (3179 ^ _166148) ^ [] : [_276546 = c_Groups_Oone__class_Oone(_276544), -(c_Rings_Oinverse__class_Oinverse(_276544, _276546) = c_Groups_Oone__class_Oone(_276544))]]], (3185 ^ _166148) ^ [_277007, _277009] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _277007, _277009), _277007)], (3187 ^ _166148) ^ [_277105, _277107] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _277105, _277107), _277107)], (3189 ^ _166148) ^ [_277262, _277264, _277266] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _277262, _277264), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _277262, _277266)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _277264, _277266))], (3195 ^ _166148) ^ [_277450, _277452, _277454] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _277452, _277454), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _277450, _277452), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _277450, _277454)))], (3201 ^ _166148) ^ [_277702, _277704, _277706] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _277702, _277704), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _277702, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _277704, _277706)))], (3207 ^ _166148) ^ [_277944, _277946, _277948] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _277944, _277946), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _277944, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _277948, _277946)))], (3213 ^ _166148) ^ [_278186, _278188, _278190] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _278186, _278188), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _278186, _278190), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _278188, _278190)))], (3219 ^ _166148) ^ [_278450, _278452, _278454, _278456] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _278450, _278452), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _278454, _278456), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _278450, _278454), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _278452, _278456)))], (3229 ^ _166148) ^ [_278819, _278821, _278823, _278825] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _278819, _278821), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _278823, _278821) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _278819, _278825), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _278823, _278825))], (3239 ^ _166148) ^ [_279172, _279174, _279176] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _279172, _279174), _279176), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _279172, _279176))], (3245 ^ _166148) ^ [_279414, _279416, _279418] : [-(_279414 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 3248 ^ _166148 : [(3249 ^ _166148) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _279416), _279414) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _279418), _279414), -(_279416 = _279418)], (3255 ^ _166148) ^ [] : [_279416 = _279418, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _279416), _279414) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _279418), _279414))]]], (3261 ^ _166148) ^ [_279943, _279945, _279947] : [-(_279943 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 3264 ^ _166148 : [(3265 ^ _166148) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _279943), _279945) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _279943), _279947), -(_279945 = _279947)], (3271 ^ _166148) ^ [] : [_279945 = _279947, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _279943), _279945) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _279943), _279947))]]], (3277 ^ _166148) ^ [_280458, _280460] : [_280458 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _280458), _280460), -(_280460 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_280458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3287 ^ _166148) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (3289 ^ _166148) ^ [_280836, _280838, _280840] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _280836, _280838), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _280840, _280836), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _280840, _280838)))], (3295 ^ _166148) ^ [_281043] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _281043) = _281043)], (3297 ^ _166148) ^ [_281152, _281154, _281156] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _281152, _281154)), _281156) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _281152), _281156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _281154), _281156)))], (3299 ^ _166148) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3301 ^ _166148) ^ [_281356, _281358, _281360] : [class_Rings_Oordered__cancel__semiring(_281356), -(c_Orderings_Oord__class_Oless__eq(_281356, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_281356), _281358), _281360), c_Groups_Ozero__class_Ozero(_281356))), 3306 ^ _166148 : [(3307 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_281356, c_Groups_Ozero__class_Ozero(_281356), _281358), c_Orderings_Oord__class_Oless__eq(_281356, _281360, c_Groups_Ozero__class_Ozero(_281356))], (3313 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_281356, _281358, c_Groups_Ozero__class_Ozero(_281356)), c_Orderings_Oord__class_Oless__eq(_281356, c_Groups_Ozero__class_Ozero(_281356), _281360)]]], (3321 ^ _166148) ^ [_281985, _281987, _281989] : [class_Rings_Oordered__ring(_281985), -(c_Orderings_Oord__class_Oless__eq(_281985, c_Groups_Ozero__class_Ozero(_281985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_281985), _281987), _281989))), 3326 ^ _166148 : [(3327 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_281985, c_Groups_Ozero__class_Ozero(_281985), _281987), c_Orderings_Oord__class_Oless__eq(_281985, c_Groups_Ozero__class_Ozero(_281985), _281989)], (3333 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_281985, _281987, c_Groups_Ozero__class_Ozero(_281985)), c_Orderings_Oord__class_Oless__eq(_281985, _281989, c_Groups_Ozero__class_Ozero(_281985))]]], (3341 ^ _166148) ^ [_282642, _282644, _282646, _282648, _282650] : [class_Rings_Oordered__semiring(_282642), c_Orderings_Oord__class_Oless__eq(_282642, _282644, _282646), c_Orderings_Oord__class_Oless__eq(_282642, _282648, _282650), c_Orderings_Oord__class_Oless__eq(_282642, c_Groups_Ozero__class_Ozero(_282642), _282646), c_Orderings_Oord__class_Oless__eq(_282642, c_Groups_Ozero__class_Ozero(_282642), _282648), -(c_Orderings_Oord__class_Oless__eq(_282642, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_282642), _282644), _282648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_282642), _282646), _282650)))], (3363 ^ _166148) ^ [_283364, _283366, _283368, _283370, _283372] : [class_Rings_Oordered__semiring(_283364), c_Orderings_Oord__class_Oless__eq(_283364, _283366, _283368), c_Orderings_Oord__class_Oless__eq(_283364, _283370, _283372), c_Orderings_Oord__class_Oless__eq(_283364, c_Groups_Ozero__class_Ozero(_283364), _283366), c_Orderings_Oord__class_Oless__eq(_283364, c_Groups_Ozero__class_Ozero(_283364), _283370), -(c_Orderings_Oord__class_Oless__eq(_283364, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283364), _283366), _283370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283364), _283368), _283372)))], (3385 ^ _166148) ^ [_284072, _284074, _284076, _284078] : [class_Rings_Oordered__ring(_284072), c_Orderings_Oord__class_Oless__eq(_284072, _284074, _284076), c_Orderings_Oord__class_Oless__eq(_284072, _284078, c_Groups_Ozero__class_Ozero(_284072)), -(c_Orderings_Oord__class_Oless__eq(_284072, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284072), _284078), _284076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284072), _284078), _284074)))], (3399 ^ _166148) ^ [_284556, _284558, _284560, _284562] : [class_Rings_Oordered__ring(_284556), c_Orderings_Oord__class_Oless__eq(_284556, _284558, _284560), c_Orderings_Oord__class_Oless__eq(_284556, _284562, c_Groups_Ozero__class_Ozero(_284556)), -(c_Orderings_Oord__class_Oless__eq(_284556, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284556), _284560), _284562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284556), _284558), _284562)))], (3413 ^ _166148) ^ [_285040, _285042, _285044, _285046] : [class_Rings_Oordered__comm__semiring(_285040), c_Orderings_Oord__class_Oless__eq(_285040, _285042, _285044), c_Orderings_Oord__class_Oless__eq(_285040, c_Groups_Ozero__class_Ozero(_285040), _285046), -(c_Orderings_Oord__class_Oless__eq(_285040, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285040), _285046), _285042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285040), _285046), _285044)))], (3427 ^ _166148) ^ [_285524, _285526, _285528, _285530] : [class_Rings_Oordered__semiring(_285524), c_Orderings_Oord__class_Oless__eq(_285524, _285526, _285528), c_Orderings_Oord__class_Oless__eq(_285524, c_Groups_Ozero__class_Ozero(_285524), _285530), -(c_Orderings_Oord__class_Oless__eq(_285524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285524), _285530), _285526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285524), _285530), _285528)))], (3441 ^ _166148) ^ [_286008, _286010, _286012, _286014] : [class_Rings_Oordered__semiring(_286008), c_Orderings_Oord__class_Oless__eq(_286008, _286010, _286012), c_Orderings_Oord__class_Oless__eq(_286008, c_Groups_Ozero__class_Ozero(_286008), _286014), -(c_Orderings_Oord__class_Oless__eq(_286008, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286008), _286010), _286014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286008), _286012), _286014)))], (3455 ^ _166148) ^ [_286478, _286480, _286482] : [class_Rings_Oordered__ring(_286478), c_Orderings_Oord__class_Oless__eq(_286478, _286480, c_Groups_Ozero__class_Ozero(_286478)), c_Orderings_Oord__class_Oless__eq(_286478, _286482, c_Groups_Ozero__class_Ozero(_286478)), -(c_Orderings_Oord__class_Oless__eq(_286478, c_Groups_Ozero__class_Ozero(_286478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286478), _286480), _286482)))], (3469 ^ _166148) ^ [_286926, _286928, _286930] : [class_Rings_Oordered__cancel__semiring(_286926), c_Orderings_Oord__class_Oless__eq(_286926, _286928, c_Groups_Ozero__class_Ozero(_286926)), c_Orderings_Oord__class_Oless__eq(_286926, c_Groups_Ozero__class_Ozero(_286926), _286930), -(c_Orderings_Oord__class_Oless__eq(_286926, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286926), _286928), _286930), c_Groups_Ozero__class_Ozero(_286926)))], (3483 ^ _166148) ^ [_287374, _287376, _287378] : [class_Rings_Oordered__cancel__semiring(_287374), c_Orderings_Oord__class_Oless__eq(_287374, c_Groups_Ozero__class_Ozero(_287374), _287376), c_Orderings_Oord__class_Oless__eq(_287374, _287378, c_Groups_Ozero__class_Ozero(_287374)), -(c_Orderings_Oord__class_Oless__eq(_287374, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287374), _287378), _287376), c_Groups_Ozero__class_Ozero(_287374)))], (3497 ^ _166148) ^ [_287822, _287824, _287826] : [class_Rings_Oordered__cancel__semiring(_287822), c_Orderings_Oord__class_Oless__eq(_287822, c_Groups_Ozero__class_Ozero(_287822), _287824), c_Orderings_Oord__class_Oless__eq(_287822, _287826, c_Groups_Ozero__class_Ozero(_287822)), -(c_Orderings_Oord__class_Oless__eq(_287822, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287822), _287824), _287826), c_Groups_Ozero__class_Ozero(_287822)))], (3511 ^ _166148) ^ [_288270, _288272, _288274] : [class_Rings_Oordered__cancel__semiring(_288270), c_Orderings_Oord__class_Oless__eq(_288270, c_Groups_Ozero__class_Ozero(_288270), _288272), c_Orderings_Oord__class_Oless__eq(_288270, c_Groups_Ozero__class_Ozero(_288270), _288274), -(c_Orderings_Oord__class_Oless__eq(_288270, c_Groups_Ozero__class_Ozero(_288270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_288270), _288272), _288274)))], (3525 ^ _166148) ^ [_288718, _288720, _288722] : [class_Rings_Olinordered__ring__strict(_288718), 3528 ^ _166148 : [(3529 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_288718, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_288718), _288720), _288722), c_Groups_Ozero__class_Ozero(_288718)), 3534 ^ _166148 : [(3535 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_288718, c_Groups_Ozero__class_Ozero(_288718), _288720))], (3537 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_288718, _288722, c_Groups_Ozero__class_Ozero(_288718)))]], 3538 ^ _166148 : [(3539 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_288718, _288720, c_Groups_Ozero__class_Ozero(_288718)))], (3541 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_288718, c_Groups_Ozero__class_Ozero(_288718), _288722))]]], (3543 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_288718, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_288718), _288720), _288722), c_Groups_Ozero__class_Ozero(_288718))), 3544 ^ _166148 : [(3545 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_288718, c_Groups_Ozero__class_Ozero(_288718), _288720), c_Orderings_Oord__class_Oless__eq(_288718, _288722, c_Groups_Ozero__class_Ozero(_288718))], (3551 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_288718, _288720, c_Groups_Ozero__class_Ozero(_288718)), c_Orderings_Oord__class_Oless__eq(_288718, c_Groups_Ozero__class_Ozero(_288718), _288722)]]]]], (3559 ^ _166148) ^ [_289767, _289769, _289771] : [class_Rings_Olinordered__ring__strict(_289767), 3562 ^ _166148 : [(3563 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289767, c_Groups_Ozero__class_Ozero(_289767), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289767), _289769), _289771)), 3568 ^ _166148 : [(3569 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_289767, c_Groups_Ozero__class_Ozero(_289767), _289769))], (3571 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_289767, c_Groups_Ozero__class_Ozero(_289767), _289771))]], 3572 ^ _166148 : [(3573 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_289767, _289769, c_Groups_Ozero__class_Ozero(_289767)))], (3575 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_289767, _289771, c_Groups_Ozero__class_Ozero(_289767)))]]], (3577 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_289767, c_Groups_Ozero__class_Ozero(_289767), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289767), _289769), _289771))), 3578 ^ _166148 : [(3579 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289767, c_Groups_Ozero__class_Ozero(_289767), _289769), c_Orderings_Oord__class_Oless__eq(_289767, c_Groups_Ozero__class_Ozero(_289767), _289771)], (3585 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289767, _289769, c_Groups_Ozero__class_Ozero(_289767)), c_Orderings_Oord__class_Oless__eq(_289767, _289771, c_Groups_Ozero__class_Ozero(_289767))]]]]], (3593 ^ _166148) ^ [_290802, _290804] : [class_Rings_Olinordered__ring(_290802), -(c_Orderings_Oord__class_Oless__eq(_290802, c_Groups_Ozero__class_Ozero(_290802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_290802), _290804), _290804)))], (3599 ^ _166148) ^ [_291032, _291034] : [class_Rings_Olinordered__ring(_291032), c_Orderings_Oord__class_Oless(_291032, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291032), _291034), _291034), c_Groups_Ozero__class_Ozero(_291032))], (3605 ^ _166148) ^ [_291291, _291293, _291295, _291297] : [class_Rings_Olinordered__ring__strict(_291291), 3608 ^ _166148 : [(3609 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_291291, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291291), _291293), _291295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291291), _291297), _291295)), 3614 ^ _166148 : [(3615 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_291291, c_Groups_Ozero__class_Ozero(_291291), _291295))], (3617 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_291291, _291293, _291297))]], 3618 ^ _166148 : [(3619 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_291291, _291295, c_Groups_Ozero__class_Ozero(_291291)))], (3621 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_291291, _291297, _291293))]]], (3623 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_291291, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291291), _291293), _291295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291291), _291297), _291295))), 3624 ^ _166148 : [(3625 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_291291, c_Groups_Ozero__class_Ozero(_291291), _291295), c_Orderings_Oord__class_Oless(_291291, _291293, _291297)], (3631 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_291291, _291295, c_Groups_Ozero__class_Ozero(_291291)), c_Orderings_Oord__class_Oless(_291291, _291297, _291293)]]]]], (3639 ^ _166148) ^ [_292394, _292396, _292398, _292400] : [class_Rings_Olinordered__ring__strict(_292394), 3642 ^ _166148 : [(3643 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_292394, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292394), _292396), _292398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292394), _292396), _292400)), 3648 ^ _166148 : [(3649 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_292394, c_Groups_Ozero__class_Ozero(_292394), _292396))], (3651 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_292394, _292398, _292400))]], 3652 ^ _166148 : [(3653 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_292394, _292396, c_Groups_Ozero__class_Ozero(_292394)))], (3655 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_292394, _292400, _292398))]]], (3657 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_292394, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292394), _292396), _292398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292394), _292396), _292400))), 3658 ^ _166148 : [(3659 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_292394, c_Groups_Ozero__class_Ozero(_292394), _292396), c_Orderings_Oord__class_Oless(_292394, _292398, _292400)], (3665 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_292394, _292396, c_Groups_Ozero__class_Ozero(_292394)), c_Orderings_Oord__class_Oless(_292394, _292400, _292398)]]]]], (3673 ^ _166148) ^ [_293497, _293499, _293501, _293503] : [class_Rings_Olinordered__ring__strict(_293497), c_Orderings_Oord__class_Oless(_293497, c_Groups_Ozero__class_Ozero(_293497), _293499), 3680 ^ _166148 : [(3681 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_293497, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293497), _293499), _293501), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293497), _293499), _293503)), -(c_Orderings_Oord__class_Oless(_293497, _293501, _293503))], (3687 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_293497, _293501, _293503), -(c_Orderings_Oord__class_Oless(_293497, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293497), _293499), _293501), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293497), _293499), _293503)))]]], (3693 ^ _166148) ^ [_294158, _294160, _294162] : [class_Rings_Olinordered__semiring__strict(_294158), c_Orderings_Oord__class_Oless(_294158, c_Groups_Ozero__class_Ozero(_294158), _294160), c_Orderings_Oord__class_Oless(_294158, c_Groups_Ozero__class_Ozero(_294158), _294162), -(c_Orderings_Oord__class_Oless(_294158, c_Groups_Ozero__class_Ozero(_294158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_294158), _294160), _294162)))], (3707 ^ _166148) ^ [_294606, _294608, _294610] : [class_Rings_Olinordered__semiring__strict(_294606), c_Orderings_Oord__class_Oless(_294606, c_Groups_Ozero__class_Ozero(_294606), _294608), c_Orderings_Oord__class_Oless(_294606, _294610, c_Groups_Ozero__class_Ozero(_294606)), -(c_Orderings_Oord__class_Oless(_294606, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_294606), _294608), _294610), c_Groups_Ozero__class_Ozero(_294606)))], (3721 ^ _166148) ^ [_295054, _295056, _295058] : [class_Rings_Olinordered__semiring__strict(_295054), c_Orderings_Oord__class_Oless(_295054, c_Groups_Ozero__class_Ozero(_295054), _295056), c_Orderings_Oord__class_Oless(_295054, _295058, c_Groups_Ozero__class_Ozero(_295054)), -(c_Orderings_Oord__class_Oless(_295054, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295054), _295058), _295056), c_Groups_Ozero__class_Ozero(_295054)))], (3735 ^ _166148) ^ [_295502, _295504, _295506] : [class_Rings_Olinordered__semiring__strict(_295502), c_Orderings_Oord__class_Oless(_295502, c_Groups_Ozero__class_Ozero(_295502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295502), _295504), _295506)), c_Orderings_Oord__class_Oless(_295502, c_Groups_Ozero__class_Ozero(_295502), _295504), -(c_Orderings_Oord__class_Oless(_295502, c_Groups_Ozero__class_Ozero(_295502), _295506))], (3749 ^ _166148) ^ [_295950, _295952, _295954] : [class_Rings_Olinordered__semiring__strict(_295950), c_Orderings_Oord__class_Oless(_295950, c_Groups_Ozero__class_Ozero(_295950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295950), _295952), _295954)), c_Orderings_Oord__class_Oless(_295950, c_Groups_Ozero__class_Ozero(_295950), _295954), -(c_Orderings_Oord__class_Oless(_295950, c_Groups_Ozero__class_Ozero(_295950), _295952))], (3763 ^ _166148) ^ [_296412, _296414, _296416, _296418] : [class_Rings_Olinordered__ring__strict(_296412), c_Orderings_Oord__class_Oless(_296412, _296414, c_Groups_Ozero__class_Ozero(_296412)), 3770 ^ _166148 : [(3771 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_296412, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296412), _296414), _296416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296412), _296414), _296418)), -(c_Orderings_Oord__class_Oless(_296412, _296418, _296416))], (3777 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_296412, _296418, _296416), -(c_Orderings_Oord__class_Oless(_296412, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296412), _296414), _296416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296412), _296414), _296418)))]]], (3783 ^ _166148) ^ [_297073, _297075, _297077] : [class_Rings_Olinordered__semiring__strict(_297073), c_Orderings_Oord__class_Oless(_297073, _297075, c_Groups_Ozero__class_Ozero(_297073)), c_Orderings_Oord__class_Oless(_297073, c_Groups_Ozero__class_Ozero(_297073), _297077), -(c_Orderings_Oord__class_Oless(_297073, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297073), _297075), _297077), c_Groups_Ozero__class_Ozero(_297073)))], (3797 ^ _166148) ^ [_297521, _297523, _297525] : [class_Rings_Olinordered__ring__strict(_297521), c_Orderings_Oord__class_Oless(_297521, _297523, c_Groups_Ozero__class_Ozero(_297521)), c_Orderings_Oord__class_Oless(_297521, _297525, c_Groups_Ozero__class_Ozero(_297521)), -(c_Orderings_Oord__class_Oless(_297521, c_Groups_Ozero__class_Ozero(_297521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297521), _297523), _297525)))], (3811 ^ _166148) ^ [_297983, _297985, _297987, _297989] : [class_Rings_Olinordered__semiring__strict(_297983), c_Orderings_Oord__class_Oless(_297983, _297985, _297987), c_Orderings_Oord__class_Oless(_297983, c_Groups_Ozero__class_Ozero(_297983), _297989), -(c_Orderings_Oord__class_Oless(_297983, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297983), _297985), _297989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297983), _297987), _297989)))], (3825 ^ _166148) ^ [_298467, _298469, _298471, _298473] : [class_Rings_Olinordered__semiring__strict(_298467), c_Orderings_Oord__class_Oless(_298467, _298469, _298471), c_Orderings_Oord__class_Oless(_298467, c_Groups_Ozero__class_Ozero(_298467), _298473), -(c_Orderings_Oord__class_Oless(_298467, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298467), _298473), _298469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298467), _298473), _298471)))], (3839 ^ _166148) ^ [_298951, _298953, _298955, _298957] : [class_Rings_Olinordered__comm__semiring__strict(_298951), c_Orderings_Oord__class_Oless(_298951, _298953, _298955), c_Orderings_Oord__class_Oless(_298951, c_Groups_Ozero__class_Ozero(_298951), _298957), -(c_Orderings_Oord__class_Oless(_298951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298951), _298957), _298953), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298951), _298957), _298955)))], (3853 ^ _166148) ^ [_299435, _299437, _299439, _299441] : [class_Rings_Olinordered__ring__strict(_299435), c_Orderings_Oord__class_Oless(_299435, _299437, _299439), c_Orderings_Oord__class_Oless(_299435, _299441, c_Groups_Ozero__class_Ozero(_299435)), -(c_Orderings_Oord__class_Oless(_299435, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299435), _299439), _299441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299435), _299437), _299441)))], (3867 ^ _166148) ^ [_299919, _299921, _299923, _299925] : [class_Rings_Olinordered__ring__strict(_299919), c_Orderings_Oord__class_Oless(_299919, _299921, _299923), c_Orderings_Oord__class_Oless(_299919, _299925, c_Groups_Ozero__class_Ozero(_299919)), -(c_Orderings_Oord__class_Oless(_299919, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299919), _299925), _299923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299919), _299925), _299921)))], (3881 ^ _166148) ^ [_300403, _300405, _300407, _300409] : [class_Rings_Olinordered__semidom(_300403), c_Orderings_Oord__class_Oless(_300403, c_Groups_Ozero__class_Ozero(_300403), _300405), c_Orderings_Oord__class_Oless(_300403, _300407, _300409), -(c_Orderings_Oord__class_Oless(_300403, _300407, c_Groups_Oplus__class_Oplus(_300403, _300405, _300409)))], (3895 ^ _166148) ^ [_300821] : [class_Rings_Olinordered__semidom(_300821), -(c_Orderings_Oord__class_Oless__eq(_300821, c_Groups_Ozero__class_Ozero(_300821), c_Groups_Oone__class_Oone(_300821)))], (3901 ^ _166148) ^ [_301019] : [class_Rings_Olinordered__semidom(_301019), c_Orderings_Oord__class_Oless__eq(_301019, c_Groups_Oone__class_Oone(_301019), c_Groups_Ozero__class_Ozero(_301019))], (3907 ^ _166148) ^ [_301218] : [class_Rings_Olinordered__semidom(_301218), c_Orderings_Oord__class_Oless(_301218, c_Groups_Oone__class_Oone(_301218), c_Groups_Ozero__class_Ozero(_301218))], (3913 ^ _166148) ^ [_301417] : [class_Rings_Olinordered__semidom(_301417), -(c_Orderings_Oord__class_Oless(_301417, c_Groups_Ozero__class_Ozero(_301417), c_Groups_Oone__class_Oone(_301417)))], (3919 ^ _166148) ^ [_301643, _301645, _301647] : [class_Rings_Olinordered__semidom(_301643), c_Orderings_Oord__class_Oless(_301643, c_Groups_Oone__class_Oone(_301643), _301645), c_Orderings_Oord__class_Oless(_301643, c_Groups_Oone__class_Oone(_301643), _301647), -(c_Orderings_Oord__class_Oless(_301643, c_Groups_Oone__class_Oone(_301643), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301643), _301645), _301647)))], (3933 ^ _166148) ^ [_302077, _302079] : [class_Rings_Olinordered__semidom(_302077), -(c_Orderings_Oord__class_Oless(_302077, _302079, c_Groups_Oplus__class_Oplus(_302077, _302079, c_Groups_Oone__class_Oone(_302077))))], (3939 ^ _166148) ^ [_302299, _302301] : [class_Fields_Olinordered__field__inverse__zero(_302299), 3942 ^ _166148 : [(3943 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_302299, c_Rings_Oinverse__class_Oinverse(_302299, _302301), c_Groups_Ozero__class_Ozero(_302299)), -(c_Orderings_Oord__class_Oless__eq(_302299, _302301, c_Groups_Ozero__class_Ozero(_302299)))], (3949 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_302299, _302301, c_Groups_Ozero__class_Ozero(_302299)), -(c_Orderings_Oord__class_Oless__eq(_302299, c_Rings_Oinverse__class_Oinverse(_302299, _302301), c_Groups_Ozero__class_Ozero(_302299)))]]], (3955 ^ _166148) ^ [_302784, _302786] : [class_Fields_Olinordered__field__inverse__zero(_302784), 3958 ^ _166148 : [(3959 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_302784, c_Groups_Ozero__class_Ozero(_302784), c_Rings_Oinverse__class_Oinverse(_302784, _302786)), -(c_Orderings_Oord__class_Oless__eq(_302784, c_Groups_Ozero__class_Ozero(_302784), _302786))], (3965 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_302784, c_Groups_Ozero__class_Ozero(_302784), _302786), -(c_Orderings_Oord__class_Oless__eq(_302784, c_Groups_Ozero__class_Ozero(_302784), c_Rings_Oinverse__class_Oinverse(_302784, _302786)))]]], (3971 ^ _166148) ^ [_303283, _303285, _303287] : [class_Fields_Olinordered__field(_303283), c_Orderings_Oord__class_Oless(_303283, c_Rings_Oinverse__class_Oinverse(_303283, _303285), c_Rings_Oinverse__class_Oinverse(_303283, _303287)), c_Orderings_Oord__class_Oless(_303283, _303287, c_Groups_Ozero__class_Ozero(_303283)), -(c_Orderings_Oord__class_Oless(_303283, _303287, _303285))], (3985 ^ _166148) ^ [_303719, _303721, _303723] : [class_Fields_Olinordered__field(_303719), c_Orderings_Oord__class_Oless(_303719, c_Rings_Oinverse__class_Oinverse(_303719, _303721), c_Rings_Oinverse__class_Oinverse(_303719, _303723)), c_Orderings_Oord__class_Oless(_303719, c_Groups_Ozero__class_Ozero(_303719), _303721), -(c_Orderings_Oord__class_Oless(_303719, _303723, _303721))], (3999 ^ _166148) ^ [_304141, _304143] : [class_Fields_Olinordered__field(_304141), c_Orderings_Oord__class_Oless(_304141, c_Rings_Oinverse__class_Oinverse(_304141, _304143), c_Groups_Ozero__class_Ozero(_304141)), -(_304143 = c_Groups_Ozero__class_Ozero(_304141)), -(c_Orderings_Oord__class_Oless(_304141, _304143, c_Groups_Ozero__class_Ozero(_304141)))], (4013 ^ _166148) ^ [_304566, _304568, _304570] : [class_Fields_Olinordered__field(_304566), c_Orderings_Oord__class_Oless(_304566, _304568, _304570), c_Orderings_Oord__class_Oless(_304566, _304570, c_Groups_Ozero__class_Ozero(_304566)), -(c_Orderings_Oord__class_Oless(_304566, c_Rings_Oinverse__class_Oinverse(_304566, _304570), c_Rings_Oinverse__class_Oinverse(_304566, _304568)))], (4027 ^ _166148) ^ [_305002, _305004, _305006] : [class_Fields_Olinordered__field(_305002), c_Orderings_Oord__class_Oless(_305002, _305004, _305006), c_Orderings_Oord__class_Oless(_305002, c_Groups_Ozero__class_Ozero(_305002), _305004), -(c_Orderings_Oord__class_Oless(_305002, c_Rings_Oinverse__class_Oinverse(_305002, _305006), c_Rings_Oinverse__class_Oinverse(_305002, _305004)))], (4041 ^ _166148) ^ [_305424, _305426] : [class_Fields_Olinordered__field(_305424), c_Orderings_Oord__class_Oless(_305424, _305426, c_Groups_Ozero__class_Ozero(_305424)), -(c_Orderings_Oord__class_Oless(_305424, c_Rings_Oinverse__class_Oinverse(_305424, _305426), c_Groups_Ozero__class_Ozero(_305424)))], (4051 ^ _166148) ^ [_305739, _305741] : [class_Fields_Olinordered__field(_305739), c_Orderings_Oord__class_Oless(_305739, c_Groups_Ozero__class_Ozero(_305739), c_Rings_Oinverse__class_Oinverse(_305739, _305741)), -(_305741 = c_Groups_Ozero__class_Ozero(_305739)), -(c_Orderings_Oord__class_Oless(_305739, c_Groups_Ozero__class_Ozero(_305739), _305741))], (4065 ^ _166148) ^ [_306150, _306152] : [class_Fields_Olinordered__field(_306150), c_Orderings_Oord__class_Oless(_306150, c_Groups_Ozero__class_Ozero(_306150), _306152), -(c_Orderings_Oord__class_Oless(_306150, c_Groups_Ozero__class_Ozero(_306150), c_Rings_Oinverse__class_Oinverse(_306150, _306152)))], (4075 ^ _166148) ^ [_306465, _306467] : [class_Fields_Olinordered__field__inverse__zero(_306465), 4078 ^ _166148 : [(4079 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_306465, c_Rings_Oinverse__class_Oinverse(_306465, _306467), c_Groups_Ozero__class_Ozero(_306465)), -(c_Orderings_Oord__class_Oless(_306465, _306467, c_Groups_Ozero__class_Ozero(_306465)))], (4085 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_306465, _306467, c_Groups_Ozero__class_Ozero(_306465)), -(c_Orderings_Oord__class_Oless(_306465, c_Rings_Oinverse__class_Oinverse(_306465, _306467), c_Groups_Ozero__class_Ozero(_306465)))]]], (4091 ^ _166148) ^ [_306950, _306952] : [class_Fields_Olinordered__field__inverse__zero(_306950), 4094 ^ _166148 : [(4095 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_306950, c_Groups_Ozero__class_Ozero(_306950), c_Rings_Oinverse__class_Oinverse(_306950, _306952)), -(c_Orderings_Oord__class_Oless(_306950, c_Groups_Ozero__class_Ozero(_306950), _306952))], (4101 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_306950, c_Groups_Ozero__class_Ozero(_306950), _306952), -(c_Orderings_Oord__class_Oless(_306950, c_Groups_Ozero__class_Ozero(_306950), c_Rings_Oinverse__class_Oinverse(_306950, _306952)))]]], (4107 ^ _166148) ^ [_307449, _307451, _307453] : [class_Rings_Odivision__ring(_307449), -(_307451 = c_Groups_Ozero__class_Ozero(_307449)), -(_307453 = c_Groups_Ozero__class_Ozero(_307449)), -(c_Rings_Oinverse__class_Oinverse(_307449, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307449), _307451), _307453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307449), c_Rings_Oinverse__class_Oinverse(_307449, _307453)), c_Rings_Oinverse__class_Oinverse(_307449, _307451)))], (4121 ^ _166148) ^ [_307927, _307929, _307931] : [class_Rings_Odivision__ring(_307927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307927), _307929), _307931) = c_Groups_Oone__class_Oone(_307927), -(c_Rings_Oinverse__class_Oinverse(_307927, _307929) = _307931)], (4141 ^ _166148) ^ [_308555, _308557] : [4142 ^ _166148 : [(4143 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _308555)], (4145 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _308557)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _308555, _308557)))], (4131 ^ _166148) ^ [_308289, _308291] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _308289, _308291)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _308289)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _308291))], (4149 ^ _166148) ^ [_308869, _308871, _308873] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _308869), 4152 ^ _166148 : [(4153 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _308871), _308869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _308873), _308869)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _308871, _308873))], (4159 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _308871, _308873), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _308871), _308869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _308873), _308869)))]]], (4165 ^ _166148) ^ [_309389, _309391] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _309389), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _309391), -(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), _309389), _309391)))], (4175 ^ _166148) ^ [_309720, _309722, _309724] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _309720), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _309722, _309724), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _309720), _309722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _309720), _309724)))], (4185 ^ _166148) ^ [_310088, _310090] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _310088), _310088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _310090), _310090)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4188 ^ _166148 : [(4189 ^ _166148) ^ [] : [-(_310088 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4191 ^ _166148) ^ [] : [-(_310090 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (4193 ^ _166148) ^ [_310357, _310359] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _310357), _310357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _310359), _310359)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _310357 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _310359 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (4203 ^ _166148) ^ [_310718, _310720, _310722, _310724] : [class_Rings_Olinordered__ring__strict(_310718), c_Orderings_Oord__class_Oless(_310718, c_Groups_Ozero__class_Ozero(_310718), _310720), 4210 ^ _166148 : [(4211 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_310718, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310718), _310720), _310722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310718), _310720), _310724)), -(c_Orderings_Oord__class_Oless__eq(_310718, _310722, _310724))], (4217 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_310718, _310722, _310724), -(c_Orderings_Oord__class_Oless__eq(_310718, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310718), _310720), _310722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310718), _310720), _310724)))]]], (4223 ^ _166148) ^ [_311393, _311395, _311397, _311399] : [class_Rings_Olinordered__ring__strict(_311393), c_Orderings_Oord__class_Oless(_311393, _311395, c_Groups_Ozero__class_Ozero(_311393)), 4230 ^ _166148 : [(4231 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_311393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311393), _311395), _311397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311393), _311395), _311399)), -(c_Orderings_Oord__class_Oless__eq(_311393, _311399, _311397))], (4237 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_311393, _311399, _311397), -(c_Orderings_Oord__class_Oless__eq(_311393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311393), _311395), _311397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311393), _311395), _311399)))]]], (4243 ^ _166148) ^ [_312082, _312084, _312086, _312088, _312090] : [class_Rings_Olinordered__semiring__strict(_312082), c_Orderings_Oord__class_Oless(_312082, _312084, _312086), c_Orderings_Oord__class_Oless(_312082, _312088, _312090), c_Orderings_Oord__class_Oless(_312082, c_Groups_Ozero__class_Ozero(_312082), _312086), c_Orderings_Oord__class_Oless__eq(_312082, c_Groups_Ozero__class_Ozero(_312082), _312088), -(c_Orderings_Oord__class_Oless(_312082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312082), _312084), _312088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312082), _312086), _312090)))], (4265 ^ _166148) ^ [_312804, _312806, _312808, _312810, _312812] : [class_Rings_Olinordered__semiring__strict(_312804), c_Orderings_Oord__class_Oless(_312804, _312806, _312808), c_Orderings_Oord__class_Oless(_312804, _312810, _312812), c_Orderings_Oord__class_Oless__eq(_312804, c_Groups_Ozero__class_Ozero(_312804), _312806), c_Orderings_Oord__class_Oless__eq(_312804, c_Groups_Ozero__class_Ozero(_312804), _312810), -(c_Orderings_Oord__class_Oless(_312804, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312804), _312806), _312810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312804), _312808), _312812)))], (4287 ^ _166148) ^ [_313526, _313528, _313530, _313532, _313534] : [class_Rings_Olinordered__semiring__strict(_313526), c_Orderings_Oord__class_Oless(_313526, _313528, _313530), c_Orderings_Oord__class_Oless__eq(_313526, _313532, _313534), c_Orderings_Oord__class_Oless__eq(_313526, c_Groups_Ozero__class_Ozero(_313526), _313528), c_Orderings_Oord__class_Oless(_313526, c_Groups_Ozero__class_Ozero(_313526), _313532), -(c_Orderings_Oord__class_Oless(_313526, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313526), _313528), _313532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313526), _313530), _313534)))], (4309 ^ _166148) ^ [_314248, _314250, _314252, _314254, _314256] : [class_Rings_Olinordered__semiring__strict(_314248), c_Orderings_Oord__class_Oless__eq(_314248, _314250, _314252), c_Orderings_Oord__class_Oless(_314248, _314254, _314256), c_Orderings_Oord__class_Oless(_314248, c_Groups_Ozero__class_Ozero(_314248), _314250), c_Orderings_Oord__class_Oless__eq(_314248, c_Groups_Ozero__class_Ozero(_314248), _314254), -(c_Orderings_Oord__class_Oless(_314248, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314248), _314250), _314254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314248), _314252), _314256)))], (4331 ^ _166148) ^ [_314956, _314958, _314960, _314962] : [class_Rings_Olinordered__semiring(_314956), c_Orderings_Oord__class_Oless(_314956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314956), _314958), _314960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314956), _314962), _314960)), c_Orderings_Oord__class_Oless__eq(_314956, c_Groups_Ozero__class_Ozero(_314956), _314960), -(c_Orderings_Oord__class_Oless(_314956, _314958, _314962))], (4345 ^ _166148) ^ [_315440, _315442, _315444, _315446] : [class_Rings_Olinordered__semiring__strict(_315440), c_Orderings_Oord__class_Oless(_315440, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315440), _315442), _315444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315440), _315446), _315444)), c_Orderings_Oord__class_Oless__eq(_315440, c_Groups_Ozero__class_Ozero(_315440), _315444), -(c_Orderings_Oord__class_Oless(_315440, _315442, _315446))], (4359 ^ _166148) ^ [_315924, _315926, _315928, _315930] : [class_Rings_Olinordered__semiring(_315924), c_Orderings_Oord__class_Oless(_315924, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315924), _315926), _315928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315924), _315926), _315930)), c_Orderings_Oord__class_Oless__eq(_315924, c_Groups_Ozero__class_Ozero(_315924), _315926), -(c_Orderings_Oord__class_Oless(_315924, _315928, _315930))], (4373 ^ _166148) ^ [_316408, _316410, _316412, _316414] : [class_Rings_Olinordered__semiring__strict(_316408), c_Orderings_Oord__class_Oless(_316408, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316408), _316410), _316412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316408), _316410), _316414)), c_Orderings_Oord__class_Oless__eq(_316408, c_Groups_Ozero__class_Ozero(_316408), _316410), -(c_Orderings_Oord__class_Oless(_316408, _316412, _316414))], (4387 ^ _166148) ^ [_316892, _316894, _316896, _316898] : [class_Rings_Olinordered__semiring__strict(_316892), c_Orderings_Oord__class_Oless__eq(_316892, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316892), _316894), _316896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316892), _316898), _316896)), c_Orderings_Oord__class_Oless(_316892, c_Groups_Ozero__class_Ozero(_316892), _316896), -(c_Orderings_Oord__class_Oless__eq(_316892, _316894, _316898))], (4401 ^ _166148) ^ [_317376, _317378, _317380, _317382] : [class_Rings_Olinordered__semiring__strict(_317376), c_Orderings_Oord__class_Oless__eq(_317376, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317376), _317378), _317380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317376), _317378), _317382)), c_Orderings_Oord__class_Oless(_317376, c_Groups_Ozero__class_Ozero(_317376), _317378), -(c_Orderings_Oord__class_Oless__eq(_317376, _317380, _317382))], (4415 ^ _166148) ^ [_317846, _317848, _317850] : [class_Rings_Olinordered__idom(_317846), c_Orderings_Oord__class_Oless__eq(_317846, c_Groups_Ozero__class_Ozero(_317846), _317848), c_Orderings_Oord__class_Oless__eq(_317846, c_Groups_Ozero__class_Ozero(_317846), _317850), c_Orderings_Oord__class_Oless__eq(_317846, _317850, c_Groups_Oone__class_Oone(_317846)), -(c_Orderings_Oord__class_Oless__eq(_317846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317846), _317848), _317850), _317848))], (4433 ^ _166148) ^ [_318389, _318391, _318393] : [class_Rings_Olinordered__idom(_318389), c_Orderings_Oord__class_Oless__eq(_318389, c_Groups_Ozero__class_Ozero(_318389), _318391), c_Orderings_Oord__class_Oless__eq(_318389, c_Groups_Ozero__class_Ozero(_318389), _318393), c_Orderings_Oord__class_Oless__eq(_318389, _318393, c_Groups_Oone__class_Oone(_318389)), -(c_Orderings_Oord__class_Oless__eq(_318389, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318389), _318393), _318391), _318391))], (4451 ^ _166148) ^ [_318904] : [class_Rings_Olinordered__semidom(_318904), -(c_Orderings_Oord__class_Oless(_318904, c_Groups_Ozero__class_Ozero(_318904), c_Groups_Oplus__class_Oplus(_318904, c_Groups_Oone__class_Oone(_318904), c_Groups_Oone__class_Oone(_318904))))], (4457 ^ _166148) ^ [_319142, _319144, _319146] : [class_Fields_Olinordered__field(_319142), c_Orderings_Oord__class_Oless__eq(_319142, c_Rings_Oinverse__class_Oinverse(_319142, _319144), c_Rings_Oinverse__class_Oinverse(_319142, _319146)), c_Orderings_Oord__class_Oless(_319142, _319146, c_Groups_Ozero__class_Ozero(_319142)), -(c_Orderings_Oord__class_Oless__eq(_319142, _319146, _319144))], (4471 ^ _166148) ^ [_319578, _319580, _319582] : [class_Fields_Olinordered__field(_319578), c_Orderings_Oord__class_Oless__eq(_319578, c_Rings_Oinverse__class_Oinverse(_319578, _319580), c_Rings_Oinverse__class_Oinverse(_319578, _319582)), c_Orderings_Oord__class_Oless(_319578, c_Groups_Ozero__class_Ozero(_319578), _319580), -(c_Orderings_Oord__class_Oless__eq(_319578, _319582, _319580))], (4485 ^ _166148) ^ [_320014, _320016, _320018] : [class_Fields_Olinordered__field(_320014), c_Orderings_Oord__class_Oless__eq(_320014, _320016, _320018), c_Orderings_Oord__class_Oless(_320014, _320018, c_Groups_Ozero__class_Ozero(_320014)), -(c_Orderings_Oord__class_Oless__eq(_320014, c_Rings_Oinverse__class_Oinverse(_320014, _320018), c_Rings_Oinverse__class_Oinverse(_320014, _320016)))], (4499 ^ _166148) ^ [_320450, _320452, _320454] : [class_Fields_Olinordered__field(_320450), c_Orderings_Oord__class_Oless__eq(_320450, _320452, _320454), c_Orderings_Oord__class_Oless(_320450, c_Groups_Ozero__class_Ozero(_320450), _320452), -(c_Orderings_Oord__class_Oless__eq(_320450, c_Rings_Oinverse__class_Oinverse(_320450, _320454), c_Rings_Oinverse__class_Oinverse(_320450, _320452)))], (4513 ^ _166148) ^ [_320872, _320874] : [class_Fields_Olinordered__field__inverse__zero(_320872), 4516 ^ _166148 : [(4527 ^ _166148) ^ [] : [4528 ^ _166148 : [(4529 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320872, _320874, c_Groups_Ozero__class_Ozero(_320872))], (4531 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320872, c_Groups_Oone__class_Oone(_320872), _320874)]], -(c_Orderings_Oord__class_Oless__eq(_320872, c_Rings_Oinverse__class_Oinverse(_320872, _320874), c_Groups_Oone__class_Oone(_320872)))], (4517 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320872, c_Rings_Oinverse__class_Oinverse(_320872, _320874), c_Groups_Oone__class_Oone(_320872)), -(c_Orderings_Oord__class_Oless__eq(_320872, _320874, c_Groups_Ozero__class_Ozero(_320872))), -(c_Orderings_Oord__class_Oless__eq(_320872, c_Groups_Oone__class_Oone(_320872), _320874))]]], (4535 ^ _166148) ^ [_321538, _321540, _321542] : [class_Rings_Odivision__ring(_321538), -(_321540 = c_Groups_Ozero__class_Ozero(_321538)), -(_321542 = c_Groups_Ozero__class_Ozero(_321538)), -(c_Groups_Oplus__class_Oplus(_321538, c_Rings_Oinverse__class_Oinverse(_321538, _321540), c_Rings_Oinverse__class_Oinverse(_321538, _321542)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_321538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_321538), c_Rings_Oinverse__class_Oinverse(_321538, _321540)), c_Groups_Oplus__class_Oplus(_321538, _321540, _321542))), c_Rings_Oinverse__class_Oinverse(_321538, _321542)))], (4549 ^ _166148) ^ [_322038, _322040, _322042] : [class_Fields_Ofield(_322038), -(_322040 = c_Groups_Ozero__class_Ozero(_322038)), -(_322042 = c_Groups_Ozero__class_Ozero(_322038)), -(c_Groups_Oplus__class_Oplus(_322038, c_Rings_Oinverse__class_Oinverse(_322038, _322040), c_Rings_Oinverse__class_Oinverse(_322038, _322042)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322038), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322038), c_Groups_Oplus__class_Oplus(_322038, _322040, _322042)), c_Rings_Oinverse__class_Oinverse(_322038, _322040))), c_Rings_Oinverse__class_Oinverse(_322038, _322042)))], (4563 ^ _166148) ^ [_322524, _322526] : [class_Fields_Olinordered__field__inverse__zero(_322524), 4566 ^ _166148 : [(4567 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_322524, c_Groups_Oone__class_Oone(_322524), c_Rings_Oinverse__class_Oinverse(_322524, _322526)), 4570 ^ _166148 : [(4571 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_322524, c_Groups_Ozero__class_Ozero(_322524), _322526))], (4573 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_322524, _322526, c_Groups_Oone__class_Oone(_322524)))]]], (4575 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_322524, c_Groups_Oone__class_Oone(_322524), c_Rings_Oinverse__class_Oinverse(_322524, _322526))), c_Orderings_Oord__class_Oless(_322524, c_Groups_Ozero__class_Ozero(_322524), _322526), c_Orderings_Oord__class_Oless(_322524, _322526, c_Groups_Oone__class_Oone(_322524))]]], (4585 ^ _166148) ^ [_323176, _323178] : [class_Fields_Olinordered__field(_323176), c_Orderings_Oord__class_Oless(_323176, c_Groups_Ozero__class_Ozero(_323176), _323178), c_Orderings_Oord__class_Oless(_323176, _323178, c_Groups_Oone__class_Oone(_323176)), -(c_Orderings_Oord__class_Oless(_323176, c_Groups_Oone__class_Oone(_323176), c_Rings_Oinverse__class_Oinverse(_323176, _323178)))], (4599 ^ _166148) ^ [_323586, _323588] : [class_Rings_Odivision__ring(_323586), -(_323588 = c_Groups_Ozero__class_Ozero(_323586)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323586), _323588), c_Rings_Oinverse__class_Oinverse(_323586, _323588)) = c_Groups_Oone__class_Oone(_323586))], (4609 ^ _166148) ^ [_323916, _323918] : [class_Fields_Ofield(_323916), -(_323918 = c_Groups_Ozero__class_Ozero(_323916)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323916), c_Rings_Oinverse__class_Oinverse(_323916, _323918)), _323918) = c_Groups_Oone__class_Oone(_323916))], (4619 ^ _166148) ^ [_324246, _324248] : [class_Rings_Odivision__ring(_324246), -(_324248 = c_Groups_Ozero__class_Ozero(_324246)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324246), c_Rings_Oinverse__class_Oinverse(_324246, _324248)), _324248) = c_Groups_Oone__class_Oone(_324246))], (4629 ^ _166148) ^ [_324590, _324592, _324594] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _324590), 4632 ^ _166148 : [(4633 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _324592), _324590), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _324594), _324590)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _324592, _324594))], (4639 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _324592, _324594), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _324592), _324590), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _324594), _324590)))]]], (4645 ^ _166148) ^ [_325124, _325126, _325128] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _325124), 4648 ^ _166148 : [(4649 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _325124), _325126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _325124), _325128)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _325126, _325128))], (4655 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _325126, _325128), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _325124), _325126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _325124), _325128)))]]], (4661 ^ _166148) ^ [_325672, _325674, _325676, _325678] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _325672), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _325674), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _325674), _325676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _325672), _325678)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _325676), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _325672)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _325678), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _325674))))], (4675 ^ _166148) ^ [_326184, _326186, _326188, _326190] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _326184), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _326186), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _326186), _326188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _326184), _326190)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _326184)), _326188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _326186)), _326190)))], (4689 ^ _166148) ^ [_326682, _326684, _326686] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _326682), 4692 ^ _166148 : [(4693 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326682), _326684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326682), _326686)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _326684, _326686))], (4699 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _326684, _326686), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326682), _326684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326682), _326686)))]]], (4705 ^ _166148) ^ [_327216, _327218, _327220] : [class_Rings_Olinordered__ring(_327216), c_Orderings_Oord__class_Oless(_327216, c_Groups_Oplus__class_Oplus(_327216, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327216), _327218), _327218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327216), _327220), _327220)), c_Groups_Ozero__class_Ozero(_327216))], (4711 ^ _166148) ^ [_327491, _327493, _327495] : [class_Rings_Olinordered__ring__strict(_327491), 4714 ^ _166148 : [(4725 ^ _166148) ^ [] : [4726 ^ _166148 : [(4727 ^ _166148) ^ [] : [-(_327493 = c_Groups_Ozero__class_Ozero(_327491))], (4729 ^ _166148) ^ [] : [-(_327495 = c_Groups_Ozero__class_Ozero(_327491))]], -(c_Orderings_Oord__class_Oless(_327491, c_Groups_Ozero__class_Ozero(_327491), c_Groups_Oplus__class_Oplus(_327491, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327491), _327493), _327493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327491), _327495), _327495))))], (4715 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_327491, c_Groups_Ozero__class_Ozero(_327491), c_Groups_Oplus__class_Oplus(_327491, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327491), _327493), _327493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327491), _327495), _327495))), _327493 = c_Groups_Ozero__class_Ozero(_327491), _327495 = c_Groups_Ozero__class_Ozero(_327491)]]], (4733 ^ _166148) ^ [_328228, _328230, _328232] : [class_Rings_Olinordered__ring(_328228), -(c_Orderings_Oord__class_Oless__eq(_328228, c_Groups_Ozero__class_Ozero(_328228), c_Groups_Oplus__class_Oplus(_328228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328228), _328230), _328230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328228), _328232), _328232))))], (4739 ^ _166148) ^ [_328502, _328504, _328506] : [class_Rings_Olinordered__ring__strict(_328502), 4742 ^ _166148 : [(4743 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_328502, c_Groups_Oplus__class_Oplus(_328502, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328502), _328504), _328504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328502), _328506), _328506)), c_Groups_Ozero__class_Ozero(_328502)), 4746 ^ _166148 : [(4747 ^ _166148) ^ [] : [-(_328504 = c_Groups_Ozero__class_Ozero(_328502))], (4749 ^ _166148) ^ [] : [-(_328506 = c_Groups_Ozero__class_Ozero(_328502))]]], (4751 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_328502, c_Groups_Oplus__class_Oplus(_328502, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328502), _328504), _328504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328502), _328506), _328506)), c_Groups_Ozero__class_Ozero(_328502))), _328504 = c_Groups_Ozero__class_Ozero(_328502), _328506 = c_Groups_Ozero__class_Ozero(_328502)]]], (4761 ^ _166148) ^ [_329235, _329237, _329239] : [class_Groups_Oordered__comm__monoid__add(_329235), c_Orderings_Oord__class_Oless(_329235, c_Groups_Ozero__class_Ozero(_329235), _329237), c_Orderings_Oord__class_Oless__eq(_329235, c_Groups_Ozero__class_Ozero(_329235), _329239), -(c_Orderings_Oord__class_Oless(_329235, c_Groups_Ozero__class_Ozero(_329235), c_Groups_Oplus__class_Oplus(_329235, _329237, _329239)))], (4775 ^ _166148) ^ [_329675, _329677, _329679] : [class_Groups_Oordered__comm__monoid__add(_329675), c_Orderings_Oord__class_Oless__eq(_329675, c_Groups_Ozero__class_Ozero(_329675), _329677), c_Orderings_Oord__class_Oless(_329675, c_Groups_Ozero__class_Ozero(_329675), _329679), -(c_Orderings_Oord__class_Oless(_329675, c_Groups_Ozero__class_Ozero(_329675), c_Groups_Oplus__class_Oplus(_329675, _329677, _329679)))], (4789 ^ _166148) ^ [_330101, _330103] : [class_Groups_Ozero(_330101), 4792 ^ _166148 : [(4793 ^ _166148) ^ [] : [c_Groups_Ozero__class_Ozero(_330101) = _330103, -(_330103 = c_Groups_Ozero__class_Ozero(_330101))], (4799 ^ _166148) ^ [] : [_330103 = c_Groups_Ozero__class_Ozero(_330101), -(c_Groups_Ozero__class_Ozero(_330101) = _330103)]]], (4805 ^ _166148) ^ [_330599, _330601, _330603, _330605] : [class_Groups_Oab__semigroup__mult(_330599), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330599), _330601), _330603)), _330605) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330599), _330601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330599), _330603), _330605)))], (4811 ^ _166148) ^ [_330911, _330913, _330915, _330917] : [class_Groups_Ocancel__semigroup__add(_330911), c_Groups_Oplus__class_Oplus(_330911, _330913, _330915) = c_Groups_Oplus__class_Oplus(_330911, _330917, _330915), -(_330913 = _330917)], (4821 ^ _166148) ^ [_331272, _331274, _331276, _331278] : [class_Groups_Ocancel__ab__semigroup__add(_331272), c_Groups_Oplus__class_Oplus(_331272, _331274, _331276) = c_Groups_Oplus__class_Oplus(_331272, _331274, _331278), -(_331276 = _331278)], (4831 ^ _166148) ^ [_331633, _331635, _331637, _331639] : [class_Groups_Ocancel__semigroup__add(_331633), c_Groups_Oplus__class_Oplus(_331633, _331635, _331637) = c_Groups_Oplus__class_Oplus(_331633, _331635, _331639), -(_331637 = _331639)], (4841 ^ _166148) ^ [_331994, _331996, _331998, _332000] : [class_Groups_Ocancel__semigroup__add(_331994), 4844 ^ _166148 : [(4845 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_331994, _331996, _331998) = c_Groups_Oplus__class_Oplus(_331994, _332000, _331998), -(_331996 = _332000)], (4851 ^ _166148) ^ [] : [_331996 = _332000, -(c_Groups_Oplus__class_Oplus(_331994, _331996, _331998) = c_Groups_Oplus__class_Oplus(_331994, _332000, _331998))]]], (4857 ^ _166148) ^ [_332536, _332538, _332540, _332542] : [class_Groups_Ocancel__semigroup__add(_332536), 4860 ^ _166148 : [(4861 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_332536, _332538, _332540) = c_Groups_Oplus__class_Oplus(_332536, _332538, _332542), -(_332540 = _332542)], (4867 ^ _166148) ^ [] : [_332540 = _332542, -(c_Groups_Oplus__class_Oplus(_332536, _332538, _332540) = c_Groups_Oplus__class_Oplus(_332536, _332538, _332542))]]], (4873 ^ _166148) ^ [_333078, _333080, _333082, _333084] : [class_Groups_Oab__semigroup__add(_333078), -(c_Groups_Oplus__class_Oplus(_333078, c_Groups_Oplus__class_Oplus(_333078, _333080, _333082), _333084) = c_Groups_Oplus__class_Oplus(_333078, _333080, c_Groups_Oplus__class_Oplus(_333078, _333082, _333084)))], (4879 ^ _166148) ^ [_333330, _333332] : [class_Groups_Oone(_333330), 4882 ^ _166148 : [(4883 ^ _166148) ^ [] : [c_Groups_Oone__class_Oone(_333330) = _333332, -(_333332 = c_Groups_Oone__class_Oone(_333330))], (4889 ^ _166148) ^ [] : [_333332 = c_Groups_Oone__class_Oone(_333330), -(c_Groups_Oone__class_Oone(_333330) = _333332)]]], (4895 ^ _166148) ^ [_333800, _333802] : [class_Groups_Ocomm__monoid__add(_333800), -(c_Groups_Oplus__class_Oplus(_333800, _333802, c_Groups_Ozero__class_Ozero(_333800)) = _333802)], (4901 ^ _166148) ^ [_334020, _334022] : [class_Groups_Omonoid__add(_334020), -(c_Groups_Oplus__class_Oplus(_334020, _334022, c_Groups_Ozero__class_Ozero(_334020)) = _334022)], (4907 ^ _166148) ^ [_334240, _334242] : [class_Groups_Olinordered__ab__group__add(_334240), 4910 ^ _166148 : [(4911 ^ _166148) ^ [] : [c_Groups_Ozero__class_Ozero(_334240) = c_Groups_Oplus__class_Oplus(_334240, _334242, _334242), -(_334242 = c_Groups_Ozero__class_Ozero(_334240))], (4917 ^ _166148) ^ [] : [_334242 = c_Groups_Ozero__class_Ozero(_334240), -(c_Groups_Ozero__class_Ozero(_334240) = c_Groups_Oplus__class_Oplus(_334240, _334242, _334242))]]], (4923 ^ _166148) ^ [_334722, _334724] : [class_Groups_Ocomm__monoid__add(_334722), -(c_Groups_Oplus__class_Oplus(_334722, c_Groups_Ozero__class_Ozero(_334722), _334724) = _334724)], (4929 ^ _166148) ^ [_334942, _334944] : [class_Groups_Omonoid__add(_334942), -(c_Groups_Oplus__class_Oplus(_334942, c_Groups_Ozero__class_Ozero(_334942), _334944) = _334944)], (4935 ^ _166148) ^ [_335190, _335192, _335194, _335196] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_335190), c_Orderings_Oord__class_Oless__eq(_335190, c_Groups_Oplus__class_Oplus(_335190, _335192, _335194), c_Groups_Oplus__class_Oplus(_335190, _335192, _335196)), -(c_Orderings_Oord__class_Oless__eq(_335190, _335194, _335196))], (4945 ^ _166148) ^ [_335555, _335557, _335559, _335561] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_335555), c_Orderings_Oord__class_Oless__eq(_335555, c_Groups_Oplus__class_Oplus(_335555, _335557, _335559), c_Groups_Oplus__class_Oplus(_335555, _335561, _335559)), -(c_Orderings_Oord__class_Oless__eq(_335555, _335557, _335561))], (4955 ^ _166148) ^ [_335934, _335936, _335938, _335940, _335942] : [class_Groups_Oordered__ab__semigroup__add(_335934), c_Orderings_Oord__class_Oless__eq(_335934, _335936, _335938), c_Orderings_Oord__class_Oless__eq(_335934, _335940, _335942), -(c_Orderings_Oord__class_Oless__eq(_335934, c_Groups_Oplus__class_Oplus(_335934, _335936, _335940), c_Groups_Oplus__class_Oplus(_335934, _335938, _335942)))], (4969 ^ _166148) ^ [_336412, _336414, _336416, _336418] : [class_Groups_Oordered__ab__semigroup__add(_336412), c_Orderings_Oord__class_Oless__eq(_336412, _336414, _336416), -(c_Orderings_Oord__class_Oless__eq(_336412, c_Groups_Oplus__class_Oplus(_336412, _336418, _336414), c_Groups_Oplus__class_Oplus(_336412, _336418, _336416)))], (4979 ^ _166148) ^ [_336777, _336779, _336781, _336783] : [class_Groups_Oordered__ab__semigroup__add(_336777), c_Orderings_Oord__class_Oless__eq(_336777, _336779, _336781), -(c_Orderings_Oord__class_Oless__eq(_336777, c_Groups_Oplus__class_Oplus(_336777, _336779, _336783), c_Groups_Oplus__class_Oplus(_336777, _336781, _336783)))], (4989 ^ _166148) ^ [_337142, _337144, _337146, _337148] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_337142), 4992 ^ _166148 : [(4993 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_337142, c_Groups_Oplus__class_Oplus(_337142, _337144, _337146), c_Groups_Oplus__class_Oplus(_337142, _337144, _337148)), -(c_Orderings_Oord__class_Oless__eq(_337142, _337146, _337148))], (4999 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_337142, _337146, _337148), -(c_Orderings_Oord__class_Oless__eq(_337142, c_Groups_Oplus__class_Oplus(_337142, _337144, _337146), c_Groups_Oplus__class_Oplus(_337142, _337144, _337148)))]]], (5005 ^ _166148) ^ [_337690, _337692, _337694, _337696] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_337690), 5008 ^ _166148 : [(5009 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_337690, c_Groups_Oplus__class_Oplus(_337690, _337692, _337694), c_Groups_Oplus__class_Oplus(_337690, _337696, _337694)), -(c_Orderings_Oord__class_Oless__eq(_337690, _337692, _337696))], (5015 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_337690, _337692, _337696), -(c_Orderings_Oord__class_Oless__eq(_337690, c_Groups_Oplus__class_Oplus(_337690, _337692, _337694), c_Groups_Oplus__class_Oplus(_337690, _337696, _337694)))]]], (5021 ^ _166148) ^ [_338238, _338240, _338242, _338244] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_338238), c_Orderings_Oord__class_Oless(_338238, c_Groups_Oplus__class_Oplus(_338238, _338240, _338242), c_Groups_Oplus__class_Oplus(_338238, _338240, _338244)), -(c_Orderings_Oord__class_Oless(_338238, _338242, _338244))], (5031 ^ _166148) ^ [_338603, _338605, _338607, _338609] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_338603), c_Orderings_Oord__class_Oless(_338603, c_Groups_Oplus__class_Oplus(_338603, _338605, _338607), c_Groups_Oplus__class_Oplus(_338603, _338609, _338607)), -(c_Orderings_Oord__class_Oless(_338603, _338605, _338609))], (5041 ^ _166148) ^ [_338982, _338984, _338986, _338988, _338990] : [class_Groups_Oordered__cancel__ab__semigroup__add(_338982), c_Orderings_Oord__class_Oless(_338982, _338984, _338986), c_Orderings_Oord__class_Oless(_338982, _338988, _338990), -(c_Orderings_Oord__class_Oless(_338982, c_Groups_Oplus__class_Oplus(_338982, _338984, _338988), c_Groups_Oplus__class_Oplus(_338982, _338986, _338990)))], (5055 ^ _166148) ^ [_339460, _339462, _339464, _339466] : [class_Groups_Oordered__cancel__ab__semigroup__add(_339460), c_Orderings_Oord__class_Oless(_339460, _339462, _339464), -(c_Orderings_Oord__class_Oless(_339460, c_Groups_Oplus__class_Oplus(_339460, _339466, _339462), c_Groups_Oplus__class_Oplus(_339460, _339466, _339464)))], (5065 ^ _166148) ^ [_339825, _339827, _339829, _339831] : [class_Groups_Oordered__cancel__ab__semigroup__add(_339825), c_Orderings_Oord__class_Oless(_339825, _339827, _339829), -(c_Orderings_Oord__class_Oless(_339825, c_Groups_Oplus__class_Oplus(_339825, _339827, _339831), c_Groups_Oplus__class_Oplus(_339825, _339829, _339831)))], (5075 ^ _166148) ^ [_340190, _340192, _340194, _340196] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_340190), 5078 ^ _166148 : [(5079 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_340190, c_Groups_Oplus__class_Oplus(_340190, _340192, _340194), c_Groups_Oplus__class_Oplus(_340190, _340192, _340196)), -(c_Orderings_Oord__class_Oless(_340190, _340194, _340196))], (5085 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_340190, _340194, _340196), -(c_Orderings_Oord__class_Oless(_340190, c_Groups_Oplus__class_Oplus(_340190, _340192, _340194), c_Groups_Oplus__class_Oplus(_340190, _340192, _340196)))]]], (5091 ^ _166148) ^ [_340738, _340740, _340742, _340744] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_340738), 5094 ^ _166148 : [(5095 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_340738, c_Groups_Oplus__class_Oplus(_340738, _340740, _340742), c_Groups_Oplus__class_Oplus(_340738, _340744, _340742)), -(c_Orderings_Oord__class_Oless(_340738, _340740, _340744))], (5101 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_340738, _340740, _340744), -(c_Orderings_Oord__class_Oless(_340738, c_Groups_Oplus__class_Oplus(_340738, _340740, _340742), c_Groups_Oplus__class_Oplus(_340738, _340744, _340742)))]]], (5107 ^ _166148) ^ [_341258, _341260] : [class_Groups_Ocomm__monoid__mult(_341258), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341258), _341260), c_Groups_Oone__class_Oone(_341258)) = _341260)], (5113 ^ _166148) ^ [_341486, _341488] : [class_Groups_Omonoid__mult(_341486), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341486), _341488), c_Groups_Oone__class_Oone(_341486)) = _341488)], (5119 ^ _166148) ^ [_341714, _341716] : [class_Groups_Ocomm__monoid__mult(_341714), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341714), c_Groups_Oone__class_Oone(_341714)), _341716) = _341716)], (5125 ^ _166148) ^ [_341942, _341944] : [class_Groups_Omonoid__mult(_341942), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341942), c_Groups_Oone__class_Oone(_341942)), _341944) = _341944)], (5141 ^ _166148) ^ [_342499, _342501, _342503] : [5142 ^ _166148 : [(5143 ^ _166148) ^ [] : [_342499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5145 ^ _166148) ^ [] : [_342501 = _342503]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _342499), _342501) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _342499), _342503))], (5131 ^ _166148) ^ [_342213, _342215, _342217] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _342213), _342215) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _342213), _342217), -(_342213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_342215 = _342217)], (5149 ^ _166148) ^ [_342830, _342832, _342834, _342836] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _342830), _342832), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _342834), _342832), _342836)) = 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, _342830, _342834)), _342832), _342836))], (5151 ^ _166148) ^ [_342977, _342979] : [class_Groups_Olinordered__ab__group__add(_342977), 5154 ^ _166148 : [(5155 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_342977, c_Groups_Ozero__class_Ozero(_342977), c_Groups_Oplus__class_Oplus(_342977, _342979, _342979)), -(c_Orderings_Oord__class_Oless__eq(_342977, c_Groups_Ozero__class_Ozero(_342977), _342979))], (5161 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_342977, c_Groups_Ozero__class_Ozero(_342977), _342979), -(c_Orderings_Oord__class_Oless__eq(_342977, c_Groups_Ozero__class_Ozero(_342977), c_Groups_Oplus__class_Oplus(_342977, _342979, _342979)))]]], (5167 ^ _166148) ^ [_343465, _343467] : [class_Groups_Olinordered__ab__group__add(_343465), 5170 ^ _166148 : [(5171 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343465, c_Groups_Oplus__class_Oplus(_343465, _343467, _343467), c_Groups_Ozero__class_Ozero(_343465)), -(c_Orderings_Oord__class_Oless__eq(_343465, _343467, c_Groups_Ozero__class_Ozero(_343465)))], (5177 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343465, _343467, c_Groups_Ozero__class_Ozero(_343465)), -(c_Orderings_Oord__class_Oless__eq(_343465, c_Groups_Oplus__class_Oplus(_343465, _343467, _343467), c_Groups_Ozero__class_Ozero(_343465)))]]], (5183 ^ _166148) ^ [_343967, _343969, _343971] : [class_Groups_Oordered__comm__monoid__add(_343967), c_Orderings_Oord__class_Oless__eq(_343967, c_Groups_Ozero__class_Ozero(_343967), _343969), c_Orderings_Oord__class_Oless__eq(_343967, c_Groups_Ozero__class_Ozero(_343967), _343971), -(c_Orderings_Oord__class_Oless__eq(_343967, c_Groups_Ozero__class_Ozero(_343967), c_Groups_Oplus__class_Oplus(_343967, _343969, _343971)))], (5197 ^ _166148) ^ [_344407, _344409, _344411] : [class_Groups_Oordered__comm__monoid__add(_344407), c_Orderings_Oord__class_Oless__eq(_344407, c_Groups_Ozero__class_Ozero(_344407), _344409), c_Orderings_Oord__class_Oless__eq(_344407, c_Groups_Ozero__class_Ozero(_344407), _344411), 5208 ^ _166148 : [(5209 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_344407, _344409, _344411) = c_Groups_Ozero__class_Ozero(_344407), 5212 ^ _166148 : [(5213 ^ _166148) ^ [] : [-(_344409 = c_Groups_Ozero__class_Ozero(_344407))], (5215 ^ _166148) ^ [] : [-(_344411 = c_Groups_Ozero__class_Ozero(_344407))]]], (5217 ^ _166148) ^ [] : [-(c_Groups_Oplus__class_Oplus(_344407, _344409, _344411) = c_Groups_Ozero__class_Ozero(_344407)), _344409 = c_Groups_Ozero__class_Ozero(_344407), _344411 = c_Groups_Ozero__class_Ozero(_344407)]]], (5227 ^ _166148) ^ [_345301, _345303, _345305, _345307] : [class_Groups_Oordered__comm__monoid__add(_345301), c_Orderings_Oord__class_Oless__eq(_345301, c_Groups_Ozero__class_Ozero(_345301), _345303), c_Orderings_Oord__class_Oless__eq(_345301, _345305, _345307), -(c_Orderings_Oord__class_Oless__eq(_345301, _345305, c_Groups_Oplus__class_Oplus(_345301, _345303, _345307)))], (5241 ^ _166148) ^ [_345761, _345763, _345765, _345767] : [class_Groups_Oordered__comm__monoid__add(_345761), c_Orderings_Oord__class_Oless__eq(_345761, c_Groups_Ozero__class_Ozero(_345761), _345763), c_Orderings_Oord__class_Oless__eq(_345761, _345765, _345767), -(c_Orderings_Oord__class_Oless__eq(_345761, _345765, c_Groups_Oplus__class_Oplus(_345761, _345767, _345763)))], (5255 ^ _166148) ^ [_346207, _346209, _346211] : [class_Groups_Oordered__comm__monoid__add(_346207), c_Orderings_Oord__class_Oless__eq(_346207, _346209, c_Groups_Ozero__class_Ozero(_346207)), c_Orderings_Oord__class_Oless__eq(_346207, _346211, c_Groups_Ozero__class_Ozero(_346207)), -(c_Orderings_Oord__class_Oless__eq(_346207, c_Groups_Oplus__class_Oplus(_346207, _346209, _346211), c_Groups_Ozero__class_Ozero(_346207)))], (5269 ^ _166148) ^ [_346647, _346649, _346651] : [class_Groups_Oordered__comm__monoid__add(_346647), c_Orderings_Oord__class_Oless(_346647, _346649, c_Groups_Ozero__class_Ozero(_346647)), c_Orderings_Oord__class_Oless(_346647, _346651, c_Groups_Ozero__class_Ozero(_346647)), -(c_Orderings_Oord__class_Oless(_346647, c_Groups_Oplus__class_Oplus(_346647, _346649, _346651), c_Groups_Ozero__class_Ozero(_346647)))], (5283 ^ _166148) ^ [_347087, _347089, _347091] : [class_Groups_Oordered__comm__monoid__add(_347087), c_Orderings_Oord__class_Oless(_347087, c_Groups_Ozero__class_Ozero(_347087), _347089), c_Orderings_Oord__class_Oless(_347087, c_Groups_Ozero__class_Ozero(_347087), _347091), -(c_Orderings_Oord__class_Oless(_347087, c_Groups_Ozero__class_Ozero(_347087), c_Groups_Oplus__class_Oplus(_347087, _347089, _347091)))], (5297 ^ _166148) ^ [_347513, _347515] : [class_Groups_Olinordered__ab__group__add(_347513), 5300 ^ _166148 : [(5301 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_347513, c_Groups_Oplus__class_Oplus(_347513, _347515, _347515), c_Groups_Ozero__class_Ozero(_347513)), -(c_Orderings_Oord__class_Oless(_347513, _347515, c_Groups_Ozero__class_Ozero(_347513)))], (5307 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_347513, _347515, c_Groups_Ozero__class_Ozero(_347513)), -(c_Orderings_Oord__class_Oless(_347513, c_Groups_Oplus__class_Oplus(_347513, _347515, _347515), c_Groups_Ozero__class_Ozero(_347513)))]]], (5313 ^ _166148) ^ [_348001, _348003] : [class_Groups_Olinordered__ab__group__add(_348001), 5316 ^ _166148 : [(5317 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_348001, c_Groups_Ozero__class_Ozero(_348001), c_Groups_Oplus__class_Oplus(_348001, _348003, _348003)), -(c_Orderings_Oord__class_Oless(_348001, c_Groups_Ozero__class_Ozero(_348001), _348003))], (5323 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_348001, c_Groups_Ozero__class_Ozero(_348001), _348003), -(c_Orderings_Oord__class_Oless(_348001, c_Groups_Ozero__class_Ozero(_348001), c_Groups_Oplus__class_Oplus(_348001, _348003, _348003)))]]], (5329 ^ _166148) ^ [_348531, _348533, _348535, _348537, _348539] : [class_Groups_Oordered__cancel__ab__semigroup__add(_348531), c_Orderings_Oord__class_Oless__eq(_348531, _348533, _348535), c_Orderings_Oord__class_Oless(_348531, _348537, _348539), -(c_Orderings_Oord__class_Oless(_348531, c_Groups_Oplus__class_Oplus(_348531, _348533, _348537), c_Groups_Oplus__class_Oplus(_348531, _348535, _348539)))], (5343 ^ _166148) ^ [_349023, _349025, _349027, _349029, _349031] : [class_Groups_Oordered__cancel__ab__semigroup__add(_349023), c_Orderings_Oord__class_Oless(_349023, _349025, _349027), c_Orderings_Oord__class_Oless__eq(_349023, _349029, _349031), -(c_Orderings_Oord__class_Oless(_349023, c_Groups_Oplus__class_Oplus(_349023, _349025, _349029), c_Groups_Oplus__class_Oplus(_349023, _349027, _349031)))], (5357 ^ _166148) ^ [_349487, _349489, _349491] : [class_Rings_Olinordered__ring__strict(_349487), 5360 ^ _166148 : [(5361 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_349487, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349487), _349489), _349489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349487), _349491), _349491)) = c_Groups_Ozero__class_Ozero(_349487), 5364 ^ _166148 : [(5365 ^ _166148) ^ [] : [-(_349489 = c_Groups_Ozero__class_Ozero(_349487))], (5367 ^ _166148) ^ [] : [-(_349491 = c_Groups_Ozero__class_Ozero(_349487))]]], (5369 ^ _166148) ^ [] : [-(c_Groups_Oplus__class_Oplus(_349487, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349487), _349489), _349489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349487), _349491), _349491)) = c_Groups_Ozero__class_Ozero(_349487)), _349489 = c_Groups_Ozero__class_Ozero(_349487), _349491 = c_Groups_Ozero__class_Ozero(_349487)]]], (5379 ^ _166148) ^ [_350217, _350219, _350221] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _350217), 5382 ^ _166148 : [(5383 ^ _166148) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350217), _350219) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350217), _350221), -(_350219 = _350221)], (5389 ^ _166148) ^ [] : [_350219 = _350221, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350217), _350219) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350217), _350221))]]], (5395 ^ _166148) ^ [_350745, _350747, _350749] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _350745), 5398 ^ _166148 : [(5399 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350745), _350747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350745), _350749)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _350747, _350749))], (5405 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _350747, _350749), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350745), _350747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350745), _350749)))]]], (5411 ^ _166148) ^ [_351279, _351281, _351283] : [class_Groups_Oordered__comm__monoid__add(_351279), c_Orderings_Oord__class_Oless__eq(_351279, _351281, c_Groups_Ozero__class_Ozero(_351279)), c_Orderings_Oord__class_Oless(_351279, _351283, c_Groups_Ozero__class_Ozero(_351279)), -(c_Orderings_Oord__class_Oless(_351279, c_Groups_Oplus__class_Oplus(_351279, _351281, _351283), c_Groups_Ozero__class_Ozero(_351279)))], (5425 ^ _166148) ^ [_351719, _351721, _351723] : [class_Groups_Oordered__comm__monoid__add(_351719), c_Orderings_Oord__class_Oless(_351719, _351721, c_Groups_Ozero__class_Ozero(_351719)), c_Orderings_Oord__class_Oless__eq(_351719, _351723, c_Groups_Ozero__class_Ozero(_351719)), -(c_Orderings_Oord__class_Oless(_351719, c_Groups_Oplus__class_Oplus(_351719, _351721, _351723), c_Groups_Ozero__class_Ozero(_351719)))], (5439 ^ _166148) ^ [_352173, _352175, _352177, _352179] : [class_Groups_Oordered__comm__monoid__add(_352173), c_Orderings_Oord__class_Oless__eq(_352173, c_Groups_Ozero__class_Ozero(_352173), _352175), c_Orderings_Oord__class_Oless(_352173, _352177, _352179), -(c_Orderings_Oord__class_Oless(_352173, _352177, c_Groups_Oplus__class_Oplus(_352173, _352175, _352179)))], (5453 ^ _166148) ^ [_352633, _352635, _352637, _352639] : [class_Groups_Oordered__comm__monoid__add(_352633), c_Orderings_Oord__class_Oless(_352633, c_Groups_Ozero__class_Ozero(_352633), _352635), c_Orderings_Oord__class_Oless__eq(_352633, _352637, _352639), -(c_Orderings_Oord__class_Oless(_352633, _352637, c_Groups_Oplus__class_Oplus(_352633, _352635, _352639)))], (5468 ^ _166148) ^ [] : [-(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 5466 ^ []), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (5470 ^ _166148) ^ [] : [-(c_Groups_Ominus__class_Ominus(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____)), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (5472 ^ _166148) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (5474 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)))], (5476 ^ _166148) ^ [_353332, _353334] : [-(_353332 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_353334 = 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), _353332), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 5483 ^ [_353332, _353334]), _353334)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (5497 ^ _166148) ^ [_354051, _354053] : [5498 ^ _166148 : [(5499 ^ _166148) ^ [] : [_354053 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5501 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _354051)]], -(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), _354051), _354053)))], (5487 ^ _166148) ^ [_353783, _353785] : [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), _353783), _353785)), -(_353785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _353783))], (5505 ^ _166148) ^ [_354353, _354355] : [class_Groups_Ogroup__add(_354353), -(c_Groups_Ominus__class_Ominus(_354353, c_Groups_Ozero__class_Ozero(_354353), _354355) = c_Groups_Ouminus__class_Ouminus(_354353, _354355))], (5511 ^ _166148) ^ [_354593, _354595, _354597] : [class_Groups_Ogroup__add(_354593), -(c_Groups_Ominus__class_Ominus(_354593, _354595, _354597) = c_Groups_Oplus__class_Oplus(_354593, _354595, c_Groups_Ouminus__class_Ouminus(_354593, _354597)))], (5517 ^ _166148) ^ [_354843, _354845, _354847] : [class_Groups_Oab__group__add(_354843), -(c_Groups_Ominus__class_Ominus(_354843, _354845, _354847) = c_Groups_Oplus__class_Oplus(_354843, _354845, c_Groups_Ouminus__class_Ouminus(_354843, _354847)))], (5523 ^ _166148) ^ [_355093, _355095, _355097] : [class_Groups_Ogroup__add(_355093), -(c_Groups_Ominus__class_Ominus(_355093, _355095, c_Groups_Ouminus__class_Ouminus(_355093, _355097)) = c_Groups_Oplus__class_Oplus(_355093, _355095, _355097))], (5529 ^ _166148) ^ [_355329, _355331] : [class_Groups_Ogroup__add(_355329), -(c_Groups_Ouminus__class_Ouminus(_355329, c_Groups_Ouminus__class_Ouminus(_355329, _355331)) = _355331)], (5535 ^ _166148) ^ [_355563, _355565, _355567] : [class_Groups_Oab__group__add(_355563), -(c_Groups_Ouminus__class_Ouminus(_355563, c_Groups_Ominus__class_Ominus(_355563, _355565, _355567)) = c_Groups_Ominus__class_Ominus(_355563, _355567, _355565))], (5541 ^ _166148) ^ [_355813, _355815, _355817] : [class_Groups_Ogroup__add(_355813), 5544 ^ _166148 : [(5545 ^ _166148) ^ [] : [_355815 = c_Groups_Ouminus__class_Ouminus(_355813, _355817), -(_355817 = c_Groups_Ouminus__class_Ouminus(_355813, _355815))], (5551 ^ _166148) ^ [] : [_355817 = c_Groups_Ouminus__class_Ouminus(_355813, _355815), -(_355815 = c_Groups_Ouminus__class_Ouminus(_355813, _355817))]]], (5557 ^ _166148) ^ [_356319, _356321, _356323] : [class_Groups_Ogroup__add(_356319), 5560 ^ _166148 : [(5561 ^ _166148) ^ [] : [c_Groups_Ouminus__class_Ouminus(_356319, _356321) = _356323, -(c_Groups_Ouminus__class_Ouminus(_356319, _356323) = _356321)], (5567 ^ _166148) ^ [] : [c_Groups_Ouminus__class_Ouminus(_356319, _356323) = _356321, -(c_Groups_Ouminus__class_Ouminus(_356319, _356321) = _356323)]]], (5573 ^ _166148) ^ [_356825, _356827, _356829] : [class_Groups_Ogroup__add(_356825), 5576 ^ _166148 : [(5577 ^ _166148) ^ [] : [c_Groups_Ouminus__class_Ouminus(_356825, _356827) = c_Groups_Ouminus__class_Ouminus(_356825, _356829), -(_356827 = _356829)], (5583 ^ _166148) ^ [] : [_356827 = _356829, -(c_Groups_Ouminus__class_Ouminus(_356825, _356827) = c_Groups_Ouminus__class_Ouminus(_356825, _356829))]]], (5589 ^ _166148) ^ [_357359, _357361, _357363, _357365, _357367] : [class_Groups_Oab__group__add(_357359), c_Groups_Ominus__class_Ominus(_357359, _357361, _357363) = c_Groups_Ominus__class_Ominus(_357359, _357365, _357367), 5596 ^ _166148 : [(5597 ^ _166148) ^ [] : [_357361 = _357363, -(_357365 = _357367)], (5603 ^ _166148) ^ [] : [_357365 = _357367, -(_357361 = _357363)]]], (5609 ^ _166148) ^ [_357996, _357998, _358000] : [class_RealVector_Oreal__normed__vector(_357996), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_357996, _357998), c_RealVector_Onorm__class_Onorm(_357996, _358000)), c_RealVector_Onorm__class_Onorm(_357996, c_Groups_Ominus__class_Ominus(_357996, _357998, _358000))))], (5615 ^ _166148) ^ [_358246, _358248] : [class_RealVector_Oreal__algebra__1(_358246), -(c_RealVector_Oof__real(_358246, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _358248)) = c_Groups_Ouminus__class_Ouminus(_358246, c_RealVector_Oof__real(_358246, _358248)))], (5621 ^ _166148) ^ [_358478, _358480] : [-(c_RealVector_Oof__real(_358478, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _358480)) = c_Groups_Ouminus__class_Ouminus(_358478, c_RealVector_Oof__real(_358478, _358480))), class_RealVector_Oreal__algebra__1(_358478), class_RealVector_Oreal__normed__vector(_358478)], (5631 ^ _166148) ^ [_358811, _358813, _358815] : [class_RealVector_Oreal__algebra__1(_358811), -(c_RealVector_Oof__real(_358811, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _358813, _358815)) = c_Groups_Ominus__class_Ominus(_358811, c_RealVector_Oof__real(_358811, _358813), c_RealVector_Oof__real(_358811, _358815)))], (5637 ^ _166148) ^ [_359073, _359075, _359077] : [-(c_RealVector_Oof__real(_359073, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _359075, _359077)) = c_Groups_Ominus__class_Ominus(_359073, c_RealVector_Oof__real(_359073, _359075), c_RealVector_Oof__real(_359073, _359077))), class_RealVector_Oreal__algebra__1(_359073), class_RealVector_Oreal__normed__vector(_359073)], (5647 ^ _166148) ^ [_359426, _359428, _359430] : [class_RealVector_Oreal__algebra__1(_359426), 5650 ^ _166148 : [(5651 ^ _166148) ^ [] : [c_RealVector_Oof__real(_359426, _359428) = c_RealVector_Oof__real(_359426, _359430), -(_359428 = _359430)], (5657 ^ _166148) ^ [] : [_359428 = _359430, -(c_RealVector_Oof__real(_359426, _359428) = c_RealVector_Oof__real(_359426, _359430))]]], (5663 ^ _166148) ^ [_359932, _359934, _359936] : [class_Rings_Ocomm__ring__1(_359932), -(c_Groups_Ominus__class_Ominus(_359932, _359934, _359936) = c_Groups_Oplus__class_Oplus(_359932, _359934, c_Groups_Ouminus__class_Ouminus(_359932, _359936)))], (5669 ^ _166148) ^ [_360168, _360170] : [class_Groups_Ogroup__add(_360168), -(c_Groups_Ominus__class_Ominus(_360168, _360170, c_Groups_Ozero__class_Ozero(_360168)) = _360170)], (5675 ^ _166148) ^ [_360388, _360390] : [class_Groups_Ogroup__add(_360388), -(c_Groups_Ominus__class_Ominus(_360388, _360390, _360390) = c_Groups_Ozero__class_Ozero(_360388))], (5681 ^ _166148) ^ [_360622, _360624, _360626] : [class_Groups_Oab__group__add(_360622), 5684 ^ _166148 : [(5685 ^ _166148) ^ [] : [_360624 = _360626, -(c_Groups_Ominus__class_Ominus(_360622, _360624, _360626) = c_Groups_Ozero__class_Ozero(_360622))], (5691 ^ _166148) ^ [] : [c_Groups_Ominus__class_Ominus(_360622, _360624, _360626) = c_Groups_Ozero__class_Ozero(_360622), -(_360624 = _360626)]]], (5697 ^ _166148) ^ [_361128, _361130, _361132] : [class_Groups_Ogroup__add(_361128), 5700 ^ _166148 : [(5701 ^ _166148) ^ [] : [c_Groups_Ominus__class_Ominus(_361128, _361130, _361132) = c_Groups_Ozero__class_Ozero(_361128), -(_361130 = _361132)], (5707 ^ _166148) ^ [] : [_361130 = _361132, -(c_Groups_Ominus__class_Ominus(_361128, _361130, _361132) = c_Groups_Ozero__class_Ozero(_361128))]]], (5713 ^ _166148) ^ [_361662, _361664, _361666, _361668, _361670] : [class_Groups_Oordered__ab__group__add(_361662), c_Groups_Ominus__class_Ominus(_361662, _361664, _361666) = c_Groups_Ominus__class_Ominus(_361662, _361668, _361670), 5720 ^ _166148 : [(5721 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_361662, _361664, _361666), -(c_Orderings_Oord__class_Oless__eq(_361662, _361668, _361670))], (5727 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_361662, _361668, _361670), -(c_Orderings_Oord__class_Oless__eq(_361662, _361664, _361666))]]], (5733 ^ _166148) ^ [_362277] : [class_Groups_Ogroup__add(_362277), -(c_Groups_Ouminus__class_Ouminus(_362277, c_Groups_Ozero__class_Ozero(_362277)) = c_Groups_Ozero__class_Ozero(_362277))], (5739 ^ _166148) ^ [_362493, _362495] : [class_Groups_Ogroup__add(_362493), 5742 ^ _166148 : [(5743 ^ _166148) ^ [] : [c_Groups_Ozero__class_Ozero(_362493) = c_Groups_Ouminus__class_Ouminus(_362493, _362495), -(c_Groups_Ozero__class_Ozero(_362493) = _362495)], (5749 ^ _166148) ^ [] : [c_Groups_Ozero__class_Ozero(_362493) = _362495, -(c_Groups_Ozero__class_Ozero(_362493) = c_Groups_Ouminus__class_Ouminus(_362493, _362495))]]], (5755 ^ _166148) ^ [_362972, _362974] : [class_Groups_Olinordered__ab__group__add(_362972), 5758 ^ _166148 : [(5759 ^ _166148) ^ [] : [_362974 = c_Groups_Ouminus__class_Ouminus(_362972, _362974), -(_362974 = c_Groups_Ozero__class_Ozero(_362972))], (5765 ^ _166148) ^ [] : [_362974 = c_Groups_Ozero__class_Ozero(_362972), -(_362974 = c_Groups_Ouminus__class_Ouminus(_362972, _362974))]]], (5771 ^ _166148) ^ [_363445, _363447] : [class_Groups_Ogroup__add(_363445), 5774 ^ _166148 : [(5775 ^ _166148) ^ [] : [c_Groups_Ouminus__class_Ouminus(_363445, _363447) = c_Groups_Ozero__class_Ozero(_363445), -(_363447 = c_Groups_Ozero__class_Ozero(_363445))], (5781 ^ _166148) ^ [] : [_363447 = c_Groups_Ozero__class_Ozero(_363445), -(c_Groups_Ouminus__class_Ouminus(_363445, _363447) = c_Groups_Ozero__class_Ozero(_363445))]]], (5787 ^ _166148) ^ [_363924, _363926] : [class_Groups_Olinordered__ab__group__add(_363924), 5790 ^ _166148 : [(5791 ^ _166148) ^ [] : [c_Groups_Ouminus__class_Ouminus(_363924, _363926) = _363926, -(_363926 = c_Groups_Ozero__class_Ozero(_363924))], (5797 ^ _166148) ^ [] : [_363926 = c_Groups_Ozero__class_Ozero(_363924), -(c_Groups_Ouminus__class_Ouminus(_363924, _363926) = _363926)]]], (5803 ^ _166148) ^ [_364439, _364441, _364443, _364445, _364447] : [class_Groups_Oordered__ab__group__add(_364439), c_Groups_Ominus__class_Ominus(_364439, _364441, _364443) = c_Groups_Ominus__class_Ominus(_364439, _364445, _364447), 5810 ^ _166148 : [(5811 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_364439, _364441, _364443), -(c_Orderings_Oord__class_Oless(_364439, _364445, _364447))], (5817 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_364439, _364445, _364447), -(c_Orderings_Oord__class_Oless(_364439, _364441, _364443))]]], (5823 ^ _166148) ^ [_365082, _365084, _365086] : [class_Groups_Oordered__ab__group__add(_365082), 5826 ^ _166148 : [(5827 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365082, _365084, c_Groups_Ouminus__class_Ouminus(_365082, _365086)), -(c_Orderings_Oord__class_Oless__eq(_365082, _365086, c_Groups_Ouminus__class_Ouminus(_365082, _365084)))], (5833 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365082, _365086, c_Groups_Ouminus__class_Ouminus(_365082, _365084)), -(c_Orderings_Oord__class_Oless__eq(_365082, _365084, c_Groups_Ouminus__class_Ouminus(_365082, _365086)))]]], (5839 ^ _166148) ^ [_365594, _365596, _365598] : [class_Groups_Oordered__ab__group__add(_365594), 5842 ^ _166148 : [(5843 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365594, c_Groups_Ouminus__class_Ouminus(_365594, _365596), _365598), -(c_Orderings_Oord__class_Oless__eq(_365594, c_Groups_Ouminus__class_Ouminus(_365594, _365598), _365596))], (5849 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365594, c_Groups_Ouminus__class_Ouminus(_365594, _365598), _365596), -(c_Orderings_Oord__class_Oless__eq(_365594, c_Groups_Ouminus__class_Ouminus(_365594, _365596), _365598))]]], (5855 ^ _166148) ^ [_366106, _366108, _366110] : [class_Groups_Oordered__ab__group__add(_366106), 5858 ^ _166148 : [(5859 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366106, c_Groups_Ouminus__class_Ouminus(_366106, _366108), c_Groups_Ouminus__class_Ouminus(_366106, _366110)), -(c_Orderings_Oord__class_Oless__eq(_366106, _366110, _366108))], (5865 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366106, _366110, _366108), -(c_Orderings_Oord__class_Oless__eq(_366106, c_Groups_Ouminus__class_Ouminus(_366106, _366108), c_Groups_Ouminus__class_Ouminus(_366106, _366110)))]]], (5871 ^ _166148) ^ [_366618, _366620, _366622] : [class_Groups_Oordered__ab__group__add(_366618), c_Orderings_Oord__class_Oless__eq(_366618, _366620, _366622), -(c_Orderings_Oord__class_Oless__eq(_366618, c_Groups_Ouminus__class_Ouminus(_366618, _366622), c_Groups_Ouminus__class_Ouminus(_366618, _366620)))], (5881 ^ _166148) ^ [_366955, _366957, _366959] : [class_Groups_Oordered__ab__group__add(_366955), 5884 ^ _166148 : [(5885 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_366955, c_Groups_Ouminus__class_Ouminus(_366955, _366957), c_Groups_Ouminus__class_Ouminus(_366955, _366959)), -(c_Orderings_Oord__class_Oless(_366955, _366959, _366957))], (5891 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_366955, _366959, _366957), -(c_Orderings_Oord__class_Oless(_366955, c_Groups_Ouminus__class_Ouminus(_366955, _366957), c_Groups_Ouminus__class_Ouminus(_366955, _366959)))]]], (5897 ^ _166148) ^ [_367467, _367469, _367471] : [class_Groups_Oordered__ab__group__add(_367467), 5900 ^ _166148 : [(5901 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_367467, c_Groups_Ouminus__class_Ouminus(_367467, _367469), _367471), -(c_Orderings_Oord__class_Oless(_367467, c_Groups_Ouminus__class_Ouminus(_367467, _367471), _367469))], (5907 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_367467, c_Groups_Ouminus__class_Ouminus(_367467, _367471), _367469), -(c_Orderings_Oord__class_Oless(_367467, c_Groups_Ouminus__class_Ouminus(_367467, _367469), _367471))]]], (5913 ^ _166148) ^ [_367979, _367981, _367983] : [class_Groups_Oordered__ab__group__add(_367979), 5916 ^ _166148 : [(5917 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_367979, _367981, c_Groups_Ouminus__class_Ouminus(_367979, _367983)), -(c_Orderings_Oord__class_Oless(_367979, _367983, c_Groups_Ouminus__class_Ouminus(_367979, _367981)))], (5923 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_367979, _367983, c_Groups_Ouminus__class_Ouminus(_367979, _367981)), -(c_Orderings_Oord__class_Oless(_367979, _367981, c_Groups_Ouminus__class_Ouminus(_367979, _367983)))]]], (5929 ^ _166148) ^ [_368505, _368507, _368509, _368511] : [class_RealVector_Oreal__normed__algebra(_368505), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368505), _368507), c_Groups_Ominus__class_Ominus(_368505, _368509, _368511)) = c_Groups_Ominus__class_Ominus(_368505, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368505), _368507), _368509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368505), _368507), _368511)))], (5935 ^ _166148) ^ [_368817, _368819, _368821, _368823] : [class_RealVector_Oreal__normed__algebra(_368817), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368817), _368819), c_Groups_Ominus__class_Ominus(_368817, _368821, _368823)) = c_Groups_Ominus__class_Ominus(_368817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368817), _368819), _368821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368817), _368819), _368823)))], (5941 ^ _166148) ^ [_369129, _369131, _369133, _369135] : [class_RealVector_Oreal__normed__algebra(_369129), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369129), c_Groups_Ominus__class_Ominus(_369129, _369131, _369133)), _369135) = c_Groups_Ominus__class_Ominus(_369129, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369129), _369131), _369135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369129), _369133), _369135)))], (5947 ^ _166148) ^ [_369441, _369443, _369445, _369447] : [class_RealVector_Oreal__normed__algebra(_369441), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369441), c_Groups_Ominus__class_Ominus(_369441, _369443, _369445)), _369447) = c_Groups_Ominus__class_Ominus(_369441, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369441), _369443), _369447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369441), _369445), _369447)))], (5953 ^ _166148) ^ [_369739, _369741, _369743] : [class_Rings_Oring(_369739), -(c_Groups_Ouminus__class_Ouminus(_369739, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369739), _369741), _369743)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369739), _369741), c_Groups_Ouminus__class_Ouminus(_369739, _369743)))], (5959 ^ _166148) ^ [_370011, _370013, _370015] : [class_Rings_Oring(_370011), -(c_Groups_Ouminus__class_Ouminus(_370011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370011), _370013), _370015)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370011), c_Groups_Ouminus__class_Ouminus(_370011, _370013)), _370015))], (5965 ^ _166148) ^ [_370283, _370285, _370287] : [class_Rings_Oring(_370283), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370283), c_Groups_Ouminus__class_Ouminus(_370283, _370285)), _370287) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370283), _370285), c_Groups_Ouminus__class_Ouminus(_370283, _370287)))], (5971 ^ _166148) ^ [_370555, _370557, _370559] : [class_Rings_Oring(_370555), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370555), c_Groups_Ouminus__class_Ouminus(_370555, _370557)), c_Groups_Ouminus__class_Ouminus(_370555, _370559)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370555), _370557), _370559))], (5977 ^ _166148) ^ [_370827, _370829, _370831] : [class_Rings_Oidom(_370827), 5980 ^ _166148 : [(5991 ^ _166148) ^ [] : [5992 ^ _166148 : [(5993 ^ _166148) ^ [] : [_370829 = _370831], (5995 ^ _166148) ^ [] : [_370829 = c_Groups_Ouminus__class_Ouminus(_370827, _370831)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370827), _370829), _370829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370827), _370831), _370831))], (5981 ^ _166148) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370827), _370829), _370829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370827), _370831), _370831), -(_370829 = _370831), -(_370829 = c_Groups_Ouminus__class_Ouminus(_370827, _370831))]]], (5999 ^ _166148) ^ [_371536, _371538, _371540] : [class_RealVector_Oreal__normed__algebra(_371536), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371536), _371538), c_Groups_Ouminus__class_Ouminus(_371536, _371540)) = c_Groups_Ouminus__class_Ouminus(_371536, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371536), _371538), _371540)))], (6005 ^ _166148) ^ [_371808, _371810, _371812] : [class_RealVector_Oreal__normed__algebra(_371808), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371808), _371810), c_Groups_Ouminus__class_Ouminus(_371808, _371812)) = c_Groups_Ouminus__class_Ouminus(_371808, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371808), _371810), _371812)))], (6011 ^ _166148) ^ [_372080, _372082, _372084] : [class_RealVector_Oreal__normed__algebra(_372080), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372080), c_Groups_Ouminus__class_Ouminus(_372080, _372082)), _372084) = c_Groups_Ouminus__class_Ouminus(_372080, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372080), _372082), _372084)))], (6017 ^ _166148) ^ [_372352, _372354, _372356] : [class_RealVector_Oreal__normed__algebra(_372352), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372352), c_Groups_Ouminus__class_Ouminus(_372352, _372354)), _372356) = c_Groups_Ouminus__class_Ouminus(_372352, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372352), _372354), _372356)))], (6023 ^ _166148) ^ [_372624, _372626, _372628] : [class_Groups_Ogroup__add(_372624), -(c_Groups_Ominus__class_Ominus(_372624, c_Groups_Oplus__class_Oplus(_372624, _372626, _372628), _372628) = _372626)], (6029 ^ _166148) ^ [_372868, _372870, _372872] : [class_Groups_Ogroup__add(_372868), -(c_Groups_Oplus__class_Oplus(_372868, c_Groups_Ominus__class_Ominus(_372868, _372870, _372872), _372872) = _372870)], (6035 ^ _166148) ^ [_373112, _373114, _373116] : [class_Groups_Ogroup__add(_373112), -(c_Groups_Oplus__class_Oplus(_373112, c_Groups_Ouminus__class_Ouminus(_373112, _373114), c_Groups_Oplus__class_Oplus(_373112, _373114, _373116)) = _373116)], (6041 ^ _166148) ^ [_373362, _373364, _373366] : [class_Groups_Ogroup__add(_373362), -(c_Groups_Oplus__class_Oplus(_373362, _373364, c_Groups_Oplus__class_Oplus(_373362, c_Groups_Ouminus__class_Ouminus(_373362, _373364), _373366)) = _373366)], (6047 ^ _166148) ^ [_373612, _373614, _373616] : [class_Groups_Ogroup__add(_373612), -(c_Groups_Ouminus__class_Ouminus(_373612, c_Groups_Oplus__class_Oplus(_373612, _373614, _373616)) = c_Groups_Oplus__class_Oplus(_373612, c_Groups_Ouminus__class_Ouminus(_373612, _373616), c_Groups_Ouminus__class_Ouminus(_373612, _373614)))], (6053 ^ _166148) ^ [_373874, _373876, _373878] : [class_Groups_Oab__group__add(_373874), -(c_Groups_Ouminus__class_Ouminus(_373874, c_Groups_Oplus__class_Oplus(_373874, _373876, _373878)) = c_Groups_Oplus__class_Oplus(_373874, c_Groups_Ouminus__class_Ouminus(_373874, _373876), c_Groups_Ouminus__class_Ouminus(_373874, _373878)))], (6059 ^ _166148) ^ [_374136, _374138, _374140] : [class_RealVector_Oreal__normed__vector(_374136), -(c_RealVector_Onorm__class_Onorm(_374136, c_Groups_Ominus__class_Ominus(_374136, _374138, _374140)) = c_RealVector_Onorm__class_Onorm(_374136, c_Groups_Ominus__class_Ominus(_374136, _374140, _374138)))], (6065 ^ _166148) ^ [_374378, _374380] : [class_RealVector_Oreal__normed__vector(_374378), -(c_RealVector_Onorm__class_Onorm(_374378, c_Groups_Ouminus__class_Ouminus(_374378, _374380)) = c_RealVector_Onorm__class_Onorm(_374378, _374380))], (6071 ^ _166148) ^ [_374604, _374606] : [class_Rings_Odivision__ring__inverse__zero(_374604), -(c_Rings_Oinverse__class_Oinverse(_374604, c_Groups_Ouminus__class_Ouminus(_374604, _374606)) = c_Groups_Ouminus__class_Ouminus(_374604, c_Rings_Oinverse__class_Oinverse(_374604, _374606)))], (6077 ^ _166148) ^ [_374850, _374852, _374854] : [class_Groups_Oordered__ab__group__add(_374850), 6080 ^ _166148 : [(6081 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_374850, _374852, _374854), -(c_Orderings_Oord__class_Oless__eq(_374850, c_Groups_Ominus__class_Ominus(_374850, _374852, _374854), c_Groups_Ozero__class_Ozero(_374850)))], (6087 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_374850, c_Groups_Ominus__class_Ominus(_374850, _374852, _374854), c_Groups_Ozero__class_Ozero(_374850)), -(c_Orderings_Oord__class_Oless__eq(_374850, _374852, _374854))]]], (6093 ^ _166148) ^ [_375362, _375364, _375366] : [class_Groups_Oordered__ab__group__add(_375362), 6096 ^ _166148 : [(6097 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_375362, _375364, _375366), -(c_Orderings_Oord__class_Oless(_375362, c_Groups_Ominus__class_Ominus(_375362, _375364, _375366), c_Groups_Ozero__class_Ozero(_375362)))], (6103 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_375362, c_Groups_Ominus__class_Ominus(_375362, _375364, _375366), c_Groups_Ozero__class_Ozero(_375362)), -(c_Orderings_Oord__class_Oless(_375362, _375364, _375366))]]], (6109 ^ _166148) ^ [_375860, _375862] : [class_Groups_Olinordered__ab__group__add(_375860), 6112 ^ _166148 : [(6113 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_375860, c_Groups_Ouminus__class_Ouminus(_375860, _375862), _375862), -(c_Orderings_Oord__class_Oless__eq(_375860, c_Groups_Ozero__class_Ozero(_375860), _375862))], (6119 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_375860, c_Groups_Ozero__class_Ozero(_375860), _375862), -(c_Orderings_Oord__class_Oless__eq(_375860, c_Groups_Ouminus__class_Ouminus(_375860, _375862), _375862))]]], (6125 ^ _166148) ^ [_376339, _376341] : [class_Groups_Oordered__ab__group__add(_376339), 6128 ^ _166148 : [(6129 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_376339, c_Groups_Ouminus__class_Ouminus(_376339, _376341), c_Groups_Ozero__class_Ozero(_376339)), -(c_Orderings_Oord__class_Oless__eq(_376339, c_Groups_Ozero__class_Ozero(_376339), _376341))], (6135 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_376339, c_Groups_Ozero__class_Ozero(_376339), _376341), -(c_Orderings_Oord__class_Oless__eq(_376339, c_Groups_Ouminus__class_Ouminus(_376339, _376341), c_Groups_Ozero__class_Ozero(_376339)))]]], (6141 ^ _166148) ^ [_376824, _376826] : [class_Groups_Olinordered__ab__group__add(_376824), 6144 ^ _166148 : [(6145 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_376824, _376826, c_Groups_Ouminus__class_Ouminus(_376824, _376826)), -(c_Orderings_Oord__class_Oless__eq(_376824, _376826, c_Groups_Ozero__class_Ozero(_376824)))], (6151 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_376824, _376826, c_Groups_Ozero__class_Ozero(_376824)), -(c_Orderings_Oord__class_Oless__eq(_376824, _376826, c_Groups_Ouminus__class_Ouminus(_376824, _376826)))]]], (6157 ^ _166148) ^ [_377303, _377305] : [class_Groups_Oordered__ab__group__add(_377303), 6160 ^ _166148 : [(6161 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_377303, c_Groups_Ozero__class_Ozero(_377303), c_Groups_Ouminus__class_Ouminus(_377303, _377305)), -(c_Orderings_Oord__class_Oless__eq(_377303, _377305, c_Groups_Ozero__class_Ozero(_377303)))], (6167 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_377303, _377305, c_Groups_Ozero__class_Ozero(_377303)), -(c_Orderings_Oord__class_Oless__eq(_377303, c_Groups_Ozero__class_Ozero(_377303), c_Groups_Ouminus__class_Ouminus(_377303, _377305)))]]], (6173 ^ _166148) ^ [_377788, _377790] : [class_Rings_Olinordered__idom(_377788), 6176 ^ _166148 : [(6177 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_377788, _377790, c_Groups_Ouminus__class_Ouminus(_377788, _377790)), -(c_Orderings_Oord__class_Oless(_377788, _377790, c_Groups_Ozero__class_Ozero(_377788)))], (6183 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_377788, _377790, c_Groups_Ozero__class_Ozero(_377788)), -(c_Orderings_Oord__class_Oless(_377788, _377790, c_Groups_Ouminus__class_Ouminus(_377788, _377790)))]]], (6189 ^ _166148) ^ [_378267, _378269] : [class_Groups_Olinordered__ab__group__add(_378267), 6192 ^ _166148 : [(6193 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_378267, c_Groups_Ouminus__class_Ouminus(_378267, _378269), _378269), -(c_Orderings_Oord__class_Oless(_378267, c_Groups_Ozero__class_Ozero(_378267), _378269))], (6199 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_378267, c_Groups_Ozero__class_Ozero(_378267), _378269), -(c_Orderings_Oord__class_Oless(_378267, c_Groups_Ouminus__class_Ouminus(_378267, _378269), _378269))]]], (6205 ^ _166148) ^ [_378746, _378748] : [class_Groups_Oordered__ab__group__add(_378746), 6208 ^ _166148 : [(6209 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_378746, c_Groups_Ouminus__class_Ouminus(_378746, _378748), c_Groups_Ozero__class_Ozero(_378746)), -(c_Orderings_Oord__class_Oless(_378746, c_Groups_Ozero__class_Ozero(_378746), _378748))], (6215 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_378746, c_Groups_Ozero__class_Ozero(_378746), _378748), -(c_Orderings_Oord__class_Oless(_378746, c_Groups_Ouminus__class_Ouminus(_378746, _378748), c_Groups_Ozero__class_Ozero(_378746)))]]], (6221 ^ _166148) ^ [_379231, _379233] : [class_Groups_Oordered__ab__group__add(_379231), 6224 ^ _166148 : [(6225 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_379231, c_Groups_Ozero__class_Ozero(_379231), c_Groups_Ouminus__class_Ouminus(_379231, _379233)), -(c_Orderings_Oord__class_Oless(_379231, _379233, c_Groups_Ozero__class_Ozero(_379231)))], (6231 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_379231, _379233, c_Groups_Ozero__class_Ozero(_379231)), -(c_Orderings_Oord__class_Oless(_379231, c_Groups_Ozero__class_Ozero(_379231), c_Groups_Ouminus__class_Ouminus(_379231, _379233)))]]], (6237 ^ _166148) ^ [_379716, _379718] : [class_RealVector_Oreal__algebra__1(_379716), 6240 ^ _166148 : [(6241 ^ _166148) ^ [] : [c_RealVector_Oof__real(_379716, _379718) = c_Groups_Ozero__class_Ozero(_379716), -(_379718 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6247 ^ _166148) ^ [] : [_379718 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_RealVector_Oof__real(_379716, _379718) = c_Groups_Ozero__class_Ozero(_379716))]]], (6253 ^ _166148) ^ [_380175] : [-(c_RealVector_Oof__real(_380175, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(_380175)), class_RealVector_Oreal__algebra__1(_380175), class_RealVector_Oreal__normed__vector(_380175)], (6263 ^ _166148) ^ [_380456] : [class_RealVector_Oreal__algebra__1(_380456), -(c_RealVector_Oof__real(_380456, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(_380456))], (6269 ^ _166148) ^ [_380682, _380684, _380686] : [class_Groups_Ogroup__add(_380682), 6272 ^ _166148 : [(6273 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_380682, _380684, _380686) = c_Groups_Ozero__class_Ozero(_380682), -(_380686 = c_Groups_Ouminus__class_Ouminus(_380682, _380684))], (6279 ^ _166148) ^ [] : [_380686 = c_Groups_Ouminus__class_Ouminus(_380682, _380684), -(c_Groups_Oplus__class_Oplus(_380682, _380684, _380686) = c_Groups_Ozero__class_Ozero(_380682))]]], (6285 ^ _166148) ^ [_381197, _381199, _381201] : [class_Groups_Ogroup__add(_381197), c_Groups_Oplus__class_Oplus(_381197, _381199, _381201) = c_Groups_Ozero__class_Ozero(_381197), -(c_Groups_Ouminus__class_Ouminus(_381197, _381199) = _381201)], (6295 ^ _166148) ^ [_381522, _381524] : [class_Groups_Oab__group__add(_381522), -(c_Groups_Oplus__class_Oplus(_381522, c_Groups_Ouminus__class_Ouminus(_381522, _381524), _381524) = c_Groups_Ozero__class_Ozero(_381522))], (6301 ^ _166148) ^ [_381748, _381750] : [class_Groups_Ogroup__add(_381748), -(c_Groups_Oplus__class_Oplus(_381748, c_Groups_Ouminus__class_Ouminus(_381748, _381750), _381750) = c_Groups_Ozero__class_Ozero(_381748))], (6307 ^ _166148) ^ [_381988, _381990, _381992] : [class_Groups_Ogroup__add(_381988), 6310 ^ _166148 : [(6311 ^ _166148) ^ [] : [_381990 = c_Groups_Ouminus__class_Ouminus(_381988, _381992), -(c_Groups_Oplus__class_Oplus(_381988, _381990, _381992) = c_Groups_Ozero__class_Ozero(_381988))], (6317 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_381988, _381990, _381992) = c_Groups_Ozero__class_Ozero(_381988), -(_381990 = c_Groups_Ouminus__class_Ouminus(_381988, _381992))]]], (6323 ^ _166148) ^ [_382489, _382491] : [class_Groups_Ogroup__add(_382489), -(c_Groups_Oplus__class_Oplus(_382489, _382491, c_Groups_Ouminus__class_Ouminus(_382489, _382491)) = c_Groups_Ozero__class_Ozero(_382489))], (6329 ^ _166148) ^ [_382757, _382759, _382761, _382763, _382765] : [class_Rings_Oring(_382757), -(c_Groups_Ominus__class_Ominus(_382757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382757), _382759), _382761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382757), _382763), _382765)) = c_Groups_Oplus__class_Oplus(_382757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382757), _382759), c_Groups_Ominus__class_Ominus(_382757, _382761, _382765)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382757), c_Groups_Ominus__class_Ominus(_382757, _382759, _382763)), _382765)))], (6335 ^ _166148) ^ [_383135, _383137, _383139, _383141, _383143, _383145] : [class_Rings_Oring(_383135), 6338 ^ _166148 : [(6339 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_383135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383135), _383137), _383139), _383141) = c_Groups_Oplus__class_Oplus(_383135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383135), _383143), _383139), _383145), -(_383141 = c_Groups_Oplus__class_Oplus(_383135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383135), c_Groups_Ominus__class_Ominus(_383135, _383143, _383137)), _383139), _383145))], (6345 ^ _166148) ^ [] : [_383141 = c_Groups_Oplus__class_Oplus(_383135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383135), c_Groups_Ominus__class_Ominus(_383135, _383143, _383137)), _383139), _383145), -(c_Groups_Oplus__class_Oplus(_383135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383135), _383137), _383139), _383141) = c_Groups_Oplus__class_Oplus(_383135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383135), _383143), _383139), _383145))]]], (6351 ^ _166148) ^ [_383833, _383835, _383837, _383839, _383841, _383843] : [class_Rings_Oring(_383833), 6354 ^ _166148 : [(6355 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_383833, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383833), _383835), _383837), _383839) = c_Groups_Oplus__class_Oplus(_383833, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383833), _383841), _383837), _383843), -(c_Groups_Oplus__class_Oplus(_383833, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383833), c_Groups_Ominus__class_Ominus(_383833, _383835, _383841)), _383837), _383839) = _383843)], (6361 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_383833, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383833), c_Groups_Ominus__class_Ominus(_383833, _383835, _383841)), _383837), _383839) = _383843, -(c_Groups_Oplus__class_Oplus(_383833, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383833), _383835), _383837), _383839) = c_Groups_Oplus__class_Oplus(_383833, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383833), _383841), _383837), _383843))]]], (6367 ^ _166148) ^ [_384517, _384519, _384521, _384523, _384525] : [class_RealVector_Oreal__normed__algebra(_384517), -(c_Groups_Ominus__class_Ominus(_384517, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384517), _384519), _384521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384517), _384523), _384525)) = c_Groups_Oplus__class_Oplus(_384517, c_Groups_Oplus__class_Oplus(_384517, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384517), c_Groups_Ominus__class_Ominus(_384517, _384519, _384523)), c_Groups_Ominus__class_Ominus(_384517, _384521, _384525)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384517), c_Groups_Ominus__class_Ominus(_384517, _384519, _384523)), _384525)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384517), _384523), c_Groups_Ominus__class_Ominus(_384517, _384521, _384525))))], (6373 ^ _166148) ^ [_384879, _384881] : [class_Rings_Oring__1__no__zero__divisors(_384879), 6376 ^ _166148 : [(6387 ^ _166148) ^ [] : [6388 ^ _166148 : [(6389 ^ _166148) ^ [] : [_384881 = c_Groups_Oone__class_Oone(_384879)], (6391 ^ _166148) ^ [] : [_384881 = c_Groups_Ouminus__class_Ouminus(_384879, c_Groups_Oone__class_Oone(_384879))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384879), _384881), _384881) = c_Groups_Oone__class_Oone(_384879))], (6377 ^ _166148) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384879), _384881), _384881) = c_Groups_Oone__class_Oone(_384879), -(_384881 = c_Groups_Oone__class_Oone(_384879)), -(_384881 = c_Groups_Ouminus__class_Ouminus(_384879, c_Groups_Oone__class_Oone(_384879)))]]], (6395 ^ _166148) ^ [_385546, _385548] : [class_Rings_Ocomm__ring__1(_385546), -(c_Groups_Ouminus__class_Ouminus(_385546, _385548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385546), c_Groups_Ouminus__class_Ouminus(_385546, c_Groups_Oone__class_Oone(_385546))), _385548))], (6401 ^ _166148) ^ [_385800, _385802, _385804] : [class_RealVector_Oreal__algebra__1(_385800), -(c_RealVector_Oof__real(_385800, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _385802), _385804)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385800), c_RealVector_Oof__real(_385800, _385802)), c_RealVector_Oof__real(_385800, _385804)))], (6407 ^ _166148) ^ [_386074, _386076, _386078] : [class_RealVector_Oreal__algebra__1(_386074), -(c_RealVector_Oof__real(_386074, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _386076, _386078)) = c_Groups_Oplus__class_Oplus(_386074, c_RealVector_Oof__real(_386074, _386076), c_RealVector_Oof__real(_386074, _386078)))], (6413 ^ _166148) ^ [_386336, _386338, _386340] : [-(c_RealVector_Oof__real(_386336, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _386338, _386340)) = c_Groups_Oplus__class_Oplus(_386336, c_RealVector_Oof__real(_386336, _386338), c_RealVector_Oof__real(_386336, _386340))), class_RealVector_Oreal__algebra__1(_386336), class_RealVector_Oreal__normed__vector(_386336)], (6423 ^ _166148) ^ [_386661] : [class_RealVector_Oreal__algebra__1(_386661), -(c_RealVector_Oof__real(_386661, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(_386661))], (6429 ^ _166148) ^ [_386873, _386875] : [class_Rings_Odivision__ring(_386873), -(_386875 = c_Groups_Ozero__class_Ozero(_386873)), -(c_Rings_Oinverse__class_Oinverse(_386873, c_Groups_Ouminus__class_Ouminus(_386873, _386875)) = c_Groups_Ouminus__class_Ouminus(_386873, c_Rings_Oinverse__class_Oinverse(_386873, _386875)))], (6439 ^ _166148) ^ [_387215, _387217, _387219] : [class_RealVector_Oreal__algebra__1(_387215), -(c_RealVector_Oof__real(_387215, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _387217), _387219)) = hAPP(hAPP(c_Power_Opower__class_Opower(_387215), c_RealVector_Oof__real(_387215, _387217)), _387219))], (6445 ^ _166148) ^ [_387469, _387471] : [-(c_RealVector_Oof__real(_387469, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _387471)) = c_Rings_Oinverse__class_Oinverse(_387469, c_RealVector_Oof__real(_387469, _387471))), class_RealVector_Oreal__div__algebra(_387469), class_Rings_Odivision__ring__inverse__zero(_387469)], (6455 ^ _166148) ^ [_387773, _387775] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, _387773)), _387775) = c_RealVector_Oof__real(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _387773), _387775)))], (6457 ^ _166148) ^ [_387956, _387958, _387960, _387962, _387964, _387966] : [class_Rings_Oordered__ring(_387956), 6460 ^ _166148 : [(6461 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_387956, c_Groups_Oplus__class_Oplus(_387956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387956), _387958), _387960), _387962), c_Groups_Oplus__class_Oplus(_387956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387956), _387964), _387960), _387966)), -(c_Orderings_Oord__class_Oless__eq(_387956, _387962, c_Groups_Oplus__class_Oplus(_387956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387956), c_Groups_Ominus__class_Ominus(_387956, _387964, _387958)), _387960), _387966)))], (6467 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_387956, _387962, c_Groups_Oplus__class_Oplus(_387956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387956), c_Groups_Ominus__class_Ominus(_387956, _387964, _387958)), _387960), _387966)), -(c_Orderings_Oord__class_Oless__eq(_387956, c_Groups_Oplus__class_Oplus(_387956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387956), _387958), _387960), _387962), c_Groups_Oplus__class_Oplus(_387956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387956), _387964), _387960), _387966)))]]], (6473 ^ _166148) ^ [_388660, _388662, _388664, _388666, _388668, _388670] : [class_Rings_Oordered__ring(_388660), 6476 ^ _166148 : [(6477 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_388660, c_Groups_Oplus__class_Oplus(_388660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388660), _388662), _388664), _388666), c_Groups_Oplus__class_Oplus(_388660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388660), _388668), _388664), _388670)), -(c_Orderings_Oord__class_Oless__eq(_388660, c_Groups_Oplus__class_Oplus(_388660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388660), c_Groups_Ominus__class_Ominus(_388660, _388662, _388668)), _388664), _388666), _388670))], (6483 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_388660, c_Groups_Oplus__class_Oplus(_388660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388660), c_Groups_Ominus__class_Ominus(_388660, _388662, _388668)), _388664), _388666), _388670), -(c_Orderings_Oord__class_Oless__eq(_388660, c_Groups_Oplus__class_Oplus(_388660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388660), _388662), _388664), _388666), c_Groups_Oplus__class_Oplus(_388660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388660), _388668), _388664), _388670)))]]], (6489 ^ _166148) ^ [_389364, _389366, _389368, _389370, _389372, _389374] : [class_Rings_Oordered__ring(_389364), 6492 ^ _166148 : [(6493 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_389364, c_Groups_Oplus__class_Oplus(_389364, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389364), _389366), _389368), _389370), c_Groups_Oplus__class_Oplus(_389364, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389364), _389372), _389368), _389374)), -(c_Orderings_Oord__class_Oless(_389364, _389370, c_Groups_Oplus__class_Oplus(_389364, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389364), c_Groups_Ominus__class_Ominus(_389364, _389372, _389366)), _389368), _389374)))], (6499 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_389364, _389370, c_Groups_Oplus__class_Oplus(_389364, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389364), c_Groups_Ominus__class_Ominus(_389364, _389372, _389366)), _389368), _389374)), -(c_Orderings_Oord__class_Oless(_389364, c_Groups_Oplus__class_Oplus(_389364, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389364), _389366), _389368), _389370), c_Groups_Oplus__class_Oplus(_389364, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389364), _389372), _389368), _389374)))]]], (6505 ^ _166148) ^ [_390068, _390070, _390072, _390074, _390076, _390078] : [class_Rings_Oordered__ring(_390068), 6508 ^ _166148 : [(6509 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_390068, c_Groups_Oplus__class_Oplus(_390068, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390068), _390070), _390072), _390074), c_Groups_Oplus__class_Oplus(_390068, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390068), _390076), _390072), _390078)), -(c_Orderings_Oord__class_Oless(_390068, c_Groups_Oplus__class_Oplus(_390068, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390068), c_Groups_Ominus__class_Ominus(_390068, _390070, _390076)), _390072), _390074), _390078))], (6515 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_390068, c_Groups_Oplus__class_Oplus(_390068, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390068), c_Groups_Ominus__class_Ominus(_390068, _390070, _390076)), _390072), _390074), _390078), -(c_Orderings_Oord__class_Oless(_390068, c_Groups_Oplus__class_Oplus(_390068, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390068), _390070), _390072), _390074), c_Groups_Oplus__class_Oplus(_390068, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390068), _390076), _390072), _390078)))]]], (6521 ^ _166148) ^ [_390716, _390718] : [class_Rings_Oring__1(_390716), -(c_Groups_Ominus__class_Ominus(_390716, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390716), _390718), _390718), c_Groups_Oone__class_Oone(_390716)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390716), c_Groups_Oplus__class_Oplus(_390716, _390718, c_Groups_Oone__class_Oone(_390716))), c_Groups_Ominus__class_Ominus(_390716, _390718, c_Groups_Oone__class_Oone(_390716))))], (6527 ^ _166148) ^ [_391006, _391008, _391010] : [class_Rings_Odivision__ring(_391006), -(_391008 = c_Groups_Ozero__class_Ozero(_391006)), -(_391010 = c_Groups_Ozero__class_Ozero(_391006)), -(c_Groups_Ominus__class_Ominus(_391006, c_Rings_Oinverse__class_Oinverse(_391006, _391008), c_Rings_Oinverse__class_Oinverse(_391006, _391010)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391006), c_Rings_Oinverse__class_Oinverse(_391006, _391008)), c_Groups_Ominus__class_Ominus(_391006, _391010, _391008))), c_Rings_Oinverse__class_Oinverse(_391006, _391010)))], (6541 ^ _166148) ^ [_391506, _391508, _391510] : [class_Rings_Oring__1(_391506), -(hAPP(hAPP(c_Power_Opower__class_Opower(_391506), c_Groups_Ouminus__class_Ouminus(_391506, _391508)), _391510) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391506), hAPP(hAPP(c_Power_Opower__class_Opower(_391506), c_Groups_Ouminus__class_Ouminus(_391506, c_Groups_Oone__class_Oone(_391506))), _391510)), hAPP(hAPP(c_Power_Opower__class_Opower(_391506), _391508), _391510)))], (6547 ^ _166148) ^ [_391814, _391816, _391818] : [class_RealVector_Oreal__normed__vector(_391814), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_391814, c_Groups_Ominus__class_Ominus(_391814, _391816, _391818)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_391814, _391816), c_RealVector_Onorm__class_Onorm(_391814, _391818))))], (6553 ^ _166148) ^ [_392064, _392066] : [class_RealVector_Oreal__div__algebra(_392064), -(_392066 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RealVector_Oof__real(_392064, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _392066)) = c_Rings_Oinverse__class_Oinverse(_392064, c_RealVector_Oof__real(_392064, _392066)))], (6563 ^ _166148) ^ [_392430, _392432, _392434, _392436, _392438] : [class_RealVector_Oreal__normed__vector(_392430), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_392430, c_Groups_Ominus__class_Ominus(_392430, c_Groups_Oplus__class_Oplus(_392430, _392432, _392434), c_Groups_Oplus__class_Oplus(_392430, _392436, _392438))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_392430, c_Groups_Ominus__class_Ominus(_392430, _392432, _392436)), c_RealVector_Onorm__class_Onorm(_392430, c_Groups_Ominus__class_Ominus(_392430, _392434, _392438)))))], (6569 ^ _166148) ^ [_392738, _392740, _392742] : [class_Rings_Odivision__ring(_392738), -(_392740 = c_Groups_Ozero__class_Ozero(_392738)), -(_392742 = c_Groups_Ozero__class_Ozero(_392738)), -(c_Groups_Ominus__class_Ominus(_392738, c_Rings_Oinverse__class_Oinverse(_392738, _392740), c_Rings_Oinverse__class_Oinverse(_392738, _392742)) = c_Groups_Ouminus__class_Ouminus(_392738, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392738), c_Rings_Oinverse__class_Oinverse(_392738, _392740)), c_Groups_Ominus__class_Ominus(_392738, _392740, _392742))), c_Rings_Oinverse__class_Oinverse(_392738, _392742))))], (6583 ^ _166148) ^ [_393215, _393217] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _393215, _393217) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _393215, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _393217)))], (6585 ^ _166148) ^ [_393350] : [-(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), _393350), _393350))), -(_393350 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6591 ^ _166148) ^ [_393523] : [_393523 = 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), _393523), _393523))], (6597 ^ _166148) ^ [_393744, _393746] : [class_Rings_Olinordered__idom(_393744), 6600 ^ _166148 : [(6601 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_393744, c_Groups_Oplus__class_Oplus(_393744, _393746, _393746), c_Groups_Ozero__class_Ozero(_393744)), -(c_Orderings_Oord__class_Oless(_393744, _393746, c_Groups_Ozero__class_Ozero(_393744)))], (6607 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_393744, _393746, c_Groups_Ozero__class_Ozero(_393744)), -(c_Orderings_Oord__class_Oless(_393744, c_Groups_Oplus__class_Oplus(_393744, _393746, _393746), c_Groups_Ozero__class_Ozero(_393744)))]]], (6613 ^ _166148) ^ [_394218] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _394218) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _394218, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _394218, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _394218, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _394218, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (6631 ^ _166148) ^ [_394735, _394737] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _394735, _394737) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _394735, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _394737)))], (6633 ^ _166148) ^ [_394840, _394842] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _394840, _394842) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _394840, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _394842)))], (6635 ^ _166148) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Complex_Oii))], (6637 ^ _166148) ^ [_395013, _395015] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395013, _395015) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395015, _395013) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_395013 = _395015)], (6647 ^ _166148) ^ [_395299] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395299, _395299) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6649 ^ _166148) ^ [_395381] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395381, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _395381)], (6651 ^ _166148) ^ [_395463] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _395463) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6653 ^ _166148) ^ [_395588, _395590, _395592] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395588, _395590), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395588, _395592), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395592, _395590), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395592, _395588)))], (6663 ^ _166148) ^ [_395933, _395935, _395937] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395933, _395935), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395933, _395937), _395935))], (6669 ^ _166148) ^ [_396146, _396148] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396146, _396148), _396148) = _396146)], (6671 ^ _166148) ^ [_396248, _396250] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396248, _396250), _396248) = _396250)], (6673 ^ _166148) ^ [_396364, _396366, _396368] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396364, _396366), _396368) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396364, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396366, _396368)))], (6675 ^ _166148) ^ [_396490, _396492, _396494] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396490, _396492), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396490, _396494)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396492, _396494))], (6677 ^ _166148) ^ [_396616, _396618, _396620] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396616, _396618), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396620, _396618)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396616, _396620))], (6679 ^ _166148) ^ [_396728, _396730] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396728, _396730), _396728))], (6681 ^ _166148) ^ [_396856, _396858, _396860] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _396856, _396858), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396860, _396858), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396860, _396856)))], (6687 ^ _166148) ^ [_397106, _397108, _397110] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397106, _397108), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397106, _397110), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397108, _397110)))], (6693 ^ _166148) ^ [_397342, _397344] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397342, _397344), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397344, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397344, _397342)) = _397342)], (6699 ^ _166148) ^ [_397584, _397586, _397588] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397584, _397586), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397584, _397588), 6706 ^ _166148 : [(6707 ^ _166148) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397586, _397584) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397588, _397584), -(_397586 = _397588)], (6713 ^ _166148) ^ [] : [_397586 = _397588, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397586, _397584) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397588, _397584))]]], (6719 ^ _166148) ^ [_398195, _398197, _398199] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398195, _398197), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398195, _398199), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398197, _398195), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398199, _398195)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398197, _398199))], (6729 ^ _166148) ^ [_398554, _398556, _398558] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398554, _398556), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398554, _398558), 6736 ^ _166148 : [(6737 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398556, _398554), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398558, _398554)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398556, _398558))], (6743 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398556, _398558), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398556, _398554), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398558, _398554)))]]], (6749 ^ _166148) ^ [_399156, _399158, _399160] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399156), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _399158, _399160)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399156), _399158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399156), _399160)))], (6751 ^ _166148) ^ [_399292, _399294, _399296] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _399292, _399294)), _399296) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399292), _399296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399294), _399296)))], (6753 ^ _166148) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (6755 ^ _166148) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (6757 ^ _166148) ^ [_399504] : [-(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, _399504)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _399504)))], (6759 ^ _166148) ^ [_399592] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oii), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oii), _399592)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _399592))], (6761 ^ _166148) ^ [_399737, _399739] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _399737, _399739), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _399737, _399739), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (6767 ^ _166148) ^ [_399911, _399913] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _399911, _399913), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _399911, _399913))], (6773 ^ _166148) ^ [_400164, _400166] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _400164, _400166)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _400166, _400164))], (6779 ^ _166148) ^ [_400338, _400340] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _400340, _400338), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _400338, _400340)))], (6785 ^ _166148) ^ [_400562, _400564] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400562), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400564), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _400564, _400562), _400564))], (6795 ^ _166148) ^ [_400860, _400862] : [-(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), _400860), _400860)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _400862), _400862)))], (6797 ^ _166148) ^ [_400970, _400972] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _400970, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400970, _400972)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6799 ^ _166148) ^ [_401087, _401089] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401087, _401089), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401087, _401089) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6805 ^ _166148) ^ [_401336, _401338] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401336, _401338) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401336, _401338))], (6811 ^ _166148) ^ [_401508, _401510] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401508, _401510), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401508, _401510) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6817 ^ _166148) ^ [_401773, _401775, _401777] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _401773, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401775, _401777)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401773, _401777), _401775))], (6823 ^ _166148) ^ [_401961, _401963, _401965] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401961, _401965), _401963), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _401961, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401963, _401965)))], (6829 ^ _166148) ^ [_402199, _402201] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _402199, _402201)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _402201, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _402199, _402201)) = _402199)], (6835 ^ _166148) ^ [_402444, _402446, _402448] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402444, _402446), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402444, _402448), 6842 ^ _166148 : [(6843 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _402446, _402444), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _402448, _402444)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _402446, _402448))], (6849 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _402446, _402448), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _402446, _402444), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _402448, _402444)))]]], (6855 ^ _166148) ^ [_403061, _403063, _403065] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _403061, _403063), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403065, _403061), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _403061, _403065), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _403063, _403065)))], (6865 ^ _166148) ^ [_403421, _403423] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _403421, _403423) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_403423 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _403421))], (6871 ^ _166148) ^ [_403597, _403599] : [_403599 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _403597), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _403597, _403599) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6877 ^ _166148) ^ [_403852, _403854] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _403852, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _403854)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_403852 = _403854)], (6883 ^ _166148) ^ [_404028, _404030] : [_404028 = _404030, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _404028, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _404030)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6889 ^ _166148) ^ [_404268, _404270, _404272] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _404268, _404270), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404270, _404272), _404268) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _404270, _404268), _404272))], (6895 ^ _166148) ^ [_404532, _404534, _404536] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _404532, _404534), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _404534, _404532), _404536) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404534, _404536), _404532))], (6901 ^ _166148) ^ [_404796, _404798, _404800] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _404796, _404798), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404800, _404798), _404796) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404800, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _404798, _404796)))], (6907 ^ _166148) ^ [_405060, _405062, _405064] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _405060, _405062), 6910 ^ _166148 : [(6911 ^ _166148) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _405062, _405060) = _405064, -(_405062 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405064, _405060))], (6917 ^ _166148) ^ [] : [_405062 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405064, _405060), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _405062, _405060) = _405064)]]], (6923 ^ _166148) ^ [_405562, _405564] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _405562, _405564), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _405564, _405562), _405562) = _405564)], (6929 ^ _166148) ^ [_405804, _405806, _405808] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _405804, _405806), 6932 ^ _166148 : [(6933 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _405808, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _405806, _405804)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405808, _405804), _405806))], (6939 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405808, _405804), _405806), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _405808, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _405806, _405804)))]]], (6945 ^ _166148) ^ [_406326, _406328, _406330] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406326, _406328), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406330, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _406328, _406326)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406330, _406328), _406326))], (6951 ^ _166148) ^ [_406576, _406578] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406576, _406578), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406576, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _406578, _406576)) = _406578)], (6957 ^ _166148) ^ [_406818, _406820, _406822] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406818, _406820), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406822, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406820, _406822), _406818)))], (6963 ^ _166148) ^ [_407097, _407099, _407101] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _407097, _407099), _407101), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _407097, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _407101, _407099)))], (6969 ^ _166148) ^ [_407285, _407287, _407289] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _407285, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _407289, _407287)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _407285, _407287), _407289))], (6975 ^ _166148) ^ [_407537, _407539, _407541] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _407537, _407539), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _407541, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _407539, _407537)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _407541, _407537), _407539))], (6981 ^ _166148) ^ [_407772, _407774] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _407772, _407774)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _407772)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _407774)))], (6983 ^ _166148) ^ [_407913, _407915, _407917] : [class_RealVector_Oreal__normed__vector(_407913), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_407913, _407915), c_RealVector_Onorm__class_Onorm(_407913, _407917)), c_RealVector_Onorm__class_Onorm(_407913, c_Groups_Oplus__class_Oplus(_407913, _407915, _407917))))], (7005 ^ _166148) ^ [_408745, _408747, _408749] : [-(hBOOL(hAPP(_408745, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _408747, _408749)))), 7008 ^ _166148 : [(7009 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408747, _408749))], (7011 ^ _166148) ^ [] : [hBOOL(hAPP(_408745, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 7013 ^ _166148 : [(7014 ^ _166148) ^ [] : [-(_408747 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _408749, 7012 ^ [_408745, _408747, _408749]))], (7016 ^ _166148) ^ [] : [hBOOL(hAPP(_408745, 7012 ^ [_408745, _408747, _408749]))]]], (6989 ^ _166148) ^ [_408206, _408208, _408210] : [hBOOL(hAPP(_408206, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _408208, _408210))), 6992 ^ _166148 : [(6993 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408208, _408210), -(hBOOL(hAPP(_408206, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6999 ^ _166148) ^ [_408544] : [_408208 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _408210, _408544), -(hBOOL(hAPP(_408206, _408544)))]]], (7036 ^ _166148) ^ [_409906, _409908, _409910] : [-(hBOOL(hAPP(_409906, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _409908, _409910)))), 7039 ^ _166148 : [(7040 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409908, _409910))], (7042 ^ _166148) ^ [] : [hBOOL(hAPP(_409906, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 7044 ^ _166148 : [(7045 ^ _166148) ^ [] : [-(_409908 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409910, 7043 ^ [_409906, _409908, _409910]))], (7047 ^ _166148) ^ [] : [hBOOL(hAPP(_409906, 7043 ^ [_409906, _409908, _409910]))]]], (7020 ^ _166148) ^ [_409375, _409377, _409379] : [hBOOL(hAPP(_409375, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _409377, _409379))), 7023 ^ _166148 : [(7024 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409377, _409379), -(hBOOL(hAPP(_409375, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7030 ^ _166148) ^ [_409707] : [_409377 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409379, _409707), -(hBOOL(hAPP(_409375, _409707)))]]], (7051 ^ _166148) ^ [_410514, _410516] : [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, _410514, _410516)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _410514), _410516))], (7057 ^ _166148) ^ [_410694, _410696] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _410694), _410696), -(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, _410694, _410696)))], (7063 ^ _166148) ^ [_410953, _410955] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _410953, _410955), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410955, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _410953)))], (7069 ^ _166148) ^ [_411133, _411135] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _411135, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _411133)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _411133, _411135), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7075 ^ _166148) ^ [_411392, _411394] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _411392, _411394)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _411392), _411394))], (7081 ^ _166148) ^ [_411572, _411574] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _411572), _411574), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _411572, _411574)))], (7087 ^ _166148) ^ [_411831, _411833] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _411831, _411833), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _411833, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _411831)))], (7093 ^ _166148) ^ [_412011, _412013] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _412013, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _412011)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _412011, _412013), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7099 ^ _166148) ^ [_412283, _412285, _412287, _412289, _412291] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412283, _412285), 7102 ^ _166148 : [(7103 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412285), _412287), _412289), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412283), _412287), _412291)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _412285, _412283)), _412287), _412289), _412291))], (7109 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _412285, _412283)), _412287), _412289), _412291), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412285), _412287), _412289), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412283), _412287), _412291)))]]], (7115 ^ _166148) ^ [_412943, _412945, _412947, _412949, _412951] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412943, _412945), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412945), _412947), _412949), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412943), _412947), _412951)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _412945, _412943)), _412947), _412949), _412951))], (7121 ^ _166148) ^ [_413299, _413301, _413303, _413305, _413307] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413299, _413301), 7124 ^ _166148 : [(7125 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413301), _413303), _413305) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413299), _413303), _413307), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _413301, _413299)), _413303), _413305) = _413307)], (7131 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _413301, _413299)), _413303), _413305) = _413307, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413301), _413303), _413305) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413299), _413303), _413307))]]], (7137 ^ _166148) ^ [_413953, _413955, _413957, _413959, _413961] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413953, _413955), 7140 ^ _166148 : [(7141 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413953), _413957), _413959), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413955), _413957), _413961)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413959, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _413955, _413953)), _413957), _413961)))], (7147 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413959, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _413955, _413953)), _413957), _413961)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413953), _413957), _413959), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413955), _413957), _413961)))]]], (7153 ^ _166148) ^ [_414613, _414615, _414617, _414619, _414621] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _414613, _414615), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _414613), _414617), _414619), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _414615), _414617), _414621)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _414619, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _414615, _414613)), _414617), _414621)))], (7159 ^ _166148) ^ [_414969, _414971, _414973, _414975, _414977] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _414969, _414971), 7162 ^ _166148 : [(7163 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _414969), _414973), _414975) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _414971), _414973), _414977), -(_414975 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _414971, _414969)), _414973), _414977))], (7169 ^ _166148) ^ [] : [_414975 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _414971, _414969)), _414973), _414977), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _414969), _414973), _414975) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _414971), _414973), _414977))]]], (7175 ^ _166148) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oii), c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (7177 ^ _166148) ^ [] : [-(c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (7179 ^ _166148) ^ [_415686, _415688, _415690] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _415686), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415688, _415690)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _415686), _415688)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _415686), _415690)))], (7181 ^ _166148) ^ [_415824, _415826, _415828] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _415824), _415826)), _415828) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _415824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _415826), _415828)))], (7183 ^ _166148) ^ [_416001, _416003, _416005, _416007, _416009] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416001, _416003), 7186 ^ _166148 : [(7187 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416001), _416005), _416007), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416003), _416005), _416009)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _416007, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _416003, _416001)), _416005), _416009)))], (7193 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _416007, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _416003, _416001)), _416005), _416009)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416001), _416005), _416007), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416003), _416005), _416009)))]]], (7199 ^ _166148) ^ [_416661, _416663, _416665, _416667, _416669] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416661, _416663), 7202 ^ _166148 : [(7203 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416663), _416665), _416667), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416661), _416665), _416669)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _416663, _416661)), _416665), _416667), _416669))], (7209 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _416663, _416661)), _416665), _416667), _416669), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416663), _416665), _416667), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416661), _416665), _416669)))]]], (7215 ^ _166148) ^ [_417299, _417301] : [_417299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417299), _417301) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7221 ^ _166148) ^ [_417473, _417475] : [-(_417473 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417473), _417475) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417475, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _417473, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _417475)))], (7227 ^ _166148) ^ [_417748, _417750] : [_417748 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _417750), _417748) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7233 ^ _166148) ^ [_417922, _417924] : [-(_417922 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _417924), _417922) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417924), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _417924), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _417922, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (7239 ^ _166148) ^ [_418195, _418197, _418199] : [class_Power_Opower(_418195), 7242 ^ _166148 : [(7243 ^ _166148) ^ [] : [_418197 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_418195), _418199), _418197) = c_Groups_Oone__class_Oone(_418195))], (7249 ^ _166148) ^ [] : [-(_418197 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_418195), _418199), _418197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418195), _418199), hAPP(hAPP(c_Power_Opower__class_Opower(_418195), _418199), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _418197, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (7255 ^ _166148) ^ [_418765, _418767, _418769] : [class_Groups_Omonoid__mult(_418765), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _418767), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418765), hAPP(hAPP(c_Power_Opower__class_Opower(_418765), _418769), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _418767, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _418769) = hAPP(hAPP(c_Power_Opower__class_Opower(_418765), _418769), _418767))], (7265 ^ _166148) ^ [_419130, _419132] : [class_Groups_Olinordered__ab__group__add(_419130), 7268 ^ _166148 : [(7269 ^ _166148) ^ [] : [c_Groups_Oplus__class_Oplus(_419130, _419132, _419132) = c_Groups_Ozero__class_Ozero(_419130), -(_419132 = c_Groups_Ozero__class_Ozero(_419130))], (7275 ^ _166148) ^ [] : [_419132 = c_Groups_Ozero__class_Ozero(_419130), -(c_Groups_Oplus__class_Oplus(_419130, _419132, _419132) = c_Groups_Ozero__class_Ozero(_419130))]]], (7281 ^ _166148) ^ [_419654, _419656, _419658, _419660, _419662] : [class_Groups_Oab__group__add(_419654), -(c_Groups_Ominus__class_Ominus(_419654, c_Groups_Oplus__class_Oplus(_419654, _419656, _419658), c_Groups_Oplus__class_Oplus(_419654, _419660, _419662)) = c_Groups_Oplus__class_Oplus(_419654, c_Groups_Ominus__class_Ominus(_419654, _419656, _419660), c_Groups_Ominus__class_Ominus(_419654, _419658, _419662)))], (7287 ^ _166148) ^ [_419928, _419930] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _419928), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _419928, _419930), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _419930, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _419930)), _419928), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7301 ^ _166148) ^ [] : [-(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))], (7303 ^ _166148) ^ [] : [-(c_Groups_Oplus__class_Oplus(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (7305 ^ _166148) ^ [] : [-(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (7307 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p))], (7309 ^ _166148) ^ [_420543] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _420543), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(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_s____), _420543)), v_m____))], (7315 ^ _166148) ^ [] : [-(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))) = c_Groups_Oplus__class_Oplus(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (7317 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))))], (7319 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))))], (7321 ^ _166148) ^ [_420927, _420929, _420931] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _420927), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _420929, _420931)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _420927), _420929), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _420927), _420931)))], (7323 ^ _166148) ^ [_421049, _421051] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _421049)), _421051) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _421049), _421051)))], (7325 ^ _166148) ^ [_421175, _421177, _421179] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _421175, _421177)), _421179) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _421175), _421179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _421177), _421179)))], (7327 ^ _166148) ^ [_421312, _421314] : [class_Groups_Oordered__ab__group__add__abs(_421312), -(c_Groups_Oabs__class_Oabs(_421312, c_Groups_Ouminus__class_Ouminus(_421312, _421314)) = c_Groups_Oabs__class_Oabs(_421312, _421314))], (7333 ^ _166148) ^ [_421552, _421554, _421556] : [class_Groups_Oordered__ab__group__add__abs(_421552), -(c_Groups_Oabs__class_Oabs(_421552, c_Groups_Ominus__class_Ominus(_421552, _421554, _421556)) = c_Groups_Oabs__class_Oabs(_421552, c_Groups_Ominus__class_Ominus(_421552, _421556, _421554)))], (7339 ^ _166148) ^ [_421793, _421795, _421797] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _421793, _421795), _421797) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _421793, _421797), _421795))], (7341 ^ _166148) ^ [_421934, _421936, _421938] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _421934, _421936), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _421938), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _421938), _421934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _421938), _421936)))], (7351 ^ _166148) ^ [_422273, _422275] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _422273), 7354 ^ _166148 : [(7355 ^ _166148) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _422273), _422275) = c_Groups_Oone__class_Oone(tc_Int_Oint), 7358 ^ _166148 : [(7359 ^ _166148) ^ [] : [-(_422273 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7361 ^ _166148) ^ [] : [-(_422275 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (7363 ^ _166148) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _422273), _422275) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _422273 = c_Groups_Oone__class_Oone(tc_Int_Oint), _422275 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (7373 ^ _166148) ^ [_422910, _422912, _422914] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _422910, _422912)), _422914) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _422910), _422914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _422912), _422914)))], (7375 ^ _166148) ^ [_423046, _423048, _423050] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423046), _423048)), _423050) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423048), _423050)))], (7377 ^ _166148) ^ [_423180, _423182, _423184] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423180), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _423182, _423184)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423180), _423182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423180), _423184)))], (7379 ^ _166148) ^ [_423302, _423304] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423302), _423304) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423304), _423302))], (7381 ^ _166148) ^ [_423394] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _423394), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _423394)], (7383 ^ _166148) ^ [_423478] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _423478) = _423478)], (7385 ^ _166148) ^ [_423588, _423590] : [class_Groups_Oordered__ab__group__add__abs(_423588), 7388 ^ _166148 : [(7389 ^ _166148) ^ [] : [c_Groups_Oabs__class_Oabs(_423588, _423590) = c_Groups_Ozero__class_Ozero(_423588), -(_423590 = c_Groups_Ozero__class_Ozero(_423588))], (7395 ^ _166148) ^ [] : [_423590 = c_Groups_Ozero__class_Ozero(_423588), -(c_Groups_Oabs__class_Oabs(_423588, _423590) = c_Groups_Ozero__class_Ozero(_423588))]]], (7401 ^ _166148) ^ [_424053] : [class_Groups_Oordered__ab__group__add__abs(_424053), -(c_Groups_Oabs__class_Oabs(_424053, c_Groups_Ozero__class_Ozero(_424053)) = c_Groups_Ozero__class_Ozero(_424053))], (7407 ^ _166148) ^ [_424283, _424285, _424287] : [class_Groups_Oordered__ab__group__add__abs(_424283), c_Orderings_Oord__class_Oless__eq(_424283, c_Groups_Oabs__class_Oabs(_424283, _424285), _424287), -(c_Orderings_Oord__class_Oless__eq(_424283, _424285, _424287))], (7417 ^ _166148) ^ [_424600, _424602] : [class_Groups_Oordered__ab__group__add__abs(_424600), -(c_Orderings_Oord__class_Oless__eq(_424600, _424602, c_Groups_Oabs__class_Oabs(_424600, _424602)))], (7423 ^ _166148) ^ [_424830, _424832, _424834] : [class_Groups_Oordered__ab__group__add__abs(_424830), -(c_Groups_Oabs__class_Oabs(_424830, c_Groups_Oplus__class_Oplus(_424830, c_Groups_Oabs__class_Oabs(_424830, _424832), c_Groups_Oabs__class_Oabs(_424830, _424834))) = c_Groups_Oplus__class_Oplus(_424830, c_Groups_Oabs__class_Oabs(_424830, _424832), c_Groups_Oabs__class_Oabs(_424830, _424834)))], (7429 ^ _166148) ^ [_425090, _425092] : [class_Groups_Oordered__ab__group__add__abs(_425090), -(c_Groups_Oabs__class_Oabs(_425090, c_Groups_Oabs__class_Oabs(_425090, _425092)) = c_Groups_Oabs__class_Oabs(_425090, _425092))], (7435 ^ _166148) ^ [_425316, _425318] : [class_Rings_Olinordered__idom(_425316), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425316), c_Groups_Oabs__class_Oabs(_425316, _425318)), c_Groups_Oabs__class_Oabs(_425316, _425318)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425316), _425318), _425318))], (7441 ^ _166148) ^ [_425582, _425584, _425586] : [class_Rings_Olinordered__idom(_425582), -(c_Groups_Oabs__class_Oabs(_425582, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425582), _425584), _425586)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425582), c_Groups_Oabs__class_Oabs(_425582, _425584)), c_Groups_Oabs__class_Oabs(_425582, _425586)))], (7447 ^ _166148) ^ [_425832] : [class_Rings_Olinordered__idom(_425832), -(c_Groups_Oabs__class_Oabs(_425832, c_Groups_Oone__class_Oone(_425832)) = c_Groups_Oone__class_Oone(_425832))], (7453 ^ _166148) ^ [_426019] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _426019) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _426019))], (7455 ^ _166148) ^ [_426132, _426134] : [class_RealVector_Oreal__normed__vector(_426132), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_426132, _426134)) = c_RealVector_Onorm__class_Onorm(_426132, _426134))], (7461 ^ _166148) ^ [_426358, _426360] : [class_Fields_Olinordered__field__inverse__zero(_426358), -(c_Groups_Oabs__class_Oabs(_426358, c_Rings_Oinverse__class_Oinverse(_426358, _426360)) = c_Rings_Oinverse__class_Oinverse(_426358, c_Groups_Oabs__class_Oabs(_426358, _426360)))], (7467 ^ _166148) ^ [_426604, _426606, _426608] : [class_Rings_Olinordered__idom(_426604), -(c_Groups_Oabs__class_Oabs(_426604, hAPP(hAPP(c_Power_Opower__class_Opower(_426604), _426606), _426608)) = hAPP(hAPP(c_Power_Opower__class_Opower(_426604), c_Groups_Oabs__class_Oabs(_426604, _426606)), _426608))], (7473 ^ _166148) ^ [_426862, _426864] : [class_Groups_Oordered__ab__group__add__abs(_426862), c_Orderings_Oord__class_Oless__eq(_426862, c_Groups_Ozero__class_Ozero(_426862), _426864), -(c_Groups_Oabs__class_Oabs(_426862, _426864) = _426864)], (7483 ^ _166148) ^ [_427171, _427173] : [class_Groups_Oordered__ab__group__add__abs(_427171), 7486 ^ _166148 : [(7487 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_427171, c_Groups_Oabs__class_Oabs(_427171, _427173), c_Groups_Ozero__class_Ozero(_427171)), -(_427173 = c_Groups_Ozero__class_Ozero(_427171))], (7493 ^ _166148) ^ [] : [_427173 = c_Groups_Ozero__class_Ozero(_427171), -(c_Orderings_Oord__class_Oless__eq(_427171, c_Groups_Oabs__class_Oabs(_427171, _427173), c_Groups_Ozero__class_Ozero(_427171)))]]], (7499 ^ _166148) ^ [_427653, _427655] : [class_Groups_Oordered__ab__group__add__abs(_427653), -(c_Orderings_Oord__class_Oless__eq(_427653, c_Groups_Ozero__class_Ozero(_427653), c_Groups_Oabs__class_Oabs(_427653, _427655)))], (7505 ^ _166148) ^ [_427873, _427875] : [class_Groups_Oordered__ab__group__add__abs(_427873), c_Orderings_Oord__class_Oless(_427873, c_Groups_Ozero__class_Ozero(_427873), _427875), -(c_Groups_Oabs__class_Oabs(_427873, _427875) = _427875)], (7515 ^ _166148) ^ [_428182, _428184] : [class_Groups_Oordered__ab__group__add__abs(_428182), 7518 ^ _166148 : [(7519 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_428182, c_Groups_Ozero__class_Ozero(_428182), c_Groups_Oabs__class_Oabs(_428182, _428184)), _428184 = c_Groups_Ozero__class_Ozero(_428182)], (7525 ^ _166148) ^ [] : [-(_428184 = c_Groups_Ozero__class_Ozero(_428182)), -(c_Orderings_Oord__class_Oless(_428182, c_Groups_Ozero__class_Ozero(_428182), c_Groups_Oabs__class_Oabs(_428182, _428184)))]]], (7531 ^ _166148) ^ [_428666, _428668] : [class_Groups_Oordered__ab__group__add__abs(_428666), c_Orderings_Oord__class_Oless(_428666, c_Groups_Oabs__class_Oabs(_428666, _428668), c_Groups_Ozero__class_Ozero(_428666))], (7537 ^ _166148) ^ [_428929, _428931, _428933, _428935, _428937] : [class_Rings_Olinordered__idom(_428929), c_Orderings_Oord__class_Oless(_428929, c_Groups_Oabs__class_Oabs(_428929, _428931), _428933), c_Orderings_Oord__class_Oless(_428929, c_Groups_Oabs__class_Oabs(_428929, _428935), _428937), -(c_Orderings_Oord__class_Oless(_428929, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428929), c_Groups_Oabs__class_Oabs(_428929, _428931)), c_Groups_Oabs__class_Oabs(_428929, _428935)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428929), _428933), _428937)))], (7551 ^ _166148) ^ [_429433, _429435, _429437] : [class_Groups_Oordered__ab__group__add__abs(_429433), -(c_Orderings_Oord__class_Oless__eq(_429433, c_Groups_Oabs__class_Oabs(_429433, c_Groups_Oplus__class_Oplus(_429433, _429435, _429437)), c_Groups_Oplus__class_Oplus(_429433, c_Groups_Oabs__class_Oabs(_429433, _429435), c_Groups_Oabs__class_Oabs(_429433, _429437))))], (7557 ^ _166148) ^ [_429697, _429699, _429701] : [class_Groups_Oordered__ab__group__add__abs(_429697), -(c_Orderings_Oord__class_Oless__eq(_429697, c_Groups_Oabs__class_Oabs(_429697, c_Groups_Ominus__class_Ominus(_429697, c_Groups_Oabs__class_Oabs(_429697, _429699), c_Groups_Oabs__class_Oabs(_429697, _429701))), c_Groups_Oabs__class_Oabs(_429697, c_Groups_Ominus__class_Ominus(_429697, _429699, _429701))))], (7563 ^ _166148) ^ [_429967, _429969, _429971] : [class_Groups_Oordered__ab__group__add__abs(_429967), -(c_Orderings_Oord__class_Oless__eq(_429967, c_Groups_Ominus__class_Ominus(_429967, c_Groups_Oabs__class_Oabs(_429967, _429969), c_Groups_Oabs__class_Oabs(_429967, _429971)), c_Groups_Oabs__class_Oabs(_429967, c_Groups_Ominus__class_Ominus(_429967, _429969, _429971))))], (7569 ^ _166148) ^ [_430231, _430233, _430235] : [class_Groups_Oordered__ab__group__add__abs(_430231), -(c_Orderings_Oord__class_Oless__eq(_430231, c_Groups_Ominus__class_Ominus(_430231, c_Groups_Oabs__class_Oabs(_430231, _430233), c_Groups_Oabs__class_Oabs(_430231, _430235)), c_Groups_Oabs__class_Oabs(_430231, c_Groups_Ominus__class_Ominus(_430231, _430235, _430233))))], (7575 ^ _166148) ^ [_430481, _430483] : [class_Groups_Oordered__ab__group__add__abs(_430481), -(c_Orderings_Oord__class_Oless__eq(_430481, c_Groups_Ouminus__class_Ouminus(_430481, _430483), c_Groups_Oabs__class_Oabs(_430481, _430483)))], (7581 ^ _166148) ^ [_430717, _430719, _430721] : [class_Groups_Oordered__ab__group__add__abs(_430717), 7584 ^ _166148 : [(7585 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_430717, c_Groups_Oabs__class_Oabs(_430717, _430719), _430721), 7588 ^ _166148 : [(7589 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_430717, _430719, _430721))], (7591 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_430717, c_Groups_Ouminus__class_Ouminus(_430717, _430719), _430721))]]], (7593 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_430717, c_Groups_Oabs__class_Oabs(_430717, _430719), _430721)), c_Orderings_Oord__class_Oless__eq(_430717, _430719, _430721), c_Orderings_Oord__class_Oless__eq(_430717, c_Groups_Ouminus__class_Ouminus(_430717, _430719), _430721)]]], (7603 ^ _166148) ^ [_431396, _431398, _431400] : [class_Groups_Oordered__ab__group__add__abs(_431396), c_Orderings_Oord__class_Oless__eq(_431396, _431398, _431400), c_Orderings_Oord__class_Oless__eq(_431396, c_Groups_Ouminus__class_Ouminus(_431396, _431398), _431400), -(c_Orderings_Oord__class_Oless__eq(_431396, c_Groups_Oabs__class_Oabs(_431396, _431398), _431400))], (7617 ^ _166148) ^ [_431828, _431830, _431832] : [class_Groups_Oordered__ab__group__add__abs(_431828), c_Orderings_Oord__class_Oless__eq(_431828, c_Groups_Oabs__class_Oabs(_431828, _431830), _431832), -(c_Orderings_Oord__class_Oless__eq(_431828, c_Groups_Ouminus__class_Ouminus(_431828, _431830), _431832))], (7627 ^ _166148) ^ [_432165, _432167, _432169] : [class_Rings_Olinordered__idom(_432165), 7630 ^ _166148 : [(7631 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_432165, c_Groups_Oabs__class_Oabs(_432165, _432167), _432169), 7634 ^ _166148 : [(7635 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_432165, _432167, _432169))], (7637 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_432165, c_Groups_Ouminus__class_Ouminus(_432165, _432167), _432169))]]], (7639 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_432165, c_Groups_Oabs__class_Oabs(_432165, _432167), _432169)), c_Orderings_Oord__class_Oless(_432165, _432167, _432169), c_Orderings_Oord__class_Oless(_432165, c_Groups_Ouminus__class_Ouminus(_432165, _432167), _432169)]]], (7649 ^ _166148) ^ [_432830, _432832] : [class_Fields_Olinordered__field(_432830), -(_432832 = c_Groups_Ozero__class_Ozero(_432830)), -(c_Groups_Oabs__class_Oabs(_432830, c_Rings_Oinverse__class_Oinverse(_432830, _432832)) = c_Rings_Oinverse__class_Oinverse(_432830, c_Groups_Oabs__class_Oabs(_432830, _432832)))], (7659 ^ _166148) ^ [_433172, _433174, _433176] : [class_Rings_Olinordered__idom(_433172), -(c_Groups_Oabs__class_Oabs(_433172, hAPP(hAPP(c_Power_Opower__class_Opower(_433172), c_Groups_Ouminus__class_Ouminus(_433172, _433174)), _433176)) = c_Groups_Oabs__class_Oabs(_433172, hAPP(hAPP(c_Power_Opower__class_Opower(_433172), _433174), _433176)))], (7665 ^ _166148) ^ [_433465, _433467] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _433465), _433467), 7668 ^ _166148 : [(7669 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _433467), _433465))], (7671 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _433465, _433467))]]], (7673 ^ _166148) ^ [_433720, _433722] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _433720), _433722)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _433722), _433720), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _433720, _433722)], (7683 ^ _166148) ^ [_434039, _434041] : [class_RealVector_Oreal__normed__algebra__1(_434039), -(c_RealVector_Onorm__class_Onorm(_434039, c_RealVector_Oof__real(_434039, _434041)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _434041))], (7689 ^ _166148) ^ [_434250, _434252] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _434250, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _434252))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _434252, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _434250))))], (7691 ^ _166148) ^ [_434393, _434395, _434397] : [class_Rings_Oordered__ring__abs(_434393), -(c_Groups_Oabs__class_Oabs(_434393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_434393), _434395), _434397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_434393), c_Groups_Oabs__class_Oabs(_434393, _434395)), c_Groups_Oabs__class_Oabs(_434393, _434397))), 7698 ^ _166148 : [(7699 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_434393, c_Groups_Ozero__class_Ozero(_434393), _434395)], (7701 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_434393, _434395, c_Groups_Ozero__class_Ozero(_434393))]], 7702 ^ _166148 : [(7703 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_434393, c_Groups_Ozero__class_Ozero(_434393), _434397)], (7705 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_434393, _434397, c_Groups_Ozero__class_Ozero(_434393))]]], (7709 ^ _166148) ^ [_435033, _435035, _435037] : [class_Rings_Olinordered__idom(_435033), c_Orderings_Oord__class_Oless__eq(_435033, c_Groups_Ozero__class_Ozero(_435033), _435035), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_435033), c_Groups_Oabs__class_Oabs(_435033, _435037)), _435035) = c_Groups_Oabs__class_Oabs(_435033, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_435033), _435037), _435035)))], (7719 ^ _166148) ^ [_435390, _435392] : [class_Groups_Oordered__ab__group__add__abs(_435390), -(c_Orderings_Oord__class_Oless__eq(_435390, c_Groups_Ouminus__class_Ouminus(_435390, c_Groups_Oabs__class_Oabs(_435390, _435392)), c_Groups_Ozero__class_Ozero(_435390)))], (7725 ^ _166148) ^ [_435616, _435618] : [class_Groups_Oordered__ab__group__add__abs(_435616), c_Orderings_Oord__class_Oless__eq(_435616, _435618, c_Groups_Ozero__class_Ozero(_435616)), -(c_Groups_Oabs__class_Oabs(_435616, _435618) = c_Groups_Ouminus__class_Ouminus(_435616, _435618))], (7735 ^ _166148) ^ [_435945, _435947, _435949] : [class_Rings_Olinordered__idom(_435945), -(c_Orderings_Oord__class_Oless__eq(_435945, c_Groups_Ozero__class_Ozero(_435945), hAPP(hAPP(c_Power_Opower__class_Opower(_435945), c_Groups_Oabs__class_Oabs(_435945, _435947)), _435949)))], (7741 ^ _166148) ^ [_436187, _436189] : [class_Groups_Oabs__if(_436187), 7744 ^ _166148 : [(7745 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_436187, _436189, c_Groups_Ozero__class_Ozero(_436187)), -(c_Groups_Oabs__class_Oabs(_436187, _436189) = c_Groups_Ouminus__class_Ouminus(_436187, _436189))], (7751 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_436187, _436189, c_Groups_Ozero__class_Ozero(_436187))), -(c_Groups_Oabs__class_Oabs(_436187, _436189) = _436189)]]], (7757 ^ _166148) ^ [_436681, _436683] : [class_Groups_Oordered__ab__group__add__abs(_436681), c_Orderings_Oord__class_Oless(_436681, _436683, c_Groups_Ozero__class_Ozero(_436681)), -(c_Groups_Oabs__class_Oabs(_436681, _436683) = c_Groups_Ouminus__class_Ouminus(_436681, _436683))], (7767 ^ _166148) ^ [_437010, _437012, _437014] : [class_Groups_Oordered__ab__group__add__abs(_437010), -(c_Orderings_Oord__class_Oless__eq(_437010, c_Groups_Oabs__class_Oabs(_437010, c_Groups_Ominus__class_Ominus(_437010, _437012, _437014)), c_Groups_Oplus__class_Oplus(_437010, c_Groups_Oabs__class_Oabs(_437010, _437012), c_Groups_Oabs__class_Oabs(_437010, _437014))))], (7773 ^ _166148) ^ [_437302, _437304, _437306, _437308, _437310] : [class_Groups_Oordered__ab__group__add__abs(_437302), -(c_Orderings_Oord__class_Oless__eq(_437302, c_Groups_Oabs__class_Oabs(_437302, c_Groups_Ominus__class_Ominus(_437302, c_Groups_Oplus__class_Oplus(_437302, _437304, _437306), c_Groups_Oplus__class_Oplus(_437302, _437308, _437310))), c_Groups_Oplus__class_Oplus(_437302, c_Groups_Oabs__class_Oabs(_437302, c_Groups_Ominus__class_Ominus(_437302, _437304, _437308)), c_Groups_Oabs__class_Oabs(_437302, c_Groups_Ominus__class_Ominus(_437302, _437306, _437310)))))], (7779 ^ _166148) ^ [_437610, _437612, _437614] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _437610, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _437612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _437610), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _437614))), -(_437612 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7789 ^ _166148) ^ [_437953] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _437953, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _437953) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _437953))], (7795 ^ _166148) ^ [_438123] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _438123, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _438123) = _438123)], (7801 ^ _166148) ^ [_438346] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _438346, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _438346) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _438346))], (7807 ^ _166148) ^ [_438516] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _438516, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _438516) = _438516)], (7813 ^ _166148) ^ [_438703] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _438703), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _438703)], (7815 ^ _166148) ^ [_438831, _438833, _438835, _438837] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _438831, _438833), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _438835), c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _438837)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _438831, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _438835))), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _438833, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _438837))))))], (7817 ^ _166148) ^ [_439004, _439006, _439008] : [class_RealVector_Oreal__normed__vector(_439004), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_439004, _439006), c_RealVector_Onorm__class_Onorm(_439004, _439008))), c_RealVector_Onorm__class_Onorm(_439004, c_Groups_Ominus__class_Ominus(_439004, _439006, _439008))))], (7823 ^ _166148) ^ [_439231] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _439231))))], (7826 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7824 ^ []))], (7828 ^ _166148) ^ [_439451] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _439451), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(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_s____), _439451)), 7824 ^ []))], (7834 ^ _166148) ^ [_439707, _439709, _439711, _439713] : [class_Rings_Olinordered__idom(_439707), 7837 ^ _166148 : [(7838 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_439707, c_Groups_Oabs__class_Oabs(_439707, c_Groups_Ominus__class_Ominus(_439707, _439709, _439711)), _439713), 7841 ^ _166148 : [(7842 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_439707, c_Groups_Ominus__class_Ominus(_439707, _439711, _439713), _439709))], (7844 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_439707, _439709, c_Groups_Oplus__class_Oplus(_439707, _439711, _439713)))]]], (7846 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_439707, c_Groups_Oabs__class_Oabs(_439707, c_Groups_Ominus__class_Ominus(_439707, _439709, _439711)), _439713)), c_Orderings_Oord__class_Oless(_439707, c_Groups_Ominus__class_Ominus(_439707, _439711, _439713), _439709), c_Orderings_Oord__class_Oless(_439707, _439709, c_Groups_Oplus__class_Oplus(_439707, _439711, _439713))]]], (7857 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7855 ^ []))], (7859 ^ _166148) ^ [_440528] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _440528), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(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_s____), _440528)), 7855 ^ []))], (7865 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____))], (7867 ^ _166148) ^ [_440814] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _440814, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _440814) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _440814))], (7873 ^ _166148) ^ [_440984] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _440984, c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _440984) = _440984)], (7879 ^ _166148) ^ [_441230, _441232] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _441230, _441232), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _441230, _441232), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7885 ^ _166148) ^ [_441404, _441406] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _441404, _441406), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _441404, _441406))], (7891 ^ _166148) ^ [_441657, _441659] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _441657, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _441659, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _441657, _441659))], (7897 ^ _166148) ^ [_441831, _441833] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _441831, _441833), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _441831, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _441833, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7903 ^ _166148) ^ [_442040, _442042] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442040, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _442042)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _442040, _442042))], (7905 ^ _166148) ^ [_442145, _442147] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _442145, _442147) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442145, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _442147)))], (7907 ^ _166148) ^ [_442265, _442267] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _442265), _442267)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _442265) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7913 ^ _166148) ^ [_442514] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _442514), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_442514 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7919 ^ _166148) ^ [_442678] : [_442678 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _442678), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7925 ^ _166148) ^ [_442877, _442879] : [-(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), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _442877)), _442879)))], (7927 ^ _166148) ^ [_443039, _443041, _443043] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_443039, _443041, _443043), 7930 ^ _166148 : [(7931 ^ _166148) ^ [_443186, _443188] : [-(hAPP(_443043, _443188) = hAPP(_443043, _443186))]]], (7933 ^ _166148) ^ [_443264, _443266, _443268] : [hAPP(_443268, 7934 ^ [_443264, _443266, _443268]) = hAPP(_443268, 7935 ^ [_443264, _443266, _443268]), -(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_443264, _443266, _443268))], (7941 ^ _166148) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (7943 ^ _166148) ^ [_443670] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _443670), _443670) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (7945 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7947 ^ _166148) ^ [_443809] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _443809) = _443809)], (7949 ^ _166148) ^ [_443935] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _443935), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _443935))], (7955 ^ _166148) ^ [_444095] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _444095), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _444095))], (7961 ^ _166148) ^ [_444276] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _444276, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _444276)], (7963 ^ _166148) ^ [_444416, _444418] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _444416, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _444418, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _444416, _444418))], (7969 ^ _166148) ^ [_444590, _444592] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _444590, _444592), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _444590, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _444592, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7985 ^ _166148) ^ [_445107, _445109] : [7986 ^ _166148 : [(7987 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _445107, _445109)], (7989 ^ _166148) ^ [] : [_445107 = _445109]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _445107, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _445109, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7975 ^ _166148) ^ [_444843, _444845] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _444843, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _444845, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _444843, _444845)), -(_444843 = _444845)], (7993 ^ _166148) ^ [_445434, _445436] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _445434, c_Groups_Oone__class_Oone(tc_Int_Oint)), _445436), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _445434, _445436))], (7999 ^ _166148) ^ [_445608, _445610] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _445608, _445610), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _445608, c_Groups_Oone__class_Oone(tc_Int_Oint)), _445610))], (8005 ^ _166148) ^ [_445847] : [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), _445847), _445847), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _445847, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8011 ^ _166148) ^ [_446023] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _446023, 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), _446023), _446023), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8017 ^ _166148) ^ [_446235] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _446235), -(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), _446235)))], (8023 ^ _166148) ^ [_446451, _446453] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _446451, _446453), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _446451, c_Groups_Oone__class_Oone(tc_Int_Oint)), _446453))], (8029 ^ _166148) ^ [_446673, _446675] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _446673, _446675)), -(_446673 = _446675), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _446675, _446673))], (8039 ^ _166148) ^ [_447006, _447008, _447010, _447012] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _447006, _447008), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _447010, _447012), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447006, _447010), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447008, _447012)))], (8049 ^ _166148) ^ [_447361, _447363, _447365] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _447361, _447363), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447365, _447361), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447365, _447363)))], (8055 ^ _166148) ^ [_447611, _447613, _447615] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _447611, _447613), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447611, _447615), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447613, _447615)))], (8061 ^ _166148) ^ [_447846, _447848, _447850] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447846, _447848), _447850) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447846, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447848, _447850)))], (8063 ^ _166148) ^ [_447972, _447974, _447976] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447972, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447974, _447976)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447974, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447972, _447976)))], (8065 ^ _166148) ^ [_448128, _448130] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _448128, _448130), 8068 ^ _166148 : [(8069 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _448128, _448130))], (8071 ^ _166148) ^ [] : [_448128 = _448130]]], (8073 ^ _166148) ^ [_448370, _448372] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _448370, _448372)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _448370, _448372), -(_448370 = _448372)], (8083 ^ _166148) ^ [_448663, _448665] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _448663, _448665) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _448665, _448663))], (8085 ^ _166148) ^ [_448765, _448767] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _448765, _448767)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _448765), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _448767)))], (8087 ^ _166148) ^ [_448862] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _448862)) = _448862)], (8089 ^ _166148) ^ [_448946] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _448946), _448946) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8091 ^ _166148) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8103 ^ _166148) ^ [_449415, _449417] : [8104 ^ _166148 : [(8105 ^ _166148) ^ [] : [-(_449415 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8107 ^ _166148) ^ [] : [_449417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _449415)), _449417)))], (8093 ^ _166148) ^ [_449142, _449144] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _449142)), _449144)), _449142 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_449144 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8111 ^ _166148) ^ [_449738, _449740, _449742] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _449738), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _449740, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _449742, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _449742, _449740)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _449738))))], (8117 ^ _166148) ^ [_450014, _450016, _450018] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _450014), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _450016, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _450016, _450018)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _450014)), _450018))], (8123 ^ _166148) ^ [_450290, _450292, _450294] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _450290), _450290 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _450292, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _450290), _450294)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _450292, _450290), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _450294))], (8137 ^ _166148) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (8139 ^ _166148) ^ [_450741] : [-(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_pa____), v_c____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), _450741))))], (8141 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8143 ^ _166148) ^ [_450878] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _450878, _450878))], (8145 ^ _166148) ^ [_450986, _450988] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _450986, _450988)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _450988, _450986))], (8151 ^ _166148) ^ [_451215, _451217, _451219] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _451215, _451217), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _451217, _451219), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _451215, _451219))], (8161 ^ _166148) ^ [_451530, _451532] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _451530, _451532), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _451532, _451530), -(_451530 = _451532)], (8171 ^ _166148) ^ [_451847, _451849, _451851] : [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), _451847), _451849), _451851)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _451851, _451847), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _451847), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _451849))], (8185 ^ _166148) ^ [_452291, _452293, _452295] : [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), _452291), _452293), _452295), 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), _452295), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _452291), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _452293, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8199 ^ _166148) ^ [_452763, _452765, _452767, _452769, _452771] : [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), _452763), _452765), _452767), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _452763), _452769), _452771)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _452767), c_Orderings_Oord__class_Oless(tc_Int_Oint, _452767, _452763), c_Orderings_Oord__class_Oless(tc_Int_Oint, _452771, _452763), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _452765, _452769))], (8217 ^ _166148) ^ [_453400, _453402, _453404, _453406, _453408, _453410] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _453400), _453402), _453404) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _453406), _453408), _453410), 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), _453406), _453408), _453410)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _453410, _453406), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _453404), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _453406), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _453406, _453400), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _453402, _453408))], (8243 ^ _166148) ^ [_454273, _454275, _454277, _454279, _454281] : [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), _454273), _454275), _454277), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _454273), _454279), _454281)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _454281, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _454273, _454281), c_Orderings_Oord__class_Oless(tc_Int_Oint, _454273, _454277), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _454279, _454275))], (8261 ^ _166148) ^ [_454910, _454912, _454914, _454916, _454918, _454920] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _454910), _454912), _454914) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _454916), _454918), _454920), 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), _454916), _454918), _454920), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _454914, _454910), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _454920), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _454916), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _454916, _454910), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _454918, _454912))], (8287 ^ _166148) ^ [_455755, _455757, _455759] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _455755), _455755 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _455757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _455755), _455759)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _455757), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _455759, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8301 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____)))], (8303 ^ _166148) ^ [_456236, _456238] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _456236), -(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), _456236), _456238)))], (8309 ^ _166148) ^ [_456462, _456464] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _456462), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _456464), -(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), _456462), _456464)))], (8319 ^ _166148) ^ [_456779, _456781] : [class_Groups_Ozero(_456779), 8322 ^ _166148 : [(8323 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_456779, _456781) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_456781 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456779)))], (8329 ^ _166148) ^ [] : [_456781 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456779)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_456779, _456781) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8335 ^ _166148) ^ [] : [-(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)))], (8337 ^ _166148) ^ [] : [-(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)))], (8339 ^ _166148) ^ [_457364, _457366] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _457364), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _457366), -(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, _457364, _457366)))], (8349 ^ _166148) ^ [_457648] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _457648) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _457648)))], (8351 ^ _166148) ^ [_457751] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, _457751), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, _457751))), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _457751), 8358 ^ [_457751]) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8363 ^ _166148) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 8361 ^ []) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (8365 ^ _166148) ^ [_458216] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 8361 ^ []), _458216) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _458216)))], (8367 ^ _166148) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (8369 ^ _166148) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (8371 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____))], (8373 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____))], (8375 ^ _166148) ^ [_458515] : [-(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_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), _458515))))], (8377 ^ _166148) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))], (8379 ^ _166148) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_s____), v_k____), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (8381 ^ _166148) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), 8384 ^ []) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8388 ^ _166148) ^ [_458909] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _458909)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _458909)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))], (8394 ^ _166148) ^ [_459093] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _459093)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _459093)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8400 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (8402 ^ _166148) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))], (8404 ^ _166148) ^ [_459403] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _459403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _459403)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))], (8406 ^ _166148) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (8408 ^ _166148) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (8410 ^ _166148) ^ [_459599] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _459599) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), _459599), v_k____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a____, v_s____)), _459599))))], (8412 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 8415 ^ [])), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8421 ^ _166148) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 8418 ^ []) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 8419 ^ [])], (8423 ^ _166148) ^ [_460059, _460061, _460063, _460065] : [class_Rings_Ocomm__semiring__0(_460059), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_460059), c_Polynomial_Osmult(_460059, _460061, _460063), c_Polynomial_OpCons(_460059, _460065, _460063)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460059)), -(_460063 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460059)))], (8433 ^ _166148) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))], (8435 ^ _166148) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))], (8437 ^ _166148) ^ [_460553, _460555, _460557, _460559] : [class_Rings_Ocomm__ring__1(_460553), -(hAPP(c_Polynomial_Opoly(_460553, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_460553)), c_Polynomial_Omonom(_460553, c_Groups_Oone__class_Oone(_460553), _460555)), _460557)), _460559) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_460553), hAPP(hAPP(c_Power_Opower__class_Opower(_460553), _460559), _460555)), hAPP(c_Polynomial_Opoly(_460553, _460557), _460559)))], (8444 ^ _166148) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), 8442 ^ []) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8446 ^ _166148) ^ [_460954, _460956] : [class_Groups_Ozero(_460954), -(c_Polynomial_Omonom(_460954, _460956, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_460954, _460956, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460954))))], (8452 ^ _166148) ^ [_461186, _461188] : [class_Groups_Oab__group__add(_461186), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_461186), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_461186)), _461188) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_461186), _461188))], (8458 ^ _166148) ^ [_461424, _461426] : [class_Groups_Oab__group__add(_461424), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_461424), _461426, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_461424))) = _461426)], (8464 ^ _166148) ^ [_461652, _461654] : [class_Rings_Ocomm__semiring__0(_461652), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_461652)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_461652))), _461654) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_461652)))], (8470 ^ _166148) ^ [_461896, _461898] : [class_Rings_Ocomm__semiring__0(_461896), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_461896)), _461898), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_461896))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_461896)))], (8476 ^ _166148) ^ [_462126] : [class_Groups_Oab__group__add(_462126), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_462126), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_462126))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_462126)))], (8482 ^ _166148) ^ [_462354, _462356] : [class_Rings_Olinordered__idom(_462354), 8485 ^ _166148 : [(8486 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_462354), _462356, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_462354))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_462354), _462356) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_462354), _462356))], (8492 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_462354), _462356, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_462354)))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_462354), _462356) = _462356)]]], (8498 ^ _166148) ^ [_462890, _462892, _462894] : [class_Int_Oring__char__0(_462890), class_Rings_Oidom(_462890), 8505 ^ _166148 : [(8506 ^ _166148) ^ [] : [c_Polynomial_Opoly(_462890, _462892) = c_Polynomial_Opoly(_462890, _462894), -(_462892 = _462894)], (8512 ^ _166148) ^ [] : [_462892 = _462894, -(c_Polynomial_Opoly(_462890, _462892) = c_Polynomial_Opoly(_462890, _462894))]]], (8518 ^ _166148) ^ [_463517, _463519, _463521, _463523, _463525] : [class_Groups_Ozero(_463517), 8521 ^ _166148 : [(8522 ^ _166148) ^ [] : [c_Polynomial_OpCons(_463517, _463519, _463521) = c_Polynomial_OpCons(_463517, _463523, _463525), 8525 ^ _166148 : [(8526 ^ _166148) ^ [] : [-(_463519 = _463523)], (8528 ^ _166148) ^ [] : [-(_463521 = _463525)]]], (8530 ^ _166148) ^ [] : [-(c_Polynomial_OpCons(_463517, _463519, _463521) = c_Polynomial_OpCons(_463517, _463523, _463525)), _463519 = _463523, _463521 = _463525]]], (8540 ^ _166148) ^ [_464251, _464253, _464255, _464257] : [class_Rings_Ocomm__ring(_464251), -(c_Polynomial_Osmult(_464251, _464253, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_464251), _464255, _464257)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_464251), c_Polynomial_Osmult(_464251, _464253, _464255), c_Polynomial_Osmult(_464251, _464253, _464257)))], (8546 ^ _166148) ^ [_464533, _464535, _464537] : [class_Rings_Ocomm__ring(_464533), -(c_Polynomial_Osmult(_464533, _464535, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_464533), _464537)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_464533), c_Polynomial_Osmult(_464533, _464535, _464537)))], (8552 ^ _166148) ^ [_464811, _464813, _464815, _464817] : [class_Rings_Ocomm__semiring__0(_464811), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_464811)), c_Polynomial_Osmult(_464811, _464813, _464815)), _464817) = c_Polynomial_Osmult(_464811, _464813, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_464811)), _464815), _464817)))], (8558 ^ _166148) ^ [_465115, _465117, _465119, _465121] : [class_Rings_Ocomm__semiring__0(_465115), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_465115)), _465117), c_Polynomial_Osmult(_465115, _465119, _465121)) = c_Polynomial_Osmult(_465115, _465119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_465115)), _465117), _465121)))], (8564 ^ _166148) ^ [_465419, _465421, _465423, _465425] : [class_Rings_Ocomm__semiring__0(_465419), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_465419)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_465419), _465421, _465423)), _465425) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_465419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_465419)), _465421), _465425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_465419)), _465423), _465425)))], (8570 ^ _166148) ^ [_465751, _465753, _465755, _465757] : [class_Groups_Ozero(_465751), 8573 ^ _166148 : [(8574 ^ _166148) ^ [] : [c_Polynomial_Omonom(_465751, _465753, _465755) = c_Polynomial_Omonom(_465751, _465757, _465755), -(_465753 = _465757)], (8580 ^ _166148) ^ [] : [_465753 = _465757, -(c_Polynomial_Omonom(_465751, _465753, _465755) = c_Polynomial_Omonom(_465751, _465757, _465755))]]], (8586 ^ _166148) ^ [_466293, _466295, _466297, _466299] : [class_Rings_Ocomm__semiring__0(_466293), -(hAPP(c_Polynomial_Opoly(_466293, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_466293)), _466295), _466297)), _466299) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466293), hAPP(c_Polynomial_Opoly(_466293, _466295), _466299)), hAPP(c_Polynomial_Opoly(_466293, _466297), _466299)))], (8592 ^ _166148) ^ [_466585, _466587] : [class_Rings_Ocomm__semiring__1(_466585), -(hAPP(c_Polynomial_Opoly(_466585, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_466585))), _466587) = c_Groups_Oone__class_Oone(_466585))], (8598 ^ _166148) ^ [_466845, _466847, _466849, _466851] : [class_Rings_Ocomm__ring(_466845), -(hAPP(c_Polynomial_Opoly(_466845, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_466845), _466847, _466849)), _466851) = c_Groups_Ominus__class_Ominus(_466845, hAPP(c_Polynomial_Opoly(_466845, _466847), _466851), hAPP(c_Polynomial_Opoly(_466845, _466849), _466851)))], (8604 ^ _166148) ^ [_467135, _467137, _467139] : [class_Rings_Ocomm__ring(_467135), -(hAPP(c_Polynomial_Opoly(_467135, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_467135), _467137)), _467139) = c_Groups_Ouminus__class_Ouminus(_467135, hAPP(c_Polynomial_Opoly(_467135, _467137), _467139)))], (8610 ^ _166148) ^ [_467417, _467419, _467421, _467423] : [class_Rings_Ocomm__semiring__1(_467417), -(hAPP(c_Polynomial_Opoly(_467417, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_467417)), _467419), _467421)), _467423) = hAPP(hAPP(c_Power_Opower__class_Opower(_467417), hAPP(c_Polynomial_Opoly(_467417, _467419), _467423)), _467421))], (8616 ^ _166148) ^ [_467739, _467741, _467743, _467745, _467747] : [class_Groups_Oab__group__add(_467739), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_467739), c_Polynomial_OpCons(_467739, _467741, _467743), c_Polynomial_OpCons(_467739, _467745, _467747)) = c_Polynomial_OpCons(_467739, c_Groups_Ominus__class_Ominus(_467739, _467741, _467745), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_467739), _467743, _467747)))], (8622 ^ _166148) ^ [_468049, _468051, _468053, _468055] : [class_Rings_Ocomm__semiring__0(_468049), -(c_Polynomial_Osmult(_468049, _468051, c_Polynomial_Osmult(_468049, _468053, _468055)) = c_Polynomial_Osmult(_468049, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468049), _468051), _468053), _468055))], (8628 ^ _166148) ^ [_468309, _468311] : [class_Rings_Ocomm__semiring__1(_468309), -(c_Polynomial_Osmult(_468309, c_Groups_Oone__class_Oone(_468309), _468311) = _468311)], (8634 ^ _166148) ^ [_468543, _468545, _468547] : [class_Groups_Oab__group__add(_468543), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_468543), c_Polynomial_OpCons(_468543, _468545, _468547)) = c_Polynomial_OpCons(_468543, c_Groups_Ouminus__class_Ouminus(_468543, _468545), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_468543), _468547)))], (8640 ^ _166148) ^ [_468813, _468815, _468817] : [class_Groups_Oab__group__add(_468813), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_468813), c_Polynomial_OpCons(_468813, _468815, _468817)) = c_Polynomial_OpCons(_468813, c_Groups_Ouminus__class_Ouminus(_468813, _468815), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_468813), _468817)))], (8646 ^ _166148) ^ [_469097, _469099, _469101, _469103] : [class_Rings_Ocomm__ring(_469097), -(c_Polynomial_Osmult(_469097, c_Groups_Ominus__class_Ominus(_469097, _469099, _469101), _469103) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_469097), c_Polynomial_Osmult(_469097, _469099, _469103), c_Polynomial_Osmult(_469097, _469101, _469103)))], (8652 ^ _166148) ^ [_469375, _469377, _469379] : [class_Rings_Ocomm__ring(_469375), -(c_Polynomial_Osmult(_469375, c_Groups_Ouminus__class_Ouminus(_469375, _469377), _469379) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_469375), c_Polynomial_Osmult(_469375, _469377, _469379)))], (8658 ^ _166148) ^ [_469621, _469623] : [class_Int_Oring__char__0(_469621), class_Rings_Oidom(_469621), 8665 ^ _166148 : [(8666 ^ _166148) ^ [] : [c_Polynomial_Opoly(_469621, _469623) = c_Polynomial_Opoly(_469621, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_469621))), -(_469623 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_469621)))], (8672 ^ _166148) ^ [] : [_469623 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_469621)), -(c_Polynomial_Opoly(_469621, _469623) = c_Polynomial_Opoly(_469621, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_469621))))]]], (8678 ^ _166148) ^ [_470210, _470212] : [class_Rings_Ocomm__semiring__0(_470210), -(c_Polynomial_Osmult(_470210, _470212, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_470210))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_470210)))], (8684 ^ _166148) ^ [_470470, _470472, _470474, _470476] : [class_Groups_Oab__group__add(_470470), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_470470), c_Polynomial_Omonom(_470470, _470472, _470474), c_Polynomial_Omonom(_470470, _470476, _470474)) = c_Polynomial_Omonom(_470470, c_Groups_Ominus__class_Ominus(_470470, _470472, _470476), _470474))], (8690 ^ _166148) ^ [_470748, _470750, _470752] : [class_Groups_Oab__group__add(_470748), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_470748), c_Polynomial_Omonom(_470748, _470750, _470752)) = c_Polynomial_Omonom(_470748, c_Groups_Ouminus__class_Ouminus(_470748, _470750), _470752))], (8696 ^ _166148) ^ [_470994, _470996] : [class_Groups_Ocomm__monoid__add(_470994), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_470994), _470996, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_470994))) = _470996)], (8702 ^ _166148) ^ [_471222, _471224] : [class_Groups_Ocomm__monoid__add(_471222), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_471222), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471222)), _471224) = _471224)], (8708 ^ _166148) ^ [_471478, _471480, _471482, _471484] : [class_Rings_Ocomm__semiring__0(_471478), -(c_Polynomial_Osmult(_471478, _471480, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_471478), _471482, _471484)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_471478), c_Polynomial_Osmult(_471478, _471480, _471482), c_Polynomial_Osmult(_471478, _471480, _471484)))], (8714 ^ _166148) ^ [_471746, _471748] : [class_Rings_Ocomm__semiring__0(_471746), -(hAPP(c_Polynomial_Opoly(_471746, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471746))), _471748) = c_Groups_Ozero__class_Ozero(_471746))], (8720 ^ _166148) ^ [_471992, _471994, _471996] : [class_Groups_Ozero(_471992), 8723 ^ _166148 : [(8724 ^ _166148) ^ [] : [c_Polynomial_OpCons(_471992, _471994, _471996) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471992)), 8727 ^ _166148 : [(8728 ^ _166148) ^ [] : [-(_471994 = c_Groups_Ozero__class_Ozero(_471992))], (8730 ^ _166148) ^ [] : [-(_471996 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471992)))]]], (8732 ^ _166148) ^ [] : [-(c_Polynomial_OpCons(_471992, _471994, _471996) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471992))), _471994 = c_Groups_Ozero__class_Ozero(_471992), _471996 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471992))]]], (8742 ^ _166148) ^ [_472658] : [class_Groups_Ozero(_472658), -(c_Polynomial_OpCons(_472658, c_Groups_Ozero__class_Ozero(_472658), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472658))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472658)))], (8748 ^ _166148) ^ [_472902, _472904, _472906] : [class_Rings_Oidom(_472902), 8751 ^ _166148 : [(8762 ^ _166148) ^ [] : [8763 ^ _166148 : [(8764 ^ _166148) ^ [] : [_472904 = c_Groups_Ozero__class_Ozero(_472902)], (8766 ^ _166148) ^ [] : [_472906 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472902))]], -(c_Polynomial_Osmult(_472902, _472904, _472906) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472902)))], (8752 ^ _166148) ^ [] : [c_Polynomial_Osmult(_472902, _472904, _472906) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472902)), -(_472904 = c_Groups_Ozero__class_Ozero(_472902)), -(_472906 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472902)))]]], (8770 ^ _166148) ^ [_473582, _473584] : [class_Rings_Ocomm__semiring__0(_473582), -(c_Polynomial_Osmult(_473582, c_Groups_Ozero__class_Ozero(_473582), _473584) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473582)))], (8776 ^ _166148) ^ [_473796] : [class_Rings_Ocomm__semiring__1(_473796), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_473796)) = c_Polynomial_OpCons(_473796, c_Groups_Oone__class_Oone(_473796), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473796))))], (8782 ^ _166148) ^ [_474054, _474056, _474058, _474060] : [class_Rings_Ocomm__semiring__0(_474054), -(hAPP(c_Polynomial_Opoly(_474054, c_Polynomial_Osmult(_474054, _474056, _474058)), _474060) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474054), _474056), hAPP(c_Polynomial_Opoly(_474054, _474058), _474060)))], (8788 ^ _166148) ^ [_474350, _474352, _474354, _474356] : [class_Rings_Ocomm__semiring__0(_474350), -(c_Polynomial_Osmult(_474350, _474352, c_Polynomial_OpCons(_474350, _474354, _474356)) = c_Polynomial_OpCons(_474350, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474350), _474352), _474354), c_Polynomial_Osmult(_474350, _474352, _474356)))], (8794 ^ _166148) ^ [_474660, _474662, _474664, _474666, _474668] : [class_Rings_Ocomm__semiring__0(_474660), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_474660)), c_Polynomial_Omonom(_474660, _474662, _474664)), c_Polynomial_Omonom(_474660, _474666, _474668)) = c_Polynomial_Omonom(_474660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474660), _474662), _474666), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _474664, _474668)))], (8800 ^ _166148) ^ [_474954, _474956] : [class_Groups_Ozero(_474954), -(c_Polynomial_Omonom(_474954, c_Groups_Ozero__class_Ozero(_474954), _474956) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474954)))], (8806 ^ _166148) ^ [_475196, _475198, _475200] : [class_Groups_Ozero(_475196), 8809 ^ _166148 : [(8810 ^ _166148) ^ [] : [c_Polynomial_Omonom(_475196, _475198, _475200) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475196)), -(_475198 = c_Groups_Ozero__class_Ozero(_475196))], (8816 ^ _166148) ^ [] : [_475198 = c_Groups_Ozero__class_Ozero(_475196), -(c_Polynomial_Omonom(_475196, _475198, _475200) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475196)))]]], (8822 ^ _166148) ^ [_475728, _475730, _475732, _475734] : [class_Rings_Ocomm__semiring__0(_475728), -(hAPP(c_Polynomial_Opoly(_475728, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_475728), _475730, _475732)), _475734) = c_Groups_Oplus__class_Oplus(_475728, hAPP(c_Polynomial_Opoly(_475728, _475730), _475734), hAPP(c_Polynomial_Opoly(_475728, _475732), _475734)))], (8828 ^ _166148) ^ [_476046, _476048, _476050, _476052, _476054] : [class_Groups_Ocomm__monoid__add(_476046), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_476046), c_Polynomial_OpCons(_476046, _476048, _476050), c_Polynomial_OpCons(_476046, _476052, _476054)) = c_Polynomial_OpCons(_476046, c_Groups_Oplus__class_Oplus(_476046, _476048, _476052), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_476046), _476050, _476054)))], (8834 ^ _166148) ^ [_476356, _476358, _476360, _476362] : [class_Rings_Ocomm__semiring__0(_476356), c_Polynomial_Osmult(_476356, _476358, _476360) = c_Polynomial_OpCons(_476356, _476362, _476360), -(_476360 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_476356)))], (8844 ^ _166148) ^ [_476725, _476727, _476729, _476731] : [class_Rings_Ocomm__semiring__0(_476725), -(c_Polynomial_Osmult(_476725, c_Groups_Oplus__class_Oplus(_476725, _476727, _476729), _476731) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_476725), c_Polynomial_Osmult(_476725, _476727, _476731), c_Polynomial_Osmult(_476725, _476729, _476731)))], (8850 ^ _166148) ^ [_477017, _477019, _477021, _477023] : [class_Rings_Ocomm__semiring__0(_477017), -(c_Polynomial_Osmult(_477017, _477019, c_Polynomial_Omonom(_477017, _477021, _477023)) = c_Polynomial_Omonom(_477017, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477017), _477019), _477021), _477023))], (8856 ^ _166148) ^ [_477305, _477307, _477309, _477311] : [class_Groups_Ocomm__monoid__add(_477305), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_477305), c_Polynomial_Omonom(_477305, _477307, _477309), c_Polynomial_Omonom(_477305, _477311, _477309)) = c_Polynomial_Omonom(_477305, c_Groups_Oplus__class_Oplus(_477305, _477307, _477311), _477309))], (8862 ^ _166148) ^ [_477597, _477599, _477601, _477603] : [class_Rings_Ocomm__semiring__0(_477597), -(hAPP(c_Polynomial_Opoly(_477597, c_Polynomial_OpCons(_477597, _477599, _477601)), _477603) = c_Groups_Oplus__class_Oplus(_477597, _477599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477597), _477603), hAPP(c_Polynomial_Opoly(_477597, _477601), _477603))))], (8868 ^ _166148) ^ [_477901, _477903, _477905, _477907] : [class_Rings_Ocomm__semiring__1(_477901), -(hAPP(c_Polynomial_Opoly(_477901, c_Polynomial_Omonom(_477901, _477903, _477905)), _477907) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477901), _477903), hAPP(hAPP(c_Power_Opower__class_Opower(_477901), _477907), _477905)))], (8874 ^ _166148) ^ [_478201, _478203, _478205, _478207] : [class_Rings_Ocomm__semiring__0(_478201), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_478201)), _478203), c_Polynomial_OpCons(_478201, _478205, _478207)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478201), c_Polynomial_Osmult(_478201, _478205, _478203), c_Polynomial_OpCons(_478201, c_Groups_Ozero__class_Ozero(_478201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_478201)), _478203), _478207))))], (8880 ^ _166148) ^ [_478529, _478531, _478533, _478535] : [class_Rings_Ocomm__semiring__0(_478529), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_478529)), c_Polynomial_OpCons(_478529, _478531, _478533)), _478535) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478529), c_Polynomial_Osmult(_478529, _478531, _478535), c_Polynomial_OpCons(_478529, c_Groups_Ozero__class_Ozero(_478529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_478529)), _478533), _478535))))], (8886 ^ _166148) ^ [_478843, _478845, _478847] : [class_Rings_Ocomm__ring__1(_478843), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_478843)), c_Polynomial_OpCons(_478843, c_Groups_Ouminus__class_Ouminus(_478843, _478845), c_Polynomial_OpCons(_478843, c_Groups_Oone__class_Oone(_478843), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_478843))))), c_Polynomial_Osynthetic__div(_478843, _478847, _478845)), c_Polynomial_OpCons(_478843, hAPP(c_Polynomial_Opoly(_478843, _478847), _478845), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_478843)))) = _478847)], (8892 ^ _166148) ^ [_479187, _479189, _479191, _479193] : [class_Rings_Ocomm__semiring__0(_479187), -(c_Polynomial_Opcompose(_479187, c_Polynomial_OpCons(_479187, _479189, _479191), _479193) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_479187), c_Polynomial_OpCons(_479187, _479189, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_479187))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_479187)), _479193), c_Polynomial_Opcompose(_479187, _479191, _479193))))], (8898 ^ _166148) ^ [_479479, _479481] : [class_Rings_Ocomm__semiring__0(_479479), -(c_Polynomial_Osynthetic__div(_479479, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_479479)), _479481) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_479479)))], (8904 ^ _166148) ^ [_479711, _479713] : [class_Rings_Ocomm__semiring__0(_479711), -(c_Polynomial_Opcompose(_479711, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_479711)), _479713) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_479711)))], (8910 ^ _166148) ^ [_479971, _479973, _479975, _479977] : [class_Rings_Ocomm__semiring__0(_479971), -(hAPP(c_Polynomial_Opoly(_479971, c_Polynomial_Opcompose(_479971, _479973, _479975)), _479977) = hAPP(c_Polynomial_Opoly(_479971, _479973), hAPP(c_Polynomial_Opoly(_479971, _479975), _479977)))], (8916 ^ _166148) ^ [_480263, _480265, _480267, _480269] : [class_Rings_Ocomm__semiring__0(_480263), -(c_Polynomial_Osynthetic__div(_480263, c_Polynomial_OpCons(_480263, _480265, _480267), _480269) = c_Polynomial_OpCons(_480263, hAPP(c_Polynomial_Opoly(_480263, _480267), _480269), c_Polynomial_Osynthetic__div(_480263, _480267, _480269)))], (8922 ^ _166148) ^ [_480569, _480571, _480573, _480575, _480577] : [class_Rings_Ocomm__semiring__0(_480569), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_480569), _480571, c_Polynomial_Osmult(_480569, _480573, _480575)) = c_Polynomial_OpCons(_480569, _480577, _480575), 8929 ^ _166148 : [(8930 ^ _166148) ^ [] : [-(_480577 = hAPP(c_Polynomial_Opoly(_480569, _480571), _480573))], (8932 ^ _166148) ^ [] : [-(_480575 = c_Polynomial_Osynthetic__div(_480569, _480571, _480573))]]], (8934 ^ _166148) ^ [_481039, _481041, _481043] : [class_Rings_Ocomm__semiring__0(_481039), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_481039), _481041, c_Polynomial_Osmult(_481039, _481043, c_Polynomial_Osynthetic__div(_481039, _481041, _481043))) = c_Polynomial_OpCons(_481039, hAPP(c_Polynomial_Opoly(_481039, _481041), _481043), c_Polynomial_Osynthetic__div(_481039, _481041, _481043)))], (8940 ^ _166148) ^ [_481295] : [8948 ^ _166148 : [(8949 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8947 ^ [_481295]))], (8951 ^ _166148) ^ [_481655] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_481295, c_RealVector_Oof__real(_481295, _481655)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _481655)), 8947 ^ [_481295])))]], class_RealVector_Oreal__algebra__1(_481295), class_RealVector_Oreal__normed__vector(_481295)], (8953 ^ _166148) ^ [_481806, _481808, _481810] : [class_Rings_Oidom(_481806), 8956 ^ _166148 : [(8967 ^ _166148) ^ [] : [8968 ^ _166148 : [(8969 ^ _166148) ^ [] : [_481808 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481806))], (8971 ^ _166148) ^ [] : [-(c_Polynomial_Oorder(_481806, _481810, _481808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_481806, _481808), _481810) = c_Groups_Ozero__class_Ozero(_481806))], (8957 ^ _166148) ^ [] : [hAPP(c_Polynomial_Opoly(_481806, _481808), _481810) = c_Groups_Ozero__class_Ozero(_481806), -(_481808 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481806))), c_Polynomial_Oorder(_481806, _481810, _481808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (8975 ^ _166148) ^ [_482494, _482496] : [class_Orderings_Opreorder(_482494), -(c_Orderings_Oord__class_Oless__eq(_482494, _482496, _482496))], (8983 ^ _166148) ^ [] : [8981 ^ [] = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (8985 ^ _166148) ^ [] : [8980 ^ [] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8988 ^ _166148) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 8986 ^ []), 8980 ^ []), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (8990 ^ _166148) ^ [_483138] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _483138) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), _483138), 8980 ^ [])), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, 8981 ^ [], 8986 ^ [])), _483138))))], (8992 ^ _166148) ^ [_483301, _483303, _483305, _483307] : [class_Orderings_Oord(_483301), 8995 ^ _166148 : [(8996 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_483303, _483301), _483305, _483307), 8999 ^ _166148 : [(9000 ^ _166148) ^ [_483560] : [-(c_Orderings_Oord__class_Oless__eq(_483301, hAPP(_483305, _483560), hAPP(_483307, _483560)))]]], (9002 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_483301, hAPP(_483305, 9003 ^ [_483301, _483303, _483305, _483307]), hAPP(_483307, 9003 ^ [_483301, _483303, _483305, _483307])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_483303, _483301), _483305, _483307))]]], (9009 ^ _166148) ^ [_483942, _483944, _483946] : [class_Orderings_Olinorder(_483942), -(c_Orderings_Oord__class_Oless__eq(_483942, _483944, _483946)), -(c_Orderings_Oord__class_Oless__eq(_483942, _483946, _483944))], (9019 ^ _166148) ^ [_484268, _484270, _484272] : [class_Orderings_Oorder(_484268), 9022 ^ _166148 : [(9023 ^ _166148) ^ [] : [_484270 = _484272, 9026 ^ _166148 : [(9027 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_484268, _484270, _484272))], (9029 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_484268, _484272, _484270))]]], (9031 ^ _166148) ^ [] : [-(_484270 = _484272), c_Orderings_Oord__class_Oless__eq(_484268, _484270, _484272), c_Orderings_Oord__class_Oless__eq(_484268, _484272, _484270)]]], (9041 ^ _166148) ^ [_484926, _484928, _484930] : [class_Orderings_Opreorder(_484926), _484928 = _484930, -(c_Orderings_Oord__class_Oless__eq(_484926, _484928, _484930))], (9051 ^ _166148) ^ [_485277, _485279, _485281, _485283, _485285] : [class_Orderings_Oord(_485277), c_Orderings_Oord__class_Oless__eq(tc_fun(_485279, _485277), _485281, _485283), -(c_Orderings_Oord__class_Oless__eq(_485277, hAPP(_485281, _485285), hAPP(_485283, _485285)))], (9061 ^ _166148) ^ [_485640, _485642, _485644] : [class_Orderings_Oorder(_485640), c_Orderings_Oord__class_Oless__eq(_485640, _485642, _485644), 9068 ^ _166148 : [(9069 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_485640, _485644, _485642), -(_485644 = _485642)], (9075 ^ _166148) ^ [] : [_485644 = _485642, -(c_Orderings_Oord__class_Oless__eq(_485640, _485644, _485642))]]], (9081 ^ _166148) ^ [_486240, _486242, _486244, _486246] : [class_Orderings_Oord(_486240), _486242 = _486244, c_Orderings_Oord__class_Oless__eq(_486240, _486244, _486246), -(c_Orderings_Oord__class_Oless__eq(_486240, _486242, _486246))], (9095 ^ _166148) ^ [_486686, _486688, _486690, _486692] : [class_Orderings_Oorder(_486686), _486688 = _486690, c_Orderings_Oord__class_Oless__eq(_486686, _486692, _486690), -(c_Orderings_Oord__class_Oless__eq(_486686, _486692, _486688))], (9109 ^ _166148) ^ [_487132, _487134, _487136, _487138] : [class_Orderings_Oord(_487132), c_Orderings_Oord__class_Oless__eq(_487132, _487134, _487136), _487136 = _487138, -(c_Orderings_Oord__class_Oless__eq(_487132, _487134, _487138))], (9123 ^ _166148) ^ [_487578, _487580, _487582, _487584] : [class_Orderings_Oorder(_487578), c_Orderings_Oord__class_Oless__eq(_487578, _487580, _487582), _487580 = _487584, -(c_Orderings_Oord__class_Oless__eq(_487578, _487584, _487582))], (9137 ^ _166148) ^ [_488010, _488012, _488014] : [class_Orderings_Oorder(_488010), c_Orderings_Oord__class_Oless__eq(_488010, _488012, _488014), c_Orderings_Oord__class_Oless__eq(_488010, _488014, _488012), -(_488012 = _488014)], (9151 ^ _166148) ^ [_488442, _488444, _488446, _488448] : [class_Orderings_Opreorder(_488442), c_Orderings_Oord__class_Oless__eq(_488442, _488444, _488446), c_Orderings_Oord__class_Oless__eq(_488442, _488446, _488448), -(c_Orderings_Oord__class_Oless__eq(_488442, _488444, _488448))], (9165 ^ _166148) ^ [_488876, _488878, _488880] : [class_Orderings_Oorder(_488876), c_Orderings_Oord__class_Oless__eq(_488876, _488878, _488880), c_Orderings_Oord__class_Oless__eq(_488876, _488880, _488878), -(_488880 = _488878)], (9179 ^ _166148) ^ [_489308, _489310, _489312, _489314] : [class_Orderings_Oorder(_489308), c_Orderings_Oord__class_Oless__eq(_489308, _489310, _489312), c_Orderings_Oord__class_Oless__eq(_489308, _489314, _489310), -(c_Orderings_Oord__class_Oless__eq(_489308, _489314, _489312))], (9193 ^ _166148) ^ [_489770, _489772, _489774, _489776, _489778] : [class_Orderings_Oord(_489770), c_Orderings_Oord__class_Oless__eq(tc_fun(_489772, _489770), _489774, _489776), -(c_Orderings_Oord__class_Oless__eq(_489770, hAPP(_489774, _489778), hAPP(_489776, _489778)))], (9203 ^ _166148) ^ [_490133, _490135, _490137] : [class_Orderings_Olinorder(_490133), -(c_Orderings_Oord__class_Oless__eq(_490133, _490135, _490137)), -(c_Orderings_Oord__class_Oless__eq(_490133, _490137, _490135))], (9213 ^ _166148) ^ [_490461, _490463, _490465] : [class_Orderings_Olinorder(_490461), -(c_Orderings_Oord__class_Oless(_490461, _490463, _490465)), -(_490463 = _490465), -(c_Orderings_Oord__class_Oless(_490461, _490465, _490463))], (9227 ^ _166148) ^ [_490885, _490887, _490889] : [class_Orderings_Opreorder(_490885), c_Orderings_Oord__class_Oless(_490885, _490887, _490889), c_Orderings_Oord__class_Oless(_490885, _490889, _490887)], (9237 ^ _166148) ^ [_491225, _491227, _491229, _491231] : [class_Orderings_Oorder(_491225), c_Orderings_Oord__class_Oless(_491225, _491227, _491229), c_Orderings_Oord__class_Oless(_491225, _491231, _491227), -(c_Orderings_Oord__class_Oless(_491225, _491231, _491229))], (9251 ^ _166148) ^ [_491673, _491675, _491677, _491679] : [class_Orderings_Opreorder(_491673), c_Orderings_Oord__class_Oless(_491673, _491675, _491677), c_Orderings_Oord__class_Oless(_491673, _491677, _491679), -(c_Orderings_Oord__class_Oless(_491673, _491675, _491679))], (9265 ^ _166148) ^ [_492121, _492123, _492125, _492127] : [class_Orderings_Oorder(_492121), c_Orderings_Oord__class_Oless(_492121, _492123, _492125), _492123 = _492127, -(c_Orderings_Oord__class_Oless(_492121, _492127, _492125))], (9279 ^ _166148) ^ [_492567, _492569, _492571, _492573] : [class_Orderings_Oord(_492567), c_Orderings_Oord__class_Oless(_492567, _492569, _492571), _492571 = _492573, -(c_Orderings_Oord__class_Oless(_492567, _492569, _492573))], (9293 ^ _166148) ^ [_493013, _493015, _493017, _493019] : [class_Orderings_Oorder(_493013), _493015 = _493017, c_Orderings_Oord__class_Oless(_493013, _493019, _493017), -(c_Orderings_Oord__class_Oless(_493013, _493019, _493015))], (9307 ^ _166148) ^ [_493459, _493461, _493463, _493465] : [class_Orderings_Oord(_493459), _493461 = _493463, c_Orderings_Oord__class_Oless(_493459, _493463, _493465), -(c_Orderings_Oord__class_Oless(_493459, _493461, _493465))], (9321 ^ _166148) ^ [_493891, _493893, _493895] : [class_Orderings_Oorder(_493891), c_Orderings_Oord__class_Oless(_493891, _493893, _493895), c_Orderings_Oord__class_Oless(_493891, _493895, _493893)], (9331 ^ _166148) ^ [_494217, _494219, _494221] : [class_Orderings_Opreorder(_494217), c_Orderings_Oord__class_Oless(_494217, _494219, _494221), c_Orderings_Oord__class_Oless(_494217, _494221, _494219)], (9341 ^ _166148) ^ [_494543, _494545, _494547] : [class_Orderings_Oorder(_494543), c_Orderings_Oord__class_Oless(_494543, _494545, _494547), _494547 = _494545], (9351 ^ _166148) ^ [_494867, _494869, _494871] : [class_Orderings_Oorder(_494867), c_Orderings_Oord__class_Oless(_494867, _494869, _494871), _494869 = _494871], (9361 ^ _166148) ^ [_495191, _495193, _495195] : [class_Orderings_Opreorder(_495191), c_Orderings_Oord__class_Oless(_495191, _495193, _495195), c_Orderings_Oord__class_Oless(_495191, _495195, _495193)], (9371 ^ _166148) ^ [_495517, _495519, _495521] : [class_Orderings_Opreorder(_495517), c_Orderings_Oord__class_Oless(_495517, _495519, _495521), c_Orderings_Oord__class_Oless(_495517, _495521, _495519)], (9381 ^ _166148) ^ [_495843, _495845, _495847] : [class_Orderings_Oorder(_495843), c_Orderings_Oord__class_Oless(_495843, _495845, _495847), _495845 = _495847], (9391 ^ _166148) ^ [_496167, _496169, _496171] : [class_Orderings_Olinorder(_496167), -(_496169 = _496171), -(c_Orderings_Oord__class_Oless(_496167, _496169, _496171)), -(c_Orderings_Oord__class_Oless(_496167, _496171, _496169))], (9405 ^ _166148) ^ [_496591, _496593, _496595] : [class_Orderings_Olinorder(_496591), -(c_Orderings_Oord__class_Oless(_496591, _496593, _496595)), 9412 ^ _166148 : [(9413 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_496591, _496595, _496593)), -(_496595 = _496593)], (9419 ^ _166148) ^ [] : [_496595 = _496593, c_Orderings_Oord__class_Oless(_496591, _496595, _496593)]]], (9425 ^ _166148) ^ [_497182, _497184, _497186] : [class_Orderings_Olinorder(_497182), -(c_Orderings_Oord__class_Oless(_497182, _497184, _497186)), -(_497184 = _497186), -(c_Orderings_Oord__class_Oless(_497182, _497186, _497184))], (9439 ^ _166148) ^ [_497602, _497604, _497606] : [class_Orderings_Olinorder(_497602), 9442 ^ _166148 : [(9453 ^ _166148) ^ [] : [9454 ^ _166148 : [(9455 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_497602, _497606, _497604)], (9457 ^ _166148) ^ [] : [_497604 = _497606]], c_Orderings_Oord__class_Oless(_497602, _497604, _497606)], (9443 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_497602, _497604, _497606)), -(c_Orderings_Oord__class_Oless(_497602, _497606, _497604)), -(_497604 = _497606)]]], (9461 ^ _166148) ^ [_498262, _498264, _498266] : [class_Orderings_Olinorder(_498262), 9464 ^ _166148 : [(9475 ^ _166148) ^ [] : [9476 ^ _166148 : [(9477 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_498262, _498264, _498266)], (9479 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_498262, _498266, _498264)]], _498264 = _498266], (9465 ^ _166148) ^ [] : [-(_498264 = _498266), -(c_Orderings_Oord__class_Oless(_498262, _498264, _498266)), -(c_Orderings_Oord__class_Oless(_498262, _498266, _498264))]]], (9483 ^ _166148) ^ [_498908, _498910] : [class_Orderings_Opreorder(_498908), c_Orderings_Oord__class_Oless(_498908, _498910, _498910)], (9489 ^ _166148) ^ [_499147, _499149, _499151, _499153] : [class_Orderings_Oorder(_499147), c_Orderings_Oord__class_Oless__eq(_499147, _499149, _499151), c_Orderings_Oord__class_Oless(_499147, _499153, _499149), -(c_Orderings_Oord__class_Oless(_499147, _499153, _499151))], (9503 ^ _166148) ^ [_499595, _499597, _499599, _499601] : [class_Orderings_Opreorder(_499595), c_Orderings_Oord__class_Oless__eq(_499595, _499597, _499599), c_Orderings_Oord__class_Oless(_499595, _499599, _499601), -(c_Orderings_Oord__class_Oless(_499595, _499597, _499601))], (9517 ^ _166148) ^ [_500043, _500045, _500047, _500049] : [class_Orderings_Oorder(_500043), c_Orderings_Oord__class_Oless(_500043, _500045, _500047), c_Orderings_Oord__class_Oless__eq(_500043, _500049, _500045), -(c_Orderings_Oord__class_Oless(_500043, _500049, _500047))], (9531 ^ _166148) ^ [_500491, _500493, _500495, _500497] : [class_Orderings_Opreorder(_500491), c_Orderings_Oord__class_Oless(_500491, _500493, _500495), c_Orderings_Oord__class_Oless__eq(_500491, _500495, _500497), -(c_Orderings_Oord__class_Oless(_500491, _500493, _500497))], (9545 ^ _166148) ^ [_500925, _500927, _500929] : [class_Orderings_Oorder(_500925), c_Orderings_Oord__class_Oless__eq(_500925, _500927, _500929), -(_500929 = _500927), -(c_Orderings_Oord__class_Oless(_500925, _500927, _500929))], (9559 ^ _166148) ^ [_501346, _501348, _501350] : [class_Orderings_Oorder(_501346), c_Orderings_Oord__class_Oless__eq(_501346, _501348, _501350), -(_501348 = _501350), -(c_Orderings_Oord__class_Oless(_501346, _501348, _501350))], (9573 ^ _166148) ^ [_501767, _501769, _501771] : [class_Orderings_Oorder(_501767), c_Orderings_Oord__class_Oless__eq(_501767, _501769, _501771), -(c_Orderings_Oord__class_Oless(_501767, _501769, _501771)), -(_501769 = _501771)], (9587 ^ _166148) ^ [_502186, _502188, _502190] : [class_Orderings_Olinorder(_502186), c_Orderings_Oord__class_Oless__eq(_502186, _502188, _502190), 9594 ^ _166148 : [(9595 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_502186, _502188, _502190)), -(_502188 = _502190)], (9601 ^ _166148) ^ [] : [_502188 = _502190, c_Orderings_Oord__class_Oless(_502186, _502188, _502190)]]], (9607 ^ _166148) ^ [_502774, _502776, _502778] : [class_Orderings_Opreorder(_502774), c_Orderings_Oord__class_Oless(_502774, _502776, _502778), -(c_Orderings_Oord__class_Oless__eq(_502774, _502776, _502778))], (9617 ^ _166148) ^ [_503099, _503101, _503103] : [class_Orderings_Olinorder(_503099), c_Orderings_Oord__class_Oless__eq(_503099, _503101, _503103), c_Orderings_Oord__class_Oless(_503099, _503103, _503101)], (9627 ^ _166148) ^ [_503425, _503427, _503429] : [class_Orderings_Oorder(_503425), -(_503427 = _503429), c_Orderings_Oord__class_Oless__eq(_503425, _503429, _503427), -(c_Orderings_Oord__class_Oless(_503425, _503429, _503427))], (9641 ^ _166148) ^ [_503846, _503848, _503850] : [class_Orderings_Oorder(_503846), -(_503848 = _503850), c_Orderings_Oord__class_Oless__eq(_503846, _503848, _503850), -(c_Orderings_Oord__class_Oless(_503846, _503848, _503850))], (9655 ^ _166148) ^ [_504267, _504269, _504271] : [class_Orderings_Olinorder(_504267), -(c_Orderings_Oord__class_Oless(_504267, _504269, _504271)), 9662 ^ _166148 : [(9663 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_504267, _504269, _504271), -(_504269 = _504271)], (9669 ^ _166148) ^ [] : [_504269 = _504271, -(c_Orderings_Oord__class_Oless__eq(_504267, _504269, _504271))]]], (9675 ^ _166148) ^ [_504856, _504858, _504860] : [class_Orderings_Olinorder(_504856), -(c_Orderings_Oord__class_Oless__eq(_504856, _504858, _504860)), -(c_Orderings_Oord__class_Oless(_504856, _504860, _504858))], (9685 ^ _166148) ^ [_505184, _505186, _505188] : [class_Orderings_Olinorder(_505184), -(c_Orderings_Oord__class_Oless(_505184, _505186, _505188)), -(c_Orderings_Oord__class_Oless__eq(_505184, _505188, _505186))], (9695 ^ _166148) ^ [_505512, _505514, _505516] : [class_Orderings_Oorder(_505512), 9698 ^ _166148 : [(9709 ^ _166148) ^ [] : [9710 ^ _166148 : [(9711 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_505512, _505514, _505516)], (9713 ^ _166148) ^ [] : [_505514 = _505516]], -(c_Orderings_Oord__class_Oless__eq(_505512, _505514, _505516))], (9699 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_505512, _505514, _505516), -(c_Orderings_Oord__class_Oless(_505512, _505514, _505516)), -(_505514 = _505516)]]], (9717 ^ _166148) ^ [_506170, _506172, _506174] : [class_Orderings_Opreorder(_506170), 9720 ^ _166148 : [(9721 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_506170, _506172, _506174), 9724 ^ _166148 : [(9725 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_506170, _506172, _506174))], (9727 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_506170, _506174, _506172)]]], (9729 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_506170, _506172, _506174)), c_Orderings_Oord__class_Oless__eq(_506170, _506172, _506174), -(c_Orderings_Oord__class_Oless__eq(_506170, _506174, _506172))]]], (9739 ^ _166148) ^ [_506833, _506835, _506837] : [class_Orderings_Oorder(_506833), 9742 ^ _166148 : [(9743 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_506833, _506835, _506837), 9746 ^ _166148 : [(9747 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_506833, _506835, _506837))], (9749 ^ _166148) ^ [] : [_506835 = _506837]]], (9751 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_506833, _506835, _506837)), c_Orderings_Oord__class_Oless__eq(_506833, _506835, _506837), -(_506835 = _506837)]]], (9761 ^ _166148) ^ [_507493, _507495, _507497] : [class_Orderings_Olinorder(_507493), -(c_Orderings_Oord__class_Oless__eq(_507493, _507495, _507497)), -(c_Orderings_Oord__class_Oless(_507493, _507497, _507495))], (9771 ^ _166148) ^ [_507819, _507821, _507823] : [class_Orderings_Olinorder(_507819), 9774 ^ _166148 : [(9775 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_507819, _507821, _507823)), -(c_Orderings_Oord__class_Oless(_507819, _507823, _507821))], (9781 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_507819, _507823, _507821), c_Orderings_Oord__class_Oless__eq(_507819, _507821, _507823)]]], (9787 ^ _166148) ^ [_508315, _508317, _508319] : [class_Orderings_Olinorder(_508315), 9790 ^ _166148 : [(9791 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_508315, _508317, _508319)), -(c_Orderings_Oord__class_Oless__eq(_508315, _508319, _508317))], (9797 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_508315, _508319, _508317), c_Orderings_Oord__class_Oless(_508315, _508317, _508319)]]], (9803 ^ _166148) ^ [_508783] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _508783), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _508783, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_508783), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9809 ^ _166148) ^ [_508999] : [class_Power_Opower(_508999), -(c_Power_Opower__class_Opower(_508999) = c_Power_Opower_Opower(_508999, c_Groups_Oone__class_Oone(_508999), c_Groups_Otimes__class_Otimes(_508999)))], (9815 ^ _166148) ^ [_509249, _509251, _509253, _509255] : [class_Orderings_Oord(_509249), 9818 ^ _166148 : [(9819 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_509251, _509249), _509253, _509255), 9822 ^ _166148 : [(9823 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_509251, _509249), _509253, _509255))], (9825 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_509251, _509249), _509255, _509253)]]], (9827 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_509251, _509249), _509253, _509255)), c_Orderings_Oord__class_Oless__eq(tc_fun(_509251, _509249), _509253, _509255), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_509251, _509249), _509255, _509253))]]], (9837 ^ _166148) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9839 ^ _166148) ^ [_509971] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_509971)))], (9841 ^ _166148) ^ [_510081, _510083] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _510081, _510083), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_510081), c_RComplete_Onatceiling(_510083)))], (9847 ^ _166148) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9849 ^ _166148) ^ [_510369, _510371, _510373, _510375] : [-(hAPP(hAPP(c_Power_Opower_Opower(_510369, _510371, _510373), _510375), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _510371)], (9851 ^ _166148) ^ [_510478] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _510478, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_510478) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9857 ^ _166148) ^ [_510703] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_510703), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _510703, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9863 ^ _166148) ^ [_510867] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _510867, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_510867), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9869 ^ _166148) ^ [_511067] : [9877 ^ _166148 : [(9878 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9876 ^ [_511067]))], (9880 ^ _166148) ^ [_511427] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_511067, c_RealVector_Oof__real(_511067, _511427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _511427)), 9876 ^ [_511067])))]], class_RealVector_Oreal__algebra__1(_511067), class_RealVector_Oreal__normed__vector(_511067)], (9882 ^ _166148) ^ [_511592, _511594, _511596, _511598] : [class_RealVector_Oreal__normed__vector(_511592), class_Orderings_Oord(_511594), 9892 ^ _166148 : [(9893 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_511594, _511596, 9891 ^ [_511592, _511594, _511596, _511598]))], (9895 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_511592, c_Groups_Ominus__class_Ominus(_511592, hAPP(_511598, _511596), hAPP(_511598, 9891 ^ [_511592, _511594, _511596, _511598]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]], 9896 ^ _166148 : [(9897 ^ _166148) ^ [_512150] : [c_Orderings_Oord__class_Oless__eq(_511594, _511596, _512150), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_511592, hAPP(_511598, _512150)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_511592, hAPP(_511598, _511596)))))]]], (9903 ^ _166148) ^ [_512434, _512436] : [class_RealVector_Oreal__normed__algebra(_512434), 9907 ^ _166148 : [(9908 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9906 ^ [_512434, _512436]))], (9910 ^ _166148) ^ [_512733] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_512434, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512434), _512733), _512436)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_512434, _512733)), 9906 ^ [_512434, _512436])))]]], (9912 ^ _166148) ^ [_512879, _512881] : [class_RealVector_Oreal__normed__algebra(_512879), 9916 ^ _166148 : [(9917 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9915 ^ [_512879, _512881]))], (9919 ^ _166148) ^ [_513178] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_512879, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512879), _512881), _513178)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_512879, _513178)), 9915 ^ [_512879, _512881])))]]], (9921 ^ _166148) ^ [_513310] : [class_RealVector_Oreal__normed__algebra(_513310), 9925 ^ _166148 : [(9926 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9924 ^ [_513310]))], (9928 ^ _166148) ^ [_513639, _513641] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_513310, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513310), _513641), _513639)), 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(_513310, _513641)), c_RealVector_Onorm__class_Onorm(_513310, _513639))), 9924 ^ [_513310])))]]], (9931 ^ _166148) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 9929 ^ []) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (9933 ^ _166148) ^ [_513882] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 9929 ^ []), _513882) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _513882)))], (9935 ^ _166148) ^ [_513987] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _513987), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _513987, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_513987), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9941 ^ _166148) ^ [_514237, _514239] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _514237, _514239), -(c_Nat__Transfer_Otsub(_514239, _514237) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _514239, _514237))], (9947 ^ _166148) ^ [_514415, _514417] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _514415, _514417)), -(c_Nat__Transfer_Otsub(_514417, _514415) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9953 ^ _166148) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9955 ^ _166148) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9957 ^ _166148) ^ [_514744, _514746] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _514744, _514746), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_514744), c_RComplete_Onatfloor(_514746)))], (9963 ^ _166148) ^ [_514937] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_514937)))], (9965 ^ _166148) ^ [_515033] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _515033, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_515033) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9971 ^ _166148) ^ [_515243, _515245] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515243), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515245), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_515243, _515245)))], (9981 ^ _166148) ^ [_515569] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_515569)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _515569))], (9987 ^ _166148) ^ [_515733] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _515733), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_515733)))], (9993 ^ _166148) ^ [_515947, _515949] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _515947, _515949), -(c_Nat__Transfer_Otsub(_515949, _515947) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _515949, _515947))], (9999 ^ _166148) ^ [_516173, _516175] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _516173), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _516175), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_516173)), c_RComplete_Onatfloor(_516175)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _516173), _516175))))], (10009 ^ _166148) ^ [_516528, _516530, _516532] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _516528, _516530), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _516528, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _516530, _516532)))], (10015 ^ _166148) ^ [_516770, _516772, _516774] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _516770, _516772), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _516770, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _516774, _516772)))], (10021 ^ _166148) ^ [_517012, _517014, _517016] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _517012, _517014), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _517012, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _517016, _517014)))], (10027 ^ _166148) ^ [_517254, _517256, _517258] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _517254, _517256), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _517254, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _517256, _517258)))], (10033 ^ _166148) ^ [_517482, _517484] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _517482, _517484), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _517482, _517484))], (10039 ^ _166148) ^ [_517696, _517698] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _517696), _517698), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _517698, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _517696), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_517698) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _517696, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10049 ^ _166148) ^ [_518045, _518047, _518049] : [class_Rings_Olinordered__idom(_518045), 10052 ^ _166148 : [(10053 ^ _166148) ^ [] : [c_Polynomial_Opos__poly(_518045, c_Polynomial_OpCons(_518045, _518047, _518049)), -(c_Polynomial_Opos__poly(_518045, _518049)), 10060 ^ _166148 : [(10061 ^ _166148) ^ [] : [-(_518049 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_518045)))], (10063 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_518045, c_Groups_Ozero__class_Ozero(_518045), _518047))]]], (10065 ^ _166148) ^ [] : [-(c_Polynomial_Opos__poly(_518045, c_Polynomial_OpCons(_518045, _518047, _518049))), 10066 ^ _166148 : [(10067 ^ _166148) ^ [] : [c_Polynomial_Opos__poly(_518045, _518049)], (10069 ^ _166148) ^ [] : [_518049 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_518045)), c_Orderings_Oord__class_Oless(_518045, c_Groups_Ozero__class_Ozero(_518045), _518047)]]]]], (10077 ^ _166148) ^ [_518851] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _518851)))], (10079 ^ _166148) ^ [_518962, _518964] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _518962, _518964), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _518964, _518962)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _518964), c_RealDef_Oreal(tc_Nat_Onat, _518962)))], (10085 ^ _166148) ^ [_519237, _519239] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _519237), c_RealDef_Oreal(tc_Nat_Onat, _519239)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _519237, _519239))], (10091 ^ _166148) ^ [_519415, _519417] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _519415, _519417), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _519415), c_RealDef_Oreal(tc_Nat_Onat, _519417)))], (10097 ^ _166148) ^ [_519613] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _519613), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10099 ^ _166148) ^ [_519695] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _519695)) = c_RealDef_Oreal(tc_Nat_Onat, _519695))], (10101 ^ _166148) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10103 ^ _166148) ^ [_519849, _519851] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _519849)), _519851) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _519849), _519851)))], (10105 ^ _166148) ^ [_519961, _519963] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _519961), _519963)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _519961)), _519963))], (10107 ^ _166148) ^ [_520073, _520075] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _520073, _520075)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _520073), c_RealDef_Oreal(tc_Nat_Onat, _520075)))], (10109 ^ _166148) ^ [_520228, _520230] : [c_RealDef_Oreal(tc_Nat_Onat, _520228) = c_RealDef_Oreal(tc_Nat_Onat, _520230), -(_520228 = _520230)], (10115 ^ _166148) ^ [_520402, _520404] : [_520402 = _520404, -(c_RealDef_Oreal(tc_Nat_Onat, _520402) = c_RealDef_Oreal(tc_Nat_Onat, _520404))], (10121 ^ _166148) ^ [_520641] : [c_RealDef_Oreal(tc_Nat_Onat, _520641) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_520641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10127 ^ _166148) ^ [_520803] : [_520803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _520803) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10133 ^ _166148) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10135 ^ _166148) ^ [_521054] : [class_Rings_Olinordered__idom(_521054), c_Polynomial_Opos__poly(_521054, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_521054)))], (10141 ^ _166148) ^ [_521250, _521252] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _521250), _521252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _521250)), c_RealDef_Oreal(tc_Nat_Onat, _521252)))], (10143 ^ _166148) ^ [_521394, _521396, _521398] : [class_Rings_Olinordered__idom(_521394), c_Polynomial_Opos__poly(_521394, _521396), c_Polynomial_Opos__poly(_521394, _521398), -(c_Polynomial_Opos__poly(_521394, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_521394)), _521396), _521398)))], (10157 ^ _166148) ^ [_521828, _521830, _521832] : [class_Rings_Olinordered__idom(_521828), c_Polynomial_Opos__poly(_521828, _521830), c_Polynomial_Opos__poly(_521828, _521832), -(c_Polynomial_Opos__poly(_521828, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_521828), _521830, _521832)))], (10171 ^ _166148) ^ [_522255] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _522255), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_522255 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10177 ^ _166148) ^ [_522419] : [_522419 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _522419), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10183 ^ _166148) ^ [_522604] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _522604, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_522604))))], (10185 ^ _166148) ^ [_522746, _522748] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _522746), c_RealDef_Oreal(tc_Nat_Onat, _522748)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _522746, _522748))], (10191 ^ _166148) ^ [_522924, _522926] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _522924, _522926), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _522924), c_RealDef_Oreal(tc_Nat_Onat, _522926)))], (10197 ^ _166148) ^ [_523123] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _523123)) = _523123)], (10199 ^ _166148) ^ [_523249, _523251, _523253] : [class_Rings_Olinordered__idom(_523249), 10202 ^ _166148 : [(10213 ^ _166148) ^ [] : [10214 ^ _166148 : [(10215 ^ _166148) ^ [] : [_523251 = _523253], (10217 ^ _166148) ^ [] : [c_Polynomial_Opos__poly(_523249, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_523249), _523253, _523251))]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_523249), _523251, _523253))], (10203 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_523249), _523251, _523253), -(_523251 = _523253), -(c_Polynomial_Opos__poly(_523249, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_523249), _523253, _523251)))]]], (10221 ^ _166148) ^ [_523885] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _523885)) = _523885)], (10223 ^ _166148) ^ [_523983] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _523983), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_523983)), _523983))], (10229 ^ _166148) ^ [_524201, _524203] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _524201), _524203), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _524201, c_RComplete_Onatfloor(_524203)))], (10235 ^ _166148) ^ [_524425, _524427] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _524425, c_RealDef_Oreal(tc_Nat_Onat, _524427)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_524425), _524427))], (10241 ^ _166148) ^ [_524649, _524651] : [_524649 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_524649)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _524649), _524651)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_524649)), _524651))], (10247 ^ _166148) ^ [_524916] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _524916)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _524916))], (10253 ^ _166148) ^ [_525082] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _525082), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _525082)))], (10259 ^ _166148) ^ [_525327, _525329] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _525327, _525329), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525327), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _525329)))], (10265 ^ _166148) ^ [_525513, _525515] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525513), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _525515)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _525513, _525515))], (10271 ^ _166148) ^ [_525778, _525780] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525778, _525780), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525778), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525780), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10277 ^ _166148) ^ [_525964, _525966] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525964), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525966), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525964, _525966))], (10283 ^ _166148) ^ [_526200, _526202] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _526200), 10286 ^ _166148 : [(10287 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _526202, c_RComplete_Onatfloor(_526200)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _526202), _526200))], (10293 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _526202), _526200), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _526202, c_RComplete_Onatfloor(_526200)))]]], (10299 ^ _166148) ^ [_526683, _526685] : [class_Rings_Olinordered__idom(_526683), -(_526685 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_526683))), -(c_Polynomial_Opos__poly(_526683, _526685)), -(c_Polynomial_Opos__poly(_526683, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_526683), _526685)))], (10313 ^ _166148) ^ [_527089, _527091] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _527089), 10316 ^ _166148 : [(10317 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_527089), _527091), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _527089, c_RealDef_Oreal(tc_Nat_Onat, _527091)))], (10323 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _527089, c_RealDef_Oreal(tc_Nat_Onat, _527091)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_527089), _527091))]]], (10329 ^ _166148) ^ [_527543] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _527543, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_527543)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10331 ^ _166148) ^ [_527660, _527662] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527660), _527662), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _527662, c_RealDef_Oreal(tc_Nat_Onat, _527660))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_527662), _527660))], (10337 ^ _166148) ^ [_527879] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _527879, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_527879))))], (10339 ^ _166148) ^ [_527996, _527998] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527996), _527998), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _527998, c_RealDef_Oreal(tc_Nat_Onat, _527996))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_527998), _527996))], (10345 ^ _166148) ^ [_528244, _528246] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _528244), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _528244, c_RealDef_Oreal(tc_Nat_Onat, _528246)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_528244), _528246))], (10355 ^ _166148) ^ [_528559, _528561] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _528559), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _528559, c_RealDef_Oreal(tc_Nat_Onat, _528561))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_528559), _528561))], (10361 ^ _166148) ^ [_528801, _528803] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_528801), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _528803), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _528801, c_RealDef_Oreal(tc_Nat_Onat, _528803)))], (10367 ^ _166148) ^ [_529033, _529035] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _529033), _529035), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _529035, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _529033), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_529035) = _529033)], (10377 ^ _166148) ^ [_529360, _529362] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _529360), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _529360, c_RealDef_Oreal(tc_Nat_Onat, _529362))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_529360), _529362))], (10383 ^ _166148) ^ [_529616, _529618, _529620] : [class_Rings_Olinordered__idom(_529616), 10386 ^ _166148 : [(10387 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_529616), _529618, _529620), -(c_Polynomial_Opos__poly(_529616, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_529616), _529620, _529618)))], (10393 ^ _166148) ^ [] : [c_Polynomial_Opos__poly(_529616, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_529616), _529620, _529618)), -(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_529616), _529618, _529620))]]], (10399 ^ _166148) ^ [_530117, _530119] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _530117), -(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, _530119)), _530117), 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, _530117, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _530119)))], (10405 ^ _166148) ^ [_530363] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _530363), 10409 ^ _166148 : [(10410 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 10408 ^ [_530363], c_Groups_Oone__class_Oone(tc_Nat_Onat))), _530363))], (10412 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _530363, c_RealDef_Oreal(tc_Nat_Onat, 10408 ^ [_530363])))]]], (10414 ^ _166148) ^ [_530754, _530756, _530758] : [class_Groups_Oab__group__add(_530754), -(c_Groups_Ominus__class_Ominus(_530754, c_Groups_Ouminus__class_Ouminus(_530754, _530756), c_Groups_Ouminus__class_Ouminus(_530754, _530758)) = c_Groups_Ouminus__class_Ouminus(_530754, c_Groups_Ominus__class_Ominus(_530754, _530756, _530758)))], (10420 ^ _166148) ^ [_531016, _531018, _531020] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _531016), 10424 ^ _166148 : [(10425 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10423 ^ [_531016, _531018, _531020]))], (10427 ^ _166148) ^ [_531400] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _531020), _531400), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _531020), _531018))), _531016)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _531400, _531018))), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _531400, _531018)), 10423 ^ [_531016, _531018, _531020])]]], (10437 ^ _166148) ^ [_531822, _531824] : [class_Orderings_Oorder(_531822), 10440 ^ _166148 : [(10451 ^ _166148) ^ [] : [10454 ^ _166148 : [(10455 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 10452 ^ [_531822, _531824], 10453 ^ [_531822, _531824]))], (10457 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_531822, hAPP(_531824, 10453 ^ [_531822, _531824]), hAPP(_531824, 10452 ^ [_531822, _531824]))]], -(c_SEQ_Odecseq(_531822, _531824))], (10441 ^ _166148) ^ [] : [c_SEQ_Odecseq(_531822, _531824), 10444 ^ _166148 : [(10445 ^ _166148) ^ [_532098, _532100] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _532100, _532098), -(c_Orderings_Oord__class_Oless__eq(_531822, hAPP(_531824, _532098), hAPP(_531824, _532100)))]]]]], (10461 ^ _166148) ^ [_532737, _532739, _532741] : [class_Lattices_Oboolean__algebra(_532737), 10464 ^ _166148 : [(10465 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_532737, c_Groups_Ouminus__class_Ouminus(_532737, _532739), c_Groups_Ouminus__class_Ouminus(_532737, _532741)), -(c_Orderings_Oord__class_Oless__eq(_532737, _532741, _532739))], (10471 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless__eq(_532737, _532741, _532739), -(c_Orderings_Oord__class_Oless__eq(_532737, c_Groups_Ouminus__class_Ouminus(_532737, _532739), c_Groups_Ouminus__class_Ouminus(_532737, _532741)))]]], (10477 ^ _166148) ^ [_533249, _533251, _533253] : [class_Lattices_Oboolean__algebra(_533249), c_Orderings_Oord__class_Oless__eq(_533249, _533251, _533253), -(c_Orderings_Oord__class_Oless__eq(_533249, c_Groups_Ouminus__class_Ouminus(_533249, _533253), c_Groups_Ouminus__class_Ouminus(_533249, _533251)))], (10487 ^ _166148) ^ [_533614, _533616, _533618, _533620, _533622] : [class_Groups_Ominus(_533614), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_533616, _533614), _533618, _533620), _533622) = c_Groups_Ominus__class_Ominus(_533614, hAPP(_533618, _533622), hAPP(_533620, _533622)))], (10493 ^ _166148) ^ [_533880, _533882] : [class_Lattices_Oab__semigroup__idem__mult(_533880), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533880), _533882), _533882) = _533882)], (10499 ^ _166148) ^ [_534104, _534106] : [class_Lattices_Oab__semigroup__idem__mult(_534104), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534104), _534106), _534106) = _534106)], (10505 ^ _166148) ^ [_534342, _534344, _534346] : [class_Lattices_Oab__semigroup__idem__mult(_534342), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534342), _534344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534342), _534344), _534346)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534342), _534344), _534346))], (10511 ^ _166148) ^ [_534604, _534606] : [class_Lattices_Oboolean__algebra(_534604), -(c_Groups_Ouminus__class_Ouminus(_534604, c_Groups_Ouminus__class_Ouminus(_534604, _534606)) = _534606)], (10517 ^ _166148) ^ [_534852, _534854, _534856, _534858] : [class_Groups_Ouminus(_534852), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_534854, _534852), _534856), _534858) = c_Groups_Ouminus__class_Ouminus(_534852, hAPP(_534856, _534858)))], (10523 ^ _166148) ^ [_535116, _535118, _535120] : [class_Lattices_Oboolean__algebra(_535116), 10526 ^ _166148 : [(10527 ^ _166148) ^ [] : [c_Groups_Ouminus__class_Ouminus(_535116, _535118) = c_Groups_Ouminus__class_Ouminus(_535116, _535120), -(_535118 = _535120)], (10533 ^ _166148) ^ [] : [_535118 = _535120, -(c_Groups_Ouminus__class_Ouminus(_535116, _535118) = c_Groups_Ouminus__class_Ouminus(_535116, _535120))]]], (10539 ^ _166148) ^ [_535594] : [10547 ^ _166148 : [(10548 ^ _166148) ^ [_535870] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_535594, c_RealVector_Oof__real(_535594, _535870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _535870)), 10546 ^ [_535594])))]], class_RealVector_Oreal__algebra__1(_535594), class_RealVector_Oreal__normed__vector(_535594)], (10550 ^ _166148) ^ [_536005, _536007] : [class_Rings_Olinordered__idom(_536005), 10553 ^ _166148 : [(10554 ^ _166148) ^ [] : [_536007 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_536005)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_536005), _536007) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_536005)))], (10560 ^ _166148) ^ [] : [-(_536007 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_536005))), 10563 ^ _166148 : [(10564 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_536005), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_536005)), _536007), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_536005), _536007) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_536005)))], (10570 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_536005), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_536005)), _536007)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_536005), _536007) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_536005), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_536005))))]]]]], (10576 ^ _166148) ^ [_536833, _536835] : [class_Rings_Olinordered__idom(_536833), 10579 ^ _166148 : [(10580 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_536833, c_Groups_Osgn__class_Osgn(_536833, _536835), c_Groups_Ozero__class_Ozero(_536833)), -(c_Orderings_Oord__class_Oless(_536833, _536835, c_Groups_Ozero__class_Ozero(_536833)))], (10586 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_536833, _536835, c_Groups_Ozero__class_Ozero(_536833)), -(c_Orderings_Oord__class_Oless(_536833, c_Groups_Osgn__class_Osgn(_536833, _536835), c_Groups_Ozero__class_Ozero(_536833)))]]], (10592 ^ _166148) ^ [_537318, _537320] : [class_Rings_Olinordered__idom(_537318), 10595 ^ _166148 : [(10596 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_537318, c_Groups_Ozero__class_Ozero(_537318), c_Groups_Osgn__class_Osgn(_537318, _537320)), -(c_Orderings_Oord__class_Oless(_537318, c_Groups_Ozero__class_Ozero(_537318), _537320))], (10602 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_537318, c_Groups_Ozero__class_Ozero(_537318), _537320), -(c_Orderings_Oord__class_Oless(_537318, c_Groups_Ozero__class_Ozero(_537318), c_Groups_Osgn__class_Osgn(_537318, _537320)))]]], (10608 ^ _166148) ^ [_537789] : [class_RealVector_Oreal__normed__algebra__1(_537789), -(c_Groups_Osgn__class_Osgn(_537789, c_Groups_Oone__class_Oone(_537789)) = c_Groups_Oone__class_Oone(_537789))], (10614 ^ _166148) ^ [_538005, _538007] : [class_RealVector_Oreal__normed__vector(_538005), -(c_Groups_Osgn__class_Osgn(_538005, c_Groups_Ouminus__class_Ouminus(_538005, _538007)) = c_Groups_Ouminus__class_Ouminus(_538005, c_Groups_Osgn__class_Osgn(_538005, _538007)))], (10620 ^ _166148) ^ [_538237, _538239] : [class_Rings_Olinordered__idom(_538237), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538237), c_Groups_Osgn__class_Osgn(_538237, _538239)), c_Groups_Oabs__class_Oabs(_538237, _538239)) = _538239)], (10626 ^ _166148) ^ [_538473, _538475] : [class_Rings_Olinordered__idom(_538473), -(c_Groups_Oabs__class_Oabs(_538473, _538475) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538473), _538475), c_Groups_Osgn__class_Osgn(_538473, _538475)))], (10632 ^ _166148) ^ [_538709, _538711] : [class_RealVector_Oreal__normed__algebra__1(_538709), -(c_Groups_Osgn__class_Osgn(_538709, c_RealVector_Oof__real(_538709, _538711)) = c_RealVector_Oof__real(_538709, c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _538711)))], (10638 ^ _166148) ^ [_538941, _538943] : [class_Rings_Olinordered__idom(_538941), -(c_Groups_Osgn__class_Osgn(_538941, c_Groups_Osgn__class_Osgn(_538941, _538943)) = c_Groups_Osgn__class_Osgn(_538941, _538943))], (10644 ^ _166148) ^ [_539153] : [class_Groups_Osgn__if(_539153), -(c_Groups_Osgn__class_Osgn(_539153, c_Groups_Ozero__class_Ozero(_539153)) = c_Groups_Ozero__class_Ozero(_539153))], (10650 ^ _166148) ^ [_539355] : [class_RealVector_Oreal__normed__vector(_539355), -(c_Groups_Osgn__class_Osgn(_539355, c_Groups_Ozero__class_Ozero(_539355)) = c_Groups_Ozero__class_Ozero(_539355))], (10656 ^ _166148) ^ [_539571, _539573] : [class_RealVector_Oreal__normed__vector(_539571), 10659 ^ _166148 : [(10660 ^ _166148) ^ [] : [c_Groups_Osgn__class_Osgn(_539571, _539573) = c_Groups_Ozero__class_Ozero(_539571), -(_539573 = c_Groups_Ozero__class_Ozero(_539571))], (10666 ^ _166148) ^ [] : [_539573 = c_Groups_Ozero__class_Ozero(_539571), -(c_Groups_Osgn__class_Osgn(_539571, _539573) = c_Groups_Ozero__class_Ozero(_539571))]]], (10672 ^ _166148) ^ [_540050, _540052] : [class_Rings_Olinordered__idom(_540050), 10675 ^ _166148 : [(10676 ^ _166148) ^ [] : [c_Groups_Osgn__class_Osgn(_540050, _540052) = c_Groups_Ozero__class_Ozero(_540050), -(_540052 = c_Groups_Ozero__class_Ozero(_540050))], (10682 ^ _166148) ^ [] : [_540052 = c_Groups_Ozero__class_Ozero(_540050), -(c_Groups_Osgn__class_Osgn(_540050, _540052) = c_Groups_Ozero__class_Ozero(_540050))]]], (10688 ^ _166148) ^ [_540543, _540545, _540547] : [class_RealVector_Oreal__normed__div__algebra(_540543), -(c_Groups_Osgn__class_Osgn(_540543, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540543), _540545), _540547)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540543), c_Groups_Osgn__class_Osgn(_540543, _540545)), c_Groups_Osgn__class_Osgn(_540543, _540547)))], (10694 ^ _166148) ^ [_540821, _540823, _540825] : [class_Rings_Olinordered__idom(_540821), -(c_Groups_Osgn__class_Osgn(_540821, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540821), _540823), _540825)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540821), c_Groups_Osgn__class_Osgn(_540821, _540823)), c_Groups_Osgn__class_Osgn(_540821, _540825)))], (10700 ^ _166148) ^ [_541085, _541087] : [class_Rings_Olinordered__idom(_541085), 10703 ^ _166148 : [(10704 ^ _166148) ^ [] : [c_Groups_Osgn__class_Osgn(_541085, _541087) = c_Groups_Oone__class_Oone(_541085), -(c_Orderings_Oord__class_Oless(_541085, c_Groups_Ozero__class_Ozero(_541085), _541087))], (10710 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_541085, c_Groups_Ozero__class_Ozero(_541085), _541087), -(c_Groups_Osgn__class_Osgn(_541085, _541087) = c_Groups_Oone__class_Oone(_541085))]]], (10716 ^ _166148) ^ [_541567, _541569] : [class_Rings_Olinordered__idom(_541567), c_Orderings_Oord__class_Oless(_541567, c_Groups_Ozero__class_Ozero(_541567), _541569), -(c_Groups_Osgn__class_Osgn(_541567, _541569) = c_Groups_Oone__class_Oone(_541567))], (10726 ^ _166148) ^ [_541880, _541882] : [class_Rings_Olinordered__idom(_541880), 10729 ^ _166148 : [(10730 ^ _166148) ^ [] : [c_Groups_Osgn__class_Osgn(_541880, _541882) = c_Groups_Ouminus__class_Ouminus(_541880, c_Groups_Oone__class_Oone(_541880)), -(c_Orderings_Oord__class_Oless(_541880, _541882, c_Groups_Ozero__class_Ozero(_541880)))], (10736 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_541880, _541882, c_Groups_Ozero__class_Ozero(_541880)), -(c_Groups_Osgn__class_Osgn(_541880, _541882) = c_Groups_Ouminus__class_Ouminus(_541880, c_Groups_Oone__class_Oone(_541880)))]]], (10742 ^ _166148) ^ [_542371, _542373] : [class_Rings_Olinordered__idom(_542371), c_Orderings_Oord__class_Oless(_542371, _542373, c_Groups_Ozero__class_Ozero(_542371)), -(c_Groups_Osgn__class_Osgn(_542371, _542373) = c_Groups_Ouminus__class_Ouminus(_542371, c_Groups_Oone__class_Oone(_542371)))], (10752 ^ _166148) ^ [_542690, _542692] : [class_Groups_Osgn__if(_542690), 10755 ^ _166148 : [(10756 ^ _166148) ^ [] : [_542692 = c_Groups_Ozero__class_Ozero(_542690), -(c_Groups_Osgn__class_Osgn(_542690, _542692) = c_Groups_Ozero__class_Ozero(_542690))], (10762 ^ _166148) ^ [] : [-(_542692 = c_Groups_Ozero__class_Ozero(_542690)), 10765 ^ _166148 : [(10766 ^ _166148) ^ [] : [c_Orderings_Oord__class_Oless(_542690, c_Groups_Ozero__class_Ozero(_542690), _542692), -(c_Groups_Osgn__class_Osgn(_542690, _542692) = c_Groups_Oone__class_Oone(_542690))], (10772 ^ _166148) ^ [] : [-(c_Orderings_Oord__class_Oless(_542690, c_Groups_Ozero__class_Ozero(_542690), _542692)), -(c_Groups_Osgn__class_Osgn(_542690, _542692) = c_Groups_Ouminus__class_Ouminus(_542690, c_Groups_Oone__class_Oone(_542690)))]]]]], (10778 ^ _166148) ^ [_543466, _543468] : [class_RealVector_Oreal__normed__vector(_543466), 10781 ^ _166148 : [(10782 ^ _166148) ^ [] : [_543468 = c_Groups_Ozero__class_Ozero(_543466), -(c_RealVector_Onorm__class_Onorm(_543466, c_Groups_Osgn__class_Osgn(_543466, _543468)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10788 ^ _166148) ^ [] : [-(_543468 = c_Groups_Ozero__class_Ozero(_543466)), -(c_RealVector_Onorm__class_Onorm(_543466, c_Groups_Osgn__class_Osgn(_543466, _543468)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (10794 ^ _166148) ^ [_543976, _543978, _543980] : [class_Rings_Oidom(_543976), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_543976), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_543976)), c_Polynomial_OpCons(_543976, c_Groups_Ouminus__class_Ouminus(_543976, _543978), c_Polynomial_OpCons(_543976, c_Groups_Oone__class_Oone(_543976), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_543976))))), c_Polynomial_Oorder(_543976, _543978, _543980)), _543980))], (10800 ^ _166148) ^ [_544286, _544288, _544290, _544292] : [class_Rings_Ocomm__semiring__0(_544286), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_544286, c_Polynomial_OpCons(_544286, _544288, _544290), _544292) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_544286), c_Polynomial_Osmult(_544286, _544292, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_544286, _544290, _544292)), c_Polynomial_OpCons(_544286, _544288, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_544286, _544290, _544292))))], (10806 ^ _166148) ^ [_544566, _544568] : [class_Rings_Ocomm__semiring__1(_544566), -(c_Rings_Odvd__class_Odvd(_544566, _544568, c_Groups_Ozero__class_Ozero(_544566)))], (10812 ^ _166148) ^ [_544794, _544796, _544798] : [class_Rings_Ocomm__ring__1(_544794), 10815 ^ _166148 : [(10816 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(_544794, _544796, c_Groups_Ouminus__class_Ouminus(_544794, _544798)), -(c_Rings_Odvd__class_Odvd(_544794, _544796, _544798))], (10822 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(_544794, _544796, _544798), -(c_Rings_Odvd__class_Odvd(_544794, _544796, c_Groups_Ouminus__class_Ouminus(_544794, _544798)))]]], (10828 ^ _166148) ^ [_545297, _545299, _545301] : [class_Rings_Ocomm__ring__1(_545297), 10831 ^ _166148 : [(10832 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(_545297, c_Groups_Ouminus__class_Ouminus(_545297, _545299), _545301), -(c_Rings_Odvd__class_Odvd(_545297, _545299, _545301))], (10838 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(_545297, _545299, _545301), -(c_Rings_Odvd__class_Odvd(_545297, c_Groups_Ouminus__class_Ouminus(_545297, _545299), _545301))]]], (10844 ^ _166148) ^ [_545814, _545816, _545818, _545820] : [class_Rings_Ocomm__ring__1(_545814), c_Rings_Odvd__class_Odvd(_545814, _545816, _545818), c_Rings_Odvd__class_Odvd(_545814, _545816, _545820), -(c_Rings_Odvd__class_Odvd(_545814, _545816, c_Groups_Ominus__class_Ominus(_545814, _545818, _545820)))], (10858 ^ _166148) ^ [_546270, _546272, _546274, _546276] : [class_Rings_Ocomm__ring(_546270), class_Rings_Odvd(_546270), c_Rings_Odvd__class_Odvd(_546270, _546272, _546274), 10869 ^ _166148 : [(10870 ^ _166148) ^ [_546673, _546675] : [c_Rings_Odvd__class_Odvd(_546270, _546272, c_Groups_Oplus__class_Oplus(_546270, _546675, _546276)), -(c_Rings_Odvd__class_Odvd(_546270, _546272, c_Groups_Oplus__class_Oplus(_546270, c_Groups_Ominus__class_Ominus(_546270, _546675, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546270), _546673), _546274)), _546276)))], (10876 ^ _166148) ^ [_546911, _546913] : [c_Rings_Odvd__class_Odvd(_546270, _546272, c_Groups_Oplus__class_Oplus(_546270, c_Groups_Ominus__class_Ominus(_546270, _546913, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546270), _546911), _546274)), _546276)), -(c_Rings_Odvd__class_Odvd(_546270, _546272, c_Groups_Oplus__class_Oplus(_546270, _546913, _546276)))]]], (10882 ^ _166148) ^ [_547238, _547240, _547242, _547244] : [class_Rings_Ocomm__ring(_547238), class_Rings_Odvd(_547238), c_Rings_Odvd__class_Odvd(_547238, _547240, _547242), 10893 ^ _166148 : [(10894 ^ _166148) ^ [_547641, _547643] : [c_Rings_Odvd__class_Odvd(_547238, _547240, c_Groups_Oplus__class_Oplus(_547238, _547643, _547244)), -(c_Rings_Odvd__class_Odvd(_547238, _547240, c_Groups_Oplus__class_Oplus(_547238, c_Groups_Ominus__class_Ominus(_547238, _547643, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547238), _547641), _547242)), _547244)))], (10900 ^ _166148) ^ [_547879, _547881] : [c_Rings_Odvd__class_Odvd(_547238, _547240, c_Groups_Oplus__class_Oplus(_547238, c_Groups_Ominus__class_Ominus(_547238, _547881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547238), _547879), _547242)), _547244)), -(c_Rings_Odvd__class_Odvd(_547238, _547240, c_Groups_Oplus__class_Oplus(_547238, _547881, _547244)))]]], (10906 ^ _166148) ^ [_548206, _548208, _548210, _548212] : [class_Fields_Ofield(_548206), 10909 ^ _166148 : [(10926 ^ _166148) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_548206), c_Polynomial_Osmult(_548206, _548208, _548210), _548212)), 10929 ^ _166148 : [(10930 ^ _166148) ^ [] : [-(_548208 = c_Groups_Ozero__class_Ozero(_548206))], (10932 ^ _166148) ^ [] : [_548212 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548206))]], 10933 ^ _166148 : [(10934 ^ _166148) ^ [] : [_548208 = c_Groups_Ozero__class_Ozero(_548206)], (10936 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_548206), _548210, _548212)]]], (10910 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_548206), c_Polynomial_Osmult(_548206, _548208, _548210), _548212), 10913 ^ _166148 : [(10914 ^ _166148) ^ [] : [_548208 = c_Groups_Ozero__class_Ozero(_548206), -(_548212 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548206)))], (10920 ^ _166148) ^ [] : [-(_548208 = c_Groups_Ozero__class_Ozero(_548206)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_548206), _548210, _548212))]]]]], (10940 ^ _166148) ^ [_549276, _549278, _549280] : [class_Rings_Odvd(_549276), class_Rings_Osemiring__0(_549276), 10947 ^ _166148 : [(10948 ^ _166148) ^ [] : [10949 ^ _166148 : [(10950 ^ _166148) ^ [_549585] : [hBOOL(hAPP(_549278, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549276), _549280), _549585)))]], 10952 ^ _166148 : [(10953 ^ _166148) ^ [] : [-(c_Rings_Odvd__class_Odvd(_549276, _549280, c_Groups_Oplus__class_Oplus(_549276, 10951 ^ [_549276, _549278, _549280], c_Groups_Ozero__class_Ozero(_549276))))], (10955 ^ _166148) ^ [] : [-(hBOOL(hAPP(_549278, 10951 ^ [_549276, _549278, _549280])))]]], (10957 ^ _166148) ^ [] : [-(hBOOL(hAPP(_549278, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549276), _549280), 10964 ^ [_549276, _549278, _549280])))), 10958 ^ _166148 : [(10959 ^ _166148) ^ [_549925] : [c_Rings_Odvd__class_Odvd(_549276, _549280, c_Groups_Oplus__class_Oplus(_549276, _549925, c_Groups_Ozero__class_Ozero(_549276))), hBOOL(hAPP(_549278, _549925))]]]]], (10968 ^ _166148) ^ [_550338, _550340, _550342, _550344] : [class_Rings_Ocomm__semiring__1(_550338), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_550338), c_Polynomial_Osmult(_550338, _550340, _550342), _550344), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_550338), _550342, _550344))], (10978 ^ _166148) ^ [_550703, _550705, _550707, _550709] : [class_Rings_Ocomm__semiring__1(_550703), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_550703), _550705, _550707), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_550703), _550705, c_Polynomial_Osmult(_550703, _550709, _550707)))], (10988 ^ _166148) ^ [_551068, _551070, _551072, _551074] : [class_Fields_Ofield(_551068), -(_551070 = c_Groups_Ozero__class_Ozero(_551068)), 10995 ^ _166148 : [(10996 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_551068), _551072, c_Polynomial_Osmult(_551068, _551070, _551074)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_551068), _551072, _551074))], (11002 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_551068), _551072, _551074), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_551068), _551072, c_Polynomial_Osmult(_551068, _551070, _551074)))]]], (11008 ^ _166148) ^ [_551720, _551722, _551724, _551726] : [class_Fields_Ofield(_551720), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_551720), _551722, _551724), -(_551726 = c_Groups_Ozero__class_Ozero(_551720)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_551720), c_Polynomial_Osmult(_551720, _551726, _551722), _551724))], (11022 ^ _166148) ^ [_552189, _552191, _552193, _552195] : [class_Fields_Ofield(_552189), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_552189), _552191, c_Polynomial_Osmult(_552189, _552193, _552195)), -(_552193 = c_Groups_Ozero__class_Ozero(_552189)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_552189), _552191, _552195))], (11036 ^ _166148) ^ [_552644, _552646, _552648] : [class_Rings_Ocomm__semiring__1(_552644), -(c_Rings_Odvd__class_Odvd(_552644, _552646, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552644), _552646), _552648)))], (11042 ^ _166148) ^ [_552890, _552892, _552894] : [class_Rings_Ocomm__semiring__1(_552890), -(c_Rings_Odvd__class_Odvd(_552890, _552892, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552890), _552894), _552892)))], (11048 ^ _166148) ^ [_553150, _553152, _553154, _553156] : [class_Rings_Ocomm__semiring__1(_553150), c_Rings_Odvd__class_Odvd(_553150, _553152, _553154), -(c_Rings_Odvd__class_Odvd(_553150, _553152, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553150), _553154), _553156)))], (11058 ^ _166148) ^ [_553515, _553517, _553519, _553521] : [class_Rings_Ocomm__semiring__1(_553515), c_Rings_Odvd__class_Odvd(_553515, _553517, _553519), -(c_Rings_Odvd__class_Odvd(_553515, _553517, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553515), _553521), _553519)))], (11068 ^ _166148) ^ [_553894, _553896, _553898, _553900, _553902] : [class_Rings_Ocomm__semiring__1(_553894), c_Rings_Odvd__class_Odvd(_553894, _553896, _553898), c_Rings_Odvd__class_Odvd(_553894, _553900, _553902), -(c_Rings_Odvd__class_Odvd(_553894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553894), _553896), _553900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553894), _553898), _553902)))], (11082 ^ _166148) ^ [_554388, _554390, _554392, _554394] : [class_Rings_Odvd(_554388), _554390 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554388), _554392), _554394), -(c_Rings_Odvd__class_Odvd(_554388, _554392, _554390))], (11092 ^ _166148) ^ [_554751, _554753, _554755, _554757] : [class_Rings_Ocomm__semiring__1(_554751), c_Rings_Odvd__class_Odvd(_554751, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554751), _554753), _554755), _554757), -(c_Rings_Odvd__class_Odvd(_554751, _554753, _554757))], (11102 ^ _166148) ^ [_555116, _555118, _555120, _555122] : [class_Rings_Ocomm__semiring__1(_555116), c_Rings_Odvd__class_Odvd(_555116, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555116), _555118), _555120), _555122), -(c_Rings_Odvd__class_Odvd(_555116, _555120, _555122))], (11112 ^ _166148) ^ [_555481, _555483, _555485, _555487] : [class_Rings_Oidom(_555481), 11115 ^ _166148 : [(11126 ^ _166148) ^ [] : [11127 ^ _166148 : [(11128 ^ _166148) ^ [] : [_555483 = c_Groups_Ozero__class_Ozero(_555481)], (11130 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(_555481, _555485, _555487)]], -(c_Rings_Odvd__class_Odvd(_555481, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555481), _555483), _555485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555481), _555483), _555487)))], (11116 ^ _166148) ^ [] : [c_Rings_Odvd__class_Odvd(_555481, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555481), _555483), _555485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555481), _555483), _555487)), -(_555483 = c_Groups_Ozero__class_Ozero(_555481)), -(c_Rings_Odvd__class_Odvd(_555481, _555485, _555487))]]], (11134 ^ _166148) ^ [_556187] : [class_Groups_Ocancel__comm__monoid__add(_556187), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_556187)))], (11140 ^ _166148) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11142 ^ _166148) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11144 ^ _166148) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11146 ^ _166148) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11148 ^ _166148) ^ [_556603, _556605] : [class_Lattices_Oboolean__algebra(_556603), -(class_Lattices_Oboolean__algebra(tc_fun(_556605, _556603)))], (11154 ^ _166148) ^ [_556815, _556817] : [class_Orderings_Opreorder(_556815), -(class_Orderings_Opreorder(tc_fun(_556817, _556815)))], (11160 ^ _166148) ^ [_557027, _557029] : [class_Orderings_Oorder(_557027), -(class_Orderings_Oorder(tc_fun(_557029, _557027)))], (11166 ^ _166148) ^ [_557239, _557241] : [class_Orderings_Oord(_557239), -(class_Orderings_Oord(tc_fun(_557241, _557239)))], (11172 ^ _166148) ^ [_557451, _557453] : [class_Groups_Ouminus(_557451), -(class_Groups_Ouminus(tc_fun(_557453, _557451)))], (11178 ^ _166148) ^ [_557663, _557665] : [class_Groups_Ominus(_557663), -(class_Groups_Ominus(tc_fun(_557665, _557663)))], (11184 ^ _166148) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11186 ^ _166148) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11188 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11190 ^ _166148) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11192 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11194 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11196 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11198 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (11200 ^ _166148) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11202 ^ _166148) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11204 ^ _166148) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11206 ^ _166148) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11208 ^ _166148) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11210 ^ _166148) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11212 ^ _166148) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11214 ^ _166148) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11216 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11218 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11220 ^ _166148) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11222 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11224 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11226 ^ _166148) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11228 ^ _166148) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11230 ^ _166148) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11232 ^ _166148) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (11234 ^ _166148) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (11236 ^ _166148) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11238 ^ _166148) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11240 ^ _166148) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11242 ^ _166148) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11244 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11246 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (11248 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11250 ^ _166148) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11252 ^ _166148) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11254 ^ _166148) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (11256 ^ _166148) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (11258 ^ _166148) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (11260 ^ _166148) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11262 ^ _166148) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11264 ^ _166148) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (11266 ^ _166148) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11268 ^ _166148) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11270 ^ _166148) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11272 ^ _166148) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11274 ^ _166148) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (11276 ^ _166148) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (11278 ^ _166148) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (11280 ^ _166148) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (11282 ^ _166148) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (11284 ^ _166148) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (11286 ^ _166148) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (11288 ^ _166148) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11290 ^ _166148) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (11292 ^ _166148) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11294 ^ _166148) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11296 ^ _166148) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11298 ^ _166148) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11300 ^ _166148) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11302 ^ _166148) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (11304 ^ _166148) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11306 ^ _166148) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11308 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11310 ^ _166148) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11312 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11314 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11316 ^ _166148) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11318 ^ _166148) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11320 ^ _166148) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11322 ^ _166148) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (11324 ^ _166148) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11326 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11328 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11330 ^ _166148) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11332 ^ _166148) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11334 ^ _166148) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11336 ^ _166148) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (11338 ^ _166148) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11340 ^ _166148) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11342 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11344 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (11346 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (11348 ^ _166148) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (11350 ^ _166148) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (11352 ^ _166148) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11354 ^ _166148) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (11356 ^ _166148) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11358 ^ _166148) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (11360 ^ _166148) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (11362 ^ _166148) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11364 ^ _166148) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (11366 ^ _166148) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (11368 ^ _166148) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (11370 ^ _166148) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (11372 ^ _166148) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11374 ^ _166148) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (11376 ^ _166148) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (11378 ^ _166148) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (11380 ^ _166148) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (11382 ^ _166148) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11384 ^ _166148) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (11386 ^ _166148) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (11388 ^ _166148) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (11390 ^ _166148) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (11392 ^ _166148) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (11394 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (11396 ^ _166148) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (11398 ^ _166148) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (11400 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (11402 ^ _166148) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (11404 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (11406 ^ _166148) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (11408 ^ _166148) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (11410 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (11412 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (11414 ^ _166148) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (11416 ^ _166148) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (11418 ^ _166148) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (11420 ^ _166148) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (11422 ^ _166148) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (11424 ^ _166148) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11426 ^ _166148) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11428 ^ _166148) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (11430 ^ _166148) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (11432 ^ _166148) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11434 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (11436 ^ _166148) ^ [] : [-(class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal))], (11438 ^ _166148) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11440 ^ _166148) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11442 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (11444 ^ _166148) ^ [] : [-(class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal))], (11446 ^ _166148) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (11448 ^ _166148) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (11450 ^ _166148) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (11452 ^ _166148) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11454 ^ _166148) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11456 ^ _166148) ^ [] : [-(class_Fields_Olinordered__field(tc_RealDef_Oreal))], (11458 ^ _166148) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (11460 ^ _166148) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (11462 ^ _166148) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (11464 ^ _166148) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11466 ^ _166148) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11468 ^ _166148) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (11470 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (11472 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (11474 ^ _166148) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (11476 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11478 ^ _166148) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11480 ^ _166148) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11482 ^ _166148) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (11484 ^ _166148) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11486 ^ _166148) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11488 ^ _166148) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11490 ^ _166148) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (11492 ^ _166148) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11494 ^ _166148) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11496 ^ _166148) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11498 ^ _166148) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (11500 ^ _166148) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (11502 ^ _166148) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (11504 ^ _166148) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (11506 ^ _166148) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11508 ^ _166148) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11510 ^ _166148) ^ [] : [-(class_Groups_Ouminus(tc_RealDef_Oreal))], (11512 ^ _166148) ^ [] : [-(class_Groups_Osgn__if(tc_RealDef_Oreal))], (11514 ^ _166148) ^ [] : [-(class_Groups_Oabs__if(tc_RealDef_Oreal))], (11516 ^ _166148) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11518 ^ _166148) ^ [] : [-(class_Groups_Ominus(tc_RealDef_Oreal))], (11520 ^ _166148) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11522 ^ _166148) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11524 ^ _166148) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11526 ^ _166148) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11528 ^ _166148) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11530 ^ _166148) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11532 ^ _166148) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (11534 ^ _166148) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11536 ^ _166148) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11538 ^ _166148) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (11540 ^ _166148) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11542 ^ _166148) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11544 ^ _166148) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11546 ^ _166148) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11548 ^ _166148) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11550 ^ _166148) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11552 ^ _166148) ^ [] : [-(class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex))], (11554 ^ _166148) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11556 ^ _166148) ^ [] : [-(class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex))], (11558 ^ _166148) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (11560 ^ _166148) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11562 ^ _166148) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11564 ^ _166148) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11566 ^ _166148) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11568 ^ _166148) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11570 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11572 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (11574 ^ _166148) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (11576 ^ _166148) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11578 ^ _166148) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11580 ^ _166148) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11582 ^ _166148) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11584 ^ _166148) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11586 ^ _166148) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (11588 ^ _166148) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11590 ^ _166148) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11592 ^ _166148) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11594 ^ _166148) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (11596 ^ _166148) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (11598 ^ _166148) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (11600 ^ _166148) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (11602 ^ _166148) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11604 ^ _166148) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (11606 ^ _166148) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (11608 ^ _166148) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (11610 ^ _166148) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11612 ^ _166148) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11614 ^ _166148) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (11616 ^ _166148) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (11618 ^ _166148) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (11620 ^ _166148) ^ [_569415] : [class_Rings_Oidom(_569415), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_569415)))], (11626 ^ _166148) ^ [_569605] : [class_Rings_Olinordered__idom(_569605), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_569605)))], (11632 ^ _166148) ^ [_569795] : [class_Rings_Olinordered__idom(_569795), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_569795)))], (11638 ^ _166148) ^ [_569985] : [class_Rings_Olinordered__idom(_569985), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_569985)))], (11644 ^ _166148) ^ [_570175] : [class_Rings_Olinordered__idom(_570175), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_570175)))], (11650 ^ _166148) ^ [_570365] : [class_Rings_Olinordered__idom(_570365), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_570365)))], (11656 ^ _166148) ^ [_570555] : [class_Rings_Olinordered__idom(_570555), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_570555)))], (11662 ^ _166148) ^ [_570745] : [class_Rings_Olinordered__idom(_570745), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_570745)))], (11668 ^ _166148) ^ [_570935] : [class_Rings_Olinordered__idom(_570935), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_570935)))], (11674 ^ _166148) ^ [_571125] : [class_Rings_Olinordered__idom(_571125), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_571125)))], (11680 ^ _166148) ^ [_571315] : [class_Groups_Ocancel__comm__monoid__add(_571315), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_571315)))], (11686 ^ _166148) ^ [_571505] : [class_Rings_Oidom(_571505), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_571505)))], (11692 ^ _166148) ^ [_571695] : [class_Rings_Olinordered__idom(_571695), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_571695)))], (11698 ^ _166148) ^ [_571885] : [class_Rings_Olinordered__idom(_571885), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_571885)))], (11704 ^ _166148) ^ [_572075] : [class_Rings_Oidom(_572075), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_572075)))], (11710 ^ _166148) ^ [_572265] : [class_Rings_Olinordered__idom(_572265), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_572265)))], (11716 ^ _166148) ^ [_572455] : [class_Rings_Olinordered__idom(_572455), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_572455)))], (11722 ^ _166148) ^ [_572645] : [class_Rings_Olinordered__idom(_572645), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_572645)))], (11728 ^ _166148) ^ [_572835] : [class_Groups_Ocancel__comm__monoid__add(_572835), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_572835)))], (11734 ^ _166148) ^ [_573025] : [class_Rings_Olinordered__idom(_573025), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_573025)))], (11740 ^ _166148) ^ [_573215] : [class_Rings_Olinordered__idom(_573215), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_573215)))], (11746 ^ _166148) ^ [_573405] : [class_Rings_Ocomm__semiring__0(_573405), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_573405)))], (11752 ^ _166148) ^ [_573595] : [class_Rings_Ocomm__semiring__1(_573595), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_573595)))], (11758 ^ _166148) ^ [_573785] : [class_Groups_Ocomm__monoid__add(_573785), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_573785)))], (11764 ^ _166148) ^ [_573975] : [class_Rings_Olinordered__idom(_573975), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_573975)))], (11770 ^ _166148) ^ [_574165] : [class_Rings_Olinordered__idom(_574165), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_574165)))], (11776 ^ _166148) ^ [_574355] : [class_Rings_Oidom(_574355), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_574355)))], (11782 ^ _166148) ^ [_574545] : [class_Groups_Ocomm__monoid__add(_574545), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_574545)))], (11788 ^ _166148) ^ [_574735] : [class_Rings_Olinordered__idom(_574735), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_574735)))], (11794 ^ _166148) ^ [_574925] : [class_Rings_Olinordered__idom(_574925), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_574925)))], (11800 ^ _166148) ^ [_575115] : [class_Rings_Ocomm__semiring__1(_575115), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_575115)))], (11806 ^ _166148) ^ [_575305] : [class_Rings_Ocomm__semiring__0(_575305), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_575305)))], (11812 ^ _166148) ^ [_575495] : [class_Rings_Ocomm__semiring__0(_575495), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_575495)))], (11818 ^ _166148) ^ [_575685] : [class_Groups_Oab__group__add(_575685), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_575685)))], (11824 ^ _166148) ^ [_575875] : [class_Rings_Ocomm__semiring__1(_575875), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_575875)))], (11830 ^ _166148) ^ [_576065] : [class_Rings_Olinordered__idom(_576065), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_576065)))], (11836 ^ _166148) ^ [_576255] : [class_Rings_Olinordered__idom(_576255), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_576255)))], (11842 ^ _166148) ^ [_576445] : [class_Rings_Olinordered__idom(_576445), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_576445)))], (11848 ^ _166148) ^ [_576635] : [class_Rings_Ocomm__semiring__1(_576635), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_576635)))], (11854 ^ _166148) ^ [_576825] : [class_Rings_Ocomm__ring__1(_576825), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_576825)))], (11860 ^ _166148) ^ [_577015] : [class_Groups_Ocomm__monoid__add(_577015), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_577015)))], (11866 ^ _166148) ^ [_577205] : [class_Rings_Ocomm__semiring__0(_577205), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_577205)))], (11872 ^ _166148) ^ [_577395] : [class_Groups_Oab__group__add(_577395), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_577395)))], (11878 ^ _166148) ^ [_577585] : [class_Rings_Ocomm__semiring__0(_577585), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_577585)))], (11884 ^ _166148) ^ [_577775] : [class_Rings_Ocomm__ring(_577775), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_577775)))], (11890 ^ _166148) ^ [_577965] : [class_Rings_Olinordered__idom(_577965), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_577965)))], (11896 ^ _166148) ^ [_578155] : [class_Rings_Olinordered__idom(_578155), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_578155)))], (11902 ^ _166148) ^ [_578345] : [class_Rings_Ocomm__semiring__0(_578345), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_578345)))], (11908 ^ _166148) ^ [_578535] : [class_Rings_Olinordered__idom(_578535), -(class_Orderings_Oord(tc_Polynomial_Opoly(_578535)))], (11914 ^ _166148) ^ [_578725] : [class_Groups_Oab__group__add(_578725), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_578725)))], (11920 ^ _166148) ^ [_578915] : [class_Rings_Olinordered__idom(_578915), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_578915)))], (11926 ^ _166148) ^ [_579105] : [class_Rings_Olinordered__idom(_579105), -(class_Groups_Oabs__if(tc_Polynomial_Opoly(_579105)))], (11932 ^ _166148) ^ [_579295] : [class_Rings_Ocomm__ring__1(_579295), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_579295)))], (11938 ^ _166148) ^ [_579485] : [class_Groups_Oab__group__add(_579485), -(class_Groups_Ominus(tc_Polynomial_Opoly(_579485)))], (11944 ^ _166148) ^ [_579675] : [class_Rings_Ocomm__semiring__1(_579675), -(class_Power_Opower(tc_Polynomial_Opoly(_579675)))], (11950 ^ _166148) ^ [_579865] : [class_Groups_Ozero(_579865), -(class_Groups_Ozero(tc_Polynomial_Opoly(_579865)))], (11956 ^ _166148) ^ [_580055] : [class_Rings_Ocomm__ring(_580055), -(class_Rings_Oring(tc_Polynomial_Opoly(_580055)))], (11962 ^ _166148) ^ [_580245] : [class_Rings_Oidom(_580245), -(class_Rings_Oidom(tc_Polynomial_Opoly(_580245)))], (11968 ^ _166148) ^ [_580435] : [class_Rings_Ocomm__semiring__1(_580435), -(class_Groups_Oone(tc_Polynomial_Opoly(_580435)))], (11974 ^ _166148) ^ [_580605] : [class_Rings_Ocomm__semiring__1(_580605), -(class_Rings_Odvd(tc_Polynomial_Opoly(_580605)))]], input).
% 0.42/1.33  ncf('1',plain,[c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))],start(11980 ^ 0)).
% 0.42/1.33  ncf('1.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), 3659 : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), 3659 : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), 3657 : class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal)],extension(3639 ^ 1,bind([[_292394, _292396, _292398, _292400], [tc_RealDef_Oreal, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)]]))).
% 0.42/1.33  ncf('1.1.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))],extension(1191 ^ 6)).
% 0.42/1.33  ncf('1.1.2',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))],extension(1193 ^ 6)).
% 0.42/1.33  ncf('1.1.3',plain,[-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))],extension(11428 ^ 2)).
% 0.42/1.33  %-----------------------------------------------------
% 0.42/1.33  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------