TSTP Solution File: SWW232+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW232+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n021.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 12:25:48 EDT 2023

% Result   : Theorem 4.64s 5.53s
% Output   : Proof 4.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW232+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 22:07:27 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 4.64/5.53  
% 4.64/5.53  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 4.64/5.53  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.64/5.53  %-----------------------------------------------------
% 4.64/5.53  ncf(matrix, plain, [(12160 ^ _124236) ^ [] : [v_thesis____], (718 ^ _124236) ^ [_146315, _146317, _146319, _146321, _146323, _146325, _146327, _146329] : [-(c_If(_146329, _146325, _146321, _146317) = c_If(_146327, _146323, _146319, _146315)), _146329 = _146327, _146325 = _146323, _146321 = _146319, _146317 = _146315], (736 ^ _124236) ^ [_147032, _147034, _147036, _147038, _147040, _147042, _147044, _147046, _147048, _147050] : [-(c_Polynomial_Opoly__rec(_147050, _147046, _147042, _147038, _147034) = c_Polynomial_Opoly__rec(_147048, _147044, _147040, _147036, _147032)), _147050 = _147048, _147046 = _147044, _147042 = _147040, _147038 = _147036, _147034 = _147032], (758 ^ _124236) ^ [_147826, _147828, _147830, _147832] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_147832, _147828) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_147830, _147826)), _147832 = _147830, _147828 = _147826], (768 ^ _124236) ^ [_148213, _148215, _148217, _148219, _148221, _148223] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_148223, _148219, _148215) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_148221, _148217, _148213)), _148223 = _148221, _148219 = _148217, _148215 = _148213], (782 ^ _124236) ^ [_148729, _148731, _148733, _148735, _148737, _148739] : [-(c_Polynomial_Opcompose(_148739, _148735, _148731) = c_Polynomial_Opcompose(_148737, _148733, _148729)), _148739 = _148737, _148735 = _148733, _148731 = _148729], (796 ^ _124236) ^ [_149245, _149247, _149249, _149251, _149253, _149255] : [-(c_Polynomial_Osynthetic__div(_149255, _149251, _149247) = c_Polynomial_Osynthetic__div(_149253, _149249, _149245)), _149255 = _149253, _149251 = _149249, _149247 = _149245], (810 ^ _124236) ^ [_149761, _149763, _149765, _149767, _149769, _149771] : [-(c_Polynomial_Omonom(_149771, _149767, _149763) = c_Polynomial_Omonom(_149769, _149765, _149761)), _149771 = _149769, _149767 = _149765, _149763 = _149761], (824 ^ _124236) ^ [_150277, _150279, _150281, _150283, _150285, _150287] : [-(c_Power_Opower_Opower(_150287, _150283, _150279) = c_Power_Opower_Opower(_150285, _150281, _150277)), _150287 = _150285, _150283 = _150281, _150279 = _150277], (838 ^ _124236) ^ [_150793, _150795, _150797, _150799, _150801, _150803] : [-(c_Polynomial_Osmult(_150803, _150799, _150795) = c_Polynomial_Osmult(_150801, _150797, _150793)), _150803 = _150801, _150799 = _150797, _150795 = _150793], (852 ^ _124236) ^ [_151309, _151311, _151313, _151315, _151317, _151319] : [-(c_Polynomial_Oorder(_151319, _151315, _151311) = c_Polynomial_Oorder(_151317, _151313, _151309)), _151319 = _151317, _151315 = _151313, _151311 = _151309], (866 ^ _124236) ^ [_151797, _151799, _151801, _151803] : [-(c_Nat__Transfer_Otsub(_151803, _151799) = c_Nat__Transfer_Otsub(_151801, _151797)), _151803 = _151801, _151799 = _151797], (876 ^ _124236) ^ [_152128, _152130] : [_152130 = _152128, -(c_RComplete_Onatfloor(_152130) = c_RComplete_Onatfloor(_152128))], (882 ^ _124236) ^ [_152346, _152348] : [_152348 = _152346, -(c_RComplete_Onatceiling(_152348) = c_RComplete_Onatceiling(_152346))], (888 ^ _124236) ^ [_152592, _152594, _152596, _152598] : [-(c_RealDef_Oreal(_152598, _152594) = c_RealDef_Oreal(_152596, _152592)), _152598 = _152596, _152594 = _152592], (898 ^ _124236) ^ [_152979, _152981, _152983, _152985, _152987, _152989] : [-(c_Groups_Ominus__class_Ominus(_152989, _152985, _152981) = c_Groups_Ominus__class_Ominus(_152987, _152983, _152979)), _152989 = _152987, _152985 = _152983, _152981 = _152979], (912 ^ _124236) ^ [_153439, _153441] : [_153441 = _153439, -(c_Nat_OSuc(_153441) = c_Nat_OSuc(_153439))], (918 ^ _124236) ^ [_153685, _153687, _153689, _153691] : [-(c_Groups_Ouminus__class_Ouminus(_153691, _153687) = c_Groups_Ouminus__class_Ouminus(_153689, _153685)), _153691 = _153689, _153687 = _153685], (928 ^ _124236) ^ [_154016, _154018] : [_154018 = _154016, -(c_Groups_Otimes__class_Otimes(_154018) = c_Groups_Otimes__class_Otimes(_154016))], (934 ^ _124236) ^ [_154234, _154236] : [_154236 = _154234, -(c_Power_Opower__class_Opower(_154236) = c_Power_Opower__class_Opower(_154234))], (940 ^ _124236) ^ [_154452, _154454] : [_154454 = _154452, -(c_Groups_Ozero__class_Ozero(_154454) = c_Groups_Ozero__class_Ozero(_154452))], (946 ^ _124236) ^ [_154670, _154672] : [_154672 = _154670, -(c_Groups_Oone__class_Oone(_154672) = c_Groups_Oone__class_Oone(_154670))], (952 ^ _124236) ^ [_154944, _154946, _154948, _154950, _154952, _154954] : [-(c_Divides_Odiv__class_Odiv(_154954, _154950, _154946) = c_Divides_Odiv__class_Odiv(_154952, _154948, _154944)), _154954 = _154952, _154950 = _154948, _154946 = _154944], (966 ^ _124236) ^ [_155432, _155434, _155436, _155438] : [-(tc_fun(_155438, _155434) = tc_fun(_155436, _155432)), _155438 = _155436, _155434 = _155432], (976 ^ _124236) ^ [_155763, _155765] : [_155765 = _155763, -(tc_Polynomial_Opoly(_155765) = tc_Polynomial_Opoly(_155763))], (982 ^ _124236) ^ [_156009, _156011, _156013, _156015] : [-(c_fequal(_156015, _156011) = c_fequal(_156013, _156009)), _156015 = _156013, _156011 = _156009], (992 ^ _124236) ^ [_156396, _156398, _156400, _156402, _156404, _156406] : [-(c_Groups_Oplus__class_Oplus(_156406, _156402, _156398) = c_Groups_Oplus__class_Oplus(_156404, _156400, _156396)), _156406 = _156404, _156402 = _156400, _156398 = _156396], (1006 ^ _124236) ^ [_156884, _156886, _156888, _156890] : [-(c_RealVector_Onorm__class_Onorm(_156890, _156886) = c_RealVector_Onorm__class_Onorm(_156888, _156884)), _156890 = _156888, _156886 = _156884], (1016 ^ _124236) ^ [_157243, _157245, _157247, _157249] : [-(hAPP(_157249, _157245) = hAPP(_157247, _157243)), _157249 = _157247, _157245 = _157243], (1026 ^ _124236) ^ [_157602, _157604, _157606, _157608] : [-(c_Polynomial_Opoly(_157608, _157604) = c_Polynomial_Opoly(_157606, _157602)), _157608 = _157606, _157604 = _157602], (1036 ^ _124236) ^ [_157969, _157971, _157973, _157975, _157977, _157979] : [-(c_Polynomial_OpCons(_157979, _157975, _157971) = c_Polynomial_OpCons(_157977, _157973, _157969)), _157979 = _157977, _157975 = _157973, _157971 = _157969], (2 ^ _124236) ^ [_124380] : [-(_124380 = _124380)], (4 ^ _124236) ^ [_124487, _124489] : [_124489 = _124487, -(_124487 = _124489)], (10 ^ _124236) ^ [_124691, _124693, _124695] : [-(_124695 = _124691), _124695 = _124693, _124693 = _124691], (20 ^ _124236) ^ [_125032, _125034, _125036, _125038] : [-(c_Polynomial_Opos__poly(_125036, _125032)), c_Polynomial_Opos__poly(_125038, _125034), _125038 = _125036, _125034 = _125032], (34 ^ _124236) ^ [_125504, _125506, _125508, _125510, _125512, _125514] : [-(c_Rings_Odvd__class_Odvd(_125512, _125508, _125504)), c_Rings_Odvd__class_Odvd(_125514, _125510, _125506), _125514 = _125512, _125510 = _125508, _125506 = _125504], (52 ^ _124236) ^ [_126113, _126115, _126117, _126119, _126121, _126123] : [-(c_Orderings_Oord__class_Oless(_126121, _126117, _126113)), c_Orderings_Oord__class_Oless(_126123, _126119, _126115), _126123 = _126121, _126119 = _126117, _126115 = _126113], (70 ^ _124236) ^ [_126666, _126668] : [-(class_RealVector_Oreal__normed__div__algebra(_126666)), _126668 = _126666, class_RealVector_Oreal__normed__div__algebra(_126668)], (80 ^ _124236) ^ [_126961, _126963] : [-(class_RealVector_Oreal__normed__algebra__1(_126961)), _126963 = _126961, class_RealVector_Oreal__normed__algebra__1(_126963)], (90 ^ _124236) ^ [_127256, _127258] : [-(class_RealVector_Oreal__normed__algebra(_127256)), _127258 = _127256, class_RealVector_Oreal__normed__algebra(_127258)], (100 ^ _124236) ^ [_127551, _127553] : [-(class_RealVector_Oreal__normed__vector(_127551)), _127553 = _127551, class_RealVector_Oreal__normed__vector(_127553)], (110 ^ _124236) ^ [_127846, _127848] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_127846)), _127848 = _127846, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_127848)], (120 ^ _124236) ^ [_128141, _128143] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_128141)), _128143 = _128141, class_Groups_Oordered__cancel__ab__semigroup__add(_128143)], (130 ^ _124236) ^ [_128436, _128438] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_128436)), _128438 = _128436, class_Groups_Oordered__ab__semigroup__add__imp__le(_128438)], (140 ^ _124236) ^ [_128731, _128733] : [-(class_Rings_Olinordered__comm__semiring__strict(_128731)), _128733 = _128731, class_Rings_Olinordered__comm__semiring__strict(_128733)], (150 ^ _124236) ^ [_129026, _129028] : [-(class_Rings_Olinordered__semiring__1__strict(_129026)), _129028 = _129026, class_Rings_Olinordered__semiring__1__strict(_129028)], (160 ^ _124236) ^ [_129321, _129323] : [-(class_Rings_Olinordered__semiring__strict(_129321)), _129323 = _129321, class_Rings_Olinordered__semiring__strict(_129323)], (170 ^ _124236) ^ [_129616, _129618] : [-(class_Groups_Oordered__ab__semigroup__add(_129616)), _129618 = _129616, class_Groups_Oordered__ab__semigroup__add(_129618)], (180 ^ _124236) ^ [_129911, _129913] : [-(class_Groups_Oordered__comm__monoid__add(_129911)), _129913 = _129911, class_Groups_Oordered__comm__monoid__add(_129913)], (190 ^ _124236) ^ [_130206, _130208] : [-(class_Groups_Olinordered__ab__group__add(_130206)), _130208 = _130206, class_Groups_Olinordered__ab__group__add(_130208)], (200 ^ _124236) ^ [_130501, _130503] : [-(class_Groups_Ocancel__ab__semigroup__add(_130501)), _130503 = _130501, class_Groups_Ocancel__ab__semigroup__add(_130503)], (210 ^ _124236) ^ [_130796, _130798] : [-(class_Rings_Oring__1__no__zero__divisors(_130796)), _130798 = _130796, class_Rings_Oring__1__no__zero__divisors(_130798)], (220 ^ _124236) ^ [_131091, _131093] : [-(class_Rings_Oordered__cancel__semiring(_131091)), _131093 = _131091, class_Rings_Oordered__cancel__semiring(_131093)], (230 ^ _124236) ^ [_131386, _131388] : [-(class_Rings_Olinordered__ring__strict(_131386)), _131388 = _131386, class_Rings_Olinordered__ring__strict(_131388)], (240 ^ _124236) ^ [_131681, _131683] : [-(class_Rings_Oring__no__zero__divisors(_131681)), _131683 = _131681, class_Rings_Oring__no__zero__divisors(_131683)], (250 ^ _124236) ^ [_131976, _131978] : [-(class_Rings_Oordered__comm__semiring(_131976)), _131978 = _131976, class_Rings_Oordered__comm__semiring(_131978)], (260 ^ _124236) ^ [_132271, _132273] : [-(class_Rings_Olinordered__semiring__1(_132271)), _132273 = _132271, class_Rings_Olinordered__semiring__1(_132273)], (270 ^ _124236) ^ [_132566, _132568] : [-(class_Groups_Oordered__ab__group__add(_132566)), _132568 = _132566, class_Groups_Oordered__ab__group__add(_132568)], (280 ^ _124236) ^ [_132861, _132863] : [-(class_Groups_Ocancel__comm__monoid__add(_132861)), _132863 = _132861, class_Groups_Ocancel__comm__monoid__add(_132863)], (290 ^ _124236) ^ [_133156, _133158] : [-(class_Groups_Ocancel__semigroup__add(_133156)), _133158 = _133156, class_Groups_Ocancel__semigroup__add(_133158)], (300 ^ _124236) ^ [_133451, _133453] : [-(class_Rings_Olinordered__semiring(_133451)), _133453 = _133451, class_Rings_Olinordered__semiring(_133453)], (310 ^ _124236) ^ [_133746, _133748] : [-(class_Rings_Olinordered__semidom(_133746)), _133748 = _133746, class_Rings_Olinordered__semidom(_133748)], (320 ^ _124236) ^ [_134041, _134043] : [-(class_Groups_Oab__semigroup__mult(_134041)), _134043 = _134041, class_Groups_Oab__semigroup__mult(_134043)], (330 ^ _124236) ^ [_134336, _134338] : [-(class_Groups_Ocomm__monoid__mult(_134336)), _134338 = _134336, class_Groups_Ocomm__monoid__mult(_134338)], (340 ^ _124236) ^ [_134631, _134633] : [-(class_Groups_Oab__semigroup__add(_134631)), _134633 = _134631, class_Groups_Oab__semigroup__add(_134633)], (350 ^ _124236) ^ [_134926, _134928] : [-(class_Rings_Oordered__semiring(_134926)), _134928 = _134926, class_Rings_Oordered__semiring(_134928)], (360 ^ _124236) ^ [_135221, _135223] : [-(class_Rings_Ono__zero__divisors(_135221)), _135223 = _135221, class_Rings_Ono__zero__divisors(_135223)], (370 ^ _124236) ^ [_135516, _135518] : [-(class_Rings_Olinordered__ring(_135516)), _135518 = _135516, class_Rings_Olinordered__ring(_135518)], (380 ^ _124236) ^ [_135811, _135813] : [-(class_Divides_Osemiring__div(_135811)), _135813 = _135811, class_Divides_Osemiring__div(_135813)], (390 ^ _124236) ^ [_136106, _136108] : [-(class_Rings_Ocomm__semiring(_136106)), _136108 = _136106, class_Rings_Ocomm__semiring(_136108)], (400 ^ _124236) ^ [_136401, _136403] : [-(class_Rings_Ozero__neq__one(_136401)), _136403 = _136401, class_Rings_Ozero__neq__one(_136403)], (410 ^ _124236) ^ [_136696, _136698] : [-(class_Rings_Oordered__ring(_136696)), _136698 = _136696, class_Rings_Oordered__ring(_136698)], (420 ^ _124236) ^ [_136991, _136993] : [-(class_Orderings_Opreorder(_136991)), _136993 = _136991, class_Orderings_Opreorder(_136993)], (430 ^ _124236) ^ [_137286, _137288] : [-(class_Orderings_Olinorder(_137286)), _137288 = _137286, class_Orderings_Olinorder(_137288)], (440 ^ _124236) ^ [_137581, _137583] : [-(class_Groups_Omonoid__mult(_137581)), _137583 = _137581, class_Groups_Omonoid__mult(_137583)], (450 ^ _124236) ^ [_137876, _137878] : [-(class_Groups_Ocomm__monoid__add(_137876)), _137878 = _137876, class_Groups_Ocomm__monoid__add(_137878)], (460 ^ _124236) ^ [_138171, _138173] : [-(class_Groups_Omonoid__add(_138171)), _138173 = _138171, class_Groups_Omonoid__add(_138173)], (470 ^ _124236) ^ [_138466, _138468] : [-(class_Rings_Osemiring__0(_138466)), _138468 = _138466, class_Rings_Osemiring__0(_138468)], (480 ^ _124236) ^ [_138761, _138763] : [-(class_Groups_Oab__group__add(_138761)), _138763 = _138761, class_Groups_Oab__group__add(_138763)], (490 ^ _124236) ^ [_139056, _139058] : [-(class_Groups_Ogroup__add(_139056)), _139058 = _139056, class_Groups_Ogroup__add(_139058)], (500 ^ _124236) ^ [_139351, _139353] : [-(class_Fields_Ofield(_139351)), _139353 = _139351, class_Fields_Ofield(_139353)], (510 ^ _124236) ^ [_139646, _139648] : [-(class_Divides_Oring__div(_139646)), _139648 = _139646, class_Divides_Oring__div(_139648)], (520 ^ _124236) ^ [_139941, _139943] : [-(class_Rings_Omult__zero(_139941)), _139943 = _139941, class_Rings_Omult__zero(_139943)], (530 ^ _124236) ^ [_140236, _140238] : [-(class_Orderings_Oorder(_140236)), _140238 = _140236, class_Orderings_Oorder(_140238)], (540 ^ _124236) ^ [_140531, _140533] : [-(class_Int_Oring__char__0(_140531)), _140533 = _140531, class_Int_Oring__char__0(_140533)], (550 ^ _124236) ^ [_140826, _140828] : [-(class_Rings_Ocomm__semiring__0(_140826)), _140828 = _140826, class_Rings_Ocomm__semiring__0(_140828)], (560 ^ _124236) ^ [_141121, _141123] : [-(class_Rings_Osemiring(_141121)), _141123 = _141121, class_Rings_Osemiring(_141123)], (570 ^ _124236) ^ [_141416, _141418] : [-(class_Rings_Olinordered__idom(_141416)), _141418 = _141416, class_Rings_Olinordered__idom(_141418)], (580 ^ _124236) ^ [_141711, _141713] : [-(class_Orderings_Oord(_141711)), _141713 = _141711, class_Orderings_Oord(_141713)], (590 ^ _124236) ^ [_142006, _142008] : [-(class_Rings_Ocomm__ring__1(_142006)), _142008 = _142006, class_Rings_Ocomm__ring__1(_142008)], (600 ^ _124236) ^ [_142301, _142303] : [-(class_Rings_Oring__1(_142301)), _142303 = _142301, class_Rings_Oring__1(_142303)], (610 ^ _124236) ^ [_142596, _142598] : [-(class_Power_Opower(_142596)), _142598 = _142596, class_Power_Opower(_142598)], (620 ^ _124236) ^ [_142891, _142893] : [-(class_Groups_Ozero(_142891)), _142893 = _142891, class_Groups_Ozero(_142893)], (630 ^ _124236) ^ [_143186, _143188] : [-(class_Rings_Ocomm__ring(_143186)), _143188 = _143186, class_Rings_Ocomm__ring(_143188)], (640 ^ _124236) ^ [_143481, _143483] : [-(class_Rings_Oring(_143481)), _143483 = _143481, class_Rings_Oring(_143483)], (650 ^ _124236) ^ [_143776, _143778] : [-(class_Rings_Oidom(_143776)), _143778 = _143776, class_Rings_Oidom(_143778)], (660 ^ _124236) ^ [_144071, _144073] : [-(class_Groups_Oone(_144071)), _144073 = _144071, class_Groups_Oone(_144073)], (670 ^ _124236) ^ [_144366, _144368] : [-(class_Rings_Ocomm__semiring__1(_144366)), _144368 = _144366, class_Rings_Ocomm__semiring__1(_144368)], (680 ^ _124236) ^ [_144661, _144663] : [-(class_Rings_Odvd(_144661)), _144663 = _144661, class_Rings_Odvd(_144663)], (690 ^ _124236) ^ [_144956, _144958] : [-(hBOOL(_144956)), _144958 = _144956, hBOOL(_144958)], (700 ^ _124236) ^ [_145287, _145289, _145291, _145293, _145295, _145297] : [-(c_Orderings_Oord__class_Oless__eq(_145295, _145291, _145287)), c_Orderings_Oord__class_Oless__eq(_145297, _145293, _145289), _145297 = _145295, _145293 = _145291, _145289 = _145287], (1050 ^ _124236) ^ [_158615, _158617] : [hAPP(_158615, 1051 ^ [_158615, _158617]) = hAPP(_158617, 1051 ^ [_158615, _158617]), -(_158615 = _158617)], (1057 ^ _124236) ^ [] : [v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1059 ^ _124236) ^ [] : [c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1061 ^ _124236) ^ [_159011, _159013] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), 1065 ^ _124236 : [(1066 ^ _124236) ^ [_159240] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 1064 ^ [_159011, _159013], c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _159240)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _159011, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, _159013, v_cs____)), _159240))))]]], (1072 ^ _124236) ^ [] : [v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1074 ^ _124236) ^ [_159581, _159583, _159585] : [class_RealVector_Oreal__normed__vector(_159581), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_159581, c_Groups_Oplus__class_Oplus(_159581, _159583, _159585)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_159581, _159583), c_RealVector_Onorm__class_Onorm(_159581, _159585))))], (1080 ^ _124236) ^ [_159831, _159833] : [class_Orderings_Opreorder(_159831), -(c_Orderings_Oord__class_Oless__eq(_159831, _159833, _159833))], (1086 ^ _124236) ^ [_160069, _160071, _160073, _160075] : [class_Rings_Ocomm__semiring__0(_160069), -(hAPP(c_Polynomial_Opoly(_160069, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_160069), _160071, _160073)), _160075) = c_Groups_Oplus__class_Oplus(_160069, hAPP(c_Polynomial_Opoly(_160069, _160071), _160075), hAPP(c_Polynomial_Opoly(_160069, _160073), _160075)))], (1092 ^ _124236) ^ [_160387, _160389, _160391, _160393, _160395] : [class_Groups_Ocomm__monoid__add(_160387), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_160387), c_Polynomial_OpCons(_160387, _160389, _160391), c_Polynomial_OpCons(_160387, _160393, _160395)) = c_Polynomial_OpCons(_160387, c_Groups_Oplus__class_Oplus(_160387, _160389, _160393), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_160387), _160391, _160395)))], (1098 ^ _124236) ^ [_160683, _160685, _160687] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _160683, _160685), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _160687, _160683), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _160687, _160685)))], (1104 ^ _124236) ^ [_160947, _160949, _160951, _160953] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_160947), 1107 ^ _124236 : [(1108 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_160947, c_Groups_Oplus__class_Oplus(_160947, _160949, _160951), c_Groups_Oplus__class_Oplus(_160947, _160953, _160951)), -(c_Orderings_Oord__class_Oless__eq(_160947, _160949, _160953))], (1114 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_160947, _160949, _160953), -(c_Orderings_Oord__class_Oless__eq(_160947, c_Groups_Oplus__class_Oplus(_160947, _160949, _160951), c_Groups_Oplus__class_Oplus(_160947, _160953, _160951)))]]], (1120 ^ _124236) ^ [_161495, _161497, _161499, _161501] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_161495), 1123 ^ _124236 : [(1124 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_161495, c_Groups_Oplus__class_Oplus(_161495, _161497, _161499), c_Groups_Oplus__class_Oplus(_161495, _161497, _161501)), -(c_Orderings_Oord__class_Oless__eq(_161495, _161499, _161501))], (1130 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_161495, _161499, _161501), -(c_Orderings_Oord__class_Oless__eq(_161495, c_Groups_Oplus__class_Oplus(_161495, _161497, _161499), c_Groups_Oplus__class_Oplus(_161495, _161497, _161501)))]]], (1136 ^ _124236) ^ [_162043, _162045, _162047, _162049] : [class_Groups_Oordered__ab__semigroup__add(_162043), c_Orderings_Oord__class_Oless__eq(_162043, _162045, _162047), -(c_Orderings_Oord__class_Oless__eq(_162043, c_Groups_Oplus__class_Oplus(_162043, _162045, _162049), c_Groups_Oplus__class_Oplus(_162043, _162047, _162049)))], (1146 ^ _124236) ^ [_162408, _162410, _162412, _162414] : [class_Groups_Oordered__ab__semigroup__add(_162408), c_Orderings_Oord__class_Oless__eq(_162408, _162410, _162412), -(c_Orderings_Oord__class_Oless__eq(_162408, c_Groups_Oplus__class_Oplus(_162408, _162414, _162410), c_Groups_Oplus__class_Oplus(_162408, _162414, _162412)))], (1156 ^ _124236) ^ [_162787, _162789, _162791, _162793, _162795] : [class_Groups_Oordered__ab__semigroup__add(_162787), c_Orderings_Oord__class_Oless__eq(_162787, _162789, _162791), c_Orderings_Oord__class_Oless__eq(_162787, _162793, _162795), -(c_Orderings_Oord__class_Oless__eq(_162787, c_Groups_Oplus__class_Oplus(_162787, _162789, _162793), c_Groups_Oplus__class_Oplus(_162787, _162791, _162795)))], (1170 ^ _124236) ^ [_163223] : [class_RealVector_Oreal__normed__vector(_163223), -(c_RealVector_Onorm__class_Onorm(_163223, c_Groups_Ozero__class_Ozero(_163223)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1176 ^ _124236) ^ [_163421] : [class_Groups_Ozero(_163421), -(c_Polynomial_OpCons(_163421, c_Groups_Ozero__class_Ozero(_163421), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_163421))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_163421)))], (1182 ^ _124236) ^ [_163651, _163653] : [class_Rings_Ocomm__semiring__0(_163651), -(hAPP(c_Polynomial_Opoly(_163651, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_163651))), _163653) = c_Groups_Ozero__class_Ozero(_163651))], (1188 ^ _124236) ^ [_163883, _163885] : [class_Groups_Ocomm__monoid__add(_163883), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_163883), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_163883)), _163885) = _163885)], (1194 ^ _124236) ^ [_164111, _164113] : [class_Groups_Ozero(_164111), 1197 ^ _124236 : [(1198 ^ _124236) ^ [] : [c_Groups_Ozero__class_Ozero(_164111) = _164113, -(_164113 = c_Groups_Ozero__class_Ozero(_164111))], (1204 ^ _124236) ^ [] : [_164113 = c_Groups_Ozero__class_Ozero(_164111), -(c_Groups_Ozero__class_Ozero(_164111) = _164113)]]], (1210 ^ _124236) ^ [_164581, _164583] : [class_Groups_Ocomm__monoid__add(_164581), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_164581), _164583, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_164581))) = _164583)], (1216 ^ _124236) ^ [_164809, _164811] : [class_RealVector_Oreal__normed__vector(_164809), 1219 ^ _124236 : [(1220 ^ _124236) ^ [] : [c_RealVector_Onorm__class_Onorm(_164809, _164811) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_164811 = c_Groups_Ozero__class_Ozero(_164809))], (1226 ^ _124236) ^ [] : [_164811 = c_Groups_Ozero__class_Ozero(_164809), -(c_RealVector_Onorm__class_Onorm(_164809, _164811) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1232 ^ _124236) ^ [_165296, _165298, _165300] : [class_Groups_Ozero(_165296), 1235 ^ _124236 : [(1236 ^ _124236) ^ [] : [c_Polynomial_OpCons(_165296, _165298, _165300) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_165296)), 1239 ^ _124236 : [(1240 ^ _124236) ^ [] : [-(_165298 = c_Groups_Ozero__class_Ozero(_165296))], (1242 ^ _124236) ^ [] : [-(_165300 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_165296)))]]], (1244 ^ _124236) ^ [] : [-(c_Polynomial_OpCons(_165296, _165298, _165300) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_165296))), _165298 = c_Groups_Ozero__class_Ozero(_165296), _165300 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_165296))]]], (1254 ^ _124236) ^ [_165976, _165978] : [class_Groups_Ocomm__monoid__add(_165976), -(c_Groups_Oplus__class_Oplus(_165976, _165978, c_Groups_Ozero__class_Ozero(_165976)) = _165978)], (1260 ^ _124236) ^ [_166196, _166198] : [class_Groups_Omonoid__add(_166196), -(c_Groups_Oplus__class_Oplus(_166196, _166198, c_Groups_Ozero__class_Ozero(_166196)) = _166198)], (1266 ^ _124236) ^ [_166416, _166418] : [class_Groups_Olinordered__ab__group__add(_166416), 1269 ^ _124236 : [(1270 ^ _124236) ^ [] : [c_Groups_Ozero__class_Ozero(_166416) = c_Groups_Oplus__class_Oplus(_166416, _166418, _166418), -(_166418 = c_Groups_Ozero__class_Ozero(_166416))], (1276 ^ _124236) ^ [] : [_166418 = c_Groups_Ozero__class_Ozero(_166416), -(c_Groups_Ozero__class_Ozero(_166416) = c_Groups_Oplus__class_Oplus(_166416, _166418, _166418))]]], (1282 ^ _124236) ^ [_166898, _166900] : [class_Groups_Ocomm__monoid__add(_166898), -(c_Groups_Oplus__class_Oplus(_166898, c_Groups_Ozero__class_Ozero(_166898), _166900) = _166900)], (1288 ^ _124236) ^ [_167118, _167120] : [class_Groups_Omonoid__add(_167118), -(c_Groups_Oplus__class_Oplus(_167118, c_Groups_Ozero__class_Ozero(_167118), _167120) = _167120)], (1294 ^ _124236) ^ [_167338, _167340] : [class_RealVector_Oreal__normed__vector(_167338), 1297 ^ _124236 : [(1298 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_167338, _167340), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_167340 = c_Groups_Ozero__class_Ozero(_167338))], (1304 ^ _124236) ^ [] : [_167340 = c_Groups_Ozero__class_Ozero(_167338), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_167338, _167340), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (1310 ^ _124236) ^ [_167814, _167816] : [class_Int_Oring__char__0(_167814), class_Rings_Oidom(_167814), 1317 ^ _124236 : [(1318 ^ _124236) ^ [] : [c_Polynomial_Opoly(_167814, _167816) = c_Polynomial_Opoly(_167814, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_167814))), -(_167816 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_167814)))], (1324 ^ _124236) ^ [] : [_167816 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_167814)), -(c_Polynomial_Opoly(_167814, _167816) = c_Polynomial_Opoly(_167814, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_167814))))]]], (1330 ^ _124236) ^ [_168417, _168419, _168421] : [class_Groups_Oordered__comm__monoid__add(_168417), c_Orderings_Oord__class_Oless__eq(_168417, _168419, c_Groups_Ozero__class_Ozero(_168417)), c_Orderings_Oord__class_Oless__eq(_168417, _168421, c_Groups_Ozero__class_Ozero(_168417)), -(c_Orderings_Oord__class_Oless__eq(_168417, c_Groups_Oplus__class_Oplus(_168417, _168419, _168421), c_Groups_Ozero__class_Ozero(_168417)))], (1344 ^ _124236) ^ [_168871, _168873, _168875, _168877] : [class_Groups_Oordered__comm__monoid__add(_168871), c_Orderings_Oord__class_Oless__eq(_168871, c_Groups_Ozero__class_Ozero(_168871), _168873), c_Orderings_Oord__class_Oless__eq(_168871, _168875, _168877), -(c_Orderings_Oord__class_Oless__eq(_168871, _168875, c_Groups_Oplus__class_Oplus(_168871, _168877, _168873)))], (1358 ^ _124236) ^ [_169331, _169333, _169335, _169337] : [class_Groups_Oordered__comm__monoid__add(_169331), c_Orderings_Oord__class_Oless__eq(_169331, c_Groups_Ozero__class_Ozero(_169331), _169333), c_Orderings_Oord__class_Oless__eq(_169331, _169335, _169337), -(c_Orderings_Oord__class_Oless__eq(_169331, _169335, c_Groups_Oplus__class_Oplus(_169331, _169333, _169337)))], (1372 ^ _124236) ^ [_169777, _169779, _169781] : [class_Groups_Oordered__comm__monoid__add(_169777), c_Orderings_Oord__class_Oless__eq(_169777, c_Groups_Ozero__class_Ozero(_169777), _169779), c_Orderings_Oord__class_Oless__eq(_169777, c_Groups_Ozero__class_Ozero(_169777), _169781), 1383 ^ _124236 : [(1384 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_169777, _169779, _169781) = c_Groups_Ozero__class_Ozero(_169777), 1387 ^ _124236 : [(1388 ^ _124236) ^ [] : [-(_169779 = c_Groups_Ozero__class_Ozero(_169777))], (1390 ^ _124236) ^ [] : [-(_169781 = c_Groups_Ozero__class_Ozero(_169777))]]], (1392 ^ _124236) ^ [] : [-(c_Groups_Oplus__class_Oplus(_169777, _169779, _169781) = c_Groups_Ozero__class_Ozero(_169777)), _169779 = c_Groups_Ozero__class_Ozero(_169777), _169781 = c_Groups_Ozero__class_Ozero(_169777)]]], (1402 ^ _124236) ^ [_170657, _170659, _170661] : [class_Groups_Oordered__comm__monoid__add(_170657), c_Orderings_Oord__class_Oless__eq(_170657, c_Groups_Ozero__class_Ozero(_170657), _170659), c_Orderings_Oord__class_Oless__eq(_170657, c_Groups_Ozero__class_Ozero(_170657), _170661), -(c_Orderings_Oord__class_Oless__eq(_170657, c_Groups_Ozero__class_Ozero(_170657), c_Groups_Oplus__class_Oplus(_170657, _170659, _170661)))], (1416 ^ _124236) ^ [_171083, _171085] : [class_Groups_Olinordered__ab__group__add(_171083), 1419 ^ _124236 : [(1420 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_171083, c_Groups_Oplus__class_Oplus(_171083, _171085, _171085), c_Groups_Ozero__class_Ozero(_171083)), -(c_Orderings_Oord__class_Oless__eq(_171083, _171085, c_Groups_Ozero__class_Ozero(_171083)))], (1426 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_171083, _171085, c_Groups_Ozero__class_Ozero(_171083)), -(c_Orderings_Oord__class_Oless__eq(_171083, c_Groups_Oplus__class_Oplus(_171083, _171085, _171085), c_Groups_Ozero__class_Ozero(_171083)))]]], (1432 ^ _124236) ^ [_171571, _171573] : [class_Groups_Olinordered__ab__group__add(_171571), 1435 ^ _124236 : [(1436 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_171571, c_Groups_Ozero__class_Ozero(_171571), c_Groups_Oplus__class_Oplus(_171571, _171573, _171573)), -(c_Orderings_Oord__class_Oless__eq(_171571, c_Groups_Ozero__class_Ozero(_171571), _171573))], (1442 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_171571, c_Groups_Ozero__class_Ozero(_171571), _171573), -(c_Orderings_Oord__class_Oless__eq(_171571, c_Groups_Ozero__class_Ozero(_171571), c_Groups_Oplus__class_Oplus(_171571, _171573, _171573)))]]], (1448 ^ _124236) ^ [_172073, _172075, _172077] : [class_Orderings_Olinorder(_172073), -(c_Orderings_Oord__class_Oless__eq(_172073, _172075, _172077)), -(c_Orderings_Oord__class_Oless__eq(_172073, _172077, _172075))], (1458 ^ _124236) ^ [_172429, _172431, _172433, _172435, _172437] : [class_Orderings_Oord(_172429), c_Orderings_Oord__class_Oless__eq(tc_fun(_172431, _172429), _172433, _172435), -(c_Orderings_Oord__class_Oless__eq(_172429, hAPP(_172433, _172437), hAPP(_172435, _172437)))], (1468 ^ _124236) ^ [_172806, _172808, _172810, _172812] : [class_Orderings_Oorder(_172806), c_Orderings_Oord__class_Oless__eq(_172806, _172808, _172810), c_Orderings_Oord__class_Oless__eq(_172806, _172812, _172808), -(c_Orderings_Oord__class_Oless__eq(_172806, _172812, _172810))], (1482 ^ _124236) ^ [_173240, _173242, _173244] : [class_Orderings_Oorder(_173240), c_Orderings_Oord__class_Oless__eq(_173240, _173242, _173244), c_Orderings_Oord__class_Oless__eq(_173240, _173244, _173242), -(_173244 = _173242)], (1496 ^ _124236) ^ [_173672, _173674, _173676, _173678] : [class_Orderings_Opreorder(_173672), c_Orderings_Oord__class_Oless__eq(_173672, _173674, _173676), c_Orderings_Oord__class_Oless__eq(_173672, _173676, _173678), -(c_Orderings_Oord__class_Oless__eq(_173672, _173674, _173678))], (1510 ^ _124236) ^ [_174106, _174108, _174110] : [class_Orderings_Oorder(_174106), c_Orderings_Oord__class_Oless__eq(_174106, _174108, _174110), c_Orderings_Oord__class_Oless__eq(_174106, _174110, _174108), -(_174108 = _174110)], (1524 ^ _124236) ^ [_174538, _174540, _174542, _174544] : [class_Orderings_Oorder(_174538), c_Orderings_Oord__class_Oless__eq(_174538, _174540, _174542), _174540 = _174544, -(c_Orderings_Oord__class_Oless__eq(_174538, _174544, _174542))], (1538 ^ _124236) ^ [_174984, _174986, _174988, _174990] : [class_Orderings_Oord(_174984), c_Orderings_Oord__class_Oless__eq(_174984, _174986, _174988), _174988 = _174990, -(c_Orderings_Oord__class_Oless__eq(_174984, _174986, _174990))], (1552 ^ _124236) ^ [_175430, _175432, _175434, _175436] : [class_Orderings_Oorder(_175430), _175432 = _175434, c_Orderings_Oord__class_Oless__eq(_175430, _175436, _175434), -(c_Orderings_Oord__class_Oless__eq(_175430, _175436, _175432))], (1566 ^ _124236) ^ [_175876, _175878, _175880, _175882] : [class_Orderings_Oord(_175876), _175878 = _175880, c_Orderings_Oord__class_Oless__eq(_175876, _175880, _175882), -(c_Orderings_Oord__class_Oless__eq(_175876, _175878, _175882))], (1580 ^ _124236) ^ [_176308, _176310, _176312] : [class_Orderings_Oorder(_176308), c_Orderings_Oord__class_Oless__eq(_176308, _176310, _176312), 1587 ^ _124236 : [(1588 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_176308, _176312, _176310), -(_176312 = _176310)], (1594 ^ _124236) ^ [] : [_176312 = _176310, -(c_Orderings_Oord__class_Oless__eq(_176308, _176312, _176310))]]], (1600 ^ _124236) ^ [_176922, _176924, _176926, _176928, _176930] : [class_Orderings_Oord(_176922), c_Orderings_Oord__class_Oless__eq(tc_fun(_176924, _176922), _176926, _176928), -(c_Orderings_Oord__class_Oless__eq(_176922, hAPP(_176926, _176930), hAPP(_176928, _176930)))], (1610 ^ _124236) ^ [_177285, _177287, _177289] : [class_Orderings_Opreorder(_177285), _177287 = _177289, -(c_Orderings_Oord__class_Oless__eq(_177285, _177287, _177289))], (1620 ^ _124236) ^ [_177608, _177610, _177612] : [class_Orderings_Oorder(_177608), 1623 ^ _124236 : [(1624 ^ _124236) ^ [] : [_177610 = _177612, 1627 ^ _124236 : [(1628 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_177608, _177610, _177612))], (1630 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_177608, _177612, _177610))]]], (1632 ^ _124236) ^ [] : [-(_177610 = _177612), c_Orderings_Oord__class_Oless__eq(_177608, _177610, _177612), c_Orderings_Oord__class_Oless__eq(_177608, _177612, _177610)]]], (1642 ^ _124236) ^ [_178266, _178268, _178270] : [class_Orderings_Olinorder(_178266), -(c_Orderings_Oord__class_Oless__eq(_178266, _178268, _178270)), -(c_Orderings_Oord__class_Oless__eq(_178266, _178270, _178268))], (1652 ^ _124236) ^ [_178606, _178608, _178610, _178612] : [class_Orderings_Oord(_178606), 1655 ^ _124236 : [(1656 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_178608, _178606), _178610, _178612), 1659 ^ _124236 : [(1660 ^ _124236) ^ [_178865] : [-(c_Orderings_Oord__class_Oless__eq(_178606, hAPP(_178610, _178865), hAPP(_178612, _178865)))]]], (1662 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_178606, hAPP(_178610, 1663 ^ [_178606, _178608, _178610, _178612]), hAPP(_178612, 1663 ^ [_178606, _178608, _178610, _178612])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_178608, _178606), _178610, _178612))]]], (1669 ^ _124236) ^ [_179218, _179220] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _179218), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _179218, _179220)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _179220))))], (1671 ^ _124236) ^ [_179373, _179375, _179377, _179379] : [class_Groups_Ocancel__semigroup__add(_179373), c_Groups_Oplus__class_Oplus(_179373, _179375, _179377) = c_Groups_Oplus__class_Oplus(_179373, _179379, _179377), -(_179375 = _179379)], (1681 ^ _124236) ^ [_179734, _179736, _179738, _179740] : [class_Groups_Ocancel__ab__semigroup__add(_179734), c_Groups_Oplus__class_Oplus(_179734, _179736, _179738) = c_Groups_Oplus__class_Oplus(_179734, _179736, _179740), -(_179738 = _179740)], (1691 ^ _124236) ^ [_180095, _180097, _180099, _180101] : [class_Groups_Ocancel__semigroup__add(_180095), c_Groups_Oplus__class_Oplus(_180095, _180097, _180099) = c_Groups_Oplus__class_Oplus(_180095, _180097, _180101), -(_180099 = _180101)], (1701 ^ _124236) ^ [_180456, _180458, _180460, _180462] : [class_Groups_Ocancel__semigroup__add(_180456), 1704 ^ _124236 : [(1705 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_180456, _180458, _180460) = c_Groups_Oplus__class_Oplus(_180456, _180462, _180460), -(_180458 = _180462)], (1711 ^ _124236) ^ [] : [_180458 = _180462, -(c_Groups_Oplus__class_Oplus(_180456, _180458, _180460) = c_Groups_Oplus__class_Oplus(_180456, _180462, _180460))]]], (1717 ^ _124236) ^ [_180998, _181000, _181002, _181004] : [class_Groups_Ocancel__semigroup__add(_180998), 1720 ^ _124236 : [(1721 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_180998, _181000, _181002) = c_Groups_Oplus__class_Oplus(_180998, _181000, _181004), -(_181002 = _181004)], (1727 ^ _124236) ^ [] : [_181002 = _181004, -(c_Groups_Oplus__class_Oplus(_180998, _181000, _181002) = c_Groups_Oplus__class_Oplus(_180998, _181000, _181004))]]], (1733 ^ _124236) ^ [_181540, _181542, _181544, _181546] : [class_Groups_Oab__semigroup__add(_181540), -(c_Groups_Oplus__class_Oplus(_181540, c_Groups_Oplus__class_Oplus(_181540, _181542, _181544), _181546) = c_Groups_Oplus__class_Oplus(_181540, _181542, c_Groups_Oplus__class_Oplus(_181540, _181544, _181546)))], (1739 ^ _124236) ^ [_181792, _181794] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _181792, _181794), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _181794, _181792), -(_181792 = _181794)], (1749 ^ _124236) ^ [_182109, _182111, _182113] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _182109, _182111), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _182111, _182113), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _182109, _182113))], (1759 ^ _124236) ^ [_182424, _182426] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _182424, _182426)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _182426, _182424))], (1765 ^ _124236) ^ [_182610] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _182610, _182610))], (1767 ^ _124236) ^ [_182760, _182762, _182764, _182766, _182768] : [class_Groups_Ozero(_182760), 1770 ^ _124236 : [(1771 ^ _124236) ^ [] : [c_Polynomial_OpCons(_182760, _182762, _182764) = c_Polynomial_OpCons(_182760, _182766, _182768), 1774 ^ _124236 : [(1775 ^ _124236) ^ [] : [-(_182762 = _182766)], (1777 ^ _124236) ^ [] : [-(_182764 = _182768)]]], (1779 ^ _124236) ^ [] : [-(c_Polynomial_OpCons(_182760, _182762, _182764) = c_Polynomial_OpCons(_182760, _182766, _182768)), _182762 = _182766, _182764 = _182768]]], (1789 ^ _124236) ^ [_183480, _183482, _183484] : [class_Int_Oring__char__0(_183480), class_Rings_Oidom(_183480), 1796 ^ _124236 : [(1797 ^ _124236) ^ [] : [c_Polynomial_Opoly(_183480, _183482) = c_Polynomial_Opoly(_183480, _183484), -(_183482 = _183484)], (1803 ^ _124236) ^ [] : [_183482 = _183484, -(c_Polynomial_Opoly(_183480, _183482) = c_Polynomial_Opoly(_183480, _183484))]]], (1809 ^ _124236) ^ [_184093, _184095, _184097, _184099] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_184093), c_Orderings_Oord__class_Oless__eq(_184093, c_Groups_Oplus__class_Oplus(_184093, _184095, _184097), c_Groups_Oplus__class_Oplus(_184093, _184095, _184099)), -(c_Orderings_Oord__class_Oless__eq(_184093, _184097, _184099))], (1819 ^ _124236) ^ [_184458, _184460, _184462, _184464] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_184458), c_Orderings_Oord__class_Oless__eq(_184458, c_Groups_Oplus__class_Oplus(_184458, _184460, _184462), c_Groups_Oplus__class_Oplus(_184458, _184464, _184462)), -(c_Orderings_Oord__class_Oless__eq(_184458, _184460, _184464))], (1829 ^ _124236) ^ [_184809, _184811, _184813] : [class_Rings_Oidom(_184809), 1832 ^ _124236 : [(1843 ^ _124236) ^ [] : [1844 ^ _124236 : [(1845 ^ _124236) ^ [] : [_184811 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_184809))], (1847 ^ _124236) ^ [] : [-(c_Polynomial_Oorder(_184809, _184813, _184811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_184809, _184811), _184813) = c_Groups_Ozero__class_Ozero(_184809))], (1833 ^ _124236) ^ [] : [hAPP(c_Polynomial_Opoly(_184809, _184811), _184813) = c_Groups_Ozero__class_Ozero(_184809), -(_184811 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_184809))), c_Polynomial_Oorder(_184809, _184813, _184811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (1851 ^ _124236) ^ [_185497, _185499] : [class_Groups_Olinordered__ab__group__add(_185497), 1854 ^ _124236 : [(1855 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_185497, _185499, _185499) = c_Groups_Ozero__class_Ozero(_185497), -(_185499 = c_Groups_Ozero__class_Ozero(_185497))], (1861 ^ _124236) ^ [] : [_185499 = c_Groups_Ozero__class_Ozero(_185497), -(c_Groups_Oplus__class_Oplus(_185497, _185499, _185499) = c_Groups_Ozero__class_Ozero(_185497))]]], (1867 ^ _124236) ^ [_185993, _185995, _185997] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_185993), 1870 ^ _124236 : [(1871 ^ _124236) ^ [] : [_185995 = c_Groups_Oplus__class_Oplus(_185993, _185995, _185997), -(_185997 = c_Groups_Ozero__class_Ozero(_185993))], (1877 ^ _124236) ^ [] : [_185997 = c_Groups_Ozero__class_Ozero(_185993), -(_185995 = c_Groups_Oplus__class_Oplus(_185993, _185995, _185997))]]], (1883 ^ _124236) ^ [_186485, _186487] : [class_Rings_Ocomm__semiring__1(_186485), -(c_Groups_Oplus__class_Oplus(_186485, _186487, c_Groups_Ozero__class_Ozero(_186485)) = _186487)], (1889 ^ _124236) ^ [_186705, _186707] : [class_Rings_Ocomm__semiring__1(_186705), -(c_Groups_Oplus__class_Oplus(_186705, c_Groups_Ozero__class_Ozero(_186705), _186707) = _186707)], (1895 ^ _124236) ^ [_186981, _186983, _186985, _186987, _186989, _186991] : [class_Groups_Ozero(_186981), hAPP(hAPP(hAPP(_186983, c_Groups_Ozero__class_Ozero(_186981)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_186981))), _186985) = _186985, -(c_Polynomial_Opoly__rec(_186987, _186981, _186985, _186983, c_Polynomial_OpCons(_186981, _186989, _186991)) = hAPP(hAPP(hAPP(_186983, _186989), _186991), c_Polynomial_Opoly__rec(_186987, _186981, _186985, _186983, _186991)))], (1905 ^ _124236) ^ [_187454, _187456, _187458, _187460, _187462, _187464] : [class_Groups_Ozero(_187454), -(c_Polynomial_Opoly__rec(_187456, _187454, _187458, _187460, c_Polynomial_OpCons(_187454, _187462, _187464)) = hAPP(hAPP(hAPP(_187460, _187462), _187464), c_If(_187456, c_fequal(_187464, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_187454))), _187458, c_Polynomial_Opoly__rec(_187456, _187454, _187458, _187460, _187464))))], (1912 ^ _124236) ^ [_187849, _187851, _187853] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _187849), _187851), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _187853), 1910 ^ [_187851, _187853])), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _187853), _187849))))], (1918 ^ _124236) ^ [_188139, _188141, _188143] : [class_Rings_Ocomm__semiring__0(_188139), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_188139, c_Polynomial_OpCons(_188139, _188141, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_188139))), _188143) = c_Polynomial_OpCons(_188139, _188141, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_188139))))], (1924 ^ _124236) ^ [_188421, _188423, _188425, _188427] : [class_Groups_Ozero(_188421), hAPP(hAPP(hAPP(_188423, c_Groups_Ozero__class_Ozero(_188421)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_188421))), _188425) = _188425, -(c_Polynomial_Opoly__rec(_188427, _188421, _188425, _188423, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_188421))) = _188425)], (1934 ^ _124236) ^ [_188816, _188818, _188820, _188822] : [class_Rings_Ocomm__semiring__0(_188816), -(c_Polynomial_Osynthetic__div(_188816, c_Polynomial_OpCons(_188816, _188818, _188820), _188822) = c_Polynomial_OpCons(_188816, hAPP(c_Polynomial_Opoly(_188816, _188820), _188822), c_Polynomial_Osynthetic__div(_188816, _188820, _188822)))], (1940 ^ _124236) ^ [_189108, _189110, _189112, _189114] : [class_Rings_Ocomm__semiring__0(_189108), -(hAPP(c_Polynomial_Opoly(_189108, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_189108, _189110, _189112)), _189114) = hAPP(c_Polynomial_Opoly(_189108, _189110), c_Groups_Oplus__class_Oplus(_189108, _189112, _189114)))], (1946 ^ _124236) ^ [_189368, _189370] : [class_Rings_Ocomm__semiring__0(_189368), -(c_Polynomial_Osynthetic__div(_189368, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_189368)), _189370) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_189368)))], (1952 ^ _124236) ^ [_189600, _189602] : [class_RealVector_Oreal__normed__vector(_189600), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_189600, _189602)))], (1958 ^ _124236) ^ [_189830, _189832, _189834] : [class_Rings_Ocomm__semiring__0(_189830), 1961 ^ _124236 : [(1962 ^ _124236) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_189830, _189832, _189834) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_189830)), -(_189832 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_189830)))], (1968 ^ _124236) ^ [] : [_189832 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_189830)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_189830, _189832, _189834) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_189830)))]]], (1974 ^ _124236) ^ [_190340, _190342] : [class_Rings_Ocomm__semiring__0(_190340), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_190340, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_190340)), _190342) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_190340)))], (1980 ^ _124236) ^ [_190586, _190588, _190590] : [class_Rings_Ocomm__semiring__1(_190586), -(c_Groups_Oplus__class_Oplus(_190586, _190588, _190590) = c_Groups_Oplus__class_Oplus(_190586, _190590, _190588))], (1986 ^ _124236) ^ [_190844, _190846, _190848, _190850] : [class_Rings_Ocomm__semiring__1(_190844), -(c_Groups_Oplus__class_Oplus(_190844, _190846, c_Groups_Oplus__class_Oplus(_190844, _190848, _190850)) = c_Groups_Oplus__class_Oplus(_190844, _190848, c_Groups_Oplus__class_Oplus(_190844, _190846, _190850)))], (1992 ^ _124236) ^ [_191124, _191126, _191128, _191130] : [class_Rings_Ocomm__semiring__1(_191124), -(c_Groups_Oplus__class_Oplus(_191124, _191126, c_Groups_Oplus__class_Oplus(_191124, _191128, _191130)) = c_Groups_Oplus__class_Oplus(_191124, c_Groups_Oplus__class_Oplus(_191124, _191126, _191128), _191130))], (1998 ^ _124236) ^ [_191404, _191406, _191408, _191410] : [class_Rings_Ocomm__semiring__1(_191404), -(c_Groups_Oplus__class_Oplus(_191404, c_Groups_Oplus__class_Oplus(_191404, _191406, _191408), _191410) = c_Groups_Oplus__class_Oplus(_191404, _191406, c_Groups_Oplus__class_Oplus(_191404, _191408, _191410)))], (2004 ^ _124236) ^ [_191684, _191686, _191688, _191690] : [class_Rings_Ocomm__semiring__1(_191684), -(c_Groups_Oplus__class_Oplus(_191684, c_Groups_Oplus__class_Oplus(_191684, _191686, _191688), _191690) = c_Groups_Oplus__class_Oplus(_191684, c_Groups_Oplus__class_Oplus(_191684, _191686, _191690), _191688))], (2010 ^ _124236) ^ [_191978, _191980, _191982, _191984, _191986] : [class_Rings_Ocomm__semiring__1(_191978), -(c_Groups_Oplus__class_Oplus(_191978, c_Groups_Oplus__class_Oplus(_191978, _191980, _191982), c_Groups_Oplus__class_Oplus(_191978, _191984, _191986)) = c_Groups_Oplus__class_Oplus(_191978, c_Groups_Oplus__class_Oplus(_191978, _191980, _191984), c_Groups_Oplus__class_Oplus(_191978, _191982, _191986)))], (2016 ^ _124236) ^ [_192252, _192254] : [class_Groups_Ozero(_192252), 2019 ^ _124236 : [(2020 ^ _124236) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_192252, _192254) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_192254 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_192252)))], (2026 ^ _124236) ^ [] : [_192254 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_192252)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_192252, _192254) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2032 ^ _124236) ^ [_192702] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _192702))], (2034 ^ _124236) ^ [_192824, _192826, _192828] : [class_Rings_Ocomm__semiring__0(_192824), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_192824), _192826, c_Polynomial_Osmult(_192824, _192828, c_Polynomial_Osynthetic__div(_192824, _192826, _192828))) = c_Polynomial_OpCons(_192824, hAPP(c_Polynomial_Opoly(_192824, _192826), _192828), c_Polynomial_Osynthetic__div(_192824, _192826, _192828)))], (2040 ^ _124236) ^ [_193136, _193138, _193140, _193142, _193144] : [class_Rings_Ocomm__semiring__0(_193136), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_193136), _193138, c_Polynomial_Osmult(_193136, _193140, _193142)) = c_Polynomial_OpCons(_193136, _193144, _193142), 2047 ^ _124236 : [(2048 ^ _124236) ^ [] : [-(_193144 = hAPP(c_Polynomial_Opoly(_193136, _193138), _193140))], (2050 ^ _124236) ^ [] : [-(_193142 = c_Polynomial_Osynthetic__div(_193136, _193138, _193140))]]], (2052 ^ _124236) ^ [_193592, _193594] : [class_Groups_Ozero(_193592), -(c_Polynomial_Omonom(_193592, _193594, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_193592, _193594, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_193592))))], (2058 ^ _124236) ^ [_193866, _193868, _193870, _193872, _193874] : [class_RealVector_Oreal__normed__vector(_193866), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_193866, c_Groups_Ominus__class_Ominus(_193866, c_Groups_Oplus__class_Oplus(_193866, _193868, _193870), c_Groups_Oplus__class_Oplus(_193866, _193872, _193874))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_193866, c_Groups_Ominus__class_Ominus(_193866, _193868, _193872)), c_RealVector_Onorm__class_Onorm(_193866, c_Groups_Ominus__class_Ominus(_193866, _193870, _193874)))))], (2064 ^ _124236) ^ [_194188, _194190, _194192, _194194] : [class_Rings_Ocomm__semiring__0(_194188), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_194188, c_Polynomial_OpCons(_194188, _194190, _194192), _194194) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_194188), c_Polynomial_Osmult(_194188, _194194, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_194188, _194192, _194194)), c_Polynomial_OpCons(_194188, _194190, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_194188, _194192, _194194))))], (2070 ^ _124236) ^ [_194496, _194498, _194500, _194502] : [class_Rings_Ocomm__semiring__0(_194496), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_194496), c_Polynomial_Osmult(_194496, _194498, _194500), c_Polynomial_OpCons(_194496, _194502, _194500)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_194496)), -(_194500 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_194496)))], (2080 ^ _124236) ^ [_194885, _194887, _194889, _194891] : [class_Rings_Ocomm__semiring__0(_194885), -(hAPP(c_Polynomial_Opoly(_194885, c_Polynomial_OpCons(_194885, _194887, _194889)), _194891) = c_Groups_Oplus__class_Oplus(_194885, _194887, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_194885), _194891), hAPP(c_Polynomial_Opoly(_194885, _194889), _194891))))], (2086 ^ _124236) ^ [_195132] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _195132))], (2088 ^ _124236) ^ [_195211] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _195211, _195211))], (2090 ^ _124236) ^ [_195290] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _195290, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195290), _195290)))], (2092 ^ _124236) ^ [_195389, _195391] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _195389, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _195391, _195389)))], (2094 ^ _124236) ^ [_195488, _195490] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _195488, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _195488, _195490)))], (2096 ^ _124236) ^ [_195573] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _195573, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195573), _195573))))], (2098 ^ _124236) ^ [_195678, _195680] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _195678, _195680), _195678))], (2100 ^ _124236) ^ [_195821, _195823] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _195821, _195823), -(_195823 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _195821, 2103 ^ [_195821, _195823]))], (2107 ^ _124236) ^ [_196054, _196056] : [2108 ^ _124236 : [(2109 ^ _124236) ^ [_196129] : [_196056 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _196054, _196129)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _196054, _196056))], (2113 ^ _124236) ^ [_196298, _196300] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _196298, _196300)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _196300, _196298))], (2119 ^ _124236) ^ [_196527, _196529, _196531] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _196527, _196529), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _196531, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _196529, _196527)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _196531, _196527), _196529))], (2125 ^ _124236) ^ [_196820, _196822, _196824] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _196820, _196822), _196824), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _196820, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _196824, _196822)))], (2131 ^ _124236) ^ [_197008, _197010, _197012] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _197008, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _197012, _197010)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _197008, _197010), _197012))], (2137 ^ _124236) ^ [_197289, _197291, _197293] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _197289, _197291), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _197289, _197293)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _197291, _197293))], (2143 ^ _124236) ^ [_197477, _197479, _197481] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _197479, _197481), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _197477, _197479), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _197477, _197481)))], (2149 ^ _124236) ^ [_197757, _197759, _197761, _197763, _197765] : [class_Rings_Ocomm__semiring__0(_197757), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_197757)), c_Polynomial_Omonom(_197757, _197759, _197761)), c_Polynomial_Omonom(_197757, _197763, _197765)) = c_Polynomial_Omonom(_197757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197757), _197759), _197763), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _197761, _197765)))], (2155 ^ _124236) ^ [_198051, _198053] : [_198051 = _198053, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _198051, _198053))], (2161 ^ _124236) ^ [_198277, _198279, _198281] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _198277, _198279), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _198277, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _198279, _198281)))], (2167 ^ _124236) ^ [_198519, _198521, _198523] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _198519, _198521), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _198519, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _198523, _198521)))], (2173 ^ _124236) ^ [_198761, _198763, _198765] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _198761, _198763), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _198765, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _198763, _198765), _198761)))], (2179 ^ _124236) ^ [_199011, _199013, _199015] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _199011, _199013), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _199011, _199015), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _199013, _199015)))], (2185 ^ _124236) ^ [_199261, _199263, _199265] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _199261, _199263), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _199261), _199265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _199263), _199265)))], (2191 ^ _124236) ^ [_199519, _199521, _199523] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _199519, _199521), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _199523), _199519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _199523), _199521)))], (2197 ^ _124236) ^ [_199777, _199779, _199781] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _199777, _199779), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _199781, _199779), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _199781, _199777)))], (2203 ^ _124236) ^ [_200027, _200029, _200031] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _200027, _200029), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _200027, _200031), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _200029, _200031)))], (2209 ^ _124236) ^ [_200263, _200265] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _200263, _200265), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _200265, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _200265, _200263)) = _200263)], (2215 ^ _124236) ^ [_200491, _200493] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _200491, _200493), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _200491, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _200493, _200491)) = _200493)], (2221 ^ _124236) ^ [_200733, _200735, _200737] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _200733, _200735), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _200737, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _200735, _200733)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _200737, _200735), _200733))], (2227 ^ _124236) ^ [_200997, _200999, _201001] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _200997, _200999), 2230 ^ _124236 : [(2231 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _201001, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _200999, _200997)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _201001, _200997), _200999))], (2237 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _201001, _200997), _200999), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _201001, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _200999, _200997)))]]], (2243 ^ _124236) ^ [_201505, _201507] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _201505, _201507), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _201507, _201505), _201505) = _201507)], (2249 ^ _124236) ^ [_201747, _201749, _201751] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _201747, _201749), 2252 ^ _124236 : [(2253 ^ _124236) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _201749, _201747) = _201751, -(_201749 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _201751, _201747))], (2259 ^ _124236) ^ [] : [_201749 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _201751, _201747), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _201749, _201747) = _201751)]]], (2265 ^ _124236) ^ [_202263, _202265, _202267] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _202263, _202265), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _202267, _202265), _202263) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _202267, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _202265, _202263)))], (2271 ^ _124236) ^ [_202527, _202529, _202531] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _202527, _202529), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _202529, _202527), _202531) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _202529, _202531), _202527))], (2277 ^ _124236) ^ [_202791, _202793, _202795] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _202791, _202793), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _202793, _202795), _202791) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _202793, _202791), _202795))], (2283 ^ _124236) ^ [_203055, _203057, _203059] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _203055, _203057), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _203057, _203059), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _203055, _203059))], (2293 ^ _124236) ^ [_203370, _203372] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _203370, _203372), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _203372, _203370), -(_203370 = _203372)], (2303 ^ _124236) ^ [_203701, _203703, _203705, _203707] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _203701, _203703), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _203705, _203707), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _203701, _203705), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _203703, _203707)))], (2313 ^ _124236) ^ [_204070, _204072, _204074, _204076] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _204070, _204072), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _204074, _204076), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _204070), _204074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _204072), _204076)))], (2323 ^ _124236) ^ [_204433, _204435, _204437] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _204433, _204435), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _204433, _204437), 2330 ^ _124236 : [(2331 ^ _124236) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _204435, _204433) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _204437, _204433), -(_204435 = _204437)], (2337 ^ _124236) ^ [] : [_204435 = _204437, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _204435, _204433) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _204437, _204433))]]], (2343 ^ _124236) ^ [_205044, _205046, _205048] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _205044, _205046), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _205044, _205048), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _205046, _205044), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _205048, _205044)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _205046, _205048))], (2353 ^ _124236) ^ [_205403, _205405, _205407] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _205403, _205405), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _205403, _205407), 2360 ^ _124236 : [(2361 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _205405, _205403), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _205407, _205403)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _205405, _205407))], (2367 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _205405, _205407), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _205405, _205403), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _205407, _205403)))]]], (2373 ^ _124236) ^ [_206020, _206022, _206024] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _206020, _206022), _206024), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _206022, _206024))], (2379 ^ _124236) ^ [_206262, _206264, _206266] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _206262, _206264), _206266), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _206262, _206266))], (2385 ^ _124236) ^ [_206504, _206506, _206508] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _206504, _206506), _206508), 2388 ^ _124236 : [(2389 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _206504, _206508))], (2391 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _206506, _206508))]]], (2393 ^ _124236) ^ [_206857, _206859, _206861, _206863, _206865] : [class_Rings_Ocomm__semiring__1(_206857), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_206857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_206857), _206859), _206861)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_206857), _206863), _206865)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_206857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_206857), _206859), _206863)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_206857), _206861), _206865)))], (2399 ^ _124236) ^ [_207221, _207223, _207225, _207227, _207229] : [class_Rings_Ocomm__semiring__1(_207221), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207221), _207223), _207225)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207221), _207227), _207229)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207221), _207227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207221), _207223), _207225)), _207229)))], (2405 ^ _124236) ^ [_207585, _207587, _207589, _207591, _207593] : [class_Rings_Ocomm__semiring__1(_207585), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207585), _207587), _207589)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207585), _207591), _207593)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207585), _207587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207585), _207589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207585), _207591), _207593))))], (2411 ^ _124236) ^ [_207935, _207937, _207939, _207941] : [class_Rings_Ocomm__semiring__1(_207935), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207935), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207935), _207937), _207939)), _207941) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207935), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207935), _207937), _207941)), _207939))], (2417 ^ _124236) ^ [_208247, _208249, _208251, _208253] : [class_Rings_Ocomm__semiring__1(_208247), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208247), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208247), _208249), _208251)), _208253) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208247), _208249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208247), _208251), _208253)))], (2423 ^ _124236) ^ [_208559, _208561, _208563, _208565] : [class_Rings_Ocomm__semiring__1(_208559), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208559), _208561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208559), _208563), _208565)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208559), _208561), _208563)), _208565))], (2429 ^ _124236) ^ [_208871, _208873, _208875, _208877] : [class_Rings_Ocomm__semiring__1(_208871), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208871), _208873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208871), _208875), _208877)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208871), _208875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208871), _208873), _208877)))], (2435 ^ _124236) ^ [_209169, _209171, _209173] : [class_Rings_Ocomm__semiring__1(_209169), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209169), _209171), _209173) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209169), _209173), _209171))], (2441 ^ _124236) ^ [_209457, _209459, _209461, _209463, _209465] : [class_RealVector_Oreal__normed__algebra(_209457), -(c_Groups_Ominus__class_Ominus(_209457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209457), _209459), _209461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209457), _209463), _209465)) = c_Groups_Oplus__class_Oplus(_209457, c_Groups_Oplus__class_Oplus(_209457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209457), c_Groups_Ominus__class_Ominus(_209457, _209459, _209463)), c_Groups_Ominus__class_Ominus(_209457, _209461, _209465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209457), c_Groups_Ominus__class_Ominus(_209457, _209459, _209463)), _209465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209457), _209463), c_Groups_Ominus__class_Ominus(_209457, _209461, _209465))))], (2447 ^ _124236) ^ [_209861, _209863, _209865, _209867, _209869] : [class_Rings_Oring(_209861), -(c_Groups_Ominus__class_Ominus(_209861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209861), _209863), _209865), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209861), _209867), _209869)) = c_Groups_Oplus__class_Oplus(_209861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209861), _209863), c_Groups_Ominus__class_Ominus(_209861, _209865, _209869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209861), c_Groups_Ominus__class_Ominus(_209861, _209863, _209867)), _209869)))], (2453 ^ _124236) ^ [_210225, _210227, _210229, _210231, _210233] : [class_Groups_Oab__group__add(_210225), c_Groups_Ominus__class_Ominus(_210225, _210227, _210229) = c_Groups_Ominus__class_Ominus(_210225, _210231, _210233), 2460 ^ _124236 : [(2461 ^ _124236) ^ [] : [_210227 = _210229, -(_210231 = _210233)], (2467 ^ _124236) ^ [] : [_210231 = _210233, -(_210227 = _210229)]]], (2473 ^ _124236) ^ [_210876, _210878, _210880, _210882] : [class_Groups_Oab__group__add(_210876), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_210876), c_Polynomial_Omonom(_210876, _210878, _210880), c_Polynomial_Omonom(_210876, _210882, _210880)) = c_Polynomial_Omonom(_210876, c_Groups_Ominus__class_Ominus(_210876, _210878, _210882), _210880))], (2479 ^ _124236) ^ [_211168, _211170, _211172, _211174] : [class_Groups_Ozero(_211168), 2482 ^ _124236 : [(2483 ^ _124236) ^ [] : [c_Polynomial_Omonom(_211168, _211170, _211172) = c_Polynomial_Omonom(_211168, _211174, _211172), -(_211170 = _211174)], (2489 ^ _124236) ^ [] : [_211170 = _211174, -(c_Polynomial_Omonom(_211168, _211170, _211172) = c_Polynomial_Omonom(_211168, _211174, _211172))]]], (2495 ^ _124236) ^ [_211710, _211712, _211714, _211716] : [class_RealVector_Oreal__normed__algebra(_211710), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_211710), c_Groups_Ominus__class_Ominus(_211710, _211712, _211714)), _211716) = c_Groups_Ominus__class_Ominus(_211710, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_211710), _211712), _211716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_211710), _211714), _211716)))], (2501 ^ _124236) ^ [_212022, _212024, _212026, _212028] : [class_RealVector_Oreal__normed__algebra(_212022), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212022), c_Groups_Ominus__class_Ominus(_212022, _212024, _212026)), _212028) = c_Groups_Ominus__class_Ominus(_212022, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212022), _212024), _212028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212022), _212026), _212028)))], (2507 ^ _124236) ^ [_212334, _212336, _212338, _212340] : [class_Rings_Ocomm__ring(_212334), -(c_Polynomial_Osmult(_212334, c_Groups_Ominus__class_Ominus(_212334, _212336, _212338), _212340) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_212334), c_Polynomial_Osmult(_212334, _212336, _212340), c_Polynomial_Osmult(_212334, _212338, _212340)))], (2513 ^ _124236) ^ [_212626, _212628, _212630, _212632] : [class_Groups_Oab__semigroup__mult(_212626), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212626), _212628), _212630)), _212632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212626), _212628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212626), _212630), _212632)))], (2519 ^ _124236) ^ [_212938, _212940, _212942, _212944] : [class_Rings_Ocomm__semiring__0(_212938), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_212938)), c_Polynomial_Osmult(_212938, _212940, _212942)), _212944) = c_Polynomial_Osmult(_212938, _212940, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_212938)), _212942), _212944)))], (2525 ^ _124236) ^ [_213242, _213244, _213246, _213248] : [class_RealVector_Oreal__normed__algebra(_213242), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213242), _213244), c_Groups_Ominus__class_Ominus(_213242, _213246, _213248)) = c_Groups_Ominus__class_Ominus(_213242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213242), _213244), _213246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213242), _213244), _213248)))], (2531 ^ _124236) ^ [_213554, _213556, _213558, _213560] : [class_RealVector_Oreal__normed__algebra(_213554), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213554), _213556), c_Groups_Ominus__class_Ominus(_213554, _213558, _213560)) = c_Groups_Ominus__class_Ominus(_213554, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213554), _213556), _213558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213554), _213556), _213560)))], (2537 ^ _124236) ^ [_213866, _213868, _213870, _213872] : [class_Rings_Ocomm__ring(_213866), -(c_Polynomial_Osmult(_213866, _213868, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_213866), _213870, _213872)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_213866), c_Polynomial_Osmult(_213866, _213868, _213870), c_Polynomial_Osmult(_213866, _213868, _213872)))], (2543 ^ _124236) ^ [_214162, _214164, _214166, _214168] : [class_Rings_Ocomm__semiring__0(_214162), -(c_Polynomial_Osmult(_214162, _214164, c_Polynomial_Osmult(_214162, _214166, _214168)) = c_Polynomial_Osmult(_214162, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_214162), _214164), _214166), _214168))], (2549 ^ _124236) ^ [_214450, _214452, _214454, _214456] : [class_Rings_Ocomm__semiring__0(_214450), -(c_Polynomial_Osmult(_214450, _214452, c_Polynomial_Omonom(_214450, _214454, _214456)) = c_Polynomial_Omonom(_214450, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_214450), _214452), _214454), _214456))], (2555 ^ _124236) ^ [_214738, _214740, _214742, _214744] : [class_Rings_Ocomm__semiring__0(_214738), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_214738)), _214740), c_Polynomial_Osmult(_214738, _214742, _214744)) = c_Polynomial_Osmult(_214738, _214742, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_214738)), _214740), _214744)))], (2561 ^ _124236) ^ [_215056, _215058, _215060, _215062, _215064] : [class_Groups_Oab__group__add(_215056), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_215056), c_Polynomial_OpCons(_215056, _215058, _215060), c_Polynomial_OpCons(_215056, _215062, _215064)) = c_Polynomial_OpCons(_215056, c_Groups_Ominus__class_Ominus(_215056, _215058, _215062), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_215056), _215060, _215064)))], (2567 ^ _124236) ^ [_215352, _215354, _215356] : [class_RealVector_Oreal__normed__div__algebra(_215352), -(c_RealVector_Onorm__class_Onorm(_215352, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_215352), _215354), _215356)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_215352, _215354)), c_RealVector_Onorm__class_Onorm(_215352, _215356)))], (2573 ^ _124236) ^ [_215640, _215642, _215644, _215646] : [class_Rings_Ocomm__semiring__0(_215640), -(c_Polynomial_Osmult(_215640, _215642, c_Polynomial_OpCons(_215640, _215644, _215646)) = c_Polynomial_OpCons(_215640, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_215640), _215642), _215644), c_Polynomial_Osmult(_215640, _215642, _215646)))], (2579 ^ _124236) ^ [_215936, _215938, _215940, _215942] : [class_Rings_Ocomm__ring(_215936), -(hAPP(c_Polynomial_Opoly(_215936, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_215936), _215938, _215940)), _215942) = c_Groups_Ominus__class_Ominus(_215936, hAPP(c_Polynomial_Opoly(_215936, _215938), _215942), hAPP(c_Polynomial_Opoly(_215936, _215940), _215942)))], (2585 ^ _124236) ^ [_216240, _216242, _216244, _216246] : [class_Rings_Ocomm__semiring__0(_216240), -(hAPP(c_Polynomial_Opoly(_216240, c_Polynomial_Osmult(_216240, _216242, _216244)), _216246) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216240), _216242), hAPP(c_Polynomial_Opoly(_216240, _216244), _216246)))], (2591 ^ _124236) ^ [_216508, _216510] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _216508, _216510) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _216510, _216508) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_216508 = _216510)], (2601 ^ _124236) ^ [_216823, _216825] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _216823, _216825), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _216823, _216825) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2607 ^ _124236) ^ [_217072, _217074] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _217072, _217074) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _217072, _217074))], (2613 ^ _124236) ^ [_217244, _217246] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _217244, _217246), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _217244, _217246) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2619 ^ _124236) ^ [_217451, _217453] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _217451, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _217451, _217453)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2621 ^ _124236) ^ [_217539] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _217539, _217539) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2623 ^ _124236) ^ [_217621] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _217621, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _217621)], (2625 ^ _124236) ^ [_217703] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _217703) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2627 ^ _124236) ^ [_217842, _217844, _217846, _217848] : [class_Rings_Ocomm__semiring__0(_217842), -(hAPP(c_Polynomial_Opoly(_217842, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_217842)), _217844), _217846)), _217848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_217842), hAPP(c_Polynomial_Opoly(_217842, _217844), _217848)), hAPP(c_Polynomial_Opoly(_217842, _217846), _217848)))], (2643 ^ _124236) ^ [_218463, _218465, _218467] : [2644 ^ _124236 : [(2645 ^ _124236) ^ [] : [_218463 = _218467], (2647 ^ _124236) ^ [] : [_218465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _218463), _218465) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _218467), _218465))], (2633 ^ _124236) ^ [_218177, _218179, _218181] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _218177), _218179) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _218181), _218179), -(_218177 = _218181), -(_218179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2661 ^ _124236) ^ [_219110, _219112, _219114] : [2662 ^ _124236 : [(2663 ^ _124236) ^ [] : [_219112 = _219114], (2665 ^ _124236) ^ [] : [_219110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _219110), _219112) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _219110), _219114))], (2651 ^ _124236) ^ [_218824, _218826, _218828] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _218824), _218826) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _218824), _218828), -(_218826 = _218828), -(_218824 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2679 ^ _124236) ^ [_219721, _219723] : [2680 ^ _124236 : [(2681 ^ _124236) ^ [] : [_219721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2683 ^ _124236) ^ [] : [_219723 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _219721), _219723) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2669 ^ _124236) ^ [_219457, _219459] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _219457), _219459) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_219457 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_219459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2687 ^ _124236) ^ [_219990] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _219990), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2689 ^ _124236) ^ [_220074] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _220074) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2691 ^ _124236) ^ [_220198, _220200, _220202] : [class_RealVector_Oreal__normed__vector(_220198), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_220198, _220200), c_RealVector_Onorm__class_Onorm(_220198, _220202)), c_RealVector_Onorm__class_Onorm(_220198, c_Groups_Ominus__class_Ominus(_220198, _220200, _220202))))], (2697 ^ _124236) ^ [_220462, _220464, _220466] : [class_RealVector_Oreal__normed__algebra(_220462), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_220462, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_220462), _220464), _220466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_220462, _220464)), c_RealVector_Onorm__class_Onorm(_220462, _220466))))], (2703 ^ _124236) ^ [_220724, _220726] : [class_Groups_Ogroup__add(_220724), -(c_Groups_Ominus__class_Ominus(_220724, _220726, c_Groups_Ozero__class_Ozero(_220724)) = _220726)], (2709 ^ _124236) ^ [_220944, _220946] : [class_Groups_Ogroup__add(_220944), -(c_Groups_Ominus__class_Ominus(_220944, _220946, _220946) = c_Groups_Ozero__class_Ozero(_220944))], (2715 ^ _124236) ^ [_221178, _221180, _221182] : [class_Groups_Oab__group__add(_221178), 2718 ^ _124236 : [(2719 ^ _124236) ^ [] : [_221180 = _221182, -(c_Groups_Ominus__class_Ominus(_221178, _221180, _221182) = c_Groups_Ozero__class_Ozero(_221178))], (2725 ^ _124236) ^ [] : [c_Groups_Ominus__class_Ominus(_221178, _221180, _221182) = c_Groups_Ozero__class_Ozero(_221178), -(_221180 = _221182)]]], (2731 ^ _124236) ^ [_221684, _221686, _221688] : [class_Groups_Ogroup__add(_221684), 2734 ^ _124236 : [(2735 ^ _124236) ^ [] : [c_Groups_Ominus__class_Ominus(_221684, _221686, _221688) = c_Groups_Ozero__class_Ozero(_221684), -(_221686 = _221688)], (2741 ^ _124236) ^ [] : [_221686 = _221688, -(c_Groups_Ominus__class_Ominus(_221684, _221686, _221688) = c_Groups_Ozero__class_Ozero(_221684))]]], (2747 ^ _124236) ^ [_222218, _222220, _222222, _222224, _222226] : [class_Groups_Oordered__ab__group__add(_222218), c_Groups_Ominus__class_Ominus(_222218, _222220, _222222) = c_Groups_Ominus__class_Ominus(_222218, _222224, _222226), 2754 ^ _124236 : [(2755 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_222218, _222220, _222222), -(c_Orderings_Oord__class_Oless__eq(_222218, _222224, _222226))], (2761 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_222218, _222224, _222226), -(c_Orderings_Oord__class_Oless__eq(_222218, _222220, _222222))]]], (2767 ^ _124236) ^ [_222861, _222863, _222865] : [class_Groups_Ogroup__add(_222861), -(c_Groups_Ominus__class_Ominus(_222861, c_Groups_Oplus__class_Oplus(_222861, _222863, _222865), _222865) = _222863)], (2773 ^ _124236) ^ [_223105, _223107, _223109] : [class_Groups_Ogroup__add(_223105), -(c_Groups_Oplus__class_Oplus(_223105, c_Groups_Ominus__class_Ominus(_223105, _223107, _223109), _223109) = _223107)], (2779 ^ _124236) ^ [_223335, _223337] : [class_RealVector_Oreal__normed__algebra(_223335), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223335), c_Groups_Ozero__class_Ozero(_223335)), _223337) = c_Groups_Ozero__class_Ozero(_223335))], (2785 ^ _124236) ^ [_223567, _223569] : [class_RealVector_Oreal__normed__algebra(_223567), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223567), c_Groups_Ozero__class_Ozero(_223567)), _223569) = c_Groups_Ozero__class_Ozero(_223567))], (2791 ^ _124236) ^ [_223799, _223801] : [class_RealVector_Oreal__normed__algebra(_223799), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223799), _223801), c_Groups_Ozero__class_Ozero(_223799)) = c_Groups_Ozero__class_Ozero(_223799))], (2797 ^ _124236) ^ [_224031, _224033] : [class_RealVector_Oreal__normed__algebra(_224031), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224031), _224033), c_Groups_Ozero__class_Ozero(_224031)) = c_Groups_Ozero__class_Ozero(_224031))], (2803 ^ _124236) ^ [_224263, _224265] : [class_Rings_Ocomm__semiring__1(_224263), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224263), c_Groups_Ozero__class_Ozero(_224263)), _224265) = c_Groups_Ozero__class_Ozero(_224263))], (2809 ^ _124236) ^ [_224495, _224497] : [class_Rings_Ocomm__semiring__1(_224495), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224495), _224497), c_Groups_Ozero__class_Ozero(_224495)) = c_Groups_Ozero__class_Ozero(_224495))], (2815 ^ _124236) ^ [_224741, _224743, _224745] : [class_RealVector_Oreal__normed__vector(_224741), -(c_RealVector_Onorm__class_Onorm(_224741, c_Groups_Ominus__class_Ominus(_224741, _224743, _224745)) = c_RealVector_Onorm__class_Onorm(_224741, c_Groups_Ominus__class_Ominus(_224741, _224745, _224743)))], (2821 ^ _124236) ^ [_225011, _225013, _225015, _225017] : [class_RealVector_Oreal__normed__algebra(_225011), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225011), c_Groups_Oplus__class_Oplus(_225011, _225013, _225015)), _225017) = c_Groups_Oplus__class_Oplus(_225011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225011), _225013), _225017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225011), _225015), _225017)))], (2827 ^ _124236) ^ [_225323, _225325, _225327, _225329] : [class_RealVector_Oreal__normed__algebra(_225323), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225323), c_Groups_Oplus__class_Oplus(_225323, _225325, _225327)), _225329) = c_Groups_Oplus__class_Oplus(_225323, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225323), _225325), _225329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225323), _225327), _225329)))], (2833 ^ _124236) ^ [_225635, _225637, _225639, _225641] : [class_RealVector_Oreal__normed__algebra(_225635), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225635), _225637), c_Groups_Oplus__class_Oplus(_225635, _225639, _225641)) = c_Groups_Oplus__class_Oplus(_225635, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225635), _225637), _225639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225635), _225637), _225641)))], (2839 ^ _124236) ^ [_225947, _225949, _225951, _225953] : [class_RealVector_Oreal__normed__algebra(_225947), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225947), _225949), c_Groups_Oplus__class_Oplus(_225947, _225951, _225953)) = c_Groups_Oplus__class_Oplus(_225947, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225947), _225949), _225951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225947), _225949), _225953)))], (2845 ^ _124236) ^ [_226273, _226275, _226277, _226279, _226281] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_226273), 2848 ^ _124236 : [(2859 ^ _124236) ^ [] : [2860 ^ _124236 : [(2861 ^ _124236) ^ [] : [_226275 = _226279], (2863 ^ _124236) ^ [] : [_226277 = _226281]], -(c_Groups_Oplus__class_Oplus(_226273, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226273), _226275), _226277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226273), _226279), _226281)) = c_Groups_Oplus__class_Oplus(_226273, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226273), _226275), _226281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226273), _226279), _226277)))], (2849 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_226273, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226273), _226275), _226277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226273), _226279), _226281)) = c_Groups_Oplus__class_Oplus(_226273, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226273), _226275), _226281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226273), _226279), _226277)), -(_226275 = _226279), -(_226277 = _226281)]]], (2867 ^ _124236) ^ [_227103, _227105, _227107, _227109] : [class_Rings_Ocomm__semiring__1(_227103), -(c_Groups_Oplus__class_Oplus(_227103, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227103), _227105), _227107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227103), _227109), _227107)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227103), c_Groups_Oplus__class_Oplus(_227103, _227105, _227109)), _227107))], (2873 ^ _124236) ^ [_227415, _227417, _227419, _227421] : [class_Rings_Ocomm__semiring__1(_227415), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227415), c_Groups_Oplus__class_Oplus(_227415, _227417, _227419)), _227421) = c_Groups_Oplus__class_Oplus(_227415, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227415), _227417), _227421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227415), _227419), _227421)))], (2879 ^ _124236) ^ [_227741, _227743, _227745, _227747, _227749] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_227741), 2882 ^ _124236 : [(2893 ^ _124236) ^ [] : [-(c_Groups_Oplus__class_Oplus(_227741, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227741), _227743), _227747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227741), _227745), _227749)) = c_Groups_Oplus__class_Oplus(_227741, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227741), _227743), _227749), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227741), _227745), _227747))), 2896 ^ _124236 : [(2897 ^ _124236) ^ [] : [_227743 = _227745], (2899 ^ _124236) ^ [] : [_227747 = _227749]]], (2883 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_227741, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227741), _227743), _227747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227741), _227745), _227749)) = c_Groups_Oplus__class_Oplus(_227741, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227741), _227743), _227749), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227741), _227745), _227747)), -(_227743 = _227745), -(_227747 = _227749)]]], (2901 ^ _124236) ^ [_228577, _228579, _228581, _228583] : [class_Rings_Ocomm__semiring__1(_228577), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228577), _228579), c_Groups_Oplus__class_Oplus(_228577, _228581, _228583)) = c_Groups_Oplus__class_Oplus(_228577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228577), _228579), _228581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228577), _228579), _228583)))], (2907 ^ _124236) ^ [_228861, _228863] : [class_Groups_Oab__group__add(_228861), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_228861), _228863, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_228861))) = _228863)], (2913 ^ _124236) ^ [_229103, _229105, _229107] : [-(_229103 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 2916 ^ _124236 : [(2917 ^ _124236) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _229103), _229105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _229103), _229107), -(_229105 = _229107)], (2923 ^ _124236) ^ [] : [_229105 = _229107, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _229103), _229105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _229103), _229107))]]], (2929 ^ _124236) ^ [_229632, _229634, _229636] : [-(_229632 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 2932 ^ _124236 : [(2933 ^ _124236) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _229634), _229632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _229636), _229632), -(_229634 = _229636)], (2939 ^ _124236) ^ [] : [_229634 = _229636, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _229634), _229632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _229636), _229632))]]], (2945 ^ _124236) ^ [_230147, _230149] : [class_Rings_Ocomm__semiring__0(_230147), -(c_Polynomial_Osmult(_230147, _230149, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_230147))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_230147)))], (2951 ^ _124236) ^ [_230378, _230380, _230382] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _230378, _230380)), _230382) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _230378), _230382), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _230380), _230382)))], (2953 ^ _124236) ^ [_230515, _230517] : [class_Rings_Ocomm__semiring__0(_230515), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_230515)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_230515))), _230517) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_230515)))], (2959 ^ _124236) ^ [_230759, _230761] : [class_Rings_Ocomm__semiring__0(_230759), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_230759)), _230761), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_230759))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_230759)))], (2965 ^ _124236) ^ [_231031, _231033, _231035, _231037] : [class_Rings_Ocomm__semiring__0(_231031), -(c_Polynomial_Osmult(_231031, _231033, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_231031), _231035, _231037)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_231031), c_Polynomial_Osmult(_231031, _231033, _231035), c_Polynomial_Osmult(_231031, _231033, _231037)))], (2971 ^ _124236) ^ [_231327, _231329, _231331, _231333] : [class_Rings_Ocomm__semiring__0(_231327), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_231327)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_231327), _231329, _231331)), _231333) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_231327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_231327)), _231329), _231333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_231327)), _231331), _231333)))], (2977 ^ _124236) ^ [_231659, _231661, _231663, _231665] : [class_Rings_Ocomm__semiring__0(_231659), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_231659)), _231661), c_Polynomial_OpCons(_231659, _231663, _231665)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_231659), c_Polynomial_Osmult(_231659, _231663, _231661), c_Polynomial_OpCons(_231659, c_Groups_Ozero__class_Ozero(_231659), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_231659)), _231661), _231665))))], (2983 ^ _124236) ^ [_231987, _231989, _231991, _231993] : [class_Rings_Ocomm__semiring__0(_231987), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_231987)), c_Polynomial_OpCons(_231987, _231989, _231991)), _231993) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_231987), c_Polynomial_Osmult(_231987, _231989, _231993), c_Polynomial_OpCons(_231987, c_Groups_Ozero__class_Ozero(_231987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_231987)), _231991), _231993))))], (2989 ^ _124236) ^ [_232301, _232303, _232305] : [class_Groups_Oordered__ab__group__add(_232301), 2992 ^ _124236 : [(2993 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_232301, _232303, _232305), -(c_Orderings_Oord__class_Oless__eq(_232301, c_Groups_Ominus__class_Ominus(_232301, _232303, _232305), c_Groups_Ozero__class_Ozero(_232301)))], (2999 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_232301, c_Groups_Ominus__class_Ominus(_232301, _232303, _232305), c_Groups_Ozero__class_Ozero(_232301)), -(c_Orderings_Oord__class_Oless__eq(_232301, _232303, _232305))]]], (3005 ^ _124236) ^ [_232855, _232857, _232859, _232861, _232863, _232865] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_232855), -(_232857 = c_Groups_Ozero__class_Ozero(_232855)), c_Groups_Oplus__class_Oplus(_232855, _232859, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232855), _232857), _232863)) = c_Groups_Oplus__class_Oplus(_232855, _232861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232855), _232857), _232865)), _232859 = _232861, -(_232863 = _232865)], (3023 ^ _124236) ^ [_233490, _233492] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _233490, _233492), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _233490, _233492), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (3029 ^ _124236) ^ [_233664, _233666] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _233664, _233666), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _233664, _233666))], (3035 ^ _124236) ^ [_233888, _233890] : [class_Rings_Ocomm__semiring__0(_233888), -(c_Polynomial_Osmult(_233888, c_Groups_Ozero__class_Ozero(_233888), _233890) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_233888)))], (3041 ^ _124236) ^ [_234130, _234132, _234134] : [class_Rings_Oidom(_234130), 3044 ^ _124236 : [(3055 ^ _124236) ^ [] : [3056 ^ _124236 : [(3057 ^ _124236) ^ [] : [_234132 = c_Groups_Ozero__class_Ozero(_234130)], (3059 ^ _124236) ^ [] : [_234134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_234130))]], -(c_Polynomial_Osmult(_234130, _234132, _234134) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_234130)))], (3045 ^ _124236) ^ [] : [c_Polynomial_Osmult(_234130, _234132, _234134) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_234130)), -(_234132 = c_Groups_Ozero__class_Ozero(_234130)), -(_234134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_234130)))]]], (3063 ^ _124236) ^ [_234839, _234841] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _234839), _234839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _234841), _234841)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3066 ^ _124236 : [(3067 ^ _124236) ^ [] : [-(_234839 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3069 ^ _124236) ^ [] : [-(_234841 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (3071 ^ _124236) ^ [_235108, _235110] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _235108), _235108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _235110), _235110)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _235108 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _235110 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (3081 ^ _124236) ^ [_235469, _235471, _235473, _235475] : [class_Rings_Ocomm__semiring__0(_235469), c_Polynomial_Osmult(_235469, _235471, _235473) = c_Polynomial_OpCons(_235469, _235475, _235473), -(_235473 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_235469)))], (3091 ^ _124236) ^ [_235838, _235840, _235842, _235844] : [class_Rings_Ocomm__semiring__0(_235838), -(c_Polynomial_Osmult(_235838, c_Groups_Oplus__class_Oplus(_235838, _235840, _235842), _235844) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_235838), c_Polynomial_Osmult(_235838, _235840, _235844), c_Polynomial_Osmult(_235838, _235842, _235844)))], (3097 ^ _124236) ^ [_236102, _236104] : [class_Groups_Ozero(_236102), -(c_Polynomial_Omonom(_236102, c_Groups_Ozero__class_Ozero(_236102), _236104) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_236102)))], (3103 ^ _124236) ^ [_236344, _236346, _236348] : [class_Groups_Ozero(_236344), 3106 ^ _124236 : [(3107 ^ _124236) ^ [] : [c_Polynomial_Omonom(_236344, _236346, _236348) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_236344)), -(_236346 = c_Groups_Ozero__class_Ozero(_236344))], (3113 ^ _124236) ^ [] : [_236346 = c_Groups_Ozero__class_Ozero(_236344), -(c_Polynomial_Omonom(_236344, _236346, _236348) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_236344)))]]], (3119 ^ _124236) ^ [_236876, _236878, _236880, _236882] : [class_Groups_Ocomm__monoid__add(_236876), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_236876), c_Polynomial_Omonom(_236876, _236878, _236880), c_Polynomial_Omonom(_236876, _236882, _236880)) = c_Polynomial_Omonom(_236876, c_Groups_Oplus__class_Oplus(_236876, _236878, _236882), _236880))], (3125 ^ _124236) ^ [_237154, _237156, _237158] : [class_RealVector_Oreal__normed__vector(_237154), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_237154, _237156), c_RealVector_Onorm__class_Onorm(_237154, _237158)), c_RealVector_Onorm__class_Onorm(_237154, c_Groups_Oplus__class_Oplus(_237154, _237156, _237158))))], (3131 ^ _124236) ^ [_237418, _237420, _237422] : [class_RealVector_Oreal__normed__vector(_237418), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_237418, c_Groups_Ominus__class_Ominus(_237418, _237420, _237422)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_237418, _237420), c_RealVector_Onorm__class_Onorm(_237418, _237422))))], (3137 ^ _124236) ^ [_237668, _237670] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _237668, _237670) = _237668, -(_237670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3143 ^ _124236) ^ [_237915, _237917] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _237915, _237917) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 3146 ^ _124236 : [(3147 ^ _124236) ^ [] : [-(_237915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3149 ^ _124236) ^ [] : [-(_237917 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3151 ^ _124236) ^ [_238160, _238162] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238160, _238162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _238160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _238162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3161 ^ _124236) ^ [_238484] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _238484, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_238484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3167 ^ _124236) ^ [_238642] : [_238642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _238642, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3173 ^ _124236) ^ [_238821] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238821, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _238821)], (3175 ^ _124236) ^ [_238903] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _238903) = _238903)], (3177 ^ _124236) ^ [_239042, _239044, _239046, _239048] : [class_RealVector_Oreal__normed__vector(_239042), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _239044, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_239042, _239046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _239044), c_RealVector_Onorm__class_Onorm(_239042, _239048))), -(_239046 = c_Groups_Ozero__class_Ozero(_239042))], (3191 ^ _124236) ^ [_239544, _239546, _239548, _239550, _239552, _239554] : [class_Rings_Oordered__ring(_239544), 3194 ^ _124236 : [(3195 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_239544, c_Groups_Oplus__class_Oplus(_239544, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239544), _239546), _239548), _239550), c_Groups_Oplus__class_Oplus(_239544, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239544), _239552), _239548), _239554)), -(c_Orderings_Oord__class_Oless__eq(_239544, c_Groups_Oplus__class_Oplus(_239544, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239544), c_Groups_Ominus__class_Ominus(_239544, _239546, _239552)), _239548), _239550), _239554))], (3201 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_239544, c_Groups_Oplus__class_Oplus(_239544, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239544), c_Groups_Ominus__class_Ominus(_239544, _239546, _239552)), _239548), _239550), _239554), -(c_Orderings_Oord__class_Oless__eq(_239544, c_Groups_Oplus__class_Oplus(_239544, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239544), _239546), _239548), _239550), c_Groups_Oplus__class_Oplus(_239544, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239544), _239552), _239548), _239554)))]]], (3207 ^ _124236) ^ [_240248, _240250, _240252, _240254, _240256, _240258] : [class_Rings_Oordered__ring(_240248), 3210 ^ _124236 : [(3211 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_240248, c_Groups_Oplus__class_Oplus(_240248, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240248), _240250), _240252), _240254), c_Groups_Oplus__class_Oplus(_240248, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240248), _240256), _240252), _240258)), -(c_Orderings_Oord__class_Oless__eq(_240248, _240254, c_Groups_Oplus__class_Oplus(_240248, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240248), c_Groups_Ominus__class_Ominus(_240248, _240256, _240250)), _240252), _240258)))], (3217 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_240248, _240254, c_Groups_Oplus__class_Oplus(_240248, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240248), c_Groups_Ominus__class_Ominus(_240248, _240256, _240250)), _240252), _240258)), -(c_Orderings_Oord__class_Oless__eq(_240248, c_Groups_Oplus__class_Oplus(_240248, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240248), _240250), _240252), _240254), c_Groups_Oplus__class_Oplus(_240248, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240248), _240256), _240252), _240258)))]]], (3223 ^ _124236) ^ [_240910, _240912, _240914] : [class_Rings_Olinordered__ring__strict(_240910), 3226 ^ _124236 : [(3227 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_240910, c_Groups_Oplus__class_Oplus(_240910, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240910), _240912), _240912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240910), _240914), _240914)), c_Groups_Ozero__class_Ozero(_240910)), 3230 ^ _124236 : [(3231 ^ _124236) ^ [] : [-(_240912 = c_Groups_Ozero__class_Ozero(_240910))], (3233 ^ _124236) ^ [] : [-(_240914 = c_Groups_Ozero__class_Ozero(_240910))]]], (3235 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_240910, c_Groups_Oplus__class_Oplus(_240910, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240910), _240912), _240912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240910), _240914), _240914)), c_Groups_Ozero__class_Ozero(_240910))), _240912 = c_Groups_Ozero__class_Ozero(_240910), _240914 = c_Groups_Ozero__class_Ozero(_240910)]]], (3245 ^ _124236) ^ [_241643, _241645, _241647] : [class_Rings_Olinordered__ring(_241643), -(c_Orderings_Oord__class_Oless__eq(_241643, c_Groups_Ozero__class_Ozero(_241643), c_Groups_Oplus__class_Oplus(_241643, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_241643), _241645), _241645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_241643), _241647), _241647))))], (3251 ^ _124236) ^ [_241888, _241890] : [-(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, _241888, _241890)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _241888)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _241890)))], (3253 ^ _124236) ^ [_242071, _242073, _242075, _242077, _242079, _242081] : [class_Rings_Oring(_242071), 3256 ^ _124236 : [(3257 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_242071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242071), _242073), _242075), _242077) = c_Groups_Oplus__class_Oplus(_242071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242071), _242079), _242075), _242081), -(_242077 = c_Groups_Oplus__class_Oplus(_242071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242071), c_Groups_Ominus__class_Ominus(_242071, _242079, _242073)), _242075), _242081))], (3263 ^ _124236) ^ [] : [_242077 = c_Groups_Oplus__class_Oplus(_242071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242071), c_Groups_Ominus__class_Ominus(_242071, _242079, _242073)), _242075), _242081), -(c_Groups_Oplus__class_Oplus(_242071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242071), _242073), _242075), _242077) = c_Groups_Oplus__class_Oplus(_242071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242071), _242079), _242075), _242081))]]], (3269 ^ _124236) ^ [_242769, _242771, _242773, _242775, _242777, _242779] : [class_Rings_Oring(_242769), 3272 ^ _124236 : [(3273 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_242769, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242769), _242771), _242773), _242775) = c_Groups_Oplus__class_Oplus(_242769, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242769), _242777), _242773), _242779), -(c_Groups_Oplus__class_Oplus(_242769, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242769), c_Groups_Ominus__class_Ominus(_242769, _242771, _242777)), _242773), _242775) = _242779)], (3279 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_242769, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242769), c_Groups_Ominus__class_Ominus(_242769, _242771, _242777)), _242773), _242775) = _242779, -(c_Groups_Oplus__class_Oplus(_242769, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242769), _242771), _242773), _242775) = c_Groups_Oplus__class_Oplus(_242769, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242769), _242777), _242773), _242779))]]], (3285 ^ _124236) ^ [_243425, _243427, _243429] : [class_Rings_Olinordered__ring__strict(_243425), 3288 ^ _124236 : [(3289 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_243425, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_243425), _243427), _243427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_243425), _243429), _243429)) = c_Groups_Ozero__class_Ozero(_243425), 3292 ^ _124236 : [(3293 ^ _124236) ^ [] : [-(_243427 = c_Groups_Ozero__class_Ozero(_243425))], (3295 ^ _124236) ^ [] : [-(_243429 = c_Groups_Ozero__class_Ozero(_243425))]]], (3297 ^ _124236) ^ [] : [-(c_Groups_Oplus__class_Oplus(_243425, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_243425), _243427), _243427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_243425), _243429), _243429)) = c_Groups_Ozero__class_Ozero(_243425)), _243427 = c_Groups_Ozero__class_Ozero(_243425), _243429 = c_Groups_Ozero__class_Ozero(_243425)]]], (3307 ^ _124236) ^ [_244141, _244143] : [class_Rings_Olinordered__ring(_244141), -(c_Orderings_Oord__class_Oless__eq(_244141, c_Groups_Ozero__class_Ozero(_244141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_244141), _244143), _244143)))], (3313 ^ _124236) ^ [_244356, _244358] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244356, _244358) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244358, _244356))], (3315 ^ _124236) ^ [_244472, _244474, _244476] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244472, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244474, _244476)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244474, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244472, _244476)))], (3317 ^ _124236) ^ [_244598, _244600, _244602] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244598), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244600, _244602)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244598), _244600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244598), _244602)))], (3319 ^ _124236) ^ [_244720, _244722] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244720, _244722), _244722) = _244720)], (3321 ^ _124236) ^ [_244822, _244824] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244822, _244824), _244822) = _244824)], (3323 ^ _124236) ^ [_244938, _244940, _244942] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244938, _244940), _244942) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244938, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244940, _244942)))], (3325 ^ _124236) ^ [_245064, _245066, _245068] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _245064, _245066), _245068) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _245064, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245066, _245068)))], (3327 ^ _124236) ^ [_245190, _245192, _245194] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245190, _245192)), _245194) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245190), _245194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245192), _245194)))], (3329 ^ _124236) ^ [_245370, _245372, _245374] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245370, _245372) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245370, _245374), -(_245372 = _245374)], (3335 ^ _124236) ^ [_245554, _245556, _245558] : [_245556 = _245558, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245554, _245556) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245554, _245558))], (3341 ^ _124236) ^ [_245831, _245833, _245835] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245831, _245833) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245835, _245833), -(_245831 = _245835)], (3347 ^ _124236) ^ [_246015, _246017, _246019] : [_246015 = _246019, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246015, _246017) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246019, _246017))], (3353 ^ _124236) ^ [_246248, _246250, _246252] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246248, _246250), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246248, _246252)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _246250, _246252))], (3355 ^ _124236) ^ [_246374, _246376, _246378] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246374, _246376), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246378, _246376)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _246374, _246378))], (3357 ^ _124236) ^ [_246486, _246488] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246486), _246488) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246488), _246486))], (3359 ^ _124236) ^ [_246606, _246608, _246610] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246606), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _246608, _246610)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246606), _246608), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246606), _246610)))], (3361 ^ _124236) ^ [_246742, _246744, _246746] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246742), _246744)), _246746) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _246744), _246746)))], (3363 ^ _124236) ^ [_246876, _246878, _246880] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _246876, _246878), _246880) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _246876, _246880), _246878))], (3365 ^ _124236) ^ [_247002, _247004, _247006] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _247002, _247004)), _247006) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _247002), _247006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _247004), _247006)))], (3367 ^ _124236) ^ [_247138, _247140, _247142] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _247138), _247140)), _247142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _247138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _247140), _247142)))], (3369 ^ _124236) ^ [_247258, _247260] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _247258), _247260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _247260), _247258))], (3371 ^ _124236) ^ [_247408, _247410] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _247408, _247410), -(_247410 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _247408, 3374 ^ [_247408, _247410]))], (3378 ^ _124236) ^ [_247641, _247643] : [3379 ^ _124236 : [(3380 ^ _124236) ^ [_247716] : [_247643 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _247641, _247716)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _247641, _247643))], (3384 ^ _124236) ^ [_247899, _247901, _247903] : [class_Rings_Ono__zero__divisors(_247899), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_247899), _247901), _247903) = c_Groups_Ozero__class_Ozero(_247899), -(_247901 = c_Groups_Ozero__class_Ozero(_247899)), -(_247903 = c_Groups_Ozero__class_Ozero(_247899))], (3398 ^ _124236) ^ [_248342, _248344, _248346] : [class_Rings_Ono__zero__divisors(_248342), -(_248344 = c_Groups_Ozero__class_Ozero(_248342)), -(_248346 = c_Groups_Ozero__class_Ozero(_248342)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248342), _248344), _248346) = c_Groups_Ozero__class_Ozero(_248342)], (3412 ^ _124236) ^ [_248791, _248793, _248795] : [class_Rings_Oring__no__zero__divisors(_248791), 3415 ^ _124236 : [(3426 ^ _124236) ^ [] : [3427 ^ _124236 : [(3428 ^ _124236) ^ [] : [_248793 = c_Groups_Ozero__class_Ozero(_248791)], (3430 ^ _124236) ^ [] : [_248795 = c_Groups_Ozero__class_Ozero(_248791)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248791), _248793), _248795) = c_Groups_Ozero__class_Ozero(_248791))], (3416 ^ _124236) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248791), _248793), _248795) = c_Groups_Ozero__class_Ozero(_248791), -(_248793 = c_Groups_Ozero__class_Ozero(_248791)), -(_248795 = c_Groups_Ozero__class_Ozero(_248791))]]], (3434 ^ _124236) ^ [_249471, _249473] : [class_Rings_Omult__zero(_249471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249471), _249473), c_Groups_Ozero__class_Ozero(_249471)) = c_Groups_Ozero__class_Ozero(_249471))], (3440 ^ _124236) ^ [_249703, _249705] : [class_Rings_Omult__zero(_249703), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249703), c_Groups_Ozero__class_Ozero(_249703)), _249705) = c_Groups_Ozero__class_Ozero(_249703))], (3446 ^ _124236) ^ [_249963, _249965, _249967, _249969] : [class_Rings_Ocomm__semiring(_249963), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249963), c_Groups_Oplus__class_Oplus(_249963, _249965, _249967)), _249969) = c_Groups_Oplus__class_Oplus(_249963, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249963), _249965), _249969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249963), _249967), _249969)))], (3452 ^ _124236) ^ [_250289, _250291, _250293, _250295, _250297] : [class_Rings_Osemiring(_250289), -(c_Groups_Oplus__class_Oplus(_250289, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250289), _250291), _250293), c_Groups_Oplus__class_Oplus(_250289, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250289), _250295), _250293), _250297)) = c_Groups_Oplus__class_Oplus(_250289, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250289), c_Groups_Oplus__class_Oplus(_250289, _250291, _250295)), _250293), _250297))], (3458 ^ _124236) ^ [_250609, _250611, _250613] : [class_Rings_Oordered__cancel__semiring(_250609), -(c_Orderings_Oord__class_Oless__eq(_250609, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250609), _250611), _250613), c_Groups_Ozero__class_Ozero(_250609))), 3463 ^ _124236 : [(3464 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_250609, c_Groups_Ozero__class_Ozero(_250609), _250611), c_Orderings_Oord__class_Oless__eq(_250609, _250613, c_Groups_Ozero__class_Ozero(_250609))], (3470 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_250609, _250611, c_Groups_Ozero__class_Ozero(_250609)), c_Orderings_Oord__class_Oless__eq(_250609, c_Groups_Ozero__class_Ozero(_250609), _250613)]]], (3478 ^ _124236) ^ [_251238, _251240, _251242] : [class_Rings_Oordered__ring(_251238), -(c_Orderings_Oord__class_Oless__eq(_251238, c_Groups_Ozero__class_Ozero(_251238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251238), _251240), _251242))), 3483 ^ _124236 : [(3484 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_251238, c_Groups_Ozero__class_Ozero(_251238), _251240), c_Orderings_Oord__class_Oless__eq(_251238, c_Groups_Ozero__class_Ozero(_251238), _251242)], (3490 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_251238, _251240, c_Groups_Ozero__class_Ozero(_251238)), c_Orderings_Oord__class_Oless__eq(_251238, _251242, c_Groups_Ozero__class_Ozero(_251238))]]], (3498 ^ _124236) ^ [_251895, _251897, _251899, _251901, _251903] : [class_Rings_Oordered__semiring(_251895), c_Orderings_Oord__class_Oless__eq(_251895, _251897, _251899), c_Orderings_Oord__class_Oless__eq(_251895, _251901, _251903), c_Orderings_Oord__class_Oless__eq(_251895, c_Groups_Ozero__class_Ozero(_251895), _251899), c_Orderings_Oord__class_Oless__eq(_251895, c_Groups_Ozero__class_Ozero(_251895), _251901), -(c_Orderings_Oord__class_Oless__eq(_251895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251895), _251897), _251901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251895), _251899), _251903)))], (3520 ^ _124236) ^ [_252617, _252619, _252621, _252623, _252625] : [class_Rings_Oordered__semiring(_252617), c_Orderings_Oord__class_Oless__eq(_252617, _252619, _252621), c_Orderings_Oord__class_Oless__eq(_252617, _252623, _252625), c_Orderings_Oord__class_Oless__eq(_252617, c_Groups_Ozero__class_Ozero(_252617), _252619), c_Orderings_Oord__class_Oless__eq(_252617, c_Groups_Ozero__class_Ozero(_252617), _252623), -(c_Orderings_Oord__class_Oless__eq(_252617, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252617), _252619), _252623), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252617), _252621), _252625)))], (3542 ^ _124236) ^ [_253325, _253327, _253329, _253331] : [class_Rings_Oordered__ring(_253325), c_Orderings_Oord__class_Oless__eq(_253325, _253327, _253329), c_Orderings_Oord__class_Oless__eq(_253325, _253331, c_Groups_Ozero__class_Ozero(_253325)), -(c_Orderings_Oord__class_Oless__eq(_253325, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253325), _253331), _253329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253325), _253331), _253327)))], (3556 ^ _124236) ^ [_253809, _253811, _253813, _253815] : [class_Rings_Oordered__ring(_253809), c_Orderings_Oord__class_Oless__eq(_253809, _253811, _253813), c_Orderings_Oord__class_Oless__eq(_253809, _253815, c_Groups_Ozero__class_Ozero(_253809)), -(c_Orderings_Oord__class_Oless__eq(_253809, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253809), _253813), _253815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253809), _253811), _253815)))], (3570 ^ _124236) ^ [_254293, _254295, _254297, _254299] : [class_Rings_Oordered__comm__semiring(_254293), c_Orderings_Oord__class_Oless__eq(_254293, _254295, _254297), c_Orderings_Oord__class_Oless__eq(_254293, c_Groups_Ozero__class_Ozero(_254293), _254299), -(c_Orderings_Oord__class_Oless__eq(_254293, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254293), _254299), _254295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254293), _254299), _254297)))], (3584 ^ _124236) ^ [_254777, _254779, _254781, _254783] : [class_Rings_Oordered__semiring(_254777), c_Orderings_Oord__class_Oless__eq(_254777, _254779, _254781), c_Orderings_Oord__class_Oless__eq(_254777, c_Groups_Ozero__class_Ozero(_254777), _254783), -(c_Orderings_Oord__class_Oless__eq(_254777, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254777), _254783), _254779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254777), _254783), _254781)))], (3598 ^ _124236) ^ [_255261, _255263, _255265, _255267] : [class_Rings_Oordered__semiring(_255261), c_Orderings_Oord__class_Oless__eq(_255261, _255263, _255265), c_Orderings_Oord__class_Oless__eq(_255261, c_Groups_Ozero__class_Ozero(_255261), _255267), -(c_Orderings_Oord__class_Oless__eq(_255261, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_255261), _255263), _255267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_255261), _255265), _255267)))], (3612 ^ _124236) ^ [_255731, _255733, _255735] : [class_Rings_Oordered__ring(_255731), c_Orderings_Oord__class_Oless__eq(_255731, _255733, c_Groups_Ozero__class_Ozero(_255731)), c_Orderings_Oord__class_Oless__eq(_255731, _255735, c_Groups_Ozero__class_Ozero(_255731)), -(c_Orderings_Oord__class_Oless__eq(_255731, c_Groups_Ozero__class_Ozero(_255731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_255731), _255733), _255735)))], (3626 ^ _124236) ^ [_256179, _256181, _256183] : [class_Rings_Oordered__cancel__semiring(_256179), c_Orderings_Oord__class_Oless__eq(_256179, _256181, c_Groups_Ozero__class_Ozero(_256179)), c_Orderings_Oord__class_Oless__eq(_256179, c_Groups_Ozero__class_Ozero(_256179), _256183), -(c_Orderings_Oord__class_Oless__eq(_256179, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_256179), _256181), _256183), c_Groups_Ozero__class_Ozero(_256179)))], (3640 ^ _124236) ^ [_256627, _256629, _256631] : [class_Rings_Oordered__cancel__semiring(_256627), c_Orderings_Oord__class_Oless__eq(_256627, c_Groups_Ozero__class_Ozero(_256627), _256629), c_Orderings_Oord__class_Oless__eq(_256627, _256631, c_Groups_Ozero__class_Ozero(_256627)), -(c_Orderings_Oord__class_Oless__eq(_256627, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_256627), _256631), _256629), c_Groups_Ozero__class_Ozero(_256627)))], (3654 ^ _124236) ^ [_257075, _257077, _257079] : [class_Rings_Oordered__cancel__semiring(_257075), c_Orderings_Oord__class_Oless__eq(_257075, c_Groups_Ozero__class_Ozero(_257075), _257077), c_Orderings_Oord__class_Oless__eq(_257075, _257079, c_Groups_Ozero__class_Ozero(_257075)), -(c_Orderings_Oord__class_Oless__eq(_257075, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257075), _257077), _257079), c_Groups_Ozero__class_Ozero(_257075)))], (3668 ^ _124236) ^ [_257523, _257525, _257527] : [class_Rings_Oordered__cancel__semiring(_257523), c_Orderings_Oord__class_Oless__eq(_257523, c_Groups_Ozero__class_Ozero(_257523), _257525), c_Orderings_Oord__class_Oless__eq(_257523, c_Groups_Ozero__class_Ozero(_257523), _257527), -(c_Orderings_Oord__class_Oless__eq(_257523, c_Groups_Ozero__class_Ozero(_257523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257523), _257525), _257527)))], (3682 ^ _124236) ^ [_257971, _257973, _257975] : [class_Rings_Olinordered__ring__strict(_257971), 3685 ^ _124236 : [(3686 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_257971, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257971), _257973), _257975), c_Groups_Ozero__class_Ozero(_257971)), 3691 ^ _124236 : [(3692 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_257971, c_Groups_Ozero__class_Ozero(_257971), _257973))], (3694 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_257971, _257975, c_Groups_Ozero__class_Ozero(_257971)))]], 3695 ^ _124236 : [(3696 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_257971, _257973, c_Groups_Ozero__class_Ozero(_257971)))], (3698 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_257971, c_Groups_Ozero__class_Ozero(_257971), _257975))]]], (3700 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_257971, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257971), _257973), _257975), c_Groups_Ozero__class_Ozero(_257971))), 3701 ^ _124236 : [(3702 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_257971, c_Groups_Ozero__class_Ozero(_257971), _257973), c_Orderings_Oord__class_Oless__eq(_257971, _257975, c_Groups_Ozero__class_Ozero(_257971))], (3708 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_257971, _257973, c_Groups_Ozero__class_Ozero(_257971)), c_Orderings_Oord__class_Oless__eq(_257971, c_Groups_Ozero__class_Ozero(_257971), _257975)]]]]], (3716 ^ _124236) ^ [_259020, _259022, _259024] : [class_Rings_Olinordered__ring__strict(_259020), 3719 ^ _124236 : [(3720 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_259020, c_Groups_Ozero__class_Ozero(_259020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259020), _259022), _259024)), 3725 ^ _124236 : [(3726 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_259020, c_Groups_Ozero__class_Ozero(_259020), _259022))], (3728 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_259020, c_Groups_Ozero__class_Ozero(_259020), _259024))]], 3729 ^ _124236 : [(3730 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_259020, _259022, c_Groups_Ozero__class_Ozero(_259020)))], (3732 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_259020, _259024, c_Groups_Ozero__class_Ozero(_259020)))]]], (3734 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_259020, c_Groups_Ozero__class_Ozero(_259020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259020), _259022), _259024))), 3735 ^ _124236 : [(3736 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_259020, c_Groups_Ozero__class_Ozero(_259020), _259022), c_Orderings_Oord__class_Oless__eq(_259020, c_Groups_Ozero__class_Ozero(_259020), _259024)], (3742 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_259020, _259022, c_Groups_Ozero__class_Ozero(_259020)), c_Orderings_Oord__class_Oless__eq(_259020, _259024, c_Groups_Ozero__class_Ozero(_259020))]]]]], (3750 ^ _124236) ^ [_260097, _260099, _260101, _260103, _260105] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260097, _260099), 3753 ^ _124236 : [(3754 ^ _124236) ^ [] : [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), _260099), _260101), _260103), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _260097), _260101), _260105)), -(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, _260099, _260097)), _260101), _260103), _260105))], (3760 ^ _124236) ^ [] : [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, _260099, _260097)), _260101), _260103), _260105), -(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), _260099), _260101), _260103), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _260097), _260101), _260105)))]]], (3766 ^ _124236) ^ [_260757, _260759, _260761, _260763, _260765] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260757, _260759), -(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), _260759), _260761), _260763), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _260757), _260761), _260765)) = 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, _260759, _260757)), _260761), _260763), _260765))], (3772 ^ _124236) ^ [_261113, _261115, _261117, _261119, _261121] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _261113, _261115), 3775 ^ _124236 : [(3776 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261115), _261117), _261119) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261113), _261117), _261121), -(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, _261115, _261113)), _261117), _261119) = _261121)], (3782 ^ _124236) ^ [] : [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, _261115, _261113)), _261117), _261119) = _261121, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261115), _261117), _261119) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261113), _261117), _261121))]]], (3788 ^ _124236) ^ [_261767, _261769, _261771, _261773, _261775] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _261767, _261769), 3791 ^ _124236 : [(3792 ^ _124236) ^ [] : [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), _261767), _261771), _261773), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261769), _261771), _261775)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _261773, 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, _261769, _261767)), _261771), _261775)))], (3798 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _261773, 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, _261769, _261767)), _261771), _261775)), -(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), _261767), _261771), _261773), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261769), _261771), _261775)))]]], (3804 ^ _124236) ^ [_262427, _262429, _262431, _262433, _262435] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _262427, _262429), -(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), _262427), _262431), _262433), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262429), _262431), _262435)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _262433, 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, _262429, _262427)), _262431), _262435)))], (3810 ^ _124236) ^ [_262783, _262785, _262787, _262789, _262791] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _262783, _262785), 3813 ^ _124236 : [(3814 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262783), _262787), _262789) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262785), _262787), _262791), -(_262789 = 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, _262785, _262783)), _262787), _262791))], (3820 ^ _124236) ^ [] : [_262789 = 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, _262785, _262783)), _262787), _262791), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262783), _262787), _262789) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262785), _262787), _262791))]]], (3826 ^ _124236) ^ [_263423, _263425, _263427, _263429] : [class_Rings_Ocomm__semiring__0(_263423), -(c_Polynomial_Opcompose(_263423, c_Polynomial_OpCons(_263423, _263425, _263427), _263429) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_263423), c_Polynomial_OpCons(_263423, _263425, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_263423))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_263423)), _263429), c_Polynomial_Opcompose(_263423, _263427, _263429))))], (3832 ^ _124236) ^ [_263715, _263717] : [class_Rings_Ocomm__semiring__0(_263715), -(c_Polynomial_Opcompose(_263715, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_263715)), _263717) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_263715)))], (3838 ^ _124236) ^ [_263975, _263977, _263979, _263981] : [class_Rings_Ocomm__semiring__0(_263975), -(hAPP(c_Polynomial_Opoly(_263975, c_Polynomial_Opcompose(_263975, _263977, _263979)), _263981) = hAPP(c_Polynomial_Opoly(_263975, _263977), hAPP(c_Polynomial_Opoly(_263975, _263979), _263981)))], (3854 ^ _124236) ^ [_264568, _264570, _264572] : [3855 ^ _124236 : [(3856 ^ _124236) ^ [] : [_264568 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3858 ^ _124236) ^ [] : [_264570 = _264572]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264568), _264570) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264568), _264572))], (3844 ^ _124236) ^ [_264282, _264284, _264286] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264282), _264284) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264282), _264286), -(_264282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_264284 = _264286)], (3862 ^ _124236) ^ [_264899, _264901, _264903, _264905] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264899), _264901), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264903), _264901), _264905)) = 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, _264899, _264903)), _264901), _264905))], (3864 ^ _124236) ^ [_265060, _265062, _265064] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _265060, _265062), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _265060, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265062, _265064)))], (3870 ^ _124236) ^ [_265302, _265304, _265306] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _265302, _265304), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _265302, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265306, _265304)))], (3876 ^ _124236) ^ [_265572, _265574, _265576, _265578, _265580] : [class_Groups_Oab__group__add(_265572), -(c_Groups_Ominus__class_Ominus(_265572, c_Groups_Oplus__class_Oplus(_265572, _265574, _265576), c_Groups_Oplus__class_Oplus(_265572, _265578, _265580)) = c_Groups_Oplus__class_Oplus(_265572, c_Groups_Ominus__class_Ominus(_265572, _265574, _265578), c_Groups_Ominus__class_Ominus(_265572, _265576, _265580)))], (3882 ^ _124236) ^ [_265832] : [class_RealVector_Oreal__normed__algebra(_265832), 3886 ^ _124236 : [(3887 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3885 ^ [_265832]))], (3889 ^ _124236) ^ [_266161, _266163] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_265832, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265832), _266163), _266161)), 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(_265832, _266163)), c_RealVector_Onorm__class_Onorm(_265832, _266161))), 3885 ^ [_265832])))]]], (3891 ^ _124236) ^ [_266314, _266316] : [class_RealVector_Oreal__normed__algebra(_266314), 3895 ^ _124236 : [(3896 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3894 ^ [_266314, _266316]))], (3898 ^ _124236) ^ [_266613] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_266314, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266314), _266316), _266613)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_266314, _266613)), 3894 ^ [_266314, _266316])))]]], (3900 ^ _124236) ^ [_266759, _266761] : [class_RealVector_Oreal__normed__algebra(_266759), 3904 ^ _124236 : [(3905 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3903 ^ [_266759, _266761]))], (3907 ^ _124236) ^ [_267058] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_266759, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266759), _267058), _266761)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_266759, _267058)), 3903 ^ [_266759, _266761])))]]], (3909 ^ _124236) ^ [_267190] : [class_RealVector_Oreal__normed__algebra(_267190), 3913 ^ _124236 : [(3914 ^ _124236) ^ [_267435, _267437] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_267190, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267190), _267437), _267435)), 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(_267190, _267437)), c_RealVector_Onorm__class_Onorm(_267190, _267435))), 3912 ^ [_267190])))]]], (3916 ^ _124236) ^ [_267586, _267588] : [class_RealVector_Oreal__normed__algebra(_267586), 3920 ^ _124236 : [(3921 ^ _124236) ^ [_267797] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_267586, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267586), _267588), _267797)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_267586, _267797)), 3919 ^ [_267586, _267588])))]]], (3923 ^ _124236) ^ [_267941, _267943] : [class_RealVector_Oreal__normed__algebra(_267941), 3927 ^ _124236 : [(3928 ^ _124236) ^ [_268152] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_267941, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267941), _268152), _267943)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_267941, _268152)), 3926 ^ [_267941, _267943])))]]], (3930 ^ _124236) ^ [_268316, _268318] : [_268316 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _268316), _268318) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3936 ^ _124236) ^ [_268490, _268492] : [-(_268490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _268490), _268492) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _268492, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _268490, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _268492)))], (3942 ^ _124236) ^ [_268787, _268789, _268791, _268793, _268795] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _268787, _268789), 3945 ^ _124236 : [(3946 ^ _124236) ^ [] : [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), _268789), _268791), _268793), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _268787), _268791), _268795)), -(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, _268789, _268787)), _268791), _268793), _268795))], (3952 ^ _124236) ^ [] : [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, _268789, _268787)), _268791), _268793), _268795), -(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), _268789), _268791), _268793), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _268787), _268791), _268795)))]]], (3958 ^ _124236) ^ [_269447, _269449, _269451, _269453, _269455] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _269447, _269449), 3961 ^ _124236 : [(3962 ^ _124236) ^ [] : [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), _269447), _269451), _269453), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _269449), _269451), _269455)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _269453, 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, _269449, _269447)), _269451), _269455)))], (3968 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _269453, 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, _269449, _269447)), _269451), _269455)), -(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), _269447), _269451), _269453), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _269449), _269451), _269455)))]]], (3974 ^ _124236) ^ [_270035] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _270035, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3976 ^ _124236) ^ [_270157, _270159, _270161] : [class_Rings_Olinordered__semidom(_270157), c_Orderings_Oord__class_Oless(_270157, c_Groups_Oone__class_Oone(_270157), _270159), c_Orderings_Oord__class_Oless(_270157, c_Groups_Oone__class_Oone(_270157), _270161), -(c_Orderings_Oord__class_Oless(_270157, c_Groups_Oone__class_Oone(_270157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270157), _270159), _270161)))], (3990 ^ _124236) ^ [_270605, _270607, _270609] : [class_Rings_Olinordered__idom(_270605), -(_270607 = _270609), -(c_Orderings_Oord__class_Oless(_270605, _270607, _270609)), -(c_Orderings_Oord__class_Oless(_270605, _270609, _270607))], (4004 ^ _124236) ^ [_271015, _271017] : [class_Rings_Olinordered__semidom(_271015), -(c_Orderings_Oord__class_Oless(_271015, _271017, c_Groups_Oplus__class_Oplus(_271015, _271017, c_Groups_Oone__class_Oone(_271015))))], (4010 ^ _124236) ^ [_271223] : [class_Rings_Olinordered__semidom(_271223), -(c_Orderings_Oord__class_Oless(_271223, c_Groups_Ozero__class_Ozero(_271223), c_Groups_Oone__class_Oone(_271223)))], (4016 ^ _124236) ^ [_271421] : [class_Rings_Olinordered__semidom(_271421), c_Orderings_Oord__class_Oless(_271421, c_Groups_Oone__class_Oone(_271421), c_Groups_Ozero__class_Ozero(_271421))], (4022 ^ _124236) ^ [_271634, _271636] : [class_Rings_Ocomm__semiring__1(_271634), -(hAPP(c_Polynomial_Opoly(_271634, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_271634))), _271636) = c_Groups_Oone__class_Oone(_271634))], (4028 ^ _124236) ^ [_271880, _271882, _271884] : [class_Orderings_Olinorder(_271880), -(c_Orderings_Oord__class_Oless(_271880, _271882, _271884)), -(_271882 = _271884), -(c_Orderings_Oord__class_Oless(_271880, _271884, _271882))], (4042 ^ _124236) ^ [_272304, _272306, _272308] : [class_Orderings_Opreorder(_272304), c_Orderings_Oord__class_Oless(_272304, _272306, _272308), c_Orderings_Oord__class_Oless(_272304, _272308, _272306)], (4052 ^ _124236) ^ [_272644, _272646, _272648, _272650] : [class_Orderings_Oorder(_272644), c_Orderings_Oord__class_Oless(_272644, _272646, _272648), c_Orderings_Oord__class_Oless(_272644, _272650, _272646), -(c_Orderings_Oord__class_Oless(_272644, _272650, _272648))], (4066 ^ _124236) ^ [_273092, _273094, _273096, _273098] : [class_Orderings_Opreorder(_273092), c_Orderings_Oord__class_Oless(_273092, _273094, _273096), c_Orderings_Oord__class_Oless(_273092, _273096, _273098), -(c_Orderings_Oord__class_Oless(_273092, _273094, _273098))], (4080 ^ _124236) ^ [_273540, _273542, _273544, _273546] : [class_Orderings_Oorder(_273540), c_Orderings_Oord__class_Oless(_273540, _273542, _273544), _273542 = _273546, -(c_Orderings_Oord__class_Oless(_273540, _273546, _273544))], (4094 ^ _124236) ^ [_273986, _273988, _273990, _273992] : [class_Orderings_Oord(_273986), c_Orderings_Oord__class_Oless(_273986, _273988, _273990), _273990 = _273992, -(c_Orderings_Oord__class_Oless(_273986, _273988, _273992))], (4108 ^ _124236) ^ [_274432, _274434, _274436, _274438] : [class_Orderings_Oorder(_274432), _274434 = _274436, c_Orderings_Oord__class_Oless(_274432, _274438, _274436), -(c_Orderings_Oord__class_Oless(_274432, _274438, _274434))], (4122 ^ _124236) ^ [_274878, _274880, _274882, _274884] : [class_Orderings_Oord(_274878), _274880 = _274882, c_Orderings_Oord__class_Oless(_274878, _274882, _274884), -(c_Orderings_Oord__class_Oless(_274878, _274880, _274884))], (4136 ^ _124236) ^ [_275310, _275312, _275314] : [class_Orderings_Oorder(_275310), c_Orderings_Oord__class_Oless(_275310, _275312, _275314), c_Orderings_Oord__class_Oless(_275310, _275314, _275312)], (4146 ^ _124236) ^ [_275636, _275638, _275640] : [class_Orderings_Opreorder(_275636), c_Orderings_Oord__class_Oless(_275636, _275638, _275640), c_Orderings_Oord__class_Oless(_275636, _275640, _275638)], (4156 ^ _124236) ^ [_275962, _275964, _275966] : [class_Orderings_Oorder(_275962), c_Orderings_Oord__class_Oless(_275962, _275964, _275966), _275966 = _275964], (4166 ^ _124236) ^ [_276286, _276288, _276290] : [class_Orderings_Oorder(_276286), c_Orderings_Oord__class_Oless(_276286, _276288, _276290), _276288 = _276290], (4176 ^ _124236) ^ [_276610, _276612, _276614] : [class_Orderings_Opreorder(_276610), c_Orderings_Oord__class_Oless(_276610, _276612, _276614), c_Orderings_Oord__class_Oless(_276610, _276614, _276612)], (4186 ^ _124236) ^ [_276936, _276938, _276940] : [class_Orderings_Opreorder(_276936), c_Orderings_Oord__class_Oless(_276936, _276938, _276940), c_Orderings_Oord__class_Oless(_276936, _276940, _276938)], (4196 ^ _124236) ^ [_277262, _277264, _277266] : [class_Orderings_Oorder(_277262), c_Orderings_Oord__class_Oless(_277262, _277264, _277266), _277264 = _277266], (4206 ^ _124236) ^ [_277586, _277588, _277590] : [class_Orderings_Olinorder(_277586), -(_277588 = _277590), -(c_Orderings_Oord__class_Oless(_277586, _277588, _277590)), -(c_Orderings_Oord__class_Oless(_277586, _277590, _277588))], (4220 ^ _124236) ^ [_278010, _278012, _278014] : [class_Orderings_Olinorder(_278010), -(c_Orderings_Oord__class_Oless(_278010, _278012, _278014)), 4227 ^ _124236 : [(4228 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_278010, _278014, _278012)), -(_278014 = _278012)], (4234 ^ _124236) ^ [] : [_278014 = _278012, c_Orderings_Oord__class_Oless(_278010, _278014, _278012)]]], (4240 ^ _124236) ^ [_278601, _278603, _278605] : [class_Orderings_Olinorder(_278601), -(c_Orderings_Oord__class_Oless(_278601, _278603, _278605)), -(_278603 = _278605), -(c_Orderings_Oord__class_Oless(_278601, _278605, _278603))], (4254 ^ _124236) ^ [_279007, _279009] : [class_Groups_Oone(_279007), 4257 ^ _124236 : [(4258 ^ _124236) ^ [] : [c_Groups_Oone__class_Oone(_279007) = _279009, -(_279009 = c_Groups_Oone__class_Oone(_279007))], (4264 ^ _124236) ^ [] : [_279009 = c_Groups_Oone__class_Oone(_279007), -(c_Groups_Oone__class_Oone(_279007) = _279009)]]], (4270 ^ _124236) ^ [_279491, _279493, _279495] : [class_Orderings_Olinorder(_279491), 4273 ^ _124236 : [(4284 ^ _124236) ^ [] : [4285 ^ _124236 : [(4286 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_279491, _279495, _279493)], (4288 ^ _124236) ^ [] : [_279493 = _279495]], c_Orderings_Oord__class_Oless(_279491, _279493, _279495)], (4274 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_279491, _279493, _279495)), -(c_Orderings_Oord__class_Oless(_279491, _279495, _279493)), -(_279493 = _279495)]]], (4292 ^ _124236) ^ [_280151, _280153, _280155] : [class_Orderings_Olinorder(_280151), 4295 ^ _124236 : [(4306 ^ _124236) ^ [] : [4307 ^ _124236 : [(4308 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_280151, _280153, _280155)], (4310 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_280151, _280155, _280153)]], _280153 = _280155], (4296 ^ _124236) ^ [] : [-(_280153 = _280155), -(c_Orderings_Oord__class_Oless(_280151, _280153, _280155)), -(c_Orderings_Oord__class_Oless(_280151, _280155, _280153))]]], (4314 ^ _124236) ^ [_280797, _280799] : [class_Orderings_Opreorder(_280797), c_Orderings_Oord__class_Oless(_280797, _280799, _280799)], (4320 ^ _124236) ^ [_280994] : [class_RealVector_Oreal__normed__algebra__1(_280994), -(c_RealVector_Onorm__class_Onorm(_280994, c_Groups_Oone__class_Oone(_280994)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (4326 ^ _124236) ^ [_281220, _281222, _281224] : [4327 ^ _124236 : [(4328 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _281220, _281222))], (4330 ^ _124236) ^ [] : [hBOOL(hAPP(hAPP(_281224, _281222), _281220))]], 4333 ^ _124236 : [(4334 ^ _124236) ^ [] : [-(_281220 = _281222)], (4336 ^ _124236) ^ [] : [hBOOL(hAPP(hAPP(_281224, _281222), _281220))]], 4339 ^ _124236 : [(4340 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _281222, _281220))], (4342 ^ _124236) ^ [] : [hBOOL(hAPP(hAPP(_281224, _281222), _281220))]], -(hBOOL(hAPP(hAPP(_281224, _281222), _281220)))], (4346 ^ _124236) ^ [_281897, _281899] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _281897, _281899), _281897 = _281899], (4352 ^ _124236) ^ [_282110, _282112] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282110, _282112), _282112 = _282110], (4358 ^ _124236) ^ [_282293] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282293, _282293)], (4360 ^ _124236) ^ [_282401, _282403] : [-(_282401 = _282403), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282401, _282403)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282403, _282401))], (4380 ^ _124236) ^ [_282998, _283000] : [4381 ^ _124236 : [(4382 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282998, _283000)], (4384 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _283000, _282998)]], _282998 = _283000], (4370 ^ _124236) ^ [_282739, _282741] : [-(_282739 = _282741), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282739, _282741)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282741, _282739))], (4388 ^ _124236) ^ [_283259] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _283259, _283259)], (4390 ^ _124236) ^ [_283353] : [class_Rings_Olinordered__semidom(_283353), -(c_Orderings_Oord__class_Oless(_283353, c_Groups_Ozero__class_Ozero(_283353), c_Groups_Oplus__class_Oplus(_283353, c_Groups_Oone__class_Oone(_283353), c_Groups_Oone__class_Oone(_283353))))], (4396 ^ _124236) ^ [_283563] : [class_Rings_Ocomm__semiring__1(_283563), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_283563)) = c_Polynomial_OpCons(_283563, c_Groups_Oone__class_Oone(_283563), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_283563))))], (4402 ^ _124236) ^ [_283821, _283823, _283825, _283827] : [class_Orderings_Oorder(_283821), c_Orderings_Oord__class_Oless__eq(_283821, _283823, _283825), c_Orderings_Oord__class_Oless(_283821, _283827, _283823), -(c_Orderings_Oord__class_Oless(_283821, _283827, _283825))], (4416 ^ _124236) ^ [_284269, _284271, _284273, _284275] : [class_Orderings_Opreorder(_284269), c_Orderings_Oord__class_Oless__eq(_284269, _284271, _284273), c_Orderings_Oord__class_Oless(_284269, _284273, _284275), -(c_Orderings_Oord__class_Oless(_284269, _284271, _284275))], (4430 ^ _124236) ^ [_284717, _284719, _284721, _284723] : [class_Orderings_Oorder(_284717), c_Orderings_Oord__class_Oless(_284717, _284719, _284721), c_Orderings_Oord__class_Oless__eq(_284717, _284723, _284719), -(c_Orderings_Oord__class_Oless(_284717, _284723, _284721))], (4444 ^ _124236) ^ [_285165, _285167, _285169, _285171] : [class_Orderings_Opreorder(_285165), c_Orderings_Oord__class_Oless(_285165, _285167, _285169), c_Orderings_Oord__class_Oless__eq(_285165, _285169, _285171), -(c_Orderings_Oord__class_Oless(_285165, _285167, _285171))], (4458 ^ _124236) ^ [_285599, _285601, _285603] : [class_Orderings_Oorder(_285599), c_Orderings_Oord__class_Oless__eq(_285599, _285601, _285603), -(_285603 = _285601), -(c_Orderings_Oord__class_Oless(_285599, _285601, _285603))], (4472 ^ _124236) ^ [_286020, _286022, _286024] : [class_Orderings_Oorder(_286020), c_Orderings_Oord__class_Oless__eq(_286020, _286022, _286024), -(_286022 = _286024), -(c_Orderings_Oord__class_Oless(_286020, _286022, _286024))], (4486 ^ _124236) ^ [_286441, _286443, _286445] : [class_Orderings_Oorder(_286441), c_Orderings_Oord__class_Oless__eq(_286441, _286443, _286445), -(c_Orderings_Oord__class_Oless(_286441, _286443, _286445)), -(_286443 = _286445)], (4500 ^ _124236) ^ [_286860, _286862, _286864] : [class_Orderings_Olinorder(_286860), c_Orderings_Oord__class_Oless__eq(_286860, _286862, _286864), 4507 ^ _124236 : [(4508 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_286860, _286862, _286864)), -(_286862 = _286864)], (4514 ^ _124236) ^ [] : [_286862 = _286864, c_Orderings_Oord__class_Oless(_286860, _286862, _286864)]]], (4520 ^ _124236) ^ [_287448, _287450, _287452] : [class_Orderings_Opreorder(_287448), c_Orderings_Oord__class_Oless(_287448, _287450, _287452), -(c_Orderings_Oord__class_Oless__eq(_287448, _287450, _287452))], (4530 ^ _124236) ^ [_287773, _287775, _287777] : [class_Orderings_Olinorder(_287773), c_Orderings_Oord__class_Oless__eq(_287773, _287775, _287777), c_Orderings_Oord__class_Oless(_287773, _287777, _287775)], (4540 ^ _124236) ^ [_288099, _288101, _288103] : [class_Orderings_Oorder(_288099), -(_288101 = _288103), c_Orderings_Oord__class_Oless__eq(_288099, _288103, _288101), -(c_Orderings_Oord__class_Oless(_288099, _288103, _288101))], (4554 ^ _124236) ^ [_288520, _288522, _288524] : [class_Orderings_Oorder(_288520), -(_288522 = _288524), c_Orderings_Oord__class_Oless__eq(_288520, _288522, _288524), -(c_Orderings_Oord__class_Oless(_288520, _288522, _288524))], (4568 ^ _124236) ^ [_288941, _288943, _288945] : [class_Orderings_Olinorder(_288941), -(c_Orderings_Oord__class_Oless(_288941, _288943, _288945)), 4575 ^ _124236 : [(4576 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_288941, _288943, _288945), -(_288943 = _288945)], (4582 ^ _124236) ^ [] : [_288943 = _288945, -(c_Orderings_Oord__class_Oless__eq(_288941, _288943, _288945))]]], (4588 ^ _124236) ^ [_289530, _289532, _289534] : [class_Orderings_Olinorder(_289530), -(c_Orderings_Oord__class_Oless__eq(_289530, _289532, _289534)), -(c_Orderings_Oord__class_Oless(_289530, _289534, _289532))], (4598 ^ _124236) ^ [_289858, _289860, _289862] : [class_Orderings_Olinorder(_289858), -(c_Orderings_Oord__class_Oless(_289858, _289860, _289862)), -(c_Orderings_Oord__class_Oless__eq(_289858, _289862, _289860))], (4608 ^ _124236) ^ [_290186, _290188, _290190] : [class_Orderings_Oorder(_290186), 4611 ^ _124236 : [(4622 ^ _124236) ^ [] : [4623 ^ _124236 : [(4624 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_290186, _290188, _290190)], (4626 ^ _124236) ^ [] : [_290188 = _290190]], -(c_Orderings_Oord__class_Oless__eq(_290186, _290188, _290190))], (4612 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290186, _290188, _290190), -(c_Orderings_Oord__class_Oless(_290186, _290188, _290190)), -(_290188 = _290190)]]], (4630 ^ _124236) ^ [_290844, _290846, _290848] : [class_Orderings_Opreorder(_290844), 4633 ^ _124236 : [(4634 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_290844, _290846, _290848), 4637 ^ _124236 : [(4638 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_290844, _290846, _290848))], (4640 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290844, _290848, _290846)]]], (4642 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_290844, _290846, _290848)), c_Orderings_Oord__class_Oless__eq(_290844, _290846, _290848), -(c_Orderings_Oord__class_Oless__eq(_290844, _290848, _290846))]]], (4652 ^ _124236) ^ [_291507, _291509, _291511] : [class_Orderings_Oorder(_291507), 4655 ^ _124236 : [(4656 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_291507, _291509, _291511), 4659 ^ _124236 : [(4660 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_291507, _291509, _291511))], (4662 ^ _124236) ^ [] : [_291509 = _291511]]], (4664 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_291507, _291509, _291511)), c_Orderings_Oord__class_Oless__eq(_291507, _291509, _291511), -(_291509 = _291511)]]], (4674 ^ _124236) ^ [_292167, _292169, _292171] : [class_Orderings_Olinorder(_292167), -(c_Orderings_Oord__class_Oless__eq(_292167, _292169, _292171)), -(c_Orderings_Oord__class_Oless(_292167, _292171, _292169))], (4684 ^ _124236) ^ [_292493, _292495, _292497] : [class_Orderings_Olinorder(_292493), 4687 ^ _124236 : [(4688 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_292493, _292495, _292497)), -(c_Orderings_Oord__class_Oless(_292493, _292497, _292495))], (4694 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_292493, _292497, _292495), c_Orderings_Oord__class_Oless__eq(_292493, _292495, _292497)]]], (4700 ^ _124236) ^ [_292989, _292991, _292993] : [class_Orderings_Olinorder(_292989), 4703 ^ _124236 : [(4704 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_292989, _292991, _292993)), -(c_Orderings_Oord__class_Oless__eq(_292989, _292993, _292991))], (4710 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_292989, _292993, _292991), c_Orderings_Oord__class_Oless(_292989, _292991, _292993)]]], (4716 ^ _124236) ^ [_293457] : [class_Rings_Ozero__neq__one(_293457), c_Groups_Oone__class_Oone(_293457) = c_Groups_Ozero__class_Ozero(_293457)], (4722 ^ _124236) ^ [_293654] : [class_Rings_Ozero__neq__one(_293654), c_Groups_Ozero__class_Ozero(_293654) = c_Groups_Oone__class_Oone(_293654)], (4728 ^ _124236) ^ [_293893, _293895, _293897, _293899] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_293893), c_Orderings_Oord__class_Oless(_293893, c_Groups_Oplus__class_Oplus(_293893, _293895, _293897), c_Groups_Oplus__class_Oplus(_293893, _293895, _293899)), -(c_Orderings_Oord__class_Oless(_293893, _293897, _293899))], (4738 ^ _124236) ^ [_294258, _294260, _294262, _294264] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_294258), c_Orderings_Oord__class_Oless(_294258, c_Groups_Oplus__class_Oplus(_294258, _294260, _294262), c_Groups_Oplus__class_Oplus(_294258, _294264, _294262)), -(c_Orderings_Oord__class_Oless(_294258, _294260, _294264))], (4748 ^ _124236) ^ [_294637, _294639, _294641, _294643, _294645] : [class_Groups_Oordered__cancel__ab__semigroup__add(_294637), c_Orderings_Oord__class_Oless(_294637, _294639, _294641), c_Orderings_Oord__class_Oless(_294637, _294643, _294645), -(c_Orderings_Oord__class_Oless(_294637, c_Groups_Oplus__class_Oplus(_294637, _294639, _294643), c_Groups_Oplus__class_Oplus(_294637, _294641, _294645)))], (4762 ^ _124236) ^ [_295115, _295117, _295119, _295121] : [class_Groups_Oordered__cancel__ab__semigroup__add(_295115), c_Orderings_Oord__class_Oless(_295115, _295117, _295119), -(c_Orderings_Oord__class_Oless(_295115, c_Groups_Oplus__class_Oplus(_295115, _295121, _295117), c_Groups_Oplus__class_Oplus(_295115, _295121, _295119)))], (4772 ^ _124236) ^ [_295480, _295482, _295484, _295486] : [class_Groups_Oordered__cancel__ab__semigroup__add(_295480), c_Orderings_Oord__class_Oless(_295480, _295482, _295484), -(c_Orderings_Oord__class_Oless(_295480, c_Groups_Oplus__class_Oplus(_295480, _295482, _295486), c_Groups_Oplus__class_Oplus(_295480, _295484, _295486)))], (4782 ^ _124236) ^ [_295845, _295847, _295849, _295851] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_295845), 4785 ^ _124236 : [(4786 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_295845, c_Groups_Oplus__class_Oplus(_295845, _295847, _295849), c_Groups_Oplus__class_Oplus(_295845, _295847, _295851)), -(c_Orderings_Oord__class_Oless(_295845, _295849, _295851))], (4792 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_295845, _295849, _295851), -(c_Orderings_Oord__class_Oless(_295845, c_Groups_Oplus__class_Oplus(_295845, _295847, _295849), c_Groups_Oplus__class_Oplus(_295845, _295847, _295851)))]]], (4798 ^ _124236) ^ [_296393, _296395, _296397, _296399] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_296393), 4801 ^ _124236 : [(4802 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_296393, c_Groups_Oplus__class_Oplus(_296393, _296395, _296397), c_Groups_Oplus__class_Oplus(_296393, _296399, _296397)), -(c_Orderings_Oord__class_Oless(_296393, _296395, _296399))], (4808 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_296393, _296395, _296399), -(c_Orderings_Oord__class_Oless(_296393, c_Groups_Oplus__class_Oplus(_296393, _296395, _296397), c_Groups_Oplus__class_Oplus(_296393, _296399, _296397)))]]], (4814 ^ _124236) ^ [_296955, _296957, _296959, _296961, _296963] : [class_Groups_Oordered__ab__group__add(_296955), c_Groups_Ominus__class_Ominus(_296955, _296957, _296959) = c_Groups_Ominus__class_Ominus(_296955, _296961, _296963), 4821 ^ _124236 : [(4822 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_296955, _296957, _296959), -(c_Orderings_Oord__class_Oless(_296955, _296961, _296963))], (4828 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_296955, _296961, _296963), -(c_Orderings_Oord__class_Oless(_296955, _296957, _296959))]]], (4834 ^ _124236) ^ [_297584, _297586] : [class_Rings_Ocomm__semiring__1(_297584), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297584), _297586), c_Groups_Oone__class_Oone(_297584)) = _297586)], (4840 ^ _124236) ^ [_297812, _297814] : [class_Rings_Ocomm__semiring__1(_297812), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297812), c_Groups_Oone__class_Oone(_297812)), _297814) = _297814)], (4846 ^ _124236) ^ [_298040, _298042] : [class_Groups_Ocomm__monoid__mult(_298040), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298040), _298042), c_Groups_Oone__class_Oone(_298040)) = _298042)], (4852 ^ _124236) ^ [_298268, _298270] : [class_Groups_Omonoid__mult(_298268), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298268), _298270), c_Groups_Oone__class_Oone(_298268)) = _298270)], (4858 ^ _124236) ^ [_298496, _298498] : [class_Groups_Ocomm__monoid__mult(_298496), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298496), c_Groups_Oone__class_Oone(_298496)), _298498) = _298498)], (4864 ^ _124236) ^ [_298724, _298726] : [class_Groups_Omonoid__mult(_298724), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298724), c_Groups_Oone__class_Oone(_298724)), _298726) = _298726)], (4870 ^ _124236) ^ [_298938] : [-(_298938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _298938))], (4876 ^ _124236) ^ [_299147, _299149] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _299147, _299149), _299149 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4882 ^ _124236) ^ [_299330] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _299330, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4884 ^ _124236) ^ [_299453] : [-(_299453 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _299453))], (4890 ^ _124236) ^ [_299614] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _299614), _299614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4896 ^ _124236) ^ [_299793] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _299793, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4898 ^ _124236) ^ [_299915, _299917, _299919] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _299915, _299917), _299919), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _299915, _299919))], (4904 ^ _124236) ^ [_300171, _300173, _300175, _300177] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _300171, _300173), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300175, _300173) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300171, _300177), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _300175, _300177))], (4914 ^ _124236) ^ [_300538, _300540, _300542, _300544] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _300538, _300540), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _300542, _300544), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300538, _300542), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300540, _300544)))], (4924 ^ _124236) ^ [_300893, _300895, _300897] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _300893, _300895), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300893, _300897), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300895, _300897)))], (4930 ^ _124236) ^ [_301143, _301145, _301147] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301143, _301145), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301143, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301147, _301145)))], (4936 ^ _124236) ^ [_301385, _301387, _301389] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301385, _301387), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301385, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301387, _301389)))], (4942 ^ _124236) ^ [_301656, _301658, _301660] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301656, _301658), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301656, _301660)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301658, _301660))], (4948 ^ _124236) ^ [_301844, _301846, _301848] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301846, _301848), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301844, _301846), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301844, _301848)))], (4954 ^ _124236) ^ [_302066, _302068] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _302066, _302068), _302068)], (4956 ^ _124236) ^ [_302164, _302166] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _302164, _302166), _302164)], (4958 ^ _124236) ^ [_302292, _302294, _302296] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _302292, _302294), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _302292, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _302296, _302294)))], (4964 ^ _124236) ^ [_302534, _302536, _302538] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _302534, _302536), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _302534, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _302536, _302538)))], (4970 ^ _124236) ^ [_302791, _302793] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _302791, _302793), 4973 ^ _124236 : [(4974 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _302791, _302793))], (4976 ^ _124236) ^ [] : [_302791 = _302793]]], (4978 ^ _124236) ^ [_303033, _303035] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _303033, _303035)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _303033, _303035), -(_303033 = _303035)], (4998 ^ _124236) ^ [_303626, _303628] : [4999 ^ _124236 : [(5000 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _303626, _303628)], (5002 ^ _124236) ^ [] : [_303626 = _303628]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _303626, _303628))], (4988 ^ _124236) ^ [_303370, _303372] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _303370, _303372), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _303370, _303372)), -(_303370 = _303372)], (5006 ^ _124236) ^ [_303916, _303918] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _303916, _303918), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _303916, _303918))], (5012 ^ _124236) ^ [_304130, _304132] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _304130, _304132), -(_304130 = _304132), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304130, _304132))], (5022 ^ _124236) ^ [_304436, _304438] : [5023 ^ _124236 : [(5024 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304436, _304438)], (5026 ^ _124236) ^ [] : [_304436 = _304438]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _304436, _304438))], (5030 ^ _124236) ^ [_304724, _304726] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304724, _304726), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _304724, _304726))], (5036 ^ _124236) ^ [_304952, _304954, _304956] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304952, _304954), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304952, _304956), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _304956, _304954), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _304956, _304952)))], (5046 ^ _124236) ^ [_305297, _305299, _305301] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _305297, _305299), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _305297, _305301), _305299))], (5052 ^ _124236) ^ [_305554, _305556] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _305554), _305556) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 5055 ^ _124236 : [(5056 ^ _124236) ^ [] : [-(_305554 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5058 ^ _124236) ^ [] : [-(_305556 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5060 ^ _124236) ^ [_305803, _305805] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _305803), _305805) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _305803 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _305805 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5070 ^ _124236) ^ [_306087] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _306087), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _306087)], (5072 ^ _124236) ^ [_306229, _306231] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _306229), _306231), 5075 ^ _124236 : [(5076 ^ _124236) ^ [] : [-(_306229 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5078 ^ _124236) ^ [] : [-(_306231 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5080 ^ _124236) ^ [_306478, _306480] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _306478), _306480)), _306478 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _306480 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5090 ^ _124236) ^ [_306762] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _306762) = _306762)], (5092 ^ _124236) ^ [_306872, _306874] : [class_Rings_Ocomm__semiring__1(_306872), -(c_Polynomial_Osmult(_306872, c_Groups_Oone__class_Oone(_306872), _306874) = _306874)], (5098 ^ _124236) ^ [_307148, _307150, _307152, _307154, _307156, _307158] : [class_Rings_Olinordered__semiring__1__strict(_307148), c_Orderings_Oord__class_Oless(_307148, _307150, _307152), c_Orderings_Oord__class_Oless(_307148, _307154, _307152), c_Orderings_Oord__class_Oless__eq(_307148, c_Groups_Ozero__class_Ozero(_307148), _307156), c_Orderings_Oord__class_Oless__eq(_307148, c_Groups_Ozero__class_Ozero(_307148), _307158), c_Groups_Oplus__class_Oplus(_307148, _307156, _307158) = c_Groups_Oone__class_Oone(_307148), -(c_Orderings_Oord__class_Oless(_307148, c_Groups_Oplus__class_Oplus(_307148, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307148), _307156), _307150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307148), _307158), _307154)), _307152))], (5124 ^ _124236) ^ [_307975, _307977] : [class_Rings_Olinordered__ring(_307975), c_Orderings_Oord__class_Oless(_307975, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307975), _307977), _307977), c_Groups_Ozero__class_Ozero(_307975))], (5130 ^ _124236) ^ [_308234, _308236, _308238, _308240] : [class_Rings_Olinordered__ring__strict(_308234), 5133 ^ _124236 : [(5134 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_308234, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308234), _308236), _308238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308234), _308240), _308238)), 5139 ^ _124236 : [(5140 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_308234, c_Groups_Ozero__class_Ozero(_308234), _308238))], (5142 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_308234, _308236, _308240))]], 5143 ^ _124236 : [(5144 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_308234, _308238, c_Groups_Ozero__class_Ozero(_308234)))], (5146 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_308234, _308240, _308236))]]], (5148 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_308234, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308234), _308236), _308238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308234), _308240), _308238))), 5149 ^ _124236 : [(5150 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_308234, c_Groups_Ozero__class_Ozero(_308234), _308238), c_Orderings_Oord__class_Oless(_308234, _308236, _308240)], (5156 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_308234, _308238, c_Groups_Ozero__class_Ozero(_308234)), c_Orderings_Oord__class_Oless(_308234, _308240, _308236)]]]]], (5164 ^ _124236) ^ [_309337, _309339, _309341, _309343] : [class_Rings_Olinordered__ring__strict(_309337), 5167 ^ _124236 : [(5168 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_309337, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309337), _309339), _309341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309337), _309339), _309343)), 5173 ^ _124236 : [(5174 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_309337, c_Groups_Ozero__class_Ozero(_309337), _309339))], (5176 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_309337, _309341, _309343))]], 5177 ^ _124236 : [(5178 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_309337, _309339, c_Groups_Ozero__class_Ozero(_309337)))], (5180 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_309337, _309343, _309341))]]], (5182 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_309337, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309337), _309339), _309341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309337), _309339), _309343))), 5183 ^ _124236 : [(5184 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_309337, c_Groups_Ozero__class_Ozero(_309337), _309339), c_Orderings_Oord__class_Oless(_309337, _309341, _309343)], (5190 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_309337, _309339, c_Groups_Ozero__class_Ozero(_309337)), c_Orderings_Oord__class_Oless(_309337, _309343, _309341)]]]]], (5198 ^ _124236) ^ [_310440, _310442, _310444, _310446] : [class_Rings_Olinordered__ring__strict(_310440), c_Orderings_Oord__class_Oless(_310440, c_Groups_Ozero__class_Ozero(_310440), _310442), 5205 ^ _124236 : [(5206 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_310440, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310440), _310442), _310444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310440), _310442), _310446)), -(c_Orderings_Oord__class_Oless(_310440, _310444, _310446))], (5212 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_310440, _310444, _310446), -(c_Orderings_Oord__class_Oless(_310440, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310440), _310442), _310444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310440), _310442), _310446)))]]], (5218 ^ _124236) ^ [_311101, _311103, _311105] : [class_Rings_Olinordered__semiring__strict(_311101), c_Orderings_Oord__class_Oless(_311101, c_Groups_Ozero__class_Ozero(_311101), _311103), c_Orderings_Oord__class_Oless(_311101, c_Groups_Ozero__class_Ozero(_311101), _311105), -(c_Orderings_Oord__class_Oless(_311101, c_Groups_Ozero__class_Ozero(_311101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311101), _311103), _311105)))], (5232 ^ _124236) ^ [_311549, _311551, _311553] : [class_Rings_Olinordered__semiring__strict(_311549), c_Orderings_Oord__class_Oless(_311549, c_Groups_Ozero__class_Ozero(_311549), _311551), c_Orderings_Oord__class_Oless(_311549, _311553, c_Groups_Ozero__class_Ozero(_311549)), -(c_Orderings_Oord__class_Oless(_311549, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311549), _311551), _311553), c_Groups_Ozero__class_Ozero(_311549)))], (5246 ^ _124236) ^ [_311997, _311999, _312001] : [class_Rings_Olinordered__semiring__strict(_311997), c_Orderings_Oord__class_Oless(_311997, c_Groups_Ozero__class_Ozero(_311997), _311999), c_Orderings_Oord__class_Oless(_311997, _312001, c_Groups_Ozero__class_Ozero(_311997)), -(c_Orderings_Oord__class_Oless(_311997, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311997), _312001), _311999), c_Groups_Ozero__class_Ozero(_311997)))], (5260 ^ _124236) ^ [_312445, _312447, _312449] : [class_Rings_Olinordered__semiring__strict(_312445), c_Orderings_Oord__class_Oless(_312445, c_Groups_Ozero__class_Ozero(_312445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312445), _312447), _312449)), c_Orderings_Oord__class_Oless(_312445, c_Groups_Ozero__class_Ozero(_312445), _312447), -(c_Orderings_Oord__class_Oless(_312445, c_Groups_Ozero__class_Ozero(_312445), _312449))], (5274 ^ _124236) ^ [_312893, _312895, _312897] : [class_Rings_Olinordered__semiring__strict(_312893), c_Orderings_Oord__class_Oless(_312893, c_Groups_Ozero__class_Ozero(_312893), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312893), _312895), _312897)), c_Orderings_Oord__class_Oless(_312893, c_Groups_Ozero__class_Ozero(_312893), _312897), -(c_Orderings_Oord__class_Oless(_312893, c_Groups_Ozero__class_Ozero(_312893), _312895))], (5288 ^ _124236) ^ [_313355, _313357, _313359, _313361] : [class_Rings_Olinordered__ring__strict(_313355), c_Orderings_Oord__class_Oless(_313355, _313357, c_Groups_Ozero__class_Ozero(_313355)), 5295 ^ _124236 : [(5296 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_313355, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313355), _313357), _313359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313355), _313357), _313361)), -(c_Orderings_Oord__class_Oless(_313355, _313361, _313359))], (5302 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_313355, _313361, _313359), -(c_Orderings_Oord__class_Oless(_313355, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313355), _313357), _313359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313355), _313357), _313361)))]]], (5308 ^ _124236) ^ [_314016, _314018, _314020] : [class_Rings_Olinordered__semiring__strict(_314016), c_Orderings_Oord__class_Oless(_314016, _314018, c_Groups_Ozero__class_Ozero(_314016)), c_Orderings_Oord__class_Oless(_314016, c_Groups_Ozero__class_Ozero(_314016), _314020), -(c_Orderings_Oord__class_Oless(_314016, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314016), _314018), _314020), c_Groups_Ozero__class_Ozero(_314016)))], (5322 ^ _124236) ^ [_314464, _314466, _314468] : [class_Rings_Olinordered__ring__strict(_314464), c_Orderings_Oord__class_Oless(_314464, _314466, c_Groups_Ozero__class_Ozero(_314464)), c_Orderings_Oord__class_Oless(_314464, _314468, c_Groups_Ozero__class_Ozero(_314464)), -(c_Orderings_Oord__class_Oless(_314464, c_Groups_Ozero__class_Ozero(_314464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314464), _314466), _314468)))], (5336 ^ _124236) ^ [_314926, _314928, _314930, _314932] : [class_Rings_Olinordered__semiring__strict(_314926), c_Orderings_Oord__class_Oless(_314926, _314928, _314930), c_Orderings_Oord__class_Oless(_314926, c_Groups_Ozero__class_Ozero(_314926), _314932), -(c_Orderings_Oord__class_Oless(_314926, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314926), _314928), _314932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314926), _314930), _314932)))], (5350 ^ _124236) ^ [_315410, _315412, _315414, _315416] : [class_Rings_Olinordered__semiring__strict(_315410), c_Orderings_Oord__class_Oless(_315410, _315412, _315414), c_Orderings_Oord__class_Oless(_315410, c_Groups_Ozero__class_Ozero(_315410), _315416), -(c_Orderings_Oord__class_Oless(_315410, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315410), _315416), _315412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315410), _315416), _315414)))], (5364 ^ _124236) ^ [_315894, _315896, _315898, _315900] : [class_Rings_Olinordered__comm__semiring__strict(_315894), c_Orderings_Oord__class_Oless(_315894, _315896, _315898), c_Orderings_Oord__class_Oless(_315894, c_Groups_Ozero__class_Ozero(_315894), _315900), -(c_Orderings_Oord__class_Oless(_315894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315894), _315900), _315896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315894), _315900), _315898)))], (5378 ^ _124236) ^ [_316378, _316380, _316382, _316384] : [class_Rings_Olinordered__ring__strict(_316378), c_Orderings_Oord__class_Oless(_316378, _316380, _316382), c_Orderings_Oord__class_Oless(_316378, _316384, c_Groups_Ozero__class_Ozero(_316378)), -(c_Orderings_Oord__class_Oless(_316378, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316378), _316382), _316384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316378), _316380), _316384)))], (5392 ^ _124236) ^ [_316862, _316864, _316866, _316868] : [class_Rings_Olinordered__ring__strict(_316862), c_Orderings_Oord__class_Oless(_316862, _316864, _316866), c_Orderings_Oord__class_Oless(_316862, _316868, c_Groups_Ozero__class_Ozero(_316862)), -(c_Orderings_Oord__class_Oless(_316862, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316862), _316868), _316866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316862), _316868), _316864)))], (5406 ^ _124236) ^ [_317318, _317320] : [class_Groups_Olinordered__ab__group__add(_317318), 5409 ^ _124236 : [(5410 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_317318, c_Groups_Ozero__class_Ozero(_317318), c_Groups_Oplus__class_Oplus(_317318, _317320, _317320)), -(c_Orderings_Oord__class_Oless(_317318, c_Groups_Ozero__class_Ozero(_317318), _317320))], (5416 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_317318, c_Groups_Ozero__class_Ozero(_317318), _317320), -(c_Orderings_Oord__class_Oless(_317318, c_Groups_Ozero__class_Ozero(_317318), c_Groups_Oplus__class_Oplus(_317318, _317320, _317320)))]]], (5422 ^ _124236) ^ [_317806, _317808] : [class_Groups_Olinordered__ab__group__add(_317806), 5425 ^ _124236 : [(5426 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_317806, c_Groups_Oplus__class_Oplus(_317806, _317808, _317808), c_Groups_Ozero__class_Ozero(_317806)), -(c_Orderings_Oord__class_Oless(_317806, _317808, c_Groups_Ozero__class_Ozero(_317806)))], (5432 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_317806, _317808, c_Groups_Ozero__class_Ozero(_317806)), -(c_Orderings_Oord__class_Oless(_317806, c_Groups_Oplus__class_Oplus(_317806, _317808, _317808), c_Groups_Ozero__class_Ozero(_317806)))]]], (5438 ^ _124236) ^ [_318308, _318310, _318312] : [class_Groups_Oordered__comm__monoid__add(_318308), c_Orderings_Oord__class_Oless(_318308, c_Groups_Ozero__class_Ozero(_318308), _318310), c_Orderings_Oord__class_Oless(_318308, c_Groups_Ozero__class_Ozero(_318308), _318312), -(c_Orderings_Oord__class_Oless(_318308, c_Groups_Ozero__class_Ozero(_318308), c_Groups_Oplus__class_Oplus(_318308, _318310, _318312)))], (5452 ^ _124236) ^ [_318748, _318750, _318752] : [class_Groups_Oordered__comm__monoid__add(_318748), c_Orderings_Oord__class_Oless(_318748, _318750, c_Groups_Ozero__class_Ozero(_318748)), c_Orderings_Oord__class_Oless(_318748, _318752, c_Groups_Ozero__class_Ozero(_318748)), -(c_Orderings_Oord__class_Oless(_318748, c_Groups_Oplus__class_Oplus(_318748, _318750, _318752), c_Groups_Ozero__class_Ozero(_318748)))], (5466 ^ _124236) ^ [_319174, _319176] : [class_Rings_Olinordered__idom(_319174), 5469 ^ _124236 : [(5470 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_319174, c_Groups_Oplus__class_Oplus(_319174, _319176, _319176), c_Groups_Ozero__class_Ozero(_319174)), -(c_Orderings_Oord__class_Oless(_319174, _319176, c_Groups_Ozero__class_Ozero(_319174)))], (5476 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_319174, _319176, c_Groups_Ozero__class_Ozero(_319174)), -(c_Orderings_Oord__class_Oless(_319174, c_Groups_Oplus__class_Oplus(_319174, _319176, _319176), c_Groups_Ozero__class_Ozero(_319174)))]]], (5482 ^ _124236) ^ [_319690, _319692, _319694, _319696] : [class_Rings_Olinordered__semidom(_319690), c_Orderings_Oord__class_Oless(_319690, c_Groups_Ozero__class_Ozero(_319690), _319692), c_Orderings_Oord__class_Oless(_319690, _319694, _319696), -(c_Orderings_Oord__class_Oless(_319690, _319694, c_Groups_Oplus__class_Oplus(_319690, _319692, _319696)))], (5496 ^ _124236) ^ [_320164, _320166, _320168, _320170, _320172] : [class_Groups_Oordered__cancel__ab__semigroup__add(_320164), c_Orderings_Oord__class_Oless__eq(_320164, _320166, _320168), c_Orderings_Oord__class_Oless(_320164, _320170, _320172), -(c_Orderings_Oord__class_Oless(_320164, c_Groups_Oplus__class_Oplus(_320164, _320166, _320170), c_Groups_Oplus__class_Oplus(_320164, _320168, _320172)))], (5510 ^ _124236) ^ [_320656, _320658, _320660, _320662, _320664] : [class_Groups_Oordered__cancel__ab__semigroup__add(_320656), c_Orderings_Oord__class_Oless(_320656, _320658, _320660), c_Orderings_Oord__class_Oless__eq(_320656, _320662, _320664), -(c_Orderings_Oord__class_Oless(_320656, c_Groups_Oplus__class_Oplus(_320656, _320658, _320662), c_Groups_Oplus__class_Oplus(_320656, _320660, _320664)))], (5524 ^ _124236) ^ [_321120, _321122, _321124] : [class_Groups_Oordered__ab__group__add(_321120), 5527 ^ _124236 : [(5528 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_321120, _321122, _321124), -(c_Orderings_Oord__class_Oless(_321120, c_Groups_Ominus__class_Ominus(_321120, _321122, _321124), c_Groups_Ozero__class_Ozero(_321120)))], (5534 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_321120, c_Groups_Ominus__class_Ominus(_321120, _321122, _321124), c_Groups_Ozero__class_Ozero(_321120)), -(c_Orderings_Oord__class_Oless(_321120, _321122, _321124))]]], (5540 ^ _124236) ^ [_321604] : [class_Rings_Olinordered__semidom(_321604), c_Orderings_Oord__class_Oless__eq(_321604, c_Groups_Oone__class_Oone(_321604), c_Groups_Ozero__class_Ozero(_321604))], (5546 ^ _124236) ^ [_321803] : [class_Rings_Olinordered__semidom(_321803), -(c_Orderings_Oord__class_Oless__eq(_321803, c_Groups_Ozero__class_Ozero(_321803), c_Groups_Oone__class_Oone(_321803)))], (5552 ^ _124236) ^ [_322015, _322017] : [class_Rings_Ocomm__semiring__1(_322015), -(c_Groups_Oplus__class_Oplus(_322015, _322017, _322017) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322015), c_Groups_Oplus__class_Oplus(_322015, c_Groups_Oone__class_Oone(_322015), c_Groups_Oone__class_Oone(_322015))), _322017))], (5558 ^ _124236) ^ [_322277, _322279, _322281] : [class_Rings_Ocomm__semiring__1(_322277), -(c_Groups_Oplus__class_Oplus(_322277, _322279, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322277), _322281), _322279)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322277), c_Groups_Oplus__class_Oplus(_322277, _322281, c_Groups_Oone__class_Oone(_322277))), _322279))], (5564 ^ _124236) ^ [_322557, _322559, _322561] : [class_Rings_Ocomm__semiring__1(_322557), -(c_Groups_Oplus__class_Oplus(_322557, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322557), _322559), _322561), _322561) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322557), c_Groups_Oplus__class_Oplus(_322557, _322559, c_Groups_Oone__class_Oone(_322557))), _322561))], (5580 ^ _124236) ^ [_323118, _323120] : [5581 ^ _124236 : [(5582 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _323118)], (5584 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _323120)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _323118, _323120)))], (5570 ^ _124236) ^ [_322852, _322854] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _322852, _322854)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _322852)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _322854))], (5588 ^ _124236) ^ [_323432, _323434, _323436] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _323432), 5591 ^ _124236 : [(5592 ^ _124236) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _323432), _323434) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _323432), _323436), -(_323434 = _323436)], (5598 ^ _124236) ^ [] : [_323434 = _323436, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _323432), _323434) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _323432), _323436))]]], (5604 ^ _124236) ^ [_323960, _323962, _323964] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _323960), 5607 ^ _124236 : [(5608 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _323960), _323962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _323960), _323964)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323962, _323964))], (5614 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323962, _323964), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _323960), _323962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _323960), _323964)))]]], (5620 ^ _124236) ^ [_324509, _324511] : [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), _324509), _324511)), 5623 ^ _124236 : [(5624 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _324509))], (5626 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _324511))]]], (5628 ^ _124236) ^ [_324764, _324766] : [-(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), _324764), _324766))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _324764), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _324766)], (5638 ^ _124236) ^ [_325126, _325128, _325130] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _325126), _325128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _325126), _325130)), 5641 ^ _124236 : [(5642 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _325126))], (5644 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _325128, _325130))]]], (5646 ^ _124236) ^ [_325401, _325403, _325405] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _325401), _325403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _325401), _325405))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _325401), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _325403, _325405)], (5656 ^ _124236) ^ [_325785, _325787, _325789] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _325785), _325787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _325789), _325787)), 5659 ^ _124236 : [(5660 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _325787))], (5662 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _325785, _325789))]]], (5664 ^ _124236) ^ [_326060, _326062, _326064] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326060), _326062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326064), _326062))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _326062), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326060, _326064)], (5674 ^ _124236) ^ [_326415, _326417, _326419] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326415, _326417), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _326419), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326415), _326419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326417), _326419)))], (5684 ^ _124236) ^ [_326768, _326770, _326772] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326768, _326770), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _326772), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326772), _326768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326772), _326770)))], (5694 ^ _124236) ^ [_327136, _327138] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _327136, _327138)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327138, _327136))], (5700 ^ _124236) ^ [_327310, _327312] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327312, _327310), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _327310, _327312)))], (5706 ^ _124236) ^ [_327534, _327536] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _327534), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _327536), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _327536, _327534), _327536))], (5716 ^ _124236) ^ [_327847, _327849] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327847, _327849)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _327849, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _327847, _327849)) = _327847)], (5722 ^ _124236) ^ [_328121, _328123, _328125] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _328121, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328123, _328125)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _328121, _328125), _328123))], (5728 ^ _124236) ^ [_328309, _328311, _328313] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _328309, _328313), _328311), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _328309, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328311, _328313)))], (5734 ^ _124236) ^ [_328561, _328563, _328565] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _328561, _328563), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _328565, _328561), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328561, _328565), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328563, _328565)))], (5744 ^ _124236) ^ [_328906, _328908, _328910] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _328906, _328908), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _328906, _328910), 5751 ^ _124236 : [(5752 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328908, _328906), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328910, _328906)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _328908, _328910))], (5758 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _328908, _328910), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328908, _328906), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328910, _328906)))]]], (5764 ^ _124236) ^ [_329509, _329511] : [_329509 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _329509), _329511), -(_329511 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_329509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5774 ^ _124236) ^ [_329849, _329851, _329853, _329855] : [class_Rings_Olinordered__ring__strict(_329849), c_Orderings_Oord__class_Oless(_329849, c_Groups_Ozero__class_Ozero(_329849), _329851), 5781 ^ _124236 : [(5782 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_329849, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329849), _329851), _329853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329849), _329851), _329855)), -(c_Orderings_Oord__class_Oless__eq(_329849, _329853, _329855))], (5788 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_329849, _329853, _329855), -(c_Orderings_Oord__class_Oless__eq(_329849, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329849), _329851), _329853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329849), _329851), _329855)))]]], (5794 ^ _124236) ^ [_330524, _330526, _330528, _330530] : [class_Rings_Olinordered__ring__strict(_330524), c_Orderings_Oord__class_Oless(_330524, _330526, c_Groups_Ozero__class_Ozero(_330524)), 5801 ^ _124236 : [(5802 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330524), _330526), _330528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330524), _330526), _330530)), -(c_Orderings_Oord__class_Oless__eq(_330524, _330530, _330528))], (5808 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330524, _330530, _330528), -(c_Orderings_Oord__class_Oless__eq(_330524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330524), _330526), _330528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330524), _330526), _330530)))]]], (5814 ^ _124236) ^ [_331213, _331215, _331217, _331219, _331221] : [class_Rings_Olinordered__semiring__strict(_331213), c_Orderings_Oord__class_Oless(_331213, _331215, _331217), c_Orderings_Oord__class_Oless(_331213, _331219, _331221), c_Orderings_Oord__class_Oless(_331213, c_Groups_Ozero__class_Ozero(_331213), _331217), c_Orderings_Oord__class_Oless__eq(_331213, c_Groups_Ozero__class_Ozero(_331213), _331219), -(c_Orderings_Oord__class_Oless(_331213, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_331213), _331215), _331219), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_331213), _331217), _331221)))], (5836 ^ _124236) ^ [_331935, _331937, _331939, _331941, _331943] : [class_Rings_Olinordered__semiring__strict(_331935), c_Orderings_Oord__class_Oless(_331935, _331937, _331939), c_Orderings_Oord__class_Oless(_331935, _331941, _331943), c_Orderings_Oord__class_Oless__eq(_331935, c_Groups_Ozero__class_Ozero(_331935), _331937), c_Orderings_Oord__class_Oless__eq(_331935, c_Groups_Ozero__class_Ozero(_331935), _331941), -(c_Orderings_Oord__class_Oless(_331935, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_331935), _331937), _331941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_331935), _331939), _331943)))], (5858 ^ _124236) ^ [_332657, _332659, _332661, _332663, _332665] : [class_Rings_Olinordered__semiring__strict(_332657), c_Orderings_Oord__class_Oless(_332657, _332659, _332661), c_Orderings_Oord__class_Oless__eq(_332657, _332663, _332665), c_Orderings_Oord__class_Oless__eq(_332657, c_Groups_Ozero__class_Ozero(_332657), _332659), c_Orderings_Oord__class_Oless(_332657, c_Groups_Ozero__class_Ozero(_332657), _332663), -(c_Orderings_Oord__class_Oless(_332657, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332657), _332659), _332663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332657), _332661), _332665)))], (5880 ^ _124236) ^ [_333379, _333381, _333383, _333385, _333387] : [class_Rings_Olinordered__semiring__strict(_333379), c_Orderings_Oord__class_Oless__eq(_333379, _333381, _333383), c_Orderings_Oord__class_Oless(_333379, _333385, _333387), c_Orderings_Oord__class_Oless(_333379, c_Groups_Ozero__class_Ozero(_333379), _333381), c_Orderings_Oord__class_Oless__eq(_333379, c_Groups_Ozero__class_Ozero(_333379), _333385), -(c_Orderings_Oord__class_Oless(_333379, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333379), _333381), _333385), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333379), _333383), _333387)))], (5902 ^ _124236) ^ [_334087, _334089, _334091, _334093] : [class_Rings_Olinordered__semiring(_334087), c_Orderings_Oord__class_Oless(_334087, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334087), _334089), _334091), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334087), _334093), _334091)), c_Orderings_Oord__class_Oless__eq(_334087, c_Groups_Ozero__class_Ozero(_334087), _334091), -(c_Orderings_Oord__class_Oless(_334087, _334089, _334093))], (5916 ^ _124236) ^ [_334571, _334573, _334575, _334577] : [class_Rings_Olinordered__semiring__strict(_334571), c_Orderings_Oord__class_Oless(_334571, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334571), _334573), _334575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334571), _334577), _334575)), c_Orderings_Oord__class_Oless__eq(_334571, c_Groups_Ozero__class_Ozero(_334571), _334575), -(c_Orderings_Oord__class_Oless(_334571, _334573, _334577))], (5930 ^ _124236) ^ [_335055, _335057, _335059, _335061] : [class_Rings_Olinordered__semiring(_335055), c_Orderings_Oord__class_Oless(_335055, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335055), _335057), _335059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335055), _335057), _335061)), c_Orderings_Oord__class_Oless__eq(_335055, c_Groups_Ozero__class_Ozero(_335055), _335057), -(c_Orderings_Oord__class_Oless(_335055, _335059, _335061))], (5944 ^ _124236) ^ [_335539, _335541, _335543, _335545] : [class_Rings_Olinordered__semiring__strict(_335539), c_Orderings_Oord__class_Oless(_335539, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335539), _335541), _335543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335539), _335541), _335545)), c_Orderings_Oord__class_Oless__eq(_335539, c_Groups_Ozero__class_Ozero(_335539), _335541), -(c_Orderings_Oord__class_Oless(_335539, _335543, _335545))], (5958 ^ _124236) ^ [_336023, _336025, _336027, _336029] : [class_Rings_Olinordered__semiring__strict(_336023), c_Orderings_Oord__class_Oless__eq(_336023, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336023), _336025), _336027), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336023), _336029), _336027)), c_Orderings_Oord__class_Oless(_336023, c_Groups_Ozero__class_Ozero(_336023), _336027), -(c_Orderings_Oord__class_Oless__eq(_336023, _336025, _336029))], (5972 ^ _124236) ^ [_336507, _336509, _336511, _336513] : [class_Rings_Olinordered__semiring__strict(_336507), c_Orderings_Oord__class_Oless__eq(_336507, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336507), _336509), _336511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336507), _336509), _336513)), c_Orderings_Oord__class_Oless(_336507, c_Groups_Ozero__class_Ozero(_336507), _336509), -(c_Orderings_Oord__class_Oless__eq(_336507, _336511, _336513))], (5986 ^ _124236) ^ [_336977, _336979, _336981] : [class_Groups_Oordered__comm__monoid__add(_336977), c_Orderings_Oord__class_Oless__eq(_336977, _336979, c_Groups_Ozero__class_Ozero(_336977)), c_Orderings_Oord__class_Oless(_336977, _336981, c_Groups_Ozero__class_Ozero(_336977)), -(c_Orderings_Oord__class_Oless(_336977, c_Groups_Oplus__class_Oplus(_336977, _336979, _336981), c_Groups_Ozero__class_Ozero(_336977)))], (6000 ^ _124236) ^ [_337417, _337419, _337421] : [class_Groups_Oordered__comm__monoid__add(_337417), c_Orderings_Oord__class_Oless(_337417, _337419, c_Groups_Ozero__class_Ozero(_337417)), c_Orderings_Oord__class_Oless__eq(_337417, _337421, c_Groups_Ozero__class_Ozero(_337417)), -(c_Orderings_Oord__class_Oless(_337417, c_Groups_Oplus__class_Oplus(_337417, _337419, _337421), c_Groups_Ozero__class_Ozero(_337417)))], (6014 ^ _124236) ^ [_337871, _337873, _337875, _337877] : [class_Groups_Oordered__comm__monoid__add(_337871), c_Orderings_Oord__class_Oless__eq(_337871, c_Groups_Ozero__class_Ozero(_337871), _337873), c_Orderings_Oord__class_Oless(_337871, _337875, _337877), -(c_Orderings_Oord__class_Oless(_337871, _337875, c_Groups_Oplus__class_Oplus(_337871, _337873, _337877)))], (6028 ^ _124236) ^ [_338331, _338333, _338335, _338337] : [class_Groups_Oordered__comm__monoid__add(_338331), c_Orderings_Oord__class_Oless(_338331, c_Groups_Ozero__class_Ozero(_338331), _338333), c_Orderings_Oord__class_Oless__eq(_338331, _338335, _338337), -(c_Orderings_Oord__class_Oless(_338331, _338335, c_Groups_Oplus__class_Oplus(_338331, _338333, _338337)))], (6042 ^ _124236) ^ [_338777, _338779, _338781] : [class_Groups_Oordered__comm__monoid__add(_338777), c_Orderings_Oord__class_Oless__eq(_338777, c_Groups_Ozero__class_Ozero(_338777), _338779), c_Orderings_Oord__class_Oless(_338777, c_Groups_Ozero__class_Ozero(_338777), _338781), -(c_Orderings_Oord__class_Oless(_338777, c_Groups_Ozero__class_Ozero(_338777), c_Groups_Oplus__class_Oplus(_338777, _338779, _338781)))], (6056 ^ _124236) ^ [_339217, _339219, _339221] : [class_Groups_Oordered__comm__monoid__add(_339217), c_Orderings_Oord__class_Oless(_339217, c_Groups_Ozero__class_Ozero(_339217), _339219), c_Orderings_Oord__class_Oless__eq(_339217, c_Groups_Ozero__class_Ozero(_339217), _339221), -(c_Orderings_Oord__class_Oless(_339217, c_Groups_Ozero__class_Ozero(_339217), c_Groups_Oplus__class_Oplus(_339217, _339219, _339221)))], (6070 ^ _124236) ^ [_339657, _339659, _339661] : [class_Rings_Olinordered__ring(_339657), c_Orderings_Oord__class_Oless(_339657, c_Groups_Oplus__class_Oplus(_339657, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339657), _339659), _339659), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339657), _339661), _339661)), c_Groups_Ozero__class_Ozero(_339657))], (6076 ^ _124236) ^ [_339932, _339934, _339936] : [class_Rings_Olinordered__ring__strict(_339932), 6079 ^ _124236 : [(6090 ^ _124236) ^ [] : [6091 ^ _124236 : [(6092 ^ _124236) ^ [] : [-(_339934 = c_Groups_Ozero__class_Ozero(_339932))], (6094 ^ _124236) ^ [] : [-(_339936 = c_Groups_Ozero__class_Ozero(_339932))]], -(c_Orderings_Oord__class_Oless(_339932, c_Groups_Ozero__class_Ozero(_339932), c_Groups_Oplus__class_Oplus(_339932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339932), _339934), _339934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339932), _339936), _339936))))], (6080 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_339932, c_Groups_Ozero__class_Ozero(_339932), c_Groups_Oplus__class_Oplus(_339932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339932), _339934), _339934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339932), _339936), _339936))), _339934 = c_Groups_Ozero__class_Ozero(_339932), _339936 = c_Groups_Ozero__class_Ozero(_339932)]]], (6098 ^ _124236) ^ [_340669, _340671, _340673] : [class_Rings_Olinordered__idom(_340669), c_Orderings_Oord__class_Oless__eq(_340669, c_Groups_Ozero__class_Ozero(_340669), _340671), c_Orderings_Oord__class_Oless__eq(_340669, c_Groups_Ozero__class_Ozero(_340669), _340673), c_Orderings_Oord__class_Oless__eq(_340669, _340673, c_Groups_Oone__class_Oone(_340669)), -(c_Orderings_Oord__class_Oless__eq(_340669, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340669), _340671), _340673), _340671))], (6116 ^ _124236) ^ [_341212, _341214, _341216] : [class_Rings_Olinordered__idom(_341212), c_Orderings_Oord__class_Oless__eq(_341212, c_Groups_Ozero__class_Ozero(_341212), _341214), c_Orderings_Oord__class_Oless__eq(_341212, c_Groups_Ozero__class_Ozero(_341212), _341216), c_Orderings_Oord__class_Oless__eq(_341212, _341216, c_Groups_Oone__class_Oone(_341212)), -(c_Orderings_Oord__class_Oless__eq(_341212, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341212), _341216), _341214), _341214))], (6134 ^ _124236) ^ [_341797, _341799, _341801, _341803, _341805, _341807] : [class_Rings_Oordered__ring(_341797), 6137 ^ _124236 : [(6138 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_341797, c_Groups_Oplus__class_Oplus(_341797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341797), _341799), _341801), _341803), c_Groups_Oplus__class_Oplus(_341797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341797), _341805), _341801), _341807)), -(c_Orderings_Oord__class_Oless(_341797, _341803, c_Groups_Oplus__class_Oplus(_341797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341797), c_Groups_Ominus__class_Ominus(_341797, _341805, _341799)), _341801), _341807)))], (6144 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_341797, _341803, c_Groups_Oplus__class_Oplus(_341797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341797), c_Groups_Ominus__class_Ominus(_341797, _341805, _341799)), _341801), _341807)), -(c_Orderings_Oord__class_Oless(_341797, c_Groups_Oplus__class_Oplus(_341797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341797), _341799), _341801), _341803), c_Groups_Oplus__class_Oplus(_341797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341797), _341805), _341801), _341807)))]]], (6150 ^ _124236) ^ [_342501, _342503, _342505, _342507, _342509, _342511] : [class_Rings_Oordered__ring(_342501), 6153 ^ _124236 : [(6154 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_342501, c_Groups_Oplus__class_Oplus(_342501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342501), _342503), _342505), _342507), c_Groups_Oplus__class_Oplus(_342501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342501), _342509), _342505), _342511)), -(c_Orderings_Oord__class_Oless(_342501, c_Groups_Oplus__class_Oplus(_342501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342501), c_Groups_Ominus__class_Ominus(_342501, _342503, _342509)), _342505), _342507), _342511))], (6160 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_342501, c_Groups_Oplus__class_Oplus(_342501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342501), c_Groups_Ominus__class_Ominus(_342501, _342503, _342509)), _342505), _342507), _342511), -(c_Orderings_Oord__class_Oless(_342501, c_Groups_Oplus__class_Oplus(_342501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342501), _342503), _342505), _342507), c_Groups_Oplus__class_Oplus(_342501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342501), _342509), _342505), _342511)))]]], (6166 ^ _124236) ^ [_343149, _343151] : [class_Rings_Oring__1(_343149), -(c_Groups_Ominus__class_Ominus(_343149, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343149), _343151), _343151), c_Groups_Oone__class_Oone(_343149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343149), c_Groups_Oplus__class_Oplus(_343149, _343151, c_Groups_Oone__class_Oone(_343149))), c_Groups_Ominus__class_Ominus(_343149, _343151, c_Groups_Oone__class_Oone(_343149))))], (6172 ^ _124236) ^ [_343439, _343441, _343443] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _343439), 6175 ^ _124236 : [(6176 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343439), _343441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343439), _343443)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _343441, _343443))], (6182 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _343441, _343443), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343439), _343441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343439), _343443)))]]], (6198 ^ _124236) ^ [_344293, _344295, _344297] : [6199 ^ _124236 : [(6200 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _344293))], (6202 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _344295, _344297)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344293), _344295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344293), _344297)))], (6188 ^ _124236) ^ [_344002, _344004, _344006] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344002), _344004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344002), _344006)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _344002), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _344004, _344006))], (6216 ^ _124236) ^ [_344952, _344954, _344956] : [6217 ^ _124236 : [(6218 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _344954))], (6220 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _344952, _344956)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344952), _344954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344956), _344954)))], (6206 ^ _124236) ^ [_344661, _344663, _344665] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344661), _344663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344665), _344663)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _344663), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _344661, _344665))], (6240 ^ _124236) ^ [_345859, _345861, _345863] : [-(hBOOL(hAPP(_345859, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _345861, _345863)))), 6243 ^ _124236 : [(6244 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _345861, _345863))], (6246 ^ _124236) ^ [] : [hBOOL(hAPP(_345859, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6248 ^ _124236 : [(6249 ^ _124236) ^ [] : [-(_345861 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _345863, 6247 ^ [_345859, _345861, _345863]))], (6251 ^ _124236) ^ [] : [hBOOL(hAPP(_345859, 6247 ^ [_345859, _345861, _345863]))]]], (6224 ^ _124236) ^ [_345320, _345322, _345324] : [hBOOL(hAPP(_345320, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _345322, _345324))), 6227 ^ _124236 : [(6228 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _345322, _345324), -(hBOOL(hAPP(_345320, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6234 ^ _124236) ^ [_345658] : [_345322 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _345324, _345658), -(hBOOL(hAPP(_345320, _345658)))]]], (6271 ^ _124236) ^ [_347020, _347022, _347024] : [-(hBOOL(hAPP(_347020, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _347022, _347024)))), 6274 ^ _124236 : [(6275 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _347022, _347024))], (6277 ^ _124236) ^ [] : [hBOOL(hAPP(_347020, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6279 ^ _124236 : [(6280 ^ _124236) ^ [] : [-(_347022 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _347024, 6278 ^ [_347020, _347022, _347024]))], (6282 ^ _124236) ^ [] : [hBOOL(hAPP(_347020, 6278 ^ [_347020, _347022, _347024]))]]], (6255 ^ _124236) ^ [_346489, _346491, _346493] : [hBOOL(hAPP(_346489, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _346491, _346493))), 6258 ^ _124236 : [(6259 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _346491, _346493), -(hBOOL(hAPP(_346489, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6265 ^ _124236) ^ [_346821] : [_346491 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _346493, _346821), -(hBOOL(hAPP(_346489, _346821)))]]], (6286 ^ _124236) ^ [_347655, _347657, _347659, _347661, _347663, _347665] : [class_Rings_Olinordered__semiring__1(_347655), c_Orderings_Oord__class_Oless__eq(_347655, _347657, _347659), c_Orderings_Oord__class_Oless__eq(_347655, _347661, _347659), c_Orderings_Oord__class_Oless__eq(_347655, c_Groups_Ozero__class_Ozero(_347655), _347663), c_Orderings_Oord__class_Oless__eq(_347655, c_Groups_Ozero__class_Ozero(_347655), _347665), c_Groups_Oplus__class_Oplus(_347655, _347663, _347665) = c_Groups_Oone__class_Oone(_347655), -(c_Orderings_Oord__class_Oless__eq(_347655, c_Groups_Oplus__class_Oplus(_347655, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347655), _347663), _347657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347655), _347665), _347661)), _347659))], (6312 ^ _124236) ^ [_348496, _348498, _348500] : [class_Rings_Ocomm__ring__1(_348496), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_348496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_348496)), c_Polynomial_OpCons(_348496, c_Groups_Ouminus__class_Ouminus(_348496, _348498), c_Polynomial_OpCons(_348496, c_Groups_Oone__class_Oone(_348496), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_348496))))), c_Polynomial_Osynthetic__div(_348496, _348500, _348498)), c_Polynomial_OpCons(_348496, hAPP(c_Polynomial_Opoly(_348496, _348500), _348498), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_348496)))) = _348500)], (6318 ^ _124236) ^ [_348826, _348828, _348830] : [class_Rings_Olinordered__idom(_348826), 6321 ^ _124236 : [(6322 ^ _124236) ^ [] : [c_Polynomial_Opos__poly(_348826, c_Polynomial_OpCons(_348826, _348828, _348830)), -(c_Polynomial_Opos__poly(_348826, _348830)), 6329 ^ _124236 : [(6330 ^ _124236) ^ [] : [-(_348830 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_348826)))], (6332 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(_348826, c_Groups_Ozero__class_Ozero(_348826), _348828))]]], (6334 ^ _124236) ^ [] : [-(c_Polynomial_Opos__poly(_348826, c_Polynomial_OpCons(_348826, _348828, _348830))), 6335 ^ _124236 : [(6336 ^ _124236) ^ [] : [c_Polynomial_Opos__poly(_348826, _348830)], (6338 ^ _124236) ^ [] : [_348830 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_348826)), c_Orderings_Oord__class_Oless(_348826, c_Groups_Ozero__class_Ozero(_348826), _348828)]]]]], (6346 ^ _124236) ^ [_349661, _349663] : [-(hBOOL(hAPP(_349661, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_349661, _349663)), 6354 ^ _124236 : [(6355 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 6353 ^ [_349661, _349663], _349663))], (6363 ^ _124236) ^ [] : [-(hBOOL(hAPP(_349661, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 6353 ^ [_349661, _349663], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (6357 ^ _124236) ^ [_350097] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _350097, 6353 ^ [_349661, _349663]), hBOOL(hAPP(_349661, _350097))]]], (6365 ^ _124236) ^ [_350424, _350426, _350428] : [class_Groups_Omonoid__mult(_350424), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _350426), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350424), hAPP(hAPP(c_Power_Opower__class_Opower(_350424), _350428), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _350426, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _350428) = hAPP(hAPP(c_Power_Opower__class_Opower(_350424), _350428), _350426))], (6375 ^ _124236) ^ [_350789, _350791] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _350789), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _350791), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_350789)), c_RComplete_Onatfloor(_350791)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _350789), _350791))))], (6385 ^ _124236) ^ [_351150, _351152] : [_351150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _351150, _351152) = _351152)], (6391 ^ _124236) ^ [_351320, _351322] : [-(_351320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _351320, _351322) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _351320, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _351322)))], (6397 ^ _124236) ^ [_351534] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _351534, c_Nat_OSuc(_351534)))], (6399 ^ _124236) ^ [_351644, _351646] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _351644, _351646), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_351644), c_Nat_OSuc(_351646)))], (6405 ^ _124236) ^ [_351837] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_351837)))], (6407 ^ _124236) ^ [_351961, _351963, _351965] : [class_Rings_Olinordered__idom(_351961), 6410 ^ _124236 : [(6411 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_351961), _351963, _351965), -(c_Polynomial_Opos__poly(_351961, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_351961), _351965, _351963)))], (6417 ^ _124236) ^ [] : [c_Polynomial_Opos__poly(_351961, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_351961), _351965, _351963)), -(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_351961), _351963, _351965))]]], (6423 ^ _124236) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6425 ^ _124236) ^ [_352485] : [_352485 = c_Nat_OSuc(_352485)], (6427 ^ _124236) ^ [_352564] : [c_Nat_OSuc(_352564) = _352564], (6429 ^ _124236) ^ [_352702, _352704] : [c_Nat_OSuc(_352702) = c_Nat_OSuc(_352704), -(_352702 = _352704)], (6435 ^ _124236) ^ [_352872, _352874] : [_352872 = _352874, -(c_Nat_OSuc(_352872) = c_Nat_OSuc(_352874))], (6441 ^ _124236) ^ [_353092, _353094] : [c_Nat_OSuc(_353092) = c_Nat_OSuc(_353094), -(_353092 = _353094)], (6447 ^ _124236) ^ [_353324, _353326, _353328] : [class_Rings_Ocomm__ring(_353324), -(c_Polynomial_Osmult(_353324, c_Groups_Ouminus__class_Ouminus(_353324, _353326), _353328) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_353324), c_Polynomial_Osmult(_353324, _353326, _353328)))], (6453 ^ _124236) ^ [_353584, _353586, _353588] : [class_Groups_Oab__group__add(_353584), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_353584), c_Polynomial_OpCons(_353584, _353586, _353588)) = c_Polynomial_OpCons(_353584, c_Groups_Ouminus__class_Ouminus(_353584, _353586), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_353584), _353588)))], (6459 ^ _124236) ^ [_353854, _353856, _353858] : [class_Groups_Oab__group__add(_353854), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_353854), c_Polynomial_OpCons(_353854, _353856, _353858)) = c_Polynomial_OpCons(_353854, c_Groups_Ouminus__class_Ouminus(_353854, _353856), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_353854), _353858)))], (6465 ^ _124236) ^ [_354110, _354112] : [class_Groups_Ogroup__add(_354110), -(c_Groups_Ouminus__class_Ouminus(_354110, c_Groups_Ouminus__class_Ouminus(_354110, _354112)) = _354112)], (6471 ^ _124236) ^ [_354344, _354346, _354348] : [class_Groups_Ogroup__add(_354344), 6474 ^ _124236 : [(6475 ^ _124236) ^ [] : [_354346 = c_Groups_Ouminus__class_Ouminus(_354344, _354348), -(_354348 = c_Groups_Ouminus__class_Ouminus(_354344, _354346))], (6481 ^ _124236) ^ [] : [_354348 = c_Groups_Ouminus__class_Ouminus(_354344, _354346), -(_354346 = c_Groups_Ouminus__class_Ouminus(_354344, _354348))]]], (6487 ^ _124236) ^ [_354850, _354852, _354854] : [class_Groups_Ogroup__add(_354850), 6490 ^ _124236 : [(6491 ^ _124236) ^ [] : [c_Groups_Ouminus__class_Ouminus(_354850, _354852) = _354854, -(c_Groups_Ouminus__class_Ouminus(_354850, _354854) = _354852)], (6497 ^ _124236) ^ [] : [c_Groups_Ouminus__class_Ouminus(_354850, _354854) = _354852, -(c_Groups_Ouminus__class_Ouminus(_354850, _354852) = _354854)]]], (6503 ^ _124236) ^ [_355356, _355358, _355360] : [class_Groups_Ogroup__add(_355356), 6506 ^ _124236 : [(6507 ^ _124236) ^ [] : [c_Groups_Ouminus__class_Ouminus(_355356, _355358) = c_Groups_Ouminus__class_Ouminus(_355356, _355360), -(_355358 = _355360)], (6513 ^ _124236) ^ [] : [_355358 = _355360, -(c_Groups_Ouminus__class_Ouminus(_355356, _355358) = c_Groups_Ouminus__class_Ouminus(_355356, _355360))]]], (6519 ^ _124236) ^ [_355862, _355864, _355866] : [class_RealVector_Oreal__normed__div__algebra(_355862), -(c_RealVector_Onorm__class_Onorm(_355862, hAPP(hAPP(c_Power_Opower__class_Opower(_355862), _355864), _355866)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_355862, _355864)), _355866))], (6525 ^ _124236) ^ [_356130, _356132, _356134] : [class_Rings_Oidom(_356130), 6528 ^ _124236 : [(6539 ^ _124236) ^ [] : [6540 ^ _124236 : [(6541 ^ _124236) ^ [] : [_356132 = _356134], (6543 ^ _124236) ^ [] : [_356132 = c_Groups_Ouminus__class_Ouminus(_356130, _356134)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_356130), _356132), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_356130), _356134), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (6529 ^ _124236) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_356130), _356132), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_356130), _356134), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_356132 = _356134), -(_356132 = c_Groups_Ouminus__class_Ouminus(_356130, _356134))]]], (6547 ^ _124236) ^ [_356825, _356827] : [class_Rings_Olinordered__idom(_356825), -(_356827 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_356825))), -(c_Polynomial_Opos__poly(_356825, _356827)), -(c_Polynomial_Opos__poly(_356825, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_356825), _356827)))], (6561 ^ _124236) ^ [_357245, _357247, _357249] : [class_Groups_Oab__group__add(_357245), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_357245), c_Polynomial_Omonom(_357245, _357247, _357249)) = c_Polynomial_Omonom(_357245, c_Groups_Ouminus__class_Ouminus(_357245, _357247), _357249))], (6567 ^ _124236) ^ [_357519, _357521, _357523, _357525] : [class_Rings_Ocomm__semiring__1(_357519), -(hAPP(c_Polynomial_Opoly(_357519, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_357519)), _357521), _357523)), _357525) = hAPP(hAPP(c_Power_Opower__class_Opower(_357519), hAPP(c_Polynomial_Opoly(_357519, _357521), _357525)), _357523))], (6573 ^ _124236) ^ [_357813, _357815, _357817] : [class_Rings_Ocomm__ring(_357813), -(hAPP(c_Polynomial_Opoly(_357813, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_357813), _357815)), _357817) = c_Groups_Ouminus__class_Ouminus(_357813, hAPP(c_Polynomial_Opoly(_357813, _357815), _357817)))], (6579 ^ _124236) ^ [_358081, _358083, _358085] : [class_Rings_Ocomm__semiring__1(_358081), -(hAPP(hAPP(c_Power_Opower__class_Opower(_358081), _358083), c_Nat_OSuc(_358085)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358081), _358083), hAPP(hAPP(c_Power_Opower__class_Opower(_358081), _358083), _358085)))], (6585 ^ _124236) ^ [_358361, _358363, _358365] : [class_Rings_Ocomm__semiring__1(_358361), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358361), _358363), hAPP(hAPP(c_Power_Opower__class_Opower(_358361), _358363), _358365)) = hAPP(hAPP(c_Power_Opower__class_Opower(_358361), _358363), c_Nat_OSuc(_358365)))], (6591 ^ _124236) ^ [_358641, _358643, _358645] : [class_Rings_Ocomm__semiring__1(_358641), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358641), hAPP(hAPP(c_Power_Opower__class_Opower(_358641), _358643), _358645)), _358643) = hAPP(hAPP(c_Power_Opower__class_Opower(_358641), _358643), c_Nat_OSuc(_358645)))], (6597 ^ _124236) ^ [_358921, _358923, _358925] : [class_RealVector_Oreal__normed__algebra__1(_358921), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_358921, hAPP(hAPP(c_Power_Opower__class_Opower(_358921), _358923), _358925)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_358921, _358923)), _358925)))], (6603 ^ _124236) ^ [_359206, _359208] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _359206, _359208)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _359206), _359208))], (6609 ^ _124236) ^ [_359386, _359388] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _359386), _359388), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _359386, _359388)))], (6615 ^ _124236) ^ [_359645, _359647] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _359645, _359647), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _359647, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _359645)))], (6621 ^ _124236) ^ [_359825, _359827] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _359827, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _359825)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _359825, _359827), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (6627 ^ _124236) ^ [_360055, _360057] : [class_Groups_Olinordered__ab__group__add(_360055), 6630 ^ _124236 : [(6631 ^ _124236) ^ [] : [c_Groups_Ouminus__class_Ouminus(_360055, _360057) = _360057, -(_360057 = c_Groups_Ozero__class_Ozero(_360055))], (6637 ^ _124236) ^ [] : [_360057 = c_Groups_Ozero__class_Ozero(_360055), -(c_Groups_Ouminus__class_Ouminus(_360055, _360057) = _360057)]]], (6643 ^ _124236) ^ [_360528, _360530] : [class_Groups_Ogroup__add(_360528), 6646 ^ _124236 : [(6647 ^ _124236) ^ [] : [c_Groups_Ouminus__class_Ouminus(_360528, _360530) = c_Groups_Ozero__class_Ozero(_360528), -(_360530 = c_Groups_Ozero__class_Ozero(_360528))], (6653 ^ _124236) ^ [] : [_360530 = c_Groups_Ozero__class_Ozero(_360528), -(c_Groups_Ouminus__class_Ouminus(_360528, _360530) = c_Groups_Ozero__class_Ozero(_360528))]]], (6659 ^ _124236) ^ [_361007, _361009] : [class_Groups_Olinordered__ab__group__add(_361007), 6662 ^ _124236 : [(6663 ^ _124236) ^ [] : [_361009 = c_Groups_Ouminus__class_Ouminus(_361007, _361009), -(_361009 = c_Groups_Ozero__class_Ozero(_361007))], (6669 ^ _124236) ^ [] : [_361009 = c_Groups_Ozero__class_Ozero(_361007), -(_361009 = c_Groups_Ouminus__class_Ouminus(_361007, _361009))]]], (6675 ^ _124236) ^ [_361480, _361482] : [class_Groups_Ogroup__add(_361480), 6678 ^ _124236 : [(6679 ^ _124236) ^ [] : [c_Groups_Ozero__class_Ozero(_361480) = c_Groups_Ouminus__class_Ouminus(_361480, _361482), -(c_Groups_Ozero__class_Ozero(_361480) = _361482)], (6685 ^ _124236) ^ [] : [c_Groups_Ozero__class_Ozero(_361480) = _361482, -(c_Groups_Ozero__class_Ozero(_361480) = c_Groups_Ouminus__class_Ouminus(_361480, _361482))]]], (6691 ^ _124236) ^ [_361945] : [class_Groups_Ogroup__add(_361945), -(c_Groups_Ouminus__class_Ouminus(_361945, c_Groups_Ozero__class_Ozero(_361945)) = c_Groups_Ozero__class_Ozero(_361945))], (6697 ^ _124236) ^ [_362175, _362177, _362179] : [class_Groups_Oordered__ab__group__add(_362175), 6700 ^ _124236 : [(6701 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_362175, _362177, c_Groups_Ouminus__class_Ouminus(_362175, _362179)), -(c_Orderings_Oord__class_Oless__eq(_362175, _362179, c_Groups_Ouminus__class_Ouminus(_362175, _362177)))], (6707 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_362175, _362179, c_Groups_Ouminus__class_Ouminus(_362175, _362177)), -(c_Orderings_Oord__class_Oless__eq(_362175, _362177, c_Groups_Ouminus__class_Ouminus(_362175, _362179)))]]], (6713 ^ _124236) ^ [_362687, _362689, _362691] : [class_Groups_Oordered__ab__group__add(_362687), 6716 ^ _124236 : [(6717 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_362687, c_Groups_Ouminus__class_Ouminus(_362687, _362689), _362691), -(c_Orderings_Oord__class_Oless__eq(_362687, c_Groups_Ouminus__class_Ouminus(_362687, _362691), _362689))], (6723 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_362687, c_Groups_Ouminus__class_Ouminus(_362687, _362691), _362689), -(c_Orderings_Oord__class_Oless__eq(_362687, c_Groups_Ouminus__class_Ouminus(_362687, _362689), _362691))]]], (6729 ^ _124236) ^ [_363199, _363201, _363203] : [class_Groups_Oordered__ab__group__add(_363199), 6732 ^ _124236 : [(6733 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_363199, c_Groups_Ouminus__class_Ouminus(_363199, _363201), c_Groups_Ouminus__class_Ouminus(_363199, _363203)), -(c_Orderings_Oord__class_Oless__eq(_363199, _363203, _363201))], (6739 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_363199, _363203, _363201), -(c_Orderings_Oord__class_Oless__eq(_363199, c_Groups_Ouminus__class_Ouminus(_363199, _363201), c_Groups_Ouminus__class_Ouminus(_363199, _363203)))]]], (6745 ^ _124236) ^ [_363711, _363713, _363715] : [class_Groups_Oordered__ab__group__add(_363711), c_Orderings_Oord__class_Oless__eq(_363711, _363713, _363715), -(c_Orderings_Oord__class_Oless__eq(_363711, c_Groups_Ouminus__class_Ouminus(_363711, _363715), c_Groups_Ouminus__class_Ouminus(_363711, _363713)))], (6755 ^ _124236) ^ [_364048, _364050, _364052] : [class_Groups_Oordered__ab__group__add(_364048), 6758 ^ _124236 : [(6759 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_364048, _364050, c_Groups_Ouminus__class_Ouminus(_364048, _364052)), -(c_Orderings_Oord__class_Oless(_364048, _364052, c_Groups_Ouminus__class_Ouminus(_364048, _364050)))], (6765 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_364048, _364052, c_Groups_Ouminus__class_Ouminus(_364048, _364050)), -(c_Orderings_Oord__class_Oless(_364048, _364050, c_Groups_Ouminus__class_Ouminus(_364048, _364052)))]]], (6771 ^ _124236) ^ [_364560, _364562, _364564] : [class_Groups_Oordered__ab__group__add(_364560), 6774 ^ _124236 : [(6775 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_364560, c_Groups_Ouminus__class_Ouminus(_364560, _364562), _364564), -(c_Orderings_Oord__class_Oless(_364560, c_Groups_Ouminus__class_Ouminus(_364560, _364564), _364562))], (6781 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_364560, c_Groups_Ouminus__class_Ouminus(_364560, _364564), _364562), -(c_Orderings_Oord__class_Oless(_364560, c_Groups_Ouminus__class_Ouminus(_364560, _364562), _364564))]]], (6787 ^ _124236) ^ [_365072, _365074, _365076] : [class_Groups_Oordered__ab__group__add(_365072), 6790 ^ _124236 : [(6791 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_365072, c_Groups_Ouminus__class_Ouminus(_365072, _365074), c_Groups_Ouminus__class_Ouminus(_365072, _365076)), -(c_Orderings_Oord__class_Oless(_365072, _365076, _365074))], (6797 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_365072, _365076, _365074), -(c_Orderings_Oord__class_Oless(_365072, c_Groups_Ouminus__class_Ouminus(_365072, _365074), c_Groups_Ouminus__class_Ouminus(_365072, _365076)))]]], (6803 ^ _124236) ^ [_365584, _365586, _365588] : [class_Rings_Oring(_365584), -(c_Groups_Ouminus__class_Ouminus(_365584, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365584), _365586), _365588)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365584), _365586), c_Groups_Ouminus__class_Ouminus(_365584, _365588)))], (6809 ^ _124236) ^ [_365856, _365858, _365860] : [class_Rings_Oring(_365856), -(c_Groups_Ouminus__class_Ouminus(_365856, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365856), _365858), _365860)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365856), c_Groups_Ouminus__class_Ouminus(_365856, _365858)), _365860))], (6815 ^ _124236) ^ [_366128, _366130, _366132] : [class_Rings_Oring(_366128), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366128), c_Groups_Ouminus__class_Ouminus(_366128, _366130)), _366132) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366128), _366130), c_Groups_Ouminus__class_Ouminus(_366128, _366132)))], (6821 ^ _124236) ^ [_366400, _366402, _366404] : [class_Rings_Oring(_366400), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366400), c_Groups_Ouminus__class_Ouminus(_366400, _366402)), c_Groups_Ouminus__class_Ouminus(_366400, _366404)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366400), _366402), _366404))], (6827 ^ _124236) ^ [_366672, _366674, _366676] : [class_Rings_Oidom(_366672), 6830 ^ _124236 : [(6841 ^ _124236) ^ [] : [6842 ^ _124236 : [(6843 ^ _124236) ^ [] : [_366674 = _366676], (6845 ^ _124236) ^ [] : [_366674 = c_Groups_Ouminus__class_Ouminus(_366672, _366676)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366672), _366674), _366674) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366672), _366676), _366676))], (6831 ^ _124236) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366672), _366674), _366674) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366672), _366676), _366676), -(_366674 = _366676), -(_366674 = c_Groups_Ouminus__class_Ouminus(_366672, _366676))]]], (6849 ^ _124236) ^ [_367381, _367383, _367385] : [class_RealVector_Oreal__normed__algebra(_367381), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367381), _367383), c_Groups_Ouminus__class_Ouminus(_367381, _367385)) = c_Groups_Ouminus__class_Ouminus(_367381, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367381), _367383), _367385)))], (6855 ^ _124236) ^ [_367653, _367655, _367657] : [class_RealVector_Oreal__normed__algebra(_367653), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367653), _367655), c_Groups_Ouminus__class_Ouminus(_367653, _367657)) = c_Groups_Ouminus__class_Ouminus(_367653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367653), _367655), _367657)))], (6861 ^ _124236) ^ [_367925, _367927, _367929] : [class_RealVector_Oreal__normed__algebra(_367925), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367925), c_Groups_Ouminus__class_Ouminus(_367925, _367927)), _367929) = c_Groups_Ouminus__class_Ouminus(_367925, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367925), _367927), _367929)))], (6867 ^ _124236) ^ [_368197, _368199, _368201] : [class_RealVector_Oreal__normed__algebra(_368197), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368197), c_Groups_Ouminus__class_Ouminus(_368197, _368199)), _368201) = c_Groups_Ouminus__class_Ouminus(_368197, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368197), _368199), _368201)))], (6873 ^ _124236) ^ [_368483, _368485, _368487, _368489] : [class_Rings_Ocomm__semiring__1(_368483), -(hAPP(hAPP(c_Power_Opower__class_Opower(_368483), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368483), _368485), _368487)), _368489) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368483), hAPP(hAPP(c_Power_Opower__class_Opower(_368483), _368485), _368489)), hAPP(hAPP(c_Power_Opower__class_Opower(_368483), _368487), _368489)))], (6879 ^ _124236) ^ [_368797, _368799, _368801] : [class_Groups_Oab__group__add(_368797), -(c_Groups_Ouminus__class_Ouminus(_368797, c_Groups_Oplus__class_Oplus(_368797, _368799, _368801)) = c_Groups_Oplus__class_Oplus(_368797, c_Groups_Ouminus__class_Ouminus(_368797, _368799), c_Groups_Ouminus__class_Ouminus(_368797, _368801)))], (6885 ^ _124236) ^ [_369059, _369061, _369063] : [class_Groups_Ogroup__add(_369059), -(c_Groups_Ouminus__class_Ouminus(_369059, c_Groups_Oplus__class_Oplus(_369059, _369061, _369063)) = c_Groups_Oplus__class_Oplus(_369059, c_Groups_Ouminus__class_Ouminus(_369059, _369063), c_Groups_Ouminus__class_Ouminus(_369059, _369061)))], (6891 ^ _124236) ^ [_369321, _369323, _369325] : [class_Groups_Ogroup__add(_369321), -(c_Groups_Oplus__class_Oplus(_369321, _369323, c_Groups_Oplus__class_Oplus(_369321, c_Groups_Ouminus__class_Ouminus(_369321, _369323), _369325)) = _369325)], (6897 ^ _124236) ^ [_369571, _369573, _369575] : [class_Groups_Ogroup__add(_369571), -(c_Groups_Oplus__class_Oplus(_369571, c_Groups_Ouminus__class_Ouminus(_369571, _369573), c_Groups_Oplus__class_Oplus(_369571, _369573, _369575)) = _369575)], (6903 ^ _124236) ^ [_369821, _369823, _369825] : [class_Groups_Oab__group__add(_369821), -(c_Groups_Ouminus__class_Ouminus(_369821, c_Groups_Ominus__class_Ominus(_369821, _369823, _369825)) = c_Groups_Ominus__class_Ominus(_369821, _369825, _369823))], (6909 ^ _124236) ^ [_370085, _370087, _370089, _370091] : [class_Orderings_Oord(_370085), 6912 ^ _124236 : [(6913 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_370087, _370085), _370089, _370091), 6916 ^ _124236 : [(6917 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_370087, _370085), _370089, _370091))], (6919 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_370087, _370085), _370091, _370089)]]], (6921 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_370087, _370085), _370089, _370091)), c_Orderings_Oord__class_Oless__eq(tc_fun(_370087, _370085), _370089, _370091), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_370087, _370085), _370091, _370089))]]], (6931 ^ _124236) ^ [_370782, _370784, _370786] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _370782), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _370784, _370786)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _370782), _370784)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _370782), _370786)))], (6933 ^ _124236) ^ [_370921, _370923] : [class_RealVector_Oreal__normed__vector(_370921), -(c_RealVector_Onorm__class_Onorm(_370921, c_Groups_Ouminus__class_Ouminus(_370921, _370923)) = c_RealVector_Onorm__class_Onorm(_370921, _370923))], (6939 ^ _124236) ^ [_371117] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_371117)], (6941 ^ _124236) ^ [_371196] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_371196)], (6943 ^ _124236) ^ [_371275] : [c_Nat_OSuc(_371275) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6945 ^ _124236) ^ [_371354] : [c_Nat_OSuc(_371354) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6947 ^ _124236) ^ [_371433] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_371433)], (6949 ^ _124236) ^ [_371512] : [c_Nat_OSuc(_371512) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6951 ^ _124236) ^ [_371649, _371651, _371653, _371655] : [class_Rings_Ocomm__semiring__1(_371649), -(hAPP(hAPP(c_Power_Opower__class_Opower(_371649), hAPP(hAPP(c_Power_Opower__class_Opower(_371649), _371651), _371653)), _371655) = hAPP(hAPP(c_Power_Opower__class_Opower(_371649), _371651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371653), _371655)))], (6957 ^ _124236) ^ [_371928, _371930, _371932] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _371928), _371930)), _371932) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _371928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371930), _371932)))], (6959 ^ _124236) ^ [_372063, _372065] : [class_Rings_Ocomm__semiring__1(_372063), -(hAPP(hAPP(c_Power_Opower__class_Opower(_372063), _372065), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _372065)], (6965 ^ _124236) ^ [_372316, _372318] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372316, _372318)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372318, c_Nat_OSuc(_372316)))], (6971 ^ _124236) ^ [_372489, _372491] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372491, c_Nat_OSuc(_372489)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372489, _372491)], (6987 ^ _124236) ^ [_372999, _373001] : [6988 ^ _124236 : [(6989 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372999, _373001)], (6991 ^ _124236) ^ [] : [_372999 = _373001]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372999, c_Nat_OSuc(_373001)))], (6977 ^ _124236) ^ [_372739, _372741] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372739, c_Nat_OSuc(_372741)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372739, _372741)), -(_372739 = _372741)], (6995 ^ _124236) ^ [_373322, _373324] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_373322), c_Nat_OSuc(_373324)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373322, _373324))], (7001 ^ _124236) ^ [_373496, _373498] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373496, _373498), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_373496), c_Nat_OSuc(_373498)))], (7007 ^ _124236) ^ [_373720, _373722] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373720, _373722)), 7010 ^ _124236 : [(7011 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373720, c_Nat_OSuc(_373722)), -(_373720 = _373722)], (7017 ^ _124236) ^ [] : [_373720 = _373722, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373720, c_Nat_OSuc(_373722)))]]], (7023 ^ _124236) ^ [_374194, _374196] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374194, _374196)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374194, c_Nat_OSuc(_374196)), -(_374196 = _374194)], (7033 ^ _124236) ^ [_374504, _374506] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374504, _374506), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374504, c_Nat_OSuc(_374506)))], (7039 ^ _124236) ^ [_374722, _374724] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374722, _374724), -(c_Nat_OSuc(_374722) = _374724), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_374722), _374724))], (7049 ^ _124236) ^ [_375050, _375052, _375054] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375050, _375052), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375052, _375054), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_375050), _375054))], (7059 ^ _124236) ^ [_375369, _375371] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375369, c_Nat_OSuc(_375371)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375369, _375371)), -(_375369 = _375371)], (7069 ^ _124236) ^ [_375679, _375681] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_375679), _375681), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375679, _375681))], (7075 ^ _124236) ^ [_375897, _375899] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_375897), c_Nat_OSuc(_375899)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375897, _375899))], (7081 ^ _124236) ^ [_376104, _376106] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _376104, c_Nat_OSuc(_376106)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _376104, _376106)))], (7083 ^ _124236) ^ [_376210, _376212] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_376210), _376212) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _376210, _376212)))], (7085 ^ _124236) ^ [_376316, _376318] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_376316), _376318) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _376316, c_Nat_OSuc(_376318)))], (7087 ^ _124236) ^ [_376437, _376439] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_376437), _376439), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _376437, _376439))], (7093 ^ _124236) ^ [_376655, _376657] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _376655, c_Nat_OSuc(_376657)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _376655, _376657)), -(_376655 = c_Nat_OSuc(_376657))], (7103 ^ _124236) ^ [_376969, _376971] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _376969, _376971), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _376969, c_Nat_OSuc(_376971)))], (7109 ^ _124236) ^ [_377216, _377218] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_377216), c_Nat_OSuc(_377218)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377216, _377218))], (7115 ^ _124236) ^ [_377390, _377392] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377390, _377392), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_377390), c_Nat_OSuc(_377392)))], (7131 ^ _124236) ^ [_377907, _377909] : [7132 ^ _124236 : [(7133 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377907, _377909)], (7135 ^ _124236) ^ [] : [_377907 = c_Nat_OSuc(_377909)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377907, c_Nat_OSuc(_377909)))], (7121 ^ _124236) ^ [_377643, _377645] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377643, c_Nat_OSuc(_377645)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377643, _377645)), -(_377643 = c_Nat_OSuc(_377645))], (7139 ^ _124236) ^ [_378234, _378236] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378234, _378236)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_378236), _378234))], (7145 ^ _124236) ^ [_378407, _378409] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_378409), _378407), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378407, _378409)], (7151 ^ _124236) ^ [_378598] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_378598), _378598)], (7153 ^ _124236) ^ [_378751, _378753, _378755] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_378751)), _378753) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_378751)), _378755), -(_378753 = _378755)], (7159 ^ _124236) ^ [_378951, _378953, _378955] : [_378953 = _378955, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_378951)), _378953) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_378951)), _378955))], (7165 ^ _124236) ^ [_379187] : [class_Groups_Oab__group__add(_379187), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_379187), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_379187))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_379187)))], (7171 ^ _124236) ^ [_379444, _379446] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _379444, _379446), 7174 ^ _124236 : [(7175 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _379444, _379446))], (7177 ^ _124236) ^ [] : [_379444 = _379446]]], (7179 ^ _124236) ^ [_379686, _379688] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _379686, _379688)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _379686, _379688), -(_379686 = _379688)], (7199 ^ _124236) ^ [_380279, _380281] : [7200 ^ _124236 : [(7201 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _380279, _380281)], (7203 ^ _124236) ^ [] : [_380279 = _380281]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _380279, _380281))], (7189 ^ _124236) ^ [_380023, _380025] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _380023, _380025), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _380023, _380025)), -(_380023 = _380025)], (7207 ^ _124236) ^ [_380554, _380556] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_380554), c_Nat_OSuc(_380556)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _380554, _380556))], (7209 ^ _124236) ^ [_380674, _380676, _380678] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_380674), _380676), c_Nat_OSuc(_380678)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _380674, _380676), _380678))], (7211 ^ _124236) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (7213 ^ _124236) ^ [_380828] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _380828) = _380828)], (7215 ^ _124236) ^ [_380952, _380954, _380956] : [class_Rings_Ocomm__ring(_380952), -(c_Polynomial_Osmult(_380952, _380954, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_380952), _380956)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_380952), c_Polynomial_Osmult(_380952, _380954, _380956)))], (7221 ^ _124236) ^ [_381217] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_381217)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _381217))], (7227 ^ _124236) ^ [_381381] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _381381), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_381381)))], (7233 ^ _124236) ^ [_381609, _381611, _381613] : [class_Rings_Olinordered__semidom(_381609), c_Orderings_Oord__class_Oless__eq(_381609, c_Groups_Ozero__class_Ozero(_381609), _381611), c_Orderings_Oord__class_Oless__eq(_381609, _381611, c_Groups_Oone__class_Oone(_381609)), -(c_Orderings_Oord__class_Oless__eq(_381609, hAPP(hAPP(c_Power_Opower__class_Opower(_381609), _381611), c_Nat_OSuc(_381613)), _381611))], (7247 ^ _124236) ^ [_382028, _382030] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _382028, _382030) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _382028, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _382030)))], (7249 ^ _124236) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7251 ^ _124236) ^ [_382172] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_382172)))], (7253 ^ _124236) ^ [_382282, _382284] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _382282, _382284), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_382282), c_RComplete_Onatfloor(_382284)))], (7259 ^ _124236) ^ [_382518, _382520, _382522] : [class_Rings_Ocomm__ring__1(_382518), -(c_Groups_Ominus__class_Ominus(_382518, hAPP(hAPP(c_Power_Opower__class_Opower(_382518), _382520), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_382518), _382522), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382518), c_Groups_Ominus__class_Ominus(_382518, _382520, _382522)), c_Groups_Oplus__class_Oplus(_382518, _382520, _382522)))], (7265 ^ _124236) ^ [_382804, _382806] : [class_Groups_Olinordered__ab__group__add(_382804), 7268 ^ _124236 : [(7269 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_382804, c_Groups_Ouminus__class_Ouminus(_382804, _382806), _382806), -(c_Orderings_Oord__class_Oless__eq(_382804, c_Groups_Ozero__class_Ozero(_382804), _382806))], (7275 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_382804, c_Groups_Ozero__class_Ozero(_382804), _382806), -(c_Orderings_Oord__class_Oless__eq(_382804, c_Groups_Ouminus__class_Ouminus(_382804, _382806), _382806))]]], (7281 ^ _124236) ^ [_383283, _383285] : [class_Groups_Oordered__ab__group__add(_383283), 7284 ^ _124236 : [(7285 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_383283, c_Groups_Ouminus__class_Ouminus(_383283, _383285), c_Groups_Ozero__class_Ozero(_383283)), -(c_Orderings_Oord__class_Oless__eq(_383283, c_Groups_Ozero__class_Ozero(_383283), _383285))], (7291 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_383283, c_Groups_Ozero__class_Ozero(_383283), _383285), -(c_Orderings_Oord__class_Oless__eq(_383283, c_Groups_Ouminus__class_Ouminus(_383283, _383285), c_Groups_Ozero__class_Ozero(_383283)))]]], (7297 ^ _124236) ^ [_383768, _383770] : [class_Groups_Olinordered__ab__group__add(_383768), 7300 ^ _124236 : [(7301 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_383768, _383770, c_Groups_Ouminus__class_Ouminus(_383768, _383770)), -(c_Orderings_Oord__class_Oless__eq(_383768, _383770, c_Groups_Ozero__class_Ozero(_383768)))], (7307 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_383768, _383770, c_Groups_Ozero__class_Ozero(_383768)), -(c_Orderings_Oord__class_Oless__eq(_383768, _383770, c_Groups_Ouminus__class_Ouminus(_383768, _383770)))]]], (7313 ^ _124236) ^ [_384247, _384249] : [class_Groups_Oordered__ab__group__add(_384247), 7316 ^ _124236 : [(7317 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_384247, c_Groups_Ozero__class_Ozero(_384247), c_Groups_Ouminus__class_Ouminus(_384247, _384249)), -(c_Orderings_Oord__class_Oless__eq(_384247, _384249, c_Groups_Ozero__class_Ozero(_384247)))], (7323 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_384247, _384249, c_Groups_Ozero__class_Ozero(_384247)), -(c_Orderings_Oord__class_Oless__eq(_384247, c_Groups_Ozero__class_Ozero(_384247), c_Groups_Ouminus__class_Ouminus(_384247, _384249)))]]], (7329 ^ _124236) ^ [_384732, _384734] : [class_Groups_Oordered__ab__group__add(_384732), 7332 ^ _124236 : [(7333 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_384732, c_Groups_Ozero__class_Ozero(_384732), c_Groups_Ouminus__class_Ouminus(_384732, _384734)), -(c_Orderings_Oord__class_Oless(_384732, _384734, c_Groups_Ozero__class_Ozero(_384732)))], (7339 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_384732, _384734, c_Groups_Ozero__class_Ozero(_384732)), -(c_Orderings_Oord__class_Oless(_384732, c_Groups_Ozero__class_Ozero(_384732), c_Groups_Ouminus__class_Ouminus(_384732, _384734)))]]], (7345 ^ _124236) ^ [_385217, _385219] : [class_Groups_Oordered__ab__group__add(_385217), 7348 ^ _124236 : [(7349 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_385217, c_Groups_Ouminus__class_Ouminus(_385217, _385219), c_Groups_Ozero__class_Ozero(_385217)), -(c_Orderings_Oord__class_Oless(_385217, c_Groups_Ozero__class_Ozero(_385217), _385219))], (7355 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_385217, c_Groups_Ozero__class_Ozero(_385217), _385219), -(c_Orderings_Oord__class_Oless(_385217, c_Groups_Ouminus__class_Ouminus(_385217, _385219), c_Groups_Ozero__class_Ozero(_385217)))]]], (7361 ^ _124236) ^ [_385702, _385704] : [class_Groups_Olinordered__ab__group__add(_385702), 7364 ^ _124236 : [(7365 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_385702, c_Groups_Ouminus__class_Ouminus(_385702, _385704), _385704), -(c_Orderings_Oord__class_Oless(_385702, c_Groups_Ozero__class_Ozero(_385702), _385704))], (7371 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_385702, c_Groups_Ozero__class_Ozero(_385702), _385704), -(c_Orderings_Oord__class_Oless(_385702, c_Groups_Ouminus__class_Ouminus(_385702, _385704), _385704))]]], (7377 ^ _124236) ^ [_386181, _386183] : [class_Rings_Olinordered__idom(_386181), 7380 ^ _124236 : [(7381 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_386181, _386183, c_Groups_Ouminus__class_Ouminus(_386181, _386183)), -(c_Orderings_Oord__class_Oless(_386181, _386183, c_Groups_Ozero__class_Ozero(_386181)))], (7387 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_386181, _386183, c_Groups_Ozero__class_Ozero(_386181)), -(c_Orderings_Oord__class_Oless(_386181, _386183, c_Groups_Ouminus__class_Ouminus(_386181, _386183)))]]], (7393 ^ _124236) ^ [_386674, _386676, _386678] : [class_Groups_Ogroup__add(_386674), c_Groups_Oplus__class_Oplus(_386674, _386676, _386678) = c_Groups_Ozero__class_Ozero(_386674), -(c_Groups_Ouminus__class_Ouminus(_386674, _386676) = _386678)], (7403 ^ _124236) ^ [_387013, _387015, _387017] : [class_Groups_Ogroup__add(_387013), 7406 ^ _124236 : [(7407 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_387013, _387015, _387017) = c_Groups_Ozero__class_Ozero(_387013), -(_387017 = c_Groups_Ouminus__class_Ouminus(_387013, _387015))], (7413 ^ _124236) ^ [] : [_387017 = c_Groups_Ouminus__class_Ouminus(_387013, _387015), -(c_Groups_Oplus__class_Oplus(_387013, _387015, _387017) = c_Groups_Ozero__class_Ozero(_387013))]]], (7419 ^ _124236) ^ [_387514, _387516] : [class_Groups_Oab__group__add(_387514), -(c_Groups_Oplus__class_Oplus(_387514, c_Groups_Ouminus__class_Ouminus(_387514, _387516), _387516) = c_Groups_Ozero__class_Ozero(_387514))], (7425 ^ _124236) ^ [_387740, _387742] : [class_Groups_Ogroup__add(_387740), -(c_Groups_Oplus__class_Oplus(_387740, c_Groups_Ouminus__class_Ouminus(_387740, _387742), _387742) = c_Groups_Ozero__class_Ozero(_387740))], (7431 ^ _124236) ^ [_387980, _387982, _387984] : [class_Groups_Ogroup__add(_387980), 7434 ^ _124236 : [(7435 ^ _124236) ^ [] : [_387982 = c_Groups_Ouminus__class_Ouminus(_387980, _387984), -(c_Groups_Oplus__class_Oplus(_387980, _387982, _387984) = c_Groups_Ozero__class_Ozero(_387980))], (7441 ^ _124236) ^ [] : [c_Groups_Oplus__class_Oplus(_387980, _387982, _387984) = c_Groups_Ozero__class_Ozero(_387980), -(_387982 = c_Groups_Ouminus__class_Ouminus(_387980, _387984))]]], (7447 ^ _124236) ^ [_388481, _388483] : [class_Groups_Ogroup__add(_388481), -(c_Groups_Oplus__class_Oplus(_388481, _388483, c_Groups_Ouminus__class_Ouminus(_388481, _388483)) = c_Groups_Ozero__class_Ozero(_388481))], (7453 ^ _124236) ^ [_388707, _388709] : [class_Groups_Ogroup__add(_388707), -(c_Groups_Ominus__class_Ominus(_388707, c_Groups_Ozero__class_Ozero(_388707), _388709) = c_Groups_Ouminus__class_Ouminus(_388707, _388709))], (7459 ^ _124236) ^ [_388933, _388935] : [class_Rings_Oring__1__no__zero__divisors(_388933), 7462 ^ _124236 : [(7473 ^ _124236) ^ [] : [7474 ^ _124236 : [(7475 ^ _124236) ^ [] : [_388935 = c_Groups_Oone__class_Oone(_388933)], (7477 ^ _124236) ^ [] : [_388935 = c_Groups_Ouminus__class_Ouminus(_388933, c_Groups_Oone__class_Oone(_388933))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388933), _388935), _388935) = c_Groups_Oone__class_Oone(_388933))], (7463 ^ _124236) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388933), _388935), _388935) = c_Groups_Oone__class_Oone(_388933), -(_388935 = c_Groups_Oone__class_Oone(_388933)), -(_388935 = c_Groups_Ouminus__class_Ouminus(_388933, c_Groups_Oone__class_Oone(_388933)))]]], (7481 ^ _124236) ^ [_389600, _389602] : [class_Rings_Ocomm__ring__1(_389600), -(c_Groups_Ouminus__class_Ouminus(_389600, _389602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389600), c_Groups_Ouminus__class_Ouminus(_389600, c_Groups_Oone__class_Oone(_389600))), _389602))], (7487 ^ _124236) ^ [_389854, _389856, _389858] : [class_Groups_Ogroup__add(_389854), -(c_Groups_Ominus__class_Ominus(_389854, _389856, _389858) = c_Groups_Oplus__class_Oplus(_389854, _389856, c_Groups_Ouminus__class_Ouminus(_389854, _389858)))], (7493 ^ _124236) ^ [_390104, _390106, _390108] : [class_Groups_Oab__group__add(_390104), -(c_Groups_Ominus__class_Ominus(_390104, _390106, _390108) = c_Groups_Oplus__class_Oplus(_390104, _390106, c_Groups_Ouminus__class_Ouminus(_390104, _390108)))], (7499 ^ _124236) ^ [_390354, _390356, _390358] : [class_Groups_Ogroup__add(_390354), -(c_Groups_Ominus__class_Ominus(_390354, _390356, c_Groups_Ouminus__class_Ouminus(_390354, _390358)) = c_Groups_Oplus__class_Oplus(_390354, _390356, _390358))], (7505 ^ _124236) ^ [_390604, _390606, _390608] : [class_Rings_Ocomm__ring__1(_390604), -(c_Groups_Ominus__class_Ominus(_390604, _390606, _390608) = c_Groups_Oplus__class_Oplus(_390604, _390606, c_Groups_Ouminus__class_Ouminus(_390604, _390608)))], (7511 ^ _124236) ^ [_390840, _390842] : [class_Rings_Ocomm__semiring__1(_390840), -(hAPP(hAPP(c_Power_Opower__class_Opower(_390840), _390842), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_390840))], (7517 ^ _124236) ^ [_391096, _391098, _391100, _391102] : [class_Rings_Ocomm__semiring__1(_391096), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391096), hAPP(hAPP(c_Power_Opower__class_Opower(_391096), _391098), _391100)), hAPP(hAPP(c_Power_Opower__class_Opower(_391096), _391098), _391102)) = hAPP(hAPP(c_Power_Opower__class_Opower(_391096), _391098), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _391100, _391102)))], (7523 ^ _124236) ^ [_391373, _391375] : [-(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), _391373), _391373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _391375), _391375)))], (7525 ^ _124236) ^ [_391484] : [class_Rings_Olinordered__idom(_391484), c_Polynomial_Opos__poly(_391484, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_391484)))], (7531 ^ _124236) ^ [_391710] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _391710), -(_391710 = c_Nat_OSuc(7534 ^ [_391710]))], (7538 ^ _124236) ^ [_391925] : [7539 ^ _124236 : [(7540 ^ _124236) ^ [_391996] : [_391925 = c_Nat_OSuc(_391996)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _391925))], (7544 ^ _124236) ^ [_392174] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _392174, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_392174 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7550 ^ _124236) ^ [_392332] : [_392332 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _392332, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7556 ^ _124236) ^ [_392569, _392571] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _392569, c_Nat_OSuc(_392571)), -(_392569 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7564 ^ _124236 : [(7565 ^ _124236) ^ [] : [-(_392569 = c_Nat_OSuc(7563 ^ [_392569, _392571]))], (7567 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 7563 ^ [_392569, _392571], _392571))]]], (7569 ^ _124236) ^ [_392981, _392983] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _392981, c_Nat_OSuc(_392983))), 7570 ^ _124236 : [(7571 ^ _124236) ^ [] : [_392981 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7573 ^ _124236) ^ [_393150] : [_392981 = c_Nat_OSuc(_393150), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _393150, _392983)]]], (7581 ^ _124236) ^ [_393462, _393464] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393462, _393464), 7586 ^ _124236 : [(7587 ^ _124236) ^ [] : [-(_393462 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7589 ^ _124236) ^ [] : [-(_393464 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7590 ^ _124236 : [(7591 ^ _124236) ^ [] : [-(_393462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7593 ^ _124236) ^ [] : [-(_393464 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7595 ^ _124236) ^ [_393872, _393874] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393872, _393874)), 7596 ^ _124236 : [(7597 ^ _124236) ^ [] : [_393872 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _393874 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7603 ^ _124236) ^ [] : [_393872 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _393874 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7611 ^ _124236) ^ [_394373, _394375] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _394373, _394375) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7616 ^ _124236 : [(7617 ^ _124236) ^ [] : [-(_394373 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7619 ^ _124236) ^ [] : [-(_394375 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7620 ^ _124236 : [(7621 ^ _124236) ^ [] : [-(_394373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7623 ^ _124236) ^ [] : [-(_394375 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7625 ^ _124236) ^ [_394783, _394785] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _394783, _394785) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7626 ^ _124236 : [(7627 ^ _124236) ^ [] : [_394783 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _394785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7633 ^ _124236) ^ [] : [_394783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _394785 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7641 ^ _124236) ^ [_395284, _395286] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _395284, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _395286)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_395284 = _395286)], (7647 ^ _124236) ^ [_395460, _395462] : [_395460 = _395462, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _395460, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _395462)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7653 ^ _124236) ^ [_395715, _395717] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _395715, _395717) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_395717 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _395715))], (7659 ^ _124236) ^ [_395891, _395893] : [_395893 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _395891), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _395891, _395893) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7665 ^ _124236) ^ [_396146, _396148] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396146), _396148) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7668 ^ _124236 : [(7669 ^ _124236) ^ [] : [-(_396146 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7671 ^ _124236) ^ [] : [-(_396148 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7673 ^ _124236) ^ [_396395, _396397] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396395), _396397) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _396395 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _396397 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7683 ^ _124236) ^ [_396737, _396739] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396737, _396739), -(_396739 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396737, 7686 ^ [_396737, _396739])))], (7690 ^ _124236) ^ [_396976, _396978] : [7691 ^ _124236 : [(7692 ^ _124236) ^ [_397053] : [_396978 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396976, _397053))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396976, _396978))], (7696 ^ _124236) ^ [_397209, _397211] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397209, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397211, _397209))))], (7698 ^ _124236) ^ [_397310, _397312] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397310, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397310, _397312))))], (7700 ^ _124236) ^ [_397455, _397457] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397455, _397457), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_397455), _397457))], (7706 ^ _124236) ^ [_397625, _397627] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_397625), _397627), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397625, _397627))], (7712 ^ _124236) ^ [_397874, _397876] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397874, c_Nat_OSuc(_397876)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397874, _397876))], (7718 ^ _124236) ^ [_398044, _398046] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398044, _398046), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398044, c_Nat_OSuc(_398046)))], (7724 ^ _124236) ^ [_398293, _398295] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_398293), _398295), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398293, _398295))], (7730 ^ _124236) ^ [_398463, _398465] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398463, _398465), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_398463), _398465))], (7736 ^ _124236) ^ [_398683, _398685] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398683, _398685), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398683, c_Nat_OSuc(_398685)))], (7742 ^ _124236) ^ [_398901, _398903] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398901, _398903), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_398901), _398903))], (7748 ^ _124236) ^ [_399119, _399121] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399119, _399121), 7751 ^ _124236 : [(7752 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _399121, c_Nat_OSuc(_399119)), -(_399121 = _399119)], (7758 ^ _124236) ^ [] : [_399121 = _399119, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _399121, c_Nat_OSuc(_399119)))]]], (7764 ^ _124236) ^ [_399590, _399592] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_399590), _399592), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _399590, _399592))], (7770 ^ _124236) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7772 ^ _124236) ^ [_399904, _399906, _399908] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_399904)), _399906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_399904)), _399908)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _399906, _399908))], (7778 ^ _124236) ^ [_400108, _400110, _400112] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _400110, _400112), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_400108)), _400110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_400108)), _400112)))], (7784 ^ _124236) ^ [_400347, _400349] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _400347, _400349), c_Nat_OSuc(_400347)))], (7786 ^ _124236) ^ [_400448, _400450] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400448), c_Nat_OSuc(_400450)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400448, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400448), _400450)))], (7788 ^ _124236) ^ [_400560, _400562] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_400560)), _400562) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400560), _400562)))], (7790 ^ _124236) ^ [_400730, _400732, _400734] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_400730)), _400732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_400730)), _400734)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400732, _400734))], (7796 ^ _124236) ^ [_400934, _400936, _400938] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400936, _400938), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_400934)), _400936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_400934)), _400938)))], (7802 ^ _124236) ^ [_401188, _401190] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401188, _401190), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_401190), _401188) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401190, _401188)))], (7808 ^ _124236) ^ [_401395] : [-(c_Nat_OSuc(_401395) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _401395))], (7810 ^ _124236) ^ [_401479] : [-(c_Nat_OSuc(_401479) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401479, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7812 ^ _124236) ^ [_401578] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _401578), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _401578, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_401578), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7818 ^ _124236) ^ [_401779] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_401779), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _401779)], (7820 ^ _124236) ^ [_401877, _401879] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401877, c_Nat_OSuc(_401879)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401877, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _401879))], (7822 ^ _124236) ^ [_401985, _401987] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _401985, _401987) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _401985, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _401987)))], (7824 ^ _124236) ^ [_402090, _402092] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _402090, _402092) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _402090, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _402092)))], (7826 ^ _124236) ^ [_402224, _402226, _402228] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _402224), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _402226, _402228), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _402224), _402226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _402224), _402228)))], (7836 ^ _124236) ^ [_402563, _402565] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _402563), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _402565), -(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), _402563), _402565)))], (7846 ^ _124236) ^ [_402894, _402896, _402898] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _402894), 7849 ^ _124236 : [(7850 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _402896), _402894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _402898), _402894)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _402896, _402898))], (7856 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _402896, _402898), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _402896), _402894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _402898), _402894)))]]], (7862 ^ _124236) ^ [_403414, _403416] : [class_RealVector_Oreal__normed__vector(_403414), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_403414, _403416), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7868 ^ _124236) ^ [_403602] : [-(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, _403602)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _403602)))], (7870 ^ _124236) ^ [_403733, _403735, _403737] : [class_Rings_Olinordered__idom(_403733), c_Polynomial_Opos__poly(_403733, _403735), c_Polynomial_Opos__poly(_403733, _403737), -(c_Polynomial_Opos__poly(_403733, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_403733), _403735, _403737)))], (7884 ^ _124236) ^ [_404159, _404161, _404163] : [class_Rings_Olinordered__idom(_404159), c_Polynomial_Opos__poly(_404159, _404161), c_Polynomial_Opos__poly(_404159, _404163), -(c_Polynomial_Opos__poly(_404159, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_404159)), _404161), _404163)))], (7898 ^ _124236) ^ [_404579, _404581] : [class_Groups_Oab__group__add(_404579), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_404579), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_404579)), _404581) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_404579), _404581))], (7904 ^ _124236) ^ [_404803] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _404803, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_404803) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7910 ^ _124236) ^ [_405027, _405029, _405031] : [class_Rings_Olinordered__idom(_405027), 7913 ^ _124236 : [(7924 ^ _124236) ^ [] : [7925 ^ _124236 : [(7926 ^ _124236) ^ [] : [_405029 = _405031], (7928 ^ _124236) ^ [] : [c_Polynomial_Opos__poly(_405027, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_405027), _405031, _405029))]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_405027), _405029, _405031))], (7914 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_405027), _405029, _405031), -(_405029 = _405031), -(c_Polynomial_Opos__poly(_405027, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_405027), _405031, _405029)))]]], (7932 ^ _124236) ^ [_405721, _405723] : [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, _405721, _405723)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _405721), _405723))], (7938 ^ _124236) ^ [_405901, _405903] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _405901), _405903), -(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, _405901, _405903)))], (7944 ^ _124236) ^ [_406160, _406162] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _406160, _406162), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _406162, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _406160)))], (7950 ^ _124236) ^ [_406340, _406342] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _406342, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _406340)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _406340, _406342), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7956 ^ _124236) ^ [_406570, _406572] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _406570), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _406572), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406570, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _406572), _406570)))], (7966 ^ _124236) ^ [_406887, _406889] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _406887), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _406889), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406887, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _406887), _406889)))], (7976 ^ _124236) ^ [_407204, _407206] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _407204), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _407206), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _407206), _407204)))], (7986 ^ _124236) ^ [_407507] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _407507), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _407507, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _407507)], (7992 ^ _124236) ^ [_407725, _407727] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _407725), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _407725, c_Nat_OSuc(_407727)), _407725))], (7998 ^ _124236) ^ [_407980, _407982] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _407980), _407982)), 8001 ^ _124236 : [(8002 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _407980))], (8004 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _407982))]]], (8006 ^ _124236) ^ [_408235, _408237] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _408235), _408237))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _408235), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _408237)], (8016 ^ _124236) ^ [_408554, _408556] : [class_RealVector_Oreal__normed__vector(_408554), 8019 ^ _124236 : [(8020 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_408554, _408556)), _408556 = c_Groups_Ozero__class_Ozero(_408554)], (8026 ^ _124236) ^ [] : [-(_408556 = c_Groups_Ozero__class_Ozero(_408554)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_408554, _408556)))]]], (8032 ^ _124236) ^ [_409046, _409048, _409050] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409046, _409048), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _409048, _409046)), _409050) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_409048), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409046, _409050)))], (8038 ^ _124236) ^ [_409318, _409320, _409322] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409318, _409320), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _409322, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _409320, _409318))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409322, _409318), c_Nat_OSuc(_409320)))], (8044 ^ _124236) ^ [_409618, _409620, _409622, _409624, _409626] : [class_RealVector_Oreal__normed__algebra(_409618), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_409618, _409620), _409622), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_409618, _409624), _409626), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_409618, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_409618), _409620), _409624)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _409622), _409626)))], (8058 ^ _124236) ^ [_410112, _410114, _410116] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _410112), 8061 ^ _124236 : [(8062 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _410114), _410112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _410116), _410112)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410114, _410116))], (8068 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410114, _410116), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _410114), _410112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _410116), _410112)))]]], (8074 ^ _124236) ^ [_410646, _410648, _410650] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _410646), 8077 ^ _124236 : [(8078 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _410646), _410648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _410646), _410650)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410648, _410650))], (8084 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _410648, _410650), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _410646), _410648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _410646), _410650)))]]], (8090 ^ _124236) ^ [_411208, _411210, _411212, _411214, _411216] : [class_RealVector_Oreal__normed__vector(_411208), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_411208, _411210), _411212), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_411208, _411214), _411216), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_411208, c_Groups_Oplus__class_Oplus(_411208, _411210, _411214)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _411212, _411216)))], (8104 ^ _124236) ^ [_411704, _411706, _411708, _411710] : [class_Rings_Ocomm__semiring__1(_411704), -(hAPP(c_Polynomial_Opoly(_411704, c_Polynomial_Omonom(_411704, _411706, _411708)), _411710) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411704), _411706), hAPP(hAPP(c_Power_Opower__class_Opower(_411704), _411710), _411708)))], (8110 ^ _124236) ^ [_411990, _411992, _411994] : [class_Groups_Ozero(_411990), -(c_Polynomial_Omonom(_411990, _411992, c_Nat_OSuc(_411994)) = c_Polynomial_OpCons(_411990, c_Groups_Ozero__class_Ozero(_411990), c_Polynomial_Omonom(_411990, _411992, _411994)))], (8116 ^ _124236) ^ [_412256, _412258] : [_412256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _412258), _412256) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8122 ^ _124236) ^ [_412430, _412432] : [-(_412430 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _412432), _412430) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412432), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _412432), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _412430, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (8128 ^ _124236) ^ [_412675] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _412675), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _412675, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _412675)], (8134 ^ _124236) ^ [_412879] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _412879), -(_412879 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _412879, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (8140 ^ _124236) ^ [_413111, _413113, _413115] : [class_Power_Opower(_413111), 8143 ^ _124236 : [(8144 ^ _124236) ^ [] : [_413113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_413111), _413115), _413113) = c_Groups_Oone__class_Oone(_413111))], (8150 ^ _124236) ^ [] : [-(_413113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_413111), _413115), _413113) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413111), _413115), hAPP(hAPP(c_Power_Opower__class_Opower(_413111), _413115), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _413113, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (8156 ^ _124236) ^ [_413695, _413697, _413699, _413701] : [class_Rings_Olinordered__semidom(_413695), c_Orderings_Oord__class_Oless(_413695, _413697, _413699), c_Orderings_Oord__class_Oless__eq(_413695, c_Groups_Ozero__class_Ozero(_413695), _413697), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _413701), -(c_Orderings_Oord__class_Oless(_413695, hAPP(hAPP(c_Power_Opower__class_Opower(_413695), _413697), _413701), hAPP(hAPP(c_Power_Opower__class_Opower(_413695), _413699), _413701)))], (8174 ^ _124236) ^ [_414278, _414280, _414282, _414284] : [class_Groups_Omonoid__mult(_414278), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _414280, _414282), -(hAPP(hAPP(c_Power_Opower__class_Opower(_414278), _414284), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_414282), _414280)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414278), hAPP(hAPP(c_Power_Opower__class_Opower(_414278), _414284), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _414282, _414280))), _414284))], (8184 ^ _124236) ^ [_414679, _414681, _414683] : [class_Rings_Olinordered__semidom(_414679), c_Orderings_Oord__class_Oless(_414679, c_Groups_Oone__class_Oone(_414679), _414681), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414683), -(c_Orderings_Oord__class_Oless(_414679, c_Groups_Oone__class_Oone(_414679), hAPP(hAPP(c_Power_Opower__class_Opower(_414679), _414681), _414683)))], (8198 ^ _124236) ^ [_415109, _415111] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _415109), 8201 ^ _124236 : [(8202 ^ _124236) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _415109), _415111) = c_Groups_Oone__class_Oone(tc_Int_Oint), 8205 ^ _124236 : [(8206 ^ _124236) ^ [] : [-(_415109 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8208 ^ _124236) ^ [] : [-(_415111 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (8210 ^ _124236) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _415109), _415111) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _415109 = c_Groups_Oone__class_Oone(tc_Int_Oint), _415111 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (8220 ^ _124236) ^ [_415761, _415763, _415765] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _415761, _415763), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _415765), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _415765), _415761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _415765), _415763)))], (8230 ^ _124236) ^ [_416071] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416071), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _416071)], (8232 ^ _124236) ^ [_416155] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _416155) = _416155)], (8234 ^ _124236) ^ [_416250, _416252] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _416250)), _416252) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416250), _416252)))], (8236 ^ _124236) ^ [_416376, _416378, _416380] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416376), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _416378, _416380)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416376), _416378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416376), _416380)))], (8238 ^ _124236) ^ [_416512, _416514, _416516] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _416512, _416514)), _416516) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416512), _416516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416514), _416516)))], (8240 ^ _124236) ^ [_416648, _416650, _416652] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _416648, _416650)), _416652) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416648), _416652), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416650), _416652)))], (8242 ^ _124236) ^ [_416784, _416786, _416788] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416784), _416786)), _416788) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416786), _416788)))], (8244 ^ _124236) ^ [_416918, _416920, _416922] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416918), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _416920, _416922)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416918), _416920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _416918), _416922)))], (8246 ^ _124236) ^ [_417040, _417042] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _417040), _417042) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _417042), _417040))], (8248 ^ _124236) ^ [_417175, _417177, _417179] : [class_Rings_Oring__1__no__zero__divisors(_417175), -(_417177 = c_Groups_Ozero__class_Ozero(_417175)), hAPP(hAPP(c_Power_Opower__class_Opower(_417175), _417177), _417179) = c_Groups_Ozero__class_Ozero(_417175)], (8258 ^ _124236) ^ [_417524, _417526, _417528] : [class_Groups_Omonoid__mult(_417524), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417524), hAPP(hAPP(c_Power_Opower__class_Opower(_417524), _417526), _417528)), _417526) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417524), _417526), hAPP(hAPP(c_Power_Opower__class_Opower(_417524), _417526), _417528)))], (8264 ^ _124236) ^ [_417830, _417832, _417834, _417836] : [class_Groups_Ocomm__monoid__mult(_417830), -(hAPP(hAPP(c_Power_Opower__class_Opower(_417830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417830), _417832), _417834)), _417836) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417830), hAPP(hAPP(c_Power_Opower__class_Opower(_417830), _417832), _417836)), hAPP(hAPP(c_Power_Opower__class_Opower(_417830), _417834), _417836)))], (8270 ^ _124236) ^ [_418130, _418132] : [class_Groups_Omonoid__mult(_418130), -(hAPP(hAPP(c_Power_Opower__class_Opower(_418130), c_Groups_Oone__class_Oone(_418130)), _418132) = c_Groups_Oone__class_Oone(_418130))], (8276 ^ _124236) ^ [_418333] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _418333) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8288 ^ _124236) ^ [_418736, _418738] : [8289 ^ _124236 : [(8290 ^ _124236) ^ [] : [_418738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8292 ^ _124236) ^ [] : [_418736 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _418736), _418738) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8278 ^ _124236) ^ [_418472, _418474] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _418472), _418474) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_418474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_418472 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8306 ^ _124236) ^ [_419331, _419333] : [8307 ^ _124236 : [(8308 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _419331)], (8310 ^ _124236) ^ [] : [_419333 = 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), _419331), _419333)))], (8296 ^ _124236) ^ [_419063, _419065] : [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), _419063), _419065)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _419063)), -(_419065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8314 ^ _124236) ^ [_419647, _419649, _419651] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _419647), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _419647), _419649), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _419647), _419651)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419649, _419651))], (8324 ^ _124236) ^ [_420014, _420016, _420018, _420020] : [class_Groups_Omonoid__mult(_420014), -(hAPP(hAPP(c_Power_Opower__class_Opower(_420014), _420016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420018), _420020)) = hAPP(hAPP(c_Power_Opower__class_Opower(_420014), hAPP(hAPP(c_Power_Opower__class_Opower(_420014), _420016), _420018)), _420020))], (8330 ^ _124236) ^ [_420294, _420296] : [class_Groups_Omonoid__mult(_420294), -(hAPP(hAPP(c_Power_Opower__class_Opower(_420294), _420296), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _420296)], (8336 ^ _124236) ^ [_420532, _420534, _420536] : [class_Rings_Olinordered__semidom(_420532), c_Orderings_Oord__class_Oless__eq(_420532, c_Groups_Ozero__class_Ozero(_420532), _420534), -(c_Orderings_Oord__class_Oless__eq(_420532, c_Groups_Ozero__class_Ozero(_420532), hAPP(hAPP(c_Power_Opower__class_Opower(_420532), _420534), _420536)))], (8346 ^ _124236) ^ [_420895, _420897, _420899, _420901] : [class_Rings_Olinordered__semidom(_420895), c_Orderings_Oord__class_Oless__eq(_420895, _420897, _420899), c_Orderings_Oord__class_Oless__eq(_420895, c_Groups_Ozero__class_Ozero(_420895), _420897), -(c_Orderings_Oord__class_Oless__eq(_420895, hAPP(hAPP(c_Power_Opower__class_Opower(_420895), _420897), _420901), hAPP(hAPP(c_Power_Opower__class_Opower(_420895), _420899), _420901)))], (8360 ^ _124236) ^ [_421365, _421367, _421369] : [class_Rings_Olinordered__semidom(_421365), c_Orderings_Oord__class_Oless(_421365, c_Groups_Ozero__class_Ozero(_421365), _421367), -(c_Orderings_Oord__class_Oless(_421365, c_Groups_Ozero__class_Ozero(_421365), hAPP(hAPP(c_Power_Opower__class_Opower(_421365), _421367), _421369)))], (8370 ^ _124236) ^ [_421714, _421716, _421718] : [class_Rings_Olinordered__semidom(_421714), c_Orderings_Oord__class_Oless__eq(_421714, c_Groups_Oone__class_Oone(_421714), _421716), -(c_Orderings_Oord__class_Oless__eq(_421714, c_Groups_Oone__class_Oone(_421714), hAPP(hAPP(c_Power_Opower__class_Opower(_421714), _421716), _421718)))], (8380 ^ _124236) ^ [_422063, _422065, _422067] : [class_Power_Opower(_422063), class_Rings_Omult__zero(_422063), class_Rings_Ono__zero__divisors(_422063), class_Rings_Ozero__neq__one(_422063), 8395 ^ _124236 : [(8396 ^ _124236) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_422063), _422065), _422067) = c_Groups_Ozero__class_Ozero(_422063), 8399 ^ _124236 : [(8400 ^ _124236) ^ [] : [-(_422065 = c_Groups_Ozero__class_Ozero(_422063))], (8402 ^ _124236) ^ [] : [_422067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (8404 ^ _124236) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_422063), _422065), _422067) = c_Groups_Ozero__class_Ozero(_422063)), _422065 = c_Groups_Ozero__class_Ozero(_422063), -(_422067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8414 ^ _124236) ^ [_423046, _423048, _423050, _423052] : [class_Rings_Olinordered__semidom(_423046), c_Orderings_Oord__class_Oless(_423046, c_Groups_Oone__class_Oone(_423046), _423048), 8421 ^ _124236 : [(8422 ^ _124236) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_423046), _423048), _423050) = hAPP(hAPP(c_Power_Opower__class_Opower(_423046), _423048), _423052), -(_423050 = _423052)], (8428 ^ _124236) ^ [] : [_423050 = _423052, -(hAPP(hAPP(c_Power_Opower__class_Opower(_423046), _423048), _423050) = hAPP(hAPP(c_Power_Opower__class_Opower(_423046), _423048), _423052))]]], (8434 ^ _124236) ^ [_423687, _423689] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_423687), c_Groups_Ozero__class_Ozero(_423687)), c_Nat_OSuc(_423689)) = c_Groups_Ozero__class_Ozero(_423687)), class_Power_Opower(_423687), class_Rings_Osemiring__0(_423687)], (8444 ^ _124236) ^ [_424024, _424026, _424028] : [class_Power_Opower(_424024), -(hAPP(hAPP(c_Power_Opower__class_Opower(_424024), _424026), c_Nat_OSuc(_424028)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_424024), _424026), hAPP(hAPP(c_Power_Opower__class_Opower(_424024), _424026), _424028)))], (8450 ^ _124236) ^ [_424304, _424306, _424308] : [class_Groups_Omonoid__mult(_424304), -(hAPP(hAPP(c_Power_Opower__class_Opower(_424304), _424306), c_Nat_OSuc(_424308)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_424304), hAPP(hAPP(c_Power_Opower__class_Opower(_424304), _424306), _424308)), _424306))], (8456 ^ _124236) ^ [_424570, _424572] : [class_Power_Opower(_424570), -(hAPP(hAPP(c_Power_Opower__class_Opower(_424570), _424572), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_424570))], (8462 ^ _124236) ^ [_424826, _424828, _424830, _424832] : [class_Groups_Omonoid__mult(_424826), -(hAPP(hAPP(c_Power_Opower__class_Opower(_424826), _424828), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _424830, _424832)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_424826), hAPP(hAPP(c_Power_Opower__class_Opower(_424826), _424828), _424830)), hAPP(hAPP(c_Power_Opower__class_Opower(_424826), _424828), _424832)))], (8468 ^ _124236) ^ [_425118, _425120] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _425118), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _425118), _425120)))], (8474 ^ _124236) ^ [_425372, _425374, _425376, _425378] : [class_Rings_Olinordered__semidom(_425372), c_Orderings_Oord__class_Oless(_425372, hAPP(hAPP(c_Power_Opower__class_Opower(_425372), _425374), _425376), hAPP(hAPP(c_Power_Opower__class_Opower(_425372), _425378), _425376)), c_Orderings_Oord__class_Oless__eq(_425372, c_Groups_Ozero__class_Ozero(_425372), _425378), -(c_Orderings_Oord__class_Oless(_425372, _425374, _425378))], (8488 ^ _124236) ^ [_425856, _425858, _425860, _425862] : [class_Rings_Olinordered__semidom(_425856), hAPP(hAPP(c_Power_Opower__class_Opower(_425856), _425858), c_Nat_OSuc(_425860)) = hAPP(hAPP(c_Power_Opower__class_Opower(_425856), _425862), c_Nat_OSuc(_425860)), c_Orderings_Oord__class_Oless__eq(_425856, c_Groups_Ozero__class_Ozero(_425856), _425858), c_Orderings_Oord__class_Oless__eq(_425856, c_Groups_Ozero__class_Ozero(_425856), _425862), -(_425858 = _425862)], (8506 ^ _124236) ^ [_426447, _426449, _426451, _426453] : [class_Rings_Olinordered__semidom(_426447), c_Orderings_Oord__class_Oless__eq(_426447, hAPP(hAPP(c_Power_Opower__class_Opower(_426447), _426449), c_Nat_OSuc(_426451)), hAPP(hAPP(c_Power_Opower__class_Opower(_426447), _426453), c_Nat_OSuc(_426451))), c_Orderings_Oord__class_Oless__eq(_426447, c_Groups_Ozero__class_Ozero(_426447), _426453), -(c_Orderings_Oord__class_Oless__eq(_426447, _426449, _426453))], (8520 ^ _124236) ^ [_426925, _426927, _426929] : [class_Rings_Olinordered__semidom(_426925), c_Orderings_Oord__class_Oless(_426925, c_Groups_Oone__class_Oone(_426925), _426927), -(c_Orderings_Oord__class_Oless(_426925, c_Groups_Oone__class_Oone(_426925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_426925), _426927), hAPP(hAPP(c_Power_Opower__class_Opower(_426925), _426927), _426929))))], (8530 ^ _124236) ^ [_427290, _427292, _427294] : [class_Rings_Olinordered__semidom(_427290), c_Orderings_Oord__class_Oless(_427290, c_Groups_Oone__class_Oone(_427290), _427292), -(c_Orderings_Oord__class_Oless(_427290, hAPP(hAPP(c_Power_Opower__class_Opower(_427290), _427292), _427294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427290), _427292), hAPP(hAPP(c_Power_Opower__class_Opower(_427290), _427292), _427294))))], (8540 ^ _124236) ^ [_427653, _427655] : [class_Power_Opower(_427653), class_Rings_Osemiring__0(_427653), 8547 ^ _124236 : [(8548 ^ _124236) ^ [] : [_427655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_427653), c_Groups_Ozero__class_Ozero(_427653)), _427655) = c_Groups_Oone__class_Oone(_427653))], (8554 ^ _124236) ^ [] : [-(_427655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_427653), c_Groups_Ozero__class_Ozero(_427653)), _427655) = c_Groups_Ozero__class_Ozero(_427653))]]], (8560 ^ _124236) ^ [_428268, _428270, _428272] : [class_Rings_Olinordered__semidom(_428268), c_Orderings_Oord__class_Oless(_428268, c_Groups_Oone__class_Oone(_428268), _428270), -(c_Orderings_Oord__class_Oless(_428268, c_Groups_Oone__class_Oone(_428268), hAPP(hAPP(c_Power_Opower__class_Opower(_428268), _428270), c_Nat_OSuc(_428272))))], (8570 ^ _124236) ^ [_428621, _428623, _428625] : [class_Rings_Oring__1(_428621), -(hAPP(hAPP(c_Power_Opower__class_Opower(_428621), c_Groups_Ouminus__class_Ouminus(_428621, _428623)), _428625) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428621), hAPP(hAPP(c_Power_Opower__class_Opower(_428621), c_Groups_Ouminus__class_Ouminus(_428621, c_Groups_Oone__class_Oone(_428621))), _428625)), hAPP(hAPP(c_Power_Opower__class_Opower(_428621), _428623), _428625)))], (8576 ^ _124236) ^ [_428943, _428945, _428947, _428949] : [class_Rings_Olinordered__semidom(_428943), c_Orderings_Oord__class_Oless(_428943, c_Groups_Oone__class_Oone(_428943), _428945), 8583 ^ _124236 : [(8584 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(_428943, hAPP(hAPP(c_Power_Opower__class_Opower(_428943), _428945), _428947), hAPP(hAPP(c_Power_Opower__class_Opower(_428943), _428945), _428949)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _428947, _428949))], (8590 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _428947, _428949), -(c_Orderings_Oord__class_Oless(_428943, hAPP(hAPP(c_Power_Opower__class_Opower(_428943), _428945), _428947), hAPP(hAPP(c_Power_Opower__class_Opower(_428943), _428945), _428949)))]]], (8596 ^ _124236) ^ [_429618, _429620, _429622, _429624] : [class_Rings_Olinordered__semidom(_429618), c_Orderings_Oord__class_Oless(_429618, c_Groups_Oone__class_Oone(_429618), _429620), c_Orderings_Oord__class_Oless(_429618, hAPP(hAPP(c_Power_Opower__class_Opower(_429618), _429620), _429622), hAPP(hAPP(c_Power_Opower__class_Opower(_429618), _429620), _429624)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _429622, _429624))], (8610 ^ _124236) ^ [_430102, _430104, _430106, _430108] : [class_Rings_Olinordered__semidom(_430102), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _430104, _430106), c_Orderings_Oord__class_Oless(_430102, c_Groups_Oone__class_Oone(_430102), _430108), -(c_Orderings_Oord__class_Oless(_430102, hAPP(hAPP(c_Power_Opower__class_Opower(_430102), _430108), _430104), hAPP(hAPP(c_Power_Opower__class_Opower(_430102), _430108), _430106)))], (8624 ^ _124236) ^ [_430586, _430588, _430590, _430592] : [class_Rings_Olinordered__semidom(_430586), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _430588, _430590), c_Orderings_Oord__class_Oless__eq(_430586, c_Groups_Oone__class_Oone(_430586), _430592), -(c_Orderings_Oord__class_Oless__eq(_430586, hAPP(hAPP(c_Power_Opower__class_Opower(_430586), _430592), _430588), hAPP(hAPP(c_Power_Opower__class_Opower(_430586), _430592), _430590)))], (8638 ^ _124236) ^ [_431056, _431058, _431060] : [class_Rings_Olinordered__semidom(_431056), c_Orderings_Oord__class_Oless(_431056, c_Groups_Ozero__class_Ozero(_431056), _431058), c_Orderings_Oord__class_Oless(_431056, _431058, c_Groups_Oone__class_Oone(_431056)), -(c_Orderings_Oord__class_Oless(_431056, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_431056), _431058), hAPP(hAPP(c_Power_Opower__class_Opower(_431056), _431058), _431060)), hAPP(hAPP(c_Power_Opower__class_Opower(_431056), _431058), _431060)))], (8652 ^ _124236) ^ [_431532, _431534, _431536] : [class_Rings_Olinordered__semidom(_431532), c_Orderings_Oord__class_Oless(_431532, c_Groups_Ozero__class_Ozero(_431532), _431534), c_Orderings_Oord__class_Oless(_431532, _431534, c_Groups_Oone__class_Oone(_431532)), -(c_Orderings_Oord__class_Oless(_431532, hAPP(hAPP(c_Power_Opower__class_Opower(_431532), _431534), c_Nat_OSuc(_431536)), c_Groups_Oone__class_Oone(_431532)))], (8666 ^ _124236) ^ [_431998, _432000, _432002, _432004] : [class_Rings_Olinordered__semidom(_431998), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432000, _432002), c_Orderings_Oord__class_Oless(_431998, c_Groups_Ozero__class_Ozero(_431998), _432004), c_Orderings_Oord__class_Oless(_431998, _432004, c_Groups_Oone__class_Oone(_431998)), -(c_Orderings_Oord__class_Oless(_431998, hAPP(hAPP(c_Power_Opower__class_Opower(_431998), _432004), _432002), hAPP(hAPP(c_Power_Opower__class_Opower(_431998), _432004), _432000)))], (8684 ^ _124236) ^ [_432585, _432587, _432589, _432591] : [class_Rings_Olinordered__semidom(_432585), hAPP(hAPP(c_Power_Opower__class_Opower(_432585), _432587), _432589) = hAPP(hAPP(c_Power_Opower__class_Opower(_432585), _432591), _432589), c_Orderings_Oord__class_Oless__eq(_432585, c_Groups_Ozero__class_Ozero(_432585), _432587), c_Orderings_Oord__class_Oless__eq(_432585, c_Groups_Ozero__class_Ozero(_432585), _432591), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _432589), -(_432587 = _432591)], (8706 ^ _124236) ^ [_433267, _433269, _433271, _433273] : [class_Rings_Olinordered__semidom(_433267), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433269, _433271), c_Orderings_Oord__class_Oless__eq(_433267, c_Groups_Ozero__class_Ozero(_433267), _433273), c_Orderings_Oord__class_Oless__eq(_433267, _433273, c_Groups_Oone__class_Oone(_433267)), -(c_Orderings_Oord__class_Oless__eq(_433267, hAPP(hAPP(c_Power_Opower__class_Opower(_433267), _433273), _433271), hAPP(hAPP(c_Power_Opower__class_Opower(_433267), _433273), _433269)))], (8724 ^ _124236) ^ [_433854, _433856, _433858, _433860] : [class_Rings_Olinordered__semidom(_433854), c_Orderings_Oord__class_Oless(_433854, c_Groups_Oone__class_Oone(_433854), _433856), c_Orderings_Oord__class_Oless__eq(_433854, hAPP(hAPP(c_Power_Opower__class_Opower(_433854), _433856), _433858), hAPP(hAPP(c_Power_Opower__class_Opower(_433854), _433856), _433860)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433858, _433860))], (8738 ^ _124236) ^ [_434338, _434340, _434342, _434344] : [class_Rings_Olinordered__semidom(_434338), c_Orderings_Oord__class_Oless(_434338, c_Groups_Oone__class_Oone(_434338), _434340), 8745 ^ _124236 : [(8746 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(_434338, hAPP(hAPP(c_Power_Opower__class_Opower(_434338), _434340), _434342), hAPP(hAPP(c_Power_Opower__class_Opower(_434338), _434340), _434344)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _434342, _434344))], (8752 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _434342, _434344), -(c_Orderings_Oord__class_Oless__eq(_434338, hAPP(hAPP(c_Power_Opower__class_Opower(_434338), _434340), _434342), hAPP(hAPP(c_Power_Opower__class_Opower(_434338), _434340), _434344)))]]], (8768 ^ _124236) ^ [_435282, _435284] : [8769 ^ _124236 : [(8770 ^ _124236) ^ [] : [_435284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8772 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _435282)]], -(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), _435282), _435284)))], (8758 ^ _124236) ^ [_435014, _435016] : [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), _435014), _435016)), -(_435016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _435014))], (8776 ^ _124236) ^ [_435599] : [-(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), _435599), _435599))), -(_435599 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8782 ^ _124236) ^ [_435772] : [_435772 = 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), _435772), _435772))], (8788 ^ _124236) ^ [_435979] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _435979, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_435979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_435979 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8798 ^ _124236) ^ [_436300, _436302] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _436300, _436302), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _436300, _436302), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8804 ^ _124236) ^ [_436474, _436476] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _436474, _436476), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _436474, _436476))], (8810 ^ _124236) ^ [_436727, _436729] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _436727, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _436729, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _436727, _436729))], (8816 ^ _124236) ^ [_436901, _436903] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _436901, _436903), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _436901, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _436903, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8822 ^ _124236) ^ [_437154, _437156] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _437154, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _437156, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _437154, _437156))], (8828 ^ _124236) ^ [_437328, _437330] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _437328, _437330), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _437328, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _437330, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8834 ^ _124236) ^ [_437581, _437583] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _437581, c_Groups_Oone__class_Oone(tc_Int_Oint)), _437583), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _437581, _437583))], (8840 ^ _124236) ^ [_437755, _437757] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _437755, _437757), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _437755, c_Groups_Oone__class_Oone(tc_Int_Oint)), _437757))], (8846 ^ _124236) ^ [_437965] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _437965), -(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), _437965)))], (8852 ^ _124236) ^ [_438181, _438183] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _438181, _438183), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _438181, c_Groups_Oone__class_Oone(tc_Int_Oint)), _438183))], (8858 ^ _124236) ^ [_438431, _438433, _438435, _438437] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _438431, _438433), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _438435, _438437), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _438431, _438435), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _438433, _438437)))], (8868 ^ _124236) ^ [_438786, _438788, _438790] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _438786, _438788), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _438786, _438790), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _438788, _438790)))], (8874 ^ _124236) ^ [_439037] : [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), _439037), _439037), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _439037, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8880 ^ _124236) ^ [_439213] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _439213, 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), _439213), _439213), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8896 ^ _124236) ^ [_439732, _439734] : [8897 ^ _124236 : [(8898 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _439732, _439734)], (8900 ^ _124236) ^ [] : [_439732 = _439734]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _439732, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _439734, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8886 ^ _124236) ^ [_439468, _439470] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _439468, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _439470, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _439468, _439470)), -(_439468 = _439470)], (8904 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8906 ^ _124236) ^ [_440083, _440085] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _440083, _440085)), -(_440083 = _440085), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _440085, _440083))], (8916 ^ _124236) ^ [_440417, _440419] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _440417, _440419), 8919 ^ _124236 : [(8920 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _440417, _440419))], (8922 ^ _124236) ^ [] : [_440417 = _440419]]], (8924 ^ _124236) ^ [_440659, _440661] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _440659, _440661)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _440659, _440661), -(_440659 = _440661)], (8934 ^ _124236) ^ [_440982] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _440982), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _440982))], (8940 ^ _124236) ^ [_441142] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _441142), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _441142))], (8946 ^ _124236) ^ [_441323] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _441323)) = _441323)], (8948 ^ _124236) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8950 ^ _124236) ^ [_441474, _441476] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _441474, _441476)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _441474), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _441476)))], (8952 ^ _124236) ^ [_441571] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _441571), _441571) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8954 ^ _124236) ^ [_441670, _441672] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _441670, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _441672)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _441670, _441672))], (8956 ^ _124236) ^ [_441775, _441777] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _441775, _441777) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _441775, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _441777)))], (8958 ^ _124236) ^ [_441909, _441911, _441913] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _441909, _441911), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _441913, _441909), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _441913, _441911)))], (8964 ^ _124236) ^ [_442116] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _442116) = _442116)], (8966 ^ _124236) ^ [_442198] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442198, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _442198)], (8968 ^ _124236) ^ [_442294, _442296] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442294, _442296) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442296, _442294))], (8970 ^ _124236) ^ [_442410, _442412, _442414] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442410, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442412, _442414)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442412, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442410, _442414)))], (8972 ^ _124236) ^ [_442536, _442538, _442540] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442536, _442538), _442540) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442536, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442538, _442540)))], (8974 ^ _124236) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (8976 ^ _124236) ^ [_442685] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _442685), _442685) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (8978 ^ _124236) ^ [_442814, _442816, _442818] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _442814), _442814 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _442816, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _442814), _442818)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _442816, _442814), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _442818))], (8992 ^ _124236) ^ [_443256, _443258, _443260] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _443256), _443256 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _443258, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _443256), _443260)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _443258), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _443260, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9006 ^ _124236) ^ [_443655] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _443655, _443655))], (9008 ^ _124236) ^ [_443763, _443765] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _443763, _443765)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _443765, _443763))], (9014 ^ _124236) ^ [_443992, _443994, _443996] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _443992, _443994), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _443994, _443996), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _443992, _443996))], (9024 ^ _124236) ^ [_444307, _444309] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _444307, _444309), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _444309, _444307), -(_444307 = _444309)], (9034 ^ _124236) ^ [_444624, _444626, _444628] : [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), _444624), _444626), _444628)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _444628, _444624), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _444624), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _444626))], (9048 ^ _124236) ^ [_445068, _445070, _445072] : [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), _445068), _445070), _445072), 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), _445072), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _445068), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _445070, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9062 ^ _124236) ^ [_445540, _445542, _445544, _445546, _445548] : [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), _445540), _445542), _445544), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _445540), _445546), _445548)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _445544), c_Orderings_Oord__class_Oless(tc_Int_Oint, _445544, _445540), c_Orderings_Oord__class_Oless(tc_Int_Oint, _445548, _445540), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _445542, _445546))], (9080 ^ _124236) ^ [_446177, _446179, _446181, _446183, _446185, _446187] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _446177), _446179), _446181) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _446183), _446185), _446187), 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), _446183), _446185), _446187)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _446187, _446183), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _446181), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _446183), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _446183, _446177), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _446179, _446185))], (9106 ^ _124236) ^ [_447050, _447052, _447054, _447056, _447058] : [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), _447050), _447052), _447054), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447050), _447056), _447058)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _447058, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _447050, _447058), c_Orderings_Oord__class_Oless(tc_Int_Oint, _447050, _447054), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _447056, _447052))], (9124 ^ _124236) ^ [_447687, _447689, _447691, _447693, _447695, _447697] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447687), _447689), _447691) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447693), _447695), _447697), 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), _447693), _447695), _447697), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _447691, _447687), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _447697), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _447693), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _447693, _447687), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _447695, _447689))], (9150 ^ _124236) ^ [_448518, _448520] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _448518), -(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), _448518), _448520)))], (9156 ^ _124236) ^ [_448744, _448746] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _448744), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _448746), -(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), _448744), _448746)))], (9166 ^ _124236) ^ [] : [-(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)))], (9168 ^ _124236) ^ [] : [-(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)))], (9170 ^ _124236) ^ [_449167, _449169] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _449167), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _449169), -(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, _449167, _449169)))], (9180 ^ _124236) ^ [_449466] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _449466), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _449466, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_449466), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9186 ^ _124236) ^ [_449682] : [class_Power_Opower(_449682), -(c_Power_Opower__class_Opower(_449682) = c_Power_Opower_Opower(_449682, c_Groups_Oone__class_Oone(_449682), c_Groups_Otimes__class_Otimes(_449682)))], (9192 ^ _124236) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9194 ^ _124236) ^ [_449928] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_449928)))], (9196 ^ _124236) ^ [_450038, _450040] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _450038, _450040), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_450038), c_RComplete_Onatceiling(_450040)))], (9202 ^ _124236) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9204 ^ _124236) ^ [_450326, _450328, _450330, _450332] : [-(hAPP(hAPP(c_Power_Opower_Opower(_450326, _450328, _450330), _450332), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _450328)], (9206 ^ _124236) ^ [_450476, _450478, _450480, _450482, _450484] : [-(hAPP(hAPP(c_Power_Opower_Opower(_450476, _450478, _450480), _450482), c_Nat_OSuc(_450484)) = hAPP(hAPP(_450480, _450482), hAPP(hAPP(c_Power_Opower_Opower(_450476, _450478, _450480), _450482), _450484)))], (9208 ^ _124236) ^ [_450605] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _450605, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_450605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9214 ^ _124236) ^ [_450830] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_450830), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _450830, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9220 ^ _124236) ^ [_450994] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _450994, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_450994), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9226 ^ _124236) ^ [_451194] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _451194) = 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, _451194, 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, _451194, 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, _451194, 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, _451194, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9244 ^ _124236) ^ [_451740, _451742, _451744] : [class_Rings_Oidom(_451740), -(_451742 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_451740))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_451740), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_451740)), c_Polynomial_OpCons(_451740, c_Groups_Ouminus__class_Ouminus(_451740, _451744), c_Polynomial_OpCons(_451740, c_Groups_Oone__class_Oone(_451740), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_451740))))), c_Nat_OSuc(c_Polynomial_Oorder(_451740, _451744, _451742))), _451742)], (9254 ^ _124236) ^ [_452131, _452133] : [class_Rings_Ocomm__semiring__1(_452131), -(c_Rings_Odvd__class_Odvd(_452131, _452133, c_Groups_Ozero__class_Ozero(_452131)))], (9260 ^ _124236) ^ [_452387, _452389, _452391, _452393, _452395] : [class_Rings_Ocomm__semiring__1(_452387), c_Rings_Odvd__class_Odvd(_452387, hAPP(hAPP(c_Power_Opower__class_Opower(_452387), _452389), _452391), _452393), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _452395, _452391), -(c_Rings_Odvd__class_Odvd(_452387, hAPP(hAPP(c_Power_Opower__class_Opower(_452387), _452389), _452395), _452393))], (9274 ^ _124236) ^ [_452895, _452897, _452899, _452901, _452903] : [class_Rings_Ocomm__semiring__1(_452895), c_Rings_Odvd__class_Odvd(_452895, _452897, _452899), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _452901, _452903), -(c_Rings_Odvd__class_Odvd(_452895, hAPP(hAPP(c_Power_Opower__class_Opower(_452895), _452897), _452901), hAPP(hAPP(c_Power_Opower__class_Opower(_452895), _452899), _452903)))], (9288 ^ _124236) ^ [_453389, _453391, _453393, _453395] : [class_Rings_Ocomm__semiring__1(_453389), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _453391, _453393), -(c_Rings_Odvd__class_Odvd(_453389, hAPP(hAPP(c_Power_Opower__class_Opower(_453389), _453395), _453391), hAPP(hAPP(c_Power_Opower__class_Opower(_453389), _453395), _453393)))], (9298 ^ _124236) ^ [_453770, _453772, _453774, _453776] : [class_Rings_Ocomm__semiring__1(_453770), c_Rings_Odvd__class_Odvd(_453770, _453772, _453774), -(c_Rings_Odvd__class_Odvd(_453770, hAPP(hAPP(c_Power_Opower__class_Opower(_453770), _453772), _453776), hAPP(hAPP(c_Power_Opower__class_Opower(_453770), _453774), _453776)))], (9308 ^ _124236) ^ [_454137, _454139, _454141] : [class_Rings_Ocomm__semiring__1(_454137), -(c_Rings_Odvd__class_Odvd(_454137, _454139, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454137), _454139), _454141)))], (9314 ^ _124236) ^ [_454383, _454385, _454387] : [class_Rings_Ocomm__semiring__1(_454383), -(c_Rings_Odvd__class_Odvd(_454383, _454385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454383), _454387), _454385)))], (9320 ^ _124236) ^ [_454643, _454645, _454647, _454649] : [class_Rings_Ocomm__semiring__1(_454643), c_Rings_Odvd__class_Odvd(_454643, _454645, _454647), -(c_Rings_Odvd__class_Odvd(_454643, _454645, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454643), _454647), _454649)))], (9330 ^ _124236) ^ [_455008, _455010, _455012, _455014] : [class_Rings_Ocomm__semiring__1(_455008), c_Rings_Odvd__class_Odvd(_455008, _455010, _455012), -(c_Rings_Odvd__class_Odvd(_455008, _455010, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455008), _455014), _455012)))], (9340 ^ _124236) ^ [_455387, _455389, _455391, _455393, _455395] : [class_Rings_Ocomm__semiring__1(_455387), c_Rings_Odvd__class_Odvd(_455387, _455389, _455391), c_Rings_Odvd__class_Odvd(_455387, _455393, _455395), -(c_Rings_Odvd__class_Odvd(_455387, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455387), _455389), _455393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455387), _455391), _455395)))], (9354 ^ _124236) ^ [_455881, _455883, _455885, _455887] : [class_Rings_Odvd(_455881), _455883 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455881), _455885), _455887), -(c_Rings_Odvd__class_Odvd(_455881, _455885, _455883))], (9364 ^ _124236) ^ [_456244, _456246, _456248, _456250] : [class_Rings_Ocomm__semiring__1(_456244), c_Rings_Odvd__class_Odvd(_456244, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_456244), _456246), _456248), _456250), -(c_Rings_Odvd__class_Odvd(_456244, _456246, _456250))], (9374 ^ _124236) ^ [_456609, _456611, _456613, _456615] : [class_Rings_Ocomm__semiring__1(_456609), c_Rings_Odvd__class_Odvd(_456609, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_456609), _456611), _456613), _456615), -(c_Rings_Odvd__class_Odvd(_456609, _456613, _456615))], (9384 ^ _124236) ^ [_456946, _456948] : [class_Rings_Ocomm__semiring__1(_456946), -(c_Rings_Odvd__class_Odvd(_456946, _456948, _456948))], (9390 ^ _124236) ^ [_457184, _457186, _457188, _457190] : [class_Rings_Ocomm__semiring__1(_457184), c_Rings_Odvd__class_Odvd(_457184, _457186, _457188), c_Rings_Odvd__class_Odvd(_457184, _457188, _457190), -(c_Rings_Odvd__class_Odvd(_457184, _457186, _457190))], (9404 ^ _124236) ^ [_457632, _457634, _457636, _457638] : [class_Rings_Ocomm__semiring__1(_457632), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_457632), c_Polynomial_Osmult(_457632, _457634, _457636), _457638), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_457632), _457636, _457638))], (9414 ^ _124236) ^ [_457997, _457999, _458001, _458003] : [class_Rings_Ocomm__semiring__1(_457997), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_457997), _457999, _458001), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_457997), _457999, c_Polynomial_Osmult(_457997, _458003, _458001)))], (9424 ^ _124236) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (9426 ^ _124236) ^ [_458386, _458388] : [class_Rings_Ocomm__semiring__1(_458386), c_Rings_Odvd__class_Odvd(_458386, c_Groups_Ozero__class_Ozero(_458386), _458388), -(_458388 = c_Groups_Ozero__class_Ozero(_458386))], (9436 ^ _124236) ^ [_458721, _458723, _458725, _458727] : [class_Rings_Ocomm__semiring__1(_458721), c_Rings_Odvd__class_Odvd(_458721, _458723, _458725), c_Rings_Odvd__class_Odvd(_458721, _458723, _458727), -(c_Rings_Odvd__class_Odvd(_458721, _458723, c_Groups_Oplus__class_Oplus(_458721, _458725, _458727)))], (9450 ^ _124236) ^ [_459149, _459151] : [class_Rings_Ocomm__semiring__1(_459149), -(c_Rings_Odvd__class_Odvd(_459149, c_Groups_Oone__class_Oone(_459149), _459151))], (9456 ^ _124236) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (9458 ^ _124236) ^ [_459443, _459445, _459447, _459449] : [class_Fields_Ofield(_459443), -(_459445 = c_Groups_Ozero__class_Ozero(_459443)), 9465 ^ _124236 : [(9466 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_459443), _459447, c_Polynomial_Osmult(_459443, _459445, _459449)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_459443), _459447, _459449))], (9472 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_459443), _459447, _459449), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_459443), _459447, c_Polynomial_Osmult(_459443, _459445, _459449)))]]], (9478 ^ _124236) ^ [_460095, _460097, _460099, _460101] : [class_Fields_Ofield(_460095), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_460095), _460097, _460099), -(_460101 = c_Groups_Ozero__class_Ozero(_460095)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_460095), c_Polynomial_Osmult(_460095, _460101, _460097), _460099))], (9492 ^ _124236) ^ [_460564, _460566, _460568, _460570] : [class_Fields_Ofield(_460564), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_460564), _460566, c_Polynomial_Osmult(_460564, _460568, _460570)), -(_460568 = c_Groups_Ozero__class_Ozero(_460564)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_460564), _460566, _460570))], (9506 ^ _124236) ^ [_461033, _461035, _461037, _461039] : [class_Rings_Oidom(_461033), 9509 ^ _124236 : [(9520 ^ _124236) ^ [] : [9521 ^ _124236 : [(9522 ^ _124236) ^ [] : [_461035 = c_Groups_Ozero__class_Ozero(_461033)], (9524 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_461033, _461037, _461039)]], -(c_Rings_Odvd__class_Odvd(_461033, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461033), _461035), _461037), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461033), _461035), _461039)))], (9510 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_461033, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461033), _461035), _461037), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461033), _461035), _461039)), -(_461035 = c_Groups_Ozero__class_Ozero(_461033)), -(c_Rings_Odvd__class_Odvd(_461033, _461037, _461039))]]], (9528 ^ _124236) ^ [_461781, _461783, _461785, _461787] : [class_Rings_Oidom(_461781), 9531 ^ _124236 : [(9542 ^ _124236) ^ [] : [9543 ^ _124236 : [(9544 ^ _124236) ^ [] : [_461785 = c_Groups_Ozero__class_Ozero(_461781)], (9546 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_461781, _461783, _461787)]], -(c_Rings_Odvd__class_Odvd(_461781, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461781), _461783), _461785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461781), _461787), _461785)))], (9532 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_461781, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461781), _461783), _461785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461781), _461787), _461785)), -(_461785 = c_Groups_Ozero__class_Ozero(_461781)), -(c_Rings_Odvd__class_Odvd(_461781, _461783, _461787))]]], (9550 ^ _124236) ^ [_462529, _462531, _462533, _462535] : [class_Rings_Ocomm__ring__1(_462529), c_Rings_Odvd__class_Odvd(_462529, _462531, _462533), c_Rings_Odvd__class_Odvd(_462529, _462531, _462535), -(c_Rings_Odvd__class_Odvd(_462529, _462531, c_Groups_Ominus__class_Ominus(_462529, _462533, _462535)))], (9564 ^ _124236) ^ [_462928] : [-(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), _462928)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _462928))], (9566 ^ _124236) ^ [_463058, _463060, _463062] : [class_Rings_Ocomm__ring__1(_463058), 9569 ^ _124236 : [(9570 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_463058, c_Groups_Ouminus__class_Ouminus(_463058, _463060), _463062), -(c_Rings_Odvd__class_Odvd(_463058, _463060, _463062))], (9576 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_463058, _463060, _463062), -(c_Rings_Odvd__class_Odvd(_463058, c_Groups_Ouminus__class_Ouminus(_463058, _463060), _463062))]]], (9582 ^ _124236) ^ [_463561, _463563, _463565] : [class_Rings_Ocomm__ring__1(_463561), 9585 ^ _124236 : [(9586 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_463561, _463563, c_Groups_Ouminus__class_Ouminus(_463561, _463565)), -(c_Rings_Odvd__class_Odvd(_463561, _463563, _463565))], (9592 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_463561, _463563, _463565), -(c_Rings_Odvd__class_Odvd(_463561, _463563, c_Groups_Ouminus__class_Ouminus(_463561, _463565)))]]], (9598 ^ _124236) ^ [] : [-(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)))], (9600 ^ _124236) ^ [_464131, _464133, _464135, _464137] : [class_Fields_Ofield(_464131), 9603 ^ _124236 : [(9620 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_464131), c_Polynomial_Osmult(_464131, _464133, _464135), _464137)), 9623 ^ _124236 : [(9624 ^ _124236) ^ [] : [-(_464133 = c_Groups_Ozero__class_Ozero(_464131))], (9626 ^ _124236) ^ [] : [_464137 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464131))]], 9627 ^ _124236 : [(9628 ^ _124236) ^ [] : [_464133 = c_Groups_Ozero__class_Ozero(_464131)], (9630 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_464131), _464135, _464137)]]], (9604 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_464131), c_Polynomial_Osmult(_464131, _464133, _464135), _464137), 9607 ^ _124236 : [(9608 ^ _124236) ^ [] : [_464133 = c_Groups_Ozero__class_Ozero(_464131), -(_464137 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464131)))], (9614 ^ _124236) ^ [] : [-(_464133 = c_Groups_Ozero__class_Ozero(_464131)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_464131), _464135, _464137))]]]]], (9634 ^ _124236) ^ [_465201, _465203, _465205] : [class_Rings_Ocomm__semiring__1(_465201), 9639 ^ _124236 : [(9640 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _465203)], (9642 ^ _124236) ^ [] : [_465205 = c_Groups_Oone__class_Oone(_465201)]], -(c_Rings_Odvd__class_Odvd(_465201, _465205, hAPP(hAPP(c_Power_Opower__class_Opower(_465201), _465205), _465203)))], (9646 ^ _124236) ^ [_465622, _465624, _465626] : [class_Rings_Oidom(_465622), 9649 ^ _124236 : [(9650 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_465622), c_Polynomial_OpCons(_465622, _465624, c_Polynomial_OpCons(_465622, c_Groups_Oone__class_Oone(_465622), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_465622)))), _465626), -(hAPP(c_Polynomial_Opoly(_465622, _465626), c_Groups_Ouminus__class_Ouminus(_465622, _465624)) = c_Groups_Ozero__class_Ozero(_465622))], (9656 ^ _124236) ^ [] : [hAPP(c_Polynomial_Opoly(_465622, _465626), c_Groups_Ouminus__class_Ouminus(_465622, _465624)) = c_Groups_Ozero__class_Ozero(_465622), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_465622), c_Polynomial_OpCons(_465622, _465624, c_Polynomial_OpCons(_465622, c_Groups_Oone__class_Oone(_465622), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_465622)))), _465626))]]], (9662 ^ _124236) ^ [_466194, _466196, _466198] : [class_Rings_Oidom(_466194), 9665 ^ _124236 : [(9666 ^ _124236) ^ [] : [hAPP(c_Polynomial_Opoly(_466194, _466196), _466198) = c_Groups_Ozero__class_Ozero(_466194), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_466194), c_Polynomial_OpCons(_466194, c_Groups_Ouminus__class_Ouminus(_466194, _466198), c_Polynomial_OpCons(_466194, c_Groups_Oone__class_Oone(_466194), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_466194)))), _466196))], (9672 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_466194), c_Polynomial_OpCons(_466194, c_Groups_Ouminus__class_Ouminus(_466194, _466198), c_Polynomial_OpCons(_466194, c_Groups_Oone__class_Oone(_466194), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_466194)))), _466196), -(hAPP(c_Polynomial_Opoly(_466194, _466196), _466198) = c_Groups_Ozero__class_Ozero(_466194))]]], (9678 ^ _124236) ^ [_466766, _466768, _466770] : [class_Rings_Oidom(_466766), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_466766), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_466766)), c_Polynomial_OpCons(_466766, c_Groups_Ouminus__class_Ouminus(_466766, _466768), c_Polynomial_OpCons(_466766, c_Groups_Oone__class_Oone(_466766), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_466766))))), c_Polynomial_Oorder(_466766, _466768, _466770)), _466770))], (9684 ^ _124236) ^ [_467062, _467064, _467066] : [class_Rings_Oidom(_467062), -(_467064 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_467062))), 9691 ^ _124236 : [(9692 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_467062), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_467062)), c_Polynomial_OpCons(_467062, c_Groups_Ouminus__class_Ouminus(_467062, _467066), c_Polynomial_OpCons(_467062, c_Groups_Oone__class_Oone(_467062), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_467062))))), c_Polynomial_Oorder(_467062, _467066, _467064)), _467064))], (9694 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_467062), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_467062)), c_Polynomial_OpCons(_467062, c_Groups_Ouminus__class_Ouminus(_467062, _467066), c_Polynomial_OpCons(_467062, c_Groups_Oone__class_Oone(_467062), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_467062))))), c_Nat_OSuc(c_Polynomial_Oorder(_467062, _467066, _467064))), _467064)]]], (9696 ^ _124236) ^ [_467626, _467628, _467630, _467632] : [class_Rings_Ocomm__ring(_467626), class_Rings_Odvd(_467626), c_Rings_Odvd__class_Odvd(_467626, _467628, _467630), 9707 ^ _124236 : [(9708 ^ _124236) ^ [_468029, _468031] : [c_Rings_Odvd__class_Odvd(_467626, _467628, c_Groups_Oplus__class_Oplus(_467626, _468031, _467632)), -(c_Rings_Odvd__class_Odvd(_467626, _467628, c_Groups_Oplus__class_Oplus(_467626, c_Groups_Ominus__class_Ominus(_467626, _468031, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467626), _468029), _467630)), _467632)))], (9714 ^ _124236) ^ [_468267, _468269] : [c_Rings_Odvd__class_Odvd(_467626, _467628, c_Groups_Oplus__class_Oplus(_467626, c_Groups_Ominus__class_Ominus(_467626, _468269, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467626), _468267), _467630)), _467632)), -(c_Rings_Odvd__class_Odvd(_467626, _467628, c_Groups_Oplus__class_Oplus(_467626, _468269, _467632)))]]], (9720 ^ _124236) ^ [_468594, _468596, _468598, _468600] : [class_Rings_Ocomm__ring(_468594), class_Rings_Odvd(_468594), c_Rings_Odvd__class_Odvd(_468594, _468596, _468598), 9731 ^ _124236 : [(9732 ^ _124236) ^ [_468997, _468999] : [c_Rings_Odvd__class_Odvd(_468594, _468596, c_Groups_Oplus__class_Oplus(_468594, _468999, _468600)), -(c_Rings_Odvd__class_Odvd(_468594, _468596, c_Groups_Oplus__class_Oplus(_468594, c_Groups_Ominus__class_Ominus(_468594, _468999, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468594), _468997), _468598)), _468600)))], (9738 ^ _124236) ^ [_469235, _469237] : [c_Rings_Odvd__class_Odvd(_468594, _468596, c_Groups_Oplus__class_Oplus(_468594, c_Groups_Ominus__class_Ominus(_468594, _469237, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468594), _469235), _468598)), _468600)), -(c_Rings_Odvd__class_Odvd(_468594, _468596, c_Groups_Oplus__class_Oplus(_468594, _469237, _468600)))]]], (9744 ^ _124236) ^ [_469505] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _469505))], (9746 ^ _124236) ^ [_469613, _469615] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _469613), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _469615), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _469613, _469615), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _469615, _469613), -(_469613 = _469615)], (9764 ^ _124236) ^ [_470112, _470114, _470116] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470112, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _470114, _470116)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470112, _470114), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _470116, _470114), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470112, _470116))], (9778 ^ _124236) ^ [_470544, _470546, _470548] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470544, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _470546, _470548)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470544, _470548), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _470548, _470546), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470544, _470546))], (9792 ^ _124236) ^ [_470991, _470993] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470991, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _470993, _470991)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470991, _470993))], (9798 ^ _124236) ^ [_471165, _471167] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471165, _471167), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471165, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _471167, _471165)))], (9804 ^ _124236) ^ [_471404] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471404, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_471404 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9810 ^ _124236) ^ [_471562] : [_471562 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471562, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9826 ^ _124236) ^ [_472103, _472105, _472107] : [9827 ^ _124236 : [(9828 ^ _124236) ^ [] : [_472103 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9830 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472105, _472107)]], -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472103), _472105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472103), _472107)))], (9816 ^ _124236) ^ [_471813, _471815, _471817] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _471813), _471815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _471813), _471817)), -(_471813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471815, _471817))], (9834 ^ _124236) ^ [_472425, _472427] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _472425), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _472425, _472427), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472427, _472425)], (9844 ^ _124236) ^ [_472746] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472746, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_472746 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9850 ^ _124236) ^ [_472904] : [_472904 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472904, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9856 ^ _124236) ^ [_473126, _473128, _473130] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473126, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _473128, _473130)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473126, _473130), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473126, _473128))], (9866 ^ _124236) ^ [_473463, _473465, _473467] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _473463), _473465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _473463), _473467)), -(_473463 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473465, _473467))], (9876 ^ _124236) ^ [_473845, _473847, _473849, _473851, _473853] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473845, _473847), 9879 ^ _124236 : [(9880 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473845, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _473849, _473851)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473845, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _473849, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _473853), _473847)), _473851)))], (9886 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473845, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _473849, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _473853), _473847)), _473851)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _473845, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _473849, _473851)))]]], (9892 ^ _124236) ^ [_474429, _474431, _474433] : [-(_474429 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9895 ^ _124236 : [(9896 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _474431, _474433), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474429), _474431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474429), _474433)))], (9902 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474429), _474431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474429), _474433)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _474431, _474433))]]], (9908 ^ _124236) ^ [_474993, _474995, _474997] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _474993, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _474995, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474993), _474997))), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _474993, _474995))], (9914 ^ _124236) ^ [_475185, _475187, _475189] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _475185, _475187), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _475185, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _475187, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _475185), _475189))))], (9920 ^ _124236) ^ [_475441, _475443, _475445] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475441, _475443), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475441, _475445), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475441, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _475443, _475445)))], (9930 ^ _124236) ^ [_475793, _475795] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _475793, _475795), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _475793, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _475795)))], (9936 ^ _124236) ^ [_475965, _475967] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _475965, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _475967)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _475965, _475967))], (9942 ^ _124236) ^ [_476216, _476218] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _476216, _476218), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _476216), _476218))], (9948 ^ _124236) ^ [_476388, _476390] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _476388), _476390), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _476388, _476390))], (9954 ^ _124236) ^ [_476610, _476612] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _476610), c_Orderings_Oord__class_Oless(tc_Int_Oint, _476610, _476612), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _476612, _476610)], (9964 ^ _124236) ^ [_476916, _476918] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _476916, _476918), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _476918), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _476916, _476918))], (9974 ^ _124236) ^ [_477221, _477223] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477221, _477223), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _477223), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _477221, _477223))], (9984 ^ _124236) ^ [_477540, _477542, _477544] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _477540), 9987 ^ _124236 : [(9988 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _477540), _477542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _477540), _477544)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477542, _477544))], (9994 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477542, _477544), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _477540), _477542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _477540), _477544)))]]], (10000 ^ _124236) ^ [_478074, _478076, _478078] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _478074), _478076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _478074), _478078)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478074), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _478076, _478078))], (10010 ^ _124236) ^ [_478413, _478415] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478413), 10013 ^ _124236 : [(10014 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _478413), _478415), _478413), -(_478415 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10020 ^ _124236) ^ [] : [_478415 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _478413), _478415), _478413))]]], (10026 ^ _124236) ^ [_478896, _478898] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478896), 10029 ^ _124236 : [(10030 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _478898), _478896), _478896), -(_478898 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10036 ^ _124236) ^ [] : [_478898 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _478898), _478896), _478896))]]], (10042 ^ _124236) ^ [_479393, _479395, _479397] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _479393), _479395), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _479393), _479397)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _479393), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _479395, _479397))], (10052 ^ _124236) ^ [_479746, _479748, _479750] : [class_Rings_Odvd(_479746), class_Rings_Osemiring__0(_479746), 10059 ^ _124236 : [(10060 ^ _124236) ^ [] : [10061 ^ _124236 : [(10062 ^ _124236) ^ [_480055] : [hBOOL(hAPP(_479748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479746), _479750), _480055)))]], 10064 ^ _124236 : [(10065 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(_479746, _479750, c_Groups_Oplus__class_Oplus(_479746, 10063 ^ [_479746, _479748, _479750], c_Groups_Ozero__class_Ozero(_479746))))], (10067 ^ _124236) ^ [] : [-(hBOOL(hAPP(_479748, 10063 ^ [_479746, _479748, _479750])))]]], (10069 ^ _124236) ^ [] : [-(hBOOL(hAPP(_479748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479746), _479750), 10076 ^ [_479746, _479748, _479750])))), 10070 ^ _124236 : [(10071 ^ _124236) ^ [_480395] : [c_Rings_Odvd__class_Odvd(_479746, _479750, c_Groups_Oplus__class_Oplus(_479746, _480395, c_Groups_Ozero__class_Ozero(_479746))), hBOOL(hAPP(_479748, _480395))]]]]], (10080 ^ _124236) ^ [_480780, _480782] : [-(_480780 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_480782 = 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), _480780), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 10087 ^ [_480780, _480782]), _480782)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10091 ^ _124236) ^ [_481216, _481218, _481220] : [-(_481216 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10094 ^ _124236 : [(10095 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _481218), _481216), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _481220), _481216)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481218, _481220))], (10101 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481218, _481220), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _481218), _481216), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _481220), _481216)))]]], (10107 ^ _124236) ^ [_481708] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481708, _481708))], (10109 ^ _124236) ^ [_481845, _481847] : [_481845 = _481847, 10112 ^ _124236 : [(10113 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481845, _481847))], (10115 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481847, _481845))]]], (10117 ^ _124236) ^ [_482086, _482088] : [-(_482086 = _482088), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _482086, _482088), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _482088, _482086)], (10127 ^ _124236) ^ [_482420, _482422] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _482420, _482422), 10132 ^ _124236 : [(10133 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _482420, _482422))], (10135 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _482422, _482420)]], -(_482420 = _482422)], (10139 ^ _124236) ^ [_482754, _482756] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _482754, _482756)), 10140 ^ _124236 : [(10147 ^ _124236) ^ [] : [_482754 = _482756], (10141 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _482754, _482756), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _482756, _482754))]]], (10151 ^ _124236) ^ [_483167, _483169] : [10158 ^ _124236 : [(10159 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483167, _483169))], (10161 ^ _124236) ^ [] : [_483167 = _483169]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483167, _483169), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483169, _483167))], (10163 ^ _124236) ^ [_483503, _483505] : [10170 ^ _124236 : [(10171 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483503, _483505))], (10173 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483505, _483503)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483503, _483505), -(_483503 = _483505)], (10175 ^ _124236) ^ [_483889, _483891] : [-(_483889 = _483891), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483889, _483891), 10182 ^ _124236 : [(10183 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483889, _483891))], (10185 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483891, _483889)]]], (10187 ^ _124236) ^ [_484273, _484275] : [_484273 = _484275, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484273, _484275))], (10193 ^ _124236) ^ [_484485, _484487] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484485, _484487), 10196 ^ _124236 : [(10197 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484487, _484485), -(_484487 = _484485)], (10203 ^ _124236) ^ [] : [_484487 = _484485, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484487, _484485))]]], (10209 ^ _124236) ^ [_484950, _484952] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484950, _484952), 10214 ^ _124236 : [(10215 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484950, _484952))], (10217 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484952, _484950)]], -(_484950 = _484952)], (10221 ^ _124236) ^ [_485332, _485334] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485332, _485334), -(_485332 = _485334), 10228 ^ _124236 : [(10229 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485332, _485334))], (10231 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485334, _485332)]]], (10233 ^ _124236) ^ [_485730, _485732, _485734] : [_485730 = _485732, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485732, _485734), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485730, _485734))], (10243 ^ _124236) ^ [_486057, _486059, _486061] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486057, _486059), _486059 = _486061, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486057, _486061))], (10253 ^ _124236) ^ [_486370, _486372] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486370, _486372), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486372, _486370), -(_486370 = _486372)], (10263 ^ _124236) ^ [_486673, _486675] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486673, _486675), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486675, _486673), -(_486673 = _486675)], (10273 ^ _124236) ^ [_486990, _486992, _486994] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486990, _486992), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486992, _486994), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486990, _486994))], (10283 ^ _124236) ^ [_487319, _487321, _487323] : [_487319 = _487321, 10294 ^ _124236 : [(10295 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487319, _487323))], (10297 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487323, _487319)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487321, _487323), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487323, _487321))], (10299 ^ _124236) ^ [_487824, _487826, _487828] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487824, _487826), 10310 ^ _124236 : [(10311 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487824, _487828))], (10313 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487828, _487824)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487826, _487828), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487828, _487826))], (10315 ^ _124236) ^ [_488317, _488319] : [_488317 = _488319, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488317, _488319), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488319, _488317))], (10325 ^ _124236) ^ [_488624, _488626] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488624, _488626), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488626, _488624)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488626, _488624), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488624, _488626))], (10339 ^ _124236) ^ [_489029, _489031] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489029, _489031)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489029, _489031), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489031, _489029))], (10349 ^ _124236) ^ [_489337, _489339] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489337, _489339), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489339, _489337)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489339, _489337), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489337, _489339))], (10363 ^ _124236) ^ [_489742, _489744] : [_489742 = _489744, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489742, _489744), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489744, _489742))], (10373 ^ _124236) ^ [_490049, _490051] : [_490051 = _490049, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490049, _490051), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490051, _490049))], (10383 ^ _124236) ^ [_490370, _490372, _490374] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490370, _490372), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490372, _490370)), _490372 = _490374, 10394 ^ _124236 : [(10395 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490370, _490374))], (10397 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490374, _490370)]]], (10399 ^ _124236) ^ [_490877, _490879, _490881] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490877, _490879), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490879, _490877)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490879, _490881), 10410 ^ _124236 : [(10411 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490877, _490881))], (10413 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490881, _490877)]]], (10415 ^ _124236) ^ [_491372, _491374] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491372, _491374), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491374, _491372)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491374, _491372), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491372, _491374))], (10429 ^ _124236) ^ [_491791, _491793, _491795] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491791, _491793), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491793, _491791)), 10444 ^ _124236 : [(10445 ^ _124236) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491791, _491795))], (10447 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491795, _491791)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491793, _491795), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491795, _491793))], (10449 ^ _124236) ^ [_492384, _492386] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492384, _492386), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492386, _492384)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492386, _492384), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492384, _492386))], (10463 ^ _124236) ^ [_492760] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492760, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10465 ^ _124236) ^ [_492839] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _492839))], (10467 ^ _124236) ^ [_492947, _492949] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _492947), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492949, _492947), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _492949))], (10477 ^ _124236) ^ [_493266, _493268, _493270] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _493266), _493268), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _493270), _493268)), -(_493268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _493266, _493270))], (10487 ^ _124236) ^ [_493620, _493622, _493624] : [-(_493620 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10490 ^ _124236 : [(10491 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _493622), _493620), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _493624), _493620)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _493622, _493624))], (10497 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _493622, _493624), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _493622), _493620), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _493624), _493620)))]]], (10503 ^ _124236) ^ [_494155, _494157, _494159] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _494155), _494157), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _494159), _494157)), -(_494157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494155, _494159))], (10513 ^ _124236) ^ [_494481] : [class_RealVector_Oreal__normed__algebra(_494481), 10517 ^ _124236 : [(10518 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10516 ^ [_494481]))], (10520 ^ _124236) ^ [_494810, _494812] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_494481, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_494481), _494812), _494810)), 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(_494481, _494812)), c_RealVector_Onorm__class_Onorm(_494481, _494810))), 10516 ^ [_494481])))]]], (10522 ^ _124236) ^ [_494963, _494965] : [class_RealVector_Oreal__normed__algebra(_494963), 10526 ^ _124236 : [(10527 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10525 ^ [_494963, _494965]))], (10529 ^ _124236) ^ [_495262] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_494963, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_494963), _494965), _495262)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_494963, _495262)), 10525 ^ [_494963, _494965])))]]], (10531 ^ _124236) ^ [_495408, _495410] : [class_RealVector_Oreal__normed__algebra(_495408), 10535 ^ _124236 : [(10536 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10534 ^ [_495408, _495410]))], (10538 ^ _124236) ^ [_495707] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_495408, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_495408), _495707), _495410)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_495408, _495707)), 10534 ^ [_495408, _495410])))]]], (10540 ^ _124236) ^ [_495867, _495869, _495871] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _495867), 10544 ^ _124236 : [(10545 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10543 ^ [_495867, _495869, _495871]))], (10547 ^ _124236) ^ [_496251] : [-(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, _495871), _496251), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _495871), _495869))), _495867)), 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, _496251, _495869))), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _496251, _495869)), 10543 ^ [_495867, _495869, _495871])]]], (10557 ^ _124236) ^ [_496693, _496695] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _496693, _496695), -(c_Nat__Transfer_Otsub(_496695, _496693) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _496695, _496693))], (10563 ^ _124236) ^ [_496871, _496873] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _496871, _496873)), -(c_Nat__Transfer_Otsub(_496873, _496871) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10569 ^ _124236) ^ [_497094, _497096] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _497094), _497096), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _497096, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _497094), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_497096) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _497094, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10579 ^ _124236) ^ [_497400] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _497400)))], (10581 ^ _124236) ^ [_497496, _497498] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _497496), _497498)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _497496)), _497498))], (10583 ^ _124236) ^ [_497608, _497610] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _497608)), _497610) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _497608), _497610)))], (10585 ^ _124236) ^ [_497750] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _497750), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_497750 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10591 ^ _124236) ^ [_497914] : [_497914 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _497914), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10597 ^ _124236) ^ [_498099] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_498099))))], (10599 ^ _124236) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10601 ^ _124236) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10603 ^ _124236) ^ [_498347, _498349] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _498347), c_RealDef_Oreal(tc_Nat_Onat, _498349)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _498347, _498349))], (10609 ^ _124236) ^ [_498525, _498527] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _498525, _498527), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _498525), c_RealDef_Oreal(tc_Nat_Onat, _498527)))], (10615 ^ _124236) ^ [_498738, _498740] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _498738, _498740)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _498738), c_RealDef_Oreal(tc_Nat_Onat, _498740)))], (10617 ^ _124236) ^ [_498835] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _498835)) = _498835)], (10619 ^ _124236) ^ [_498976, _498978] : [c_RealDef_Oreal(tc_Nat_Onat, _498976) = c_RealDef_Oreal(tc_Nat_Onat, _498978), -(_498976 = _498978)], (10625 ^ _124236) ^ [_499150, _499152] : [_499150 = _499152, -(c_RealDef_Oreal(tc_Nat_Onat, _499150) = c_RealDef_Oreal(tc_Nat_Onat, _499152))], (10631 ^ _124236) ^ [_499403, _499405] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _499403), c_RealDef_Oreal(tc_Nat_Onat, _499405)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _499403, _499405))], (10637 ^ _124236) ^ [_499581, _499583] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _499581, _499583), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _499581), c_RealDef_Oreal(tc_Nat_Onat, _499583)))], (10643 ^ _124236) ^ [_499780] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _499780, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_499780))))], (10645 ^ _124236) ^ [_499864] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _499864)) = _499864)], (10647 ^ _124236) ^ [_499961, _499963] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _499961), _499963)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _499961)), c_RealDef_Oreal(tc_Nat_Onat, _499963)))], (10649 ^ _124236) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10651 ^ _124236) ^ [_500159] : [c_RealDef_Oreal(tc_Nat_Onat, _500159) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_500159 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10657 ^ _124236) ^ [_500321] : [_500321 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _500321) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10663 ^ _124236) ^ [_500503] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _500503), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10665 ^ _124236) ^ [_500614, _500616] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _500614, c_RealDef_Oreal(tc_Nat_Onat, _500616)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_500614), _500616))], (10671 ^ _124236) ^ [_500838, _500840] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _500838), _500840), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _500838, c_RComplete_Onatfloor(_500840)))], (10677 ^ _124236) ^ [_501048] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _501048), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_501048)), _501048))], (10683 ^ _124236) ^ [_501266, _501268] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _501266, _501268), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _501268, _501266)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _501268), c_RealDef_Oreal(tc_Nat_Onat, _501266)))], (10689 ^ _124236) ^ [_501483] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_501483)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _501483), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10691 ^ _124236) ^ [_501602, _501604] : [_501602 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_501602)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _501602), _501604)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_501602)), _501604))], (10697 ^ _124236) ^ [_501869] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _501869)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _501869))], (10703 ^ _124236) ^ [_502035] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _502035), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _502035)))], (10709 ^ _124236) ^ [_502280, _502282] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _502280, _502282), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _502280), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _502282)))], (10715 ^ _124236) ^ [_502466, _502468] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _502466), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _502468)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _502466, _502468))], (10721 ^ _124236) ^ [_502731, _502733] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _502731, _502733), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _502731), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _502733), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10727 ^ _124236) ^ [_502917, _502919] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _502917), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _502919), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _502917, _502919))], (10733 ^ _124236) ^ [_503153, _503155] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _503153), 10736 ^ _124236 : [(10737 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _503155, c_RComplete_Onatfloor(_503153)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _503155), _503153))], (10743 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _503155), _503153), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _503155, c_RComplete_Onatfloor(_503153)))]]], (10749 ^ _124236) ^ [_503636, _503638] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _503636), 10752 ^ _124236 : [(10753 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_503636), _503638), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _503636, c_RealDef_Oreal(tc_Nat_Onat, _503638)))], (10759 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _503636, c_RealDef_Oreal(tc_Nat_Onat, _503638)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_503636), _503638))]]], (10765 ^ _124236) ^ [_504090] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _504090, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_504090)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10767 ^ _124236) ^ [_504207, _504209] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _504207), _504209), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _504209, c_RealDef_Oreal(tc_Nat_Onat, _504207))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_504209), _504207))], (10773 ^ _124236) ^ [_504426] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _504426, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_504426))))], (10775 ^ _124236) ^ [_504543, _504545] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _504543), _504545), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _504545, c_RealDef_Oreal(tc_Nat_Onat, _504543))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_504545), _504543))], (10781 ^ _124236) ^ [_504791, _504793] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _504791), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _504793), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_504791, _504793)))], (10791 ^ _124236) ^ [_505102, _505104] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _505102), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _505102, c_RealDef_Oreal(tc_Nat_Onat, _505104)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_505102), _505104))], (10801 ^ _124236) ^ [_505417, _505419] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _505417, _505419), -(c_Nat__Transfer_Otsub(_505419, _505417) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _505419, _505417))], (10807 ^ _124236) ^ [_505643, _505645] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _505643), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _505643, c_RealDef_Oreal(tc_Nat_Onat, _505645))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_505643), _505645))], (10813 ^ _124236) ^ [_505885, _505887] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_505885), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _505887), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _505885, c_RealDef_Oreal(tc_Nat_Onat, _505887)))], (10819 ^ _124236) ^ [_506117, _506119] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _506117), _506119), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _506119, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _506117), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_506119) = _506117)], (10829 ^ _124236) ^ [_506444, _506446] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _506444), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _506444, c_RealDef_Oreal(tc_Nat_Onat, _506446))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_506444), _506446))], (10835 ^ _124236) ^ [_506686, _506688] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _506686), -(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, _506688)), _506686), 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, _506686, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _506688)))], (10841 ^ _124236) ^ [_506946, _506948] : [class_RealVector_Oreal__normed__vector(_506946), 10844 ^ _124236 : [(10857 ^ _124236) ^ [] : [10859 ^ _124236 : [(10860 ^ _124236) ^ [_507682] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_506946, hAPP(_506948, 10858 ^ [_506946, _506948, _507682])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_507682)))]], 10862 ^ _124236 : [(10863 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10861 ^ [_506946, _506948]))], (10865 ^ _124236) ^ [_507903] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_506946, hAPP(_506948, _507903)), 10861 ^ [_506946, _506948]))]]], (10845 ^ _124236) ^ [] : [10854 ^ _124236 : [(10855 ^ _124236) ^ [_507503] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_506946, hAPP(_506948, _507503)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10853 ^ [_506946, _506948]))))]], 10846 ^ _124236 : [(10847 ^ _124236) ^ [_507185] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _507185), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_506946, hAPP(_506948, 10850 ^ [_506946, _506948, _507185])), _507185)]]]]], (10867 ^ _124236) ^ [_508043, _508045] : [class_RealVector_Oreal__normed__vector(_508043), 10870 ^ _124236 : [(10883 ^ _124236) ^ [] : [10885 ^ _124236 : [(10886 ^ _124236) ^ [_508779] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_508043, hAPP(_508045, 10884 ^ [_508043, _508045, _508779])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_508779)))]], 10888 ^ _124236 : [(10889 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10887 ^ [_508043, _508045]))], (10891 ^ _124236) ^ [_509000] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_508043, hAPP(_508045, _509000)), 10887 ^ [_508043, _508045]))]]], (10871 ^ _124236) ^ [] : [10880 ^ _124236 : [(10881 ^ _124236) ^ [_508600] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_508043, hAPP(_508045, _508600)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10879 ^ [_508043, _508045]))))]], 10872 ^ _124236 : [(10873 ^ _124236) ^ [_508282] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _508282), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_508043, hAPP(_508045, 10876 ^ [_508043, _508045, _508282])), _508282)]]]]], (10893 ^ _124236) ^ [_509126] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _509126), 10897 ^ _124236 : [(10898 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 10896 ^ [_509126], c_Groups_Oone__class_Oone(tc_Nat_Onat))), _509126))], (10900 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _509126, c_RealDef_Oreal(tc_Nat_Onat, 10896 ^ [_509126])))]]], (10902 ^ _124236) ^ [_509503, _509505] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _509503), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _509505), 10910 ^ _124236 : [(10911 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 10909 ^ [_509503, _509505])), _509503), _509505))], (10913 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _509505, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10909 ^ [_509503, _509505]))), _509503)))]]], (10915 ^ _124236) ^ [_510045, _510047, _510049, _510051] : [class_RealVector_Oreal__normed__vector(_510045), class_Orderings_Oord(_510047), 10925 ^ _124236 : [(10926 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_510047, _510049, 10924 ^ [_510045, _510047, _510049, _510051]))], (10928 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_510045, c_Groups_Ominus__class_Ominus(_510045, hAPP(_510051, _510049), hAPP(_510051, 10924 ^ [_510045, _510047, _510049, _510051]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]], 10929 ^ _124236 : [(10930 ^ _124236) ^ [_510603] : [c_Orderings_Oord__class_Oless__eq(_510047, _510049, _510603), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_510045, hAPP(_510051, _510603)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_510045, hAPP(_510051, _510049)))))]]], (10937 ^ _124236) ^ [_510965, _510967] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10935 ^ [_510965, _510967]))], (10939 ^ _124236) ^ [_511048, _511050, _511052] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _511048), _511050), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _511052), _511048)), 10935 ^ [_511050, _511052]))], (10945 ^ _124236) ^ [_511322, _511324, _511326] : [class_Groups_Oab__group__add(_511322), -(c_Groups_Ominus__class_Ominus(_511322, c_Groups_Ouminus__class_Ouminus(_511322, _511324), c_Groups_Ouminus__class_Ouminus(_511322, _511326)) = c_Groups_Ouminus__class_Ouminus(_511322, c_Groups_Ominus__class_Ominus(_511322, _511324, _511326)))], (10951 ^ _124236) ^ [_511570, _511572] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _511570), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _511572), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _511572), _511570), _511572) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _511572), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _511570, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (10961 ^ _124236) ^ [_511941, _511943, _511945, _511947] : [class_Divides_Osemiring__div(_511941), -(_511943 = c_Groups_Ozero__class_Ozero(_511941)), -(c_Divides_Odiv__class_Odiv(_511941, c_Groups_Oplus__class_Oplus(_511941, _511945, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511941), _511947), _511943)), _511943) = c_Groups_Oplus__class_Oplus(_511941, _511947, c_Divides_Odiv__class_Odiv(_511941, _511945, _511943)))], (10971 ^ _124236) ^ [_512341, _512343, _512345, _512347] : [class_Divides_Osemiring__div(_512341), -(_512343 = c_Groups_Ozero__class_Ozero(_512341)), -(c_Divides_Odiv__class_Odiv(_512341, c_Groups_Oplus__class_Oplus(_512341, _512345, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512341), _512343), _512347)), _512343) = c_Groups_Oplus__class_Oplus(_512341, _512347, c_Divides_Odiv__class_Odiv(_512341, _512345, _512343)))], (10981 ^ _124236) ^ [_512727, _512729, _512731] : [class_Divides_Osemiring__div(_512727), -(_512729 = c_Groups_Ozero__class_Ozero(_512727)), -(c_Divides_Odiv__class_Odiv(_512727, c_Groups_Oplus__class_Oplus(_512727, _512731, _512729), _512729) = c_Groups_Oplus__class_Oplus(_512727, c_Divides_Odiv__class_Odiv(_512727, _512731, _512729), c_Groups_Oone__class_Oone(_512727)))], (10991 ^ _124236) ^ [_513091, _513093, _513095] : [class_Divides_Osemiring__div(_513091), -(_513093 = c_Groups_Ozero__class_Ozero(_513091)), -(c_Divides_Odiv__class_Odiv(_513091, c_Groups_Oplus__class_Oplus(_513091, _513093, _513095), _513093) = c_Groups_Oplus__class_Oplus(_513091, c_Divides_Odiv__class_Odiv(_513091, _513095, _513093), c_Groups_Oone__class_Oone(_513091)))], (11001 ^ _124236) ^ [_513469, _513471, _513473, _513475] : [class_Divides_Osemiring__div(_513469), -(_513471 = c_Groups_Ozero__class_Ozero(_513469)), c_Rings_Odvd__class_Odvd(_513469, _513471, _513473), 11012 ^ _124236 : [(11013 ^ _124236) ^ [] : [c_Divides_Odiv__class_Odiv(_513469, _513473, _513471) = _513475, -(_513473 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513469), _513475), _513471))], (11019 ^ _124236) ^ [] : [_513473 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513469), _513475), _513471), -(c_Divides_Odiv__class_Odiv(_513469, _513473, _513471) = _513475)]]], (11025 ^ _124236) ^ [_514240, _514242, _514244, _514246, _514248] : [class_Divides_Osemiring__div(_514240), -(_514242 = c_Groups_Ozero__class_Ozero(_514240)), -(_514244 = c_Groups_Ozero__class_Ozero(_514240)), c_Rings_Odvd__class_Odvd(_514240, _514242, _514246), c_Rings_Odvd__class_Odvd(_514240, _514244, _514248), 11044 ^ _124236 : [(11045 ^ _124236) ^ [] : [c_Divides_Odiv__class_Odiv(_514240, _514246, _514242) = c_Divides_Odiv__class_Odiv(_514240, _514248, _514244), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514240), _514246), _514244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514240), _514242), _514248))], (11051 ^ _124236) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514240), _514246), _514244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514240), _514242), _514248), -(c_Divides_Odiv__class_Odiv(_514240, _514246, _514242) = c_Divides_Odiv__class_Odiv(_514240, _514248, _514244))]]], (11057 ^ _124236) ^ [_515254, _515256, _515258] : [class_Divides_Oring__div(_515254), c_Rings_Odvd__class_Odvd(_515254, _515256, _515258), -(c_Divides_Odiv__class_Odiv(_515254, c_Groups_Ouminus__class_Ouminus(_515254, _515258), _515256) = c_Groups_Ouminus__class_Ouminus(_515254, c_Divides_Odiv__class_Odiv(_515254, _515258, _515256)))], (11067 ^ _124236) ^ [_515605, _515607, _515609] : [class_Divides_Oring__div(_515605), c_Rings_Odvd__class_Odvd(_515605, _515607, _515609), -(c_Divides_Odiv__class_Odiv(_515605, _515609, c_Groups_Ouminus__class_Ouminus(_515605, _515607)) = c_Groups_Ouminus__class_Ouminus(_515605, c_Divides_Odiv__class_Odiv(_515605, _515609, _515607)))], (11077 ^ _124236) ^ [_515970, _515972, _515974, _515976] : [class_Divides_Osemiring__div(_515970), c_Rings_Odvd__class_Odvd(_515970, _515972, _515974), c_Rings_Odvd__class_Odvd(_515970, _515972, _515976), -(c_Divides_Odiv__class_Odiv(_515970, c_Groups_Oplus__class_Oplus(_515970, _515974, _515976), _515972) = c_Groups_Oplus__class_Oplus(_515970, c_Divides_Odiv__class_Odiv(_515970, _515974, _515972), c_Divides_Odiv__class_Odiv(_515970, _515976, _515972)))], (11091 ^ _124236) ^ [_516456, _516458, _516460, _516462] : [class_Divides_Osemiring__div(_516456), c_Rings_Odvd__class_Odvd(_516456, _516458, _516460), c_Rings_Odvd__class_Odvd(_516456, _516458, _516462), 11102 ^ _124236 : [(11103 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_516456, c_Divides_Odiv__class_Odiv(_516456, _516460, _516458), c_Divides_Odiv__class_Odiv(_516456, _516462, _516458)), -(c_Rings_Odvd__class_Odvd(_516456, _516460, _516462))], (11109 ^ _124236) ^ [] : [c_Rings_Odvd__class_Odvd(_516456, _516460, _516462), -(c_Rings_Odvd__class_Odvd(_516456, c_Divides_Odiv__class_Odiv(_516456, _516460, _516458), c_Divides_Odiv__class_Odiv(_516456, _516462, _516458)))]]], (11115 ^ _124236) ^ [_517216, _517218, _517220, _517222, _517224] : [class_Divides_Osemiring__div(_517216), c_Rings_Odvd__class_Odvd(_517216, _517218, _517220), c_Rings_Odvd__class_Odvd(_517216, _517222, _517224), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517216), c_Divides_Odiv__class_Odiv(_517216, _517220, _517218)), c_Divides_Odiv__class_Odiv(_517216, _517224, _517222)) = c_Divides_Odiv__class_Odiv(_517216, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517216), _517220), _517224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517216), _517218), _517222)))], (11129 ^ _124236) ^ [_517748, _517750, _517752, _517754] : [class_Divides_Osemiring__div(_517748), c_Rings_Odvd__class_Odvd(_517748, _517750, _517752), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517748), c_Divides_Odiv__class_Odiv(_517748, _517752, _517750)), _517754) = c_Divides_Odiv__class_Odiv(_517748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517748), _517752), _517754), _517750))], (11139 ^ _124236) ^ [_518129, _518131, _518133] : [class_Divides_Osemiring__div(_518129), c_Rings_Odvd__class_Odvd(_518129, _518131, _518133), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518129), c_Divides_Odiv__class_Odiv(_518129, _518133, _518131)), _518131) = _518133)], (11149 ^ _124236) ^ [_518490, _518492, _518494, _518496] : [class_Divides_Osemiring__div(_518490), c_Rings_Odvd__class_Odvd(_518490, _518492, _518494), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518490), _518496), c_Divides_Odiv__class_Odiv(_518490, _518494, _518492)) = c_Divides_Odiv__class_Odiv(_518490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518490), _518496), _518494), _518492))], (11159 ^ _124236) ^ [_518857, _518859] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _518857, _518859), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _518857), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _518859, _518857)) = _518859)], (11165 ^ _124236) ^ [_519103, _519105, _519107] : [class_Divides_Osemiring__div(_519103), c_Rings_Odvd__class_Odvd(_519103, _519105, _519107), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519103), _519105), c_Divides_Odiv__class_Odiv(_519103, _519107, _519105)) = _519107)], (11175 ^ _124236) ^ [_519464, _519466, _519468, _519470] : [class_Divides_Osemiring__div(_519464), c_Rings_Odvd__class_Odvd(_519464, _519466, _519468), -(hAPP(hAPP(c_Power_Opower__class_Opower(_519464), c_Divides_Odiv__class_Odiv(_519464, _519468, _519466)), _519470) = c_Divides_Odiv__class_Odiv(_519464, hAPP(hAPP(c_Power_Opower__class_Opower(_519464), _519468), _519470), hAPP(hAPP(c_Power_Opower__class_Opower(_519464), _519466), _519470)))], (11185 ^ _124236) ^ [_519876, _519878] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _519876, _519878) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_519878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11194 ^ _124236 : [(11195 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _519876))], (11197 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _519876, _519878))]], 11198 ^ _124236 : [(11199 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _519876, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11201 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _519878, _519876))]]], (11203 ^ _124236) ^ [_520384, _520386] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _520384, _520386) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11204 ^ _124236 : [(11205 ^ _124236) ^ [] : [_520386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (11207 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _520384), c_Orderings_Oord__class_Oless(tc_Int_Oint, _520384, _520386)], (11213 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _520384, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _520386, _520384)]]], (11221 ^ _124236) ^ [_520937, _520939] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _520937), 11224 ^ _124236 : [(11225 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _520939, _520937)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _520939))], (11231 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _520939), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _520939, _520937)))]]], (11237 ^ _124236) ^ [_521417, _521419] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _521417), 11240 ^ _124236 : [(11241 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _521419, _521417)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _521417, _521419))], (11247 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _521417, _521419), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _521419, _521417)))]]], (11253 ^ _124236) ^ [_521897, _521899] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _521897), 11256 ^ _124236 : [(11257 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _521897, _521899)), 11260 ^ _124236 : [(11261 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _521899, _521897))], (11263 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _521899))]]], (11265 ^ _124236) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _521897, _521899))), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _521899, _521897), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _521899)]]], (11275 ^ _124236) ^ [_522552, _522554, _522556] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _522552), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _522554), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _522554, _522556), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _522552, _522556), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _522552, _522554)))], (11289 ^ _124236) ^ [_522978, _522980] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _522978), c_Orderings_Oord__class_Oless(tc_Int_Oint, _522980, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _522978, _522980), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11299 ^ _124236) ^ [_523291, _523293] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _523291), c_Orderings_Oord__class_Oless(tc_Int_Oint, _523291, _523293), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _523291, _523293) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11309 ^ _124236) ^ [_523602, _523604] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _523602, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11312 ^ _124236 : [(11313 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _523604, _523602)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _523604, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11319 ^ _124236) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _523604, 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), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _523604, _523602)))]]], (11325 ^ _124236) ^ [_524082, _524084] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _524082, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _524084), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _524082, _524084), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11335 ^ _124236) ^ [_524409, _524411, _524413] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _524409, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _524411), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _524411, _524413), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _524409, _524411), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _524409, _524413)))], (11349 ^ _124236) ^ [_524835, _524837] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _524835, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _524837, _524835), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _524835, _524837) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11359 ^ _124236) ^ [_525160, _525162, _525164] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _525160, _525162), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _525164), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _525160, _525164), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _525162, _525164)))], (11369 ^ _124236) ^ [_525505, _525507, _525509] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _525505, _525507), c_Orderings_Oord__class_Oless(tc_Int_Oint, _525509, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _525507, _525509), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _525505, _525509)))], (11379 ^ _124236) ^ [_525836, _525838] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _525836), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _525838), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _525836, _525838), _525836))], (11389 ^ _124236) ^ [_526135] : [class_Groups_Ocancel__comm__monoid__add(_526135), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_526135)))], (11395 ^ _124236) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11397 ^ _124236) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11399 ^ _124236) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11401 ^ _124236) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11403 ^ _124236) ^ [_526551, _526553] : [class_Orderings_Opreorder(_526551), -(class_Orderings_Opreorder(tc_fun(_526553, _526551)))], (11409 ^ _124236) ^ [_526763, _526765] : [class_Orderings_Oorder(_526763), -(class_Orderings_Oorder(tc_fun(_526765, _526763)))], (11415 ^ _124236) ^ [_526975, _526977] : [class_Orderings_Oord(_526975), -(class_Orderings_Oord(tc_fun(_526977, _526975)))], (11421 ^ _124236) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11423 ^ _124236) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11425 ^ _124236) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11427 ^ _124236) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11429 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11431 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11433 ^ _124236) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11435 ^ _124236) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11437 ^ _124236) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11439 ^ _124236) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11441 ^ _124236) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11443 ^ _124236) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11445 ^ _124236) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11447 ^ _124236) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11449 ^ _124236) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11451 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11453 ^ _124236) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11455 ^ _124236) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11457 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11459 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11461 ^ _124236) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11463 ^ _124236) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11465 ^ _124236) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11467 ^ _124236) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (11469 ^ _124236) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11471 ^ _124236) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11473 ^ _124236) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11475 ^ _124236) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11477 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11479 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (11481 ^ _124236) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (11483 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11485 ^ _124236) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11487 ^ _124236) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11489 ^ _124236) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (11491 ^ _124236) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (11493 ^ _124236) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (11495 ^ _124236) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11497 ^ _124236) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11499 ^ _124236) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (11501 ^ _124236) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11503 ^ _124236) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11505 ^ _124236) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (11507 ^ _124236) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11509 ^ _124236) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11511 ^ _124236) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (11513 ^ _124236) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (11515 ^ _124236) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (11517 ^ _124236) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (11519 ^ _124236) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11521 ^ _124236) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11523 ^ _124236) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11525 ^ _124236) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11527 ^ _124236) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11529 ^ _124236) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11531 ^ _124236) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (11533 ^ _124236) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11535 ^ _124236) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11537 ^ _124236) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11539 ^ _124236) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11541 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11543 ^ _124236) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11545 ^ _124236) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11547 ^ _124236) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11549 ^ _124236) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11551 ^ _124236) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (11553 ^ _124236) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11555 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11557 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11559 ^ _124236) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11561 ^ _124236) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11563 ^ _124236) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11565 ^ _124236) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (11567 ^ _124236) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11569 ^ _124236) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11571 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11573 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (11575 ^ _124236) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (11577 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (11579 ^ _124236) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (11581 ^ _124236) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (11583 ^ _124236) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11585 ^ _124236) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (11587 ^ _124236) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11589 ^ _124236) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (11591 ^ _124236) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (11593 ^ _124236) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11595 ^ _124236) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (11597 ^ _124236) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (11599 ^ _124236) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (11601 ^ _124236) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11603 ^ _124236) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (11605 ^ _124236) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (11607 ^ _124236) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (11609 ^ _124236) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11611 ^ _124236) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (11613 ^ _124236) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (11615 ^ _124236) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (11617 ^ _124236) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (11619 ^ _124236) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (11621 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (11623 ^ _124236) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (11625 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (11627 ^ _124236) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (11629 ^ _124236) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (11631 ^ _124236) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (11633 ^ _124236) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (11635 ^ _124236) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (11637 ^ _124236) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (11639 ^ _124236) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (11641 ^ _124236) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11643 ^ _124236) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11645 ^ _124236) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (11647 ^ _124236) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (11649 ^ _124236) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11651 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (11653 ^ _124236) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11655 ^ _124236) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11657 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (11659 ^ _124236) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (11661 ^ _124236) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (11663 ^ _124236) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11665 ^ _124236) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11667 ^ _124236) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (11669 ^ _124236) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (11671 ^ _124236) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11673 ^ _124236) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11675 ^ _124236) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (11677 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (11679 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (11681 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11683 ^ _124236) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11685 ^ _124236) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11687 ^ _124236) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (11689 ^ _124236) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11691 ^ _124236) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11693 ^ _124236) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11695 ^ _124236) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (11697 ^ _124236) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11699 ^ _124236) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11701 ^ _124236) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11703 ^ _124236) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (11705 ^ _124236) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (11707 ^ _124236) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (11709 ^ _124236) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (11711 ^ _124236) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11713 ^ _124236) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11715 ^ _124236) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11717 ^ _124236) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11719 ^ _124236) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11721 ^ _124236) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11723 ^ _124236) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11725 ^ _124236) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11727 ^ _124236) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11729 ^ _124236) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (11731 ^ _124236) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11733 ^ _124236) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11735 ^ _124236) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11737 ^ _124236) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11739 ^ _124236) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11741 ^ _124236) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11743 ^ _124236) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11745 ^ _124236) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11747 ^ _124236) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11749 ^ _124236) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11751 ^ _124236) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11753 ^ _124236) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11755 ^ _124236) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11757 ^ _124236) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11759 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11761 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (11763 ^ _124236) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11765 ^ _124236) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11767 ^ _124236) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11769 ^ _124236) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11771 ^ _124236) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11773 ^ _124236) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (11775 ^ _124236) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11777 ^ _124236) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11779 ^ _124236) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11781 ^ _124236) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (11783 ^ _124236) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (11785 ^ _124236) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (11787 ^ _124236) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11789 ^ _124236) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (11791 ^ _124236) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (11793 ^ _124236) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11795 ^ _124236) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11797 ^ _124236) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (11799 ^ _124236) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (11801 ^ _124236) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (11803 ^ _124236) ^ [_537296] : [class_Rings_Oidom(_537296), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_537296)))], (11809 ^ _124236) ^ [_537486] : [class_Rings_Olinordered__idom(_537486), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_537486)))], (11815 ^ _124236) ^ [_537676] : [class_Rings_Olinordered__idom(_537676), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_537676)))], (11821 ^ _124236) ^ [_537866] : [class_Rings_Olinordered__idom(_537866), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_537866)))], (11827 ^ _124236) ^ [_538056] : [class_Rings_Olinordered__idom(_538056), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_538056)))], (11833 ^ _124236) ^ [_538246] : [class_Rings_Olinordered__idom(_538246), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_538246)))], (11839 ^ _124236) ^ [_538436] : [class_Rings_Olinordered__idom(_538436), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_538436)))], (11845 ^ _124236) ^ [_538626] : [class_Rings_Olinordered__idom(_538626), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_538626)))], (11851 ^ _124236) ^ [_538816] : [class_Rings_Olinordered__idom(_538816), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_538816)))], (11857 ^ _124236) ^ [_539006] : [class_Groups_Ocancel__comm__monoid__add(_539006), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_539006)))], (11863 ^ _124236) ^ [_539196] : [class_Rings_Oidom(_539196), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_539196)))], (11869 ^ _124236) ^ [_539386] : [class_Rings_Olinordered__idom(_539386), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_539386)))], (11875 ^ _124236) ^ [_539576] : [class_Rings_Olinordered__idom(_539576), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_539576)))], (11881 ^ _124236) ^ [_539766] : [class_Rings_Oidom(_539766), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_539766)))], (11887 ^ _124236) ^ [_539956] : [class_Rings_Olinordered__idom(_539956), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_539956)))], (11893 ^ _124236) ^ [_540146] : [class_Rings_Olinordered__idom(_540146), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_540146)))], (11899 ^ _124236) ^ [_540336] : [class_Rings_Olinordered__idom(_540336), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_540336)))], (11905 ^ _124236) ^ [_540526] : [class_Groups_Ocancel__comm__monoid__add(_540526), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_540526)))], (11911 ^ _124236) ^ [_540716] : [class_Rings_Olinordered__idom(_540716), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_540716)))], (11917 ^ _124236) ^ [_540906] : [class_Rings_Olinordered__idom(_540906), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_540906)))], (11923 ^ _124236) ^ [_541096] : [class_Rings_Ocomm__semiring__0(_541096), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_541096)))], (11929 ^ _124236) ^ [_541286] : [class_Rings_Ocomm__semiring__1(_541286), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_541286)))], (11935 ^ _124236) ^ [_541476] : [class_Groups_Ocomm__monoid__add(_541476), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_541476)))], (11941 ^ _124236) ^ [_541666] : [class_Rings_Olinordered__idom(_541666), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_541666)))], (11947 ^ _124236) ^ [_541856] : [class_Rings_Oidom(_541856), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_541856)))], (11953 ^ _124236) ^ [_542046] : [class_Groups_Ocomm__monoid__add(_542046), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_542046)))], (11959 ^ _124236) ^ [_542236] : [class_Rings_Olinordered__idom(_542236), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_542236)))], (11965 ^ _124236) ^ [_542426] : [class_Rings_Olinordered__idom(_542426), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_542426)))], (11971 ^ _124236) ^ [_542616] : [class_Rings_Ocomm__semiring__1(_542616), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_542616)))], (11977 ^ _124236) ^ [_542806] : [class_Rings_Ocomm__semiring__0(_542806), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_542806)))], (11983 ^ _124236) ^ [_542996] : [class_Fields_Ofield(_542996), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_542996)))], (11989 ^ _124236) ^ [_543186] : [class_Rings_Ocomm__semiring__0(_543186), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_543186)))], (11995 ^ _124236) ^ [_543376] : [class_Groups_Oab__group__add(_543376), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_543376)))], (12001 ^ _124236) ^ [_543566] : [class_Rings_Ocomm__semiring__1(_543566), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_543566)))], (12007 ^ _124236) ^ [_543756] : [class_Rings_Olinordered__idom(_543756), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_543756)))], (12013 ^ _124236) ^ [_543946] : [class_Rings_Olinordered__idom(_543946), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_543946)))], (12019 ^ _124236) ^ [_544136] : [class_Rings_Olinordered__idom(_544136), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_544136)))], (12025 ^ _124236) ^ [_544326] : [class_Rings_Ocomm__semiring__1(_544326), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_544326)))], (12031 ^ _124236) ^ [_544516] : [class_Rings_Ocomm__ring__1(_544516), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_544516)))], (12037 ^ _124236) ^ [_544706] : [class_Groups_Ocomm__monoid__add(_544706), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_544706)))], (12043 ^ _124236) ^ [_544896] : [class_Rings_Ocomm__semiring__0(_544896), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_544896)))], (12049 ^ _124236) ^ [_545086] : [class_Groups_Oab__group__add(_545086), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_545086)))], (12055 ^ _124236) ^ [_545276] : [class_Fields_Ofield(_545276), -(class_Divides_Oring__div(tc_Polynomial_Opoly(_545276)))], (12061 ^ _124236) ^ [_545466] : [class_Rings_Ocomm__semiring__0(_545466), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_545466)))], (12067 ^ _124236) ^ [_545656] : [class_Rings_Ocomm__ring(_545656), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_545656)))], (12073 ^ _124236) ^ [_545846] : [class_Rings_Olinordered__idom(_545846), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_545846)))], (12079 ^ _124236) ^ [_546036] : [class_Rings_Olinordered__idom(_546036), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_546036)))], (12085 ^ _124236) ^ [_546226] : [class_Rings_Ocomm__semiring__0(_546226), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_546226)))], (12091 ^ _124236) ^ [_546416] : [class_Rings_Olinordered__idom(_546416), -(class_Orderings_Oord(tc_Polynomial_Opoly(_546416)))], (12097 ^ _124236) ^ [_546606] : [class_Rings_Ocomm__ring__1(_546606), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_546606)))], (12103 ^ _124236) ^ [_546796] : [class_Rings_Ocomm__semiring__1(_546796), -(class_Power_Opower(tc_Polynomial_Opoly(_546796)))], (12109 ^ _124236) ^ [_546986] : [class_Groups_Ozero(_546986), -(class_Groups_Ozero(tc_Polynomial_Opoly(_546986)))], (12115 ^ _124236) ^ [_547176] : [class_Rings_Ocomm__ring(_547176), -(class_Rings_Oring(tc_Polynomial_Opoly(_547176)))], (12121 ^ _124236) ^ [_547366] : [class_Rings_Oidom(_547366), -(class_Rings_Oidom(tc_Polynomial_Opoly(_547366)))], (12127 ^ _124236) ^ [_547556] : [class_Rings_Ocomm__semiring__1(_547556), -(class_Groups_Oone(tc_Polynomial_Opoly(_547556)))], (12133 ^ _124236) ^ [_547746] : [class_Rings_Ocomm__semiring__1(_547746), -(class_Rings_Odvd(tc_Polynomial_Opoly(_547746)))], (12139 ^ _124236) ^ [_547950, _547952] : [hBOOL(c_fequal(_547950, _547952)), -(_547950 = _547952)], (12145 ^ _124236) ^ [_548166, _548168] : [_548166 = _548168, -(hBOOL(c_fequal(_548166, _548168)))], (12151 ^ _124236) ^ [] : [12153 ^ _124236 : [(12154 ^ _124236) ^ [_548439] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _548439, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12152 ^ [_548439])))], (12156 ^ _124236) ^ [_548491] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____)), 12152 ^ [_548491])))]], -(v_thesis____)]], input).
% 4.64/5.53  ncf('1',plain,[v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))],start(1057 ^ 0)).
% 4.64/5.53  ncf('1.1',plain,[-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), 1066 : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____], c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12152 ^ [1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____]])), 1066 : -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____)), 12152 ^ [1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____]]))))],extension(1061 ^ 1,bind([[_159011, _159013, _159240], [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____, 12152 ^ [1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____]]]]))).
% 4.64/5.53  ncf('1.1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____], c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12152 ^ [1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____]]))), -(v_thesis____)],extension(12151 ^ 4,bind([[_548439], [1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____]]]))).
% 4.64/5.53  ncf('1.1.1.1',plain,[v_thesis____],extension(12160 ^ 5)).
% 4.64/5.53  ncf('1.1.2',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____)), 12152 ^ [1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____]]))), -(v_thesis____)],extension(12151 ^ 4,bind([[_548491], [1064 ^ [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), v_c____]]]))).
% 4.64/5.53  ncf('1.1.2.1',plain,[v_thesis____],extension(12160 ^ 5)).
% 4.64/5.53  %-----------------------------------------------------
% 4.64/5.53  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------