TSTP Solution File: SWW263+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW263+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:50 EDT 2023

% Result   : Theorem 0.52s 1.40s
% Output   : Proof 0.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW263+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 22:49:54 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.52/1.40  
% 0.52/1.40  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.52/1.40  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/1.40  %-----------------------------------------------------
% 0.52/1.40  ncf(matrix, plain, [(11988 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (880 ^ _167881) ^ [_194929, _194931, _194933, _194935, _194937, _194939] : [-(c_Polynomial_Omonom(_194939, _194935, _194931) = c_Polynomial_Omonom(_194937, _194933, _194929)), _194939 = _194937, _194935 = _194933, _194931 = _194929], (894 ^ _167881) ^ [_195445, _195447, _195449, _195451, _195453, _195455] : [-(c_Polynomial_Opcompose(_195455, _195451, _195447) = c_Polynomial_Opcompose(_195453, _195449, _195445)), _195455 = _195453, _195451 = _195449, _195447 = _195445], (908 ^ _167881) ^ [_195961, _195963, _195965, _195967, _195969, _195971] : [-(c_Polynomial_Osynthetic__div(_195971, _195967, _195963) = c_Polynomial_Osynthetic__div(_195969, _195965, _195961)), _195971 = _195969, _195967 = _195965, _195963 = _195961], (922 ^ _167881) ^ [_196449, _196451, _196453, _196455] : [-(c_Rings_Oinverse__class_Oinverse(_196455, _196451) = c_Rings_Oinverse__class_Oinverse(_196453, _196449)), _196455 = _196453, _196451 = _196449], (932 ^ _167881) ^ [_196836, _196838, _196840, _196842, _196844, _196846] : [-(c_Power_Opower_Opower(_196846, _196842, _196838) = c_Power_Opower_Opower(_196844, _196840, _196836)), _196846 = _196844, _196842 = _196840, _196838 = _196836], (946 ^ _167881) ^ [_197324, _197326, _197328, _197330] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_197330, _197326) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_197328, _197324)), _197330 = _197328, _197326 = _197324], (956 ^ _167881) ^ [_197683, _197685, _197687, _197689] : [-(c_Nat__Transfer_Otsub(_197689, _197685) = c_Nat__Transfer_Otsub(_197687, _197683)), _197689 = _197687, _197685 = _197683], (966 ^ _167881) ^ [_198014, _198016] : [_198016 = _198014, -(c_RComplete_Onatfloor(_198016) = c_RComplete_Onatfloor(_198014))], (972 ^ _167881) ^ [_198232, _198234] : [_198234 = _198232, -(c_RComplete_Onatceiling(_198234) = c_RComplete_Onatceiling(_198232))], (978 ^ _167881) ^ [_198478, _198480, _198482, _198484] : [-(c_RealDef_Oreal(_198484, _198480) = c_RealDef_Oreal(_198482, _198478)), _198484 = _198482, _198480 = _198478], (988 ^ _167881) ^ [_198837, _198839, _198841, _198843] : [-(c_Polynomial_Opoly(_198843, _198839) = c_Polynomial_Opoly(_198841, _198837)), _198843 = _198841, _198839 = _198837], (998 ^ _167881) ^ [_199196, _199198, _199200, _199202] : [-(c_RealVector_Oof__real(_199202, _199198) = c_RealVector_Oof__real(_199200, _199196)), _199202 = _199200, _199198 = _199196], (1008 ^ _167881) ^ [_199555, _199557, _199559, _199561] : [-(c_Groups_Osgn__class_Osgn(_199561, _199557) = c_Groups_Osgn__class_Osgn(_199559, _199555)), _199561 = _199559, _199557 = _199555], (1018 ^ _167881) ^ [_199942, _199944, _199946, _199948, _199950, _199952] : [-(c_Polynomial_Oorder(_199952, _199948, _199944) = c_Polynomial_Oorder(_199950, _199946, _199942)), _199952 = _199950, _199948 = _199946, _199944 = _199942], (1032 ^ _167881) ^ [_200458, _200460, _200462, _200464, _200466, _200468] : [-(c_Polynomial_OpCons(_200468, _200464, _200460) = c_Polynomial_OpCons(_200466, _200462, _200458)), _200468 = _200466, _200464 = _200462, _200460 = _200458], (1046 ^ _167881) ^ [_200946, _200948, _200950, _200952] : [-(c_Groups_Ouminus__class_Ouminus(_200952, _200948) = c_Groups_Ouminus__class_Ouminus(_200950, _200946)), _200952 = _200950, _200948 = _200946], (1056 ^ _167881) ^ [_201333, _201335, _201337, _201339, _201341, _201343] : [-(c_Groups_Ominus__class_Ominus(_201343, _201339, _201335) = c_Groups_Ominus__class_Ominus(_201341, _201337, _201333)), _201343 = _201341, _201339 = _201337, _201335 = _201333], (1070 ^ _167881) ^ [_201849, _201851, _201853, _201855, _201857, _201859] : [-(c_Polynomial_Osmult(_201859, _201855, _201851) = c_Polynomial_Osmult(_201857, _201853, _201849)), _201859 = _201857, _201855 = _201853, _201851 = _201849], (1084 ^ _167881) ^ [_202337, _202339, _202341, _202343] : [-(c_Groups_Oabs__class_Oabs(_202343, _202339) = c_Groups_Oabs__class_Oabs(_202341, _202337)), _202343 = _202341, _202339 = _202337], (1094 ^ _167881) ^ [_202724, _202726, _202728, _202730, _202732, _202734] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_202734, _202730, _202726) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_202732, _202728, _202724)), _202734 = _202732, _202730 = _202728, _202726 = _202724], (1108 ^ _167881) ^ [_203184, _203186] : [_203186 = _203184, -(c_Groups_Ozero__class_Ozero(_203186) = c_Groups_Ozero__class_Ozero(_203184))], (1114 ^ _167881) ^ [_203430, _203432, _203434, _203436] : [-(tc_fun(_203436, _203432) = tc_fun(_203434, _203430)), _203436 = _203434, _203432 = _203430], (1124 ^ _167881) ^ [_203761, _203763] : [_203763 = _203761, -(tc_Polynomial_Opoly(_203763) = tc_Polynomial_Opoly(_203761))], (1130 ^ _167881) ^ [_204007, _204009, _204011, _204013] : [-(c_RealVector_Onorm__class_Onorm(_204013, _204009) = c_RealVector_Onorm__class_Onorm(_204011, _204007)), _204013 = _204011, _204009 = _204007], (1140 ^ _167881) ^ [_204394, _204396, _204398, _204400, _204402, _204404] : [-(c_Groups_Oplus__class_Oplus(_204404, _204400, _204396) = c_Groups_Oplus__class_Oplus(_204402, _204398, _204394)), _204404 = _204402, _204400 = _204398, _204396 = _204394], (1154 ^ _167881) ^ [_204854, _204856] : [_204856 = _204854, -(c_Groups_Otimes__class_Otimes(_204856) = c_Groups_Otimes__class_Otimes(_204854))], (1160 ^ _167881) ^ [_205100, _205102, _205104, _205106] : [-(hAPP(_205106, _205102) = hAPP(_205104, _205100)), _205106 = _205104, _205102 = _205100], (1170 ^ _167881) ^ [_205431, _205433] : [_205433 = _205431, -(c_Power_Opower__class_Opower(_205433) = c_Power_Opower__class_Opower(_205431))], (1176 ^ _167881) ^ [_205629, _205631] : [_205631 = _205629, -(c_Groups_Oone__class_Oone(_205631) = c_Groups_Oone__class_Oone(_205629))], (2 ^ _167881) ^ [_168025] : [-(_168025 = _168025)], (4 ^ _167881) ^ [_168132, _168134] : [_168134 = _168132, -(_168132 = _168134)], (10 ^ _167881) ^ [_168336, _168338, _168340] : [-(_168340 = _168336), _168340 = _168338, _168338 = _168336], (20 ^ _167881) ^ [_168705, _168707, _168709, _168711, _168713, _168715] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_168713, _168709, _168705)), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_168715, _168711, _168707), _168715 = _168713, _168711 = _168709, _168707 = _168705], (38 ^ _167881) ^ [_169286, _169288, _169290, _169292] : [-(c_Polynomial_Opos__poly(_169290, _169286)), c_Polynomial_Opos__poly(_169292, _169288), _169292 = _169290, _169288 = _169286], (52 ^ _167881) ^ [_169730, _169732, _169734, _169736] : [-(c_SEQ_Odecseq(_169734, _169730)), c_SEQ_Odecseq(_169736, _169732), _169736 = _169734, _169732 = _169730], (66 ^ _167881) ^ [_170146, _170148] : [-(class_Lattices_Oab__semigroup__idem__mult(_170146)), _170148 = _170146, class_Lattices_Oab__semigroup__idem__mult(_170148)], (76 ^ _167881) ^ [_170497, _170499, _170501, _170503, _170505, _170507] : [-(c_Orderings_Oord__class_Oless__eq(_170505, _170501, _170497)), c_Orderings_Oord__class_Oless__eq(_170507, _170503, _170499), _170507 = _170505, _170503 = _170501, _170499 = _170497], (94 ^ _167881) ^ [_171050, _171052] : [-(hBOOL(_171050)), _171052 = _171050, hBOOL(_171052)], (104 ^ _167881) ^ [_171401, _171403, _171405, _171407, _171409, _171411] : [-(c_Rings_Odvd__class_Odvd(_171409, _171405, _171401)), c_Rings_Odvd__class_Odvd(_171411, _171407, _171403), _171411 = _171409, _171407 = _171405, _171403 = _171401], (122 ^ _167881) ^ [_171954, _171956] : [-(class_Lattices_Oboolean__algebra(_171954)), _171956 = _171954, class_Lattices_Oboolean__algebra(_171956)], (132 ^ _167881) ^ [_172249, _172251] : [-(class_Fields_Olinordered__field__inverse__zero(_172249)), _172251 = _172249, class_Fields_Olinordered__field__inverse__zero(_172251)], (142 ^ _167881) ^ [_172544, _172546] : [-(class_Fields_Olinordered__field(_172544)), _172546 = _172544, class_Fields_Olinordered__field(_172546)], (152 ^ _167881) ^ [_172839, _172841] : [-(class_RealVector_Oreal__normed__div__algebra(_172839)), _172841 = _172839, class_RealVector_Oreal__normed__div__algebra(_172841)], (162 ^ _167881) ^ [_173134, _173136] : [-(class_Rings_Odivision__ring__inverse__zero(_173134)), _173136 = _173134, class_Rings_Odivision__ring__inverse__zero(_173136)], (172 ^ _167881) ^ [_173429, _173431] : [-(class_RealVector_Oreal__normed__algebra__1(_173429)), _173431 = _173429, class_RealVector_Oreal__normed__algebra__1(_173431)], (182 ^ _167881) ^ [_173724, _173726] : [-(class_RealVector_Oreal__normed__algebra(_173724)), _173726 = _173724, class_RealVector_Oreal__normed__algebra(_173726)], (192 ^ _167881) ^ [_174019, _174021] : [-(class_RealVector_Oreal__normed__vector(_174019)), _174021 = _174019, class_RealVector_Oreal__normed__vector(_174021)], (202 ^ _167881) ^ [_174314, _174316] : [-(class_RealVector_Oreal__div__algebra(_174314)), _174316 = _174314, class_RealVector_Oreal__div__algebra(_174316)], (212 ^ _167881) ^ [_174609, _174611] : [-(class_RealVector_Oreal__algebra__1(_174609)), _174611 = _174609, class_RealVector_Oreal__algebra__1(_174611)], (222 ^ _167881) ^ [_174904, _174906] : [-(class_Fields_Ofield__inverse__zero(_174904)), _174906 = _174904, class_Fields_Ofield__inverse__zero(_174906)], (232 ^ _167881) ^ [_175199, _175201] : [-(class_Rings_Odivision__ring(_175199)), _175201 = _175199, class_Rings_Odivision__ring(_175201)], (242 ^ _167881) ^ [_175494, _175496] : [-(class_Fields_Ofield(_175494)), _175496 = _175494, class_Fields_Ofield(_175496)], (252 ^ _167881) ^ [_175789, _175791] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_175789)), _175791 = _175789, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_175791)], (262 ^ _167881) ^ [_176084, _176086] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_176084)), _176086 = _176084, class_Groups_Oordered__cancel__ab__semigroup__add(_176086)], (272 ^ _167881) ^ [_176379, _176381] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_176379)), _176381 = _176379, class_Groups_Oordered__ab__semigroup__add__imp__le(_176381)], (282 ^ _167881) ^ [_176674, _176676] : [-(class_Rings_Olinordered__comm__semiring__strict(_176674)), _176676 = _176674, class_Rings_Olinordered__comm__semiring__strict(_176676)], (292 ^ _167881) ^ [_176969, _176971] : [-(class_Rings_Olinordered__semiring__1__strict(_176969)), _176971 = _176969, class_Rings_Olinordered__semiring__1__strict(_176971)], (302 ^ _167881) ^ [_177264, _177266] : [-(class_Rings_Olinordered__semiring__strict(_177264)), _177266 = _177264, class_Rings_Olinordered__semiring__strict(_177266)], (312 ^ _167881) ^ [_177559, _177561] : [-(class_Groups_Oordered__ab__semigroup__add(_177559)), _177561 = _177559, class_Groups_Oordered__ab__semigroup__add(_177561)], (322 ^ _167881) ^ [_177854, _177856] : [-(class_Groups_Oordered__ab__group__add__abs(_177854)), _177856 = _177854, class_Groups_Oordered__ab__group__add__abs(_177856)], (332 ^ _167881) ^ [_178149, _178151] : [-(class_Groups_Oordered__comm__monoid__add(_178149)), _178151 = _178149, class_Groups_Oordered__comm__monoid__add(_178151)], (342 ^ _167881) ^ [_178444, _178446] : [-(class_Groups_Olinordered__ab__group__add(_178444)), _178446 = _178444, class_Groups_Olinordered__ab__group__add(_178446)], (352 ^ _167881) ^ [_178739, _178741] : [-(class_Groups_Ocancel__ab__semigroup__add(_178739)), _178741 = _178739, class_Groups_Ocancel__ab__semigroup__add(_178741)], (362 ^ _167881) ^ [_179034, _179036] : [-(class_Rings_Oring__1__no__zero__divisors(_179034)), _179036 = _179034, class_Rings_Oring__1__no__zero__divisors(_179036)], (372 ^ _167881) ^ [_179329, _179331] : [-(class_Rings_Oordered__cancel__semiring(_179329)), _179331 = _179329, class_Rings_Oordered__cancel__semiring(_179331)], (382 ^ _167881) ^ [_179624, _179626] : [-(class_Rings_Olinordered__ring__strict(_179624)), _179626 = _179624, class_Rings_Olinordered__ring__strict(_179626)], (392 ^ _167881) ^ [_179919, _179921] : [-(class_Rings_Oring__no__zero__divisors(_179919)), _179921 = _179919, class_Rings_Oring__no__zero__divisors(_179921)], (402 ^ _167881) ^ [_180214, _180216] : [-(class_Rings_Oordered__comm__semiring(_180214)), _180216 = _180214, class_Rings_Oordered__comm__semiring(_180216)], (412 ^ _167881) ^ [_180509, _180511] : [-(class_Rings_Olinordered__semiring__1(_180509)), _180511 = _180509, class_Rings_Olinordered__semiring__1(_180511)], (422 ^ _167881) ^ [_180804, _180806] : [-(class_Groups_Oordered__ab__group__add(_180804)), _180806 = _180804, class_Groups_Oordered__ab__group__add(_180806)], (432 ^ _167881) ^ [_181099, _181101] : [-(class_Groups_Ocancel__comm__monoid__add(_181099)), _181101 = _181099, class_Groups_Ocancel__comm__monoid__add(_181101)], (442 ^ _167881) ^ [_181394, _181396] : [-(class_Groups_Ocancel__semigroup__add(_181394)), _181396 = _181394, class_Groups_Ocancel__semigroup__add(_181396)], (452 ^ _167881) ^ [_181689, _181691] : [-(class_Rings_Olinordered__semiring(_181689)), _181691 = _181689, class_Rings_Olinordered__semiring(_181691)], (462 ^ _167881) ^ [_181984, _181986] : [-(class_Rings_Olinordered__semidom(_181984)), _181986 = _181984, class_Rings_Olinordered__semidom(_181986)], (472 ^ _167881) ^ [_182279, _182281] : [-(class_Groups_Oab__semigroup__mult(_182279)), _182281 = _182279, class_Groups_Oab__semigroup__mult(_182281)], (482 ^ _167881) ^ [_182574, _182576] : [-(class_Groups_Ocomm__monoid__mult(_182574)), _182576 = _182574, class_Groups_Ocomm__monoid__mult(_182576)], (492 ^ _167881) ^ [_182869, _182871] : [-(class_Groups_Oab__semigroup__add(_182869)), _182871 = _182869, class_Groups_Oab__semigroup__add(_182871)], (502 ^ _167881) ^ [_183164, _183166] : [-(class_Rings_Oordered__semiring(_183164)), _183166 = _183164, class_Rings_Oordered__semiring(_183166)], (512 ^ _167881) ^ [_183459, _183461] : [-(class_Rings_Oordered__ring__abs(_183459)), _183461 = _183459, class_Rings_Oordered__ring__abs(_183461)], (522 ^ _167881) ^ [_183754, _183756] : [-(class_Rings_Ono__zero__divisors(_183754)), _183756 = _183754, class_Rings_Ono__zero__divisors(_183756)], (532 ^ _167881) ^ [_184049, _184051] : [-(class_Rings_Olinordered__ring(_184049)), _184051 = _184049, class_Rings_Olinordered__ring(_184051)], (542 ^ _167881) ^ [_184344, _184346] : [-(class_Rings_Ocomm__semiring(_184344)), _184346 = _184344, class_Rings_Ocomm__semiring(_184346)], (552 ^ _167881) ^ [_184639, _184641] : [-(class_Rings_Ozero__neq__one(_184639)), _184641 = _184639, class_Rings_Ozero__neq__one(_184641)], (562 ^ _167881) ^ [_184934, _184936] : [-(class_Rings_Oordered__ring(_184934)), _184936 = _184934, class_Rings_Oordered__ring(_184936)], (572 ^ _167881) ^ [_185229, _185231] : [-(class_Orderings_Opreorder(_185229)), _185231 = _185229, class_Orderings_Opreorder(_185231)], (582 ^ _167881) ^ [_185524, _185526] : [-(class_Orderings_Olinorder(_185524)), _185526 = _185524, class_Orderings_Olinorder(_185526)], (592 ^ _167881) ^ [_185819, _185821] : [-(class_Groups_Omonoid__mult(_185819)), _185821 = _185819, class_Groups_Omonoid__mult(_185821)], (602 ^ _167881) ^ [_186114, _186116] : [-(class_Groups_Ocomm__monoid__add(_186114)), _186116 = _186114, class_Groups_Ocomm__monoid__add(_186116)], (612 ^ _167881) ^ [_186409, _186411] : [-(class_Groups_Omonoid__add(_186409)), _186411 = _186409, class_Groups_Omonoid__add(_186411)], (622 ^ _167881) ^ [_186704, _186706] : [-(class_Rings_Osemiring__0(_186704)), _186706 = _186704, class_Rings_Osemiring__0(_186706)], (632 ^ _167881) ^ [_186999, _187001] : [-(class_Groups_Ogroup__add(_186999)), _187001 = _186999, class_Groups_Ogroup__add(_187001)], (642 ^ _167881) ^ [_187294, _187296] : [-(class_Rings_Omult__zero(_187294)), _187296 = _187294, class_Rings_Omult__zero(_187296)], (652 ^ _167881) ^ [_187589, _187591] : [-(class_Orderings_Oorder(_187589)), _187591 = _187589, class_Orderings_Oorder(_187591)], (662 ^ _167881) ^ [_187884, _187886] : [-(class_Int_Oring__char__0(_187884)), _187886 = _187884, class_Int_Oring__char__0(_187886)], (672 ^ _167881) ^ [_188179, _188181] : [-(class_Rings_Ocomm__semiring__0(_188179)), _188181 = _188179, class_Rings_Ocomm__semiring__0(_188181)], (682 ^ _167881) ^ [_188474, _188476] : [-(class_Rings_Osemiring(_188474)), _188476 = _188474, class_Rings_Osemiring(_188476)], (692 ^ _167881) ^ [_188769, _188771] : [-(class_Orderings_Oord(_188769)), _188771 = _188769, class_Orderings_Oord(_188771)], (702 ^ _167881) ^ [_189064, _189066] : [-(class_Groups_Ouminus(_189064)), _189066 = _189064, class_Groups_Ouminus(_189066)], (712 ^ _167881) ^ [_189359, _189361] : [-(class_Groups_Osgn__if(_189359)), _189361 = _189359, class_Groups_Osgn__if(_189361)], (722 ^ _167881) ^ [_189654, _189656] : [-(class_Rings_Olinordered__idom(_189654)), _189656 = _189654, class_Rings_Olinordered__idom(_189656)], (732 ^ _167881) ^ [_189949, _189951] : [-(class_Groups_Oabs__if(_189949)), _189951 = _189949, class_Groups_Oabs__if(_189951)], (742 ^ _167881) ^ [_190244, _190246] : [-(class_Rings_Ocomm__ring__1(_190244)), _190246 = _190244, class_Rings_Ocomm__ring__1(_190246)], (752 ^ _167881) ^ [_190539, _190541] : [-(class_Rings_Oring__1(_190539)), _190541 = _190539, class_Rings_Oring__1(_190541)], (762 ^ _167881) ^ [_190834, _190836] : [-(class_Groups_Oab__group__add(_190834)), _190836 = _190834, class_Groups_Oab__group__add(_190836)], (772 ^ _167881) ^ [_191129, _191131] : [-(class_Groups_Ominus(_191129)), _191131 = _191129, class_Groups_Ominus(_191131)], (782 ^ _167881) ^ [_191424, _191426] : [-(class_Power_Opower(_191424)), _191426 = _191424, class_Power_Opower(_191426)], (792 ^ _167881) ^ [_191719, _191721] : [-(class_Groups_Ozero(_191719)), _191721 = _191719, class_Groups_Ozero(_191721)], (802 ^ _167881) ^ [_192014, _192016] : [-(class_Rings_Ocomm__ring(_192014)), _192016 = _192014, class_Rings_Ocomm__ring(_192016)], (812 ^ _167881) ^ [_192309, _192311] : [-(class_Rings_Oring(_192309)), _192311 = _192309, class_Rings_Oring(_192311)], (822 ^ _167881) ^ [_192604, _192606] : [-(class_Rings_Oidom(_192604)), _192606 = _192604, class_Rings_Oidom(_192606)], (832 ^ _167881) ^ [_192899, _192901] : [-(class_Groups_Oone(_192899)), _192901 = _192899, class_Groups_Oone(_192901)], (842 ^ _167881) ^ [_193194, _193196] : [-(class_Rings_Ocomm__semiring__1(_193194)), _193196 = _193194, class_Rings_Ocomm__semiring__1(_193196)], (852 ^ _167881) ^ [_193489, _193491] : [-(class_Rings_Odvd(_193489)), _193491 = _193489, class_Rings_Odvd(_193491)], (862 ^ _167881) ^ [_193820, _193822, _193824, _193826, _193828, _193830] : [-(c_Orderings_Oord__class_Oless(_193828, _193824, _193820)), c_Orderings_Oord__class_Oless(_193830, _193826, _193822), _193830 = _193828, _193826 = _193824, _193822 = _193820], (1182 ^ _167881) ^ [_206033, _206035] : [hAPP(_206033, 1183 ^ [_206033, _206035]) = hAPP(_206035, 1183 ^ [_206033, _206035]), -(_206033 = _206035)], (1189 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_t____))], (1191 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_t____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1193 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_m____))], (1195 ^ _167881) ^ [] : [v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1197 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))], (1199 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1201 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_t____, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (1203 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (1205 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____))))], (1207 ^ _167881) ^ [_206815, _206817, _206819] : [class_Rings_Olinordered__semidom(_206815), c_Orderings_Oord__class_Oless(_206815, c_Groups_Ozero__class_Ozero(_206815), _206817), c_Orderings_Oord__class_Oless(_206815, _206817, c_Groups_Oone__class_Oone(_206815)), -(c_Orderings_Oord__class_Oless(_206815, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_206815), _206817), hAPP(hAPP(c_Power_Opower__class_Opower(_206815), _206817), _206819)), hAPP(hAPP(c_Power_Opower__class_Opower(_206815), _206817), _206819)))], (1221 ^ _167881) ^ [_207263] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _207263), 1225 ^ _167881 : [(1226 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1224 ^ [_207263]))], (1228 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1224 ^ [_207263], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1230 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1224 ^ [_207263], _207263))]]], (1232 ^ _167881) ^ [_207738, _207740, _207742, _207744, _207746] : [class_RealVector_Oreal__normed__algebra(_207738), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_207738, _207740), _207742), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_207738, _207744), _207746), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_207738, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_207738), _207740), _207744)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _207742), _207746)))], (1246 ^ _167881) ^ [_208218, _208220] : [class_RealVector_Oreal__normed__vector(_208218), 1249 ^ _167881 : [(1250 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_208218, _208220)), _208220 = c_Groups_Ozero__class_Ozero(_208218)], (1256 ^ _167881) ^ [] : [-(_208220 = c_Groups_Ozero__class_Ozero(_208218)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_208218, _208220)))]]], (1262 ^ _167881) ^ [_208710, _208712, _208714] : [class_Rings_Olinordered__semidom(_208710), c_Orderings_Oord__class_Oless(_208710, c_Groups_Oone__class_Oone(_208710), _208712), -(c_Orderings_Oord__class_Oless(_208710, c_Groups_Oone__class_Oone(_208710), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_208710), _208712), hAPP(hAPP(c_Power_Opower__class_Opower(_208710), _208712), _208714))))], (1272 ^ _167881) ^ [_209075, _209077, _209079] : [class_Rings_Olinordered__semidom(_209075), c_Orderings_Oord__class_Oless(_209075, c_Groups_Oone__class_Oone(_209075), _209077), -(c_Orderings_Oord__class_Oless(_209075, hAPP(hAPP(c_Power_Opower__class_Opower(_209075), _209077), _209079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_209075), _209077), hAPP(hAPP(c_Power_Opower__class_Opower(_209075), _209077), _209079))))], (1282 ^ _167881) ^ [_209466, _209468, _209470, _209472] : [class_Rings_Olinordered__semidom(_209466), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _209468, _209470), c_Orderings_Oord__class_Oless(_209466, c_Groups_Ozero__class_Ozero(_209466), _209472), c_Orderings_Oord__class_Oless(_209466, _209472, c_Groups_Oone__class_Oone(_209466)), -(c_Orderings_Oord__class_Oless(_209466, hAPP(hAPP(c_Power_Opower__class_Opower(_209466), _209472), _209470), hAPP(hAPP(c_Power_Opower__class_Opower(_209466), _209472), _209468)))], (1300 ^ _167881) ^ [_210011] : [class_Rings_Olinordered__semidom(_210011), -(c_Orderings_Oord__class_Oless(_210011, c_Groups_Ozero__class_Ozero(_210011), c_Groups_Oplus__class_Oplus(_210011, c_Groups_Oone__class_Oone(_210011), c_Groups_Oone__class_Oone(_210011))))], (1306 ^ _167881) ^ [_210249, _210251, _210253] : [class_Rings_Olinordered__ring(_210249), c_Orderings_Oord__class_Oless(_210249, c_Groups_Oplus__class_Oplus(_210249, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_210249), _210251), _210251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_210249), _210253), _210253)), c_Groups_Ozero__class_Ozero(_210249))], (1312 ^ _167881) ^ [_210524, _210526, _210528] : [class_Rings_Olinordered__ring__strict(_210524), 1315 ^ _167881 : [(1326 ^ _167881) ^ [] : [1327 ^ _167881 : [(1328 ^ _167881) ^ [] : [-(_210526 = c_Groups_Ozero__class_Ozero(_210524))], (1330 ^ _167881) ^ [] : [-(_210528 = c_Groups_Ozero__class_Ozero(_210524))]], -(c_Orderings_Oord__class_Oless(_210524, c_Groups_Ozero__class_Ozero(_210524), c_Groups_Oplus__class_Oplus(_210524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_210524), _210526), _210526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_210524), _210528), _210528))))], (1316 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_210524, c_Groups_Ozero__class_Ozero(_210524), c_Groups_Oplus__class_Oplus(_210524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_210524), _210526), _210526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_210524), _210528), _210528))), _210526 = c_Groups_Ozero__class_Ozero(_210524), _210528 = c_Groups_Ozero__class_Ozero(_210524)]]], (1334 ^ _167881) ^ [] : [v_a____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (1336 ^ _167881) ^ [] : [v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (1338 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (1340 ^ _167881) ^ [_211389, _211391] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _211389), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _211389, _211391)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _211391))))], (1342 ^ _167881) ^ [_211516, _211518] : [class_Rings_Odivision__ring__inverse__zero(_211516), -(c_Rings_Oinverse__class_Oinverse(_211516, c_Rings_Oinverse__class_Oinverse(_211516, _211518)) = _211518)], (1348 ^ _167881) ^ [_211736, _211738] : [-(c_RealVector_Onorm__class_Onorm(_211736, c_Rings_Oinverse__class_Oinverse(_211736, _211738)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_211736, _211738))), class_RealVector_Oreal__normed__div__algebra(_211736), class_Rings_Odivision__ring__inverse__zero(_211736)], (1368 ^ _167881) ^ [_212352, _212354] : [1369 ^ _167881 : [(1370 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _212352)], (1372 ^ _167881) ^ [] : [_212354 = 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), _212352), _212354)))], (1358 ^ _167881) ^ [_212084, _212086] : [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), _212084), _212086)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _212084)), -(_212086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1376 ^ _167881) ^ [_212668, _212670, _212672] : [class_Rings_Odivision__ring__inverse__zero(_212668), 1379 ^ _167881 : [(1380 ^ _167881) ^ [] : [c_Rings_Oinverse__class_Oinverse(_212668, _212670) = c_Rings_Oinverse__class_Oinverse(_212668, _212672), -(_212670 = _212672)], (1386 ^ _167881) ^ [] : [_212670 = _212672, -(c_Rings_Oinverse__class_Oinverse(_212668, _212670) = c_Rings_Oinverse__class_Oinverse(_212668, _212672))]]], (1392 ^ _167881) ^ [_213174, _213176, _213178] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _213174), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _213174), _213176), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _213174), _213178)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _213176, _213178))], (1402 ^ _167881) ^ [_213527, _213529, _213531] : [class_Rings_Odivision__ring__inverse__zero(_213527), c_Rings_Oinverse__class_Oinverse(_213527, _213529) = c_Rings_Oinverse__class_Oinverse(_213527, _213531), -(_213529 = _213531)], (1412 ^ _167881) ^ [_213860, _213862, _213864] : [class_Rings_Odivision__ring(_213860), c_Rings_Oinverse__class_Oinverse(_213860, _213862) = c_Rings_Oinverse__class_Oinverse(_213860, _213864), -(_213862 = c_Groups_Ozero__class_Ozero(_213860)), -(_213864 = c_Groups_Ozero__class_Ozero(_213860)), -(_213862 = _213864)], (1430 ^ _167881) ^ [_214379, _214381] : [class_Rings_Odivision__ring(_214379), c_Rings_Oinverse__class_Oinverse(_214379, _214381) = c_Groups_Ozero__class_Ozero(_214379), -(_214381 = c_Groups_Ozero__class_Ozero(_214379))], (1440 ^ _167881) ^ [_214690, _214692] : [class_Rings_Odivision__ring(_214690), -(_214692 = c_Groups_Ozero__class_Ozero(_214690)), -(c_Rings_Oinverse__class_Oinverse(_214690, c_Rings_Oinverse__class_Oinverse(_214690, _214692)) = _214692)], (1450 ^ _167881) ^ [_215006, _215008] : [class_Rings_Odivision__ring(_215006), -(_215008 = c_Groups_Ozero__class_Ozero(_215006)), c_Rings_Oinverse__class_Oinverse(_215006, _215008) = c_Groups_Ozero__class_Ozero(_215006)], (1460 ^ _167881) ^ [_215321, _215323] : [class_Rings_Odivision__ring__inverse__zero(_215321), 1463 ^ _167881 : [(1464 ^ _167881) ^ [] : [c_Rings_Oinverse__class_Oinverse(_215321, _215323) = c_Groups_Ozero__class_Ozero(_215321), -(_215323 = c_Groups_Ozero__class_Ozero(_215321))], (1470 ^ _167881) ^ [] : [_215323 = c_Groups_Ozero__class_Ozero(_215321), -(c_Rings_Oinverse__class_Oinverse(_215321, _215323) = c_Groups_Ozero__class_Ozero(_215321))]]], (1476 ^ _167881) ^ [_215786] : [class_Rings_Odivision__ring__inverse__zero(_215786), -(c_Rings_Oinverse__class_Oinverse(_215786, c_Groups_Ozero__class_Ozero(_215786)) = c_Groups_Ozero__class_Ozero(_215786))], (1482 ^ _167881) ^ [_215988] : [class_Rings_Odivision__ring(_215988), -(c_Rings_Oinverse__class_Oinverse(_215988, c_Groups_Oone__class_Oone(_215988)) = c_Groups_Oone__class_Oone(_215988))], (1488 ^ _167881) ^ [_216218, _216220, _216222] : [class_Rings_Odivision__ring__inverse__zero(_216218), -(c_Rings_Oinverse__class_Oinverse(_216218, hAPP(hAPP(c_Power_Opower__class_Opower(_216218), _216220), _216222)) = hAPP(hAPP(c_Power_Opower__class_Opower(_216218), c_Rings_Oinverse__class_Oinverse(_216218, _216220)), _216222))], (1494 ^ _167881) ^ [_216504, _216506, _216508, _216510] : [class_Groups_Omonoid__mult(_216504), -(hAPP(hAPP(c_Power_Opower__class_Opower(_216504), _216506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _216508), _216510)) = hAPP(hAPP(c_Power_Opower__class_Opower(_216504), hAPP(hAPP(c_Power_Opower__class_Opower(_216504), _216506), _216508)), _216510))], (1500 ^ _167881) ^ [_216784, _216786] : [class_RealVector_Oreal__normed__div__algebra(_216784), -(_216786 = c_Groups_Ozero__class_Ozero(_216784)), -(c_RealVector_Onorm__class_Onorm(_216784, c_Rings_Oinverse__class_Oinverse(_216784, _216786)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_216784, _216786)))], (1510 ^ _167881) ^ [_217140, _217142, _217144, _217146] : [class_Rings_Olinordered__semidom(_217140), hAPP(hAPP(c_Power_Opower__class_Opower(_217140), _217142), _217144) = hAPP(hAPP(c_Power_Opower__class_Opower(_217140), _217146), _217144), c_Orderings_Oord__class_Oless__eq(_217140, c_Groups_Ozero__class_Ozero(_217140), _217142), c_Orderings_Oord__class_Oless__eq(_217140, c_Groups_Ozero__class_Ozero(_217140), _217146), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _217144), -(_217142 = _217146)], (1532 ^ _167881) ^ [_217822, _217824, _217826, _217828] : [class_Rings_Olinordered__semidom(_217822), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _217824, _217826), c_Orderings_Oord__class_Oless__eq(_217822, c_Groups_Oone__class_Oone(_217822), _217828), -(c_Orderings_Oord__class_Oless__eq(_217822, hAPP(hAPP(c_Power_Opower__class_Opower(_217822), _217828), _217824), hAPP(hAPP(c_Power_Opower__class_Opower(_217822), _217828), _217826)))], (1546 ^ _167881) ^ [_218306, _218308, _218310, _218312] : [class_Rings_Olinordered__semidom(_218306), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _218308, _218310), c_Orderings_Oord__class_Oless__eq(_218306, c_Groups_Ozero__class_Ozero(_218306), _218312), c_Orderings_Oord__class_Oless__eq(_218306, _218312, c_Groups_Oone__class_Oone(_218306)), -(c_Orderings_Oord__class_Oless__eq(_218306, hAPP(hAPP(c_Power_Opower__class_Opower(_218306), _218312), _218310), hAPP(hAPP(c_Power_Opower__class_Opower(_218306), _218312), _218308)))], (1564 ^ _167881) ^ [_218893, _218895, _218897, _218899] : [class_Rings_Olinordered__semidom(_218893), c_Orderings_Oord__class_Oless(_218893, c_Groups_Oone__class_Oone(_218893), _218895), c_Orderings_Oord__class_Oless__eq(_218893, hAPP(hAPP(c_Power_Opower__class_Opower(_218893), _218895), _218897), hAPP(hAPP(c_Power_Opower__class_Opower(_218893), _218895), _218899)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _218897, _218899))], (1578 ^ _167881) ^ [_219377, _219379, _219381, _219383] : [class_Rings_Olinordered__semidom(_219377), c_Orderings_Oord__class_Oless(_219377, c_Groups_Oone__class_Oone(_219377), _219379), 1585 ^ _167881 : [(1586 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_219377, hAPP(hAPP(c_Power_Opower__class_Opower(_219377), _219379), _219381), hAPP(hAPP(c_Power_Opower__class_Opower(_219377), _219379), _219383)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _219381, _219383))], (1592 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _219381, _219383), -(c_Orderings_Oord__class_Oless__eq(_219377, hAPP(hAPP(c_Power_Opower__class_Opower(_219377), _219379), _219381), hAPP(hAPP(c_Power_Opower__class_Opower(_219377), _219379), _219383)))]]], (1598 ^ _167881) ^ [_220038, _220040, _220042] : [class_Rings_Odivision__ring(_220038), -(_220040 = c_Groups_Ozero__class_Ozero(_220038)), -(_220042 = c_Groups_Ozero__class_Ozero(_220038)), -(c_Rings_Oinverse__class_Oinverse(_220038, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_220038), _220040), _220042)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_220038), c_Rings_Oinverse__class_Oinverse(_220038, _220042)), c_Rings_Oinverse__class_Oinverse(_220038, _220040)))], (1612 ^ _167881) ^ [_220516, _220518, _220520] : [class_Rings_Odivision__ring(_220516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_220516), _220518), _220520) = c_Groups_Oone__class_Oone(_220516), -(c_Rings_Oinverse__class_Oinverse(_220516, _220518) = _220520)], (1622 ^ _167881) ^ [_220863, _220865, _220867] : [class_Rings_Odivision__ring(_220863), -(_220865 = c_Groups_Ozero__class_Ozero(_220863)), -(c_Rings_Oinverse__class_Oinverse(_220863, hAPP(hAPP(c_Power_Opower__class_Opower(_220863), _220865), _220867)) = hAPP(hAPP(c_Power_Opower__class_Opower(_220863), c_Rings_Oinverse__class_Oinverse(_220863, _220865)), _220867))], (1632 ^ _167881) ^ [_221235, _221237, _221239] : [class_Rings_Oordered__cancel__semiring(_221235), -(c_Orderings_Oord__class_Oless__eq(_221235, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_221235), _221237), _221239), c_Groups_Ozero__class_Ozero(_221235))), 1637 ^ _167881 : [(1638 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_221235, c_Groups_Ozero__class_Ozero(_221235), _221237), c_Orderings_Oord__class_Oless__eq(_221235, _221239, c_Groups_Ozero__class_Ozero(_221235))], (1644 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_221235, _221237, c_Groups_Ozero__class_Ozero(_221235)), c_Orderings_Oord__class_Oless__eq(_221235, c_Groups_Ozero__class_Ozero(_221235), _221239)]]], (1652 ^ _167881) ^ [_221864, _221866, _221868] : [class_Rings_Oordered__ring(_221864), -(c_Orderings_Oord__class_Oless__eq(_221864, c_Groups_Ozero__class_Ozero(_221864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_221864), _221866), _221868))), 1657 ^ _167881 : [(1658 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_221864, c_Groups_Ozero__class_Ozero(_221864), _221866), c_Orderings_Oord__class_Oless__eq(_221864, c_Groups_Ozero__class_Ozero(_221864), _221868)], (1664 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_221864, _221866, c_Groups_Ozero__class_Ozero(_221864)), c_Orderings_Oord__class_Oless__eq(_221864, _221868, c_Groups_Ozero__class_Ozero(_221864))]]], (1672 ^ _167881) ^ [_222521, _222523, _222525, _222527, _222529] : [class_Rings_Oordered__semiring(_222521), c_Orderings_Oord__class_Oless__eq(_222521, _222523, _222525), c_Orderings_Oord__class_Oless__eq(_222521, _222527, _222529), c_Orderings_Oord__class_Oless__eq(_222521, c_Groups_Ozero__class_Ozero(_222521), _222525), c_Orderings_Oord__class_Oless__eq(_222521, c_Groups_Ozero__class_Ozero(_222521), _222527), -(c_Orderings_Oord__class_Oless__eq(_222521, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_222521), _222523), _222527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_222521), _222525), _222529)))], (1694 ^ _167881) ^ [_223243, _223245, _223247, _223249, _223251] : [class_Rings_Oordered__semiring(_223243), c_Orderings_Oord__class_Oless__eq(_223243, _223245, _223247), c_Orderings_Oord__class_Oless__eq(_223243, _223249, _223251), c_Orderings_Oord__class_Oless__eq(_223243, c_Groups_Ozero__class_Ozero(_223243), _223245), c_Orderings_Oord__class_Oless__eq(_223243, c_Groups_Ozero__class_Ozero(_223243), _223249), -(c_Orderings_Oord__class_Oless__eq(_223243, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223243), _223245), _223249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223243), _223247), _223251)))], (1716 ^ _167881) ^ [_223951, _223953, _223955, _223957] : [class_Rings_Oordered__ring(_223951), c_Orderings_Oord__class_Oless__eq(_223951, _223953, _223955), c_Orderings_Oord__class_Oless__eq(_223951, _223957, c_Groups_Ozero__class_Ozero(_223951)), -(c_Orderings_Oord__class_Oless__eq(_223951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223951), _223957), _223955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223951), _223957), _223953)))], (1730 ^ _167881) ^ [_224435, _224437, _224439, _224441] : [class_Rings_Oordered__ring(_224435), c_Orderings_Oord__class_Oless__eq(_224435, _224437, _224439), c_Orderings_Oord__class_Oless__eq(_224435, _224441, c_Groups_Ozero__class_Ozero(_224435)), -(c_Orderings_Oord__class_Oless__eq(_224435, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224435), _224439), _224441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224435), _224437), _224441)))], (1744 ^ _167881) ^ [_224919, _224921, _224923, _224925] : [class_Rings_Oordered__comm__semiring(_224919), c_Orderings_Oord__class_Oless__eq(_224919, _224921, _224923), c_Orderings_Oord__class_Oless__eq(_224919, c_Groups_Ozero__class_Ozero(_224919), _224925), -(c_Orderings_Oord__class_Oless__eq(_224919, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224919), _224925), _224921), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224919), _224925), _224923)))], (1758 ^ _167881) ^ [_225403, _225405, _225407, _225409] : [class_Rings_Oordered__semiring(_225403), c_Orderings_Oord__class_Oless__eq(_225403, _225405, _225407), c_Orderings_Oord__class_Oless__eq(_225403, c_Groups_Ozero__class_Ozero(_225403), _225409), -(c_Orderings_Oord__class_Oless__eq(_225403, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225403), _225409), _225405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225403), _225409), _225407)))], (1772 ^ _167881) ^ [_225887, _225889, _225891, _225893] : [class_Rings_Oordered__semiring(_225887), c_Orderings_Oord__class_Oless__eq(_225887, _225889, _225891), c_Orderings_Oord__class_Oless__eq(_225887, c_Groups_Ozero__class_Ozero(_225887), _225893), -(c_Orderings_Oord__class_Oless__eq(_225887, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225887), _225889), _225893), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225887), _225891), _225893)))], (1786 ^ _167881) ^ [_226357, _226359, _226361] : [class_Rings_Oordered__ring(_226357), c_Orderings_Oord__class_Oless__eq(_226357, _226359, c_Groups_Ozero__class_Ozero(_226357)), c_Orderings_Oord__class_Oless__eq(_226357, _226361, c_Groups_Ozero__class_Ozero(_226357)), -(c_Orderings_Oord__class_Oless__eq(_226357, c_Groups_Ozero__class_Ozero(_226357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226357), _226359), _226361)))], (1800 ^ _167881) ^ [_226805, _226807, _226809] : [class_Rings_Oordered__cancel__semiring(_226805), c_Orderings_Oord__class_Oless__eq(_226805, _226807, c_Groups_Ozero__class_Ozero(_226805)), c_Orderings_Oord__class_Oless__eq(_226805, c_Groups_Ozero__class_Ozero(_226805), _226809), -(c_Orderings_Oord__class_Oless__eq(_226805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226805), _226807), _226809), c_Groups_Ozero__class_Ozero(_226805)))], (1814 ^ _167881) ^ [_227253, _227255, _227257] : [class_Rings_Oordered__cancel__semiring(_227253), c_Orderings_Oord__class_Oless__eq(_227253, c_Groups_Ozero__class_Ozero(_227253), _227255), c_Orderings_Oord__class_Oless__eq(_227253, _227257, c_Groups_Ozero__class_Ozero(_227253)), -(c_Orderings_Oord__class_Oless__eq(_227253, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227253), _227257), _227255), c_Groups_Ozero__class_Ozero(_227253)))], (1828 ^ _167881) ^ [_227701, _227703, _227705] : [class_Rings_Oordered__cancel__semiring(_227701), c_Orderings_Oord__class_Oless__eq(_227701, c_Groups_Ozero__class_Ozero(_227701), _227703), c_Orderings_Oord__class_Oless__eq(_227701, _227705, c_Groups_Ozero__class_Ozero(_227701)), -(c_Orderings_Oord__class_Oless__eq(_227701, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227701), _227703), _227705), c_Groups_Ozero__class_Ozero(_227701)))], (1842 ^ _167881) ^ [_228149, _228151, _228153] : [class_Rings_Oordered__cancel__semiring(_228149), c_Orderings_Oord__class_Oless__eq(_228149, c_Groups_Ozero__class_Ozero(_228149), _228151), c_Orderings_Oord__class_Oless__eq(_228149, c_Groups_Ozero__class_Ozero(_228149), _228153), -(c_Orderings_Oord__class_Oless__eq(_228149, c_Groups_Ozero__class_Ozero(_228149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228149), _228151), _228153)))], (1856 ^ _167881) ^ [_228597, _228599, _228601] : [class_Rings_Olinordered__ring__strict(_228597), 1859 ^ _167881 : [(1860 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_228597, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228597), _228599), _228601), c_Groups_Ozero__class_Ozero(_228597)), 1865 ^ _167881 : [(1866 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_228597, c_Groups_Ozero__class_Ozero(_228597), _228599))], (1868 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_228597, _228601, c_Groups_Ozero__class_Ozero(_228597)))]], 1869 ^ _167881 : [(1870 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_228597, _228599, c_Groups_Ozero__class_Ozero(_228597)))], (1872 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_228597, c_Groups_Ozero__class_Ozero(_228597), _228601))]]], (1874 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_228597, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228597), _228599), _228601), c_Groups_Ozero__class_Ozero(_228597))), 1875 ^ _167881 : [(1876 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_228597, c_Groups_Ozero__class_Ozero(_228597), _228599), c_Orderings_Oord__class_Oless__eq(_228597, _228601, c_Groups_Ozero__class_Ozero(_228597))], (1882 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_228597, _228599, c_Groups_Ozero__class_Ozero(_228597)), c_Orderings_Oord__class_Oless__eq(_228597, c_Groups_Ozero__class_Ozero(_228597), _228601)]]]]], (1890 ^ _167881) ^ [_229646, _229648, _229650] : [class_Rings_Olinordered__ring__strict(_229646), 1893 ^ _167881 : [(1894 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_229646, c_Groups_Ozero__class_Ozero(_229646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229646), _229648), _229650)), 1899 ^ _167881 : [(1900 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_229646, c_Groups_Ozero__class_Ozero(_229646), _229648))], (1902 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_229646, c_Groups_Ozero__class_Ozero(_229646), _229650))]], 1903 ^ _167881 : [(1904 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_229646, _229648, c_Groups_Ozero__class_Ozero(_229646)))], (1906 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_229646, _229650, c_Groups_Ozero__class_Ozero(_229646)))]]], (1908 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_229646, c_Groups_Ozero__class_Ozero(_229646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229646), _229648), _229650))), 1909 ^ _167881 : [(1910 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_229646, c_Groups_Ozero__class_Ozero(_229646), _229648), c_Orderings_Oord__class_Oless__eq(_229646, c_Groups_Ozero__class_Ozero(_229646), _229650)], (1916 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_229646, _229648, c_Groups_Ozero__class_Ozero(_229646)), c_Orderings_Oord__class_Oless__eq(_229646, _229650, c_Groups_Ozero__class_Ozero(_229646))]]]]], (1924 ^ _167881) ^ [_230681, _230683] : [class_Rings_Olinordered__ring(_230681), -(c_Orderings_Oord__class_Oless__eq(_230681, c_Groups_Ozero__class_Ozero(_230681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_230681), _230683), _230683)))], (1930 ^ _167881) ^ [_230897] : [class_Rings_Olinordered__semidom(_230897), -(c_Orderings_Oord__class_Oless__eq(_230897, c_Groups_Ozero__class_Ozero(_230897), c_Groups_Oone__class_Oone(_230897)))], (1936 ^ _167881) ^ [_231095] : [class_Rings_Olinordered__semidom(_231095), c_Orderings_Oord__class_Oless__eq(_231095, c_Groups_Oone__class_Oone(_231095), c_Groups_Ozero__class_Ozero(_231095))], (1942 ^ _167881) ^ [_231336, _231338, _231340, _231342] : [class_Rings_Olinordered__semidom(_231336), c_Orderings_Oord__class_Oless__eq(_231336, _231338, _231340), c_Orderings_Oord__class_Oless__eq(_231336, c_Groups_Ozero__class_Ozero(_231336), _231338), -(c_Orderings_Oord__class_Oless__eq(_231336, hAPP(hAPP(c_Power_Opower__class_Opower(_231336), _231338), _231342), hAPP(hAPP(c_Power_Opower__class_Opower(_231336), _231340), _231342)))], (1956 ^ _167881) ^ [_231806, _231808, _231810] : [class_Rings_Olinordered__semidom(_231806), c_Orderings_Oord__class_Oless__eq(_231806, c_Groups_Ozero__class_Ozero(_231806), _231808), -(c_Orderings_Oord__class_Oless__eq(_231806, c_Groups_Ozero__class_Ozero(_231806), hAPP(hAPP(c_Power_Opower__class_Opower(_231806), _231808), _231810)))], (1966 ^ _167881) ^ [_232155, _232157, _232159] : [class_Rings_Olinordered__semidom(_232155), c_Orderings_Oord__class_Oless__eq(_232155, c_Groups_Oone__class_Oone(_232155), _232157), -(c_Orderings_Oord__class_Oless__eq(_232155, c_Groups_Oone__class_Oone(_232155), hAPP(hAPP(c_Power_Opower__class_Opower(_232155), _232157), _232159)))], (1976 ^ _167881) ^ [_232504, _232506, _232508] : [class_RealVector_Oreal__normed__vector(_232504), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_232504, c_Groups_Oplus__class_Oplus(_232504, _232506, _232508)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_232504, _232506), c_RealVector_Onorm__class_Onorm(_232504, _232508))))], (1982 ^ _167881) ^ [_232754, _232756] : [class_RealVector_Oreal__normed__vector(_232754), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_232754, _232756)))], (1988 ^ _167881) ^ [_232970, _232972] : [class_Power_Opower(_232970), -(hAPP(hAPP(c_Power_Opower__class_Opower(_232970), _232972), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_232970))], (1994 ^ _167881) ^ [_233212, _233214, _233216] : [class_Rings_Odivision__ring(_233212), -(_233214 = c_Groups_Ozero__class_Ozero(_233212)), -(_233216 = c_Groups_Ozero__class_Ozero(_233212)), -(c_Groups_Oplus__class_Oplus(_233212, c_Rings_Oinverse__class_Oinverse(_233212, _233214), c_Rings_Oinverse__class_Oinverse(_233212, _233216)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233212), c_Rings_Oinverse__class_Oinverse(_233212, _233214)), c_Groups_Oplus__class_Oplus(_233212, _233214, _233216))), c_Rings_Oinverse__class_Oinverse(_233212, _233216)))], (2008 ^ _167881) ^ [_233698, _233700] : [class_Rings_Odivision__ring(_233698), -(_233700 = c_Groups_Ozero__class_Ozero(_233698)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233698), c_Rings_Oinverse__class_Oinverse(_233698, _233700)), _233700) = c_Groups_Oone__class_Oone(_233698))], (2018 ^ _167881) ^ [_234028, _234030] : [class_Rings_Odivision__ring(_234028), -(_234030 = c_Groups_Ozero__class_Ozero(_234028)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234028), _234030), c_Rings_Oinverse__class_Oinverse(_234028, _234030)) = c_Groups_Oone__class_Oone(_234028))], (2028 ^ _167881) ^ [_234386, _234388, _234390, _234392] : [class_Rings_Olinordered__semiring__strict(_234386), c_Orderings_Oord__class_Oless__eq(_234386, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234386), _234388), _234390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234386), _234388), _234392)), c_Orderings_Oord__class_Oless(_234386, c_Groups_Ozero__class_Ozero(_234386), _234388), -(c_Orderings_Oord__class_Oless__eq(_234386, _234390, _234392))], (2042 ^ _167881) ^ [_234870, _234872, _234874, _234876] : [class_Rings_Olinordered__semiring__strict(_234870), c_Orderings_Oord__class_Oless__eq(_234870, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234870), _234872), _234874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234870), _234876), _234874)), c_Orderings_Oord__class_Oless(_234870, c_Groups_Ozero__class_Ozero(_234870), _234874), -(c_Orderings_Oord__class_Oless__eq(_234870, _234872, _234876))], (2056 ^ _167881) ^ [_235354, _235356, _235358, _235360] : [class_Rings_Olinordered__semiring__strict(_235354), c_Orderings_Oord__class_Oless(_235354, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235354), _235356), _235358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235354), _235356), _235360)), c_Orderings_Oord__class_Oless__eq(_235354, c_Groups_Ozero__class_Ozero(_235354), _235356), -(c_Orderings_Oord__class_Oless(_235354, _235358, _235360))], (2070 ^ _167881) ^ [_235838, _235840, _235842, _235844] : [class_Rings_Olinordered__semiring(_235838), c_Orderings_Oord__class_Oless(_235838, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235838), _235840), _235842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235838), _235840), _235844)), c_Orderings_Oord__class_Oless__eq(_235838, c_Groups_Ozero__class_Ozero(_235838), _235840), -(c_Orderings_Oord__class_Oless(_235838, _235842, _235844))], (2084 ^ _167881) ^ [_236322, _236324, _236326, _236328] : [class_Rings_Olinordered__semiring__strict(_236322), c_Orderings_Oord__class_Oless(_236322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236322), _236324), _236326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236322), _236328), _236326)), c_Orderings_Oord__class_Oless__eq(_236322, c_Groups_Ozero__class_Ozero(_236322), _236326), -(c_Orderings_Oord__class_Oless(_236322, _236324, _236328))], (2098 ^ _167881) ^ [_236806, _236808, _236810, _236812] : [class_Rings_Olinordered__semiring(_236806), c_Orderings_Oord__class_Oless(_236806, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236806), _236808), _236810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236806), _236812), _236810)), c_Orderings_Oord__class_Oless__eq(_236806, c_Groups_Ozero__class_Ozero(_236806), _236810), -(c_Orderings_Oord__class_Oless(_236806, _236808, _236812))], (2112 ^ _167881) ^ [_237304, _237306, _237308, _237310, _237312] : [class_Rings_Olinordered__semiring__strict(_237304), c_Orderings_Oord__class_Oless__eq(_237304, _237306, _237308), c_Orderings_Oord__class_Oless(_237304, _237310, _237312), c_Orderings_Oord__class_Oless(_237304, c_Groups_Ozero__class_Ozero(_237304), _237306), c_Orderings_Oord__class_Oless__eq(_237304, c_Groups_Ozero__class_Ozero(_237304), _237310), -(c_Orderings_Oord__class_Oless(_237304, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_237304), _237306), _237310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_237304), _237308), _237312)))], (2134 ^ _167881) ^ [_238026, _238028, _238030, _238032, _238034] : [class_Rings_Olinordered__semiring__strict(_238026), c_Orderings_Oord__class_Oless(_238026, _238028, _238030), c_Orderings_Oord__class_Oless__eq(_238026, _238032, _238034), c_Orderings_Oord__class_Oless__eq(_238026, c_Groups_Ozero__class_Ozero(_238026), _238028), c_Orderings_Oord__class_Oless(_238026, c_Groups_Ozero__class_Ozero(_238026), _238032), -(c_Orderings_Oord__class_Oless(_238026, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238026), _238028), _238032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238026), _238030), _238034)))], (2156 ^ _167881) ^ [_238748, _238750, _238752, _238754, _238756] : [class_Rings_Olinordered__semiring__strict(_238748), c_Orderings_Oord__class_Oless(_238748, _238750, _238752), c_Orderings_Oord__class_Oless(_238748, _238754, _238756), c_Orderings_Oord__class_Oless__eq(_238748, c_Groups_Ozero__class_Ozero(_238748), _238750), c_Orderings_Oord__class_Oless__eq(_238748, c_Groups_Ozero__class_Ozero(_238748), _238754), -(c_Orderings_Oord__class_Oless(_238748, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238748), _238750), _238754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238748), _238752), _238756)))], (2178 ^ _167881) ^ [_239470, _239472, _239474, _239476, _239478] : [class_Rings_Olinordered__semiring__strict(_239470), c_Orderings_Oord__class_Oless(_239470, _239472, _239474), c_Orderings_Oord__class_Oless(_239470, _239476, _239478), c_Orderings_Oord__class_Oless(_239470, c_Groups_Ozero__class_Ozero(_239470), _239474), c_Orderings_Oord__class_Oless__eq(_239470, c_Groups_Ozero__class_Ozero(_239470), _239476), -(c_Orderings_Oord__class_Oless(_239470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239470), _239472), _239476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239470), _239474), _239478)))], (2200 ^ _167881) ^ [_240178, _240180, _240182, _240184] : [class_Rings_Olinordered__ring__strict(_240178), c_Orderings_Oord__class_Oless(_240178, _240180, c_Groups_Ozero__class_Ozero(_240178)), 2207 ^ _167881 : [(2208 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_240178, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240178), _240180), _240182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240178), _240180), _240184)), -(c_Orderings_Oord__class_Oless__eq(_240178, _240184, _240182))], (2214 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_240178, _240184, _240182), -(c_Orderings_Oord__class_Oless__eq(_240178, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240178), _240180), _240182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240178), _240180), _240184)))]]], (2220 ^ _167881) ^ [_240853, _240855, _240857, _240859] : [class_Rings_Olinordered__ring__strict(_240853), c_Orderings_Oord__class_Oless(_240853, c_Groups_Ozero__class_Ozero(_240853), _240855), 2227 ^ _167881 : [(2228 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_240853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240853), _240855), _240857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240853), _240855), _240859)), -(c_Orderings_Oord__class_Oless__eq(_240853, _240857, _240859))], (2234 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_240853, _240857, _240859), -(c_Orderings_Oord__class_Oless__eq(_240853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240853), _240855), _240857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240853), _240855), _240859)))]]], (2240 ^ _167881) ^ [_241514, _241516, _241518] : [class_Rings_Olinordered__ring__strict(_241514), 2243 ^ _167881 : [(2244 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_241514, c_Groups_Oplus__class_Oplus(_241514, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_241514), _241516), _241516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_241514), _241518), _241518)), c_Groups_Ozero__class_Ozero(_241514)), 2247 ^ _167881 : [(2248 ^ _167881) ^ [] : [-(_241516 = c_Groups_Ozero__class_Ozero(_241514))], (2250 ^ _167881) ^ [] : [-(_241518 = c_Groups_Ozero__class_Ozero(_241514))]]], (2252 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_241514, c_Groups_Oplus__class_Oplus(_241514, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_241514), _241516), _241516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_241514), _241518), _241518)), c_Groups_Ozero__class_Ozero(_241514))), _241516 = c_Groups_Ozero__class_Ozero(_241514), _241518 = c_Groups_Ozero__class_Ozero(_241514)]]], (2262 ^ _167881) ^ [_242247, _242249, _242251] : [class_Rings_Olinordered__ring(_242247), -(c_Orderings_Oord__class_Oless__eq(_242247, c_Groups_Ozero__class_Ozero(_242247), c_Groups_Oplus__class_Oplus(_242247, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242247), _242249), _242249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242247), _242251), _242251))))], (2268 ^ _167881) ^ [_242521, _242523, _242525] : [class_Rings_Olinordered__idom(_242521), c_Orderings_Oord__class_Oless__eq(_242521, c_Groups_Ozero__class_Ozero(_242521), _242523), c_Orderings_Oord__class_Oless__eq(_242521, c_Groups_Ozero__class_Ozero(_242521), _242525), c_Orderings_Oord__class_Oless__eq(_242521, _242525, c_Groups_Oone__class_Oone(_242521)), -(c_Orderings_Oord__class_Oless__eq(_242521, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242521), _242525), _242523), _242523))], (2286 ^ _167881) ^ [_243064, _243066, _243068] : [class_Rings_Olinordered__idom(_243064), c_Orderings_Oord__class_Oless__eq(_243064, c_Groups_Ozero__class_Ozero(_243064), _243066), c_Orderings_Oord__class_Oless__eq(_243064, c_Groups_Ozero__class_Ozero(_243064), _243068), c_Orderings_Oord__class_Oless__eq(_243064, _243068, c_Groups_Oone__class_Oone(_243064)), -(c_Orderings_Oord__class_Oless__eq(_243064, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_243064), _243066), _243068), _243066))], (2304 ^ _167881) ^ [_243621, _243623, _243625, _243627] : [class_Rings_Olinordered__semidom(_243621), c_Orderings_Oord__class_Oless(_243621, hAPP(hAPP(c_Power_Opower__class_Opower(_243621), _243623), _243625), hAPP(hAPP(c_Power_Opower__class_Opower(_243621), _243627), _243625)), c_Orderings_Oord__class_Oless__eq(_243621, c_Groups_Ozero__class_Ozero(_243621), _243627), -(c_Orderings_Oord__class_Oless(_243621, _243623, _243627))], (2318 ^ _167881) ^ [_244105, _244107, _244109, _244111] : [class_Rings_Olinordered__semidom(_244105), c_Orderings_Oord__class_Oless(_244105, _244107, _244109), c_Orderings_Oord__class_Oless__eq(_244105, c_Groups_Ozero__class_Ozero(_244105), _244107), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _244111), -(c_Orderings_Oord__class_Oless(_244105, hAPP(hAPP(c_Power_Opower__class_Opower(_244105), _244107), _244111), hAPP(hAPP(c_Power_Opower__class_Opower(_244105), _244109), _244111)))], (2336 ^ _167881) ^ [_244660, _244662] : [class_RealVector_Oreal__normed__vector(_244660), 2339 ^ _167881 : [(2340 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_244660, _244662), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_244662 = c_Groups_Ozero__class_Ozero(_244660))], (2346 ^ _167881) ^ [] : [_244662 = c_Groups_Ozero__class_Ozero(_244660), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_244660, _244662), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (2352 ^ _167881) ^ [_245150, _245152, _245154] : [class_RealVector_Oreal__normed__algebra(_245150), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_245150, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_245150), _245152), _245154)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_245150, _245152)), c_RealVector_Onorm__class_Onorm(_245150, _245154))))], (2358 ^ _167881) ^ [_245426, _245428, _245430] : [class_Rings_Olinordered__semidom(_245426), c_Orderings_Oord__class_Oless(_245426, c_Groups_Oone__class_Oone(_245426), _245428), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _245430), -(c_Orderings_Oord__class_Oless(_245426, c_Groups_Oone__class_Oone(_245426), hAPP(hAPP(c_Power_Opower__class_Opower(_245426), _245428), _245430)))], (2372 ^ _167881) ^ [_245870, _245872, _245874] : [class_RealVector_Oreal__normed__algebra__1(_245870), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_245870, hAPP(hAPP(c_Power_Opower__class_Opower(_245870), _245872), _245874)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_245870, _245872)), _245874)))], (2378 ^ _167881) ^ [_246182, _246184, _246186, _246188, _246190, _246192] : [class_Rings_Olinordered__semiring__1(_246182), c_Orderings_Oord__class_Oless__eq(_246182, _246184, _246186), c_Orderings_Oord__class_Oless__eq(_246182, _246188, _246186), c_Orderings_Oord__class_Oless__eq(_246182, c_Groups_Ozero__class_Ozero(_246182), _246190), c_Orderings_Oord__class_Oless__eq(_246182, c_Groups_Ozero__class_Ozero(_246182), _246192), c_Groups_Oplus__class_Oplus(_246182, _246190, _246192) = c_Groups_Oone__class_Oone(_246182), -(c_Orderings_Oord__class_Oless__eq(_246182, c_Groups_Oplus__class_Oplus(_246182, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_246182), _246190), _246184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_246182), _246192), _246188)), _246186))], (2404 ^ _167881) ^ [_247023, _247025, _247027] : [class_Rings_Olinordered__idom(_247023), -(_247025 = _247027), -(c_Orderings_Oord__class_Oless(_247023, _247025, _247027)), -(c_Orderings_Oord__class_Oless(_247023, _247027, _247025))], (2418 ^ _167881) ^ [_247489, _247491, _247493, _247495, _247497, _247499] : [class_Rings_Olinordered__semiring__1__strict(_247489), c_Orderings_Oord__class_Oless(_247489, _247491, _247493), c_Orderings_Oord__class_Oless(_247489, _247495, _247493), c_Orderings_Oord__class_Oless__eq(_247489, c_Groups_Ozero__class_Ozero(_247489), _247497), c_Orderings_Oord__class_Oless__eq(_247489, c_Groups_Ozero__class_Ozero(_247489), _247499), c_Groups_Oplus__class_Oplus(_247489, _247497, _247499) = c_Groups_Oone__class_Oone(_247489), -(c_Orderings_Oord__class_Oless(_247489, c_Groups_Oplus__class_Oplus(_247489, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_247489), _247497), _247491), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_247489), _247499), _247495)), _247493))], (2444 ^ _167881) ^ [_248330, _248332, _248334] : [class_Rings_Ono__zero__divisors(_248330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248330), _248332), _248334) = c_Groups_Ozero__class_Ozero(_248330), -(_248332 = c_Groups_Ozero__class_Ozero(_248330)), -(_248334 = c_Groups_Ozero__class_Ozero(_248330))], (2458 ^ _167881) ^ [_248773, _248775, _248777] : [class_Rings_Ono__zero__divisors(_248773), -(_248775 = c_Groups_Ozero__class_Ozero(_248773)), -(_248777 = c_Groups_Ozero__class_Ozero(_248773)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248773), _248775), _248777) = c_Groups_Ozero__class_Ozero(_248773)], (2472 ^ _167881) ^ [_249222, _249224, _249226] : [class_Rings_Oring__no__zero__divisors(_249222), 2475 ^ _167881 : [(2486 ^ _167881) ^ [] : [2487 ^ _167881 : [(2488 ^ _167881) ^ [] : [_249224 = c_Groups_Ozero__class_Ozero(_249222)], (2490 ^ _167881) ^ [] : [_249226 = c_Groups_Ozero__class_Ozero(_249222)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249222), _249224), _249226) = c_Groups_Ozero__class_Ozero(_249222))], (2476 ^ _167881) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249222), _249224), _249226) = c_Groups_Ozero__class_Ozero(_249222), -(_249224 = c_Groups_Ozero__class_Ozero(_249222)), -(_249226 = c_Groups_Ozero__class_Ozero(_249222))]]], (2494 ^ _167881) ^ [_249902, _249904] : [class_RealVector_Oreal__normed__algebra(_249902), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249902), _249904), c_Groups_Ozero__class_Ozero(_249902)) = c_Groups_Ozero__class_Ozero(_249902))], (2500 ^ _167881) ^ [_250134, _250136] : [class_RealVector_Oreal__normed__algebra(_250134), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250134), _250136), c_Groups_Ozero__class_Ozero(_250134)) = c_Groups_Ozero__class_Ozero(_250134))], (2506 ^ _167881) ^ [_250366, _250368] : [class_Rings_Omult__zero(_250366), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250366), _250368), c_Groups_Ozero__class_Ozero(_250366)) = c_Groups_Ozero__class_Ozero(_250366))], (2512 ^ _167881) ^ [_250598, _250600] : [class_RealVector_Oreal__normed__algebra(_250598), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250598), c_Groups_Ozero__class_Ozero(_250598)), _250600) = c_Groups_Ozero__class_Ozero(_250598))], (2518 ^ _167881) ^ [_250830, _250832] : [class_RealVector_Oreal__normed__algebra(_250830), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250830), c_Groups_Ozero__class_Ozero(_250830)), _250832) = c_Groups_Ozero__class_Ozero(_250830))], (2524 ^ _167881) ^ [_251062, _251064] : [class_Rings_Omult__zero(_251062), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251062), c_Groups_Ozero__class_Ozero(_251062)), _251064) = c_Groups_Ozero__class_Ozero(_251062))], (2530 ^ _167881) ^ [_251280] : [class_Rings_Ozero__neq__one(_251280), c_Groups_Ozero__class_Ozero(_251280) = c_Groups_Oone__class_Oone(_251280)], (2536 ^ _167881) ^ [_251477] : [class_Rings_Ozero__neq__one(_251477), c_Groups_Oone__class_Oone(_251477) = c_Groups_Ozero__class_Ozero(_251477)], (2542 ^ _167881) ^ [_251730, _251732, _251734, _251736, _251738] : [class_Rings_Osemiring(_251730), -(c_Groups_Oplus__class_Oplus(_251730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251730), _251732), _251734), c_Groups_Oplus__class_Oplus(_251730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251730), _251736), _251734), _251738)) = c_Groups_Oplus__class_Oplus(_251730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251730), c_Groups_Oplus__class_Oplus(_251730, _251732, _251736)), _251734), _251738))], (2548 ^ _167881) ^ [_252064, _252066, _252068, _252070] : [class_RealVector_Oreal__normed__algebra(_252064), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252064), c_Groups_Oplus__class_Oplus(_252064, _252066, _252068)), _252070) = c_Groups_Oplus__class_Oplus(_252064, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252064), _252066), _252070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252064), _252068), _252070)))], (2554 ^ _167881) ^ [_252376, _252378, _252380, _252382] : [class_RealVector_Oreal__normed__algebra(_252376), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252376), c_Groups_Oplus__class_Oplus(_252376, _252378, _252380)), _252382) = c_Groups_Oplus__class_Oplus(_252376, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252376), _252378), _252382), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252376), _252380), _252382)))], (2560 ^ _167881) ^ [_252688, _252690, _252692, _252694] : [class_Rings_Ocomm__semiring(_252688), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252688), c_Groups_Oplus__class_Oplus(_252688, _252690, _252692)), _252694) = c_Groups_Oplus__class_Oplus(_252688, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252688), _252690), _252694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252688), _252692), _252694)))], (2566 ^ _167881) ^ [_253000, _253002, _253004, _253006] : [class_RealVector_Oreal__normed__algebra(_253000), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253000), _253002), c_Groups_Oplus__class_Oplus(_253000, _253004, _253006)) = c_Groups_Oplus__class_Oplus(_253000, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253000), _253002), _253004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253000), _253002), _253006)))], (2572 ^ _167881) ^ [_253312, _253314, _253316, _253318] : [class_RealVector_Oreal__normed__algebra(_253312), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253312), _253314), c_Groups_Oplus__class_Oplus(_253312, _253316, _253318)) = c_Groups_Oplus__class_Oplus(_253312, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253312), _253314), _253316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253312), _253314), _253318)))], (2578 ^ _167881) ^ [_253610, _253612, _253614] : [class_Rings_Oring__1__no__zero__divisors(_253610), -(_253612 = c_Groups_Ozero__class_Ozero(_253610)), hAPP(hAPP(c_Power_Opower__class_Opower(_253610), _253612), _253614) = c_Groups_Ozero__class_Ozero(_253610)], (2588 ^ _167881) ^ [_253959, _253961, _253963] : [class_Power_Opower(_253959), class_Rings_Omult__zero(_253959), class_Rings_Ono__zero__divisors(_253959), class_Rings_Ozero__neq__one(_253959), 2603 ^ _167881 : [(2604 ^ _167881) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_253959), _253961), _253963) = c_Groups_Ozero__class_Ozero(_253959), 2607 ^ _167881 : [(2608 ^ _167881) ^ [] : [-(_253961 = c_Groups_Ozero__class_Ozero(_253959))], (2610 ^ _167881) ^ [] : [_253963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2612 ^ _167881) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_253959), _253961), _253963) = c_Groups_Ozero__class_Ozero(_253959)), _253961 = c_Groups_Ozero__class_Ozero(_253959), -(_253963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2622 ^ _167881) ^ [_254942, _254944, _254946, _254948] : [class_Groups_Ocomm__monoid__mult(_254942), -(hAPP(hAPP(c_Power_Opower__class_Opower(_254942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254942), _254944), _254946)), _254948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254942), hAPP(hAPP(c_Power_Opower__class_Opower(_254942), _254944), _254948)), hAPP(hAPP(c_Power_Opower__class_Opower(_254942), _254946), _254948)))], (2628 ^ _167881) ^ [_255256, _255258, _255260] : [class_Groups_Omonoid__mult(_255256), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_255256), hAPP(hAPP(c_Power_Opower__class_Opower(_255256), _255258), _255260)), _255258) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_255256), _255258), hAPP(hAPP(c_Power_Opower__class_Opower(_255256), _255258), _255260)))], (2634 ^ _167881) ^ [_255534, _255536] : [class_Groups_Omonoid__mult(_255534), -(hAPP(hAPP(c_Power_Opower__class_Opower(_255534), c_Groups_Oone__class_Oone(_255534)), _255536) = c_Groups_Oone__class_Oone(_255534))], (2640 ^ _167881) ^ [_255766, _255768] : [class_Groups_Omonoid__mult(_255766), -(hAPP(hAPP(c_Power_Opower__class_Opower(_255766), _255768), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _255768)], (2646 ^ _167881) ^ [_256018, _256020, _256022, _256024] : [class_Rings_Olinordered__ring__strict(_256018), c_Orderings_Oord__class_Oless(_256018, _256020, _256022), c_Orderings_Oord__class_Oless(_256018, _256024, c_Groups_Ozero__class_Ozero(_256018)), -(c_Orderings_Oord__class_Oless(_256018, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_256018), _256024), _256022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_256018), _256024), _256020)))], (2660 ^ _167881) ^ [_256502, _256504, _256506, _256508] : [class_Rings_Olinordered__ring__strict(_256502), c_Orderings_Oord__class_Oless(_256502, _256504, _256506), c_Orderings_Oord__class_Oless(_256502, _256508, c_Groups_Ozero__class_Ozero(_256502)), -(c_Orderings_Oord__class_Oless(_256502, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_256502), _256506), _256508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_256502), _256504), _256508)))], (2674 ^ _167881) ^ [_256986, _256988, _256990, _256992] : [class_Rings_Olinordered__comm__semiring__strict(_256986), c_Orderings_Oord__class_Oless(_256986, _256988, _256990), c_Orderings_Oord__class_Oless(_256986, c_Groups_Ozero__class_Ozero(_256986), _256992), -(c_Orderings_Oord__class_Oless(_256986, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_256986), _256992), _256988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_256986), _256992), _256990)))], (2688 ^ _167881) ^ [_257470, _257472, _257474, _257476] : [class_Rings_Olinordered__semiring__strict(_257470), c_Orderings_Oord__class_Oless(_257470, _257472, _257474), c_Orderings_Oord__class_Oless(_257470, c_Groups_Ozero__class_Ozero(_257470), _257476), -(c_Orderings_Oord__class_Oless(_257470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257470), _257476), _257472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257470), _257476), _257474)))], (2702 ^ _167881) ^ [_257954, _257956, _257958, _257960] : [class_Rings_Olinordered__semiring__strict(_257954), c_Orderings_Oord__class_Oless(_257954, _257956, _257958), c_Orderings_Oord__class_Oless(_257954, c_Groups_Ozero__class_Ozero(_257954), _257960), -(c_Orderings_Oord__class_Oless(_257954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257954), _257956), _257960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257954), _257958), _257960)))], (2716 ^ _167881) ^ [_258424, _258426, _258428] : [class_Rings_Olinordered__ring__strict(_258424), c_Orderings_Oord__class_Oless(_258424, _258426, c_Groups_Ozero__class_Ozero(_258424)), c_Orderings_Oord__class_Oless(_258424, _258428, c_Groups_Ozero__class_Ozero(_258424)), -(c_Orderings_Oord__class_Oless(_258424, c_Groups_Ozero__class_Ozero(_258424), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258424), _258426), _258428)))], (2730 ^ _167881) ^ [_258872, _258874, _258876] : [class_Rings_Olinordered__semiring__strict(_258872), c_Orderings_Oord__class_Oless(_258872, _258874, c_Groups_Ozero__class_Ozero(_258872)), c_Orderings_Oord__class_Oless(_258872, c_Groups_Ozero__class_Ozero(_258872), _258876), -(c_Orderings_Oord__class_Oless(_258872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258872), _258874), _258876), c_Groups_Ozero__class_Ozero(_258872)))], (2744 ^ _167881) ^ [_259334, _259336, _259338, _259340] : [class_Rings_Olinordered__ring__strict(_259334), c_Orderings_Oord__class_Oless(_259334, _259336, c_Groups_Ozero__class_Ozero(_259334)), 2751 ^ _167881 : [(2752 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_259334, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259334), _259336), _259338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259334), _259336), _259340)), -(c_Orderings_Oord__class_Oless(_259334, _259340, _259338))], (2758 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_259334, _259340, _259338), -(c_Orderings_Oord__class_Oless(_259334, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259334), _259336), _259338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259334), _259336), _259340)))]]], (2764 ^ _167881) ^ [_259995, _259997, _259999] : [class_Rings_Olinordered__semiring__strict(_259995), c_Orderings_Oord__class_Oless(_259995, c_Groups_Ozero__class_Ozero(_259995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259995), _259997), _259999)), c_Orderings_Oord__class_Oless(_259995, c_Groups_Ozero__class_Ozero(_259995), _259999), -(c_Orderings_Oord__class_Oless(_259995, c_Groups_Ozero__class_Ozero(_259995), _259997))], (2778 ^ _167881) ^ [_260443, _260445, _260447] : [class_Rings_Olinordered__semiring__strict(_260443), c_Orderings_Oord__class_Oless(_260443, c_Groups_Ozero__class_Ozero(_260443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260443), _260445), _260447)), c_Orderings_Oord__class_Oless(_260443, c_Groups_Ozero__class_Ozero(_260443), _260445), -(c_Orderings_Oord__class_Oless(_260443, c_Groups_Ozero__class_Ozero(_260443), _260447))], (2792 ^ _167881) ^ [_260891, _260893, _260895] : [class_Rings_Olinordered__semiring__strict(_260891), c_Orderings_Oord__class_Oless(_260891, c_Groups_Ozero__class_Ozero(_260891), _260893), c_Orderings_Oord__class_Oless(_260891, _260895, c_Groups_Ozero__class_Ozero(_260891)), -(c_Orderings_Oord__class_Oless(_260891, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260891), _260895), _260893), c_Groups_Ozero__class_Ozero(_260891)))], (2806 ^ _167881) ^ [_261339, _261341, _261343] : [class_Rings_Olinordered__semiring__strict(_261339), c_Orderings_Oord__class_Oless(_261339, c_Groups_Ozero__class_Ozero(_261339), _261341), c_Orderings_Oord__class_Oless(_261339, _261343, c_Groups_Ozero__class_Ozero(_261339)), -(c_Orderings_Oord__class_Oless(_261339, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_261339), _261341), _261343), c_Groups_Ozero__class_Ozero(_261339)))], (2820 ^ _167881) ^ [_261787, _261789, _261791] : [class_Rings_Olinordered__semiring__strict(_261787), c_Orderings_Oord__class_Oless(_261787, c_Groups_Ozero__class_Ozero(_261787), _261789), c_Orderings_Oord__class_Oless(_261787, c_Groups_Ozero__class_Ozero(_261787), _261791), -(c_Orderings_Oord__class_Oless(_261787, c_Groups_Ozero__class_Ozero(_261787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_261787), _261789), _261791)))], (2834 ^ _167881) ^ [_262249, _262251, _262253, _262255] : [class_Rings_Olinordered__ring__strict(_262249), c_Orderings_Oord__class_Oless(_262249, c_Groups_Ozero__class_Ozero(_262249), _262251), 2841 ^ _167881 : [(2842 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_262249, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262249), _262251), _262253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262249), _262251), _262255)), -(c_Orderings_Oord__class_Oless(_262249, _262253, _262255))], (2848 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_262249, _262253, _262255), -(c_Orderings_Oord__class_Oless(_262249, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262249), _262251), _262253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262249), _262251), _262255)))]]], (2854 ^ _167881) ^ [_262924, _262926, _262928, _262930] : [class_Rings_Olinordered__ring__strict(_262924), 2857 ^ _167881 : [(2858 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_262924, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262924), _262926), _262928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262924), _262926), _262930)), 2863 ^ _167881 : [(2864 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_262924, c_Groups_Ozero__class_Ozero(_262924), _262926))], (2866 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_262924, _262928, _262930))]], 2867 ^ _167881 : [(2868 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_262924, _262926, c_Groups_Ozero__class_Ozero(_262924)))], (2870 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_262924, _262930, _262928))]]], (2872 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_262924, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262924), _262926), _262928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262924), _262926), _262930))), 2873 ^ _167881 : [(2874 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_262924, c_Groups_Ozero__class_Ozero(_262924), _262926), c_Orderings_Oord__class_Oless(_262924, _262928, _262930)], (2880 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_262924, _262926, c_Groups_Ozero__class_Ozero(_262924)), c_Orderings_Oord__class_Oless(_262924, _262930, _262928)]]]]], (2888 ^ _167881) ^ [_264027, _264029, _264031, _264033] : [class_Rings_Olinordered__ring__strict(_264027), 2891 ^ _167881 : [(2892 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_264027, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_264027), _264029), _264031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_264027), _264033), _264031)), 2897 ^ _167881 : [(2898 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_264027, c_Groups_Ozero__class_Ozero(_264027), _264031))], (2900 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_264027, _264029, _264033))]], 2901 ^ _167881 : [(2902 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_264027, _264031, c_Groups_Ozero__class_Ozero(_264027)))], (2904 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_264027, _264033, _264029))]]], (2906 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_264027, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_264027), _264029), _264031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_264027), _264033), _264031))), 2907 ^ _167881 : [(2908 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_264027, c_Groups_Ozero__class_Ozero(_264027), _264031), c_Orderings_Oord__class_Oless(_264027, _264029, _264033)], (2914 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_264027, _264031, c_Groups_Ozero__class_Ozero(_264027)), c_Orderings_Oord__class_Oless(_264027, _264033, _264029)]]]]], (2922 ^ _167881) ^ [_265102, _265104] : [class_Rings_Olinordered__ring(_265102), c_Orderings_Oord__class_Oless(_265102, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265102), _265104), _265104), c_Groups_Ozero__class_Ozero(_265102))], (2928 ^ _167881) ^ [_265361, _265363, _265365, _265367] : [class_Rings_Olinordered__semidom(_265361), c_Orderings_Oord__class_Oless(_265361, c_Groups_Ozero__class_Ozero(_265361), _265363), c_Orderings_Oord__class_Oless(_265361, _265365, _265367), -(c_Orderings_Oord__class_Oless(_265361, _265365, c_Groups_Oplus__class_Oplus(_265361, _265363, _265367)))], (2942 ^ _167881) ^ [_265807, _265809, _265811] : [class_Rings_Olinordered__ring__strict(_265807), 2945 ^ _167881 : [(2946 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_265807, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265807), _265809), _265809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265807), _265811), _265811)) = c_Groups_Ozero__class_Ozero(_265807), 2949 ^ _167881 : [(2950 ^ _167881) ^ [] : [-(_265809 = c_Groups_Ozero__class_Ozero(_265807))], (2952 ^ _167881) ^ [] : [-(_265811 = c_Groups_Ozero__class_Ozero(_265807))]]], (2954 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(_265807, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265807), _265809), _265809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265807), _265811), _265811)) = c_Groups_Ozero__class_Ozero(_265807)), _265809 = c_Groups_Ozero__class_Ozero(_265807), _265811 = c_Groups_Ozero__class_Ozero(_265807)]]], (2964 ^ _167881) ^ [_266509] : [class_Rings_Olinordered__semidom(_266509), -(c_Orderings_Oord__class_Oless(_266509, c_Groups_Ozero__class_Ozero(_266509), c_Groups_Oone__class_Oone(_266509)))], (2970 ^ _167881) ^ [_266707] : [class_Rings_Olinordered__semidom(_266707), c_Orderings_Oord__class_Oless(_266707, c_Groups_Oone__class_Oone(_266707), c_Groups_Ozero__class_Ozero(_266707))], (2976 ^ _167881) ^ [_266934, _266936, _266938] : [class_Rings_Olinordered__semidom(_266934), c_Orderings_Oord__class_Oless(_266934, c_Groups_Oone__class_Oone(_266934), _266936), c_Orderings_Oord__class_Oless(_266934, c_Groups_Oone__class_Oone(_266934), _266938), -(c_Orderings_Oord__class_Oless(_266934, c_Groups_Oone__class_Oone(_266934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266934), _266936), _266938)))], (2990 ^ _167881) ^ [_267382, _267384, _267386] : [class_Rings_Olinordered__semidom(_267382), c_Orderings_Oord__class_Oless(_267382, c_Groups_Ozero__class_Ozero(_267382), _267384), -(c_Orderings_Oord__class_Oless(_267382, c_Groups_Ozero__class_Ozero(_267382), hAPP(hAPP(c_Power_Opower__class_Opower(_267382), _267384), _267386)))], (3000 ^ _167881) ^ [_267717, _267719] : [class_Rings_Olinordered__semidom(_267717), -(c_Orderings_Oord__class_Oless(_267717, _267719, c_Groups_Oplus__class_Oplus(_267717, _267719, c_Groups_Oone__class_Oone(_267717))))], (3006 ^ _167881) ^ [_267939, _267941] : [class_Power_Opower(_267939), class_Rings_Osemiring__0(_267939), 3013 ^ _167881 : [(3014 ^ _167881) ^ [] : [_267941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_267939), c_Groups_Ozero__class_Ozero(_267939)), _267941) = c_Groups_Oone__class_Oone(_267939))], (3020 ^ _167881) ^ [] : [-(_267941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_267939), c_Groups_Ozero__class_Ozero(_267939)), _267941) = c_Groups_Ozero__class_Ozero(_267939))]]], (3026 ^ _167881) ^ [_268568, _268570, _268572, _268574] : [class_Rings_Olinordered__semidom(_268568), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _268570, _268572), c_Orderings_Oord__class_Oless(_268568, c_Groups_Oone__class_Oone(_268568), _268574), -(c_Orderings_Oord__class_Oless(_268568, hAPP(hAPP(c_Power_Opower__class_Opower(_268568), _268574), _268570), hAPP(hAPP(c_Power_Opower__class_Opower(_268568), _268574), _268572)))], (3040 ^ _167881) ^ [_269052, _269054, _269056, _269058] : [class_Rings_Olinordered__semidom(_269052), c_Orderings_Oord__class_Oless(_269052, c_Groups_Oone__class_Oone(_269052), _269054), c_Orderings_Oord__class_Oless(_269052, hAPP(hAPP(c_Power_Opower__class_Opower(_269052), _269054), _269056), hAPP(hAPP(c_Power_Opower__class_Opower(_269052), _269054), _269058)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _269056, _269058))], (3054 ^ _167881) ^ [_269536, _269538, _269540, _269542] : [class_Rings_Olinordered__semidom(_269536), c_Orderings_Oord__class_Oless(_269536, c_Groups_Oone__class_Oone(_269536), _269538), 3061 ^ _167881 : [(3062 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_269536, hAPP(hAPP(c_Power_Opower__class_Opower(_269536), _269538), _269540), hAPP(hAPP(c_Power_Opower__class_Opower(_269536), _269538), _269542)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _269540, _269542))], (3068 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _269540, _269542), -(c_Orderings_Oord__class_Oless(_269536, hAPP(hAPP(c_Power_Opower__class_Opower(_269536), _269538), _269540), hAPP(hAPP(c_Power_Opower__class_Opower(_269536), _269538), _269542)))]]], (3074 ^ _167881) ^ [_270211, _270213, _270215, _270217] : [class_Rings_Olinordered__semidom(_270211), c_Orderings_Oord__class_Oless(_270211, c_Groups_Oone__class_Oone(_270211), _270213), 3081 ^ _167881 : [(3082 ^ _167881) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_270211), _270213), _270215) = hAPP(hAPP(c_Power_Opower__class_Opower(_270211), _270213), _270217), -(_270215 = _270217)], (3088 ^ _167881) ^ [] : [_270215 = _270217, -(hAPP(hAPP(c_Power_Opower__class_Opower(_270211), _270213), _270215) = hAPP(hAPP(c_Power_Opower__class_Opower(_270211), _270213), _270217))]]], (3094 ^ _167881) ^ [_270838] : [class_RealVector_Oreal__normed__vector(_270838), -(c_RealVector_Onorm__class_Onorm(_270838, c_Groups_Ozero__class_Ozero(_270838)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3100 ^ _167881) ^ [_271050, _271052] : [class_RealVector_Oreal__normed__vector(_271050), 3103 ^ _167881 : [(3104 ^ _167881) ^ [] : [c_RealVector_Onorm__class_Onorm(_271050, _271052) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_271052 = c_Groups_Ozero__class_Ozero(_271050))], (3110 ^ _167881) ^ [] : [_271052 = c_Groups_Ozero__class_Ozero(_271050), -(c_RealVector_Onorm__class_Onorm(_271050, _271052) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (3116 ^ _167881) ^ [_271551, _271553, _271555, _271557] : [class_Groups_Omonoid__mult(_271551), -(hAPP(hAPP(c_Power_Opower__class_Opower(_271551), _271553), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _271555, _271557)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271551), hAPP(hAPP(c_Power_Opower__class_Opower(_271551), _271553), _271555)), hAPP(hAPP(c_Power_Opower__class_Opower(_271551), _271553), _271557)))], (3122 ^ _167881) ^ [_271885, _271887, _271889, _271891, _271893] : [class_RealVector_Oreal__normed__vector(_271885), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_271885, _271887), _271889), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_271885, _271891), _271893), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_271885, c_Groups_Oplus__class_Oplus(_271885, _271887, _271891)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _271889, _271893)))], (3136 ^ _167881) ^ [_272367, _272369, _272371] : [class_RealVector_Oreal__normed__div__algebra(_272367), -(c_RealVector_Onorm__class_Onorm(_272367, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272367), _272369), _272371)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_272367, _272369)), c_RealVector_Onorm__class_Onorm(_272367, _272371)))], (3142 ^ _167881) ^ [_272627, _272629] : [class_RealVector_Oreal__normed__vector(_272627), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_272627, _272629), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3148 ^ _167881) ^ [_272830] : [class_RealVector_Oreal__normed__algebra__1(_272830), -(c_RealVector_Onorm__class_Onorm(_272830, c_Groups_Oone__class_Oone(_272830)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (3154 ^ _167881) ^ [_273056, _273058, _273060] : [class_RealVector_Oreal__normed__div__algebra(_273056), -(c_RealVector_Onorm__class_Onorm(_273056, hAPP(hAPP(c_Power_Opower__class_Opower(_273056), _273058), _273060)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_273056, _273058)), _273060))], (3161 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3159 ^ []))], (3163 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 3159 ^ [], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (3165 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 3159 ^ [], c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (3167 ^ _167881) ^ [_273541, _273543, _273545] : [class_RealVector_Oreal__normed__div__algebra(_273541), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _273543, c_RealVector_Onorm__class_Onorm(_273541, _273545)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _273543), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_273541, c_Rings_Oinverse__class_Oinverse(_273541, _273545)), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _273543)))], (3181 ^ _167881) ^ [_273999, _274001, _274003, _274005] : [class_RealVector_Oreal__normed__vector(_273999), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _274001, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_273999, _274003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _274001), c_RealVector_Onorm__class_Onorm(_273999, _274005))), -(_274003 = c_Groups_Ozero__class_Ozero(_273999))], (3195 ^ _167881) ^ [_274415] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _274415, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3197 ^ _167881) ^ [_274523, _274525] : [class_Fields_Olinordered__field(_274523), c_Orderings_Oord__class_Oless(_274523, c_Groups_Ozero__class_Ozero(_274523), _274525), c_Orderings_Oord__class_Oless__eq(_274523, _274525, c_Groups_Oone__class_Oone(_274523)), -(c_Orderings_Oord__class_Oless__eq(_274523, c_Groups_Oone__class_Oone(_274523), c_Rings_Oinverse__class_Oinverse(_274523, _274525)))], (3211 ^ _167881) ^ [_274933, _274935] : [class_Fields_Olinordered__field__inverse__zero(_274933), 3214 ^ _167881 : [(3225 ^ _167881) ^ [] : [3226 ^ _167881 : [(3227 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_274933, _274935, c_Groups_Ozero__class_Ozero(_274933))], (3229 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_274933, c_Groups_Oone__class_Oone(_274933), _274935)]], -(c_Orderings_Oord__class_Oless(_274933, c_Rings_Oinverse__class_Oinverse(_274933, _274935), c_Groups_Oone__class_Oone(_274933)))], (3215 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_274933, c_Rings_Oinverse__class_Oinverse(_274933, _274935), c_Groups_Oone__class_Oone(_274933)), -(c_Orderings_Oord__class_Oless__eq(_274933, _274935, c_Groups_Ozero__class_Ozero(_274933))), -(c_Orderings_Oord__class_Oless(_274933, c_Groups_Oone__class_Oone(_274933), _274935))]]], (3233 ^ _167881) ^ [_275585, _275587] : [class_Fields_Olinordered__field__inverse__zero(_275585), 3236 ^ _167881 : [(3237 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_275585, c_Groups_Oone__class_Oone(_275585), c_Rings_Oinverse__class_Oinverse(_275585, _275587)), 3240 ^ _167881 : [(3241 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_275585, c_Groups_Ozero__class_Ozero(_275585), _275587))], (3243 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_275585, _275587, c_Groups_Oone__class_Oone(_275585)))]]], (3245 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_275585, c_Groups_Oone__class_Oone(_275585), c_Rings_Oinverse__class_Oinverse(_275585, _275587))), c_Orderings_Oord__class_Oless(_275585, c_Groups_Ozero__class_Ozero(_275585), _275587), c_Orderings_Oord__class_Oless__eq(_275585, _275587, c_Groups_Oone__class_Oone(_275585))]]], (3255 ^ _167881) ^ [_276223] : [-(_276223 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _276223)), _276223) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (3261 ^ _167881) ^ [_276476, _276478, _276480, _276482] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _276476), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _276478), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _276478), _276480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _276476), _276482)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _276476)), _276480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _276478)), _276482)))], (3275 ^ _167881) ^ [_276988, _276990, _276992, _276994] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _276988), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _276990), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _276990), _276992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _276988), _276994)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _276992), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _276988)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _276994), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _276990))))], (3289 ^ _167881) ^ [_277486, _277488, _277490] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _277486), 3292 ^ _167881 : [(3293 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _277486), _277488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _277486), _277490)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _277488, _277490))], (3299 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _277488, _277490), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _277486), _277488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _277486), _277490)))]]], (3305 ^ _167881) ^ [_277977] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _277977))], (3307 ^ _167881) ^ [_278056] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278056, _278056))], (3309 ^ _167881) ^ [_278135] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278135), _278135)))], (3311 ^ _167881) ^ [_278220] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278220, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278220), _278220))))], (3313 ^ _167881) ^ [_278325, _278327] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278325), _278327) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278327), _278325))], (3315 ^ _167881) ^ [_278446, _278448] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278446, _278448)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278448, _278446))], (3321 ^ _167881) ^ [_278660, _278662, _278664] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278660), _278662)), _278664) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278662), _278664)))], (3323 ^ _167881) ^ [_278795, _278797] : [_278795 = _278797, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278795, _278797))], (3329 ^ _167881) ^ [_279021, _279023, _279025] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279021, _279023), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _279021), _279025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _279023), _279025)))], (3335 ^ _167881) ^ [_279279, _279281, _279283] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279279, _279281), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _279283), _279279), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _279283), _279281)))], (3341 ^ _167881) ^ [_279537, _279539, _279541] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279537, _279539), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279539, _279541), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279537, _279541))], (3351 ^ _167881) ^ [_279852, _279854] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279852, _279854), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279854, _279852), -(_279852 = _279854)], (3361 ^ _167881) ^ [_280183, _280185, _280187, _280189] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _280183, _280185), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _280187, _280189), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _280183), _280187), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _280185), _280189)))], (3371 ^ _167881) ^ [_280547] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _280547, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_280547 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3377 ^ _167881) ^ [_280705] : [_280705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _280705, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3383 ^ _167881) ^ [_280884] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _280884))], (3385 ^ _167881) ^ [_280992, _280994] : [3386 ^ _167881 : [(3387 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _280992, _280994)], (3389 ^ _167881) ^ [] : [_280992 = _280994]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _280992, _280994))], (3393 ^ _167881) ^ [_281280, _281282] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _281280, _281282), -(_281280 = _281282), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _281280, _281282))], (3403 ^ _167881) ^ [_281586, _281588] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _281586, _281588), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _281586, _281588))], (3419 ^ _167881) ^ [_282085, _282087] : [3420 ^ _167881 : [(3421 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282085, _282087)], (3423 ^ _167881) ^ [] : [_282085 = _282087]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _282085, _282087))], (3409 ^ _167881) ^ [_281829, _281831] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _281829, _281831), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _281829, _281831)), -(_281829 = _281831)], (3427 ^ _167881) ^ [_282404, _282406] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282404, _282406), 3430 ^ _167881 : [(3431 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _282404, _282406))], (3433 ^ _167881) ^ [] : [_282404 = _282406]]], (3435 ^ _167881) ^ [_282646, _282648] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _282646, _282648)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _282646, _282648), -(_282646 = _282648)], (3445 ^ _167881) ^ [_282939, _282941] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _282939, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _282941, _282939)))], (3447 ^ _167881) ^ [_283038, _283040] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283038, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _283038, _283040)))], (3449 ^ _167881) ^ [_283181, _283183] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283181, _283183), -(_283183 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _283181, 3452 ^ [_283181, _283183]))], (3456 ^ _167881) ^ [_283414, _283416] : [3457 ^ _167881 : [(3458 ^ _167881) ^ [_283489] : [_283416 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _283414, _283489)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283414, _283416))], (3462 ^ _167881) ^ [_283687, _283689] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283687, _283689), -(_283689 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _283687, 3465 ^ [_283687, _283689]))], (3469 ^ _167881) ^ [_283920, _283922] : [3470 ^ _167881 : [(3471 ^ _167881) ^ [_283995] : [_283922 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _283920, _283995)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283920, _283922))], (3475 ^ _167881) ^ [_284207, _284209, _284211] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _284207, _284209), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _284207, _284211)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _284209, _284211))], (3481 ^ _167881) ^ [_284395, _284397, _284399] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _284397, _284399), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _284395, _284397), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _284395, _284399)))], (3487 ^ _167881) ^ [_284647, _284649, _284651] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _284647, _284649), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _284647, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _284649, _284651)))], (3493 ^ _167881) ^ [_284889, _284891, _284893] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _284889, _284891), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _284889, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _284893, _284891)))], (3499 ^ _167881) ^ [_285131, _285133, _285135] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _285131, _285133), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _285131, _285135), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _285133, _285135)))], (3505 ^ _167881) ^ [_285395, _285397, _285399, _285401] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _285395, _285397), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _285399, _285401), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _285395, _285399), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _285397, _285401)))], (3515 ^ _167881) ^ [_285750, _285752, _285754] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _285750, _285752), _285754), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _285752, _285754))], (3521 ^ _167881) ^ [_285992, _285994, _285996] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _285992, _285994), _285996), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _285992, _285996))], (3527 ^ _167881) ^ [_286234, _286236, _286238] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _286234, _286236), _286238), 3530 ^ _167881 : [(3531 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _286234, _286238))], (3533 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _286236, _286238))]]], (3545 ^ _167881) ^ [_286879, _286881, _286883] : [3546 ^ _167881 : [(3547 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _286881))], (3549 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _286879, _286883)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286879), _286881), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286883), _286881)))], (3535 ^ _167881) ^ [_286588, _286590, _286592] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286588), _286590), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286592), _286590)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _286590), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _286588, _286592))], (3563 ^ _167881) ^ [_287538, _287540, _287542] : [3564 ^ _167881 : [(3565 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _287538))], (3567 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _287540, _287542)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287538), _287540), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287538), _287542)))], (3553 ^ _167881) ^ [_287247, _287249, _287251] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287247), _287249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287247), _287251)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _287247), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _287249, _287251))], (3581 ^ _167881) ^ [_288192, _288194, _288196] : [3582 ^ _167881 : [(3583 ^ _167881) ^ [] : [_288192 = _288196], (3585 ^ _167881) ^ [] : [_288194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _288192), _288194) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _288196), _288194))], (3571 ^ _167881) ^ [_287906, _287908, _287910] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287906), _287908) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287910), _287908), -(_287906 = _287910), -(_287908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3599 ^ _167881) ^ [_288839, _288841, _288843] : [3600 ^ _167881 : [(3601 ^ _167881) ^ [] : [_288841 = _288843], (3603 ^ _167881) ^ [] : [_288839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _288839), _288841) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _288839), _288843))], (3589 ^ _167881) ^ [_288553, _288555, _288557] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _288553), _288555) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _288553), _288557), -(_288555 = _288557), -(_288553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3617 ^ _167881) ^ [_289450, _289452] : [3618 ^ _167881 : [(3619 ^ _167881) ^ [] : [_289450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3621 ^ _167881) ^ [] : [_289452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _289450), _289452) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3607 ^ _167881) ^ [_289186, _289188] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _289186), _289188) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_289186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_289188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3625 ^ _167881) ^ [_289719] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _289719), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3627 ^ _167881) ^ [_289803] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _289803) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3629 ^ _167881) ^ [_289913, _289915] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _289913, _289915), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _289915, _289913), -(_289913 = _289915)], (3639 ^ _167881) ^ [_290230, _290232, _290234] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290230, _290232), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290232, _290234), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290230, _290234))], (3649 ^ _167881) ^ [_290559, _290561, _290563] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290559, _290561), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _290563, _290559), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _290563, _290561)))], (3655 ^ _167881) ^ [_290795, _290797] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290795, _290797)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290797, _290795))], (3661 ^ _167881) ^ [_290981] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290981, _290981))], (3663 ^ _167881) ^ [_291103, _291105, _291107] : [3664 ^ _167881 : [(3665 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291103, _291105))], (3667 ^ _167881) ^ [] : [hBOOL(hAPP(hAPP(_291107, _291105), _291103))]], 3670 ^ _167881 : [(3671 ^ _167881) ^ [] : [-(_291103 = _291105)], (3673 ^ _167881) ^ [] : [hBOOL(hAPP(hAPP(_291107, _291105), _291103))]], 3676 ^ _167881 : [(3677 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291105, _291103))], (3679 ^ _167881) ^ [] : [hBOOL(hAPP(hAPP(_291107, _291105), _291103))]], -(hBOOL(hAPP(hAPP(_291107, _291105), _291103)))], (3683 ^ _167881) ^ [_291780, _291782] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291780, _291782), _291780 = _291782], (3689 ^ _167881) ^ [_291993, _291995] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291993, _291995), _291995 = _291993], (3695 ^ _167881) ^ [_292176] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292176, _292176)], (3697 ^ _167881) ^ [_292284, _292286] : [-(_292284 = _292286), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292284, _292286)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292286, _292284))], (3717 ^ _167881) ^ [_292881, _292883] : [3718 ^ _167881 : [(3719 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292881, _292883)], (3721 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292883, _292881)]], _292881 = _292883], (3707 ^ _167881) ^ [_292622, _292624] : [-(_292622 = _292624), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292622, _292624)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292624, _292622))], (3725 ^ _167881) ^ [_293142] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293142, _293142)], (3727 ^ _167881) ^ [_293235, _293237] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293235, _293237) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293237, _293235))], (3729 ^ _167881) ^ [_293351, _293353, _293355] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293351, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293353, _293355)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293353, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293351, _293355)))], (3731 ^ _167881) ^ [_293477, _293479, _293481] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293477, _293479), _293481) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293477, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293479, _293481)))], (3733 ^ _167881) ^ [_293647, _293649, _293651] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293647, _293649) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293647, _293651), -(_293649 = _293651)], (3739 ^ _167881) ^ [_293831, _293833, _293835] : [_293833 = _293835, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293831, _293833) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _293831, _293835))], (3745 ^ _167881) ^ [_294108, _294110, _294112] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _294108, _294110) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _294112, _294110), -(_294108 = _294112)], (3751 ^ _167881) ^ [_294292, _294294, _294296] : [_294292 = _294296, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _294292, _294294) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _294296, _294294))], (3757 ^ _167881) ^ [_294525, _294527, _294529] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _294525), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _294527, _294529)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _294525), _294527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _294525), _294529)))], (3759 ^ _167881) ^ [_294661, _294663, _294665] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _294661, _294663)), _294665) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _294661), _294665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _294663), _294665)))], (3761 ^ _167881) ^ [_294783, _294785] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _294783), _294785) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _294785), _294783))], (3763 ^ _167881) ^ [_294903, _294905, _294907] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _294903), _294905)), _294907) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _294903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _294905), _294907)))], (3765 ^ _167881) ^ [_295037, _295039, _295041] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _295037, _295039)), _295041) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _295037), _295041), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _295039), _295041)))], (3767 ^ _167881) ^ [_295145] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _295145) = _295145)], (3769 ^ _167881) ^ [_295284, _295286] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _295284), _295286), 3772 ^ _167881 : [(3773 ^ _167881) ^ [] : [-(_295284 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (3775 ^ _167881) ^ [] : [-(_295286 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (3777 ^ _167881) ^ [_295533, _295535] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _295533), _295535)), _295533 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _295535 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (3787 ^ _167881) ^ [_295817] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _295817), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _295817)], (3789 ^ _167881) ^ [_295959, _295961] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _295959), _295961) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 3792 ^ _167881 : [(3793 ^ _167881) ^ [] : [-(_295959 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (3795 ^ _167881) ^ [] : [-(_295961 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (3797 ^ _167881) ^ [_296208, _296210] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _296208), _296210) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _296208 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _296210 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (3807 ^ _167881) ^ [_296507] : [class_Fields_Ofield__inverse__zero(_296507), -(c_Rings_Oinverse__class_Oinverse(_296507, c_Groups_Ozero__class_Ozero(_296507)) = c_Groups_Ozero__class_Ozero(_296507))], (3813 ^ _167881) ^ [_296709] : [-(_296709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _296709))], (3819 ^ _167881) ^ [_296932, _296934, _296936] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _296932, _296934), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _296936), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _296936), _296932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _296936), _296934)))], (3829 ^ _167881) ^ [_297285, _297287, _297289] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _297285, _297287), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _297289), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297285), _297289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297287), _297289)))], (3839 ^ _167881) ^ [_297624, _297626] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _297624, _297626), _297626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3845 ^ _167881) ^ [_297880, _297882, _297884] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297880), _297882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297884), _297882)), 3848 ^ _167881 : [(3849 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _297882))], (3851 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _297880, _297884))]]], (3853 ^ _167881) ^ [_298155, _298157, _298159] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _298155), _298157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _298159), _298157))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _298157), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _298155, _298159)], (3863 ^ _167881) ^ [_298539, _298541, _298543] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _298539), _298541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _298539), _298543)), 3866 ^ _167881 : [(3867 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _298539))], (3869 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _298541, _298543))]]], (3871 ^ _167881) ^ [_298814, _298816, _298818] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _298814), _298816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _298814), _298818))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _298814), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _298816, _298818)], (3881 ^ _167881) ^ [_299125] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _299125, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3883 ^ _167881) ^ [_299262, _299264] : [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), _299262), _299264)), 3886 ^ _167881 : [(3887 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _299262))], (3889 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _299264))]]], (3891 ^ _167881) ^ [_299517, _299519] : [-(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), _299517), _299519))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _299517), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _299519)], (3901 ^ _167881) ^ [_299851] : [-(_299851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _299851))], (3907 ^ _167881) ^ [_300012] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _300012), _300012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3913 ^ _167881) ^ [_300191] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _300191, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3915 ^ _167881) ^ [_300328, _300330] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _300328, _300330), 3918 ^ _167881 : [(3919 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _300328, _300330))], (3921 ^ _167881) ^ [] : [_300328 = _300330]]], (3923 ^ _167881) ^ [_300570, _300572] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _300570, _300572)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _300570, _300572), -(_300570 = _300572)], (3943 ^ _167881) ^ [_301163, _301165] : [3944 ^ _167881 : [(3945 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _301163, _301165)], (3947 ^ _167881) ^ [] : [_301163 = _301165]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _301163, _301165))], (3933 ^ _167881) ^ [_300907, _300909] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _300907, _300909), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _300907, _300909)), -(_300907 = _300909)], (3951 ^ _167881) ^ [_301424] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _301424) = _301424)], (3953 ^ _167881) ^ [_301506] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301506, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _301506)], (3955 ^ _167881) ^ [_301646, _301648] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301646, _301648) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 3958 ^ _167881 : [(3959 ^ _167881) ^ [] : [-(_301646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3961 ^ _167881) ^ [] : [-(_301648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3963 ^ _167881) ^ [_301891, _301893] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _301891, _301893) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _301891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _301893 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3973 ^ _167881) ^ [_302200, _302202] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _302200, _302202) = _302200, -(_302202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3979 ^ _167881) ^ [_302432, _302434, _302436] : [class_Fields_Ofield__inverse__zero(_302432), -(c_Rings_Oinverse__class_Oinverse(_302432, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302432), _302434), _302436)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302432), c_Rings_Oinverse__class_Oinverse(_302432, _302434)), c_Rings_Oinverse__class_Oinverse(_302432, _302436)))], (3985 ^ _167881) ^ [_302696, _302698] : [class_Fields_Ofield__inverse__zero(_302696), 3988 ^ _167881 : [(3989 ^ _167881) ^ [] : [c_Rings_Oinverse__class_Oinverse(_302696, _302698) = c_Groups_Oone__class_Oone(_302696), -(_302698 = c_Groups_Oone__class_Oone(_302696))], (3995 ^ _167881) ^ [] : [_302698 = c_Groups_Oone__class_Oone(_302696), -(c_Rings_Oinverse__class_Oinverse(_302696, _302698) = c_Groups_Oone__class_Oone(_302696))]]], (4001 ^ _167881) ^ [_303159, _303161] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303159, _303161), _303159)], (4003 ^ _167881) ^ [_303257, _303259] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303257, _303259), _303259)], (4005 ^ _167881) ^ [_303414, _303416, _303418] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303414, _303416), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303414, _303418)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _303416, _303418))], (4011 ^ _167881) ^ [_303602, _303604, _303606] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _303604, _303606), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303602, _303604), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303602, _303606)))], (4017 ^ _167881) ^ [_303854, _303856, _303858] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _303854, _303856), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _303854, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303856, _303858)))], (4023 ^ _167881) ^ [_304096, _304098, _304100] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304096, _304098), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304096, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _304100, _304098)))], (4029 ^ _167881) ^ [_304338, _304340, _304342] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304338, _304340), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _304338, _304342), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _304340, _304342)))], (4035 ^ _167881) ^ [_304602, _304604, _304606, _304608] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304602, _304604), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304606, _304608), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _304602, _304606), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _304604, _304608)))], (4045 ^ _167881) ^ [_304971, _304973, _304975, _304977] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304971, _304973), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _304975, _304973) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _304971, _304977), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304975, _304977))], (4055 ^ _167881) ^ [_305324, _305326, _305328] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _305324, _305326), _305328), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _305324, _305328))], (4061 ^ _167881) ^ [_305566, _305568, _305570] : [-(_305566 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4064 ^ _167881 : [(4065 ^ _167881) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _305568), _305566) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _305570), _305566), -(_305568 = _305570)], (4071 ^ _167881) ^ [] : [_305568 = _305570, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _305568), _305566) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _305570), _305566))]]], (4077 ^ _167881) ^ [_306095, _306097, _306099] : [-(_306095 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4080 ^ _167881 : [(4081 ^ _167881) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306095), _306097) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306095), _306099), -(_306097 = _306099)], (4087 ^ _167881) ^ [] : [_306097 = _306099, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306095), _306097) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306095), _306099))]]], (4093 ^ _167881) ^ [_306639, _306641] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306639), _306639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306641), _306641)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4096 ^ _167881 : [(4097 ^ _167881) ^ [] : [-(_306639 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4099 ^ _167881) ^ [] : [-(_306641 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (4101 ^ _167881) ^ [_306908, _306910] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306908), _306908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306910), _306910)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _306908 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _306910 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (4111 ^ _167881) ^ [_307241, _307243] : [_307241 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _307241), _307243), -(_307243 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_307241 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4121 ^ _167881) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (4123 ^ _167881) ^ [_307576] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _307576) = _307576)], (4125 ^ _167881) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4127 ^ _167881) ^ [_307739, _307741] : [class_Fields_Olinordered__field__inverse__zero(_307739), 4130 ^ _167881 : [(4131 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_307739, c_Rings_Oinverse__class_Oinverse(_307739, _307741), c_Groups_Ozero__class_Ozero(_307739)), -(c_Orderings_Oord__class_Oless__eq(_307739, _307741, c_Groups_Ozero__class_Ozero(_307739)))], (4137 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_307739, _307741, c_Groups_Ozero__class_Ozero(_307739)), -(c_Orderings_Oord__class_Oless__eq(_307739, c_Rings_Oinverse__class_Oinverse(_307739, _307741), c_Groups_Ozero__class_Ozero(_307739)))]]], (4143 ^ _167881) ^ [_308224, _308226] : [class_Fields_Olinordered__field__inverse__zero(_308224), 4146 ^ _167881 : [(4147 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_308224, c_Groups_Ozero__class_Ozero(_308224), c_Rings_Oinverse__class_Oinverse(_308224, _308226)), -(c_Orderings_Oord__class_Oless__eq(_308224, c_Groups_Ozero__class_Ozero(_308224), _308226))], (4153 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_308224, c_Groups_Ozero__class_Ozero(_308224), _308226), -(c_Orderings_Oord__class_Oless__eq(_308224, c_Groups_Ozero__class_Ozero(_308224), c_Rings_Oinverse__class_Oinverse(_308224, _308226)))]]], (4159 ^ _167881) ^ [_308709, _308711] : [class_Fields_Olinordered__field__inverse__zero(_308709), 4162 ^ _167881 : [(4163 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_308709, c_Groups_Ozero__class_Ozero(_308709), c_Rings_Oinverse__class_Oinverse(_308709, _308711)), -(c_Orderings_Oord__class_Oless(_308709, c_Groups_Ozero__class_Ozero(_308709), _308711))], (4169 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_308709, c_Groups_Ozero__class_Ozero(_308709), _308711), -(c_Orderings_Oord__class_Oless(_308709, c_Groups_Ozero__class_Ozero(_308709), c_Rings_Oinverse__class_Oinverse(_308709, _308711)))]]], (4175 ^ _167881) ^ [_309194, _309196] : [class_Fields_Olinordered__field__inverse__zero(_309194), 4178 ^ _167881 : [(4179 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_309194, c_Rings_Oinverse__class_Oinverse(_309194, _309196), c_Groups_Ozero__class_Ozero(_309194)), -(c_Orderings_Oord__class_Oless(_309194, _309196, c_Groups_Ozero__class_Ozero(_309194)))], (4185 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_309194, _309196, c_Groups_Ozero__class_Ozero(_309194)), -(c_Orderings_Oord__class_Oless(_309194, c_Rings_Oinverse__class_Oinverse(_309194, _309196), c_Groups_Ozero__class_Ozero(_309194)))]]], (4191 ^ _167881) ^ [_309679, _309681] : [class_Fields_Olinordered__field(_309679), c_Orderings_Oord__class_Oless(_309679, c_Groups_Ozero__class_Ozero(_309679), _309681), -(c_Orderings_Oord__class_Oless(_309679, c_Groups_Ozero__class_Ozero(_309679), c_Rings_Oinverse__class_Oinverse(_309679, _309681)))], (4201 ^ _167881) ^ [_309994, _309996] : [class_Fields_Olinordered__field(_309994), c_Orderings_Oord__class_Oless(_309994, c_Groups_Ozero__class_Ozero(_309994), c_Rings_Oinverse__class_Oinverse(_309994, _309996)), -(_309996 = c_Groups_Ozero__class_Ozero(_309994)), -(c_Orderings_Oord__class_Oless(_309994, c_Groups_Ozero__class_Ozero(_309994), _309996))], (4215 ^ _167881) ^ [_310405, _310407] : [class_Fields_Olinordered__field(_310405), c_Orderings_Oord__class_Oless(_310405, _310407, c_Groups_Ozero__class_Ozero(_310405)), -(c_Orderings_Oord__class_Oless(_310405, c_Rings_Oinverse__class_Oinverse(_310405, _310407), c_Groups_Ozero__class_Ozero(_310405)))], (4225 ^ _167881) ^ [_310734, _310736, _310738] : [class_Fields_Olinordered__field(_310734), c_Orderings_Oord__class_Oless(_310734, _310736, _310738), c_Orderings_Oord__class_Oless(_310734, c_Groups_Ozero__class_Ozero(_310734), _310736), -(c_Orderings_Oord__class_Oless(_310734, c_Rings_Oinverse__class_Oinverse(_310734, _310738), c_Rings_Oinverse__class_Oinverse(_310734, _310736)))], (4239 ^ _167881) ^ [_311170, _311172, _311174] : [class_Fields_Olinordered__field(_311170), c_Orderings_Oord__class_Oless(_311170, _311172, _311174), c_Orderings_Oord__class_Oless(_311170, _311174, c_Groups_Ozero__class_Ozero(_311170)), -(c_Orderings_Oord__class_Oless(_311170, c_Rings_Oinverse__class_Oinverse(_311170, _311174), c_Rings_Oinverse__class_Oinverse(_311170, _311172)))], (4253 ^ _167881) ^ [_311592, _311594] : [class_Fields_Olinordered__field(_311592), c_Orderings_Oord__class_Oless(_311592, c_Rings_Oinverse__class_Oinverse(_311592, _311594), c_Groups_Ozero__class_Ozero(_311592)), -(_311594 = c_Groups_Ozero__class_Ozero(_311592)), -(c_Orderings_Oord__class_Oless(_311592, _311594, c_Groups_Ozero__class_Ozero(_311592)))], (4267 ^ _167881) ^ [_312017, _312019, _312021] : [class_Fields_Olinordered__field(_312017), c_Orderings_Oord__class_Oless(_312017, c_Rings_Oinverse__class_Oinverse(_312017, _312019), c_Rings_Oinverse__class_Oinverse(_312017, _312021)), c_Orderings_Oord__class_Oless(_312017, c_Groups_Ozero__class_Ozero(_312017), _312019), -(c_Orderings_Oord__class_Oless(_312017, _312021, _312019))], (4281 ^ _167881) ^ [_312453, _312455, _312457] : [class_Fields_Olinordered__field(_312453), c_Orderings_Oord__class_Oless(_312453, c_Rings_Oinverse__class_Oinverse(_312453, _312455), c_Rings_Oinverse__class_Oinverse(_312453, _312457)), c_Orderings_Oord__class_Oless(_312453, _312457, c_Groups_Ozero__class_Ozero(_312453)), -(c_Orderings_Oord__class_Oless(_312453, _312457, _312455))], (4305 ^ _167881) ^ [_313170, _313172] : [4306 ^ _167881 : [(4307 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _313170)], (4309 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _313172)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _313170, _313172)))], (4295 ^ _167881) ^ [_312904, _312906] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _312904, _312906)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _312904)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _312906))], (4313 ^ _167881) ^ [_313484, _313486, _313488] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _313484), 4316 ^ _167881 : [(4317 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _313486), _313484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _313488), _313484)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _313486, _313488))], (4323 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _313486, _313488), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _313486), _313484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _313488), _313484)))]]], (4329 ^ _167881) ^ [_314004, _314006] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _314004), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _314006), -(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), _314004), _314006)))], (4339 ^ _167881) ^ [_314335, _314337, _314339] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _314335), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _314337, _314339), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _314335), _314337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _314335), _314339)))], (4349 ^ _167881) ^ [_314688, _314690, _314692] : [class_Fields_Olinordered__field(_314688), c_Orderings_Oord__class_Oless__eq(_314688, _314690, _314692), c_Orderings_Oord__class_Oless(_314688, c_Groups_Ozero__class_Ozero(_314688), _314690), -(c_Orderings_Oord__class_Oless__eq(_314688, c_Rings_Oinverse__class_Oinverse(_314688, _314692), c_Rings_Oinverse__class_Oinverse(_314688, _314690)))], (4363 ^ _167881) ^ [_315124, _315126, _315128] : [class_Fields_Olinordered__field(_315124), c_Orderings_Oord__class_Oless__eq(_315124, _315126, _315128), c_Orderings_Oord__class_Oless(_315124, _315128, c_Groups_Ozero__class_Ozero(_315124)), -(c_Orderings_Oord__class_Oless__eq(_315124, c_Rings_Oinverse__class_Oinverse(_315124, _315128), c_Rings_Oinverse__class_Oinverse(_315124, _315126)))], (4377 ^ _167881) ^ [_315560, _315562, _315564] : [class_Fields_Olinordered__field(_315560), c_Orderings_Oord__class_Oless__eq(_315560, c_Rings_Oinverse__class_Oinverse(_315560, _315562), c_Rings_Oinverse__class_Oinverse(_315560, _315564)), c_Orderings_Oord__class_Oless(_315560, c_Groups_Ozero__class_Ozero(_315560), _315562), -(c_Orderings_Oord__class_Oless__eq(_315560, _315564, _315562))], (4391 ^ _167881) ^ [_315996, _315998, _316000] : [class_Fields_Olinordered__field(_315996), c_Orderings_Oord__class_Oless__eq(_315996, c_Rings_Oinverse__class_Oinverse(_315996, _315998), c_Rings_Oinverse__class_Oinverse(_315996, _316000)), c_Orderings_Oord__class_Oless(_315996, _316000, c_Groups_Ozero__class_Ozero(_315996)), -(c_Orderings_Oord__class_Oless__eq(_315996, _316000, _315998))], (4405 ^ _167881) ^ [_316418, _316420] : [class_Fields_Olinordered__field__inverse__zero(_316418), 4408 ^ _167881 : [(4419 ^ _167881) ^ [] : [4420 ^ _167881 : [(4421 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_316418, _316420, c_Groups_Ozero__class_Ozero(_316418))], (4423 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_316418, c_Groups_Oone__class_Oone(_316418), _316420)]], -(c_Orderings_Oord__class_Oless__eq(_316418, c_Rings_Oinverse__class_Oinverse(_316418, _316420), c_Groups_Oone__class_Oone(_316418)))], (4409 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_316418, c_Rings_Oinverse__class_Oinverse(_316418, _316420), c_Groups_Oone__class_Oone(_316418)), -(c_Orderings_Oord__class_Oless__eq(_316418, _316420, c_Groups_Ozero__class_Ozero(_316418))), -(c_Orderings_Oord__class_Oless__eq(_316418, c_Groups_Oone__class_Oone(_316418), _316420))]]], (4427 ^ _167881) ^ [_317084, _317086, _317088] : [class_Fields_Ofield(_317084), -(_317086 = c_Groups_Ozero__class_Ozero(_317084)), -(_317088 = c_Groups_Ozero__class_Ozero(_317084)), -(c_Groups_Oplus__class_Oplus(_317084, c_Rings_Oinverse__class_Oinverse(_317084, _317086), c_Rings_Oinverse__class_Oinverse(_317084, _317088)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317084), c_Groups_Oplus__class_Oplus(_317084, _317086, _317088)), c_Rings_Oinverse__class_Oinverse(_317084, _317086))), c_Rings_Oinverse__class_Oinverse(_317084, _317088)))], (4441 ^ _167881) ^ [_317570, _317572] : [class_Fields_Olinordered__field__inverse__zero(_317570), 4444 ^ _167881 : [(4445 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_317570, c_Groups_Oone__class_Oone(_317570), c_Rings_Oinverse__class_Oinverse(_317570, _317572)), 4448 ^ _167881 : [(4449 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_317570, c_Groups_Ozero__class_Ozero(_317570), _317572))], (4451 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_317570, _317572, c_Groups_Oone__class_Oone(_317570)))]]], (4453 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_317570, c_Groups_Oone__class_Oone(_317570), c_Rings_Oinverse__class_Oinverse(_317570, _317572))), c_Orderings_Oord__class_Oless(_317570, c_Groups_Ozero__class_Ozero(_317570), _317572), c_Orderings_Oord__class_Oless(_317570, _317572, c_Groups_Oone__class_Oone(_317570))]]], (4463 ^ _167881) ^ [_318222, _318224] : [class_Fields_Olinordered__field(_318222), c_Orderings_Oord__class_Oless(_318222, c_Groups_Ozero__class_Ozero(_318222), _318224), c_Orderings_Oord__class_Oless(_318222, _318224, c_Groups_Oone__class_Oone(_318222)), -(c_Orderings_Oord__class_Oless(_318222, c_Groups_Oone__class_Oone(_318222), c_Rings_Oinverse__class_Oinverse(_318222, _318224)))], (4477 ^ _167881) ^ [_318632, _318634] : [class_Fields_Ofield(_318632), -(_318634 = c_Groups_Ozero__class_Ozero(_318632)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318632), c_Rings_Oinverse__class_Oinverse(_318632, _318634)), _318634) = c_Groups_Oone__class_Oone(_318632))], (4487 ^ _167881) ^ [_318976, _318978, _318980] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _318976), 4490 ^ _167881 : [(4491 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _318978), _318976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _318980), _318976)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _318978, _318980))], (4497 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _318978, _318980), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _318978), _318976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _318980), _318976)))]]], (4504 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 4502 ^ []), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (4506 ^ _167881) ^ [] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____)), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (4508 ^ _167881) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (4510 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)))], (4512 ^ _167881) ^ [_319777, _319779, _319781] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _319777), 4515 ^ _167881 : [(4516 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _319777), _319779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _319777), _319781)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _319779, _319781))], (4522 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _319779, _319781), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _319777), _319779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _319777), _319781)))]]], (4528 ^ _167881) ^ [_320311, _320313, _320315] : [class_Groups_Oordered__comm__monoid__add(_320311), c_Orderings_Oord__class_Oless(_320311, c_Groups_Ozero__class_Ozero(_320311), _320313), c_Orderings_Oord__class_Oless__eq(_320311, c_Groups_Ozero__class_Ozero(_320311), _320315), -(c_Orderings_Oord__class_Oless(_320311, c_Groups_Ozero__class_Ozero(_320311), c_Groups_Oplus__class_Oplus(_320311, _320313, _320315)))], (4542 ^ _167881) ^ [_320751, _320753, _320755] : [class_Groups_Oordered__comm__monoid__add(_320751), c_Orderings_Oord__class_Oless__eq(_320751, c_Groups_Ozero__class_Ozero(_320751), _320753), c_Orderings_Oord__class_Oless(_320751, c_Groups_Ozero__class_Ozero(_320751), _320755), -(c_Orderings_Oord__class_Oless(_320751, c_Groups_Ozero__class_Ozero(_320751), c_Groups_Oplus__class_Oplus(_320751, _320753, _320755)))], (4556 ^ _167881) ^ [_321205, _321207, _321209, _321211] : [class_Groups_Oordered__comm__monoid__add(_321205), c_Orderings_Oord__class_Oless(_321205, c_Groups_Ozero__class_Ozero(_321205), _321207), c_Orderings_Oord__class_Oless__eq(_321205, _321209, _321211), -(c_Orderings_Oord__class_Oless(_321205, _321209, c_Groups_Oplus__class_Oplus(_321205, _321207, _321211)))], (4570 ^ _167881) ^ [_321637, _321639] : [class_Groups_Ogroup__add(_321637), -(c_Groups_Ominus__class_Ominus(_321637, c_Groups_Ozero__class_Ozero(_321637), _321639) = c_Groups_Ouminus__class_Ouminus(_321637, _321639))], (4576 ^ _167881) ^ [_321877, _321879, _321881] : [class_Groups_Ogroup__add(_321877), -(c_Groups_Ominus__class_Ominus(_321877, _321879, _321881) = c_Groups_Oplus__class_Oplus(_321877, _321879, c_Groups_Ouminus__class_Ouminus(_321877, _321881)))], (4582 ^ _167881) ^ [_322127, _322129, _322131] : [class_Groups_Oab__group__add(_322127), -(c_Groups_Ominus__class_Ominus(_322127, _322129, _322131) = c_Groups_Oplus__class_Oplus(_322127, _322129, c_Groups_Ouminus__class_Ouminus(_322127, _322131)))], (4588 ^ _167881) ^ [_322377, _322379, _322381] : [class_Groups_Ogroup__add(_322377), -(c_Groups_Ominus__class_Ominus(_322377, _322379, c_Groups_Ouminus__class_Ouminus(_322377, _322381)) = c_Groups_Oplus__class_Oplus(_322377, _322379, _322381))], (4594 ^ _167881) ^ [_322613, _322615] : [class_Groups_Ogroup__add(_322613), -(c_Groups_Ominus__class_Ominus(_322613, _322615, c_Groups_Ozero__class_Ozero(_322613)) = _322615)], (4600 ^ _167881) ^ [_322833, _322835] : [class_Groups_Ogroup__add(_322833), -(c_Groups_Ominus__class_Ominus(_322833, _322835, _322835) = c_Groups_Ozero__class_Ozero(_322833))], (4606 ^ _167881) ^ [_323067, _323069, _323071] : [class_Groups_Oab__group__add(_323067), 4609 ^ _167881 : [(4610 ^ _167881) ^ [] : [_323069 = _323071, -(c_Groups_Ominus__class_Ominus(_323067, _323069, _323071) = c_Groups_Ozero__class_Ozero(_323067))], (4616 ^ _167881) ^ [] : [c_Groups_Ominus__class_Ominus(_323067, _323069, _323071) = c_Groups_Ozero__class_Ozero(_323067), -(_323069 = _323071)]]], (4622 ^ _167881) ^ [_323573, _323575, _323577] : [class_Groups_Ogroup__add(_323573), 4625 ^ _167881 : [(4626 ^ _167881) ^ [] : [c_Groups_Ominus__class_Ominus(_323573, _323575, _323577) = c_Groups_Ozero__class_Ozero(_323573), -(_323575 = _323577)], (4632 ^ _167881) ^ [] : [_323575 = _323577, -(c_Groups_Ominus__class_Ominus(_323573, _323575, _323577) = c_Groups_Ozero__class_Ozero(_323573))]]], (4638 ^ _167881) ^ [_324051] : [class_Groups_Ogroup__add(_324051), -(c_Groups_Ouminus__class_Ouminus(_324051, c_Groups_Ozero__class_Ozero(_324051)) = c_Groups_Ozero__class_Ozero(_324051))], (4644 ^ _167881) ^ [_324267, _324269] : [class_Groups_Ogroup__add(_324267), 4647 ^ _167881 : [(4648 ^ _167881) ^ [] : [c_Groups_Ozero__class_Ozero(_324267) = c_Groups_Ouminus__class_Ouminus(_324267, _324269), -(c_Groups_Ozero__class_Ozero(_324267) = _324269)], (4654 ^ _167881) ^ [] : [c_Groups_Ozero__class_Ozero(_324267) = _324269, -(c_Groups_Ozero__class_Ozero(_324267) = c_Groups_Ouminus__class_Ouminus(_324267, _324269))]]], (4660 ^ _167881) ^ [_324746, _324748] : [class_Groups_Olinordered__ab__group__add(_324746), 4663 ^ _167881 : [(4664 ^ _167881) ^ [] : [_324748 = c_Groups_Ouminus__class_Ouminus(_324746, _324748), -(_324748 = c_Groups_Ozero__class_Ozero(_324746))], (4670 ^ _167881) ^ [] : [_324748 = c_Groups_Ozero__class_Ozero(_324746), -(_324748 = c_Groups_Ouminus__class_Ouminus(_324746, _324748))]]], (4676 ^ _167881) ^ [_325219, _325221] : [class_Groups_Ogroup__add(_325219), 4679 ^ _167881 : [(4680 ^ _167881) ^ [] : [c_Groups_Ouminus__class_Ouminus(_325219, _325221) = c_Groups_Ozero__class_Ozero(_325219), -(_325221 = c_Groups_Ozero__class_Ozero(_325219))], (4686 ^ _167881) ^ [] : [_325221 = c_Groups_Ozero__class_Ozero(_325219), -(c_Groups_Ouminus__class_Ouminus(_325219, _325221) = c_Groups_Ozero__class_Ozero(_325219))]]], (4692 ^ _167881) ^ [_325698, _325700] : [class_Groups_Olinordered__ab__group__add(_325698), 4695 ^ _167881 : [(4696 ^ _167881) ^ [] : [c_Groups_Ouminus__class_Ouminus(_325698, _325700) = _325700, -(_325700 = c_Groups_Ozero__class_Ozero(_325698))], (4702 ^ _167881) ^ [] : [_325700 = c_Groups_Ozero__class_Ozero(_325698), -(c_Groups_Ouminus__class_Ouminus(_325698, _325700) = _325700)]]], (4708 ^ _167881) ^ [_326213, _326215, _326217, _326219, _326221] : [class_Groups_Oordered__ab__group__add(_326213), c_Groups_Ominus__class_Ominus(_326213, _326215, _326217) = c_Groups_Ominus__class_Ominus(_326213, _326219, _326221), 4715 ^ _167881 : [(4716 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_326213, _326215, _326217), -(c_Orderings_Oord__class_Oless__eq(_326213, _326219, _326221))], (4722 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_326213, _326219, _326221), -(c_Orderings_Oord__class_Oless__eq(_326213, _326215, _326217))]]], (4728 ^ _167881) ^ [_326856, _326858, _326860] : [class_Groups_Oordered__ab__group__add(_326856), c_Orderings_Oord__class_Oless__eq(_326856, _326858, _326860), -(c_Orderings_Oord__class_Oless__eq(_326856, c_Groups_Ouminus__class_Ouminus(_326856, _326860), c_Groups_Ouminus__class_Ouminus(_326856, _326858)))], (4738 ^ _167881) ^ [_327193, _327195, _327197] : [class_Groups_Oordered__ab__group__add(_327193), 4741 ^ _167881 : [(4742 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_327193, c_Groups_Ouminus__class_Ouminus(_327193, _327195), c_Groups_Ouminus__class_Ouminus(_327193, _327197)), -(c_Orderings_Oord__class_Oless__eq(_327193, _327197, _327195))], (4748 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_327193, _327197, _327195), -(c_Orderings_Oord__class_Oless__eq(_327193, c_Groups_Ouminus__class_Ouminus(_327193, _327195), c_Groups_Ouminus__class_Ouminus(_327193, _327197)))]]], (4754 ^ _167881) ^ [_327705, _327707, _327709] : [class_Groups_Oordered__ab__group__add(_327705), 4757 ^ _167881 : [(4758 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_327705, c_Groups_Ouminus__class_Ouminus(_327705, _327707), _327709), -(c_Orderings_Oord__class_Oless__eq(_327705, c_Groups_Ouminus__class_Ouminus(_327705, _327709), _327707))], (4764 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_327705, c_Groups_Ouminus__class_Ouminus(_327705, _327709), _327707), -(c_Orderings_Oord__class_Oless__eq(_327705, c_Groups_Ouminus__class_Ouminus(_327705, _327707), _327709))]]], (4770 ^ _167881) ^ [_328217, _328219, _328221] : [class_Groups_Oordered__ab__group__add(_328217), 4773 ^ _167881 : [(4774 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_328217, _328219, c_Groups_Ouminus__class_Ouminus(_328217, _328221)), -(c_Orderings_Oord__class_Oless__eq(_328217, _328221, c_Groups_Ouminus__class_Ouminus(_328217, _328219)))], (4780 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_328217, _328221, c_Groups_Ouminus__class_Ouminus(_328217, _328219)), -(c_Orderings_Oord__class_Oless__eq(_328217, _328219, c_Groups_Ouminus__class_Ouminus(_328217, _328221)))]]], (4786 ^ _167881) ^ [_328757, _328759, _328761, _328763, _328765] : [class_Groups_Oordered__ab__group__add(_328757), c_Groups_Ominus__class_Ominus(_328757, _328759, _328761) = c_Groups_Ominus__class_Ominus(_328757, _328763, _328765), 4793 ^ _167881 : [(4794 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_328757, _328759, _328761), -(c_Orderings_Oord__class_Oless(_328757, _328763, _328765))], (4800 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_328757, _328763, _328765), -(c_Orderings_Oord__class_Oless(_328757, _328759, _328761))]]], (4806 ^ _167881) ^ [_329400, _329402, _329404] : [class_Groups_Oordered__ab__group__add(_329400), 4809 ^ _167881 : [(4810 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_329400, _329402, c_Groups_Ouminus__class_Ouminus(_329400, _329404)), -(c_Orderings_Oord__class_Oless(_329400, _329404, c_Groups_Ouminus__class_Ouminus(_329400, _329402)))], (4816 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_329400, _329404, c_Groups_Ouminus__class_Ouminus(_329400, _329402)), -(c_Orderings_Oord__class_Oless(_329400, _329402, c_Groups_Ouminus__class_Ouminus(_329400, _329404)))]]], (4822 ^ _167881) ^ [_329912, _329914, _329916] : [class_Groups_Oordered__ab__group__add(_329912), 4825 ^ _167881 : [(4826 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_329912, c_Groups_Ouminus__class_Ouminus(_329912, _329914), _329916), -(c_Orderings_Oord__class_Oless(_329912, c_Groups_Ouminus__class_Ouminus(_329912, _329916), _329914))], (4832 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_329912, c_Groups_Ouminus__class_Ouminus(_329912, _329916), _329914), -(c_Orderings_Oord__class_Oless(_329912, c_Groups_Ouminus__class_Ouminus(_329912, _329914), _329916))]]], (4838 ^ _167881) ^ [_330424, _330426, _330428] : [class_Groups_Oordered__ab__group__add(_330424), 4841 ^ _167881 : [(4842 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_330424, c_Groups_Ouminus__class_Ouminus(_330424, _330426), c_Groups_Ouminus__class_Ouminus(_330424, _330428)), -(c_Orderings_Oord__class_Oless(_330424, _330428, _330426))], (4848 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_330424, _330428, _330426), -(c_Orderings_Oord__class_Oless(_330424, c_Groups_Ouminus__class_Ouminus(_330424, _330426), c_Groups_Ouminus__class_Ouminus(_330424, _330428)))]]], (4854 ^ _167881) ^ [_330936, _330938, _330940] : [class_Groups_Ogroup__add(_330936), -(c_Groups_Oplus__class_Oplus(_330936, c_Groups_Ominus__class_Ominus(_330936, _330938, _330940), _330940) = _330938)], (4860 ^ _167881) ^ [_331180, _331182, _331184] : [class_Groups_Ogroup__add(_331180), -(c_Groups_Ominus__class_Ominus(_331180, c_Groups_Oplus__class_Oplus(_331180, _331182, _331184), _331184) = _331182)], (4866 ^ _167881) ^ [_331424, _331426, _331428] : [class_Groups_Oab__group__add(_331424), -(c_Groups_Ouminus__class_Ouminus(_331424, c_Groups_Oplus__class_Oplus(_331424, _331426, _331428)) = c_Groups_Oplus__class_Oplus(_331424, c_Groups_Ouminus__class_Ouminus(_331424, _331426), c_Groups_Ouminus__class_Ouminus(_331424, _331428)))], (4872 ^ _167881) ^ [_331686, _331688, _331690] : [class_Groups_Ogroup__add(_331686), -(c_Groups_Ouminus__class_Ouminus(_331686, c_Groups_Oplus__class_Oplus(_331686, _331688, _331690)) = c_Groups_Oplus__class_Oplus(_331686, c_Groups_Ouminus__class_Ouminus(_331686, _331690), c_Groups_Ouminus__class_Ouminus(_331686, _331688)))], (4878 ^ _167881) ^ [_331948, _331950, _331952] : [class_Groups_Ogroup__add(_331948), -(c_Groups_Oplus__class_Oplus(_331948, _331950, c_Groups_Oplus__class_Oplus(_331948, c_Groups_Ouminus__class_Ouminus(_331948, _331950), _331952)) = _331952)], (4884 ^ _167881) ^ [_332198, _332200, _332202] : [class_Groups_Ogroup__add(_332198), -(c_Groups_Oplus__class_Oplus(_332198, c_Groups_Ouminus__class_Ouminus(_332198, _332200), c_Groups_Oplus__class_Oplus(_332198, _332200, _332202)) = _332202)], (4890 ^ _167881) ^ [_332434, _332436] : [class_Groups_Ogroup__add(_332434), -(c_Groups_Ouminus__class_Ouminus(_332434, c_Groups_Ouminus__class_Ouminus(_332434, _332436)) = _332436)], (4896 ^ _167881) ^ [_332668, _332670, _332672] : [class_Groups_Oab__group__add(_332668), -(c_Groups_Ouminus__class_Ouminus(_332668, c_Groups_Ominus__class_Ominus(_332668, _332670, _332672)) = c_Groups_Ominus__class_Ominus(_332668, _332672, _332670))], (4902 ^ _167881) ^ [_332918, _332920, _332922] : [class_Groups_Ogroup__add(_332918), 4905 ^ _167881 : [(4906 ^ _167881) ^ [] : [_332920 = c_Groups_Ouminus__class_Ouminus(_332918, _332922), -(_332922 = c_Groups_Ouminus__class_Ouminus(_332918, _332920))], (4912 ^ _167881) ^ [] : [_332922 = c_Groups_Ouminus__class_Ouminus(_332918, _332920), -(_332920 = c_Groups_Ouminus__class_Ouminus(_332918, _332922))]]], (4918 ^ _167881) ^ [_333424, _333426, _333428] : [class_Groups_Ogroup__add(_333424), 4921 ^ _167881 : [(4922 ^ _167881) ^ [] : [c_Groups_Ouminus__class_Ouminus(_333424, _333426) = _333428, -(c_Groups_Ouminus__class_Ouminus(_333424, _333428) = _333426)], (4928 ^ _167881) ^ [] : [c_Groups_Ouminus__class_Ouminus(_333424, _333428) = _333426, -(c_Groups_Ouminus__class_Ouminus(_333424, _333426) = _333428)]]], (4934 ^ _167881) ^ [_333930, _333932, _333934] : [class_Groups_Ogroup__add(_333930), 4937 ^ _167881 : [(4938 ^ _167881) ^ [] : [c_Groups_Ouminus__class_Ouminus(_333930, _333932) = c_Groups_Ouminus__class_Ouminus(_333930, _333934), -(_333932 = _333934)], (4944 ^ _167881) ^ [] : [_333932 = _333934, -(c_Groups_Ouminus__class_Ouminus(_333930, _333932) = c_Groups_Ouminus__class_Ouminus(_333930, _333934))]]], (4950 ^ _167881) ^ [_334464, _334466, _334468, _334470, _334472] : [class_Groups_Oab__group__add(_334464), c_Groups_Ominus__class_Ominus(_334464, _334466, _334468) = c_Groups_Ominus__class_Ominus(_334464, _334470, _334472), 4957 ^ _167881 : [(4958 ^ _167881) ^ [] : [_334466 = _334468, -(_334470 = _334472)], (4964 ^ _167881) ^ [] : [_334470 = _334472, -(_334466 = _334468)]]], (4970 ^ _167881) ^ [_335101, _335103, _335105] : [class_RealVector_Oreal__algebra__1(_335101), 4973 ^ _167881 : [(4974 ^ _167881) ^ [] : [c_RealVector_Oof__real(_335101, _335103) = c_RealVector_Oof__real(_335101, _335105), -(_335103 = _335105)], (4980 ^ _167881) ^ [] : [_335103 = _335105, -(c_RealVector_Oof__real(_335101, _335103) = c_RealVector_Oof__real(_335101, _335105))]]], (4986 ^ _167881) ^ [_335607, _335609, _335611] : [-(c_RealVector_Oof__real(_335607, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _335609, _335611)) = c_Groups_Ominus__class_Ominus(_335607, c_RealVector_Oof__real(_335607, _335609), c_RealVector_Oof__real(_335607, _335611))), class_RealVector_Oreal__algebra__1(_335607), class_RealVector_Oreal__normed__vector(_335607)], (4996 ^ _167881) ^ [_335960, _335962, _335964] : [class_RealVector_Oreal__algebra__1(_335960), -(c_RealVector_Oof__real(_335960, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _335962, _335964)) = c_Groups_Ominus__class_Ominus(_335960, c_RealVector_Oof__real(_335960, _335962), c_RealVector_Oof__real(_335960, _335964)))], (5002 ^ _167881) ^ [_336208, _336210] : [-(c_RealVector_Oof__real(_336208, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _336210)) = c_Groups_Ouminus__class_Ouminus(_336208, c_RealVector_Oof__real(_336208, _336210))), class_RealVector_Oreal__algebra__1(_336208), class_RealVector_Oreal__normed__vector(_336208)], (5012 ^ _167881) ^ [_336527, _336529] : [class_RealVector_Oreal__algebra__1(_336527), -(c_RealVector_Oof__real(_336527, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _336529)) = c_Groups_Ouminus__class_Ouminus(_336527, c_RealVector_Oof__real(_336527, _336529)))], (5018 ^ _167881) ^ [_336773, _336775, _336777] : [class_RealVector_Oreal__normed__vector(_336773), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_336773, _336775), c_RealVector_Onorm__class_Onorm(_336773, _336777)), c_RealVector_Onorm__class_Onorm(_336773, c_Groups_Ominus__class_Ominus(_336773, _336775, _336777))))], (5024 ^ _167881) ^ [_337051, _337053, _337055, _337057] : [class_RealVector_Oreal__normed__algebra(_337051), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337051), c_Groups_Ominus__class_Ominus(_337051, _337053, _337055)), _337057) = c_Groups_Ominus__class_Ominus(_337051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337051), _337053), _337057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337051), _337055), _337057)))], (5030 ^ _167881) ^ [_337363, _337365, _337367, _337369] : [class_RealVector_Oreal__normed__algebra(_337363), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337363), c_Groups_Ominus__class_Ominus(_337363, _337365, _337367)), _337369) = c_Groups_Ominus__class_Ominus(_337363, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337363), _337365), _337369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337363), _337367), _337369)))], (5036 ^ _167881) ^ [_337675, _337677, _337679, _337681] : [class_RealVector_Oreal__normed__algebra(_337675), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337675), _337677), c_Groups_Ominus__class_Ominus(_337675, _337679, _337681)) = c_Groups_Ominus__class_Ominus(_337675, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337675), _337677), _337679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337675), _337677), _337681)))], (5042 ^ _167881) ^ [_337987, _337989, _337991, _337993] : [class_RealVector_Oreal__normed__algebra(_337987), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337987), _337989), c_Groups_Ominus__class_Ominus(_337987, _337991, _337993)) = c_Groups_Ominus__class_Ominus(_337987, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337987), _337989), _337991), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337987), _337989), _337993)))], (5048 ^ _167881) ^ [_338285, _338287, _338289] : [class_Rings_Oidom(_338285), 5051 ^ _167881 : [(5062 ^ _167881) ^ [] : [5063 ^ _167881 : [(5064 ^ _167881) ^ [] : [_338287 = _338289], (5066 ^ _167881) ^ [] : [_338287 = c_Groups_Ouminus__class_Ouminus(_338285, _338289)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338285), _338287), _338287) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338285), _338289), _338289))], (5052 ^ _167881) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338285), _338287), _338287) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338285), _338289), _338289), -(_338287 = _338289), -(_338287 = c_Groups_Ouminus__class_Ouminus(_338285, _338289))]]], (5070 ^ _167881) ^ [_338994, _338996, _338998] : [class_Rings_Oring(_338994), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338994), c_Groups_Ouminus__class_Ouminus(_338994, _338996)), c_Groups_Ouminus__class_Ouminus(_338994, _338998)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338994), _338996), _338998))], (5076 ^ _167881) ^ [_339266, _339268, _339270] : [class_Rings_Oring(_339266), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339266), c_Groups_Ouminus__class_Ouminus(_339266, _339268)), _339270) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339266), _339268), c_Groups_Ouminus__class_Ouminus(_339266, _339270)))], (5082 ^ _167881) ^ [_339538, _339540, _339542] : [class_RealVector_Oreal__normed__algebra(_339538), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339538), c_Groups_Ouminus__class_Ouminus(_339538, _339540)), _339542) = c_Groups_Ouminus__class_Ouminus(_339538, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339538), _339540), _339542)))], (5088 ^ _167881) ^ [_339810, _339812, _339814] : [class_RealVector_Oreal__normed__algebra(_339810), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339810), c_Groups_Ouminus__class_Ouminus(_339810, _339812)), _339814) = c_Groups_Ouminus__class_Ouminus(_339810, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339810), _339812), _339814)))], (5094 ^ _167881) ^ [_340082, _340084, _340086] : [class_RealVector_Oreal__normed__algebra(_340082), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340082), _340084), c_Groups_Ouminus__class_Ouminus(_340082, _340086)) = c_Groups_Ouminus__class_Ouminus(_340082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340082), _340084), _340086)))], (5100 ^ _167881) ^ [_340354, _340356, _340358] : [class_RealVector_Oreal__normed__algebra(_340354), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340354), _340356), c_Groups_Ouminus__class_Ouminus(_340354, _340358)) = c_Groups_Ouminus__class_Ouminus(_340354, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340354), _340356), _340358)))], (5106 ^ _167881) ^ [_340626, _340628, _340630] : [class_Rings_Oring(_340626), -(c_Groups_Ouminus__class_Ouminus(_340626, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340626), _340628), _340630)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340626), c_Groups_Ouminus__class_Ouminus(_340626, _340628)), _340630))], (5112 ^ _167881) ^ [_340898, _340900, _340902] : [class_Rings_Oring(_340898), -(c_Groups_Ouminus__class_Ouminus(_340898, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340898), _340900), _340902)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340898), _340900), c_Groups_Ouminus__class_Ouminus(_340898, _340902)))], (5118 ^ _167881) ^ [_341170, _341172, _341174] : [class_RealVector_Oreal__normed__vector(_341170), -(c_RealVector_Onorm__class_Onorm(_341170, c_Groups_Ominus__class_Ominus(_341170, _341172, _341174)) = c_RealVector_Onorm__class_Onorm(_341170, c_Groups_Ominus__class_Ominus(_341170, _341174, _341172)))], (5124 ^ _167881) ^ [_341412, _341414] : [class_RealVector_Oreal__normed__vector(_341412), -(c_RealVector_Onorm__class_Onorm(_341412, c_Groups_Ouminus__class_Ouminus(_341412, _341414)) = c_RealVector_Onorm__class_Onorm(_341412, _341414))], (5130 ^ _167881) ^ [_341638, _341640] : [class_Rings_Odivision__ring__inverse__zero(_341638), -(c_Rings_Oinverse__class_Oinverse(_341638, c_Groups_Ouminus__class_Ouminus(_341638, _341640)) = c_Groups_Ouminus__class_Ouminus(_341638, c_Rings_Oinverse__class_Oinverse(_341638, _341640)))], (5136 ^ _167881) ^ [_341884, _341886, _341888] : [class_Groups_Oordered__ab__group__add(_341884), 5139 ^ _167881 : [(5140 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_341884, _341886, _341888), -(c_Orderings_Oord__class_Oless__eq(_341884, c_Groups_Ominus__class_Ominus(_341884, _341886, _341888), c_Groups_Ozero__class_Ozero(_341884)))], (5146 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_341884, c_Groups_Ominus__class_Ominus(_341884, _341886, _341888), c_Groups_Ozero__class_Ozero(_341884)), -(c_Orderings_Oord__class_Oless__eq(_341884, _341886, _341888))]]], (5152 ^ _167881) ^ [_342396, _342398, _342400] : [class_Groups_Oordered__ab__group__add(_342396), 5155 ^ _167881 : [(5156 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_342396, _342398, _342400), -(c_Orderings_Oord__class_Oless(_342396, c_Groups_Ominus__class_Ominus(_342396, _342398, _342400), c_Groups_Ozero__class_Ozero(_342396)))], (5162 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_342396, c_Groups_Ominus__class_Ominus(_342396, _342398, _342400), c_Groups_Ozero__class_Ozero(_342396)), -(c_Orderings_Oord__class_Oless(_342396, _342398, _342400))]]], (5168 ^ _167881) ^ [_342894, _342896] : [class_Groups_Oordered__ab__group__add(_342894), 5171 ^ _167881 : [(5172 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_342894, c_Groups_Ozero__class_Ozero(_342894), c_Groups_Ouminus__class_Ouminus(_342894, _342896)), -(c_Orderings_Oord__class_Oless__eq(_342894, _342896, c_Groups_Ozero__class_Ozero(_342894)))], (5178 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_342894, _342896, c_Groups_Ozero__class_Ozero(_342894)), -(c_Orderings_Oord__class_Oless__eq(_342894, c_Groups_Ozero__class_Ozero(_342894), c_Groups_Ouminus__class_Ouminus(_342894, _342896)))]]], (5184 ^ _167881) ^ [_343379, _343381] : [class_Groups_Olinordered__ab__group__add(_343379), 5187 ^ _167881 : [(5188 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343379, _343381, c_Groups_Ouminus__class_Ouminus(_343379, _343381)), -(c_Orderings_Oord__class_Oless__eq(_343379, _343381, c_Groups_Ozero__class_Ozero(_343379)))], (5194 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343379, _343381, c_Groups_Ozero__class_Ozero(_343379)), -(c_Orderings_Oord__class_Oless__eq(_343379, _343381, c_Groups_Ouminus__class_Ouminus(_343379, _343381)))]]], (5200 ^ _167881) ^ [_343858, _343860] : [class_Groups_Oordered__ab__group__add(_343858), 5203 ^ _167881 : [(5204 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343858, c_Groups_Ouminus__class_Ouminus(_343858, _343860), c_Groups_Ozero__class_Ozero(_343858)), -(c_Orderings_Oord__class_Oless__eq(_343858, c_Groups_Ozero__class_Ozero(_343858), _343860))], (5210 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343858, c_Groups_Ozero__class_Ozero(_343858), _343860), -(c_Orderings_Oord__class_Oless__eq(_343858, c_Groups_Ouminus__class_Ouminus(_343858, _343860), c_Groups_Ozero__class_Ozero(_343858)))]]], (5216 ^ _167881) ^ [_344343, _344345] : [class_Groups_Olinordered__ab__group__add(_344343), 5219 ^ _167881 : [(5220 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_344343, c_Groups_Ouminus__class_Ouminus(_344343, _344345), _344345), -(c_Orderings_Oord__class_Oless__eq(_344343, c_Groups_Ozero__class_Ozero(_344343), _344345))], (5226 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_344343, c_Groups_Ozero__class_Ozero(_344343), _344345), -(c_Orderings_Oord__class_Oless__eq(_344343, c_Groups_Ouminus__class_Ouminus(_344343, _344345), _344345))]]], (5232 ^ _167881) ^ [_344822, _344824] : [class_Groups_Olinordered__ab__group__add(_344822), 5235 ^ _167881 : [(5236 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_344822, c_Groups_Ouminus__class_Ouminus(_344822, _344824), _344824), -(c_Orderings_Oord__class_Oless(_344822, c_Groups_Ozero__class_Ozero(_344822), _344824))], (5242 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_344822, c_Groups_Ozero__class_Ozero(_344822), _344824), -(c_Orderings_Oord__class_Oless(_344822, c_Groups_Ouminus__class_Ouminus(_344822, _344824), _344824))]]], (5248 ^ _167881) ^ [_345301, _345303] : [class_Groups_Oordered__ab__group__add(_345301), 5251 ^ _167881 : [(5252 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_345301, c_Groups_Ouminus__class_Ouminus(_345301, _345303), c_Groups_Ozero__class_Ozero(_345301)), -(c_Orderings_Oord__class_Oless(_345301, c_Groups_Ozero__class_Ozero(_345301), _345303))], (5258 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_345301, c_Groups_Ozero__class_Ozero(_345301), _345303), -(c_Orderings_Oord__class_Oless(_345301, c_Groups_Ouminus__class_Ouminus(_345301, _345303), c_Groups_Ozero__class_Ozero(_345301)))]]], (5264 ^ _167881) ^ [_345786, _345788] : [class_Groups_Oordered__ab__group__add(_345786), 5267 ^ _167881 : [(5268 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_345786, c_Groups_Ozero__class_Ozero(_345786), c_Groups_Ouminus__class_Ouminus(_345786, _345788)), -(c_Orderings_Oord__class_Oless(_345786, _345788, c_Groups_Ozero__class_Ozero(_345786)))], (5274 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_345786, _345788, c_Groups_Ozero__class_Ozero(_345786)), -(c_Orderings_Oord__class_Oless(_345786, c_Groups_Ozero__class_Ozero(_345786), c_Groups_Ouminus__class_Ouminus(_345786, _345788)))]]], (5280 ^ _167881) ^ [_346285, _346287, _346289] : [class_Groups_Ogroup__add(_346285), c_Groups_Oplus__class_Oplus(_346285, _346287, _346289) = c_Groups_Ozero__class_Ozero(_346285), -(c_Groups_Ouminus__class_Ouminus(_346285, _346287) = _346289)], (5290 ^ _167881) ^ [_346610, _346612] : [class_Groups_Oab__group__add(_346610), -(c_Groups_Oplus__class_Oplus(_346610, c_Groups_Ouminus__class_Ouminus(_346610, _346612), _346612) = c_Groups_Ozero__class_Ozero(_346610))], (5296 ^ _167881) ^ [_346836, _346838] : [class_Groups_Ogroup__add(_346836), -(c_Groups_Oplus__class_Oplus(_346836, c_Groups_Ouminus__class_Ouminus(_346836, _346838), _346838) = c_Groups_Ozero__class_Ozero(_346836))], (5302 ^ _167881) ^ [_347076, _347078, _347080] : [class_Groups_Ogroup__add(_347076), 5305 ^ _167881 : [(5306 ^ _167881) ^ [] : [_347078 = c_Groups_Ouminus__class_Ouminus(_347076, _347080), -(c_Groups_Oplus__class_Oplus(_347076, _347078, _347080) = c_Groups_Ozero__class_Ozero(_347076))], (5312 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_347076, _347078, _347080) = c_Groups_Ozero__class_Ozero(_347076), -(_347078 = c_Groups_Ouminus__class_Ouminus(_347076, _347080))]]], (5318 ^ _167881) ^ [_347577, _347579] : [class_Groups_Ogroup__add(_347577), -(c_Groups_Oplus__class_Oplus(_347577, _347579, c_Groups_Ouminus__class_Ouminus(_347577, _347579)) = c_Groups_Ozero__class_Ozero(_347577))], (5324 ^ _167881) ^ [_347803, _347805] : [class_Rings_Olinordered__idom(_347803), 5327 ^ _167881 : [(5328 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_347803, _347805, c_Groups_Ouminus__class_Ouminus(_347803, _347805)), -(c_Orderings_Oord__class_Oless(_347803, _347805, c_Groups_Ozero__class_Ozero(_347803)))], (5334 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_347803, _347805, c_Groups_Ozero__class_Ozero(_347803)), -(c_Orderings_Oord__class_Oless(_347803, _347805, c_Groups_Ouminus__class_Ouminus(_347803, _347805)))]]], (5340 ^ _167881) ^ [_348282, _348284] : [class_RealVector_Oreal__algebra__1(_348282), 5343 ^ _167881 : [(5344 ^ _167881) ^ [] : [c_RealVector_Oof__real(_348282, _348284) = c_Groups_Ozero__class_Ozero(_348282), -(_348284 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5350 ^ _167881) ^ [] : [_348284 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_RealVector_Oof__real(_348282, _348284) = c_Groups_Ozero__class_Ozero(_348282))]]], (5356 ^ _167881) ^ [_348741] : [-(c_RealVector_Oof__real(_348741, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(_348741)), class_RealVector_Oreal__algebra__1(_348741), class_RealVector_Oreal__normed__vector(_348741)], (5366 ^ _167881) ^ [_349022] : [class_RealVector_Oreal__algebra__1(_349022), -(c_RealVector_Oof__real(_349022, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(_349022))], (5372 ^ _167881) ^ [_349248, _349250, _349252] : [class_Groups_Ogroup__add(_349248), 5375 ^ _167881 : [(5376 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_349248, _349250, _349252) = c_Groups_Ozero__class_Ozero(_349248), -(_349252 = c_Groups_Ouminus__class_Ouminus(_349248, _349250))], (5382 ^ _167881) ^ [] : [_349252 = c_Groups_Ouminus__class_Ouminus(_349248, _349250), -(c_Groups_Oplus__class_Oplus(_349248, _349250, _349252) = c_Groups_Ozero__class_Ozero(_349248))]]], (5388 ^ _167881) ^ [_349805, _349807, _349809, _349811, _349813, _349815] : [class_Rings_Oring(_349805), 5391 ^ _167881 : [(5392 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_349805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349805), _349807), _349809), _349811) = c_Groups_Oplus__class_Oplus(_349805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349805), _349813), _349809), _349815), -(c_Groups_Oplus__class_Oplus(_349805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349805), c_Groups_Ominus__class_Ominus(_349805, _349807, _349813)), _349809), _349811) = _349815)], (5398 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_349805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349805), c_Groups_Ominus__class_Ominus(_349805, _349807, _349813)), _349809), _349811) = _349815, -(c_Groups_Oplus__class_Oplus(_349805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349805), _349807), _349809), _349811) = c_Groups_Oplus__class_Oplus(_349805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349805), _349813), _349809), _349815))]]], (5404 ^ _167881) ^ [_350503, _350505, _350507, _350509, _350511, _350513] : [class_Rings_Oring(_350503), 5407 ^ _167881 : [(5408 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_350503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350503), _350505), _350507), _350509) = c_Groups_Oplus__class_Oplus(_350503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350503), _350511), _350507), _350513), -(_350509 = c_Groups_Oplus__class_Oplus(_350503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350503), c_Groups_Ominus__class_Ominus(_350503, _350511, _350505)), _350507), _350513))], (5414 ^ _167881) ^ [] : [_350509 = c_Groups_Oplus__class_Oplus(_350503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350503), c_Groups_Ominus__class_Ominus(_350503, _350511, _350505)), _350507), _350513), -(c_Groups_Oplus__class_Oplus(_350503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350503), _350505), _350507), _350509) = c_Groups_Oplus__class_Oplus(_350503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350503), _350511), _350507), _350513))]]], (5420 ^ _167881) ^ [_351187, _351189, _351191, _351193, _351195] : [class_RealVector_Oreal__normed__algebra(_351187), -(c_Groups_Ominus__class_Ominus(_351187, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351187), _351189), _351191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351187), _351193), _351195)) = c_Groups_Oplus__class_Oplus(_351187, c_Groups_Oplus__class_Oplus(_351187, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351187), c_Groups_Ominus__class_Ominus(_351187, _351189, _351193)), c_Groups_Ominus__class_Ominus(_351187, _351191, _351195)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351187), c_Groups_Ominus__class_Ominus(_351187, _351189, _351193)), _351195)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351187), _351193), c_Groups_Ominus__class_Ominus(_351187, _351191, _351195))))], (5426 ^ _167881) ^ [_351591, _351593, _351595, _351597, _351599] : [class_Rings_Oring(_351591), -(c_Groups_Ominus__class_Ominus(_351591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351591), _351593), _351595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351591), _351597), _351599)) = c_Groups_Oplus__class_Oplus(_351591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351591), _351593), c_Groups_Ominus__class_Ominus(_351591, _351595, _351599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351591), c_Groups_Ominus__class_Ominus(_351591, _351593, _351597)), _351599)))], (5432 ^ _167881) ^ [_351913, _351915] : [class_Rings_Oring__1__no__zero__divisors(_351913), 5435 ^ _167881 : [(5446 ^ _167881) ^ [] : [5447 ^ _167881 : [(5448 ^ _167881) ^ [] : [_351915 = c_Groups_Oone__class_Oone(_351913)], (5450 ^ _167881) ^ [] : [_351915 = c_Groups_Ouminus__class_Ouminus(_351913, c_Groups_Oone__class_Oone(_351913))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351913), _351915), _351915) = c_Groups_Oone__class_Oone(_351913))], (5436 ^ _167881) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351913), _351915), _351915) = c_Groups_Oone__class_Oone(_351913), -(_351915 = c_Groups_Oone__class_Oone(_351913)), -(_351915 = c_Groups_Ouminus__class_Ouminus(_351913, c_Groups_Oone__class_Oone(_351913)))]]], (5454 ^ _167881) ^ [_352594, _352596, _352598] : [class_RealVector_Oreal__algebra__1(_352594), -(c_RealVector_Oof__real(_352594, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _352596), _352598)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352594), c_RealVector_Oof__real(_352594, _352596)), c_RealVector_Oof__real(_352594, _352598)))], (5460 ^ _167881) ^ [_352868, _352870, _352872] : [-(c_RealVector_Oof__real(_352868, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _352870, _352872)) = c_Groups_Oplus__class_Oplus(_352868, c_RealVector_Oof__real(_352868, _352870), c_RealVector_Oof__real(_352868, _352872))), class_RealVector_Oreal__algebra__1(_352868), class_RealVector_Oreal__normed__vector(_352868)], (5470 ^ _167881) ^ [_353221, _353223, _353225] : [class_RealVector_Oreal__algebra__1(_353221), -(c_RealVector_Oof__real(_353221, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _353223, _353225)) = c_Groups_Oplus__class_Oplus(_353221, c_RealVector_Oof__real(_353221, _353223), c_RealVector_Oof__real(_353221, _353225)))], (5476 ^ _167881) ^ [_353455] : [class_RealVector_Oreal__algebra__1(_353455), -(c_RealVector_Oof__real(_353455, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(_353455))], (5482 ^ _167881) ^ [_353667, _353669] : [class_Rings_Odivision__ring(_353667), -(_353669 = c_Groups_Ozero__class_Ozero(_353667)), -(c_Rings_Oinverse__class_Oinverse(_353667, c_Groups_Ouminus__class_Ouminus(_353667, _353669)) = c_Groups_Ouminus__class_Ouminus(_353667, c_Rings_Oinverse__class_Oinverse(_353667, _353669)))], (5492 ^ _167881) ^ [_354009, _354011, _354013] : [class_RealVector_Oreal__algebra__1(_354009), -(c_RealVector_Oof__real(_354009, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _354011), _354013)) = hAPP(hAPP(c_Power_Opower__class_Opower(_354009), c_RealVector_Oof__real(_354009, _354011)), _354013))], (5498 ^ _167881) ^ [_354263, _354265] : [-(c_RealVector_Oof__real(_354263, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _354265)) = c_Rings_Oinverse__class_Oinverse(_354263, c_RealVector_Oof__real(_354263, _354265))), class_RealVector_Oreal__div__algebra(_354263), class_Rings_Odivision__ring__inverse__zero(_354263)], (5508 ^ _167881) ^ [_354567, _354569] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, _354567)), _354569) = c_RealVector_Oof__real(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _354567), _354569)))], (5510 ^ _167881) ^ [_354750, _354752, _354754, _354756, _354758, _354760] : [class_Rings_Oordered__ring(_354750), 5513 ^ _167881 : [(5514 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_354750, c_Groups_Oplus__class_Oplus(_354750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354750), _354752), _354754), _354756), c_Groups_Oplus__class_Oplus(_354750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354750), _354758), _354754), _354760)), -(c_Orderings_Oord__class_Oless__eq(_354750, c_Groups_Oplus__class_Oplus(_354750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354750), c_Groups_Ominus__class_Ominus(_354750, _354752, _354758)), _354754), _354756), _354760))], (5520 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_354750, c_Groups_Oplus__class_Oplus(_354750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354750), c_Groups_Ominus__class_Ominus(_354750, _354752, _354758)), _354754), _354756), _354760), -(c_Orderings_Oord__class_Oless__eq(_354750, c_Groups_Oplus__class_Oplus(_354750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354750), _354752), _354754), _354756), c_Groups_Oplus__class_Oplus(_354750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354750), _354758), _354754), _354760)))]]], (5526 ^ _167881) ^ [_355454, _355456, _355458, _355460, _355462, _355464] : [class_Rings_Oordered__ring(_355454), 5529 ^ _167881 : [(5530 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_355454, c_Groups_Oplus__class_Oplus(_355454, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355454), _355456), _355458), _355460), c_Groups_Oplus__class_Oplus(_355454, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355454), _355462), _355458), _355464)), -(c_Orderings_Oord__class_Oless__eq(_355454, _355460, c_Groups_Oplus__class_Oplus(_355454, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355454), c_Groups_Ominus__class_Ominus(_355454, _355462, _355456)), _355458), _355464)))], (5536 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_355454, _355460, c_Groups_Oplus__class_Oplus(_355454, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355454), c_Groups_Ominus__class_Ominus(_355454, _355462, _355456)), _355458), _355464)), -(c_Orderings_Oord__class_Oless__eq(_355454, c_Groups_Oplus__class_Oplus(_355454, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355454), _355456), _355458), _355460), c_Groups_Oplus__class_Oplus(_355454, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355454), _355462), _355458), _355464)))]]], (5542 ^ _167881) ^ [_356158, _356160, _356162, _356164, _356166, _356168] : [class_Rings_Oordered__ring(_356158), 5545 ^ _167881 : [(5546 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_356158, c_Groups_Oplus__class_Oplus(_356158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356158), _356160), _356162), _356164), c_Groups_Oplus__class_Oplus(_356158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356158), _356166), _356162), _356168)), -(c_Orderings_Oord__class_Oless(_356158, c_Groups_Oplus__class_Oplus(_356158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356158), c_Groups_Ominus__class_Ominus(_356158, _356160, _356166)), _356162), _356164), _356168))], (5552 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_356158, c_Groups_Oplus__class_Oplus(_356158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356158), c_Groups_Ominus__class_Ominus(_356158, _356160, _356166)), _356162), _356164), _356168), -(c_Orderings_Oord__class_Oless(_356158, c_Groups_Oplus__class_Oplus(_356158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356158), _356160), _356162), _356164), c_Groups_Oplus__class_Oplus(_356158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356158), _356166), _356162), _356168)))]]], (5558 ^ _167881) ^ [_356862, _356864, _356866, _356868, _356870, _356872] : [class_Rings_Oordered__ring(_356862), 5561 ^ _167881 : [(5562 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_356862, c_Groups_Oplus__class_Oplus(_356862, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356862), _356864), _356866), _356868), c_Groups_Oplus__class_Oplus(_356862, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356862), _356870), _356866), _356872)), -(c_Orderings_Oord__class_Oless(_356862, _356868, c_Groups_Oplus__class_Oplus(_356862, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356862), c_Groups_Ominus__class_Ominus(_356862, _356870, _356864)), _356866), _356872)))], (5568 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_356862, _356868, c_Groups_Oplus__class_Oplus(_356862, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356862), c_Groups_Ominus__class_Ominus(_356862, _356870, _356864)), _356866), _356872)), -(c_Orderings_Oord__class_Oless(_356862, c_Groups_Oplus__class_Oplus(_356862, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356862), _356864), _356866), _356868), c_Groups_Oplus__class_Oplus(_356862, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356862), _356870), _356866), _356872)))]]], (5574 ^ _167881) ^ [_357510, _357512] : [class_Rings_Oring__1(_357510), -(c_Groups_Ominus__class_Ominus(_357510, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357510), _357512), _357512), c_Groups_Oone__class_Oone(_357510)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357510), c_Groups_Oplus__class_Oplus(_357510, _357512, c_Groups_Oone__class_Oone(_357510))), c_Groups_Ominus__class_Ominus(_357510, _357512, c_Groups_Oone__class_Oone(_357510))))], (5580 ^ _167881) ^ [_357800, _357802, _357804] : [class_Rings_Odivision__ring(_357800), -(_357802 = c_Groups_Ozero__class_Ozero(_357800)), -(_357804 = c_Groups_Ozero__class_Ozero(_357800)), -(c_Groups_Ominus__class_Ominus(_357800, c_Rings_Oinverse__class_Oinverse(_357800, _357802), c_Rings_Oinverse__class_Oinverse(_357800, _357804)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357800), c_Rings_Oinverse__class_Oinverse(_357800, _357802)), c_Groups_Ominus__class_Ominus(_357800, _357804, _357802))), c_Rings_Oinverse__class_Oinverse(_357800, _357804)))], (5594 ^ _167881) ^ [_358300, _358302, _358304] : [class_Rings_Oring__1(_358300), -(hAPP(hAPP(c_Power_Opower__class_Opower(_358300), c_Groups_Ouminus__class_Ouminus(_358300, _358302)), _358304) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358300), hAPP(hAPP(c_Power_Opower__class_Opower(_358300), c_Groups_Ouminus__class_Ouminus(_358300, c_Groups_Oone__class_Oone(_358300))), _358304)), hAPP(hAPP(c_Power_Opower__class_Opower(_358300), _358302), _358304)))], (5600 ^ _167881) ^ [_358608, _358610, _358612] : [class_RealVector_Oreal__normed__vector(_358608), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_358608, c_Groups_Ominus__class_Ominus(_358608, _358610, _358612)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_358608, _358610), c_RealVector_Onorm__class_Onorm(_358608, _358612))))], (5606 ^ _167881) ^ [_358858, _358860] : [class_RealVector_Oreal__div__algebra(_358858), -(_358860 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RealVector_Oof__real(_358858, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _358860)) = c_Rings_Oinverse__class_Oinverse(_358858, c_RealVector_Oof__real(_358858, _358860)))], (5616 ^ _167881) ^ [_359182, _359184] : [class_Groups_Ozero(_359182), 5619 ^ _167881 : [(5620 ^ _167881) ^ [] : [c_Groups_Ozero__class_Ozero(_359182) = _359184, -(_359184 = c_Groups_Ozero__class_Ozero(_359182))], (5626 ^ _167881) ^ [] : [_359184 = c_Groups_Ozero__class_Ozero(_359182), -(c_Groups_Ozero__class_Ozero(_359182) = _359184)]]], (5632 ^ _167881) ^ [_359680, _359682, _359684, _359686] : [class_Groups_Oab__semigroup__mult(_359680), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359680), _359682), _359684)), _359686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359680), _359682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359680), _359684), _359686)))], (5638 ^ _167881) ^ [_359992, _359994, _359996, _359998] : [class_Groups_Ocancel__semigroup__add(_359992), c_Groups_Oplus__class_Oplus(_359992, _359994, _359996) = c_Groups_Oplus__class_Oplus(_359992, _359998, _359996), -(_359994 = _359998)], (5648 ^ _167881) ^ [_360353, _360355, _360357, _360359] : [class_Groups_Ocancel__ab__semigroup__add(_360353), c_Groups_Oplus__class_Oplus(_360353, _360355, _360357) = c_Groups_Oplus__class_Oplus(_360353, _360355, _360359), -(_360357 = _360359)], (5658 ^ _167881) ^ [_360714, _360716, _360718, _360720] : [class_Groups_Ocancel__semigroup__add(_360714), c_Groups_Oplus__class_Oplus(_360714, _360716, _360718) = c_Groups_Oplus__class_Oplus(_360714, _360716, _360720), -(_360718 = _360720)], (5668 ^ _167881) ^ [_361075, _361077, _361079, _361081] : [class_Groups_Ocancel__semigroup__add(_361075), 5671 ^ _167881 : [(5672 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_361075, _361077, _361079) = c_Groups_Oplus__class_Oplus(_361075, _361081, _361079), -(_361077 = _361081)], (5678 ^ _167881) ^ [] : [_361077 = _361081, -(c_Groups_Oplus__class_Oplus(_361075, _361077, _361079) = c_Groups_Oplus__class_Oplus(_361075, _361081, _361079))]]], (5684 ^ _167881) ^ [_361617, _361619, _361621, _361623] : [class_Groups_Ocancel__semigroup__add(_361617), 5687 ^ _167881 : [(5688 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_361617, _361619, _361621) = c_Groups_Oplus__class_Oplus(_361617, _361619, _361623), -(_361621 = _361623)], (5694 ^ _167881) ^ [] : [_361621 = _361623, -(c_Groups_Oplus__class_Oplus(_361617, _361619, _361621) = c_Groups_Oplus__class_Oplus(_361617, _361619, _361623))]]], (5700 ^ _167881) ^ [_362159, _362161, _362163, _362165] : [class_Groups_Oab__semigroup__add(_362159), -(c_Groups_Oplus__class_Oplus(_362159, c_Groups_Oplus__class_Oplus(_362159, _362161, _362163), _362165) = c_Groups_Oplus__class_Oplus(_362159, _362161, c_Groups_Oplus__class_Oplus(_362159, _362163, _362165)))], (5706 ^ _167881) ^ [_362411, _362413] : [class_Groups_Oone(_362411), 5709 ^ _167881 : [(5710 ^ _167881) ^ [] : [c_Groups_Oone__class_Oone(_362411) = _362413, -(_362413 = c_Groups_Oone__class_Oone(_362411))], (5716 ^ _167881) ^ [] : [_362413 = c_Groups_Oone__class_Oone(_362411), -(c_Groups_Oone__class_Oone(_362411) = _362413)]]], (5722 ^ _167881) ^ [_362923, _362925, _362927, _362929, _362931] : [class_RealVector_Oreal__normed__vector(_362923), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_362923, c_Groups_Ominus__class_Ominus(_362923, c_Groups_Oplus__class_Oplus(_362923, _362925, _362927), c_Groups_Oplus__class_Oplus(_362923, _362929, _362931))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_362923, c_Groups_Ominus__class_Ominus(_362923, _362925, _362929)), c_RealVector_Onorm__class_Onorm(_362923, c_Groups_Ominus__class_Ominus(_362923, _362927, _362931)))))], (5728 ^ _167881) ^ [_363217, _363219] : [class_Groups_Ocomm__monoid__add(_363217), -(c_Groups_Oplus__class_Oplus(_363217, _363219, c_Groups_Ozero__class_Ozero(_363217)) = _363219)], (5734 ^ _167881) ^ [_363437, _363439] : [class_Groups_Omonoid__add(_363437), -(c_Groups_Oplus__class_Oplus(_363437, _363439, c_Groups_Ozero__class_Ozero(_363437)) = _363439)], (5740 ^ _167881) ^ [_363657, _363659] : [class_Groups_Olinordered__ab__group__add(_363657), 5743 ^ _167881 : [(5744 ^ _167881) ^ [] : [c_Groups_Ozero__class_Ozero(_363657) = c_Groups_Oplus__class_Oplus(_363657, _363659, _363659), -(_363659 = c_Groups_Ozero__class_Ozero(_363657))], (5750 ^ _167881) ^ [] : [_363659 = c_Groups_Ozero__class_Ozero(_363657), -(c_Groups_Ozero__class_Ozero(_363657) = c_Groups_Oplus__class_Oplus(_363657, _363659, _363659))]]], (5756 ^ _167881) ^ [_364139, _364141] : [class_Groups_Ocomm__monoid__add(_364139), -(c_Groups_Oplus__class_Oplus(_364139, c_Groups_Ozero__class_Ozero(_364139), _364141) = _364141)], (5762 ^ _167881) ^ [_364359, _364361] : [class_Groups_Omonoid__add(_364359), -(c_Groups_Oplus__class_Oplus(_364359, c_Groups_Ozero__class_Ozero(_364359), _364361) = _364361)], (5768 ^ _167881) ^ [_364607, _364609, _364611, _364613] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_364607), c_Orderings_Oord__class_Oless__eq(_364607, c_Groups_Oplus__class_Oplus(_364607, _364609, _364611), c_Groups_Oplus__class_Oplus(_364607, _364609, _364613)), -(c_Orderings_Oord__class_Oless__eq(_364607, _364611, _364613))], (5778 ^ _167881) ^ [_364972, _364974, _364976, _364978] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_364972), c_Orderings_Oord__class_Oless__eq(_364972, c_Groups_Oplus__class_Oplus(_364972, _364974, _364976), c_Groups_Oplus__class_Oplus(_364972, _364978, _364976)), -(c_Orderings_Oord__class_Oless__eq(_364972, _364974, _364978))], (5788 ^ _167881) ^ [_365351, _365353, _365355, _365357, _365359] : [class_Groups_Oordered__ab__semigroup__add(_365351), c_Orderings_Oord__class_Oless__eq(_365351, _365353, _365355), c_Orderings_Oord__class_Oless__eq(_365351, _365357, _365359), -(c_Orderings_Oord__class_Oless__eq(_365351, c_Groups_Oplus__class_Oplus(_365351, _365353, _365357), c_Groups_Oplus__class_Oplus(_365351, _365355, _365359)))], (5802 ^ _167881) ^ [_365829, _365831, _365833, _365835] : [class_Groups_Oordered__ab__semigroup__add(_365829), c_Orderings_Oord__class_Oless__eq(_365829, _365831, _365833), -(c_Orderings_Oord__class_Oless__eq(_365829, c_Groups_Oplus__class_Oplus(_365829, _365835, _365831), c_Groups_Oplus__class_Oplus(_365829, _365835, _365833)))], (5812 ^ _167881) ^ [_366194, _366196, _366198, _366200] : [class_Groups_Oordered__ab__semigroup__add(_366194), c_Orderings_Oord__class_Oless__eq(_366194, _366196, _366198), -(c_Orderings_Oord__class_Oless__eq(_366194, c_Groups_Oplus__class_Oplus(_366194, _366196, _366200), c_Groups_Oplus__class_Oplus(_366194, _366198, _366200)))], (5822 ^ _167881) ^ [_366559, _366561, _366563, _366565] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_366559), 5825 ^ _167881 : [(5826 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366559, c_Groups_Oplus__class_Oplus(_366559, _366561, _366563), c_Groups_Oplus__class_Oplus(_366559, _366561, _366565)), -(c_Orderings_Oord__class_Oless__eq(_366559, _366563, _366565))], (5832 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366559, _366563, _366565), -(c_Orderings_Oord__class_Oless__eq(_366559, c_Groups_Oplus__class_Oplus(_366559, _366561, _366563), c_Groups_Oplus__class_Oplus(_366559, _366561, _366565)))]]], (5838 ^ _167881) ^ [_367107, _367109, _367111, _367113] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_367107), 5841 ^ _167881 : [(5842 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_367107, c_Groups_Oplus__class_Oplus(_367107, _367109, _367111), c_Groups_Oplus__class_Oplus(_367107, _367113, _367111)), -(c_Orderings_Oord__class_Oless__eq(_367107, _367109, _367113))], (5848 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_367107, _367109, _367113), -(c_Orderings_Oord__class_Oless__eq(_367107, c_Groups_Oplus__class_Oplus(_367107, _367109, _367111), c_Groups_Oplus__class_Oplus(_367107, _367113, _367111)))]]], (5854 ^ _167881) ^ [_367655, _367657, _367659, _367661] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_367655), c_Orderings_Oord__class_Oless(_367655, c_Groups_Oplus__class_Oplus(_367655, _367657, _367659), c_Groups_Oplus__class_Oplus(_367655, _367657, _367661)), -(c_Orderings_Oord__class_Oless(_367655, _367659, _367661))], (5864 ^ _167881) ^ [_368020, _368022, _368024, _368026] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_368020), c_Orderings_Oord__class_Oless(_368020, c_Groups_Oplus__class_Oplus(_368020, _368022, _368024), c_Groups_Oplus__class_Oplus(_368020, _368026, _368024)), -(c_Orderings_Oord__class_Oless(_368020, _368022, _368026))], (5874 ^ _167881) ^ [_368399, _368401, _368403, _368405, _368407] : [class_Groups_Oordered__cancel__ab__semigroup__add(_368399), c_Orderings_Oord__class_Oless(_368399, _368401, _368403), c_Orderings_Oord__class_Oless(_368399, _368405, _368407), -(c_Orderings_Oord__class_Oless(_368399, c_Groups_Oplus__class_Oplus(_368399, _368401, _368405), c_Groups_Oplus__class_Oplus(_368399, _368403, _368407)))], (5888 ^ _167881) ^ [_368877, _368879, _368881, _368883] : [class_Groups_Oordered__cancel__ab__semigroup__add(_368877), c_Orderings_Oord__class_Oless(_368877, _368879, _368881), -(c_Orderings_Oord__class_Oless(_368877, c_Groups_Oplus__class_Oplus(_368877, _368883, _368879), c_Groups_Oplus__class_Oplus(_368877, _368883, _368881)))], (5898 ^ _167881) ^ [_369242, _369244, _369246, _369248] : [class_Groups_Oordered__cancel__ab__semigroup__add(_369242), c_Orderings_Oord__class_Oless(_369242, _369244, _369246), -(c_Orderings_Oord__class_Oless(_369242, c_Groups_Oplus__class_Oplus(_369242, _369244, _369248), c_Groups_Oplus__class_Oplus(_369242, _369246, _369248)))], (5908 ^ _167881) ^ [_369607, _369609, _369611, _369613] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_369607), 5911 ^ _167881 : [(5912 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_369607, c_Groups_Oplus__class_Oplus(_369607, _369609, _369611), c_Groups_Oplus__class_Oplus(_369607, _369609, _369613)), -(c_Orderings_Oord__class_Oless(_369607, _369611, _369613))], (5918 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_369607, _369611, _369613), -(c_Orderings_Oord__class_Oless(_369607, c_Groups_Oplus__class_Oplus(_369607, _369609, _369611), c_Groups_Oplus__class_Oplus(_369607, _369609, _369613)))]]], (5924 ^ _167881) ^ [_370155, _370157, _370159, _370161] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_370155), 5927 ^ _167881 : [(5928 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_370155, c_Groups_Oplus__class_Oplus(_370155, _370157, _370159), c_Groups_Oplus__class_Oplus(_370155, _370161, _370159)), -(c_Orderings_Oord__class_Oless(_370155, _370157, _370161))], (5934 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_370155, _370157, _370161), -(c_Orderings_Oord__class_Oless(_370155, c_Groups_Oplus__class_Oplus(_370155, _370157, _370159), c_Groups_Oplus__class_Oplus(_370155, _370161, _370159)))]]], (5940 ^ _167881) ^ [_370675, _370677] : [class_Groups_Ocomm__monoid__mult(_370675), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370675), _370677), c_Groups_Oone__class_Oone(_370675)) = _370677)], (5946 ^ _167881) ^ [_370903, _370905] : [class_Groups_Omonoid__mult(_370903), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370903), _370905), c_Groups_Oone__class_Oone(_370903)) = _370905)], (5952 ^ _167881) ^ [_371131, _371133] : [class_Groups_Ocomm__monoid__mult(_371131), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371131), c_Groups_Oone__class_Oone(_371131)), _371133) = _371133)], (5958 ^ _167881) ^ [_371359, _371361] : [class_Groups_Omonoid__mult(_371359), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371359), c_Groups_Oone__class_Oone(_371359)), _371361) = _371361)], (5974 ^ _167881) ^ [_371916, _371918, _371920] : [5975 ^ _167881 : [(5976 ^ _167881) ^ [] : [_371916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5978 ^ _167881) ^ [] : [_371918 = _371920]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371916), _371918) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371916), _371920))], (5964 ^ _167881) ^ [_371630, _371632, _371634] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371630), _371632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371630), _371634), -(_371630 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_371632 = _371634)], (5982 ^ _167881) ^ [_372247, _372249, _372251, _372253] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _372247), _372249), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _372251), _372249), _372253)) = 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, _372247, _372251)), _372249), _372253))], (5984 ^ _167881) ^ [_372408, _372410, _372412] : [class_Groups_Oordered__comm__monoid__add(_372408), c_Orderings_Oord__class_Oless__eq(_372408, _372410, c_Groups_Ozero__class_Ozero(_372408)), c_Orderings_Oord__class_Oless__eq(_372408, _372412, c_Groups_Ozero__class_Ozero(_372408)), -(c_Orderings_Oord__class_Oless__eq(_372408, c_Groups_Oplus__class_Oplus(_372408, _372410, _372412), c_Groups_Ozero__class_Ozero(_372408)))], (5998 ^ _167881) ^ [_372862, _372864, _372866, _372868] : [class_Groups_Oordered__comm__monoid__add(_372862), c_Orderings_Oord__class_Oless__eq(_372862, c_Groups_Ozero__class_Ozero(_372862), _372864), c_Orderings_Oord__class_Oless__eq(_372862, _372866, _372868), -(c_Orderings_Oord__class_Oless__eq(_372862, _372866, c_Groups_Oplus__class_Oplus(_372862, _372868, _372864)))], (6012 ^ _167881) ^ [_373322, _373324, _373326, _373328] : [class_Groups_Oordered__comm__monoid__add(_373322), c_Orderings_Oord__class_Oless__eq(_373322, c_Groups_Ozero__class_Ozero(_373322), _373324), c_Orderings_Oord__class_Oless__eq(_373322, _373326, _373328), -(c_Orderings_Oord__class_Oless__eq(_373322, _373326, c_Groups_Oplus__class_Oplus(_373322, _373324, _373328)))], (6026 ^ _167881) ^ [_373768, _373770, _373772] : [class_Groups_Oordered__comm__monoid__add(_373768), c_Orderings_Oord__class_Oless__eq(_373768, c_Groups_Ozero__class_Ozero(_373768), _373770), c_Orderings_Oord__class_Oless__eq(_373768, c_Groups_Ozero__class_Ozero(_373768), _373772), 6037 ^ _167881 : [(6038 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_373768, _373770, _373772) = c_Groups_Ozero__class_Ozero(_373768), 6041 ^ _167881 : [(6042 ^ _167881) ^ [] : [-(_373770 = c_Groups_Ozero__class_Ozero(_373768))], (6044 ^ _167881) ^ [] : [-(_373772 = c_Groups_Ozero__class_Ozero(_373768))]]], (6046 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(_373768, _373770, _373772) = c_Groups_Ozero__class_Ozero(_373768)), _373770 = c_Groups_Ozero__class_Ozero(_373768), _373772 = c_Groups_Ozero__class_Ozero(_373768)]]], (6056 ^ _167881) ^ [_374648, _374650, _374652] : [class_Groups_Oordered__comm__monoid__add(_374648), c_Orderings_Oord__class_Oless__eq(_374648, c_Groups_Ozero__class_Ozero(_374648), _374650), c_Orderings_Oord__class_Oless__eq(_374648, c_Groups_Ozero__class_Ozero(_374648), _374652), -(c_Orderings_Oord__class_Oless__eq(_374648, c_Groups_Ozero__class_Ozero(_374648), c_Groups_Oplus__class_Oplus(_374648, _374650, _374652)))], (6070 ^ _167881) ^ [_375074, _375076] : [class_Groups_Olinordered__ab__group__add(_375074), 6073 ^ _167881 : [(6074 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_375074, c_Groups_Oplus__class_Oplus(_375074, _375076, _375076), c_Groups_Ozero__class_Ozero(_375074)), -(c_Orderings_Oord__class_Oless__eq(_375074, _375076, c_Groups_Ozero__class_Ozero(_375074)))], (6080 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_375074, _375076, c_Groups_Ozero__class_Ozero(_375074)), -(c_Orderings_Oord__class_Oless__eq(_375074, c_Groups_Oplus__class_Oplus(_375074, _375076, _375076), c_Groups_Ozero__class_Ozero(_375074)))]]], (6086 ^ _167881) ^ [_375562, _375564] : [class_Groups_Olinordered__ab__group__add(_375562), 6089 ^ _167881 : [(6090 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_375562, c_Groups_Ozero__class_Ozero(_375562), c_Groups_Oplus__class_Oplus(_375562, _375564, _375564)), -(c_Orderings_Oord__class_Oless__eq(_375562, c_Groups_Ozero__class_Ozero(_375562), _375564))], (6096 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_375562, c_Groups_Ozero__class_Ozero(_375562), _375564), -(c_Orderings_Oord__class_Oless__eq(_375562, c_Groups_Ozero__class_Ozero(_375562), c_Groups_Oplus__class_Oplus(_375562, _375564, _375564)))]]], (6102 ^ _167881) ^ [_376064, _376066, _376068] : [class_Groups_Oordered__comm__monoid__add(_376064), c_Orderings_Oord__class_Oless(_376064, _376066, c_Groups_Ozero__class_Ozero(_376064)), c_Orderings_Oord__class_Oless(_376064, _376068, c_Groups_Ozero__class_Ozero(_376064)), -(c_Orderings_Oord__class_Oless(_376064, c_Groups_Oplus__class_Oplus(_376064, _376066, _376068), c_Groups_Ozero__class_Ozero(_376064)))], (6116 ^ _167881) ^ [_376504, _376506, _376508] : [class_Groups_Oordered__comm__monoid__add(_376504), c_Orderings_Oord__class_Oless(_376504, c_Groups_Ozero__class_Ozero(_376504), _376506), c_Orderings_Oord__class_Oless(_376504, c_Groups_Ozero__class_Ozero(_376504), _376508), -(c_Orderings_Oord__class_Oless(_376504, c_Groups_Ozero__class_Ozero(_376504), c_Groups_Oplus__class_Oplus(_376504, _376506, _376508)))], (6130 ^ _167881) ^ [_376930, _376932] : [class_Groups_Olinordered__ab__group__add(_376930), 6133 ^ _167881 : [(6134 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_376930, c_Groups_Oplus__class_Oplus(_376930, _376932, _376932), c_Groups_Ozero__class_Ozero(_376930)), -(c_Orderings_Oord__class_Oless(_376930, _376932, c_Groups_Ozero__class_Ozero(_376930)))], (6140 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_376930, _376932, c_Groups_Ozero__class_Ozero(_376930)), -(c_Orderings_Oord__class_Oless(_376930, c_Groups_Oplus__class_Oplus(_376930, _376932, _376932), c_Groups_Ozero__class_Ozero(_376930)))]]], (6146 ^ _167881) ^ [_377418, _377420] : [class_Groups_Olinordered__ab__group__add(_377418), 6149 ^ _167881 : [(6150 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_377418, c_Groups_Ozero__class_Ozero(_377418), c_Groups_Oplus__class_Oplus(_377418, _377420, _377420)), -(c_Orderings_Oord__class_Oless(_377418, c_Groups_Ozero__class_Ozero(_377418), _377420))], (6156 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_377418, c_Groups_Ozero__class_Ozero(_377418), _377420), -(c_Orderings_Oord__class_Oless(_377418, c_Groups_Ozero__class_Ozero(_377418), c_Groups_Oplus__class_Oplus(_377418, _377420, _377420)))]]], (6162 ^ _167881) ^ [_377948, _377950, _377952, _377954, _377956] : [class_Groups_Oordered__cancel__ab__semigroup__add(_377948), c_Orderings_Oord__class_Oless__eq(_377948, _377950, _377952), c_Orderings_Oord__class_Oless(_377948, _377954, _377956), -(c_Orderings_Oord__class_Oless(_377948, c_Groups_Oplus__class_Oplus(_377948, _377950, _377954), c_Groups_Oplus__class_Oplus(_377948, _377952, _377956)))], (6176 ^ _167881) ^ [_378440, _378442, _378444, _378446, _378448] : [class_Groups_Oordered__cancel__ab__semigroup__add(_378440), c_Orderings_Oord__class_Oless(_378440, _378442, _378444), c_Orderings_Oord__class_Oless__eq(_378440, _378446, _378448), -(c_Orderings_Oord__class_Oless(_378440, c_Groups_Oplus__class_Oplus(_378440, _378442, _378446), c_Groups_Oplus__class_Oplus(_378440, _378444, _378448)))], (6190 ^ _167881) ^ [_378904, _378906, _378908] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _378904), 6193 ^ _167881 : [(6194 ^ _167881) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _378904), _378906) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _378904), _378908), -(_378906 = _378908)], (6200 ^ _167881) ^ [] : [_378906 = _378908, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _378904), _378906) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _378904), _378908))]]], (6206 ^ _167881) ^ [_379432, _379434, _379436] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _379432), 6209 ^ _167881 : [(6210 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379432), _379434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379432), _379436)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _379434, _379436))], (6216 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _379434, _379436), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379432), _379434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379432), _379436)))]]], (6222 ^ _167881) ^ [_379966, _379968, _379970] : [class_Groups_Oordered__comm__monoid__add(_379966), c_Orderings_Oord__class_Oless__eq(_379966, _379968, c_Groups_Ozero__class_Ozero(_379966)), c_Orderings_Oord__class_Oless(_379966, _379970, c_Groups_Ozero__class_Ozero(_379966)), -(c_Orderings_Oord__class_Oless(_379966, c_Groups_Oplus__class_Oplus(_379966, _379968, _379970), c_Groups_Ozero__class_Ozero(_379966)))], (6236 ^ _167881) ^ [_380406, _380408, _380410] : [class_Groups_Oordered__comm__monoid__add(_380406), c_Orderings_Oord__class_Oless(_380406, _380408, c_Groups_Ozero__class_Ozero(_380406)), c_Orderings_Oord__class_Oless__eq(_380406, _380410, c_Groups_Ozero__class_Ozero(_380406)), -(c_Orderings_Oord__class_Oless(_380406, c_Groups_Oplus__class_Oplus(_380406, _380408, _380410), c_Groups_Ozero__class_Ozero(_380406)))], (6250 ^ _167881) ^ [_380860, _380862, _380864, _380866] : [class_Groups_Oordered__comm__monoid__add(_380860), c_Orderings_Oord__class_Oless__eq(_380860, c_Groups_Ozero__class_Ozero(_380860), _380862), c_Orderings_Oord__class_Oless(_380860, _380864, _380866), -(c_Orderings_Oord__class_Oless(_380860, _380864, c_Groups_Oplus__class_Oplus(_380860, _380862, _380866)))], (6264 ^ _167881) ^ [_381306, _381308, _381310] : [class_Rings_Odivision__ring(_381306), -(_381308 = c_Groups_Ozero__class_Ozero(_381306)), -(_381310 = c_Groups_Ozero__class_Ozero(_381306)), -(c_Groups_Ominus__class_Ominus(_381306, c_Rings_Oinverse__class_Oinverse(_381306, _381308), c_Rings_Oinverse__class_Oinverse(_381306, _381310)) = c_Groups_Ouminus__class_Ouminus(_381306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381306), c_Rings_Oinverse__class_Oinverse(_381306, _381308)), c_Groups_Ominus__class_Ominus(_381306, _381308, _381310))), c_Rings_Oinverse__class_Oinverse(_381306, _381310))))], (6278 ^ _167881) ^ [_381783, _381785] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _381783, _381785) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _381783, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _381785)))], (6280 ^ _167881) ^ [_381903, _381905] : [-(_381903 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_381905 = 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), _381903), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 6287 ^ [_381903, _381905]), _381905)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (6301 ^ _167881) ^ [_382622, _382624] : [6302 ^ _167881 : [(6303 ^ _167881) ^ [] : [_382624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6305 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _382622)]], -(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), _382622), _382624)))], (6291 ^ _167881) ^ [_382354, _382356] : [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), _382354), _382356)), -(_382356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _382354))], (6309 ^ _167881) ^ [_382939] : [-(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), _382939), _382939))), -(_382939 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6315 ^ _167881) ^ [_383112] : [_383112 = 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), _383112), _383112))], (6321 ^ _167881) ^ [_383361, _383363, _383365, _383367] : [class_Rings_Ocomm__semiring__1(_383361), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383361), hAPP(hAPP(c_Power_Opower__class_Opower(_383361), _383363), _383365)), hAPP(hAPP(c_Power_Opower__class_Opower(_383361), _383363), _383367)) = hAPP(hAPP(c_Power_Opower__class_Opower(_383361), _383363), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _383365, _383367)))], (6327 ^ _167881) ^ [_383638, _383640] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _383638, _383640) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _383638, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _383640)))], (6329 ^ _167881) ^ [_383743, _383745] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _383743, _383745) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _383743, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _383745)))], (6331 ^ _167881) ^ [_383863, _383865] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _383863, _383865) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _383865, _383863) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_383863 = _383865)], (6341 ^ _167881) ^ [_384149] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _384149, _384149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6343 ^ _167881) ^ [_384231] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _384231, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _384231)], (6345 ^ _167881) ^ [_384313] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _384313) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6347 ^ _167881) ^ [_384438, _384440, _384442] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _384438, _384440), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _384438, _384442), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _384442, _384440), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _384442, _384438)))], (6357 ^ _167881) ^ [_384783, _384785, _384787] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _384783, _384785), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _384783, _384787), _384785))], (6363 ^ _167881) ^ [_384996, _384998] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _384996, _384998), _384998) = _384996)], (6365 ^ _167881) ^ [_385098, _385100] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _385098, _385100), _385098) = _385100)], (6367 ^ _167881) ^ [_385214, _385216, _385218] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385214, _385216), _385218) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385214, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _385216, _385218)))], (6369 ^ _167881) ^ [_385340, _385342, _385344] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _385340, _385342), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _385340, _385344)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385342, _385344))], (6371 ^ _167881) ^ [_385466, _385468, _385470] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _385466, _385468), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _385470, _385468)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385466, _385470))], (6373 ^ _167881) ^ [_385578, _385580] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385578, _385580), _385578))], (6375 ^ _167881) ^ [_385706, _385708, _385710] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _385706, _385708), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385710, _385708), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385710, _385706)))], (6381 ^ _167881) ^ [_385956, _385958, _385960] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _385956, _385958), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385956, _385960), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _385958, _385960)))], (6387 ^ _167881) ^ [_386192, _386194] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _386192, _386194), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _386194, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _386194, _386192)) = _386192)], (6393 ^ _167881) ^ [_386434, _386436, _386438] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _386434, _386436), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _386434, _386438), 6400 ^ _167881 : [(6401 ^ _167881) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _386436, _386434) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _386438, _386434), -(_386436 = _386438)], (6407 ^ _167881) ^ [] : [_386436 = _386438, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _386436, _386434) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _386438, _386434))]]], (6413 ^ _167881) ^ [_387045, _387047, _387049] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387045, _387047), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387045, _387049), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _387047, _387045), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _387049, _387045)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _387047, _387049))], (6423 ^ _167881) ^ [_387404, _387406, _387408] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387404, _387406), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387404, _387408), 6430 ^ _167881 : [(6431 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _387406, _387404), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _387408, _387404)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387406, _387408))], (6437 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387406, _387408), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _387406, _387404), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _387408, _387404)))]]], (6443 ^ _167881) ^ [_388006, _388008, _388010] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388006), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _388008, _388010)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388006), _388008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388006), _388010)))], (6445 ^ _167881) ^ [_388142, _388144, _388146] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _388142, _388144)), _388146) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388142), _388146), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388144), _388146)))], (6447 ^ _167881) ^ [_388250] : [-(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, _388250)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _388250)))], (6449 ^ _167881) ^ [_388396, _388398] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _388396, _388398), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _388396, _388398), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (6455 ^ _167881) ^ [_388570, _388572] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _388570, _388572), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _388570, _388572))], (6461 ^ _167881) ^ [_388794, _388796] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _388794), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _388796), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _388796, _388794), _388796))], (6471 ^ _167881) ^ [_389136, _389138] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _389136, _389138)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _389138, _389136))], (6477 ^ _167881) ^ [_389310, _389312] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _389312, _389310), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _389310, _389312)))], (6483 ^ _167881) ^ [_389519, _389521] : [-(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), _389519), _389519)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _389521), _389521)))], (6485 ^ _167881) ^ [_389629, _389631] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _389629, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _389629, _389631)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6487 ^ _167881) ^ [_389775, _389777] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _389775, _389777) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _389775, _389777))], (6493 ^ _167881) ^ [_389947, _389949] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _389947, _389949), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _389947, _389949) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6499 ^ _167881) ^ [_390169, _390171] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _390169, _390171), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _390169, _390171) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6505 ^ _167881) ^ [_390389, _390391] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _390389, _390391)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _390391, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _390389, _390391)) = _390389)], (6511 ^ _167881) ^ [_390663, _390665, _390667] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _390663, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _390665, _390667)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _390663, _390667), _390665))], (6517 ^ _167881) ^ [_390851, _390853, _390855] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _390851, _390855), _390853), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _390851, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _390853, _390855)))], (6523 ^ _167881) ^ [_391103, _391105, _391107] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _391103, _391105), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _391107, _391103), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _391103, _391107), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _391105, _391107)))], (6533 ^ _167881) ^ [_391448, _391450, _391452] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _391448, _391450), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _391448, _391452), 6540 ^ _167881 : [(6541 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _391450, _391448), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _391452, _391448)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _391450, _391452))], (6547 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _391450, _391452), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _391450, _391448), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _391452, _391448)))]]], (6553 ^ _167881) ^ [_392080, _392082] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _392080, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _392082)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_392080 = _392082)], (6559 ^ _167881) ^ [_392256, _392258] : [_392256 = _392258, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _392256, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _392258)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6565 ^ _167881) ^ [_392511, _392513] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _392511, _392513) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_392513 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _392511))], (6571 ^ _167881) ^ [_392687, _392689] : [_392689 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _392687), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _392687, _392689) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6577 ^ _167881) ^ [_392927, _392929, _392931] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _392927, _392929), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _392931, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _392929, _392927)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _392931, _392927), _392929))], (6583 ^ _167881) ^ [_393220, _393222, _393224] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _393220, _393222), _393224), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393220, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393224, _393222)))], (6589 ^ _167881) ^ [_393408, _393410, _393412] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393408, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393412, _393410)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _393408, _393410), _393412))], (6595 ^ _167881) ^ [_393660, _393662, _393664] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393660, _393662), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393664, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393662, _393664), _393660)))], (6601 ^ _167881) ^ [_393896, _393898] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393896, _393898), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393896, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _393898, _393896)) = _393898)], (6607 ^ _167881) ^ [_394138, _394140, _394142] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _394138, _394140), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _394142, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _394140, _394138)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _394142, _394140), _394138))], (6613 ^ _167881) ^ [_394402, _394404, _394406] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _394402, _394404), 6616 ^ _167881 : [(6617 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _394406, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _394404, _394402)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _394406, _394402), _394404))], (6623 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _394406, _394402), _394404), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _394406, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _394404, _394402)))]]], (6629 ^ _167881) ^ [_394910, _394912] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _394910, _394912), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _394912, _394910), _394910) = _394912)], (6635 ^ _167881) ^ [_395152, _395154, _395156] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _395152, _395154), 6638 ^ _167881 : [(6639 ^ _167881) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395154, _395152) = _395156, -(_395154 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395156, _395152))], (6645 ^ _167881) ^ [] : [_395154 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395156, _395152), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395154, _395152) = _395156)]]], (6651 ^ _167881) ^ [_395668, _395670, _395672] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _395668, _395670), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395672, _395670), _395668) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395672, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395670, _395668)))], (6657 ^ _167881) ^ [_395932, _395934, _395936] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _395932, _395934), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _395934, _395932), _395936) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395934, _395936), _395932))], (6663 ^ _167881) ^ [_396196, _396198, _396200] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _396196, _396198), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396198, _396200), _396196) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396198, _396196), _396200))], (6669 ^ _167881) ^ [_396431, _396433] : [-(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, _396431, _396433)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _396431)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _396433)))], (6671 ^ _167881) ^ [_396572, _396574, _396576] : [class_RealVector_Oreal__normed__vector(_396572), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_396572, _396574), c_RealVector_Onorm__class_Onorm(_396572, _396576)), c_RealVector_Onorm__class_Onorm(_396572, c_Groups_Oplus__class_Oplus(_396572, _396574, _396576))))], (6693 ^ _167881) ^ [_397396, _397398, _397400] : [-(hBOOL(hAPP(_397396, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _397398, _397400)))), 6696 ^ _167881 : [(6697 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397398, _397400))], (6699 ^ _167881) ^ [] : [hBOOL(hAPP(_397396, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6701 ^ _167881 : [(6702 ^ _167881) ^ [] : [-(_397398 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397400, 6700 ^ [_397396, _397398, _397400]))], (6704 ^ _167881) ^ [] : [hBOOL(hAPP(_397396, 6700 ^ [_397396, _397398, _397400]))]]], (6677 ^ _167881) ^ [_396865, _396867, _396869] : [hBOOL(hAPP(_396865, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _396867, _396869))), 6680 ^ _167881 : [(6681 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396867, _396869), -(hBOOL(hAPP(_396865, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6687 ^ _167881) ^ [_397197] : [_396867 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396869, _397197), -(hBOOL(hAPP(_396865, _397197)))]]], (6724 ^ _167881) ^ [_398557, _398559, _398561] : [-(hBOOL(hAPP(_398557, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398559, _398561)))), 6727 ^ _167881 : [(6728 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398559, _398561))], (6730 ^ _167881) ^ [] : [hBOOL(hAPP(_398557, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6732 ^ _167881 : [(6733 ^ _167881) ^ [] : [-(_398559 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _398561, 6731 ^ [_398557, _398559, _398561]))], (6735 ^ _167881) ^ [] : [hBOOL(hAPP(_398557, 6731 ^ [_398557, _398559, _398561]))]]], (6708 ^ _167881) ^ [_398018, _398020, _398022] : [hBOOL(hAPP(_398018, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _398020, _398022))), 6711 ^ _167881 : [(6712 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398020, _398022), -(hBOOL(hAPP(_398018, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6718 ^ _167881) ^ [_398356] : [_398020 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _398022, _398356), -(hBOOL(hAPP(_398018, _398356)))]]], (6739 ^ _167881) ^ [_399173, _399175] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _399173, _399175), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _399175, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _399173)))], (6745 ^ _167881) ^ [_399353, _399355] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _399355, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _399353)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _399353, _399355), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (6751 ^ _167881) ^ [_399612, _399614] : [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, _399612, _399614)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _399612), _399614))], (6757 ^ _167881) ^ [_399792, _399794] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _399792), _399794), -(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, _399792, _399794)))], (6763 ^ _167881) ^ [_400051, _400053] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _400051, _400053)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _400051), _400053))], (6769 ^ _167881) ^ [_400231, _400233] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _400231), _400233), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _400231, _400233)))], (6775 ^ _167881) ^ [_400490, _400492] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _400490, _400492), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _400492, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _400490)))], (6781 ^ _167881) ^ [_400670, _400672] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _400672, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _400670)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _400670, _400672), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (6787 ^ _167881) ^ [_400942, _400944, _400946, _400948, _400950] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400942, _400944), 6790 ^ _167881 : [(6791 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400942), _400946), _400948) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400944), _400946), _400950), -(_400948 = 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, _400944, _400942)), _400946), _400950))], (6797 ^ _167881) ^ [] : [_400948 = 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, _400944, _400942)), _400946), _400950), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400942), _400946), _400948) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400944), _400946), _400950))]]], (6803 ^ _167881) ^ [_401596, _401598, _401600, _401602, _401604] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401596, _401598), -(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), _401596), _401600), _401602), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401598), _401600), _401604)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401602, 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, _401598, _401596)), _401600), _401604)))], (6809 ^ _167881) ^ [_401952, _401954, _401956, _401958, _401960] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401952, _401954), 6812 ^ _167881 : [(6813 ^ _167881) ^ [] : [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), _401952), _401956), _401958), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401954), _401956), _401960)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401958, 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, _401954, _401952)), _401956), _401960)))], (6819 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401958, 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, _401954, _401952)), _401956), _401960)), -(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), _401952), _401956), _401958), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401954), _401956), _401960)))]]], (6825 ^ _167881) ^ [_402612, _402614, _402616, _402618, _402620] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402612, _402614), 6828 ^ _167881 : [(6829 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402614), _402616), _402618) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402612), _402616), _402620), -(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, _402614, _402612)), _402616), _402618) = _402620)], (6835 ^ _167881) ^ [] : [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, _402614, _402612)), _402616), _402618) = _402620, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402614), _402616), _402618) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402612), _402616), _402620))]]], (6841 ^ _167881) ^ [_403266, _403268, _403270, _403272, _403274] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403266, _403268), -(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), _403268), _403270), _403272), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403266), _403270), _403274)) = 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, _403268, _403266)), _403270), _403272), _403274))], (6847 ^ _167881) ^ [_403622, _403624, _403626, _403628, _403630] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403622, _403624), 6850 ^ _167881 : [(6851 ^ _167881) ^ [] : [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), _403624), _403626), _403628), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403622), _403626), _403630)), -(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, _403624, _403622)), _403626), _403628), _403630))], (6857 ^ _167881) ^ [] : [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, _403624, _403622)), _403626), _403628), _403630), -(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), _403624), _403626), _403628), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403622), _403626), _403630)))]]], (6863 ^ _167881) ^ [_404254, _404256, _404258] : [class_Rings_Ocomm__semiring__1(_404254), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404254), _404256), _404258) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404254), _404258), _404256))], (6869 ^ _167881) ^ [_404528, _404530, _404532, _404534] : [class_Rings_Ocomm__semiring__1(_404528), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404528), _404530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404528), _404532), _404534)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404528), _404532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404528), _404530), _404534)))], (6875 ^ _167881) ^ [_404840, _404842, _404844, _404846] : [class_Rings_Ocomm__semiring__1(_404840), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404840), _404842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404840), _404844), _404846)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404840), _404842), _404844)), _404846))], (6881 ^ _167881) ^ [_405152, _405154, _405156, _405158] : [class_Rings_Ocomm__semiring__1(_405152), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405152), _405154), _405156)), _405158) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405152), _405154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405152), _405156), _405158)))], (6887 ^ _167881) ^ [_405464, _405466, _405468, _405470] : [class_Rings_Ocomm__semiring__1(_405464), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405464), _405466), _405468)), _405470) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405464), _405466), _405470)), _405468))], (6893 ^ _167881) ^ [_405790, _405792, _405794, _405796, _405798] : [class_Rings_Ocomm__semiring__1(_405790), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405790), _405792), _405794)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405790), _405796), _405798)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405790), _405792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405790), _405794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405790), _405796), _405798))))], (6899 ^ _167881) ^ [_406154, _406156, _406158, _406160, _406162] : [class_Rings_Ocomm__semiring__1(_406154), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406154), _406156), _406158)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406154), _406160), _406162)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406154), _406160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406154), _406156), _406158)), _406162)))], (6905 ^ _167881) ^ [_406518, _406520, _406522, _406524, _406526] : [class_Rings_Ocomm__semiring__1(_406518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406518), _406520), _406522)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406518), _406524), _406526)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406518), _406520), _406524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406518), _406522), _406526)))], (6911 ^ _167881) ^ [_406854, _406856, _406858] : [class_Rings_Ocomm__semiring__1(_406854), -(c_Groups_Oplus__class_Oplus(_406854, _406856, _406858) = c_Groups_Oplus__class_Oplus(_406854, _406858, _406856))], (6917 ^ _167881) ^ [_407112, _407114, _407116, _407118] : [class_Rings_Ocomm__semiring__1(_407112), -(c_Groups_Oplus__class_Oplus(_407112, _407114, c_Groups_Oplus__class_Oplus(_407112, _407116, _407118)) = c_Groups_Oplus__class_Oplus(_407112, _407116, c_Groups_Oplus__class_Oplus(_407112, _407114, _407118)))], (6923 ^ _167881) ^ [_407392, _407394, _407396, _407398] : [class_Rings_Ocomm__semiring__1(_407392), -(c_Groups_Oplus__class_Oplus(_407392, _407394, c_Groups_Oplus__class_Oplus(_407392, _407396, _407398)) = c_Groups_Oplus__class_Oplus(_407392, c_Groups_Oplus__class_Oplus(_407392, _407394, _407396), _407398))], (6929 ^ _167881) ^ [_407672, _407674, _407676, _407678] : [class_Rings_Ocomm__semiring__1(_407672), -(c_Groups_Oplus__class_Oplus(_407672, c_Groups_Oplus__class_Oplus(_407672, _407674, _407676), _407678) = c_Groups_Oplus__class_Oplus(_407672, _407674, c_Groups_Oplus__class_Oplus(_407672, _407676, _407678)))], (6935 ^ _167881) ^ [_407952, _407954, _407956, _407958] : [class_Rings_Ocomm__semiring__1(_407952), -(c_Groups_Oplus__class_Oplus(_407952, c_Groups_Oplus__class_Oplus(_407952, _407954, _407956), _407958) = c_Groups_Oplus__class_Oplus(_407952, c_Groups_Oplus__class_Oplus(_407952, _407954, _407958), _407956))], (6941 ^ _167881) ^ [_408246, _408248, _408250, _408252, _408254] : [class_Rings_Ocomm__semiring__1(_408246), -(c_Groups_Oplus__class_Oplus(_408246, c_Groups_Oplus__class_Oplus(_408246, _408248, _408250), c_Groups_Oplus__class_Oplus(_408246, _408252, _408254)) = c_Groups_Oplus__class_Oplus(_408246, c_Groups_Oplus__class_Oplus(_408246, _408248, _408252), c_Groups_Oplus__class_Oplus(_408246, _408250, _408254)))], (6947 ^ _167881) ^ [] : [-(c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (6949 ^ _167881) ^ [_408615, _408617, _408619, _408621, _408623] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _408615, _408617), 6952 ^ _167881 : [(6953 ^ _167881) ^ [] : [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), _408617), _408619), _408621), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _408615), _408619), _408623)), -(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, _408617, _408615)), _408619), _408621), _408623))], (6959 ^ _167881) ^ [] : [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, _408617, _408615)), _408619), _408621), _408623), -(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), _408617), _408619), _408621), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _408615), _408619), _408623)))]]], (6965 ^ _167881) ^ [_409275, _409277, _409279, _409281, _409283] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409275, _409277), 6968 ^ _167881 : [(6969 ^ _167881) ^ [] : [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), _409275), _409279), _409281), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _409277), _409279), _409283)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409281, 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, _409277, _409275)), _409279), _409283)))], (6975 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409281, 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, _409277, _409275)), _409279), _409283)), -(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), _409275), _409279), _409281), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _409277), _409279), _409283)))]]], (6981 ^ _167881) ^ [_409913, _409915] : [_409913 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _409913), _409915) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6987 ^ _167881) ^ [_410087, _410089] : [-(_410087 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _410087), _410089) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _410089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _410087, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _410089)))], (6993 ^ _167881) ^ [_410362, _410364] : [_410362 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _410364), _410362) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6999 ^ _167881) ^ [_410536, _410538] : [-(_410536 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _410538), _410536) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _410538), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _410538), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _410536, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (7005 ^ _167881) ^ [_410809, _410811, _410813] : [class_Power_Opower(_410809), 7008 ^ _167881 : [(7009 ^ _167881) ^ [] : [_410811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_410809), _410813), _410811) = c_Groups_Oone__class_Oone(_410809))], (7015 ^ _167881) ^ [] : [-(_410811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_410809), _410813), _410811) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410809), _410813), hAPP(hAPP(c_Power_Opower__class_Opower(_410809), _410813), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _410811, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (7021 ^ _167881) ^ [_411379, _411381, _411383] : [class_Groups_Omonoid__mult(_411379), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _411381), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411379), hAPP(hAPP(c_Power_Opower__class_Opower(_411379), _411383), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _411381, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _411383) = hAPP(hAPP(c_Power_Opower__class_Opower(_411379), _411383), _411381))], (7031 ^ _167881) ^ [_411744, _411746] : [class_Rings_Ocomm__semiring__1(_411744), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411744), c_Groups_Ozero__class_Ozero(_411744)), _411746) = c_Groups_Ozero__class_Ozero(_411744))], (7037 ^ _167881) ^ [_411976, _411978] : [class_Rings_Ocomm__semiring__1(_411976), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411976), _411978), c_Groups_Ozero__class_Ozero(_411976)) = c_Groups_Ozero__class_Ozero(_411976))], (7043 ^ _167881) ^ [_412208, _412210] : [class_Rings_Ocomm__semiring__1(_412208), -(c_Groups_Oplus__class_Oplus(_412208, c_Groups_Ozero__class_Ozero(_412208), _412210) = _412210)], (7049 ^ _167881) ^ [_412428, _412430] : [class_Rings_Ocomm__semiring__1(_412428), -(c_Groups_Oplus__class_Oplus(_412428, _412430, c_Groups_Ozero__class_Ozero(_412428)) = _412430)], (7055 ^ _167881) ^ [_412662, _412664, _412666] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_412662), 7058 ^ _167881 : [(7059 ^ _167881) ^ [] : [_412664 = c_Groups_Oplus__class_Oplus(_412662, _412664, _412666), -(_412666 = c_Groups_Ozero__class_Ozero(_412662))], (7065 ^ _167881) ^ [] : [_412666 = c_Groups_Ozero__class_Ozero(_412662), -(_412664 = c_Groups_Oplus__class_Oplus(_412662, _412664, _412666))]]], (7071 ^ _167881) ^ [_413182, _413184, _413186, _413188] : [class_Rings_Ocomm__semiring__1(_413182), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413182), _413184), c_Groups_Oplus__class_Oplus(_413182, _413186, _413188)) = c_Groups_Oplus__class_Oplus(_413182, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413182), _413184), _413186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413182), _413184), _413188)))], (7077 ^ _167881) ^ [_413508, _413510, _413512, _413514, _413516] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_413508), 7080 ^ _167881 : [(7091 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(_413508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413508), _413510), _413514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413508), _413512), _413516)) = c_Groups_Oplus__class_Oplus(_413508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413508), _413510), _413516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413508), _413512), _413514))), 7094 ^ _167881 : [(7095 ^ _167881) ^ [] : [_413510 = _413512], (7097 ^ _167881) ^ [] : [_413514 = _413516]]], (7081 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_413508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413508), _413510), _413514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413508), _413512), _413516)) = c_Groups_Oplus__class_Oplus(_413508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413508), _413510), _413516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413508), _413512), _413514)), -(_413510 = _413512), -(_413514 = _413516)]]], (7099 ^ _167881) ^ [_414344, _414346, _414348, _414350] : [class_Rings_Ocomm__semiring__1(_414344), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414344), c_Groups_Oplus__class_Oplus(_414344, _414346, _414348)), _414350) = c_Groups_Oplus__class_Oplus(_414344, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414344), _414346), _414350), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414344), _414348), _414350)))], (7105 ^ _167881) ^ [_414656, _414658, _414660, _414662] : [class_Rings_Ocomm__semiring__1(_414656), -(c_Groups_Oplus__class_Oplus(_414656, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414656), _414658), _414660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414656), _414662), _414660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414656), c_Groups_Oplus__class_Oplus(_414656, _414658, _414662)), _414660))], (7111 ^ _167881) ^ [_414982, _414984, _414986, _414988, _414990] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_414982), 7114 ^ _167881 : [(7125 ^ _167881) ^ [] : [7126 ^ _167881 : [(7127 ^ _167881) ^ [] : [_414984 = _414988], (7129 ^ _167881) ^ [] : [_414986 = _414990]], -(c_Groups_Oplus__class_Oplus(_414982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414982), _414984), _414986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414982), _414988), _414990)) = c_Groups_Oplus__class_Oplus(_414982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414982), _414984), _414990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414982), _414988), _414986)))], (7115 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_414982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414982), _414984), _414986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414982), _414988), _414990)) = c_Groups_Oplus__class_Oplus(_414982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414982), _414984), _414990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414982), _414988), _414986)), -(_414984 = _414988), -(_414986 = _414990)]]], (7133 ^ _167881) ^ [_415784, _415786] : [class_Rings_Ocomm__semiring__1(_415784), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415784), c_Groups_Oone__class_Oone(_415784)), _415786) = _415786)], (7139 ^ _167881) ^ [_416012, _416014] : [class_Rings_Ocomm__semiring__1(_416012), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416012), _416014), c_Groups_Oone__class_Oone(_416012)) = _416014)], (7145 ^ _167881) ^ [_416282, _416284, _416286, _416288, _416290] : [class_Groups_Oab__group__add(_416282), -(c_Groups_Ominus__class_Ominus(_416282, c_Groups_Oplus__class_Oplus(_416282, _416284, _416286), c_Groups_Oplus__class_Oplus(_416282, _416288, _416290)) = c_Groups_Oplus__class_Oplus(_416282, c_Groups_Ominus__class_Ominus(_416282, _416284, _416288), c_Groups_Ominus__class_Ominus(_416282, _416286, _416290)))], (7151 ^ _167881) ^ [_416584, _416586, _416588, _416590] : [class_Rings_Ocomm__semiring__1(_416584), -(hAPP(hAPP(c_Power_Opower__class_Opower(_416584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416584), _416586), _416588)), _416590) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416584), hAPP(hAPP(c_Power_Opower__class_Opower(_416584), _416586), _416590)), hAPP(hAPP(c_Power_Opower__class_Opower(_416584), _416588), _416590)))], (7157 ^ _167881) ^ [_416912, _416914, _416916, _416918] : [class_Rings_Ocomm__semiring__1(_416912), -(hAPP(hAPP(c_Power_Opower__class_Opower(_416912), hAPP(hAPP(c_Power_Opower__class_Opower(_416912), _416914), _416916)), _416918) = hAPP(hAPP(c_Power_Opower__class_Opower(_416912), _416914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416916), _416918)))], (7163 ^ _167881) ^ [_417192, _417194] : [class_Rings_Ocomm__semiring__1(_417192), -(hAPP(hAPP(c_Power_Opower__class_Opower(_417192), _417194), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _417194)], (7169 ^ _167881) ^ [_417472, _417474, _417476, _417478, _417480, _417482] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_417472), -(_417474 = c_Groups_Ozero__class_Ozero(_417472)), c_Groups_Oplus__class_Oplus(_417472, _417476, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417472), _417474), _417480)) = c_Groups_Oplus__class_Oplus(_417472, _417478, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417472), _417474), _417482)), _417476 = _417478, -(_417480 = _417482)], (7187 ^ _167881) ^ [_418078, _418080] : [class_Rings_Ocomm__semiring__1(_418078), -(c_Groups_Oplus__class_Oplus(_418078, _418080, _418080) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418078), c_Groups_Oplus__class_Oplus(_418078, c_Groups_Oone__class_Oone(_418078), c_Groups_Oone__class_Oone(_418078))), _418080))], (7193 ^ _167881) ^ [_418340, _418342, _418344] : [class_Rings_Ocomm__semiring__1(_418340), -(c_Groups_Oplus__class_Oplus(_418340, _418342, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418340), _418344), _418342)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418340), c_Groups_Oplus__class_Oplus(_418340, _418344, c_Groups_Oone__class_Oone(_418340))), _418342))], (7199 ^ _167881) ^ [_418620, _418622, _418624] : [class_Rings_Ocomm__semiring__1(_418620), -(c_Groups_Oplus__class_Oplus(_418620, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418620), _418622), _418624), _418624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418620), c_Groups_Oplus__class_Oplus(_418620, _418622, c_Groups_Oone__class_Oone(_418620))), _418624))], (7205 ^ _167881) ^ [_418886, _418888] : [class_Rings_Ocomm__ring__1(_418886), -(c_Groups_Ouminus__class_Ouminus(_418886, _418888) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418886), c_Groups_Ouminus__class_Ouminus(_418886, c_Groups_Oone__class_Oone(_418886))), _418888))], (7211 ^ _167881) ^ [_419140, _419142, _419144] : [class_Rings_Ocomm__ring__1(_419140), -(c_Groups_Ominus__class_Ominus(_419140, _419142, _419144) = c_Groups_Oplus__class_Oplus(_419140, _419142, c_Groups_Ouminus__class_Ouminus(_419140, _419144)))], (7217 ^ _167881) ^ [_419376, _419378] : [class_Rings_Ocomm__semiring__1(_419376), -(hAPP(hAPP(c_Power_Opower__class_Opower(_419376), _419378), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_419376))], (7223 ^ _167881) ^ [_419604, _419606] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _419604), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _419604, _419606), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _419606, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _419606)), _419604), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7237 ^ _167881) ^ [] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))], (7239 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (7241 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (7243 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p))], (7245 ^ _167881) ^ [_420219] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _420219), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), _420219)), v_m____))], (7251 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (7253 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))))], (7255 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))))], (7257 ^ _167881) ^ [_420603, _420605, _420607] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _420603, _420605), _420607) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _420603, _420607), _420605))], (7259 ^ _167881) ^ [_420730, _420732] : [class_Groups_Oordered__ab__group__add__abs(_420730), 7262 ^ _167881 : [(7263 ^ _167881) ^ [] : [c_Groups_Oabs__class_Oabs(_420730, _420732) = c_Groups_Ozero__class_Ozero(_420730), -(_420732 = c_Groups_Ozero__class_Ozero(_420730))], (7269 ^ _167881) ^ [] : [_420732 = c_Groups_Ozero__class_Ozero(_420730), -(c_Groups_Oabs__class_Oabs(_420730, _420732) = c_Groups_Ozero__class_Ozero(_420730))]]], (7275 ^ _167881) ^ [_421195] : [class_Groups_Oordered__ab__group__add__abs(_421195), -(c_Groups_Oabs__class_Oabs(_421195, c_Groups_Ozero__class_Ozero(_421195)) = c_Groups_Ozero__class_Ozero(_421195))], (7281 ^ _167881) ^ [_421411, _421413] : [class_Groups_Oordered__ab__group__add__abs(_421411), -(c_Orderings_Oord__class_Oless__eq(_421411, _421413, c_Groups_Oabs__class_Oabs(_421411, _421413)))], (7287 ^ _167881) ^ [_421641, _421643, _421645] : [class_Groups_Oordered__ab__group__add__abs(_421641), c_Orderings_Oord__class_Oless__eq(_421641, c_Groups_Oabs__class_Oabs(_421641, _421643), _421645), -(c_Orderings_Oord__class_Oless__eq(_421641, _421643, _421645))], (7297 ^ _167881) ^ [_421972, _421974, _421976] : [class_Rings_Olinordered__idom(_421972), -(c_Groups_Oabs__class_Oabs(_421972, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421972), _421974), _421976)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421972), c_Groups_Oabs__class_Oabs(_421972, _421974)), c_Groups_Oabs__class_Oabs(_421972, _421976)))], (7303 ^ _167881) ^ [_422236, _422238] : [class_Rings_Olinordered__idom(_422236), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422236), c_Groups_Oabs__class_Oabs(_422236, _422238)), c_Groups_Oabs__class_Oabs(_422236, _422238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422236), _422238), _422238))], (7309 ^ _167881) ^ [_422502, _422504, _422506] : [class_Groups_Oordered__ab__group__add__abs(_422502), -(c_Groups_Oabs__class_Oabs(_422502, c_Groups_Oplus__class_Oplus(_422502, c_Groups_Oabs__class_Oabs(_422502, _422504), c_Groups_Oabs__class_Oabs(_422502, _422506))) = c_Groups_Oplus__class_Oplus(_422502, c_Groups_Oabs__class_Oabs(_422502, _422504), c_Groups_Oabs__class_Oabs(_422502, _422506)))], (7315 ^ _167881) ^ [_422748] : [class_Rings_Olinordered__idom(_422748), -(c_Groups_Oabs__class_Oabs(_422748, c_Groups_Oone__class_Oone(_422748)) = c_Groups_Oone__class_Oone(_422748))], (7321 ^ _167881) ^ [_422978, _422980, _422982] : [class_Groups_Oordered__ab__group__add__abs(_422978), -(c_Groups_Oabs__class_Oabs(_422978, c_Groups_Ominus__class_Ominus(_422978, _422980, _422982)) = c_Groups_Oabs__class_Oabs(_422978, c_Groups_Ominus__class_Ominus(_422978, _422982, _422980)))], (7327 ^ _167881) ^ [_423220, _423222] : [class_Groups_Oordered__ab__group__add__abs(_423220), -(c_Groups_Oabs__class_Oabs(_423220, c_Groups_Ouminus__class_Ouminus(_423220, _423222)) = c_Groups_Oabs__class_Oabs(_423220, _423222))], (7333 ^ _167881) ^ [_423460, _423462, _423464] : [class_Rings_Olinordered__idom(_423460), -(c_Groups_Oabs__class_Oabs(_423460, hAPP(hAPP(c_Power_Opower__class_Opower(_423460), _423462), _423464)) = hAPP(hAPP(c_Power_Opower__class_Opower(_423460), c_Groups_Oabs__class_Oabs(_423460, _423462)), _423464))], (7339 ^ _167881) ^ [_423718, _423720] : [class_Fields_Olinordered__field__inverse__zero(_423718), -(c_Groups_Oabs__class_Oabs(_423718, c_Rings_Oinverse__class_Oinverse(_423718, _423720)) = c_Rings_Oinverse__class_Oinverse(_423718, c_Groups_Oabs__class_Oabs(_423718, _423720)))], (7345 ^ _167881) ^ [_423950, _423952] : [class_RealVector_Oreal__normed__vector(_423950), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_423950, _423952)) = c_RealVector_Onorm__class_Onorm(_423950, _423952))], (7351 ^ _167881) ^ [_424147] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _424147) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _424147))], (7353 ^ _167881) ^ [_424260, _424262] : [class_Groups_Oordered__ab__group__add__abs(_424260), -(c_Groups_Oabs__class_Oabs(_424260, c_Groups_Oabs__class_Oabs(_424260, _424262)) = c_Groups_Oabs__class_Oabs(_424260, _424262))], (7359 ^ _167881) ^ [_424486, _424488] : [class_Groups_Oordered__ab__group__add__abs(_424486), -(c_Orderings_Oord__class_Oless__eq(_424486, c_Groups_Ozero__class_Ozero(_424486), c_Groups_Oabs__class_Oabs(_424486, _424488)))], (7365 ^ _167881) ^ [_424706, _424708] : [class_Groups_Oordered__ab__group__add__abs(_424706), 7368 ^ _167881 : [(7369 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_424706, c_Groups_Oabs__class_Oabs(_424706, _424708), c_Groups_Ozero__class_Ozero(_424706)), -(_424708 = c_Groups_Ozero__class_Ozero(_424706))], (7375 ^ _167881) ^ [] : [_424708 = c_Groups_Ozero__class_Ozero(_424706), -(c_Orderings_Oord__class_Oless__eq(_424706, c_Groups_Oabs__class_Oabs(_424706, _424708), c_Groups_Ozero__class_Ozero(_424706)))]]], (7381 ^ _167881) ^ [_425188, _425190] : [class_Groups_Oordered__ab__group__add__abs(_425188), c_Orderings_Oord__class_Oless__eq(_425188, c_Groups_Ozero__class_Ozero(_425188), _425190), -(c_Groups_Oabs__class_Oabs(_425188, _425190) = _425190)], (7391 ^ _167881) ^ [_425497, _425499] : [class_Groups_Oordered__ab__group__add__abs(_425497), c_Orderings_Oord__class_Oless(_425497, c_Groups_Ozero__class_Ozero(_425497), _425499), -(c_Groups_Oabs__class_Oabs(_425497, _425499) = _425499)], (7401 ^ _167881) ^ [_425806, _425808] : [class_Groups_Oordered__ab__group__add__abs(_425806), 7404 ^ _167881 : [(7405 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_425806, c_Groups_Ozero__class_Ozero(_425806), c_Groups_Oabs__class_Oabs(_425806, _425808)), _425808 = c_Groups_Ozero__class_Ozero(_425806)], (7411 ^ _167881) ^ [] : [-(_425808 = c_Groups_Ozero__class_Ozero(_425806)), -(c_Orderings_Oord__class_Oless(_425806, c_Groups_Ozero__class_Ozero(_425806), c_Groups_Oabs__class_Oabs(_425806, _425808)))]]], (7417 ^ _167881) ^ [_426290, _426292] : [class_Groups_Oordered__ab__group__add__abs(_426290), c_Orderings_Oord__class_Oless(_426290, c_Groups_Oabs__class_Oabs(_426290, _426292), c_Groups_Ozero__class_Ozero(_426290))], (7423 ^ _167881) ^ [_426553, _426555, _426557, _426559, _426561] : [class_Rings_Olinordered__idom(_426553), c_Orderings_Oord__class_Oless(_426553, c_Groups_Oabs__class_Oabs(_426553, _426555), _426557), c_Orderings_Oord__class_Oless(_426553, c_Groups_Oabs__class_Oabs(_426553, _426559), _426561), -(c_Orderings_Oord__class_Oless(_426553, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_426553), c_Groups_Oabs__class_Oabs(_426553, _426555)), c_Groups_Oabs__class_Oabs(_426553, _426559)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_426553), _426557), _426561)))], (7437 ^ _167881) ^ [_427057, _427059, _427061] : [class_Groups_Oordered__ab__group__add__abs(_427057), -(c_Orderings_Oord__class_Oless__eq(_427057, c_Groups_Oabs__class_Oabs(_427057, c_Groups_Oplus__class_Oplus(_427057, _427059, _427061)), c_Groups_Oplus__class_Oplus(_427057, c_Groups_Oabs__class_Oabs(_427057, _427059), c_Groups_Oabs__class_Oabs(_427057, _427061))))], (7443 ^ _167881) ^ [_427321, _427323, _427325] : [class_Groups_Oordered__ab__group__add__abs(_427321), -(c_Orderings_Oord__class_Oless__eq(_427321, c_Groups_Oabs__class_Oabs(_427321, c_Groups_Ominus__class_Ominus(_427321, c_Groups_Oabs__class_Oabs(_427321, _427323), c_Groups_Oabs__class_Oabs(_427321, _427325))), c_Groups_Oabs__class_Oabs(_427321, c_Groups_Ominus__class_Ominus(_427321, _427323, _427325))))], (7449 ^ _167881) ^ [_427591, _427593, _427595] : [class_Groups_Oordered__ab__group__add__abs(_427591), -(c_Orderings_Oord__class_Oless__eq(_427591, c_Groups_Ominus__class_Ominus(_427591, c_Groups_Oabs__class_Oabs(_427591, _427593), c_Groups_Oabs__class_Oabs(_427591, _427595)), c_Groups_Oabs__class_Oabs(_427591, c_Groups_Ominus__class_Ominus(_427591, _427593, _427595))))], (7455 ^ _167881) ^ [_427855, _427857, _427859] : [class_Groups_Oordered__ab__group__add__abs(_427855), -(c_Orderings_Oord__class_Oless__eq(_427855, c_Groups_Ominus__class_Ominus(_427855, c_Groups_Oabs__class_Oabs(_427855, _427857), c_Groups_Oabs__class_Oabs(_427855, _427859)), c_Groups_Oabs__class_Oabs(_427855, c_Groups_Ominus__class_Ominus(_427855, _427859, _427857))))], (7461 ^ _167881) ^ [_428105, _428107] : [class_Groups_Oordered__ab__group__add__abs(_428105), -(c_Orderings_Oord__class_Oless__eq(_428105, c_Groups_Ouminus__class_Ouminus(_428105, _428107), c_Groups_Oabs__class_Oabs(_428105, _428107)))], (7467 ^ _167881) ^ [_428341, _428343, _428345] : [class_Groups_Oordered__ab__group__add__abs(_428341), 7470 ^ _167881 : [(7471 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_428341, c_Groups_Oabs__class_Oabs(_428341, _428343), _428345), 7474 ^ _167881 : [(7475 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_428341, _428343, _428345))], (7477 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_428341, c_Groups_Ouminus__class_Ouminus(_428341, _428343), _428345))]]], (7479 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_428341, c_Groups_Oabs__class_Oabs(_428341, _428343), _428345)), c_Orderings_Oord__class_Oless__eq(_428341, _428343, _428345), c_Orderings_Oord__class_Oless__eq(_428341, c_Groups_Ouminus__class_Ouminus(_428341, _428343), _428345)]]], (7489 ^ _167881) ^ [_429020, _429022, _429024] : [class_Groups_Oordered__ab__group__add__abs(_429020), c_Orderings_Oord__class_Oless__eq(_429020, _429022, _429024), c_Orderings_Oord__class_Oless__eq(_429020, c_Groups_Ouminus__class_Ouminus(_429020, _429022), _429024), -(c_Orderings_Oord__class_Oless__eq(_429020, c_Groups_Oabs__class_Oabs(_429020, _429022), _429024))], (7503 ^ _167881) ^ [_429452, _429454, _429456] : [class_Groups_Oordered__ab__group__add__abs(_429452), c_Orderings_Oord__class_Oless__eq(_429452, c_Groups_Oabs__class_Oabs(_429452, _429454), _429456), -(c_Orderings_Oord__class_Oless__eq(_429452, c_Groups_Ouminus__class_Ouminus(_429452, _429454), _429456))], (7513 ^ _167881) ^ [_429789, _429791, _429793] : [class_Rings_Olinordered__idom(_429789), 7516 ^ _167881 : [(7517 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_429789, c_Groups_Oabs__class_Oabs(_429789, _429791), _429793), 7520 ^ _167881 : [(7521 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_429789, _429791, _429793))], (7523 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_429789, c_Groups_Ouminus__class_Ouminus(_429789, _429791), _429793))]]], (7525 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_429789, c_Groups_Oabs__class_Oabs(_429789, _429791), _429793)), c_Orderings_Oord__class_Oless(_429789, _429791, _429793), c_Orderings_Oord__class_Oless(_429789, c_Groups_Ouminus__class_Ouminus(_429789, _429791), _429793)]]], (7535 ^ _167881) ^ [_430454, _430456] : [class_Fields_Olinordered__field(_430454), -(_430456 = c_Groups_Ozero__class_Ozero(_430454)), -(c_Groups_Oabs__class_Oabs(_430454, c_Rings_Oinverse__class_Oinverse(_430454, _430456)) = c_Rings_Oinverse__class_Oinverse(_430454, c_Groups_Oabs__class_Oabs(_430454, _430456)))], (7545 ^ _167881) ^ [_430796, _430798, _430800] : [class_Rings_Olinordered__idom(_430796), -(c_Groups_Oabs__class_Oabs(_430796, hAPP(hAPP(c_Power_Opower__class_Opower(_430796), c_Groups_Ouminus__class_Ouminus(_430796, _430798)), _430800)) = c_Groups_Oabs__class_Oabs(_430796, hAPP(hAPP(c_Power_Opower__class_Opower(_430796), _430798), _430800)))], (7551 ^ _167881) ^ [_431089, _431091] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _431089), _431091), 7554 ^ _167881 : [(7555 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _431091), _431089))], (7557 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _431089, _431091))]]], (7559 ^ _167881) ^ [_431344, _431346] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _431344), _431346)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _431346), _431344), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _431344, _431346)], (7569 ^ _167881) ^ [_431663, _431665] : [class_RealVector_Oreal__normed__algebra__1(_431663), -(c_RealVector_Onorm__class_Onorm(_431663, c_RealVector_Oof__real(_431663, _431665)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _431665))], (7575 ^ _167881) ^ [_431874, _431876] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _431874, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _431876))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _431876, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _431874))))], (7577 ^ _167881) ^ [_432017, _432019, _432021] : [class_Rings_Oordered__ring__abs(_432017), -(c_Groups_Oabs__class_Oabs(_432017, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_432017), _432019), _432021)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_432017), c_Groups_Oabs__class_Oabs(_432017, _432019)), c_Groups_Oabs__class_Oabs(_432017, _432021))), 7584 ^ _167881 : [(7585 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_432017, c_Groups_Ozero__class_Ozero(_432017), _432019)], (7587 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_432017, _432019, c_Groups_Ozero__class_Ozero(_432017))]], 7588 ^ _167881 : [(7589 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_432017, c_Groups_Ozero__class_Ozero(_432017), _432021)], (7591 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_432017, _432021, c_Groups_Ozero__class_Ozero(_432017))]]], (7595 ^ _167881) ^ [_432657, _432659, _432661] : [class_Rings_Olinordered__idom(_432657), c_Orderings_Oord__class_Oless__eq(_432657, c_Groups_Ozero__class_Ozero(_432657), _432659), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_432657), c_Groups_Oabs__class_Oabs(_432657, _432661)), _432659) = c_Groups_Oabs__class_Oabs(_432657, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_432657), _432661), _432659)))], (7605 ^ _167881) ^ [_433014, _433016] : [class_Groups_Oordered__ab__group__add__abs(_433014), c_Orderings_Oord__class_Oless__eq(_433014, _433016, c_Groups_Ozero__class_Ozero(_433014)), -(c_Groups_Oabs__class_Oabs(_433014, _433016) = c_Groups_Ouminus__class_Ouminus(_433014, _433016))], (7615 ^ _167881) ^ [_433329, _433331] : [class_Groups_Oordered__ab__group__add__abs(_433329), -(c_Orderings_Oord__class_Oless__eq(_433329, c_Groups_Ouminus__class_Ouminus(_433329, c_Groups_Oabs__class_Oabs(_433329, _433331)), c_Groups_Ozero__class_Ozero(_433329)))], (7621 ^ _167881) ^ [_433569, _433571, _433573] : [class_Rings_Olinordered__idom(_433569), -(c_Orderings_Oord__class_Oless__eq(_433569, c_Groups_Ozero__class_Ozero(_433569), hAPP(hAPP(c_Power_Opower__class_Opower(_433569), c_Groups_Oabs__class_Oabs(_433569, _433571)), _433573)))], (7627 ^ _167881) ^ [_433811, _433813] : [class_Groups_Oabs__if(_433811), 7630 ^ _167881 : [(7631 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_433811, _433813, c_Groups_Ozero__class_Ozero(_433811)), -(c_Groups_Oabs__class_Oabs(_433811, _433813) = c_Groups_Ouminus__class_Ouminus(_433811, _433813))], (7637 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_433811, _433813, c_Groups_Ozero__class_Ozero(_433811))), -(c_Groups_Oabs__class_Oabs(_433811, _433813) = _433813)]]], (7643 ^ _167881) ^ [_434305, _434307] : [class_Groups_Oordered__ab__group__add__abs(_434305), c_Orderings_Oord__class_Oless(_434305, _434307, c_Groups_Ozero__class_Ozero(_434305)), -(c_Groups_Oabs__class_Oabs(_434305, _434307) = c_Groups_Ouminus__class_Ouminus(_434305, _434307))], (7653 ^ _167881) ^ [_434662, _434664, _434666, _434668, _434670] : [class_Groups_Oordered__ab__group__add__abs(_434662), -(c_Orderings_Oord__class_Oless__eq(_434662, c_Groups_Oabs__class_Oabs(_434662, c_Groups_Ominus__class_Ominus(_434662, c_Groups_Oplus__class_Oplus(_434662, _434664, _434666), c_Groups_Oplus__class_Oplus(_434662, _434668, _434670))), c_Groups_Oplus__class_Oplus(_434662, c_Groups_Oabs__class_Oabs(_434662, c_Groups_Ominus__class_Ominus(_434662, _434664, _434668)), c_Groups_Oabs__class_Oabs(_434662, c_Groups_Ominus__class_Ominus(_434662, _434666, _434670)))))], (7659 ^ _167881) ^ [_434970, _434972, _434974] : [class_Groups_Oordered__ab__group__add__abs(_434970), -(c_Orderings_Oord__class_Oless__eq(_434970, c_Groups_Oabs__class_Oabs(_434970, c_Groups_Ominus__class_Ominus(_434970, _434972, _434974)), c_Groups_Oplus__class_Oplus(_434970, c_Groups_Oabs__class_Oabs(_434970, _434972), c_Groups_Oabs__class_Oabs(_434970, _434974))))], (7665 ^ _167881) ^ [_435234, _435236, _435238] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _435234, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _435236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _435234), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _435238))), -(_435236 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7675 ^ _167881) ^ [_435577] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _435577, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _435577) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _435577))], (7681 ^ _167881) ^ [_435747] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _435747, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _435747) = _435747)], (7687 ^ _167881) ^ [_435970] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _435970, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _435970) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _435970))], (7693 ^ _167881) ^ [_436140] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _436140, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _436140) = _436140)], (7699 ^ _167881) ^ [_436327] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _436327), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _436327)], (7701 ^ _167881) ^ [_436455, _436457, _436459, _436461] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _436455, _436457), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436459), c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436461)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _436455, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436459))), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _436457, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436461))))))], (7703 ^ _167881) ^ [_436628, _436630, _436632] : [class_RealVector_Oreal__normed__vector(_436628), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_436628, _436630), c_RealVector_Onorm__class_Onorm(_436628, _436632))), c_RealVector_Onorm__class_Onorm(_436628, c_Groups_Ominus__class_Ominus(_436628, _436630, _436632))))], (7709 ^ _167881) ^ [_436855] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _436855))))], (7712 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7710 ^ []))], (7714 ^ _167881) ^ [_437075] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _437075), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), _437075)), 7710 ^ []))], (7720 ^ _167881) ^ [_437331, _437333, _437335, _437337] : [class_Rings_Olinordered__idom(_437331), 7723 ^ _167881 : [(7724 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_437331, c_Groups_Oabs__class_Oabs(_437331, c_Groups_Ominus__class_Ominus(_437331, _437333, _437335)), _437337), 7727 ^ _167881 : [(7728 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_437331, c_Groups_Ominus__class_Ominus(_437331, _437335, _437337), _437333))], (7730 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_437331, _437333, c_Groups_Oplus__class_Oplus(_437331, _437335, _437337)))]]], (7732 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_437331, c_Groups_Oabs__class_Oabs(_437331, c_Groups_Ominus__class_Ominus(_437331, _437333, _437335)), _437337)), c_Orderings_Oord__class_Oless(_437331, c_Groups_Ominus__class_Ominus(_437331, _437335, _437337), _437333), c_Orderings_Oord__class_Oless(_437331, _437333, c_Groups_Oplus__class_Oplus(_437331, _437335, _437337))]]], (7742 ^ _167881) ^ [_438045, _438047] : [class_Rings_Olinordered__idom(_438045), 7745 ^ _167881 : [(7746 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_438045, c_Groups_Oplus__class_Oplus(_438045, _438047, _438047), c_Groups_Ozero__class_Ozero(_438045)), -(c_Orderings_Oord__class_Oless(_438045, _438047, c_Groups_Ozero__class_Ozero(_438045)))], (7752 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_438045, _438047, c_Groups_Ozero__class_Ozero(_438045)), -(c_Orderings_Oord__class_Oless(_438045, c_Groups_Oplus__class_Oplus(_438045, _438047, _438047), c_Groups_Ozero__class_Ozero(_438045)))]]], (7758 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____))], (7770 ^ _167881) ^ [_438887, _438889] : [7771 ^ _167881 : [(7772 ^ _167881) ^ [] : [-(_438887 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7774 ^ _167881) ^ [] : [_438889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _438887)), _438889)))], (7760 ^ _167881) ^ [_438614, _438616] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _438614)), _438616)), _438614 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_438616 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7778 ^ _167881) ^ [_439239, _439241, _439243] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_439239, _439241, _439243), 7781 ^ _167881 : [(7782 ^ _167881) ^ [_439386, _439388] : [-(hAPP(_439243, _439388) = hAPP(_439243, _439386))]]], (7784 ^ _167881) ^ [_439464, _439466, _439468] : [hAPP(_439468, 7785 ^ [_439464, _439466, _439468]) = hAPP(_439468, 7786 ^ [_439464, _439466, _439468]), -(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_439464, _439466, _439468))], (7792 ^ _167881) ^ [_439847, _439849, _439851] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _439847), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _439849, _439851)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _439847), _439849)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _439847), _439851)))], (7794 ^ _167881) ^ [_439985, _439987, _439989] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _439985), _439987)), _439989) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _439985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _439987), _439989)))], (7796 ^ _167881) ^ [_440120, _440122] : [class_Groups_Olinordered__ab__group__add(_440120), 7799 ^ _167881 : [(7800 ^ _167881) ^ [] : [c_Groups_Oplus__class_Oplus(_440120, _440122, _440122) = c_Groups_Ozero__class_Ozero(_440120), -(_440122 = c_Groups_Ozero__class_Ozero(_440120))], (7806 ^ _167881) ^ [] : [_440122 = c_Groups_Ozero__class_Ozero(_440120), -(c_Groups_Oplus__class_Oplus(_440120, _440122, _440122) = c_Groups_Ozero__class_Ozero(_440120))]]], (7812 ^ _167881) ^ [_440588] : [7820 ^ _167881 : [(7821 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7819 ^ [_440588]))], (7823 ^ _167881) ^ [_440948] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_440588, c_RealVector_Oof__real(_440588, _440948)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _440948)), 7819 ^ [_440588])))]], class_RealVector_Oreal__algebra__1(_440588), class_RealVector_Oreal__normed__vector(_440588)], (7825 ^ _167881) ^ [_441071] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _441071) = 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, _441071, 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, _441071, 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, _441071, 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, _441071, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7844 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7842 ^ []))], (7846 ^ _167881) ^ [_441710] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _441710), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), _441710)), 7842 ^ []))], (7852 ^ _167881) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (7854 ^ _167881) ^ [_441961] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), _441961))))], (7856 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7858 ^ _167881) ^ [_442133] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _442133, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _442133) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _442133))], (7864 ^ _167881) ^ [_442303] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _442303, c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _442303) = _442303)], (7870 ^ _167881) ^ [_442549, _442551] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _442549, _442551), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _442549, _442551), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7876 ^ _167881) ^ [_442723, _442725] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _442723, _442725), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _442723, _442725))], (7882 ^ _167881) ^ [_442976, _442978] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _442976, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _442978, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _442976, _442978))], (7888 ^ _167881) ^ [_443150, _443152] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _443150, _443152), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _443150, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _443152, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7894 ^ _167881) ^ [_443373, _443375, _443377] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _443373), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _443375, _443377)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _443373), _443375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _443373), _443377)))], (7896 ^ _167881) ^ [_443509, _443511, _443513] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _443509, _443511)), _443513) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _443509), _443513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _443511), _443513)))], (7898 ^ _167881) ^ [_443631, _443633] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _443631)), _443633)))], (7900 ^ _167881) ^ [_443765] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _443765), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_443765 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7906 ^ _167881) ^ [_443929] : [_443929 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _443929), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7912 ^ _167881) ^ [_444143, _444145] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _444143), _444145)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _444143) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7918 ^ _167881) ^ [_444377, _444379] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _444377, _444379)), -(_444377 = _444379), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _444379, _444377))], (7928 ^ _167881) ^ [_444710, _444712, _444714, _444716] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _444710, _444712), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _444714, _444716), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _444710, _444714), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _444712, _444716)))], (7938 ^ _167881) ^ [_445065, _445067, _445069] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _445065, _445067), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _445069), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _445069), _445065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _445069), _445067)))], (7948 ^ _167881) ^ [_445418, _445420, _445422] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _445418, _445420), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _445418, _445422), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _445420, _445422)))], (7954 ^ _167881) ^ [_445654, _445656] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _445654, _445656), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _445654, c_Groups_Oone__class_Oone(tc_Int_Oint)), _445656))], (7960 ^ _167881) ^ [_445876, _445878] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _445876), 7963 ^ _167881 : [(7964 ^ _167881) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _445876), _445878) = c_Groups_Oone__class_Oone(tc_Int_Oint), 7967 ^ _167881 : [(7968 ^ _167881) ^ [] : [-(_445876 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7970 ^ _167881) ^ [] : [-(_445878 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (7972 ^ _167881) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _445876), _445878) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _445876 = c_Groups_Oone__class_Oone(tc_Int_Oint), _445878 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (7982 ^ _167881) ^ [_446500] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _446500), -(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), _446500)))], (7988 ^ _167881) ^ [_446731] : [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), _446731), _446731), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _446731, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7994 ^ _167881) ^ [_446907] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _446907, 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), _446907), _446907), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8000 ^ _167881) ^ [_447132, _447134, _447136] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447132, _447134)), _447136) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447132), _447136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447134), _447136)))], (8002 ^ _167881) ^ [_447268, _447270, _447272] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447268), _447270)), _447272) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447270), _447272)))], (8004 ^ _167881) ^ [_447432, _447434] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447432, c_Groups_Oone__class_Oone(tc_Int_Oint)), _447434), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _447432, _447434))], (8010 ^ _167881) ^ [_447606, _447608] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _447606, _447608), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447606, c_Groups_Oone__class_Oone(tc_Int_Oint)), _447608))], (8016 ^ _167881) ^ [_447829, _447831, _447833] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447829), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447831, _447833)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447829), _447831), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447829), _447833)))], (8028 ^ _167881) ^ [_448259, _448261] : [8029 ^ _167881 : [(8030 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _448259, _448261)], (8032 ^ _167881) ^ [] : [_448259 = _448261]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _448259, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _448261, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8018 ^ _167881) ^ [_447995, _447997] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _447995, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _447997, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _447995, _447997)), -(_447995 = _447997)], (8036 ^ _167881) ^ [_448586, _448588] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _448586, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _448588, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _448586, _448588))], (8042 ^ _167881) ^ [_448760, _448762] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _448760, _448762), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _448760, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _448762, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8048 ^ _167881) ^ [_449013, _449015] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _449013, _449015), 8051 ^ _167881 : [(8052 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _449013, _449015))], (8054 ^ _167881) ^ [] : [_449013 = _449015]]], (8056 ^ _167881) ^ [_449255, _449257] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _449255, _449257)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _449255, _449257), -(_449255 = _449257)], (8066 ^ _167881) ^ [_449548, _449550] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _449548), _449550) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _449550), _449548))], (8068 ^ _167881) ^ [_449640] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _449640), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _449640)], (8070 ^ _167881) ^ [_449724] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _449724, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _449724)], (8072 ^ _167881) ^ [_449850] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _449850), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _449850))], (8078 ^ _167881) ^ [_450010] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _450010), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _450010))], (8084 ^ _167881) ^ [_450191] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _450191) = _450191)], (8086 ^ _167881) ^ [_450272] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _450272) = _450272)], (8088 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8090 ^ _167881) ^ [_450406] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _450406), _450406) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (8092 ^ _167881) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (8094 ^ _167881) ^ [_450558, _450560] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _450558)), _450560) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _450558), _450560)))], (8096 ^ _167881) ^ [_450656] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _450656), _450656) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8098 ^ _167881) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8100 ^ _167881) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (8102 ^ _167881) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (8104 ^ _167881) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Complex_Oii))], (8106 ^ _167881) ^ [_450951] : [-(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), _450951)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _450951))], (8108 ^ _167881) ^ [] : [-(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)))], (8110 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____)))], (8112 ^ _167881) ^ [_451187, _451189, _451191] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _451187), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _451189, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _451191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _451191, _451189)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _451187))))], (8118 ^ _167881) ^ [_451463, _451465, _451467] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _451463), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _451465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _451465, _451467)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _451463)), _451467))], (8124 ^ _167881) ^ [_451710, _451712] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _451710, _451712)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _451710), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _451712)))], (8126 ^ _167881) ^ [_451807] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _451807)) = _451807)], (8128 ^ _167881) ^ [_451891] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _451891, _451891))], (8130 ^ _167881) ^ [_451984, _451986] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _451984, _451986) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _451986, _451984))], (8132 ^ _167881) ^ [_452101, _452103] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _452101, _452103)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _452103, _452101))], (8138 ^ _167881) ^ [_452315, _452317, _452319] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452315, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452317, _452319)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452317, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452315, _452319)))], (8140 ^ _167881) ^ [_452441, _452443, _452445] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452441, _452443), _452445) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452441, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452443, _452445)))], (8142 ^ _167881) ^ [_452582, _452584, _452586] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _452582, _452584), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452586, _452582), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _452586, _452584)))], (8148 ^ _167881) ^ [_452832, _452834, _452836] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _452832, _452834), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _452834, _452836), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _452832, _452836))], (8158 ^ _167881) ^ [_453147, _453149] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _453147, _453149), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _453149, _453147), -(_453147 = _453149)], (8168 ^ _167881) ^ [_453435, _453437] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _453435, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _453437)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _453435, _453437))], (8170 ^ _167881) ^ [_453540, _453542] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _453540, _453542) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _453540, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _453542)))], (8172 ^ _167881) ^ [_453660, _453662] : [class_Groups_Ozero(_453660), 8175 ^ _167881 : [(8176 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_453660, _453662) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_453662 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_453660)))], (8182 ^ _167881) ^ [] : [_453662 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_453660)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_453660, _453662) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8188 ^ _167881) ^ [_454110] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _454110) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _454110)))], (8190 ^ _167881) ^ [_454213] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, _454213), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, _454213))), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _454213), 8197 ^ [_454213]) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8202 ^ _167881) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 8200 ^ []) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (8204 ^ _167881) ^ [_454678] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 8200 ^ []), _454678) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _454678)))], (8206 ^ _167881) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (8208 ^ _167881) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (8210 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____))], (8212 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____))], (8214 ^ _167881) ^ [_454977] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), _454977))))], (8216 ^ _167881) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))], (8218 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_s____), v_k____), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (8220 ^ _167881) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), 8223 ^ []) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8227 ^ _167881) ^ [_455370, _455372, _455374] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _455370), _455370 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _455372, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _455370), _455374)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _455372), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _455374, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8241 ^ _167881) ^ [_455812, _455814, _455816] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _455812), _455812 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _455814, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _455812), _455816)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _455814, _455812), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _455816))], (8255 ^ _167881) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))], (8257 ^ _167881) ^ [_456264] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _456264) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _456264)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))], (8259 ^ _167881) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (8261 ^ _167881) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (8263 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (8265 ^ _167881) ^ [_456556] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _456556)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _456556)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))], (8271 ^ _167881) ^ [_456740] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _456740)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _456740)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8277 ^ _167881) ^ [_456945] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _456945) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), _456945), v_k____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a____, v_s____)), _456945))))], (8279 ^ _167881) ^ [_457130, _457132, _457134, _457136, _457138, _457140] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _457130), _457132), _457134) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _457136), _457138), _457140), 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), _457136), _457138), _457140), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _457134, _457130), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _457140), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _457136), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _457136, _457130), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _457138, _457132))], (8305 ^ _167881) ^ [_458003, _458005, _458007, _458009, _458011] : [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), _458003), _458005), _458007), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _458003), _458009), _458011)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _458011, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _458003, _458011), c_Orderings_Oord__class_Oless(tc_Int_Oint, _458003, _458007), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _458009, _458005))], (8323 ^ _167881) ^ [_458640, _458642, _458644, _458646, _458648, _458650] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _458640), _458642), _458644) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _458646), _458648), _458650), 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), _458646), _458648), _458650)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _458650, _458646), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _458644), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _458646), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _458646, _458640), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _458642, _458648))], (8349 ^ _167881) ^ [_459513, _459515, _459517, _459519, _459521] : [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), _459513), _459515), _459517), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _459513), _459519), _459521)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _459517), c_Orderings_Oord__class_Oless(tc_Int_Oint, _459517, _459513), c_Orderings_Oord__class_Oless(tc_Int_Oint, _459521, _459513), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _459515, _459519))], (8367 ^ _167881) ^ [_460108, _460110, _460112] : [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), _460108), _460110), _460112), 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), _460112), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _460108), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _460110, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8381 ^ _167881) ^ [_460552, _460554, _460556] : [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), _460552), _460554), _460556)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _460556, _460552), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _460552), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _460554))], (8395 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 8398 ^ [])), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8404 ^ _167881) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 8401 ^ []) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 8402 ^ [])], (8406 ^ _167881) ^ [_461285, _461287] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _461285), -(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), _461285), _461287)))], (8412 ^ _167881) ^ [_461539, _461541, _461543, _461545] : [class_Rings_Ocomm__semiring__0(_461539), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_461539), c_Polynomial_Osmult(_461539, _461541, _461543), c_Polynomial_OpCons(_461539, _461545, _461543)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_461539)), -(_461543 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_461539)))], (8422 ^ _167881) ^ [] : [-(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)))], (8424 ^ _167881) ^ [] : [-(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)))], (8426 ^ _167881) ^ [_462006, _462008] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _462006), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _462008), -(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, _462006, _462008)))], (8436 ^ _167881) ^ [_462319, _462321] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _462319), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _462321), -(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), _462319), _462321)))], (8446 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))], (8448 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))], (8450 ^ _167881) ^ [_462769, _462771, _462773, _462775] : [class_Rings_Ocomm__ring__1(_462769), -(hAPP(c_Polynomial_Opoly(_462769, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_462769)), c_Polynomial_Omonom(_462769, c_Groups_Oone__class_Oone(_462769), _462771)), _462773)), _462775) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_462769), hAPP(hAPP(c_Power_Opower__class_Opower(_462769), _462775), _462771)), hAPP(c_Polynomial_Opoly(_462769, _462773), _462775)))], (8457 ^ _167881) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), 8455 ^ []) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8459 ^ _167881) ^ [_463170, _463172] : [class_Groups_Ozero(_463170), -(c_Polynomial_Omonom(_463170, _463172, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_463170, _463172, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_463170))))], (8465 ^ _167881) ^ [_463402, _463404] : [class_Rings_Olinordered__idom(_463402), 8468 ^ _167881 : [(8469 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_463402), _463404, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_463402))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_463402), _463404) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_463402), _463404))], (8475 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_463402), _463404, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_463402)))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_463402), _463404) = _463404)]]], (8481 ^ _167881) ^ [_463910] : [class_Groups_Oab__group__add(_463910), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_463910), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_463910))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_463910)))], (8487 ^ _167881) ^ [_464138, _464140] : [class_Groups_Oab__group__add(_464138), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_464138), _464140, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464138))) = _464140)], (8493 ^ _167881) ^ [_464366, _464368] : [class_Groups_Oab__group__add(_464366), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_464366), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464366)), _464368) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_464366), _464368))], (8499 ^ _167881) ^ [_464604, _464606] : [class_Rings_Ocomm__semiring__0(_464604), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_464604)), _464606), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464604))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464604)))], (8505 ^ _167881) ^ [_464848, _464850] : [class_Rings_Ocomm__semiring__0(_464848), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_464848)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464848))), _464850) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464848)))], (8511 ^ _167881) ^ [_465106, _465108, _465110] : [class_Int_Oring__char__0(_465106), class_Rings_Oidom(_465106), 8518 ^ _167881 : [(8519 ^ _167881) ^ [] : [c_Polynomial_Opoly(_465106, _465108) = c_Polynomial_Opoly(_465106, _465110), -(_465108 = _465110)], (8525 ^ _167881) ^ [] : [_465108 = _465110, -(c_Polynomial_Opoly(_465106, _465108) = c_Polynomial_Opoly(_465106, _465110))]]], (8531 ^ _167881) ^ [_465733, _465735, _465737, _465739, _465741] : [class_Groups_Ozero(_465733), 8534 ^ _167881 : [(8535 ^ _167881) ^ [] : [c_Polynomial_OpCons(_465733, _465735, _465737) = c_Polynomial_OpCons(_465733, _465739, _465741), 8538 ^ _167881 : [(8539 ^ _167881) ^ [] : [-(_465735 = _465739)], (8541 ^ _167881) ^ [] : [-(_465737 = _465741)]]], (8543 ^ _167881) ^ [] : [-(c_Polynomial_OpCons(_465733, _465735, _465737) = c_Polynomial_OpCons(_465733, _465739, _465741)), _465735 = _465739, _465737 = _465741]]], (8553 ^ _167881) ^ [_466467, _466469, _466471, _466473] : [class_Rings_Ocomm__ring(_466467), -(c_Polynomial_Osmult(_466467, _466469, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_466467), _466471, _466473)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_466467), c_Polynomial_Osmult(_466467, _466469, _466471), c_Polynomial_Osmult(_466467, _466469, _466473)))], (8559 ^ _167881) ^ [_466749, _466751, _466753] : [class_Rings_Ocomm__ring(_466749), -(c_Polynomial_Osmult(_466749, _466751, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_466749), _466753)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_466749), c_Polynomial_Osmult(_466749, _466751, _466753)))], (8565 ^ _167881) ^ [_467027, _467029, _467031, _467033] : [class_Rings_Ocomm__semiring__0(_467027), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_467027)), c_Polynomial_Osmult(_467027, _467029, _467031)), _467033) = c_Polynomial_Osmult(_467027, _467029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_467027)), _467031), _467033)))], (8571 ^ _167881) ^ [_467331, _467333, _467335, _467337] : [class_Rings_Ocomm__semiring__0(_467331), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_467331)), _467333), c_Polynomial_Osmult(_467331, _467335, _467337)) = c_Polynomial_Osmult(_467331, _467335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_467331)), _467333), _467337)))], (8577 ^ _167881) ^ [_467635, _467637, _467639, _467641] : [class_Rings_Ocomm__semiring__0(_467635), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_467635)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_467635), _467637, _467639)), _467641) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_467635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_467635)), _467637), _467641), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_467635)), _467639), _467641)))], (8583 ^ _167881) ^ [_467967, _467969, _467971, _467973] : [class_Groups_Ozero(_467967), 8586 ^ _167881 : [(8587 ^ _167881) ^ [] : [c_Polynomial_Omonom(_467967, _467969, _467971) = c_Polynomial_Omonom(_467967, _467973, _467971), -(_467969 = _467973)], (8593 ^ _167881) ^ [] : [_467969 = _467973, -(c_Polynomial_Omonom(_467967, _467969, _467971) = c_Polynomial_Omonom(_467967, _467973, _467971))]]], (8599 ^ _167881) ^ [_468509, _468511, _468513, _468515] : [class_Rings_Ocomm__semiring__0(_468509), -(hAPP(c_Polynomial_Opoly(_468509, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_468509)), _468511), _468513)), _468515) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468509), hAPP(c_Polynomial_Opoly(_468509, _468511), _468515)), hAPP(c_Polynomial_Opoly(_468509, _468513), _468515)))], (8605 ^ _167881) ^ [_468801, _468803] : [class_Rings_Ocomm__semiring__1(_468801), -(hAPP(c_Polynomial_Opoly(_468801, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_468801))), _468803) = c_Groups_Oone__class_Oone(_468801))], (8611 ^ _167881) ^ [_469061, _469063, _469065, _469067] : [class_Rings_Ocomm__ring(_469061), -(hAPP(c_Polynomial_Opoly(_469061, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_469061), _469063, _469065)), _469067) = c_Groups_Ominus__class_Ominus(_469061, hAPP(c_Polynomial_Opoly(_469061, _469063), _469067), hAPP(c_Polynomial_Opoly(_469061, _469065), _469067)))], (8617 ^ _167881) ^ [_469351, _469353, _469355] : [class_Rings_Ocomm__ring(_469351), -(hAPP(c_Polynomial_Opoly(_469351, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_469351), _469353)), _469355) = c_Groups_Ouminus__class_Ouminus(_469351, hAPP(c_Polynomial_Opoly(_469351, _469353), _469355)))], (8623 ^ _167881) ^ [_469633, _469635, _469637, _469639] : [class_Rings_Ocomm__semiring__1(_469633), -(hAPP(c_Polynomial_Opoly(_469633, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_469633)), _469635), _469637)), _469639) = hAPP(hAPP(c_Power_Opower__class_Opower(_469633), hAPP(c_Polynomial_Opoly(_469633, _469635), _469639)), _469637))], (8629 ^ _167881) ^ [_469955, _469957, _469959, _469961, _469963] : [class_Groups_Oab__group__add(_469955), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_469955), c_Polynomial_OpCons(_469955, _469957, _469959), c_Polynomial_OpCons(_469955, _469961, _469963)) = c_Polynomial_OpCons(_469955, c_Groups_Ominus__class_Ominus(_469955, _469957, _469961), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_469955), _469959, _469963)))], (8635 ^ _167881) ^ [_470265, _470267, _470269, _470271] : [class_Rings_Ocomm__semiring__0(_470265), -(c_Polynomial_Osmult(_470265, _470267, c_Polynomial_Osmult(_470265, _470269, _470271)) = c_Polynomial_Osmult(_470265, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470265), _470267), _470269), _470271))], (8641 ^ _167881) ^ [_470525, _470527] : [class_Rings_Ocomm__semiring__1(_470525), -(c_Polynomial_Osmult(_470525, c_Groups_Oone__class_Oone(_470525), _470527) = _470527)], (8647 ^ _167881) ^ [_470759, _470761, _470763] : [class_Groups_Oab__group__add(_470759), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_470759), c_Polynomial_OpCons(_470759, _470761, _470763)) = c_Polynomial_OpCons(_470759, c_Groups_Ouminus__class_Ouminus(_470759, _470761), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_470759), _470763)))], (8653 ^ _167881) ^ [_471029, _471031, _471033] : [class_Groups_Oab__group__add(_471029), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_471029), c_Polynomial_OpCons(_471029, _471031, _471033)) = c_Polynomial_OpCons(_471029, c_Groups_Ouminus__class_Ouminus(_471029, _471031), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_471029), _471033)))], (8659 ^ _167881) ^ [_471313, _471315, _471317, _471319] : [class_Rings_Ocomm__ring(_471313), -(c_Polynomial_Osmult(_471313, c_Groups_Ominus__class_Ominus(_471313, _471315, _471317), _471319) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_471313), c_Polynomial_Osmult(_471313, _471315, _471319), c_Polynomial_Osmult(_471313, _471317, _471319)))], (8665 ^ _167881) ^ [_471591, _471593, _471595] : [class_Rings_Ocomm__ring(_471591), -(c_Polynomial_Osmult(_471591, c_Groups_Ouminus__class_Ouminus(_471591, _471593), _471595) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_471591), c_Polynomial_Osmult(_471591, _471593, _471595)))], (8671 ^ _167881) ^ [_471837, _471839] : [class_Int_Oring__char__0(_471837), class_Rings_Oidom(_471837), 8678 ^ _167881 : [(8679 ^ _167881) ^ [] : [c_Polynomial_Opoly(_471837, _471839) = c_Polynomial_Opoly(_471837, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471837))), -(_471839 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471837)))], (8685 ^ _167881) ^ [] : [_471839 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471837)), -(c_Polynomial_Opoly(_471837, _471839) = c_Polynomial_Opoly(_471837, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471837))))]]], (8691 ^ _167881) ^ [_472426, _472428] : [class_Rings_Ocomm__semiring__0(_472426), -(c_Polynomial_Osmult(_472426, _472428, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472426))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472426)))], (8697 ^ _167881) ^ [_472686, _472688, _472690, _472692] : [class_Groups_Oab__group__add(_472686), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_472686), c_Polynomial_Omonom(_472686, _472688, _472690), c_Polynomial_Omonom(_472686, _472692, _472690)) = c_Polynomial_Omonom(_472686, c_Groups_Ominus__class_Ominus(_472686, _472688, _472692), _472690))], (8703 ^ _167881) ^ [_472964, _472966, _472968] : [class_Groups_Oab__group__add(_472964), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_472964), c_Polynomial_Omonom(_472964, _472966, _472968)) = c_Polynomial_Omonom(_472964, c_Groups_Ouminus__class_Ouminus(_472964, _472966), _472968))], (8709 ^ _167881) ^ [_473210, _473212] : [class_Groups_Ocomm__monoid__add(_473210), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_473210), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473210)), _473212) = _473212)], (8715 ^ _167881) ^ [_473438, _473440] : [class_Groups_Ocomm__monoid__add(_473438), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_473438), _473440, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473438))) = _473440)], (8721 ^ _167881) ^ [_473694, _473696, _473698, _473700] : [class_Rings_Ocomm__semiring__0(_473694), -(c_Polynomial_Osmult(_473694, _473696, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_473694), _473698, _473700)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_473694), c_Polynomial_Osmult(_473694, _473696, _473698), c_Polynomial_Osmult(_473694, _473696, _473700)))], (8727 ^ _167881) ^ [_473962, _473964] : [class_Rings_Ocomm__semiring__0(_473962), -(hAPP(c_Polynomial_Opoly(_473962, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473962))), _473964) = c_Groups_Ozero__class_Ozero(_473962))], (8733 ^ _167881) ^ [_474180] : [class_Groups_Ozero(_474180), -(c_Polynomial_OpCons(_474180, c_Groups_Ozero__class_Ozero(_474180), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474180))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474180)))], (8739 ^ _167881) ^ [_474424, _474426, _474428] : [class_Groups_Ozero(_474424), 8742 ^ _167881 : [(8743 ^ _167881) ^ [] : [c_Polynomial_OpCons(_474424, _474426, _474428) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474424)), 8746 ^ _167881 : [(8747 ^ _167881) ^ [] : [-(_474426 = c_Groups_Ozero__class_Ozero(_474424))], (8749 ^ _167881) ^ [] : [-(_474428 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474424)))]]], (8751 ^ _167881) ^ [] : [-(c_Polynomial_OpCons(_474424, _474426, _474428) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474424))), _474426 = c_Groups_Ozero__class_Ozero(_474424), _474428 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474424))]]], (8761 ^ _167881) ^ [_475104, _475106] : [class_Rings_Ocomm__semiring__0(_475104), -(c_Polynomial_Osmult(_475104, c_Groups_Ozero__class_Ozero(_475104), _475106) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475104)))], (8767 ^ _167881) ^ [_475346, _475348, _475350] : [class_Rings_Oidom(_475346), 8770 ^ _167881 : [(8781 ^ _167881) ^ [] : [8782 ^ _167881 : [(8783 ^ _167881) ^ [] : [_475348 = c_Groups_Ozero__class_Ozero(_475346)], (8785 ^ _167881) ^ [] : [_475350 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475346))]], -(c_Polynomial_Osmult(_475346, _475348, _475350) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475346)))], (8771 ^ _167881) ^ [] : [c_Polynomial_Osmult(_475346, _475348, _475350) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475346)), -(_475348 = c_Groups_Ozero__class_Ozero(_475346)), -(_475350 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475346)))]]], (8789 ^ _167881) ^ [_476012] : [class_Rings_Ocomm__semiring__1(_476012), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_476012)) = c_Polynomial_OpCons(_476012, c_Groups_Oone__class_Oone(_476012), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_476012))))], (8795 ^ _167881) ^ [_476270, _476272, _476274, _476276] : [class_Rings_Ocomm__semiring__0(_476270), -(hAPP(c_Polynomial_Opoly(_476270, c_Polynomial_Osmult(_476270, _476272, _476274)), _476276) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476270), _476272), hAPP(c_Polynomial_Opoly(_476270, _476274), _476276)))], (8801 ^ _167881) ^ [_476566, _476568, _476570, _476572] : [class_Rings_Ocomm__semiring__0(_476566), -(c_Polynomial_Osmult(_476566, _476568, c_Polynomial_OpCons(_476566, _476570, _476572)) = c_Polynomial_OpCons(_476566, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476566), _476568), _476570), c_Polynomial_Osmult(_476566, _476568, _476572)))], (8807 ^ _167881) ^ [_476876, _476878, _476880, _476882, _476884] : [class_Rings_Ocomm__semiring__0(_476876), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_476876)), c_Polynomial_Omonom(_476876, _476878, _476880)), c_Polynomial_Omonom(_476876, _476882, _476884)) = c_Polynomial_Omonom(_476876, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476876), _476878), _476882), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _476880, _476884)))], (8813 ^ _167881) ^ [_477170, _477172] : [class_Groups_Ozero(_477170), -(c_Polynomial_Omonom(_477170, c_Groups_Ozero__class_Ozero(_477170), _477172) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_477170)))], (8819 ^ _167881) ^ [_477412, _477414, _477416] : [class_Groups_Ozero(_477412), 8822 ^ _167881 : [(8823 ^ _167881) ^ [] : [c_Polynomial_Omonom(_477412, _477414, _477416) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_477412)), -(_477414 = c_Groups_Ozero__class_Ozero(_477412))], (8829 ^ _167881) ^ [] : [_477414 = c_Groups_Ozero__class_Ozero(_477412), -(c_Polynomial_Omonom(_477412, _477414, _477416) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_477412)))]]], (8835 ^ _167881) ^ [_477944, _477946, _477948, _477950] : [class_Rings_Ocomm__semiring__0(_477944), -(hAPP(c_Polynomial_Opoly(_477944, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_477944), _477946, _477948)), _477950) = c_Groups_Oplus__class_Oplus(_477944, hAPP(c_Polynomial_Opoly(_477944, _477946), _477950), hAPP(c_Polynomial_Opoly(_477944, _477948), _477950)))], (8841 ^ _167881) ^ [_478262, _478264, _478266, _478268, _478270] : [class_Groups_Ocomm__monoid__add(_478262), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478262), c_Polynomial_OpCons(_478262, _478264, _478266), c_Polynomial_OpCons(_478262, _478268, _478270)) = c_Polynomial_OpCons(_478262, c_Groups_Oplus__class_Oplus(_478262, _478264, _478268), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478262), _478266, _478270)))], (8847 ^ _167881) ^ [_478572, _478574, _478576, _478578] : [class_Rings_Ocomm__semiring__0(_478572), c_Polynomial_Osmult(_478572, _478574, _478576) = c_Polynomial_OpCons(_478572, _478578, _478576), -(_478576 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_478572)))], (8857 ^ _167881) ^ [_478941, _478943, _478945, _478947] : [class_Rings_Ocomm__semiring__0(_478941), -(c_Polynomial_Osmult(_478941, c_Groups_Oplus__class_Oplus(_478941, _478943, _478945), _478947) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478941), c_Polynomial_Osmult(_478941, _478943, _478947), c_Polynomial_Osmult(_478941, _478945, _478947)))], (8863 ^ _167881) ^ [_479233, _479235, _479237, _479239] : [class_Rings_Ocomm__semiring__0(_479233), -(c_Polynomial_Osmult(_479233, _479235, c_Polynomial_Omonom(_479233, _479237, _479239)) = c_Polynomial_Omonom(_479233, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479233), _479235), _479237), _479239))], (8869 ^ _167881) ^ [_479521, _479523, _479525, _479527] : [class_Groups_Ocomm__monoid__add(_479521), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_479521), c_Polynomial_Omonom(_479521, _479523, _479525), c_Polynomial_Omonom(_479521, _479527, _479525)) = c_Polynomial_Omonom(_479521, c_Groups_Oplus__class_Oplus(_479521, _479523, _479527), _479525))], (8875 ^ _167881) ^ [_479813, _479815, _479817, _479819] : [class_Rings_Ocomm__semiring__0(_479813), -(hAPP(c_Polynomial_Opoly(_479813, c_Polynomial_OpCons(_479813, _479815, _479817)), _479819) = c_Groups_Oplus__class_Oplus(_479813, _479815, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479813), _479819), hAPP(c_Polynomial_Opoly(_479813, _479817), _479819))))], (8881 ^ _167881) ^ [_480117, _480119, _480121, _480123] : [class_Rings_Ocomm__semiring__1(_480117), -(hAPP(c_Polynomial_Opoly(_480117, c_Polynomial_Omonom(_480117, _480119, _480121)), _480123) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480117), _480119), hAPP(hAPP(c_Power_Opower__class_Opower(_480117), _480123), _480121)))], (8887 ^ _167881) ^ [_480417, _480419, _480421, _480423] : [class_Rings_Ocomm__semiring__0(_480417), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_480417)), _480419), c_Polynomial_OpCons(_480417, _480421, _480423)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_480417), c_Polynomial_Osmult(_480417, _480421, _480419), c_Polynomial_OpCons(_480417, c_Groups_Ozero__class_Ozero(_480417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_480417)), _480419), _480423))))], (8893 ^ _167881) ^ [_480745, _480747, _480749, _480751] : [class_Rings_Ocomm__semiring__0(_480745), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_480745)), c_Polynomial_OpCons(_480745, _480747, _480749)), _480751) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_480745), c_Polynomial_Osmult(_480745, _480747, _480751), c_Polynomial_OpCons(_480745, c_Groups_Ozero__class_Ozero(_480745), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_480745)), _480749), _480751))))], (8899 ^ _167881) ^ [_481059, _481061, _481063] : [class_Rings_Ocomm__ring__1(_481059), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_481059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_481059)), c_Polynomial_OpCons(_481059, c_Groups_Ouminus__class_Ouminus(_481059, _481061), c_Polynomial_OpCons(_481059, c_Groups_Oone__class_Oone(_481059), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481059))))), c_Polynomial_Osynthetic__div(_481059, _481063, _481061)), c_Polynomial_OpCons(_481059, hAPP(c_Polynomial_Opoly(_481059, _481063), _481061), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481059)))) = _481063)], (8905 ^ _167881) ^ [_481403, _481405, _481407, _481409] : [class_Rings_Ocomm__semiring__0(_481403), -(c_Polynomial_Opcompose(_481403, c_Polynomial_OpCons(_481403, _481405, _481407), _481409) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_481403), c_Polynomial_OpCons(_481403, _481405, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481403))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_481403)), _481409), c_Polynomial_Opcompose(_481403, _481407, _481409))))], (8911 ^ _167881) ^ [_481695, _481697] : [class_Rings_Ocomm__semiring__0(_481695), -(c_Polynomial_Osynthetic__div(_481695, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481695)), _481697) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481695)))], (8917 ^ _167881) ^ [_481927, _481929] : [class_Rings_Ocomm__semiring__0(_481927), -(c_Polynomial_Opcompose(_481927, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481927)), _481929) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481927)))], (8923 ^ _167881) ^ [_482187, _482189, _482191, _482193] : [class_Rings_Ocomm__semiring__0(_482187), -(hAPP(c_Polynomial_Opoly(_482187, c_Polynomial_Opcompose(_482187, _482189, _482191)), _482193) = hAPP(c_Polynomial_Opoly(_482187, _482189), hAPP(c_Polynomial_Opoly(_482187, _482191), _482193)))], (8929 ^ _167881) ^ [_482479, _482481, _482483, _482485] : [class_Rings_Ocomm__semiring__0(_482479), -(c_Polynomial_Osynthetic__div(_482479, c_Polynomial_OpCons(_482479, _482481, _482483), _482485) = c_Polynomial_OpCons(_482479, hAPP(c_Polynomial_Opoly(_482479, _482483), _482485), c_Polynomial_Osynthetic__div(_482479, _482483, _482485)))], (8935 ^ _167881) ^ [_482757, _482759, _482761] : [class_Rings_Ocomm__semiring__0(_482757), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_482757), _482759, c_Polynomial_Osmult(_482757, _482761, c_Polynomial_Osynthetic__div(_482757, _482759, _482761))) = c_Polynomial_OpCons(_482757, hAPP(c_Polynomial_Opoly(_482757, _482759), _482761), c_Polynomial_Osynthetic__div(_482757, _482759, _482761)))], (8941 ^ _167881) ^ [_483069, _483071, _483073, _483075, _483077] : [class_Rings_Ocomm__semiring__0(_483069), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_483069), _483071, c_Polynomial_Osmult(_483069, _483073, _483075)) = c_Polynomial_OpCons(_483069, _483077, _483075), 8948 ^ _167881 : [(8949 ^ _167881) ^ [] : [-(_483077 = hAPP(c_Polynomial_Opoly(_483069, _483071), _483073))], (8951 ^ _167881) ^ [] : [-(_483075 = c_Polynomial_Osynthetic__div(_483069, _483071, _483073))]]], (8953 ^ _167881) ^ [_483539, _483541, _483543] : [class_Rings_Oidom(_483539), 8956 ^ _167881 : [(8967 ^ _167881) ^ [] : [8968 ^ _167881 : [(8969 ^ _167881) ^ [] : [_483541 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483539))], (8971 ^ _167881) ^ [] : [-(c_Polynomial_Oorder(_483539, _483543, _483541) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_483539, _483541), _483543) = c_Groups_Ozero__class_Ozero(_483539))], (8957 ^ _167881) ^ [] : [hAPP(c_Polynomial_Opoly(_483539, _483541), _483543) = c_Groups_Ozero__class_Ozero(_483539), -(_483541 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483539))), c_Polynomial_Oorder(_483539, _483543, _483541) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (8975 ^ _167881) ^ [_484227, _484229] : [class_Orderings_Opreorder(_484227), -(c_Orderings_Oord__class_Oless__eq(_484227, _484229, _484229))], (8981 ^ _167881) ^ [_484465, _484467, _484469, _484471] : [class_Orderings_Oord(_484465), 8984 ^ _167881 : [(8985 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_484467, _484465), _484469, _484471), 8988 ^ _167881 : [(8989 ^ _167881) ^ [_484724] : [-(c_Orderings_Oord__class_Oless__eq(_484465, hAPP(_484469, _484724), hAPP(_484471, _484724)))]]], (8991 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_484465, hAPP(_484469, 8992 ^ [_484465, _484467, _484469, _484471]), hAPP(_484471, 8992 ^ [_484465, _484467, _484469, _484471])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_484467, _484465), _484469, _484471))]]], (8998 ^ _167881) ^ [_485106, _485108, _485110] : [class_Orderings_Olinorder(_485106), -(c_Orderings_Oord__class_Oless__eq(_485106, _485108, _485110)), -(c_Orderings_Oord__class_Oless__eq(_485106, _485110, _485108))], (9008 ^ _167881) ^ [_485432, _485434, _485436] : [class_Orderings_Oorder(_485432), 9011 ^ _167881 : [(9012 ^ _167881) ^ [] : [_485434 = _485436, 9015 ^ _167881 : [(9016 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_485432, _485434, _485436))], (9018 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_485432, _485436, _485434))]]], (9020 ^ _167881) ^ [] : [-(_485434 = _485436), c_Orderings_Oord__class_Oless__eq(_485432, _485434, _485436), c_Orderings_Oord__class_Oless__eq(_485432, _485436, _485434)]]], (9030 ^ _167881) ^ [_486090, _486092, _486094] : [class_Orderings_Opreorder(_486090), _486092 = _486094, -(c_Orderings_Oord__class_Oless__eq(_486090, _486092, _486094))], (9040 ^ _167881) ^ [_486441, _486443, _486445, _486447, _486449] : [class_Orderings_Oord(_486441), c_Orderings_Oord__class_Oless__eq(tc_fun(_486443, _486441), _486445, _486447), -(c_Orderings_Oord__class_Oless__eq(_486441, hAPP(_486445, _486449), hAPP(_486447, _486449)))], (9050 ^ _167881) ^ [_486804, _486806, _486808] : [class_Orderings_Oorder(_486804), c_Orderings_Oord__class_Oless__eq(_486804, _486806, _486808), 9057 ^ _167881 : [(9058 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_486804, _486808, _486806), -(_486808 = _486806)], (9064 ^ _167881) ^ [] : [_486808 = _486806, -(c_Orderings_Oord__class_Oless__eq(_486804, _486808, _486806))]]], (9070 ^ _167881) ^ [_487404, _487406, _487408, _487410] : [class_Orderings_Oord(_487404), _487406 = _487408, c_Orderings_Oord__class_Oless__eq(_487404, _487408, _487410), -(c_Orderings_Oord__class_Oless__eq(_487404, _487406, _487410))], (9084 ^ _167881) ^ [_487850, _487852, _487854, _487856] : [class_Orderings_Oorder(_487850), _487852 = _487854, c_Orderings_Oord__class_Oless__eq(_487850, _487856, _487854), -(c_Orderings_Oord__class_Oless__eq(_487850, _487856, _487852))], (9098 ^ _167881) ^ [_488296, _488298, _488300, _488302] : [class_Orderings_Oord(_488296), c_Orderings_Oord__class_Oless__eq(_488296, _488298, _488300), _488300 = _488302, -(c_Orderings_Oord__class_Oless__eq(_488296, _488298, _488302))], (9112 ^ _167881) ^ [_488742, _488744, _488746, _488748] : [class_Orderings_Oorder(_488742), c_Orderings_Oord__class_Oless__eq(_488742, _488744, _488746), _488744 = _488748, -(c_Orderings_Oord__class_Oless__eq(_488742, _488748, _488746))], (9126 ^ _167881) ^ [_489174, _489176, _489178] : [class_Orderings_Oorder(_489174), c_Orderings_Oord__class_Oless__eq(_489174, _489176, _489178), c_Orderings_Oord__class_Oless__eq(_489174, _489178, _489176), -(_489176 = _489178)], (9140 ^ _167881) ^ [_489606, _489608, _489610, _489612] : [class_Orderings_Opreorder(_489606), c_Orderings_Oord__class_Oless__eq(_489606, _489608, _489610), c_Orderings_Oord__class_Oless__eq(_489606, _489610, _489612), -(c_Orderings_Oord__class_Oless__eq(_489606, _489608, _489612))], (9154 ^ _167881) ^ [_490040, _490042, _490044] : [class_Orderings_Oorder(_490040), c_Orderings_Oord__class_Oless__eq(_490040, _490042, _490044), c_Orderings_Oord__class_Oless__eq(_490040, _490044, _490042), -(_490044 = _490042)], (9168 ^ _167881) ^ [_490472, _490474, _490476, _490478] : [class_Orderings_Oorder(_490472), c_Orderings_Oord__class_Oless__eq(_490472, _490474, _490476), c_Orderings_Oord__class_Oless__eq(_490472, _490478, _490474), -(c_Orderings_Oord__class_Oless__eq(_490472, _490478, _490476))], (9182 ^ _167881) ^ [_490934, _490936, _490938, _490940, _490942] : [class_Orderings_Oord(_490934), c_Orderings_Oord__class_Oless__eq(tc_fun(_490936, _490934), _490938, _490940), -(c_Orderings_Oord__class_Oless__eq(_490934, hAPP(_490938, _490942), hAPP(_490940, _490942)))], (9192 ^ _167881) ^ [_491297, _491299, _491301] : [class_Orderings_Olinorder(_491297), -(c_Orderings_Oord__class_Oless__eq(_491297, _491299, _491301)), -(c_Orderings_Oord__class_Oless__eq(_491297, _491301, _491299))], (9202 ^ _167881) ^ [_491625, _491627, _491629] : [class_Orderings_Olinorder(_491625), -(c_Orderings_Oord__class_Oless(_491625, _491627, _491629)), -(_491627 = _491629), -(c_Orderings_Oord__class_Oless(_491625, _491629, _491627))], (9216 ^ _167881) ^ [_492049, _492051, _492053] : [class_Orderings_Opreorder(_492049), c_Orderings_Oord__class_Oless(_492049, _492051, _492053), c_Orderings_Oord__class_Oless(_492049, _492053, _492051)], (9226 ^ _167881) ^ [_492389, _492391, _492393, _492395] : [class_Orderings_Oorder(_492389), c_Orderings_Oord__class_Oless(_492389, _492391, _492393), c_Orderings_Oord__class_Oless(_492389, _492395, _492391), -(c_Orderings_Oord__class_Oless(_492389, _492395, _492393))], (9240 ^ _167881) ^ [_492837, _492839, _492841, _492843] : [class_Orderings_Opreorder(_492837), c_Orderings_Oord__class_Oless(_492837, _492839, _492841), c_Orderings_Oord__class_Oless(_492837, _492841, _492843), -(c_Orderings_Oord__class_Oless(_492837, _492839, _492843))], (9254 ^ _167881) ^ [_493285, _493287, _493289, _493291] : [class_Orderings_Oorder(_493285), c_Orderings_Oord__class_Oless(_493285, _493287, _493289), _493287 = _493291, -(c_Orderings_Oord__class_Oless(_493285, _493291, _493289))], (9268 ^ _167881) ^ [_493731, _493733, _493735, _493737] : [class_Orderings_Oord(_493731), c_Orderings_Oord__class_Oless(_493731, _493733, _493735), _493735 = _493737, -(c_Orderings_Oord__class_Oless(_493731, _493733, _493737))], (9282 ^ _167881) ^ [_494177, _494179, _494181, _494183] : [class_Orderings_Oorder(_494177), _494179 = _494181, c_Orderings_Oord__class_Oless(_494177, _494183, _494181), -(c_Orderings_Oord__class_Oless(_494177, _494183, _494179))], (9296 ^ _167881) ^ [_494623, _494625, _494627, _494629] : [class_Orderings_Oord(_494623), _494625 = _494627, c_Orderings_Oord__class_Oless(_494623, _494627, _494629), -(c_Orderings_Oord__class_Oless(_494623, _494625, _494629))], (9310 ^ _167881) ^ [_495055, _495057, _495059] : [class_Orderings_Oorder(_495055), c_Orderings_Oord__class_Oless(_495055, _495057, _495059), c_Orderings_Oord__class_Oless(_495055, _495059, _495057)], (9320 ^ _167881) ^ [_495381, _495383, _495385] : [class_Orderings_Opreorder(_495381), c_Orderings_Oord__class_Oless(_495381, _495383, _495385), c_Orderings_Oord__class_Oless(_495381, _495385, _495383)], (9330 ^ _167881) ^ [_495707, _495709, _495711] : [class_Orderings_Oorder(_495707), c_Orderings_Oord__class_Oless(_495707, _495709, _495711), _495711 = _495709], (9340 ^ _167881) ^ [_496031, _496033, _496035] : [class_Orderings_Oorder(_496031), c_Orderings_Oord__class_Oless(_496031, _496033, _496035), _496033 = _496035], (9350 ^ _167881) ^ [_496355, _496357, _496359] : [class_Orderings_Opreorder(_496355), c_Orderings_Oord__class_Oless(_496355, _496357, _496359), c_Orderings_Oord__class_Oless(_496355, _496359, _496357)], (9360 ^ _167881) ^ [_496681, _496683, _496685] : [class_Orderings_Opreorder(_496681), c_Orderings_Oord__class_Oless(_496681, _496683, _496685), c_Orderings_Oord__class_Oless(_496681, _496685, _496683)], (9370 ^ _167881) ^ [_497007, _497009, _497011] : [class_Orderings_Oorder(_497007), c_Orderings_Oord__class_Oless(_497007, _497009, _497011), _497009 = _497011], (9380 ^ _167881) ^ [_497331, _497333, _497335] : [class_Orderings_Olinorder(_497331), -(_497333 = _497335), -(c_Orderings_Oord__class_Oless(_497331, _497333, _497335)), -(c_Orderings_Oord__class_Oless(_497331, _497335, _497333))], (9394 ^ _167881) ^ [_497755, _497757, _497759] : [class_Orderings_Olinorder(_497755), -(c_Orderings_Oord__class_Oless(_497755, _497757, _497759)), 9401 ^ _167881 : [(9402 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_497755, _497759, _497757)), -(_497759 = _497757)], (9408 ^ _167881) ^ [] : [_497759 = _497757, c_Orderings_Oord__class_Oless(_497755, _497759, _497757)]]], (9414 ^ _167881) ^ [_498346, _498348, _498350] : [class_Orderings_Olinorder(_498346), -(c_Orderings_Oord__class_Oless(_498346, _498348, _498350)), -(_498348 = _498350), -(c_Orderings_Oord__class_Oless(_498346, _498350, _498348))], (9428 ^ _167881) ^ [_498766, _498768, _498770] : [class_Orderings_Olinorder(_498766), 9431 ^ _167881 : [(9442 ^ _167881) ^ [] : [9443 ^ _167881 : [(9444 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_498766, _498770, _498768)], (9446 ^ _167881) ^ [] : [_498768 = _498770]], c_Orderings_Oord__class_Oless(_498766, _498768, _498770)], (9432 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_498766, _498768, _498770)), -(c_Orderings_Oord__class_Oless(_498766, _498770, _498768)), -(_498768 = _498770)]]], (9450 ^ _167881) ^ [_499426, _499428, _499430] : [class_Orderings_Olinorder(_499426), 9453 ^ _167881 : [(9464 ^ _167881) ^ [] : [9465 ^ _167881 : [(9466 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_499426, _499428, _499430)], (9468 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_499426, _499430, _499428)]], _499428 = _499430], (9454 ^ _167881) ^ [] : [-(_499428 = _499430), -(c_Orderings_Oord__class_Oless(_499426, _499428, _499430)), -(c_Orderings_Oord__class_Oless(_499426, _499430, _499428))]]], (9472 ^ _167881) ^ [_500072, _500074] : [class_Orderings_Opreorder(_500072), c_Orderings_Oord__class_Oless(_500072, _500074, _500074)], (9478 ^ _167881) ^ [_500311, _500313, _500315, _500317] : [class_Orderings_Oorder(_500311), c_Orderings_Oord__class_Oless__eq(_500311, _500313, _500315), c_Orderings_Oord__class_Oless(_500311, _500317, _500313), -(c_Orderings_Oord__class_Oless(_500311, _500317, _500315))], (9492 ^ _167881) ^ [_500759, _500761, _500763, _500765] : [class_Orderings_Opreorder(_500759), c_Orderings_Oord__class_Oless__eq(_500759, _500761, _500763), c_Orderings_Oord__class_Oless(_500759, _500763, _500765), -(c_Orderings_Oord__class_Oless(_500759, _500761, _500765))], (9506 ^ _167881) ^ [_501207, _501209, _501211, _501213] : [class_Orderings_Oorder(_501207), c_Orderings_Oord__class_Oless(_501207, _501209, _501211), c_Orderings_Oord__class_Oless__eq(_501207, _501213, _501209), -(c_Orderings_Oord__class_Oless(_501207, _501213, _501211))], (9520 ^ _167881) ^ [_501655, _501657, _501659, _501661] : [class_Orderings_Opreorder(_501655), c_Orderings_Oord__class_Oless(_501655, _501657, _501659), c_Orderings_Oord__class_Oless__eq(_501655, _501659, _501661), -(c_Orderings_Oord__class_Oless(_501655, _501657, _501661))], (9534 ^ _167881) ^ [_502089, _502091, _502093] : [class_Orderings_Oorder(_502089), c_Orderings_Oord__class_Oless__eq(_502089, _502091, _502093), -(_502093 = _502091), -(c_Orderings_Oord__class_Oless(_502089, _502091, _502093))], (9548 ^ _167881) ^ [_502510, _502512, _502514] : [class_Orderings_Oorder(_502510), c_Orderings_Oord__class_Oless__eq(_502510, _502512, _502514), -(_502512 = _502514), -(c_Orderings_Oord__class_Oless(_502510, _502512, _502514))], (9562 ^ _167881) ^ [_502931, _502933, _502935] : [class_Orderings_Oorder(_502931), c_Orderings_Oord__class_Oless__eq(_502931, _502933, _502935), -(c_Orderings_Oord__class_Oless(_502931, _502933, _502935)), -(_502933 = _502935)], (9576 ^ _167881) ^ [_503350, _503352, _503354] : [class_Orderings_Olinorder(_503350), c_Orderings_Oord__class_Oless__eq(_503350, _503352, _503354), 9583 ^ _167881 : [(9584 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_503350, _503352, _503354)), -(_503352 = _503354)], (9590 ^ _167881) ^ [] : [_503352 = _503354, c_Orderings_Oord__class_Oless(_503350, _503352, _503354)]]], (9596 ^ _167881) ^ [_503938, _503940, _503942] : [class_Orderings_Opreorder(_503938), c_Orderings_Oord__class_Oless(_503938, _503940, _503942), -(c_Orderings_Oord__class_Oless__eq(_503938, _503940, _503942))], (9606 ^ _167881) ^ [_504263, _504265, _504267] : [class_Orderings_Olinorder(_504263), c_Orderings_Oord__class_Oless__eq(_504263, _504265, _504267), c_Orderings_Oord__class_Oless(_504263, _504267, _504265)], (9616 ^ _167881) ^ [_504589, _504591, _504593] : [class_Orderings_Oorder(_504589), -(_504591 = _504593), c_Orderings_Oord__class_Oless__eq(_504589, _504593, _504591), -(c_Orderings_Oord__class_Oless(_504589, _504593, _504591))], (9630 ^ _167881) ^ [_505010, _505012, _505014] : [class_Orderings_Oorder(_505010), -(_505012 = _505014), c_Orderings_Oord__class_Oless__eq(_505010, _505012, _505014), -(c_Orderings_Oord__class_Oless(_505010, _505012, _505014))], (9644 ^ _167881) ^ [_505431, _505433, _505435] : [class_Orderings_Olinorder(_505431), -(c_Orderings_Oord__class_Oless(_505431, _505433, _505435)), 9651 ^ _167881 : [(9652 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_505431, _505433, _505435), -(_505433 = _505435)], (9658 ^ _167881) ^ [] : [_505433 = _505435, -(c_Orderings_Oord__class_Oless__eq(_505431, _505433, _505435))]]], (9664 ^ _167881) ^ [_506020, _506022, _506024] : [class_Orderings_Olinorder(_506020), -(c_Orderings_Oord__class_Oless__eq(_506020, _506022, _506024)), -(c_Orderings_Oord__class_Oless(_506020, _506024, _506022))], (9674 ^ _167881) ^ [_506348, _506350, _506352] : [class_Orderings_Olinorder(_506348), -(c_Orderings_Oord__class_Oless(_506348, _506350, _506352)), -(c_Orderings_Oord__class_Oless__eq(_506348, _506352, _506350))], (9684 ^ _167881) ^ [_506676, _506678, _506680] : [class_Orderings_Oorder(_506676), 9687 ^ _167881 : [(9698 ^ _167881) ^ [] : [9699 ^ _167881 : [(9700 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_506676, _506678, _506680)], (9702 ^ _167881) ^ [] : [_506678 = _506680]], -(c_Orderings_Oord__class_Oless__eq(_506676, _506678, _506680))], (9688 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_506676, _506678, _506680), -(c_Orderings_Oord__class_Oless(_506676, _506678, _506680)), -(_506678 = _506680)]]], (9706 ^ _167881) ^ [_507334, _507336, _507338] : [class_Orderings_Opreorder(_507334), 9709 ^ _167881 : [(9710 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_507334, _507336, _507338), 9713 ^ _167881 : [(9714 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_507334, _507336, _507338))], (9716 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_507334, _507338, _507336)]]], (9718 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_507334, _507336, _507338)), c_Orderings_Oord__class_Oless__eq(_507334, _507336, _507338), -(c_Orderings_Oord__class_Oless__eq(_507334, _507338, _507336))]]], (9728 ^ _167881) ^ [_507997, _507999, _508001] : [class_Orderings_Oorder(_507997), 9731 ^ _167881 : [(9732 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_507997, _507999, _508001), 9735 ^ _167881 : [(9736 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_507997, _507999, _508001))], (9738 ^ _167881) ^ [] : [_507999 = _508001]]], (9740 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_507997, _507999, _508001)), c_Orderings_Oord__class_Oless__eq(_507997, _507999, _508001), -(_507999 = _508001)]]], (9750 ^ _167881) ^ [_508657, _508659, _508661] : [class_Orderings_Olinorder(_508657), -(c_Orderings_Oord__class_Oless__eq(_508657, _508659, _508661)), -(c_Orderings_Oord__class_Oless(_508657, _508661, _508659))], (9760 ^ _167881) ^ [_508983, _508985, _508987] : [class_Orderings_Olinorder(_508983), 9763 ^ _167881 : [(9764 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_508983, _508985, _508987)), -(c_Orderings_Oord__class_Oless(_508983, _508987, _508985))], (9770 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_508983, _508987, _508985), c_Orderings_Oord__class_Oless__eq(_508983, _508985, _508987)]]], (9776 ^ _167881) ^ [_509479, _509481, _509483] : [class_Orderings_Olinorder(_509479), 9779 ^ _167881 : [(9780 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_509479, _509481, _509483)), -(c_Orderings_Oord__class_Oless__eq(_509479, _509483, _509481))], (9786 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_509479, _509483, _509481), c_Orderings_Oord__class_Oless(_509479, _509481, _509483)]]], (9794 ^ _167881) ^ [] : [9792 ^ [] = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (9796 ^ _167881) ^ [] : [9791 ^ [] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9799 ^ _167881) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 9797 ^ []), 9791 ^ []), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (9801 ^ _167881) ^ [_510395] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _510395) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), _510395), 9791 ^ [])), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, 9792 ^ [], 9797 ^ [])), _510395))))], (9803 ^ _167881) ^ [_510516] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _510516), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _510516, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_510516), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9809 ^ _167881) ^ [_510774, _510776, _510778, _510780] : [class_Orderings_Oord(_510774), 9812 ^ _167881 : [(9813 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_510776, _510774), _510778, _510780), 9816 ^ _167881 : [(9817 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_510776, _510774), _510778, _510780))], (9819 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_510776, _510774), _510780, _510778)]]], (9821 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_510776, _510774), _510778, _510780)), c_Orderings_Oord__class_Oless__eq(tc_fun(_510776, _510774), _510778, _510780), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_510776, _510774), _510780, _510778))]]], (9831 ^ _167881) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9833 ^ _167881) ^ [_511496] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_511496)))], (9835 ^ _167881) ^ [_511606, _511608] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _511606, _511608), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_511606), c_RComplete_Onatceiling(_511608)))], (9841 ^ _167881) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9843 ^ _167881) ^ [_511867] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _511867, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_511867) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9849 ^ _167881) ^ [_512092] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_512092), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _512092, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9855 ^ _167881) ^ [_512256] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _512256, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_512256), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9861 ^ _167881) ^ [_512456] : [class_Power_Opower(_512456), -(c_Power_Opower__class_Opower(_512456) = c_Power_Opower_Opower(_512456, c_Groups_Oone__class_Oone(_512456), c_Groups_Otimes__class_Otimes(_512456)))], (9867 ^ _167881) ^ [_512664] : [9875 ^ _167881 : [(9876 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9874 ^ [_512664]))], (9878 ^ _167881) ^ [_513024] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_512664, c_RealVector_Oof__real(_512664, _513024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _513024)), 9874 ^ [_512664])))]], class_RealVector_Oreal__algebra__1(_512664), class_RealVector_Oreal__normed__vector(_512664)], (9880 ^ _167881) ^ [_513174, _513176, _513178, _513180] : [-(hAPP(hAPP(c_Power_Opower_Opower(_513174, _513176, _513178), _513180), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _513176)], (9882 ^ _167881) ^ [_513325, _513327, _513329, _513331] : [class_RealVector_Oreal__normed__vector(_513325), class_Orderings_Oord(_513327), 9892 ^ _167881 : [(9893 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_513327, _513329, 9891 ^ [_513325, _513327, _513329, _513331]))], (9895 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_513325, c_Groups_Ominus__class_Ominus(_513325, hAPP(_513331, _513329), hAPP(_513331, 9891 ^ [_513325, _513327, _513329, _513331]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]], 9896 ^ _167881 : [(9897 ^ _167881) ^ [_513883] : [c_Orderings_Oord__class_Oless__eq(_513327, _513329, _513883), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_513325, hAPP(_513331, _513883)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_513325, hAPP(_513331, _513329)))))]]], (9903 ^ _167881) ^ [_514167, _514169] : [class_RealVector_Oreal__normed__algebra(_514167), 9907 ^ _167881 : [(9908 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9906 ^ [_514167, _514169]))], (9910 ^ _167881) ^ [_514466] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_514167, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514167), _514466), _514169)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_514167, _514466)), 9906 ^ [_514167, _514169])))]]], (9912 ^ _167881) ^ [_514598] : [class_RealVector_Oreal__normed__algebra(_514598), 9916 ^ _167881 : [(9917 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9915 ^ [_514598]))], (9919 ^ _167881) ^ [_514927, _514929] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_514598, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514598), _514929), _514927)), 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(_514598, _514929)), c_RealVector_Onorm__class_Onorm(_514598, _514927))), 9915 ^ [_514598])))]]], (9921 ^ _167881) ^ [_515080, _515082] : [class_RealVector_Oreal__normed__algebra(_515080), 9925 ^ _167881 : [(9926 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9924 ^ [_515080, _515082]))], (9928 ^ _167881) ^ [_515379] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_515080, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515080), _515082), _515379)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_515080, _515379)), 9924 ^ [_515080, _515082])))]]], (9931 ^ _167881) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 9929 ^ []) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (9933 ^ _167881) ^ [_515615] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 9929 ^ []), _515615) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _515615)))], (9935 ^ _167881) ^ [_515720] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _515720), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _515720, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_515720), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9941 ^ _167881) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9943 ^ _167881) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9945 ^ _167881) ^ [_516027] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_516027)))], (9947 ^ _167881) ^ [_516137, _516139] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _516137, _516139), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_516137), c_RComplete_Onatfloor(_516139)))], (9953 ^ _167881) ^ [_516345] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _516345, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_516345) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9959 ^ _167881) ^ [_516570] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_516570)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _516570))], (9965 ^ _167881) ^ [_516734] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _516734), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_516734)))], (9971 ^ _167881) ^ [_516948, _516950] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _516948), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _516950), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_516948)), c_RComplete_Onatfloor(_516950)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _516948), _516950))))], (9981 ^ _167881) ^ [_517309, _517311] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _517309, _517311), -(c_Nat__Transfer_Otsub(_517311, _517309) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _517311, _517309))], (9987 ^ _167881) ^ [_517487, _517489] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _517487, _517489)), -(c_Nat__Transfer_Otsub(_517489, _517487) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9993 ^ _167881) ^ [_517724, _517726, _517728] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _517724, _517726), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _517724, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _517726, _517728)))], (9999 ^ _167881) ^ [_517952, _517954] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _517952), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _517954), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_517952, _517954)))], (10009 ^ _167881) ^ [_518263, _518265] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _518263, _518265), -(c_Nat__Transfer_Otsub(_518265, _518263) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _518265, _518263))], (10015 ^ _167881) ^ [_518503, _518505, _518507] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _518503, _518505), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _518503, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _518507, _518505)))], (10021 ^ _167881) ^ [_518745, _518747, _518749] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _518745, _518747), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _518745, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _518747, _518749)))], (10027 ^ _167881) ^ [_518973, _518975] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _518973, _518975), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _518973, _518975))], (10033 ^ _167881) ^ [_519201, _519203, _519205] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _519201, _519203), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _519201, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _519205, _519203)))], (10039 ^ _167881) ^ [_519429, _519431] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _519429), _519431), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _519431, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _519429), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_519431) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _519429, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10049 ^ _167881) ^ [_519778, _519780, _519782] : [class_Rings_Olinordered__idom(_519778), 10052 ^ _167881 : [(10053 ^ _167881) ^ [] : [c_Polynomial_Opos__poly(_519778, c_Polynomial_OpCons(_519778, _519780, _519782)), -(c_Polynomial_Opos__poly(_519778, _519782)), 10060 ^ _167881 : [(10061 ^ _167881) ^ [] : [-(_519782 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_519778)))], (10063 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_519778, c_Groups_Ozero__class_Ozero(_519778), _519780))]]], (10065 ^ _167881) ^ [] : [-(c_Polynomial_Opos__poly(_519778, c_Polynomial_OpCons(_519778, _519780, _519782))), 10066 ^ _167881 : [(10067 ^ _167881) ^ [] : [c_Polynomial_Opos__poly(_519778, _519782)], (10069 ^ _167881) ^ [] : [_519782 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_519778)), c_Orderings_Oord__class_Oless(_519778, c_Groups_Ozero__class_Ozero(_519778), _519780)]]]]], (10077 ^ _167881) ^ [_520584] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _520584)))], (10079 ^ _167881) ^ [_520695, _520697] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _520695, _520697), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _520697, _520695)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _520697), c_RealDef_Oreal(tc_Nat_Onat, _520695)))], (10085 ^ _167881) ^ [_520911] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _520911), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10087 ^ _167881) ^ [_521051, _521053] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _521051), c_RealDef_Oreal(tc_Nat_Onat, _521053)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _521051, _521053))], (10093 ^ _167881) ^ [_521229, _521231] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _521229, _521231), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _521229), c_RealDef_Oreal(tc_Nat_Onat, _521231)))], (10099 ^ _167881) ^ [_521471, _521473, _521475] : [class_Rings_Olinordered__idom(_521471), c_Polynomial_Opos__poly(_521471, _521473), c_Polynomial_Opos__poly(_521471, _521475), -(c_Polynomial_Opos__poly(_521471, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_521471), _521473, _521475)))], (10113 ^ _167881) ^ [_521868, _521870] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _521868), _521870)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _521868)), c_RealDef_Oreal(tc_Nat_Onat, _521870)))], (10115 ^ _167881) ^ [_522012, _522014, _522016] : [class_Rings_Olinordered__idom(_522012), c_Polynomial_Opos__poly(_522012, _522014), c_Polynomial_Opos__poly(_522012, _522016), -(c_Polynomial_Opos__poly(_522012, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_522012)), _522014), _522016)))], (10129 ^ _167881) ^ [_522418] : [class_Rings_Olinordered__idom(_522418), c_Polynomial_Opos__poly(_522418, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_522418)))], (10135 ^ _167881) ^ [_522644] : [c_RealDef_Oreal(tc_Nat_Onat, _522644) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_522644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10141 ^ _167881) ^ [_522806] : [_522806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _522806) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10147 ^ _167881) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10149 ^ _167881) ^ [_523100, _523102] : [c_RealDef_Oreal(tc_Nat_Onat, _523100) = c_RealDef_Oreal(tc_Nat_Onat, _523102), -(_523100 = _523102)], (10155 ^ _167881) ^ [_523274, _523276] : [_523274 = _523276, -(c_RealDef_Oreal(tc_Nat_Onat, _523274) = c_RealDef_Oreal(tc_Nat_Onat, _523276))], (10161 ^ _167881) ^ [_523483, _523485] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _523483, _523485)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _523483), c_RealDef_Oreal(tc_Nat_Onat, _523485)))], (10163 ^ _167881) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10165 ^ _167881) ^ [_523633] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _523633)) = c_RealDef_Oreal(tc_Nat_Onat, _523633))], (10167 ^ _167881) ^ [_523734, _523736] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _523734)), _523736) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _523734), _523736)))], (10169 ^ _167881) ^ [_523846, _523848] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _523846), _523848)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _523846)), _523848))], (10171 ^ _167881) ^ [_523988] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _523988), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_523988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10177 ^ _167881) ^ [_524152] : [_524152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _524152), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10183 ^ _167881) ^ [_524380, _524382, _524384] : [class_Rings_Olinordered__idom(_524380), 10186 ^ _167881 : [(10197 ^ _167881) ^ [] : [10198 ^ _167881 : [(10199 ^ _167881) ^ [] : [_524382 = _524384], (10201 ^ _167881) ^ [] : [c_Polynomial_Opos__poly(_524380, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_524380), _524384, _524382))]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_524380), _524382, _524384))], (10187 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_524380), _524382, _524384), -(_524382 = _524384), -(c_Polynomial_Opos__poly(_524380, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_524380), _524384, _524382)))]]], (10205 ^ _167881) ^ [_525016] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _525016, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_525016))))], (10207 ^ _167881) ^ [_525158, _525160] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525158), c_RealDef_Oreal(tc_Nat_Onat, _525160)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525158, _525160))], (10213 ^ _167881) ^ [_525336, _525338] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525336, _525338), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525336), c_RealDef_Oreal(tc_Nat_Onat, _525338)))], (10219 ^ _167881) ^ [_525535] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _525535)) = _525535)], (10221 ^ _167881) ^ [_525618] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _525618)) = _525618)], (10223 ^ _167881) ^ [_525716] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _525716), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_525716)), _525716))], (10229 ^ _167881) ^ [_525934, _525936] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _525934), _525936), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525934, c_RComplete_Onatfloor(_525936)))], (10235 ^ _167881) ^ [_526158, _526160] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _526158, c_RealDef_Oreal(tc_Nat_Onat, _526160)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_526158), _526160))], (10241 ^ _167881) ^ [_526382, _526384] : [_526382 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_526382)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _526382), _526384)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_526382)), _526384))], (10247 ^ _167881) ^ [_526649] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _526649)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _526649))], (10253 ^ _167881) ^ [_526815] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _526815), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _526815)))], (10259 ^ _167881) ^ [_527060, _527062] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _527060, _527062), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527060), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _527062)))], (10265 ^ _167881) ^ [_527246, _527248] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527246), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _527248)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _527246, _527248))], (10271 ^ _167881) ^ [_527511, _527513] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _527511, _527513), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527511), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527513), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10277 ^ _167881) ^ [_527697, _527699] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527697), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527699), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _527697, _527699))], (10283 ^ _167881) ^ [_527933, _527935] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _527933), 10286 ^ _167881 : [(10287 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _527935, c_RComplete_Onatfloor(_527933)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527935), _527933))], (10293 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _527935), _527933), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _527935, c_RComplete_Onatfloor(_527933)))]]], (10299 ^ _167881) ^ [_528416, _528418] : [class_Rings_Olinordered__idom(_528416), -(_528418 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_528416))), -(c_Polynomial_Opos__poly(_528416, _528418)), -(c_Polynomial_Opos__poly(_528416, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_528416), _528418)))], (10313 ^ _167881) ^ [_528822, _528824] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _528822), 10316 ^ _167881 : [(10317 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_528822), _528824), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _528822, c_RealDef_Oreal(tc_Nat_Onat, _528824)))], (10323 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _528822, c_RealDef_Oreal(tc_Nat_Onat, _528824)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_528822), _528824))]]], (10329 ^ _167881) ^ [_529276] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _529276, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_529276)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10331 ^ _167881) ^ [_529393, _529395] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _529393), _529395), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _529395, c_RealDef_Oreal(tc_Nat_Onat, _529393))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_529395), _529393))], (10337 ^ _167881) ^ [_529612] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _529612, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_529612))))], (10339 ^ _167881) ^ [_529729, _529731] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _529729), _529731), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _529731, c_RealDef_Oreal(tc_Nat_Onat, _529729))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_529731), _529729))], (10345 ^ _167881) ^ [_529977, _529979] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _529977), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _529977, c_RealDef_Oreal(tc_Nat_Onat, _529979)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_529977), _529979))], (10355 ^ _167881) ^ [_530292, _530294] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _530292), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _530292, c_RealDef_Oreal(tc_Nat_Onat, _530294))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_530292), _530294))], (10361 ^ _167881) ^ [_530534, _530536] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_530534), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _530536), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _530534, c_RealDef_Oreal(tc_Nat_Onat, _530536)))], (10367 ^ _167881) ^ [_530766, _530768] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _530766), _530768), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _530768, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _530766), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_530768) = _530766)], (10377 ^ _167881) ^ [_531093, _531095] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _531093), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _531093, c_RealDef_Oreal(tc_Nat_Onat, _531095))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_531093), _531095))], (10383 ^ _167881) ^ [_531349, _531351, _531353] : [class_Rings_Olinordered__idom(_531349), 10386 ^ _167881 : [(10387 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_531349), _531351, _531353), -(c_Polynomial_Opos__poly(_531349, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_531349), _531353, _531351)))], (10393 ^ _167881) ^ [] : [c_Polynomial_Opos__poly(_531349, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_531349), _531353, _531351)), -(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_531349), _531351, _531353))]]], (10399 ^ _167881) ^ [_531850, _531852] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _531850), -(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, _531852)), _531850), 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, _531850, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _531852)))], (10405 ^ _167881) ^ [_532096] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _532096), 10409 ^ _167881 : [(10410 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 10408 ^ [_532096], c_Groups_Oone__class_Oone(tc_Nat_Onat))), _532096))], (10412 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _532096, c_RealDef_Oreal(tc_Nat_Onat, 10408 ^ [_532096])))]]], (10414 ^ _167881) ^ [_532487, _532489, _532491] : [class_Groups_Oab__group__add(_532487), -(c_Groups_Ominus__class_Ominus(_532487, c_Groups_Ouminus__class_Ouminus(_532487, _532489), c_Groups_Ouminus__class_Ouminus(_532487, _532491)) = c_Groups_Ouminus__class_Ouminus(_532487, c_Groups_Ominus__class_Ominus(_532487, _532489, _532491)))], (10420 ^ _167881) ^ [_532749, _532751, _532753] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _532749), 10424 ^ _167881 : [(10425 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10423 ^ [_532749, _532751, _532753]))], (10427 ^ _167881) ^ [_533133] : [-(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, _532753), _533133), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _532753), _532751))), _532749)), 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, _533133, _532751))), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _533133, _532751)), 10423 ^ [_532749, _532751, _532753])]]], (10437 ^ _167881) ^ [_533555, _533557] : [class_Orderings_Oorder(_533555), 10440 ^ _167881 : [(10451 ^ _167881) ^ [] : [10454 ^ _167881 : [(10455 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 10452 ^ [_533555, _533557], 10453 ^ [_533555, _533557]))], (10457 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_533555, hAPP(_533557, 10453 ^ [_533555, _533557]), hAPP(_533557, 10452 ^ [_533555, _533557]))]], -(c_SEQ_Odecseq(_533555, _533557))], (10441 ^ _167881) ^ [] : [c_SEQ_Odecseq(_533555, _533557), 10444 ^ _167881 : [(10445 ^ _167881) ^ [_533831, _533833] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _533833, _533831), -(c_Orderings_Oord__class_Oless__eq(_533555, hAPP(_533557, _533831), hAPP(_533557, _533833)))]]]]], (10461 ^ _167881) ^ [_534470, _534472, _534474] : [class_Lattices_Oboolean__algebra(_534470), 10464 ^ _167881 : [(10465 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_534470, c_Groups_Ouminus__class_Ouminus(_534470, _534472), c_Groups_Ouminus__class_Ouminus(_534470, _534474)), -(c_Orderings_Oord__class_Oless__eq(_534470, _534474, _534472))], (10471 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless__eq(_534470, _534474, _534472), -(c_Orderings_Oord__class_Oless__eq(_534470, c_Groups_Ouminus__class_Ouminus(_534470, _534472), c_Groups_Ouminus__class_Ouminus(_534470, _534474)))]]], (10477 ^ _167881) ^ [_534982, _534984, _534986] : [class_Lattices_Oboolean__algebra(_534982), c_Orderings_Oord__class_Oless__eq(_534982, _534984, _534986), -(c_Orderings_Oord__class_Oless__eq(_534982, c_Groups_Ouminus__class_Ouminus(_534982, _534986), c_Groups_Ouminus__class_Ouminus(_534982, _534984)))], (10487 ^ _167881) ^ [_535347, _535349, _535351, _535353, _535355] : [class_Groups_Ominus(_535347), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_535349, _535347), _535351, _535353), _535355) = c_Groups_Ominus__class_Ominus(_535347, hAPP(_535351, _535355), hAPP(_535353, _535355)))], (10493 ^ _167881) ^ [_535613, _535615] : [class_Lattices_Oab__semigroup__idem__mult(_535613), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535613), _535615), _535615) = _535615)], (10499 ^ _167881) ^ [_535837, _535839] : [class_Lattices_Oab__semigroup__idem__mult(_535837), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535837), _535839), _535839) = _535839)], (10505 ^ _167881) ^ [_536075, _536077, _536079] : [class_Lattices_Oab__semigroup__idem__mult(_536075), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536075), _536077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536075), _536077), _536079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536075), _536077), _536079))], (10511 ^ _167881) ^ [_536337, _536339] : [class_Lattices_Oboolean__algebra(_536337), -(c_Groups_Ouminus__class_Ouminus(_536337, c_Groups_Ouminus__class_Ouminus(_536337, _536339)) = _536339)], (10517 ^ _167881) ^ [_536585, _536587, _536589, _536591] : [class_Groups_Ouminus(_536585), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_536587, _536585), _536589), _536591) = c_Groups_Ouminus__class_Ouminus(_536585, hAPP(_536589, _536591)))], (10523 ^ _167881) ^ [_536849, _536851, _536853] : [class_Lattices_Oboolean__algebra(_536849), 10526 ^ _167881 : [(10527 ^ _167881) ^ [] : [c_Groups_Ouminus__class_Ouminus(_536849, _536851) = c_Groups_Ouminus__class_Ouminus(_536849, _536853), -(_536851 = _536853)], (10533 ^ _167881) ^ [] : [_536851 = _536853, -(c_Groups_Ouminus__class_Ouminus(_536849, _536851) = c_Groups_Ouminus__class_Ouminus(_536849, _536853))]]], (10539 ^ _167881) ^ [_537327] : [10547 ^ _167881 : [(10548 ^ _167881) ^ [_537603] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_537327, c_RealVector_Oof__real(_537327, _537603)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _537603)), 10546 ^ [_537327])))]], class_RealVector_Oreal__algebra__1(_537327), class_RealVector_Oreal__normed__vector(_537327)], (10550 ^ _167881) ^ [_537738, _537740] : [class_Rings_Olinordered__idom(_537738), 10553 ^ _167881 : [(10554 ^ _167881) ^ [] : [_537740 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_537738)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_537738), _537740) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_537738)))], (10560 ^ _167881) ^ [] : [-(_537740 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_537738))), 10563 ^ _167881 : [(10564 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_537738), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_537738)), _537740), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_537738), _537740) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_537738)))], (10570 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_537738), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_537738)), _537740)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_537738), _537740) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_537738), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_537738))))]]]]], (10576 ^ _167881) ^ [_538566, _538568] : [class_Rings_Olinordered__idom(_538566), 10579 ^ _167881 : [(10580 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_538566, c_Groups_Ozero__class_Ozero(_538566), c_Groups_Osgn__class_Osgn(_538566, _538568)), -(c_Orderings_Oord__class_Oless(_538566, c_Groups_Ozero__class_Ozero(_538566), _538568))], (10586 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_538566, c_Groups_Ozero__class_Ozero(_538566), _538568), -(c_Orderings_Oord__class_Oless(_538566, c_Groups_Ozero__class_Ozero(_538566), c_Groups_Osgn__class_Osgn(_538566, _538568)))]]], (10592 ^ _167881) ^ [_539051, _539053] : [class_Rings_Olinordered__idom(_539051), 10595 ^ _167881 : [(10596 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_539051, c_Groups_Osgn__class_Osgn(_539051, _539053), c_Groups_Ozero__class_Ozero(_539051)), -(c_Orderings_Oord__class_Oless(_539051, _539053, c_Groups_Ozero__class_Ozero(_539051)))], (10602 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_539051, _539053, c_Groups_Ozero__class_Ozero(_539051)), -(c_Orderings_Oord__class_Oless(_539051, c_Groups_Osgn__class_Osgn(_539051, _539053), c_Groups_Ozero__class_Ozero(_539051)))]]], (10608 ^ _167881) ^ [_539550, _539552, _539554] : [class_RealVector_Oreal__normed__div__algebra(_539550), -(c_Groups_Osgn__class_Osgn(_539550, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539550), _539552), _539554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539550), c_Groups_Osgn__class_Osgn(_539550, _539552)), c_Groups_Osgn__class_Osgn(_539550, _539554)))], (10614 ^ _167881) ^ [_539828, _539830, _539832] : [class_Rings_Olinordered__idom(_539828), -(c_Groups_Osgn__class_Osgn(_539828, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539828), _539830), _539832)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539828), c_Groups_Osgn__class_Osgn(_539828, _539830)), c_Groups_Osgn__class_Osgn(_539828, _539832)))], (10620 ^ _167881) ^ [_540078] : [class_Groups_Osgn__if(_540078), -(c_Groups_Osgn__class_Osgn(_540078, c_Groups_Ozero__class_Ozero(_540078)) = c_Groups_Ozero__class_Ozero(_540078))], (10626 ^ _167881) ^ [_540294, _540296] : [class_RealVector_Oreal__normed__vector(_540294), 10629 ^ _167881 : [(10630 ^ _167881) ^ [] : [c_Groups_Osgn__class_Osgn(_540294, _540296) = c_Groups_Ozero__class_Ozero(_540294), -(_540296 = c_Groups_Ozero__class_Ozero(_540294))], (10636 ^ _167881) ^ [] : [_540296 = c_Groups_Ozero__class_Ozero(_540294), -(c_Groups_Osgn__class_Osgn(_540294, _540296) = c_Groups_Ozero__class_Ozero(_540294))]]], (10642 ^ _167881) ^ [_540773, _540775] : [class_Rings_Olinordered__idom(_540773), 10645 ^ _167881 : [(10646 ^ _167881) ^ [] : [c_Groups_Osgn__class_Osgn(_540773, _540775) = c_Groups_Ozero__class_Ozero(_540773), -(_540775 = c_Groups_Ozero__class_Ozero(_540773))], (10652 ^ _167881) ^ [] : [_540775 = c_Groups_Ozero__class_Ozero(_540773), -(c_Groups_Osgn__class_Osgn(_540773, _540775) = c_Groups_Ozero__class_Ozero(_540773))]]], (10658 ^ _167881) ^ [_541238] : [class_RealVector_Oreal__normed__vector(_541238), -(c_Groups_Osgn__class_Osgn(_541238, c_Groups_Ozero__class_Ozero(_541238)) = c_Groups_Ozero__class_Ozero(_541238))], (10664 ^ _167881) ^ [_541454, _541456] : [class_Rings_Olinordered__idom(_541454), -(c_Groups_Osgn__class_Osgn(_541454, c_Groups_Osgn__class_Osgn(_541454, _541456)) = c_Groups_Osgn__class_Osgn(_541454, _541456))], (10670 ^ _167881) ^ [_541680, _541682] : [class_RealVector_Oreal__normed__algebra__1(_541680), -(c_Groups_Osgn__class_Osgn(_541680, c_RealVector_Oof__real(_541680, _541682)) = c_RealVector_Oof__real(_541680, c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _541682)))], (10676 ^ _167881) ^ [_541912, _541914] : [class_Rings_Olinordered__idom(_541912), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541912), c_Groups_Osgn__class_Osgn(_541912, _541914)), c_Groups_Oabs__class_Oabs(_541912, _541914)) = _541914)], (10682 ^ _167881) ^ [_542148, _542150] : [class_Rings_Olinordered__idom(_542148), -(c_Groups_Oabs__class_Oabs(_542148, _542150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542148), _542150), c_Groups_Osgn__class_Osgn(_542148, _542150)))], (10688 ^ _167881) ^ [_542370] : [class_RealVector_Oreal__normed__algebra__1(_542370), -(c_Groups_Osgn__class_Osgn(_542370, c_Groups_Oone__class_Oone(_542370)) = c_Groups_Oone__class_Oone(_542370))], (10694 ^ _167881) ^ [_542586, _542588] : [class_RealVector_Oreal__normed__vector(_542586), -(c_Groups_Osgn__class_Osgn(_542586, c_Groups_Ouminus__class_Ouminus(_542586, _542588)) = c_Groups_Ouminus__class_Ouminus(_542586, c_Groups_Osgn__class_Osgn(_542586, _542588)))], (10700 ^ _167881) ^ [_542818, _542820] : [class_Rings_Olinordered__idom(_542818), 10703 ^ _167881 : [(10704 ^ _167881) ^ [] : [c_Groups_Osgn__class_Osgn(_542818, _542820) = c_Groups_Oone__class_Oone(_542818), -(c_Orderings_Oord__class_Oless(_542818, c_Groups_Ozero__class_Ozero(_542818), _542820))], (10710 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_542818, c_Groups_Ozero__class_Ozero(_542818), _542820), -(c_Groups_Osgn__class_Osgn(_542818, _542820) = c_Groups_Oone__class_Oone(_542818))]]], (10716 ^ _167881) ^ [_543300, _543302] : [class_Rings_Olinordered__idom(_543300), c_Orderings_Oord__class_Oless(_543300, c_Groups_Ozero__class_Ozero(_543300), _543302), -(c_Groups_Osgn__class_Osgn(_543300, _543302) = c_Groups_Oone__class_Oone(_543300))], (10726 ^ _167881) ^ [_543613, _543615] : [class_Rings_Olinordered__idom(_543613), 10729 ^ _167881 : [(10730 ^ _167881) ^ [] : [c_Groups_Osgn__class_Osgn(_543613, _543615) = c_Groups_Ouminus__class_Ouminus(_543613, c_Groups_Oone__class_Oone(_543613)), -(c_Orderings_Oord__class_Oless(_543613, _543615, c_Groups_Ozero__class_Ozero(_543613)))], (10736 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_543613, _543615, c_Groups_Ozero__class_Ozero(_543613)), -(c_Groups_Osgn__class_Osgn(_543613, _543615) = c_Groups_Ouminus__class_Ouminus(_543613, c_Groups_Oone__class_Oone(_543613)))]]], (10742 ^ _167881) ^ [_544104, _544106] : [class_Rings_Olinordered__idom(_544104), c_Orderings_Oord__class_Oless(_544104, _544106, c_Groups_Ozero__class_Ozero(_544104)), -(c_Groups_Osgn__class_Osgn(_544104, _544106) = c_Groups_Ouminus__class_Ouminus(_544104, c_Groups_Oone__class_Oone(_544104)))], (10752 ^ _167881) ^ [_544423, _544425] : [class_Groups_Osgn__if(_544423), 10755 ^ _167881 : [(10756 ^ _167881) ^ [] : [_544425 = c_Groups_Ozero__class_Ozero(_544423), -(c_Groups_Osgn__class_Osgn(_544423, _544425) = c_Groups_Ozero__class_Ozero(_544423))], (10762 ^ _167881) ^ [] : [-(_544425 = c_Groups_Ozero__class_Ozero(_544423)), 10765 ^ _167881 : [(10766 ^ _167881) ^ [] : [c_Orderings_Oord__class_Oless(_544423, c_Groups_Ozero__class_Ozero(_544423), _544425), -(c_Groups_Osgn__class_Osgn(_544423, _544425) = c_Groups_Oone__class_Oone(_544423))], (10772 ^ _167881) ^ [] : [-(c_Orderings_Oord__class_Oless(_544423, c_Groups_Ozero__class_Ozero(_544423), _544425)), -(c_Groups_Osgn__class_Osgn(_544423, _544425) = c_Groups_Ouminus__class_Ouminus(_544423, c_Groups_Oone__class_Oone(_544423)))]]]]], (10778 ^ _167881) ^ [_545199, _545201] : [class_RealVector_Oreal__normed__vector(_545199), 10781 ^ _167881 : [(10782 ^ _167881) ^ [] : [_545201 = c_Groups_Ozero__class_Ozero(_545199), -(c_RealVector_Onorm__class_Onorm(_545199, c_Groups_Osgn__class_Osgn(_545199, _545201)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10788 ^ _167881) ^ [] : [-(_545201 = c_Groups_Ozero__class_Ozero(_545199)), -(c_RealVector_Onorm__class_Onorm(_545199, c_Groups_Osgn__class_Osgn(_545199, _545201)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (10794 ^ _167881) ^ [_545709, _545711, _545713] : [class_Rings_Oidom(_545709), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_545709), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_545709)), c_Polynomial_OpCons(_545709, c_Groups_Ouminus__class_Ouminus(_545709, _545711), c_Polynomial_OpCons(_545709, c_Groups_Oone__class_Oone(_545709), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_545709))))), c_Polynomial_Oorder(_545709, _545711, _545713)), _545713))], (10800 ^ _167881) ^ [_546019, _546021, _546023, _546025] : [class_Rings_Ocomm__semiring__0(_546019), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_546019, c_Polynomial_OpCons(_546019, _546021, _546023), _546025) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_546019), c_Polynomial_Osmult(_546019, _546025, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_546019, _546023, _546025)), c_Polynomial_OpCons(_546019, _546021, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_546019, _546023, _546025))))], (10806 ^ _167881) ^ [_546299, _546301] : [class_Rings_Ocomm__semiring__1(_546299), -(c_Rings_Odvd__class_Odvd(_546299, _546301, c_Groups_Ozero__class_Ozero(_546299)))], (10812 ^ _167881) ^ [_546541, _546543, _546545, _546547] : [class_Rings_Ocomm__ring__1(_546541), c_Rings_Odvd__class_Odvd(_546541, _546543, _546545), c_Rings_Odvd__class_Odvd(_546541, _546543, _546547), -(c_Rings_Odvd__class_Odvd(_546541, _546543, c_Groups_Ominus__class_Ominus(_546541, _546545, _546547)))], (10826 ^ _167881) ^ [_546983, _546985, _546987] : [class_Rings_Ocomm__ring__1(_546983), 10829 ^ _167881 : [(10830 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_546983, c_Groups_Ouminus__class_Ouminus(_546983, _546985), _546987), -(c_Rings_Odvd__class_Odvd(_546983, _546985, _546987))], (10836 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_546983, _546985, _546987), -(c_Rings_Odvd__class_Odvd(_546983, c_Groups_Ouminus__class_Ouminus(_546983, _546985), _546987))]]], (10842 ^ _167881) ^ [_547486, _547488, _547490] : [class_Rings_Ocomm__ring__1(_547486), 10845 ^ _167881 : [(10846 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_547486, _547488, c_Groups_Ouminus__class_Ouminus(_547486, _547490)), -(c_Rings_Odvd__class_Odvd(_547486, _547488, _547490))], (10852 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_547486, _547488, _547490), -(c_Rings_Odvd__class_Odvd(_547486, _547488, c_Groups_Ouminus__class_Ouminus(_547486, _547490)))]]], (10858 ^ _167881) ^ [_548003, _548005, _548007, _548009] : [class_Rings_Ocomm__ring(_548003), class_Rings_Odvd(_548003), c_Rings_Odvd__class_Odvd(_548003, _548005, _548007), 10869 ^ _167881 : [(10870 ^ _167881) ^ [_548406, _548408] : [c_Rings_Odvd__class_Odvd(_548003, _548005, c_Groups_Oplus__class_Oplus(_548003, _548408, _548009)), -(c_Rings_Odvd__class_Odvd(_548003, _548005, c_Groups_Oplus__class_Oplus(_548003, c_Groups_Ominus__class_Ominus(_548003, _548408, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548003), _548406), _548007)), _548009)))], (10876 ^ _167881) ^ [_548644, _548646] : [c_Rings_Odvd__class_Odvd(_548003, _548005, c_Groups_Oplus__class_Oplus(_548003, c_Groups_Ominus__class_Ominus(_548003, _548646, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548003), _548644), _548007)), _548009)), -(c_Rings_Odvd__class_Odvd(_548003, _548005, c_Groups_Oplus__class_Oplus(_548003, _548646, _548009)))]]], (10882 ^ _167881) ^ [_548971, _548973, _548975, _548977] : [class_Rings_Ocomm__ring(_548971), class_Rings_Odvd(_548971), c_Rings_Odvd__class_Odvd(_548971, _548973, _548975), 10893 ^ _167881 : [(10894 ^ _167881) ^ [_549374, _549376] : [c_Rings_Odvd__class_Odvd(_548971, _548973, c_Groups_Oplus__class_Oplus(_548971, _549376, _548977)), -(c_Rings_Odvd__class_Odvd(_548971, _548973, c_Groups_Oplus__class_Oplus(_548971, c_Groups_Ominus__class_Ominus(_548971, _549376, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548971), _549374), _548975)), _548977)))], (10900 ^ _167881) ^ [_549612, _549614] : [c_Rings_Odvd__class_Odvd(_548971, _548973, c_Groups_Oplus__class_Oplus(_548971, c_Groups_Ominus__class_Ominus(_548971, _549614, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548971), _549612), _548975)), _548977)), -(c_Rings_Odvd__class_Odvd(_548971, _548973, c_Groups_Oplus__class_Oplus(_548971, _549614, _548977)))]]], (10906 ^ _167881) ^ [_549939, _549941, _549943, _549945] : [class_Fields_Ofield(_549939), 10909 ^ _167881 : [(10926 ^ _167881) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_549939), c_Polynomial_Osmult(_549939, _549941, _549943), _549945)), 10929 ^ _167881 : [(10930 ^ _167881) ^ [] : [-(_549941 = c_Groups_Ozero__class_Ozero(_549939))], (10932 ^ _167881) ^ [] : [_549945 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_549939))]], 10933 ^ _167881 : [(10934 ^ _167881) ^ [] : [_549941 = c_Groups_Ozero__class_Ozero(_549939)], (10936 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_549939), _549943, _549945)]]], (10910 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_549939), c_Polynomial_Osmult(_549939, _549941, _549943), _549945), 10913 ^ _167881 : [(10914 ^ _167881) ^ [] : [_549941 = c_Groups_Ozero__class_Ozero(_549939), -(_549945 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_549939)))], (10920 ^ _167881) ^ [] : [-(_549941 = c_Groups_Ozero__class_Ozero(_549939)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_549939), _549943, _549945))]]]]], (10940 ^ _167881) ^ [_551009, _551011, _551013] : [class_Rings_Odvd(_551009), class_Rings_Osemiring__0(_551009), 10947 ^ _167881 : [(10948 ^ _167881) ^ [] : [10949 ^ _167881 : [(10950 ^ _167881) ^ [_551318] : [hBOOL(hAPP(_551011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551009), _551013), _551318)))]], 10952 ^ _167881 : [(10953 ^ _167881) ^ [] : [-(c_Rings_Odvd__class_Odvd(_551009, _551013, c_Groups_Oplus__class_Oplus(_551009, 10951 ^ [_551009, _551011, _551013], c_Groups_Ozero__class_Ozero(_551009))))], (10955 ^ _167881) ^ [] : [-(hBOOL(hAPP(_551011, 10951 ^ [_551009, _551011, _551013])))]]], (10957 ^ _167881) ^ [] : [-(hBOOL(hAPP(_551011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551009), _551013), 10964 ^ [_551009, _551011, _551013])))), 10958 ^ _167881 : [(10959 ^ _167881) ^ [_551658] : [c_Rings_Odvd__class_Odvd(_551009, _551013, c_Groups_Oplus__class_Oplus(_551009, _551658, c_Groups_Ozero__class_Ozero(_551009))), hBOOL(hAPP(_551011, _551658))]]]]], (10968 ^ _167881) ^ [_552057, _552059, _552061] : [class_Rings_Olinordered__idom(_552057), c_Groups_Oabs__class_Oabs(_552057, _552059) = c_Groups_Oabs__class_Oabs(_552057, _552061), -(c_Rings_Odvd__class_Odvd(_552057, _552059, _552061))], (10978 ^ _167881) ^ [_552392, _552394, _552396] : [class_Rings_Olinordered__idom(_552392), 10981 ^ _167881 : [(10982 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_552392, c_Groups_Oabs__class_Oabs(_552392, _552394), _552396), -(c_Rings_Odvd__class_Odvd(_552392, _552394, _552396))], (10988 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_552392, _552394, _552396), -(c_Rings_Odvd__class_Odvd(_552392, c_Groups_Oabs__class_Oabs(_552392, _552394), _552396))]]], (10994 ^ _167881) ^ [_552895, _552897, _552899] : [class_Rings_Olinordered__idom(_552895), 10997 ^ _167881 : [(10998 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_552895, _552897, c_Groups_Oabs__class_Oabs(_552895, _552899)), -(c_Rings_Odvd__class_Odvd(_552895, _552897, _552899))], (11004 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_552895, _552897, _552899), -(c_Rings_Odvd__class_Odvd(_552895, _552897, c_Groups_Oabs__class_Oabs(_552895, _552899)))]]], (11010 ^ _167881) ^ [_553412, _553414, _553416, _553418] : [class_Rings_Ocomm__semiring__1(_553412), c_Rings_Odvd__class_Odvd(_553412, _553414, _553416), -(c_Rings_Odvd__class_Odvd(_553412, hAPP(hAPP(c_Power_Opower__class_Opower(_553412), _553414), _553418), hAPP(hAPP(c_Power_Opower__class_Opower(_553412), _553416), _553418)))], (11020 ^ _167881) ^ [_553765, _553767] : [class_Rings_Ocomm__semiring__1(_553765), -(c_Rings_Odvd__class_Odvd(_553765, c_Groups_Oone__class_Oone(_553765), _553767))], (11026 ^ _167881) ^ [_553993, _553995, _553997] : [class_Rings_Ocomm__semiring__0(_553993), 11029 ^ _167881 : [(11030 ^ _167881) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_553993, _553995, _553997) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553993)), -(_553995 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553993)))], (11036 ^ _167881) ^ [] : [_553995 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553993)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_553993, _553995, _553997) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553993)))]]], (11042 ^ _167881) ^ [_554503, _554505] : [class_Rings_Ocomm__semiring__0(_554503), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_554503, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_554503)), _554505) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_554503)))], (11048 ^ _167881) ^ [_554763, _554765, _554767, _554769] : [class_Rings_Ocomm__semiring__1(_554763), c_Rings_Odvd__class_Odvd(_554763, _554765, _554767), c_Rings_Odvd__class_Odvd(_554763, _554765, _554769), -(c_Rings_Odvd__class_Odvd(_554763, _554765, c_Groups_Oplus__class_Oplus(_554763, _554767, _554769)))], (11062 ^ _167881) ^ [_555219, _555221, _555223, _555225] : [class_Rings_Ocomm__semiring__1(_555219), c_Rings_Odvd__class_Odvd(_555219, _555221, _555223), c_Rings_Odvd__class_Odvd(_555219, _555223, _555225), -(c_Rings_Odvd__class_Odvd(_555219, _555221, _555225))], (11076 ^ _167881) ^ [_555639, _555641] : [class_Rings_Ocomm__semiring__1(_555639), -(c_Rings_Odvd__class_Odvd(_555639, _555641, _555641))], (11082 ^ _167881) ^ [_555849, _555851] : [class_Rings_Ocomm__semiring__1(_555849), c_Rings_Odvd__class_Odvd(_555849, c_Groups_Ozero__class_Ozero(_555849), _555851), -(_555851 = c_Groups_Ozero__class_Ozero(_555849))], (11092 ^ _167881) ^ [_556184, _556186, _556188, _556190] : [class_Rings_Oidom(_556184), 11095 ^ _167881 : [(11106 ^ _167881) ^ [] : [11107 ^ _167881 : [(11108 ^ _167881) ^ [] : [_556186 = c_Groups_Ozero__class_Ozero(_556184)], (11110 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_556184, _556188, _556190)]], -(c_Rings_Odvd__class_Odvd(_556184, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556184), _556186), _556188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556184), _556186), _556190)))], (11096 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_556184, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556184), _556186), _556188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556184), _556186), _556190)), -(_556186 = c_Groups_Ozero__class_Ozero(_556184)), -(c_Rings_Odvd__class_Odvd(_556184, _556188, _556190))]]], (11114 ^ _167881) ^ [_556932, _556934, _556936, _556938] : [class_Rings_Oidom(_556932), 11117 ^ _167881 : [(11128 ^ _167881) ^ [] : [11129 ^ _167881 : [(11130 ^ _167881) ^ [] : [_556936 = c_Groups_Ozero__class_Ozero(_556932)], (11132 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_556932, _556934, _556938)]], -(c_Rings_Odvd__class_Odvd(_556932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556932), _556934), _556936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556932), _556938), _556936)))], (11118 ^ _167881) ^ [] : [c_Rings_Odvd__class_Odvd(_556932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556932), _556934), _556936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556932), _556938), _556936)), -(_556936 = c_Groups_Ozero__class_Ozero(_556932)), -(c_Rings_Odvd__class_Odvd(_556932, _556934, _556938))]]], (11136 ^ _167881) ^ [_557666, _557668, _557670] : [class_Rings_Ocomm__semiring__1(_557666), -(c_Rings_Odvd__class_Odvd(_557666, _557668, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557666), _557668), _557670)))], (11142 ^ _167881) ^ [_557884] : [class_Groups_Ocancel__comm__monoid__add(_557884), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_557884)))], (11148 ^ _167881) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11150 ^ _167881) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11152 ^ _167881) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11154 ^ _167881) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11156 ^ _167881) ^ [_558300, _558302] : [class_Lattices_Oboolean__algebra(_558300), -(class_Lattices_Oboolean__algebra(tc_fun(_558302, _558300)))], (11162 ^ _167881) ^ [_558512, _558514] : [class_Orderings_Opreorder(_558512), -(class_Orderings_Opreorder(tc_fun(_558514, _558512)))], (11168 ^ _167881) ^ [_558724, _558726] : [class_Orderings_Oorder(_558724), -(class_Orderings_Oorder(tc_fun(_558726, _558724)))], (11174 ^ _167881) ^ [_558936, _558938] : [class_Orderings_Oord(_558936), -(class_Orderings_Oord(tc_fun(_558938, _558936)))], (11180 ^ _167881) ^ [_559148, _559150] : [class_Groups_Ouminus(_559148), -(class_Groups_Ouminus(tc_fun(_559150, _559148)))], (11186 ^ _167881) ^ [_559360, _559362] : [class_Groups_Ominus(_559360), -(class_Groups_Ominus(tc_fun(_559362, _559360)))], (11192 ^ _167881) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11194 ^ _167881) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11196 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11198 ^ _167881) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11200 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11202 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11204 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11206 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (11208 ^ _167881) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11210 ^ _167881) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11212 ^ _167881) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11214 ^ _167881) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11216 ^ _167881) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11218 ^ _167881) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11220 ^ _167881) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11222 ^ _167881) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11224 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11226 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11228 ^ _167881) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11230 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11232 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11234 ^ _167881) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11236 ^ _167881) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11238 ^ _167881) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11240 ^ _167881) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (11242 ^ _167881) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (11244 ^ _167881) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11246 ^ _167881) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11248 ^ _167881) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11250 ^ _167881) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11252 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11254 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (11256 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11258 ^ _167881) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11260 ^ _167881) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11262 ^ _167881) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (11264 ^ _167881) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (11266 ^ _167881) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (11268 ^ _167881) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11270 ^ _167881) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11272 ^ _167881) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (11274 ^ _167881) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11276 ^ _167881) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11278 ^ _167881) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11280 ^ _167881) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11282 ^ _167881) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (11284 ^ _167881) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (11286 ^ _167881) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (11288 ^ _167881) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (11290 ^ _167881) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (11292 ^ _167881) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (11294 ^ _167881) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (11296 ^ _167881) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11298 ^ _167881) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (11300 ^ _167881) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11302 ^ _167881) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11304 ^ _167881) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11306 ^ _167881) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11308 ^ _167881) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11310 ^ _167881) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (11312 ^ _167881) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11314 ^ _167881) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11316 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11318 ^ _167881) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11320 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11322 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11324 ^ _167881) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11326 ^ _167881) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11328 ^ _167881) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11330 ^ _167881) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (11332 ^ _167881) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11334 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11336 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11338 ^ _167881) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11340 ^ _167881) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11342 ^ _167881) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11344 ^ _167881) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (11346 ^ _167881) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11348 ^ _167881) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11350 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11352 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (11354 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (11356 ^ _167881) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (11358 ^ _167881) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (11360 ^ _167881) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11362 ^ _167881) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (11364 ^ _167881) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11366 ^ _167881) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (11368 ^ _167881) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (11370 ^ _167881) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11372 ^ _167881) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (11374 ^ _167881) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (11376 ^ _167881) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (11378 ^ _167881) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (11380 ^ _167881) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11382 ^ _167881) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (11384 ^ _167881) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (11386 ^ _167881) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (11388 ^ _167881) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (11390 ^ _167881) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11392 ^ _167881) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (11394 ^ _167881) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (11396 ^ _167881) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (11398 ^ _167881) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (11400 ^ _167881) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (11402 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (11404 ^ _167881) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (11406 ^ _167881) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (11408 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (11410 ^ _167881) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (11412 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (11414 ^ _167881) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (11416 ^ _167881) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (11418 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (11420 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (11422 ^ _167881) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (11424 ^ _167881) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (11426 ^ _167881) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (11428 ^ _167881) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (11430 ^ _167881) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (11432 ^ _167881) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11434 ^ _167881) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11436 ^ _167881) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (11438 ^ _167881) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (11440 ^ _167881) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11442 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (11444 ^ _167881) ^ [] : [-(class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal))], (11446 ^ _167881) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11448 ^ _167881) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11450 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (11452 ^ _167881) ^ [] : [-(class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal))], (11454 ^ _167881) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (11456 ^ _167881) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (11458 ^ _167881) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (11460 ^ _167881) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11462 ^ _167881) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11464 ^ _167881) ^ [] : [-(class_Fields_Olinordered__field(tc_RealDef_Oreal))], (11466 ^ _167881) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (11468 ^ _167881) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (11470 ^ _167881) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (11472 ^ _167881) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11474 ^ _167881) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11476 ^ _167881) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (11478 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (11480 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (11482 ^ _167881) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (11484 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11486 ^ _167881) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11488 ^ _167881) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11490 ^ _167881) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (11492 ^ _167881) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11494 ^ _167881) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11496 ^ _167881) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11498 ^ _167881) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (11500 ^ _167881) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11502 ^ _167881) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11504 ^ _167881) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11506 ^ _167881) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (11508 ^ _167881) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (11510 ^ _167881) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (11512 ^ _167881) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (11514 ^ _167881) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11516 ^ _167881) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11518 ^ _167881) ^ [] : [-(class_Groups_Ouminus(tc_RealDef_Oreal))], (11520 ^ _167881) ^ [] : [-(class_Groups_Osgn__if(tc_RealDef_Oreal))], (11522 ^ _167881) ^ [] : [-(class_Groups_Oabs__if(tc_RealDef_Oreal))], (11524 ^ _167881) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11526 ^ _167881) ^ [] : [-(class_Groups_Ominus(tc_RealDef_Oreal))], (11528 ^ _167881) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11530 ^ _167881) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11532 ^ _167881) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11534 ^ _167881) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11536 ^ _167881) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11538 ^ _167881) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11540 ^ _167881) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (11542 ^ _167881) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11544 ^ _167881) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11546 ^ _167881) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (11548 ^ _167881) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11550 ^ _167881) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11552 ^ _167881) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11554 ^ _167881) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11556 ^ _167881) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11558 ^ _167881) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11560 ^ _167881) ^ [] : [-(class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex))], (11562 ^ _167881) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11564 ^ _167881) ^ [] : [-(class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex))], (11566 ^ _167881) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (11568 ^ _167881) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11570 ^ _167881) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11572 ^ _167881) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11574 ^ _167881) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11576 ^ _167881) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11578 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11580 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (11582 ^ _167881) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (11584 ^ _167881) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11586 ^ _167881) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11588 ^ _167881) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11590 ^ _167881) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11592 ^ _167881) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11594 ^ _167881) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (11596 ^ _167881) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11598 ^ _167881) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11600 ^ _167881) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11602 ^ _167881) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (11604 ^ _167881) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (11606 ^ _167881) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (11608 ^ _167881) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (11610 ^ _167881) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11612 ^ _167881) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (11614 ^ _167881) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (11616 ^ _167881) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (11618 ^ _167881) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11620 ^ _167881) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11622 ^ _167881) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (11624 ^ _167881) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (11626 ^ _167881) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (11628 ^ _167881) ^ [_571112] : [class_Rings_Oidom(_571112), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_571112)))], (11634 ^ _167881) ^ [_571302] : [class_Rings_Olinordered__idom(_571302), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_571302)))], (11640 ^ _167881) ^ [_571492] : [class_Rings_Olinordered__idom(_571492), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_571492)))], (11646 ^ _167881) ^ [_571682] : [class_Rings_Olinordered__idom(_571682), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_571682)))], (11652 ^ _167881) ^ [_571872] : [class_Rings_Olinordered__idom(_571872), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_571872)))], (11658 ^ _167881) ^ [_572062] : [class_Rings_Olinordered__idom(_572062), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_572062)))], (11664 ^ _167881) ^ [_572252] : [class_Rings_Olinordered__idom(_572252), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_572252)))], (11670 ^ _167881) ^ [_572442] : [class_Rings_Olinordered__idom(_572442), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_572442)))], (11676 ^ _167881) ^ [_572632] : [class_Rings_Olinordered__idom(_572632), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_572632)))], (11682 ^ _167881) ^ [_572822] : [class_Rings_Olinordered__idom(_572822), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_572822)))], (11688 ^ _167881) ^ [_573012] : [class_Groups_Ocancel__comm__monoid__add(_573012), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_573012)))], (11694 ^ _167881) ^ [_573202] : [class_Rings_Oidom(_573202), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_573202)))], (11700 ^ _167881) ^ [_573392] : [class_Rings_Olinordered__idom(_573392), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_573392)))], (11706 ^ _167881) ^ [_573582] : [class_Rings_Olinordered__idom(_573582), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_573582)))], (11712 ^ _167881) ^ [_573772] : [class_Rings_Oidom(_573772), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_573772)))], (11718 ^ _167881) ^ [_573962] : [class_Rings_Olinordered__idom(_573962), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_573962)))], (11724 ^ _167881) ^ [_574152] : [class_Rings_Olinordered__idom(_574152), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_574152)))], (11730 ^ _167881) ^ [_574342] : [class_Rings_Olinordered__idom(_574342), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_574342)))], (11736 ^ _167881) ^ [_574532] : [class_Groups_Ocancel__comm__monoid__add(_574532), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_574532)))], (11742 ^ _167881) ^ [_574722] : [class_Rings_Olinordered__idom(_574722), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_574722)))], (11748 ^ _167881) ^ [_574912] : [class_Rings_Olinordered__idom(_574912), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_574912)))], (11754 ^ _167881) ^ [_575102] : [class_Rings_Ocomm__semiring__0(_575102), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_575102)))], (11760 ^ _167881) ^ [_575292] : [class_Rings_Ocomm__semiring__1(_575292), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_575292)))], (11766 ^ _167881) ^ [_575482] : [class_Groups_Ocomm__monoid__add(_575482), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_575482)))], (11772 ^ _167881) ^ [_575672] : [class_Rings_Olinordered__idom(_575672), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_575672)))], (11778 ^ _167881) ^ [_575862] : [class_Rings_Olinordered__idom(_575862), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_575862)))], (11784 ^ _167881) ^ [_576052] : [class_Rings_Oidom(_576052), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_576052)))], (11790 ^ _167881) ^ [_576242] : [class_Groups_Ocomm__monoid__add(_576242), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_576242)))], (11796 ^ _167881) ^ [_576432] : [class_Rings_Olinordered__idom(_576432), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_576432)))], (11802 ^ _167881) ^ [_576622] : [class_Rings_Olinordered__idom(_576622), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_576622)))], (11808 ^ _167881) ^ [_576812] : [class_Rings_Ocomm__semiring__1(_576812), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_576812)))], (11814 ^ _167881) ^ [_577002] : [class_Rings_Ocomm__semiring__0(_577002), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_577002)))], (11820 ^ _167881) ^ [_577192] : [class_Rings_Ocomm__semiring__0(_577192), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_577192)))], (11826 ^ _167881) ^ [_577382] : [class_Groups_Oab__group__add(_577382), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_577382)))], (11832 ^ _167881) ^ [_577572] : [class_Rings_Ocomm__semiring__1(_577572), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_577572)))], (11838 ^ _167881) ^ [_577762] : [class_Rings_Olinordered__idom(_577762), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_577762)))], (11844 ^ _167881) ^ [_577952] : [class_Rings_Olinordered__idom(_577952), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_577952)))], (11850 ^ _167881) ^ [_578142] : [class_Rings_Olinordered__idom(_578142), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_578142)))], (11856 ^ _167881) ^ [_578332] : [class_Rings_Ocomm__semiring__1(_578332), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_578332)))], (11862 ^ _167881) ^ [_578522] : [class_Rings_Ocomm__ring__1(_578522), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_578522)))], (11868 ^ _167881) ^ [_578712] : [class_Groups_Ocomm__monoid__add(_578712), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_578712)))], (11874 ^ _167881) ^ [_578902] : [class_Rings_Ocomm__semiring__0(_578902), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_578902)))], (11880 ^ _167881) ^ [_579092] : [class_Groups_Oab__group__add(_579092), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_579092)))], (11886 ^ _167881) ^ [_579282] : [class_Rings_Ocomm__semiring__0(_579282), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_579282)))], (11892 ^ _167881) ^ [_579472] : [class_Rings_Ocomm__ring(_579472), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_579472)))], (11898 ^ _167881) ^ [_579662] : [class_Rings_Olinordered__idom(_579662), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_579662)))], (11904 ^ _167881) ^ [_579852] : [class_Rings_Olinordered__idom(_579852), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_579852)))], (11910 ^ _167881) ^ [_580042] : [class_Rings_Ocomm__semiring__0(_580042), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_580042)))], (11916 ^ _167881) ^ [_580232] : [class_Rings_Olinordered__idom(_580232), -(class_Orderings_Oord(tc_Polynomial_Opoly(_580232)))], (11922 ^ _167881) ^ [_580422] : [class_Groups_Oab__group__add(_580422), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_580422)))], (11928 ^ _167881) ^ [_580612] : [class_Rings_Olinordered__idom(_580612), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_580612)))], (11934 ^ _167881) ^ [_580802] : [class_Rings_Olinordered__idom(_580802), -(class_Groups_Oabs__if(tc_Polynomial_Opoly(_580802)))], (11940 ^ _167881) ^ [_580992] : [class_Rings_Ocomm__ring__1(_580992), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_580992)))], (11946 ^ _167881) ^ [_581182] : [class_Groups_Oab__group__add(_581182), -(class_Groups_Ominus(tc_Polynomial_Opoly(_581182)))], (11952 ^ _167881) ^ [_581372] : [class_Rings_Ocomm__semiring__1(_581372), -(class_Power_Opower(tc_Polynomial_Opoly(_581372)))], (11958 ^ _167881) ^ [_581562] : [class_Groups_Ozero(_581562), -(class_Groups_Ozero(tc_Polynomial_Opoly(_581562)))], (11964 ^ _167881) ^ [_581752] : [class_Rings_Ocomm__ring(_581752), -(class_Rings_Oring(tc_Polynomial_Opoly(_581752)))], (11970 ^ _167881) ^ [_581942] : [class_Rings_Oidom(_581942), -(class_Rings_Oidom(tc_Polynomial_Opoly(_581942)))], (11976 ^ _167881) ^ [_582132] : [class_Rings_Ocomm__semiring__1(_582132), -(class_Groups_Oone(tc_Polynomial_Opoly(_582132)))], (11982 ^ _167881) ^ [_582302] : [class_Rings_Ocomm__semiring__1(_582302), -(class_Rings_Odvd(tc_Polynomial_Opoly(_582302)))]], input).
% 0.52/1.40  ncf('1',plain,[c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))],start(11988 ^ 0)).
% 0.52/1.40  ncf('1.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))],extension(2674 ^ 1,bind([[_256986, _256988, _256990, _256992], [tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)]]))).
% 0.52/1.40  ncf('1.1.1',plain,[-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))],extension(11404 ^ 2)).
% 0.52/1.40  ncf('1.1.2',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))],extension(1199 ^ 2)).
% 0.52/1.40  ncf('1.1.3',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))],extension(1197 ^ 2)).
% 0.52/1.40  %-----------------------------------------------------
% 0.52/1.40  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------