TSTP Solution File: SWW259+1 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW259+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n027.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 101.89s 98.79s
% Output : Proof 101.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW259+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13 % Command : nanocop.sh %s %d
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu May 18 22:41:50 EDT 2023
% 0.12/0.32 % CPUTime :
% 101.89/98.79
% 101.89/98.79 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 101.89/98.79 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.89/98.79 %-----------------------------------------------------
% 101.89/98.79 ncf(matrix, plain, [(12079 ^ _106296) ^ [] : [v_thesis____], (776 ^ _106296) ^ [_117372, _117374] : [_117374 = _117372, -(c_Complex_Oexpi(_117374) = c_Complex_Oexpi(_117372))], (782 ^ _106296) ^ [_117646, _117648, _117650, _117652, _117654, _117656] : [-(c_Power_Opower_Opower(_117656, _117652, _117648) = c_Power_Opower_Opower(_117654, _117650, _117646)), _117656 = _117654, _117652 = _117650, _117648 = _117646], (796 ^ _106296) ^ [_118162, _118164, _118166, _118168, _118170, _118172] : [-(c_Polynomial_Omonom(_118172, _118168, _118164) = c_Polynomial_Omonom(_118170, _118166, _118162)), _118172 = _118170, _118168 = _118166, _118164 = _118162], (810 ^ _106296) ^ [_118678, _118680, _118682, _118684, _118686, _118688] : [-(c_Polynomial_Osynthetic__div(_118688, _118684, _118680) = c_Polynomial_Osynthetic__div(_118686, _118682, _118678)), _118688 = _118686, _118684 = _118682, _118680 = _118678], (824 ^ _106296) ^ [_119194, _119196, _119198, _119200, _119202, _119204] : [-(c_Polynomial_Opcompose(_119204, _119200, _119196) = c_Polynomial_Opcompose(_119202, _119198, _119194)), _119204 = _119202, _119200 = _119198, _119196 = _119194], (838 ^ _106296) ^ [_119710, _119712, _119714, _119716, _119718, _119720] : [-(c_Polynomial_Osmult(_119720, _119716, _119712) = c_Polynomial_Osmult(_119718, _119714, _119710)), _119720 = _119718, _119716 = _119714, _119712 = _119710], (852 ^ _106296) ^ [_120226, _120228, _120230, _120232, _120234, _120236] : [-(c_Polynomial_Oorder(_120236, _120232, _120228) = c_Polynomial_Oorder(_120234, _120230, _120226)), _120236 = _120234, _120232 = _120230, _120228 = _120226], (866 ^ _106296) ^ [_120714, _120716, _120718, _120720] : [-(c_Groups_Ouminus__class_Ouminus(_120720, _120716) = c_Groups_Ouminus__class_Ouminus(_120718, _120714)), _120720 = _120718, _120716 = _120714], (876 ^ _106296) ^ [_121073, _121075, _121077, _121079] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_121079, _121075) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_121077, _121073)), _121079 = _121077, _121075 = _121073], (886 ^ _106296) ^ [_121432, _121434, _121436, _121438] : [-(c_Polynomial_Opoly(_121438, _121434) = c_Polynomial_Opoly(_121436, _121432)), _121438 = _121436, _121434 = _121432], (896 ^ _106296) ^ [_121791, _121793, _121795, _121797] : [-(c_Nat__Transfer_Otsub(_121797, _121793) = c_Nat__Transfer_Otsub(_121795, _121791)), _121797 = _121795, _121793 = _121791], (906 ^ _106296) ^ [_122178, _122180, _122182, _122184, _122186, _122188] : [-(c_Polynomial_OpCons(_122188, _122184, _122180) = c_Polynomial_OpCons(_122186, _122182, _122178)), _122188 = _122186, _122184 = _122182, _122180 = _122178], (920 ^ _106296) ^ [_122638, _122640] : [_122640 = _122638, -(c_Nat_OSuc(_122640) = c_Nat_OSuc(_122638))], (926 ^ _106296) ^ [_122912, _122914, _122916, _122918, _122920, _122922] : [-(c_Groups_Ominus__class_Ominus(_122922, _122918, _122914) = c_Groups_Ominus__class_Ominus(_122920, _122916, _122912)), _122922 = _122920, _122918 = _122916, _122914 = _122912], (940 ^ _106296) ^ [_123428, _123430, _123432, _123434, _123436, _123438] : [-(c_Divides_Odiv__class_Odiv(_123438, _123434, _123430) = c_Divides_Odiv__class_Odiv(_123436, _123432, _123428)), _123438 = _123436, _123434 = _123432, _123430 = _123428], (954 ^ _106296) ^ [_123916, _123918, _123920, _123922] : [-(tc_fun(_123922, _123918) = tc_fun(_123920, _123916)), _123922 = _123920, _123918 = _123916], (964 ^ _106296) ^ [_124247, _124249] : [_124249 = _124247, -(tc_Polynomial_Opoly(_124249) = tc_Polynomial_Opoly(_124247))], (970 ^ _106296) ^ [_124465, _124467] : [_124467 = _124465, -(c_Groups_Ozero__class_Ozero(_124467) = c_Groups_Ozero__class_Ozero(_124465))], (976 ^ _106296) ^ [_124711, _124713, _124715, _124717] : [-(c_Rings_Oinverse__class_Oinverse(_124717, _124713) = c_Rings_Oinverse__class_Oinverse(_124715, _124711)), _124717 = _124715, _124713 = _124711], (986 ^ _106296) ^ [_125042, _125044] : [_125044 = _125042, -(c_Groups_Otimes__class_Otimes(_125044) = c_Groups_Otimes__class_Otimes(_125042))], (992 ^ _106296) ^ [_125288, _125290, _125292, _125294] : [-(hAPP(_125294, _125290) = hAPP(_125292, _125288)), _125294 = _125292, _125290 = _125288], (1002 ^ _106296) ^ [_125619, _125621] : [_125621 = _125619, -(c_Power_Opower__class_Opower(_125621) = c_Power_Opower__class_Opower(_125619))], (1008 ^ _106296) ^ [_125865, _125867, _125869, _125871] : [-(c_RealVector_Onorm__class_Onorm(_125871, _125867) = c_RealVector_Onorm__class_Onorm(_125869, _125865)), _125871 = _125869, _125867 = _125865], (1032 ^ _106296) ^ [_126692, _126694] : [_126694 = _126692, -(c_Groups_Oone__class_Oone(_126694) = c_Groups_Oone__class_Oone(_126692))], (1018 ^ _106296) ^ [_126252, _126254, _126256, _126258, _126260, _126262] : [-(c_Groups_Oplus__class_Oplus(_126262, _126258, _126254) = c_Groups_Oplus__class_Oplus(_126260, _126256, _126252)), _126262 = _126260, _126258 = _126256, _126254 = _126252], (2 ^ _106296) ^ [_106326] : [-(_106326 = _106326)], (4 ^ _106296) ^ [_106349, _106351] : [_106351 = _106349, -(_106349 = _106351)], (10 ^ _106296) ^ [_106422, _106424, _106426] : [-(_106426 = _106422), _106426 = _106424, _106424 = _106422], (20 ^ _106296) ^ [_106559, _106561, _106563, _106565, _106567, _106569] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_106567, _106563, _106559)), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_106569, _106565, _106561), _106569 = _106567, _106565 = _106563, _106561 = _106559], (38 ^ _106296) ^ [_106828, _106830] : [-(hBOOL(_106828)), _106830 = _106828, hBOOL(_106830)], (48 ^ _106296) ^ [_106953, _106955, _106957, _106959, _106961, _106963] : [-(c_Rings_Odvd__class_Odvd(_106961, _106957, _106953)), c_Rings_Odvd__class_Odvd(_106963, _106959, _106955), _106963 = _106961, _106959 = _106957, _106955 = _106953], (66 ^ _106296) ^ [_107222, _107224, _107226, _107228, _107230, _107232] : [-(c_Orderings_Oord__class_Oless__eq(_107230, _107226, _107222)), c_Orderings_Oord__class_Oless__eq(_107232, _107228, _107224), _107232 = _107230, _107228 = _107226, _107224 = _107222], (84 ^ _106296) ^ [_107491, _107493, _107495, _107497] : [-(c_Polynomial_Opos__poly(_107495, _107491)), c_Polynomial_Opos__poly(_107497, _107493), _107497 = _107495, _107493 = _107491], (98 ^ _106296) ^ [_107684, _107686] : [-(class_Fields_Olinordered__field__inverse__zero(_107684)), _107686 = _107684, class_Fields_Olinordered__field__inverse__zero(_107686)], (108 ^ _106296) ^ [_107809, _107811] : [-(class_Fields_Olinordered__field(_107809)), _107811 = _107809, class_Fields_Olinordered__field(_107811)], (118 ^ _106296) ^ [_107934, _107936] : [-(class_RealVector_Oreal__normed__div__algebra(_107934)), _107936 = _107934, class_RealVector_Oreal__normed__div__algebra(_107936)], (128 ^ _106296) ^ [_108059, _108061] : [-(class_Rings_Odivision__ring__inverse__zero(_108059)), _108061 = _108059, class_Rings_Odivision__ring__inverse__zero(_108061)], (138 ^ _106296) ^ [_108184, _108186] : [-(class_RealVector_Oreal__normed__algebra__1(_108184)), _108186 = _108184, class_RealVector_Oreal__normed__algebra__1(_108186)], (148 ^ _106296) ^ [_108309, _108311] : [-(class_RealVector_Oreal__normed__algebra(_108309)), _108311 = _108309, class_RealVector_Oreal__normed__algebra(_108311)], (158 ^ _106296) ^ [_108434, _108436] : [-(class_RealVector_Oreal__normed__vector(_108434)), _108436 = _108434, class_RealVector_Oreal__normed__vector(_108436)], (168 ^ _106296) ^ [_108559, _108561] : [-(class_Fields_Ofield__inverse__zero(_108559)), _108561 = _108559, class_Fields_Ofield__inverse__zero(_108561)], (178 ^ _106296) ^ [_108684, _108686] : [-(class_Rings_Odivision__ring(_108684)), _108686 = _108684, class_Rings_Odivision__ring(_108686)], (188 ^ _106296) ^ [_108809, _108811] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_108809)), _108811 = _108809, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_108811)], (198 ^ _106296) ^ [_108934, _108936] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_108934)), _108936 = _108934, class_Groups_Oordered__cancel__ab__semigroup__add(_108936)], (208 ^ _106296) ^ [_109059, _109061] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_109059)), _109061 = _109059, class_Groups_Oordered__ab__semigroup__add__imp__le(_109061)], (218 ^ _106296) ^ [_109184, _109186] : [-(class_Rings_Olinordered__comm__semiring__strict(_109184)), _109186 = _109184, class_Rings_Olinordered__comm__semiring__strict(_109186)], (228 ^ _106296) ^ [_109309, _109311] : [-(class_Rings_Olinordered__semiring__1__strict(_109309)), _109311 = _109309, class_Rings_Olinordered__semiring__1__strict(_109311)], (238 ^ _106296) ^ [_109434, _109436] : [-(class_Rings_Olinordered__semiring__strict(_109434)), _109436 = _109434, class_Rings_Olinordered__semiring__strict(_109436)], (248 ^ _106296) ^ [_109559, _109561] : [-(class_Groups_Oordered__ab__semigroup__add(_109559)), _109561 = _109559, class_Groups_Oordered__ab__semigroup__add(_109561)], (258 ^ _106296) ^ [_109684, _109686] : [-(class_Groups_Oordered__comm__monoid__add(_109684)), _109686 = _109684, class_Groups_Oordered__comm__monoid__add(_109686)], (268 ^ _106296) ^ [_109809, _109811] : [-(class_Groups_Olinordered__ab__group__add(_109809)), _109811 = _109809, class_Groups_Olinordered__ab__group__add(_109811)], (278 ^ _106296) ^ [_109934, _109936] : [-(class_Groups_Ocancel__ab__semigroup__add(_109934)), _109936 = _109934, class_Groups_Ocancel__ab__semigroup__add(_109936)], (288 ^ _106296) ^ [_110059, _110061] : [-(class_Rings_Oring__1__no__zero__divisors(_110059)), _110061 = _110059, class_Rings_Oring__1__no__zero__divisors(_110061)], (298 ^ _106296) ^ [_110184, _110186] : [-(class_Rings_Oordered__cancel__semiring(_110184)), _110186 = _110184, class_Rings_Oordered__cancel__semiring(_110186)], (308 ^ _106296) ^ [_110309, _110311] : [-(class_Rings_Olinordered__ring__strict(_110309)), _110311 = _110309, class_Rings_Olinordered__ring__strict(_110311)], (318 ^ _106296) ^ [_110434, _110436] : [-(class_Rings_Oring__no__zero__divisors(_110434)), _110436 = _110434, class_Rings_Oring__no__zero__divisors(_110436)], (328 ^ _106296) ^ [_110559, _110561] : [-(class_Rings_Oordered__comm__semiring(_110559)), _110561 = _110559, class_Rings_Oordered__comm__semiring(_110561)], (338 ^ _106296) ^ [_110684, _110686] : [-(class_Rings_Olinordered__semiring__1(_110684)), _110686 = _110684, class_Rings_Olinordered__semiring__1(_110686)], (348 ^ _106296) ^ [_110809, _110811] : [-(class_Groups_Oordered__ab__group__add(_110809)), _110811 = _110809, class_Groups_Oordered__ab__group__add(_110811)], (358 ^ _106296) ^ [_110934, _110936] : [-(class_Groups_Ocancel__comm__monoid__add(_110934)), _110936 = _110934, class_Groups_Ocancel__comm__monoid__add(_110936)], (368 ^ _106296) ^ [_111059, _111061] : [-(class_Groups_Ocancel__semigroup__add(_111059)), _111061 = _111059, class_Groups_Ocancel__semigroup__add(_111061)], (378 ^ _106296) ^ [_111184, _111186] : [-(class_Rings_Olinordered__semiring(_111184)), _111186 = _111184, class_Rings_Olinordered__semiring(_111186)], (388 ^ _106296) ^ [_111309, _111311] : [-(class_Rings_Olinordered__semidom(_111309)), _111311 = _111309, class_Rings_Olinordered__semidom(_111311)], (398 ^ _106296) ^ [_111434, _111436] : [-(class_Groups_Oab__semigroup__mult(_111434)), _111436 = _111434, class_Groups_Oab__semigroup__mult(_111436)], (408 ^ _106296) ^ [_111559, _111561] : [-(class_Groups_Ocomm__monoid__mult(_111559)), _111561 = _111559, class_Groups_Ocomm__monoid__mult(_111561)], (418 ^ _106296) ^ [_111684, _111686] : [-(class_Groups_Oab__semigroup__add(_111684)), _111686 = _111684, class_Groups_Oab__semigroup__add(_111686)], (428 ^ _106296) ^ [_111809, _111811] : [-(class_Rings_Oordered__semiring(_111809)), _111811 = _111809, class_Rings_Oordered__semiring(_111811)], (438 ^ _106296) ^ [_111934, _111936] : [-(class_Rings_Ono__zero__divisors(_111934)), _111936 = _111934, class_Rings_Ono__zero__divisors(_111936)], (448 ^ _106296) ^ [_112059, _112061] : [-(class_Rings_Olinordered__ring(_112059)), _112061 = _112059, class_Rings_Olinordered__ring(_112061)], (458 ^ _106296) ^ [_112184, _112186] : [-(class_Fields_Ofield(_112184)), _112186 = _112184, class_Fields_Ofield(_112186)], (468 ^ _106296) ^ [_112309, _112311] : [-(class_Divides_Osemiring__div(_112309)), _112311 = _112309, class_Divides_Osemiring__div(_112311)], (478 ^ _106296) ^ [_112434, _112436] : [-(class_Rings_Ocomm__semiring(_112434)), _112436 = _112434, class_Rings_Ocomm__semiring(_112436)], (488 ^ _106296) ^ [_112559, _112561] : [-(class_Rings_Ozero__neq__one(_112559)), _112561 = _112559, class_Rings_Ozero__neq__one(_112561)], (498 ^ _106296) ^ [_112684, _112686] : [-(class_Rings_Oordered__ring(_112684)), _112686 = _112684, class_Rings_Oordered__ring(_112686)], (508 ^ _106296) ^ [_112809, _112811] : [-(class_Orderings_Opreorder(_112809)), _112811 = _112809, class_Orderings_Opreorder(_112811)], (518 ^ _106296) ^ [_112934, _112936] : [-(class_Orderings_Olinorder(_112934)), _112936 = _112934, class_Orderings_Olinorder(_112936)], (528 ^ _106296) ^ [_113059, _113061] : [-(class_Groups_Omonoid__mult(_113059)), _113061 = _113059, class_Groups_Omonoid__mult(_113061)], (538 ^ _106296) ^ [_113184, _113186] : [-(class_Groups_Ocomm__monoid__add(_113184)), _113186 = _113184, class_Groups_Ocomm__monoid__add(_113186)], (548 ^ _106296) ^ [_113309, _113311] : [-(class_Groups_Omonoid__add(_113309)), _113311 = _113309, class_Groups_Omonoid__add(_113311)], (558 ^ _106296) ^ [_113434, _113436] : [-(class_Rings_Osemiring__0(_113434)), _113436 = _113434, class_Rings_Osemiring__0(_113436)], (568 ^ _106296) ^ [_113559, _113561] : [-(class_Groups_Oab__group__add(_113559)), _113561 = _113559, class_Groups_Oab__group__add(_113561)], (578 ^ _106296) ^ [_113684, _113686] : [-(class_Groups_Ogroup__add(_113684)), _113686 = _113684, class_Groups_Ogroup__add(_113686)], (588 ^ _106296) ^ [_113809, _113811] : [-(class_Rings_Omult__zero(_113809)), _113811 = _113809, class_Rings_Omult__zero(_113811)], (598 ^ _106296) ^ [_113934, _113936] : [-(class_Orderings_Oorder(_113934)), _113936 = _113934, class_Orderings_Oorder(_113936)], (608 ^ _106296) ^ [_114059, _114061] : [-(class_Int_Oring__char__0(_114059)), _114061 = _114059, class_Int_Oring__char__0(_114061)], (618 ^ _106296) ^ [_114184, _114186] : [-(class_Rings_Ocomm__semiring__0(_114184)), _114186 = _114184, class_Rings_Ocomm__semiring__0(_114186)], (628 ^ _106296) ^ [_114309, _114311] : [-(class_Rings_Osemiring(_114309)), _114311 = _114309, class_Rings_Osemiring(_114311)], (638 ^ _106296) ^ [_114434, _114436] : [-(class_Rings_Olinordered__idom(_114434)), _114436 = _114434, class_Rings_Olinordered__idom(_114436)], (648 ^ _106296) ^ [_114559, _114561] : [-(class_Orderings_Oord(_114559)), _114561 = _114559, class_Orderings_Oord(_114561)], (658 ^ _106296) ^ [_114684, _114686] : [-(class_Rings_Ocomm__ring__1(_114684)), _114686 = _114684, class_Rings_Ocomm__ring__1(_114686)], (668 ^ _106296) ^ [_114809, _114811] : [-(class_Rings_Oring__1(_114809)), _114811 = _114809, class_Rings_Oring__1(_114811)], (678 ^ _106296) ^ [_114934, _114936] : [-(class_Power_Opower(_114934)), _114936 = _114934, class_Power_Opower(_114936)], (688 ^ _106296) ^ [_115059, _115061] : [-(class_Groups_Ozero(_115059)), _115061 = _115059, class_Groups_Ozero(_115061)], (698 ^ _106296) ^ [_115184, _115186] : [-(class_Rings_Ocomm__ring(_115184)), _115186 = _115184, class_Rings_Ocomm__ring(_115186)], (708 ^ _106296) ^ [_115309, _115311] : [-(class_Rings_Oring(_115309)), _115311 = _115309, class_Rings_Oring(_115311)], (718 ^ _106296) ^ [_115434, _115436] : [-(class_Rings_Oidom(_115434)), _115436 = _115434, class_Rings_Oidom(_115436)], (728 ^ _106296) ^ [_115559, _115561] : [-(class_Groups_Oone(_115559)), _115561 = _115559, class_Groups_Oone(_115561)], (738 ^ _106296) ^ [_115767, _115769] : [-(class_Rings_Ocomm__semiring__1(_115767)), _115769 = _115767, class_Rings_Ocomm__semiring__1(_115769)], (748 ^ _106296) ^ [_116062, _116064] : [-(class_Rings_Odvd(_116062)), _116064 = _116062, class_Rings_Odvd(_116064)], (758 ^ _106296) ^ [_116393, _116395, _116397, _116399, _116401, _116403] : [-(c_Orderings_Oord__class_Oless(_116401, _116397, _116393)), c_Orderings_Oord__class_Oless(_116403, _116399, _116395), _116403 = _116401, _116399 = _116397, _116395 = _116393], (1038 ^ _106296) ^ [_127060, _127062] : [hAPP(_127060, 1039 ^ [_127060, _127062]) = hAPP(_127062, 1039 ^ [_127060, _127062]), -(_127060 = _127062)], (1045 ^ _106296) ^ [_127338] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _127338), 1049 ^ _106296 : [(1050 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1048 ^ [_127338]))], (1052 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1048 ^ [_127338], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1054 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1048 ^ [_127338], _127338))]]], (1056 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_m____))], (1058 ^ _106296) ^ [] : [-(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____))))], (1060 ^ _106296) ^ [] : [v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1062 ^ _106296) ^ [_127943, _127945, _127947] : [class_Rings_Olinordered__semidom(_127943), c_Orderings_Oord__class_Oless(_127943, c_Groups_Ozero__class_Ozero(_127943), _127945), c_Orderings_Oord__class_Oless(_127943, _127945, c_Groups_Oone__class_Oone(_127943)), -(c_Orderings_Oord__class_Oless(_127943, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_127943), _127945), hAPP(hAPP(c_Power_Opower__class_Opower(_127943), _127945), _127947)), hAPP(hAPP(c_Power_Opower__class_Opower(_127943), _127945), _127947)))], (1076 ^ _106296) ^ [_128391] : [-(_128391 = 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, _128391)), _128391) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (1082 ^ _106296) ^ [_128644, _128646, _128648, _128650] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _128644), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _128646), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _128646), _128648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _128644), _128650)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _128648), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _128644)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _128650), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _128646))))], (1096 ^ _106296) ^ [_129156, _129158, _129160, _129162] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _129156), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _129158), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _129158), _129160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _129156), _129162)), -(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, _129156)), _129160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _129158)), _129162)))], (1110 ^ _106296) ^ [_129640, _129642] : [class_RealVector_Oreal__normed__div__algebra(_129640), -(_129642 = c_Groups_Ozero__class_Ozero(_129640)), -(c_RealVector_Onorm__class_Onorm(_129640, c_Rings_Oinverse__class_Oinverse(_129640, _129642)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_129640, _129642)))], (1120 ^ _106296) ^ [_130010, _130012, _130014, _130016, _130018] : [class_RealVector_Oreal__normed__algebra(_130010), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_130010, _130012), _130014), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_130010, _130016), _130018), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_130010, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_130010), _130012), _130016)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _130014), _130018)))], (1134 ^ _106296) ^ [_130490, _130492] : [class_RealVector_Oreal__normed__vector(_130490), 1137 ^ _106296 : [(1138 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_130490, _130492)), _130492 = c_Groups_Ozero__class_Ozero(_130490)], (1144 ^ _106296) ^ [] : [-(_130492 = c_Groups_Ozero__class_Ozero(_130490)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_130490, _130492)))]]], (1150 ^ _106296) ^ [_130968, _130970] : [class_Rings_Odivision__ring(_130968), -(_130970 = c_Groups_Ozero__class_Ozero(_130968)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_130968), _130970), c_Rings_Oinverse__class_Oinverse(_130968, _130970)) = c_Groups_Oone__class_Oone(_130968))], (1160 ^ _106296) ^ [_131298, _131300] : [class_Fields_Ofield(_131298), -(_131300 = c_Groups_Ozero__class_Ozero(_131298)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_131298), c_Rings_Oinverse__class_Oinverse(_131298, _131300)), _131300) = c_Groups_Oone__class_Oone(_131298))], (1170 ^ _106296) ^ [_131628, _131630] : [class_Rings_Odivision__ring(_131628), -(_131630 = c_Groups_Ozero__class_Ozero(_131628)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_131628), c_Rings_Oinverse__class_Oinverse(_131628, _131630)), _131630) = c_Groups_Oone__class_Oone(_131628))], (1180 ^ _106296) ^ [_131958, _131960] : [class_Fields_Olinordered__field__inverse__zero(_131958), 1183 ^ _106296 : [(1184 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_131958, c_Groups_Oone__class_Oone(_131958), c_Rings_Oinverse__class_Oinverse(_131958, _131960)), 1187 ^ _106296 : [(1188 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_131958, c_Groups_Ozero__class_Ozero(_131958), _131960))], (1190 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_131958, _131960, c_Groups_Oone__class_Oone(_131958)))]]], (1192 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_131958, c_Groups_Oone__class_Oone(_131958), c_Rings_Oinverse__class_Oinverse(_131958, _131960))), c_Orderings_Oord__class_Oless(_131958, c_Groups_Ozero__class_Ozero(_131958), _131960), c_Orderings_Oord__class_Oless(_131958, _131960, c_Groups_Oone__class_Oone(_131958))]]], (1202 ^ _106296) ^ [_132610, _132612] : [class_Fields_Olinordered__field(_132610), c_Orderings_Oord__class_Oless(_132610, c_Groups_Ozero__class_Ozero(_132610), _132612), c_Orderings_Oord__class_Oless(_132610, _132612, c_Groups_Oone__class_Oone(_132610)), -(c_Orderings_Oord__class_Oless(_132610, c_Groups_Oone__class_Oone(_132610), c_Rings_Oinverse__class_Oinverse(_132610, _132612)))], (1216 ^ _106296) ^ [] : [v_a____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (1218 ^ _106296) ^ [] : [v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (1230 ^ _106296) ^ [_133421, _133423] : [1231 ^ _106296 : [(1232 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _133421)], (1234 ^ _106296) ^ [] : [_133423 = 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), _133421), _133423)))], (1220 ^ _106296) ^ [_133153, _133155] : [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), _133153), _133155)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _133153)), -(_133155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1238 ^ _106296) ^ [_133737, _133739, _133741] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _133737), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _133737), _133739), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _133737), _133741)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _133739, _133741))], (1248 ^ _106296) ^ [_134104, _134106, _134108, _134110] : [class_Groups_Omonoid__mult(_134104), -(hAPP(hAPP(c_Power_Opower__class_Opower(_134104), _134106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _134108), _134110)) = hAPP(hAPP(c_Power_Opower__class_Opower(_134104), hAPP(hAPP(c_Power_Opower__class_Opower(_134104), _134106), _134108)), _134110))], (1254 ^ _106296) ^ [_134384, _134386] : [class_Power_Opower(_134384), -(hAPP(hAPP(c_Power_Opower__class_Opower(_134384), _134386), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_134384))], (1260 ^ _106296) ^ [_134626, _134628, _134630] : [class_Rings_Olinordered__semidom(_134626), c_Orderings_Oord__class_Oless(_134626, c_Groups_Oone__class_Oone(_134626), _134628), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _134630), -(c_Orderings_Oord__class_Oless(_134626, c_Groups_Oone__class_Oone(_134626), hAPP(hAPP(c_Power_Opower__class_Opower(_134626), _134628), _134630)))], (1274 ^ _106296) ^ [_135070, _135072, _135074] : [class_Rings_Olinordered__idom(_135070), -(_135072 = _135074), -(c_Orderings_Oord__class_Oless(_135070, _135072, _135074)), -(c_Orderings_Oord__class_Oless(_135070, _135074, _135072))], (1288 ^ _106296) ^ [_135479, _135481, _135483] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _135479), _135481)), _135483) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _135479), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _135481), _135483)))], (1290 ^ _106296) ^ [_135599, _135601] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _135599), _135601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _135601), _135599))], (1292 ^ _106296) ^ [_135734, _135736, _135738] : [class_Rings_Odivision__ring__inverse__zero(_135734), c_Rings_Oinverse__class_Oinverse(_135734, _135736) = c_Rings_Oinverse__class_Oinverse(_135734, _135738), -(_135736 = _135738)], (1302 ^ _106296) ^ [_136067, _136069, _136071] : [class_Rings_Odivision__ring__inverse__zero(_136067), 1305 ^ _106296 : [(1306 ^ _106296) ^ [] : [c_Rings_Oinverse__class_Oinverse(_136067, _136069) = c_Rings_Oinverse__class_Oinverse(_136067, _136071), -(_136069 = _136071)], (1312 ^ _106296) ^ [] : [_136069 = _136071, -(c_Rings_Oinverse__class_Oinverse(_136067, _136069) = c_Rings_Oinverse__class_Oinverse(_136067, _136071))]]], (1318 ^ _106296) ^ [_136559, _136561] : [class_Rings_Odivision__ring__inverse__zero(_136559), -(c_Rings_Oinverse__class_Oinverse(_136559, c_Rings_Oinverse__class_Oinverse(_136559, _136561)) = _136561)], (1324 ^ _106296) ^ [_136793, _136795, _136797] : [class_Rings_Ono__zero__divisors(_136793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_136793), _136795), _136797) = c_Groups_Ozero__class_Ozero(_136793), -(_136795 = c_Groups_Ozero__class_Ozero(_136793)), -(_136797 = c_Groups_Ozero__class_Ozero(_136793))], (1338 ^ _106296) ^ [_137236, _137238, _137240] : [class_Rings_Ono__zero__divisors(_137236), -(_137238 = c_Groups_Ozero__class_Ozero(_137236)), -(_137240 = c_Groups_Ozero__class_Ozero(_137236)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137236), _137238), _137240) = c_Groups_Ozero__class_Ozero(_137236)], (1352 ^ _106296) ^ [_137685, _137687, _137689] : [class_Rings_Oring__no__zero__divisors(_137685), 1355 ^ _106296 : [(1366 ^ _106296) ^ [] : [1367 ^ _106296 : [(1368 ^ _106296) ^ [] : [_137687 = c_Groups_Ozero__class_Ozero(_137685)], (1370 ^ _106296) ^ [] : [_137689 = c_Groups_Ozero__class_Ozero(_137685)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137685), _137687), _137689) = c_Groups_Ozero__class_Ozero(_137685))], (1356 ^ _106296) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137685), _137687), _137689) = c_Groups_Ozero__class_Ozero(_137685), -(_137687 = c_Groups_Ozero__class_Ozero(_137685)), -(_137689 = c_Groups_Ozero__class_Ozero(_137685))]]], (1374 ^ _106296) ^ [_138365, _138367] : [class_RealVector_Oreal__normed__algebra(_138365), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138365), _138367), c_Groups_Ozero__class_Ozero(_138365)) = c_Groups_Ozero__class_Ozero(_138365))], (1380 ^ _106296) ^ [_138597, _138599] : [class_RealVector_Oreal__normed__algebra(_138597), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138597), _138599), c_Groups_Ozero__class_Ozero(_138597)) = c_Groups_Ozero__class_Ozero(_138597))], (1386 ^ _106296) ^ [_138829, _138831] : [class_Rings_Omult__zero(_138829), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138829), _138831), c_Groups_Ozero__class_Ozero(_138829)) = c_Groups_Ozero__class_Ozero(_138829))], (1392 ^ _106296) ^ [_139061, _139063] : [class_RealVector_Oreal__normed__algebra(_139061), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_139061), c_Groups_Ozero__class_Ozero(_139061)), _139063) = c_Groups_Ozero__class_Ozero(_139061))], (1398 ^ _106296) ^ [_139293, _139295] : [class_RealVector_Oreal__normed__algebra(_139293), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_139293), c_Groups_Ozero__class_Ozero(_139293)), _139295) = c_Groups_Ozero__class_Ozero(_139293))], (1404 ^ _106296) ^ [_139525, _139527] : [class_Rings_Omult__zero(_139525), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_139525), c_Groups_Ozero__class_Ozero(_139525)), _139527) = c_Groups_Ozero__class_Ozero(_139525))], (1410 ^ _106296) ^ [_139743] : [class_Rings_Ozero__neq__one(_139743), c_Groups_Ozero__class_Ozero(_139743) = c_Groups_Oone__class_Oone(_139743)], (1416 ^ _106296) ^ [_139940] : [class_Rings_Ozero__neq__one(_139940), c_Groups_Oone__class_Oone(_139940) = c_Groups_Ozero__class_Ozero(_139940)], (1422 ^ _106296) ^ [_140193, _140195, _140197, _140199, _140201] : [class_Rings_Osemiring(_140193), -(c_Groups_Oplus__class_Oplus(_140193, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140193), _140195), _140197), c_Groups_Oplus__class_Oplus(_140193, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140193), _140199), _140197), _140201)) = c_Groups_Oplus__class_Oplus(_140193, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140193), c_Groups_Oplus__class_Oplus(_140193, _140195, _140199)), _140197), _140201))], (1428 ^ _106296) ^ [_140527, _140529, _140531, _140533] : [class_RealVector_Oreal__normed__algebra(_140527), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140527), c_Groups_Oplus__class_Oplus(_140527, _140529, _140531)), _140533) = c_Groups_Oplus__class_Oplus(_140527, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140527), _140529), _140533), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140527), _140531), _140533)))], (1434 ^ _106296) ^ [_140839, _140841, _140843, _140845] : [class_RealVector_Oreal__normed__algebra(_140839), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140839), c_Groups_Oplus__class_Oplus(_140839, _140841, _140843)), _140845) = c_Groups_Oplus__class_Oplus(_140839, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140839), _140841), _140845), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140839), _140843), _140845)))], (1440 ^ _106296) ^ [_141151, _141153, _141155, _141157] : [class_Rings_Ocomm__semiring(_141151), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141151), c_Groups_Oplus__class_Oplus(_141151, _141153, _141155)), _141157) = c_Groups_Oplus__class_Oplus(_141151, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141151), _141153), _141157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141151), _141155), _141157)))], (1446 ^ _106296) ^ [_141463, _141465, _141467, _141469] : [class_RealVector_Oreal__normed__algebra(_141463), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141463), _141465), c_Groups_Oplus__class_Oplus(_141463, _141467, _141469)) = c_Groups_Oplus__class_Oplus(_141463, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141463), _141465), _141467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141463), _141465), _141469)))], (1452 ^ _106296) ^ [_141775, _141777, _141779, _141781] : [class_RealVector_Oreal__normed__algebra(_141775), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141775), _141777), c_Groups_Oplus__class_Oplus(_141775, _141779, _141781)) = c_Groups_Oplus__class_Oplus(_141775, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141775), _141777), _141779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141775), _141777), _141781)))], (1458 ^ _106296) ^ [_142073, _142075, _142077] : [class_Rings_Oring__1__no__zero__divisors(_142073), -(_142075 = c_Groups_Ozero__class_Ozero(_142073)), hAPP(hAPP(c_Power_Opower__class_Opower(_142073), _142075), _142077) = c_Groups_Ozero__class_Ozero(_142073)], (1468 ^ _106296) ^ [_142422, _142424, _142426] : [class_Power_Opower(_142422), class_Rings_Omult__zero(_142422), class_Rings_Ono__zero__divisors(_142422), class_Rings_Ozero__neq__one(_142422), 1483 ^ _106296 : [(1484 ^ _106296) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_142422), _142424), _142426) = c_Groups_Ozero__class_Ozero(_142422), 1487 ^ _106296 : [(1488 ^ _106296) ^ [] : [-(_142424 = c_Groups_Ozero__class_Ozero(_142422))], (1490 ^ _106296) ^ [] : [_142426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (1492 ^ _106296) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_142422), _142424), _142426) = c_Groups_Ozero__class_Ozero(_142422)), _142424 = c_Groups_Ozero__class_Ozero(_142422), -(_142426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (1502 ^ _106296) ^ [_143405, _143407, _143409, _143411] : [class_Groups_Ocomm__monoid__mult(_143405), -(hAPP(hAPP(c_Power_Opower__class_Opower(_143405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_143405), _143407), _143409)), _143411) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_143405), hAPP(hAPP(c_Power_Opower__class_Opower(_143405), _143407), _143411)), hAPP(hAPP(c_Power_Opower__class_Opower(_143405), _143409), _143411)))], (1508 ^ _106296) ^ [_143719, _143721, _143723] : [class_Groups_Omonoid__mult(_143719), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_143719), hAPP(hAPP(c_Power_Opower__class_Opower(_143719), _143721), _143723)), _143721) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_143719), _143721), hAPP(hAPP(c_Power_Opower__class_Opower(_143719), _143721), _143723)))], (1514 ^ _106296) ^ [_143997, _143999] : [class_Groups_Omonoid__mult(_143997), -(hAPP(hAPP(c_Power_Opower__class_Opower(_143997), c_Groups_Oone__class_Oone(_143997)), _143999) = c_Groups_Oone__class_Oone(_143997))], (1520 ^ _106296) ^ [_144243, _144245, _144247] : [class_Rings_Odivision__ring(_144243), c_Rings_Oinverse__class_Oinverse(_144243, _144245) = c_Rings_Oinverse__class_Oinverse(_144243, _144247), -(_144245 = c_Groups_Ozero__class_Ozero(_144243)), -(_144247 = c_Groups_Ozero__class_Ozero(_144243)), -(_144245 = _144247)], (1538 ^ _106296) ^ [_144762, _144764] : [class_Rings_Odivision__ring(_144762), c_Rings_Oinverse__class_Oinverse(_144762, _144764) = c_Groups_Ozero__class_Ozero(_144762), -(_144764 = c_Groups_Ozero__class_Ozero(_144762))], (1548 ^ _106296) ^ [_145073, _145075] : [class_Rings_Odivision__ring(_145073), -(_145075 = c_Groups_Ozero__class_Ozero(_145073)), -(c_Rings_Oinverse__class_Oinverse(_145073, c_Rings_Oinverse__class_Oinverse(_145073, _145075)) = _145075)], (1558 ^ _106296) ^ [_145389, _145391] : [class_Rings_Odivision__ring(_145389), -(_145391 = c_Groups_Ozero__class_Ozero(_145389)), c_Rings_Oinverse__class_Oinverse(_145389, _145391) = c_Groups_Ozero__class_Ozero(_145389)], (1568 ^ _106296) ^ [_145704, _145706] : [class_Rings_Odivision__ring__inverse__zero(_145704), 1571 ^ _106296 : [(1572 ^ _106296) ^ [] : [c_Rings_Oinverse__class_Oinverse(_145704, _145706) = c_Groups_Ozero__class_Ozero(_145704), -(_145706 = c_Groups_Ozero__class_Ozero(_145704))], (1578 ^ _106296) ^ [] : [_145706 = c_Groups_Ozero__class_Ozero(_145704), -(c_Rings_Oinverse__class_Oinverse(_145704, _145706) = c_Groups_Ozero__class_Ozero(_145704))]]], (1584 ^ _106296) ^ [_146169] : [class_Rings_Odivision__ring__inverse__zero(_146169), -(c_Rings_Oinverse__class_Oinverse(_146169, c_Groups_Ozero__class_Ozero(_146169)) = c_Groups_Ozero__class_Ozero(_146169))], (1590 ^ _106296) ^ [_146371] : [class_Fields_Ofield__inverse__zero(_146371), -(c_Rings_Oinverse__class_Oinverse(_146371, c_Groups_Ozero__class_Ozero(_146371)) = c_Groups_Ozero__class_Ozero(_146371))], (1596 ^ _106296) ^ [_146601, _146603, _146605] : [class_Fields_Ofield__inverse__zero(_146601), -(c_Rings_Oinverse__class_Oinverse(_146601, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_146601), _146603), _146605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_146601), c_Rings_Oinverse__class_Oinverse(_146601, _146603)), c_Rings_Oinverse__class_Oinverse(_146601, _146605)))], (1602 ^ _106296) ^ [_146865, _146867] : [class_Fields_Ofield__inverse__zero(_146865), 1605 ^ _106296 : [(1606 ^ _106296) ^ [] : [c_Rings_Oinverse__class_Oinverse(_146865, _146867) = c_Groups_Oone__class_Oone(_146865), -(_146867 = c_Groups_Oone__class_Oone(_146865))], (1612 ^ _106296) ^ [] : [_146867 = c_Groups_Oone__class_Oone(_146865), -(c_Rings_Oinverse__class_Oinverse(_146865, _146867) = c_Groups_Oone__class_Oone(_146865))]]], (1618 ^ _106296) ^ [_147330] : [class_Rings_Odivision__ring(_147330), -(c_Rings_Oinverse__class_Oinverse(_147330, c_Groups_Oone__class_Oone(_147330)) = c_Groups_Oone__class_Oone(_147330))], (1624 ^ _106296) ^ [_147560, _147562, _147564] : [-(_147560 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 1627 ^ _106296 : [(1628 ^ _106296) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _147560), _147562) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _147560), _147564), -(_147562 = _147564)], (1634 ^ _106296) ^ [] : [_147562 = _147564, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _147560), _147562) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _147560), _147564))]]], (1640 ^ _106296) ^ [_148089, _148091, _148093] : [-(_148089 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 1643 ^ _106296 : [(1644 ^ _106296) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _148091), _148089) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _148093), _148089), -(_148091 = _148093)], (1650 ^ _106296) ^ [] : [_148091 = _148093, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _148091), _148089) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _148093), _148089))]]], (1656 ^ _106296) ^ [_148618, _148620, _148622] : [class_Rings_Odivision__ring__inverse__zero(_148618), -(c_Rings_Oinverse__class_Oinverse(_148618, hAPP(hAPP(c_Power_Opower__class_Opower(_148618), _148620), _148622)) = hAPP(hAPP(c_Power_Opower__class_Opower(_148618), c_Rings_Oinverse__class_Oinverse(_148618, _148620)), _148622))], (1662 ^ _106296) ^ [_148876, _148878] : [class_Groups_Omonoid__mult(_148876), -(hAPP(hAPP(c_Power_Opower__class_Opower(_148876), _148878), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _148878)], (1668 ^ _106296) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (1670 ^ _106296) ^ [_149123] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _149123) = _149123)], (1672 ^ _106296) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1674 ^ _106296) ^ [_149314, _149316, _149318, _149320] : [class_Rings_Olinordered__ring__strict(_149314), c_Orderings_Oord__class_Oless(_149314, _149316, _149318), c_Orderings_Oord__class_Oless(_149314, _149320, c_Groups_Ozero__class_Ozero(_149314)), -(c_Orderings_Oord__class_Oless(_149314, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_149314), _149320), _149318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_149314), _149320), _149316)))], (1688 ^ _106296) ^ [_149798, _149800, _149802, _149804] : [class_Rings_Olinordered__ring__strict(_149798), c_Orderings_Oord__class_Oless(_149798, _149800, _149802), c_Orderings_Oord__class_Oless(_149798, _149804, c_Groups_Ozero__class_Ozero(_149798)), -(c_Orderings_Oord__class_Oless(_149798, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_149798), _149802), _149804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_149798), _149800), _149804)))], (1702 ^ _106296) ^ [_150282, _150284, _150286, _150288] : [class_Rings_Olinordered__comm__semiring__strict(_150282), c_Orderings_Oord__class_Oless(_150282, _150284, _150286), c_Orderings_Oord__class_Oless(_150282, c_Groups_Ozero__class_Ozero(_150282), _150288), -(c_Orderings_Oord__class_Oless(_150282, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_150282), _150288), _150284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_150282), _150288), _150286)))], (1716 ^ _106296) ^ [_150766, _150768, _150770, _150772] : [class_Rings_Olinordered__semiring__strict(_150766), c_Orderings_Oord__class_Oless(_150766, _150768, _150770), c_Orderings_Oord__class_Oless(_150766, c_Groups_Ozero__class_Ozero(_150766), _150772), -(c_Orderings_Oord__class_Oless(_150766, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_150766), _150772), _150768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_150766), _150772), _150770)))], (1730 ^ _106296) ^ [_151250, _151252, _151254, _151256] : [class_Rings_Olinordered__semiring__strict(_151250), c_Orderings_Oord__class_Oless(_151250, _151252, _151254), c_Orderings_Oord__class_Oless(_151250, c_Groups_Ozero__class_Ozero(_151250), _151256), -(c_Orderings_Oord__class_Oless(_151250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_151250), _151252), _151256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_151250), _151254), _151256)))], (1744 ^ _106296) ^ [_151720, _151722, _151724] : [class_Rings_Olinordered__ring__strict(_151720), c_Orderings_Oord__class_Oless(_151720, _151722, c_Groups_Ozero__class_Ozero(_151720)), c_Orderings_Oord__class_Oless(_151720, _151724, c_Groups_Ozero__class_Ozero(_151720)), -(c_Orderings_Oord__class_Oless(_151720, c_Groups_Ozero__class_Ozero(_151720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_151720), _151722), _151724)))], (1758 ^ _106296) ^ [_152168, _152170, _152172] : [class_Rings_Olinordered__semiring__strict(_152168), c_Orderings_Oord__class_Oless(_152168, _152170, c_Groups_Ozero__class_Ozero(_152168)), c_Orderings_Oord__class_Oless(_152168, c_Groups_Ozero__class_Ozero(_152168), _152172), -(c_Orderings_Oord__class_Oless(_152168, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152168), _152170), _152172), c_Groups_Ozero__class_Ozero(_152168)))], (1772 ^ _106296) ^ [_152630, _152632, _152634, _152636] : [class_Rings_Olinordered__ring__strict(_152630), c_Orderings_Oord__class_Oless(_152630, _152632, c_Groups_Ozero__class_Ozero(_152630)), 1779 ^ _106296 : [(1780 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_152630, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152630), _152632), _152634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152630), _152632), _152636)), -(c_Orderings_Oord__class_Oless(_152630, _152636, _152634))], (1786 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_152630, _152636, _152634), -(c_Orderings_Oord__class_Oless(_152630, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152630), _152632), _152634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152630), _152632), _152636)))]]], (1792 ^ _106296) ^ [_153291, _153293, _153295] : [class_Rings_Olinordered__semiring__strict(_153291), c_Orderings_Oord__class_Oless(_153291, c_Groups_Ozero__class_Ozero(_153291), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153291), _153293), _153295)), c_Orderings_Oord__class_Oless(_153291, c_Groups_Ozero__class_Ozero(_153291), _153295), -(c_Orderings_Oord__class_Oless(_153291, c_Groups_Ozero__class_Ozero(_153291), _153293))], (1806 ^ _106296) ^ [_153739, _153741, _153743] : [class_Rings_Olinordered__semiring__strict(_153739), c_Orderings_Oord__class_Oless(_153739, c_Groups_Ozero__class_Ozero(_153739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153739), _153741), _153743)), c_Orderings_Oord__class_Oless(_153739, c_Groups_Ozero__class_Ozero(_153739), _153741), -(c_Orderings_Oord__class_Oless(_153739, c_Groups_Ozero__class_Ozero(_153739), _153743))], (1820 ^ _106296) ^ [_154187, _154189, _154191] : [class_Rings_Olinordered__semiring__strict(_154187), c_Orderings_Oord__class_Oless(_154187, c_Groups_Ozero__class_Ozero(_154187), _154189), c_Orderings_Oord__class_Oless(_154187, _154191, c_Groups_Ozero__class_Ozero(_154187)), -(c_Orderings_Oord__class_Oless(_154187, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_154187), _154191), _154189), c_Groups_Ozero__class_Ozero(_154187)))], (1834 ^ _106296) ^ [_154635, _154637, _154639] : [class_Rings_Olinordered__semiring__strict(_154635), c_Orderings_Oord__class_Oless(_154635, c_Groups_Ozero__class_Ozero(_154635), _154637), c_Orderings_Oord__class_Oless(_154635, _154639, c_Groups_Ozero__class_Ozero(_154635)), -(c_Orderings_Oord__class_Oless(_154635, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_154635), _154637), _154639), c_Groups_Ozero__class_Ozero(_154635)))], (1848 ^ _106296) ^ [_155083, _155085, _155087] : [class_Rings_Olinordered__semiring__strict(_155083), c_Orderings_Oord__class_Oless(_155083, c_Groups_Ozero__class_Ozero(_155083), _155085), c_Orderings_Oord__class_Oless(_155083, c_Groups_Ozero__class_Ozero(_155083), _155087), -(c_Orderings_Oord__class_Oless(_155083, c_Groups_Ozero__class_Ozero(_155083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155083), _155085), _155087)))], (1862 ^ _106296) ^ [_155545, _155547, _155549, _155551] : [class_Rings_Olinordered__ring__strict(_155545), c_Orderings_Oord__class_Oless(_155545, c_Groups_Ozero__class_Ozero(_155545), _155547), 1869 ^ _106296 : [(1870 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_155545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155545), _155547), _155549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155545), _155547), _155551)), -(c_Orderings_Oord__class_Oless(_155545, _155549, _155551))], (1876 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_155545, _155549, _155551), -(c_Orderings_Oord__class_Oless(_155545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155545), _155547), _155549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155545), _155547), _155551)))]]], (1882 ^ _106296) ^ [_156220, _156222, _156224, _156226] : [class_Rings_Olinordered__ring__strict(_156220), 1885 ^ _106296 : [(1886 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_156220, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_156220), _156222), _156224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_156220), _156222), _156226)), 1891 ^ _106296 : [(1892 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_156220, c_Groups_Ozero__class_Ozero(_156220), _156222))], (1894 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_156220, _156224, _156226))]], 1895 ^ _106296 : [(1896 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_156220, _156222, c_Groups_Ozero__class_Ozero(_156220)))], (1898 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_156220, _156226, _156224))]]], (1900 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_156220, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_156220), _156222), _156224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_156220), _156222), _156226))), 1901 ^ _106296 : [(1902 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_156220, c_Groups_Ozero__class_Ozero(_156220), _156222), c_Orderings_Oord__class_Oless(_156220, _156224, _156226)], (1908 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_156220, _156222, c_Groups_Ozero__class_Ozero(_156220)), c_Orderings_Oord__class_Oless(_156220, _156226, _156224)]]]]], (1916 ^ _106296) ^ [_157323, _157325, _157327, _157329] : [class_Rings_Olinordered__ring__strict(_157323), 1919 ^ _106296 : [(1920 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_157323, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_157323), _157325), _157327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_157323), _157329), _157327)), 1925 ^ _106296 : [(1926 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_157323, c_Groups_Ozero__class_Ozero(_157323), _157327))], (1928 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_157323, _157325, _157329))]], 1929 ^ _106296 : [(1930 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_157323, _157327, c_Groups_Ozero__class_Ozero(_157323)))], (1932 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_157323, _157329, _157325))]]], (1934 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_157323, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_157323), _157325), _157327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_157323), _157329), _157327))), 1935 ^ _106296 : [(1936 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_157323, c_Groups_Ozero__class_Ozero(_157323), _157327), c_Orderings_Oord__class_Oless(_157323, _157325, _157329)], (1942 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_157323, _157327, c_Groups_Ozero__class_Ozero(_157323)), c_Orderings_Oord__class_Oless(_157323, _157329, _157325)]]]]], (1950 ^ _106296) ^ [_158398, _158400] : [class_Rings_Olinordered__ring(_158398), c_Orderings_Oord__class_Oless(_158398, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_158398), _158400), _158400), c_Groups_Ozero__class_Ozero(_158398))], (1956 ^ _106296) ^ [_158657, _158659, _158661, _158663] : [class_Rings_Olinordered__semidom(_158657), c_Orderings_Oord__class_Oless(_158657, c_Groups_Ozero__class_Ozero(_158657), _158659), c_Orderings_Oord__class_Oless(_158657, _158661, _158663), -(c_Orderings_Oord__class_Oless(_158657, _158661, c_Groups_Oplus__class_Oplus(_158657, _158659, _158663)))], (1970 ^ _106296) ^ [_159075] : [class_Rings_Olinordered__semidom(_159075), -(c_Orderings_Oord__class_Oless(_159075, c_Groups_Ozero__class_Ozero(_159075), c_Groups_Oone__class_Oone(_159075)))], (1976 ^ _106296) ^ [_159273] : [class_Rings_Olinordered__semidom(_159273), c_Orderings_Oord__class_Oless(_159273, c_Groups_Oone__class_Oone(_159273), c_Groups_Ozero__class_Ozero(_159273))], (1982 ^ _106296) ^ [_159500, _159502, _159504] : [class_Rings_Olinordered__semidom(_159500), c_Orderings_Oord__class_Oless(_159500, c_Groups_Oone__class_Oone(_159500), _159502), c_Orderings_Oord__class_Oless(_159500, c_Groups_Oone__class_Oone(_159500), _159504), -(c_Orderings_Oord__class_Oless(_159500, c_Groups_Oone__class_Oone(_159500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_159500), _159502), _159504)))], (1996 ^ _106296) ^ [_159948, _159950, _159952] : [class_Rings_Olinordered__semidom(_159948), c_Orderings_Oord__class_Oless(_159948, c_Groups_Ozero__class_Ozero(_159948), _159950), -(c_Orderings_Oord__class_Oless(_159948, c_Groups_Ozero__class_Ozero(_159948), hAPP(hAPP(c_Power_Opower__class_Opower(_159948), _159950), _159952)))], (2006 ^ _106296) ^ [_160283, _160285] : [class_Rings_Olinordered__semidom(_160283), -(c_Orderings_Oord__class_Oless(_160283, _160285, c_Groups_Oplus__class_Oplus(_160283, _160285, c_Groups_Oone__class_Oone(_160283))))], (2012 ^ _106296) ^ [_160505, _160507] : [class_Power_Opower(_160505), class_Rings_Osemiring__0(_160505), 2019 ^ _106296 : [(2020 ^ _106296) ^ [] : [_160507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_160505), c_Groups_Ozero__class_Ozero(_160505)), _160507) = c_Groups_Oone__class_Oone(_160505))], (2026 ^ _106296) ^ [] : [-(_160507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_160505), c_Groups_Ozero__class_Ozero(_160505)), _160507) = c_Groups_Ozero__class_Ozero(_160505))]]], (2032 ^ _106296) ^ [_161134, _161136, _161138, _161140] : [class_Rings_Olinordered__semidom(_161134), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _161136, _161138), c_Orderings_Oord__class_Oless(_161134, c_Groups_Oone__class_Oone(_161134), _161140), -(c_Orderings_Oord__class_Oless(_161134, hAPP(hAPP(c_Power_Opower__class_Opower(_161134), _161140), _161136), hAPP(hAPP(c_Power_Opower__class_Opower(_161134), _161140), _161138)))], (2046 ^ _106296) ^ [_161618, _161620, _161622, _161624] : [class_Rings_Olinordered__semidom(_161618), c_Orderings_Oord__class_Oless(_161618, c_Groups_Oone__class_Oone(_161618), _161620), c_Orderings_Oord__class_Oless(_161618, hAPP(hAPP(c_Power_Opower__class_Opower(_161618), _161620), _161622), hAPP(hAPP(c_Power_Opower__class_Opower(_161618), _161620), _161624)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _161622, _161624))], (2060 ^ _106296) ^ [_162102, _162104, _162106, _162108] : [class_Rings_Olinordered__semidom(_162102), c_Orderings_Oord__class_Oless(_162102, c_Groups_Oone__class_Oone(_162102), _162104), 2067 ^ _106296 : [(2068 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_162102, hAPP(hAPP(c_Power_Opower__class_Opower(_162102), _162104), _162106), hAPP(hAPP(c_Power_Opower__class_Opower(_162102), _162104), _162108)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _162106, _162108))], (2074 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _162106, _162108), -(c_Orderings_Oord__class_Oless(_162102, hAPP(hAPP(c_Power_Opower__class_Opower(_162102), _162104), _162106), hAPP(hAPP(c_Power_Opower__class_Opower(_162102), _162104), _162108)))]]], (2080 ^ _106296) ^ [_162777, _162779, _162781, _162783] : [class_Rings_Olinordered__semidom(_162777), c_Orderings_Oord__class_Oless(_162777, c_Groups_Oone__class_Oone(_162777), _162779), 2087 ^ _106296 : [(2088 ^ _106296) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_162777), _162779), _162781) = hAPP(hAPP(c_Power_Opower__class_Opower(_162777), _162779), _162783), -(_162781 = _162783)], (2094 ^ _106296) ^ [] : [_162781 = _162783, -(hAPP(hAPP(c_Power_Opower__class_Opower(_162777), _162779), _162781) = hAPP(hAPP(c_Power_Opower__class_Opower(_162777), _162779), _162783))]]], (2100 ^ _106296) ^ [_163432, _163434, _163436] : [class_Fields_Olinordered__field(_163432), c_Orderings_Oord__class_Oless(_163432, c_Rings_Oinverse__class_Oinverse(_163432, _163434), c_Rings_Oinverse__class_Oinverse(_163432, _163436)), c_Orderings_Oord__class_Oless(_163432, _163436, c_Groups_Ozero__class_Ozero(_163432)), -(c_Orderings_Oord__class_Oless(_163432, _163436, _163434))], (2114 ^ _106296) ^ [_163868, _163870, _163872] : [class_Fields_Olinordered__field(_163868), c_Orderings_Oord__class_Oless(_163868, c_Rings_Oinverse__class_Oinverse(_163868, _163870), c_Rings_Oinverse__class_Oinverse(_163868, _163872)), c_Orderings_Oord__class_Oless(_163868, c_Groups_Ozero__class_Ozero(_163868), _163870), -(c_Orderings_Oord__class_Oless(_163868, _163872, _163870))], (2128 ^ _106296) ^ [_164290, _164292] : [class_Fields_Olinordered__field(_164290), c_Orderings_Oord__class_Oless(_164290, c_Rings_Oinverse__class_Oinverse(_164290, _164292), c_Groups_Ozero__class_Ozero(_164290)), -(_164292 = c_Groups_Ozero__class_Ozero(_164290)), -(c_Orderings_Oord__class_Oless(_164290, _164292, c_Groups_Ozero__class_Ozero(_164290)))], (2142 ^ _106296) ^ [_164715, _164717, _164719] : [class_Fields_Olinordered__field(_164715), c_Orderings_Oord__class_Oless(_164715, _164717, _164719), c_Orderings_Oord__class_Oless(_164715, _164719, c_Groups_Ozero__class_Ozero(_164715)), -(c_Orderings_Oord__class_Oless(_164715, c_Rings_Oinverse__class_Oinverse(_164715, _164719), c_Rings_Oinverse__class_Oinverse(_164715, _164717)))], (2156 ^ _106296) ^ [_165151, _165153, _165155] : [class_Fields_Olinordered__field(_165151), c_Orderings_Oord__class_Oless(_165151, _165153, _165155), c_Orderings_Oord__class_Oless(_165151, c_Groups_Ozero__class_Ozero(_165151), _165153), -(c_Orderings_Oord__class_Oless(_165151, c_Rings_Oinverse__class_Oinverse(_165151, _165155), c_Rings_Oinverse__class_Oinverse(_165151, _165153)))], (2170 ^ _106296) ^ [_165573, _165575] : [class_Fields_Olinordered__field(_165573), c_Orderings_Oord__class_Oless(_165573, _165575, c_Groups_Ozero__class_Ozero(_165573)), -(c_Orderings_Oord__class_Oless(_165573, c_Rings_Oinverse__class_Oinverse(_165573, _165575), c_Groups_Ozero__class_Ozero(_165573)))], (2180 ^ _106296) ^ [_165888, _165890] : [class_Fields_Olinordered__field(_165888), c_Orderings_Oord__class_Oless(_165888, c_Groups_Ozero__class_Ozero(_165888), c_Rings_Oinverse__class_Oinverse(_165888, _165890)), -(_165890 = c_Groups_Ozero__class_Ozero(_165888)), -(c_Orderings_Oord__class_Oless(_165888, c_Groups_Ozero__class_Ozero(_165888), _165890))], (2194 ^ _106296) ^ [_166299, _166301] : [class_Fields_Olinordered__field(_166299), c_Orderings_Oord__class_Oless(_166299, c_Groups_Ozero__class_Ozero(_166299), _166301), -(c_Orderings_Oord__class_Oless(_166299, c_Groups_Ozero__class_Ozero(_166299), c_Rings_Oinverse__class_Oinverse(_166299, _166301)))], (2204 ^ _106296) ^ [_166614, _166616] : [class_Fields_Olinordered__field__inverse__zero(_166614), 2207 ^ _106296 : [(2208 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_166614, c_Rings_Oinverse__class_Oinverse(_166614, _166616), c_Groups_Ozero__class_Ozero(_166614)), -(c_Orderings_Oord__class_Oless(_166614, _166616, c_Groups_Ozero__class_Ozero(_166614)))], (2214 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_166614, _166616, c_Groups_Ozero__class_Ozero(_166614)), -(c_Orderings_Oord__class_Oless(_166614, c_Rings_Oinverse__class_Oinverse(_166614, _166616), c_Groups_Ozero__class_Ozero(_166614)))]]], (2220 ^ _106296) ^ [_167099, _167101] : [class_Fields_Olinordered__field__inverse__zero(_167099), 2223 ^ _106296 : [(2224 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_167099, c_Groups_Ozero__class_Ozero(_167099), c_Rings_Oinverse__class_Oinverse(_167099, _167101)), -(c_Orderings_Oord__class_Oless(_167099, c_Groups_Ozero__class_Ozero(_167099), _167101))], (2230 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_167099, c_Groups_Ozero__class_Ozero(_167099), _167101), -(c_Orderings_Oord__class_Oless(_167099, c_Groups_Ozero__class_Ozero(_167099), c_Rings_Oinverse__class_Oinverse(_167099, _167101)))]]], (2236 ^ _106296) ^ [_167598, _167600, _167602] : [class_Rings_Odivision__ring(_167598), -(_167600 = c_Groups_Ozero__class_Ozero(_167598)), -(_167602 = c_Groups_Ozero__class_Ozero(_167598)), -(c_Rings_Oinverse__class_Oinverse(_167598, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_167598), _167600), _167602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_167598), c_Rings_Oinverse__class_Oinverse(_167598, _167602)), c_Rings_Oinverse__class_Oinverse(_167598, _167600)))], (2250 ^ _106296) ^ [_168062, _168064] : [class_RealVector_Oreal__normed__vector(_168062), 2253 ^ _106296 : [(2254 ^ _106296) ^ [] : [c_RealVector_Onorm__class_Onorm(_168062, _168064) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_168064 = c_Groups_Ozero__class_Ozero(_168062))], (2260 ^ _106296) ^ [] : [_168064 = c_Groups_Ozero__class_Ozero(_168062), -(c_RealVector_Onorm__class_Onorm(_168062, _168064) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (2266 ^ _106296) ^ [_168521] : [class_RealVector_Oreal__normed__vector(_168521), -(c_RealVector_Onorm__class_Onorm(_168521, c_Groups_Ozero__class_Ozero(_168521)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2272 ^ _106296) ^ [_168761, _168763, _168765, _168767] : [class_Groups_Omonoid__mult(_168761), -(hAPP(hAPP(c_Power_Opower__class_Opower(_168761), _168763), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _168765, _168767)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_168761), hAPP(hAPP(c_Power_Opower__class_Opower(_168761), _168763), _168765)), hAPP(hAPP(c_Power_Opower__class_Opower(_168761), _168763), _168767)))], (2278 ^ _106296) ^ [_169067, _169069, _169071] : [class_Rings_Odivision__ring(_169067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_169067), _169069), _169071) = c_Groups_Oone__class_Oone(_169067), -(c_Rings_Oinverse__class_Oinverse(_169067, _169069) = _169071)], (2288 ^ _106296) ^ [_169414, _169416, _169418] : [class_Rings_Odivision__ring(_169414), -(_169416 = c_Groups_Ozero__class_Ozero(_169414)), -(c_Rings_Oinverse__class_Oinverse(_169414, hAPP(hAPP(c_Power_Opower__class_Opower(_169414), _169416), _169418)) = hAPP(hAPP(c_Power_Opower__class_Opower(_169414), c_Rings_Oinverse__class_Oinverse(_169414, _169416)), _169418))], (2298 ^ _106296) ^ [_169814, _169816, _169818, _169820, _169822] : [class_RealVector_Oreal__normed__vector(_169814), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_169814, _169816), _169818), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_169814, _169820), _169822), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_169814, c_Groups_Oplus__class_Oplus(_169814, _169816, _169820)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _169818, _169822)))], (2312 ^ _106296) ^ [_170296, _170298, _170300] : [class_RealVector_Oreal__normed__div__algebra(_170296), -(c_RealVector_Onorm__class_Onorm(_170296, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_170296), _170298), _170300)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_170296, _170298)), c_RealVector_Onorm__class_Onorm(_170296, _170300)))], (2318 ^ _106296) ^ [_170570, _170572, _170574] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _170570), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _170572, _170574), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _170570), _170572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _170570), _170574)))], (2328 ^ _106296) ^ [_170909, _170911] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _170909), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _170911), -(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), _170909), _170911)))], (2338 ^ _106296) ^ [_171240, _171242, _171244] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _171240), 2341 ^ _106296 : [(2342 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _171242), _171240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _171244), _171240)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _171242, _171244))], (2348 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _171242, _171244), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _171242), _171240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _171244), _171240)))]]], (2354 ^ _106296) ^ [_171760, _171762] : [class_RealVector_Oreal__normed__vector(_171760), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_171760, _171762), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2360 ^ _106296) ^ [_171963] : [class_RealVector_Oreal__normed__algebra__1(_171963), -(c_RealVector_Onorm__class_Onorm(_171963, c_Groups_Oone__class_Oone(_171963)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (2366 ^ _106296) ^ [_172189, _172191, _172193] : [class_RealVector_Oreal__normed__div__algebra(_172189), -(c_RealVector_Onorm__class_Onorm(_172189, hAPP(hAPP(c_Power_Opower__class_Opower(_172189), _172191), _172193)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_172189, _172191)), _172193))], (2372 ^ _106296) ^ [_172443, _172445] : [-(c_RealVector_Onorm__class_Onorm(_172443, c_Rings_Oinverse__class_Oinverse(_172443, _172445)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_172443, _172445))), class_RealVector_Oreal__normed__div__algebra(_172443), class_Rings_Odivision__ring__inverse__zero(_172443)], (2382 ^ _106296) ^ [_172748] : [class_Rings_Olinordered__semidom(_172748), -(c_Orderings_Oord__class_Oless(_172748, c_Groups_Ozero__class_Ozero(_172748), c_Groups_Oplus__class_Oplus(_172748, c_Groups_Oone__class_Oone(_172748), c_Groups_Oone__class_Oone(_172748))))], (2388 ^ _106296) ^ [_173000, _173002, _173004, _173006] : [class_Rings_Olinordered__semidom(_173000), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _173002, _173004), c_Orderings_Oord__class_Oless(_173000, c_Groups_Ozero__class_Ozero(_173000), _173006), c_Orderings_Oord__class_Oless(_173000, _173006, c_Groups_Oone__class_Oone(_173000)), -(c_Orderings_Oord__class_Oless(_173000, hAPP(hAPP(c_Power_Opower__class_Opower(_173000), _173006), _173004), hAPP(hAPP(c_Power_Opower__class_Opower(_173000), _173006), _173002)))], (2406 ^ _106296) ^ [_173573, _173575, _173577] : [class_Rings_Olinordered__semidom(_173573), c_Orderings_Oord__class_Oless(_173573, c_Groups_Oone__class_Oone(_173573), _173575), -(c_Orderings_Oord__class_Oless(_173573, hAPP(hAPP(c_Power_Opower__class_Opower(_173573), _173575), _173577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_173573), _173575), hAPP(hAPP(c_Power_Opower__class_Opower(_173573), _173575), _173577))))], (2416 ^ _106296) ^ [_173950, _173952, _173954] : [class_Rings_Olinordered__semidom(_173950), c_Orderings_Oord__class_Oless(_173950, c_Groups_Oone__class_Oone(_173950), _173952), -(c_Orderings_Oord__class_Oless(_173950, c_Groups_Oone__class_Oone(_173950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_173950), _173952), hAPP(hAPP(c_Power_Opower__class_Opower(_173950), _173952), _173954))))], (2426 ^ _106296) ^ [_174315, _174317, _174319] : [class_Fields_Ofield(_174315), -(_174317 = c_Groups_Ozero__class_Ozero(_174315)), -(_174319 = c_Groups_Ozero__class_Ozero(_174315)), -(c_Groups_Oplus__class_Oplus(_174315, c_Rings_Oinverse__class_Oinverse(_174315, _174317), c_Rings_Oinverse__class_Oinverse(_174315, _174319)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_174315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_174315), c_Groups_Oplus__class_Oplus(_174315, _174317, _174319)), c_Rings_Oinverse__class_Oinverse(_174315, _174317))), c_Rings_Oinverse__class_Oinverse(_174315, _174319)))], (2440 ^ _106296) ^ [_174815, _174817, _174819] : [class_Rings_Odivision__ring(_174815), -(_174817 = c_Groups_Ozero__class_Ozero(_174815)), -(_174819 = c_Groups_Ozero__class_Ozero(_174815)), -(c_Groups_Oplus__class_Oplus(_174815, c_Rings_Oinverse__class_Oinverse(_174815, _174817), c_Rings_Oinverse__class_Oinverse(_174815, _174819)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_174815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_174815), c_Rings_Oinverse__class_Oinverse(_174815, _174817)), c_Groups_Oplus__class_Oplus(_174815, _174817, _174819))), c_Rings_Oinverse__class_Oinverse(_174815, _174819)))], (2454 ^ _106296) ^ [_175315, _175317, _175319] : [class_Rings_Olinordered__ring__strict(_175315), 2457 ^ _106296 : [(2468 ^ _106296) ^ [] : [2469 ^ _106296 : [(2470 ^ _106296) ^ [] : [-(_175317 = c_Groups_Ozero__class_Ozero(_175315))], (2472 ^ _106296) ^ [] : [-(_175319 = c_Groups_Ozero__class_Ozero(_175315))]], -(c_Orderings_Oord__class_Oless(_175315, c_Groups_Ozero__class_Ozero(_175315), c_Groups_Oplus__class_Oplus(_175315, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_175315), _175317), _175317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_175315), _175319), _175319))))], (2458 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_175315, c_Groups_Ozero__class_Ozero(_175315), c_Groups_Oplus__class_Oplus(_175315, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_175315), _175317), _175317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_175315), _175319), _175319))), _175317 = c_Groups_Ozero__class_Ozero(_175315), _175319 = c_Groups_Ozero__class_Ozero(_175315)]]], (2476 ^ _106296) ^ [_176052, _176054, _176056] : [class_Rings_Olinordered__ring(_176052), c_Orderings_Oord__class_Oless(_176052, c_Groups_Oplus__class_Oplus(_176052, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_176052), _176054), _176054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_176052), _176056), _176056)), c_Groups_Ozero__class_Ozero(_176052))], (2482 ^ _106296) ^ [_176328] : [-(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), _176328), _176328))), -(_176328 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2488 ^ _106296) ^ [_176501] : [_176501 = 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), _176501), _176501))], (2494 ^ _106296) ^ [_176750, _176752, _176754, _176756] : [class_Rings_Ocomm__semiring__1(_176750), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_176750), hAPP(hAPP(c_Power_Opower__class_Opower(_176750), _176752), _176754)), hAPP(hAPP(c_Power_Opower__class_Opower(_176750), _176752), _176756)) = hAPP(hAPP(c_Power_Opower__class_Opower(_176750), _176752), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _176754, _176756)))], (2500 ^ _106296) ^ [_177042, _177044] : [class_Rings_Ocomm__semiring__1(_177042), -(hAPP(hAPP(c_Power_Opower__class_Opower(_177042), _177044), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_177042))], (2506 ^ _106296) ^ [_177284, _177286, _177288] : [class_Rings_Ocomm__semiring__1(_177284), -(c_Groups_Oplus__class_Oplus(_177284, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177284), _177286), _177288), _177288) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177284), c_Groups_Oplus__class_Oplus(_177284, _177286, c_Groups_Oone__class_Oone(_177284))), _177288))], (2512 ^ _106296) ^ [_177564, _177566, _177568] : [class_Rings_Ocomm__semiring__1(_177564), -(c_Groups_Oplus__class_Oplus(_177564, _177566, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177564), _177568), _177566)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177564), c_Groups_Oplus__class_Oplus(_177564, _177568, c_Groups_Oone__class_Oone(_177564))), _177566))], (2518 ^ _106296) ^ [_177830, _177832] : [class_Rings_Ocomm__semiring__1(_177830), -(c_Groups_Oplus__class_Oplus(_177830, _177832, _177832) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177830), c_Groups_Oplus__class_Oplus(_177830, c_Groups_Oone__class_Oone(_177830), c_Groups_Oone__class_Oone(_177830))), _177832))], (2524 ^ _106296) ^ [_178134, _178136, _178138, _178140, _178142, _178144] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_178134), -(_178136 = c_Groups_Ozero__class_Ozero(_178134)), c_Groups_Oplus__class_Oplus(_178134, _178138, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178134), _178136), _178142)) = c_Groups_Oplus__class_Oplus(_178134, _178140, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178134), _178136), _178144)), _178138 = _178140, -(_178142 = _178144)], (2542 ^ _106296) ^ [_178754, _178756, _178758] : [class_Rings_Olinordered__ring__strict(_178754), 2545 ^ _106296 : [(2546 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_178754, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178754), _178756), _178756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178754), _178758), _178758)) = c_Groups_Ozero__class_Ozero(_178754), 2549 ^ _106296 : [(2550 ^ _106296) ^ [] : [-(_178756 = c_Groups_Ozero__class_Ozero(_178754))], (2552 ^ _106296) ^ [] : [-(_178758 = c_Groups_Ozero__class_Ozero(_178754))]]], (2554 ^ _106296) ^ [] : [-(c_Groups_Oplus__class_Oplus(_178754, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178754), _178756), _178756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178754), _178758), _178758)) = c_Groups_Ozero__class_Ozero(_178754)), _178756 = c_Groups_Ozero__class_Ozero(_178754), _178758 = c_Groups_Ozero__class_Ozero(_178754)]]], (2564 ^ _106296) ^ [_179484, _179486, _179488] : [class_Groups_Oordered__comm__monoid__add(_179484), c_Orderings_Oord__class_Oless(_179484, _179486, c_Groups_Ozero__class_Ozero(_179484)), c_Orderings_Oord__class_Oless(_179484, _179488, c_Groups_Ozero__class_Ozero(_179484)), -(c_Orderings_Oord__class_Oless(_179484, c_Groups_Oplus__class_Oplus(_179484, _179486, _179488), c_Groups_Ozero__class_Ozero(_179484)))], (2578 ^ _106296) ^ [_179924, _179926, _179928] : [class_Groups_Oordered__comm__monoid__add(_179924), c_Orderings_Oord__class_Oless(_179924, c_Groups_Ozero__class_Ozero(_179924), _179926), c_Orderings_Oord__class_Oless(_179924, c_Groups_Ozero__class_Ozero(_179924), _179928), -(c_Orderings_Oord__class_Oless(_179924, c_Groups_Ozero__class_Ozero(_179924), c_Groups_Oplus__class_Oplus(_179924, _179926, _179928)))], (2592 ^ _106296) ^ [] : [-(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))], (2594 ^ _106296) ^ [_180402, _180404, _180406] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _180402, _180404)), _180406) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _180402), _180406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _180404), _180406)))], (2596 ^ _106296) ^ [_180568, _180570] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _180568), _180568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _180570), _180570)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 2599 ^ _106296 : [(2600 ^ _106296) ^ [] : [-(_180568 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2602 ^ _106296) ^ [] : [-(_180570 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (2604 ^ _106296) ^ [_180837, _180839] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _180837), _180837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _180839), _180839)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _180837 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _180839 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (2614 ^ _106296) ^ [_181170, _181172] : [class_Groups_Ozero(_181170), 2617 ^ _106296 : [(2618 ^ _106296) ^ [] : [c_Groups_Ozero__class_Ozero(_181170) = _181172, -(_181172 = c_Groups_Ozero__class_Ozero(_181170))], (2624 ^ _106296) ^ [] : [_181172 = c_Groups_Ozero__class_Ozero(_181170), -(c_Groups_Ozero__class_Ozero(_181170) = _181172)]]], (2630 ^ _106296) ^ [_181654, _181656, _181658] : [class_Rings_Ocomm__semiring__1(_181654), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_181654), _181656), _181658) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_181654), _181658), _181656))], (2636 ^ _106296) ^ [_181928, _181930, _181932, _181934] : [class_Rings_Ocomm__semiring__1(_181928), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_181928), _181930), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_181928), _181932), _181934)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_181928), _181932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_181928), _181930), _181934)))], (2642 ^ _106296) ^ [_182240, _182242, _182244, _182246] : [class_Rings_Ocomm__semiring__1(_182240), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182240), _182242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182240), _182244), _182246)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182240), _182242), _182244)), _182246))], (2648 ^ _106296) ^ [_182552, _182554, _182556, _182558] : [class_Groups_Oab__semigroup__mult(_182552), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182552), _182554), _182556)), _182558) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182552), _182554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182552), _182556), _182558)))], (2654 ^ _106296) ^ [_182864, _182866, _182868, _182870] : [class_Rings_Ocomm__semiring__1(_182864), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182864), _182866), _182868)), _182870) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182864), _182866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182864), _182868), _182870)))], (2660 ^ _106296) ^ [_183176, _183178, _183180, _183182] : [class_Rings_Ocomm__semiring__1(_183176), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183176), _183178), _183180)), _183182) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183176), _183178), _183182)), _183180))], (2666 ^ _106296) ^ [_183502, _183504, _183506, _183508, _183510] : [class_Rings_Ocomm__semiring__1(_183502), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183502), _183504), _183506)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183502), _183508), _183510)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183502), _183504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183502), _183506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183502), _183508), _183510))))], (2672 ^ _106296) ^ [_183866, _183868, _183870, _183872, _183874] : [class_Rings_Ocomm__semiring__1(_183866), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183866), _183868), _183870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183866), _183872), _183874)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183866), _183872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_183866), _183868), _183870)), _183874)))], (2678 ^ _106296) ^ [_184230, _184232, _184234, _184236, _184238] : [class_Rings_Ocomm__semiring__1(_184230), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184230), _184232), _184234)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184230), _184236), _184238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184230), _184232), _184236)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184230), _184234), _184238)))], (2684 ^ _106296) ^ [_184566, _184568, _184570] : [class_Rings_Ocomm__semiring__1(_184566), -(c_Groups_Oplus__class_Oplus(_184566, _184568, _184570) = c_Groups_Oplus__class_Oplus(_184566, _184570, _184568))], (2690 ^ _106296) ^ [_184824, _184826, _184828, _184830] : [class_Rings_Ocomm__semiring__1(_184824), -(c_Groups_Oplus__class_Oplus(_184824, _184826, c_Groups_Oplus__class_Oplus(_184824, _184828, _184830)) = c_Groups_Oplus__class_Oplus(_184824, _184828, c_Groups_Oplus__class_Oplus(_184824, _184826, _184830)))], (2696 ^ _106296) ^ [_185104, _185106, _185108, _185110] : [class_Rings_Ocomm__semiring__1(_185104), -(c_Groups_Oplus__class_Oplus(_185104, _185106, c_Groups_Oplus__class_Oplus(_185104, _185108, _185110)) = c_Groups_Oplus__class_Oplus(_185104, c_Groups_Oplus__class_Oplus(_185104, _185106, _185108), _185110))], (2702 ^ _106296) ^ [_185384, _185386, _185388, _185390] : [class_Rings_Ocomm__semiring__1(_185384), -(c_Groups_Oplus__class_Oplus(_185384, c_Groups_Oplus__class_Oplus(_185384, _185386, _185388), _185390) = c_Groups_Oplus__class_Oplus(_185384, _185386, c_Groups_Oplus__class_Oplus(_185384, _185388, _185390)))], (2708 ^ _106296) ^ [_185664, _185666, _185668, _185670] : [class_Groups_Oab__semigroup__add(_185664), -(c_Groups_Oplus__class_Oplus(_185664, c_Groups_Oplus__class_Oplus(_185664, _185666, _185668), _185670) = c_Groups_Oplus__class_Oplus(_185664, _185666, c_Groups_Oplus__class_Oplus(_185664, _185668, _185670)))], (2714 ^ _106296) ^ [_185944, _185946, _185948, _185950] : [class_Rings_Ocomm__semiring__1(_185944), -(c_Groups_Oplus__class_Oplus(_185944, c_Groups_Oplus__class_Oplus(_185944, _185946, _185948), _185950) = c_Groups_Oplus__class_Oplus(_185944, c_Groups_Oplus__class_Oplus(_185944, _185946, _185950), _185948))], (2720 ^ _106296) ^ [_186224, _186226, _186228, _186230] : [class_Groups_Ocancel__semigroup__add(_186224), 2723 ^ _106296 : [(2724 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_186224, _186226, _186228) = c_Groups_Oplus__class_Oplus(_186224, _186226, _186230), -(_186228 = _186230)], (2730 ^ _106296) ^ [] : [_186228 = _186230, -(c_Groups_Oplus__class_Oplus(_186224, _186226, _186228) = c_Groups_Oplus__class_Oplus(_186224, _186226, _186230))]]], (2736 ^ _106296) ^ [_186766, _186768, _186770, _186772] : [class_Groups_Ocancel__semigroup__add(_186766), 2739 ^ _106296 : [(2740 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_186766, _186768, _186770) = c_Groups_Oplus__class_Oplus(_186766, _186772, _186770), -(_186768 = _186772)], (2746 ^ _106296) ^ [] : [_186768 = _186772, -(c_Groups_Oplus__class_Oplus(_186766, _186768, _186770) = c_Groups_Oplus__class_Oplus(_186766, _186772, _186770))]]], (2752 ^ _106296) ^ [_187322, _187324, _187326, _187328, _187330] : [class_Rings_Ocomm__semiring__1(_187322), -(c_Groups_Oplus__class_Oplus(_187322, c_Groups_Oplus__class_Oplus(_187322, _187324, _187326), c_Groups_Oplus__class_Oplus(_187322, _187328, _187330)) = c_Groups_Oplus__class_Oplus(_187322, c_Groups_Oplus__class_Oplus(_187322, _187324, _187328), c_Groups_Oplus__class_Oplus(_187322, _187326, _187330)))], (2758 ^ _106296) ^ [_187624, _187626, _187628, _187630] : [class_Groups_Ocancel__semigroup__add(_187624), c_Groups_Oplus__class_Oplus(_187624, _187626, _187628) = c_Groups_Oplus__class_Oplus(_187624, _187626, _187630), -(_187628 = _187630)], (2768 ^ _106296) ^ [_187985, _187987, _187989, _187991] : [class_Groups_Ocancel__ab__semigroup__add(_187985), c_Groups_Oplus__class_Oplus(_187985, _187987, _187989) = c_Groups_Oplus__class_Oplus(_187985, _187987, _187991), -(_187989 = _187991)], (2778 ^ _106296) ^ [_188346, _188348, _188350, _188352] : [class_Groups_Ocancel__semigroup__add(_188346), c_Groups_Oplus__class_Oplus(_188346, _188348, _188350) = c_Groups_Oplus__class_Oplus(_188346, _188352, _188350), -(_188348 = _188352)], (2788 ^ _106296) ^ [_188679, _188681] : [class_Groups_Oone(_188679), 2791 ^ _106296 : [(2792 ^ _106296) ^ [] : [c_Groups_Oone__class_Oone(_188679) = _188681, -(_188681 = c_Groups_Oone__class_Oone(_188679))], (2798 ^ _106296) ^ [] : [_188681 = c_Groups_Oone__class_Oone(_188679), -(c_Groups_Oone__class_Oone(_188679) = _188681)]]], (2804 ^ _106296) ^ [_189177, _189179, _189181, _189183] : [class_Rings_Ocomm__semiring__1(_189177), -(hAPP(hAPP(c_Power_Opower__class_Opower(_189177), hAPP(hAPP(c_Power_Opower__class_Opower(_189177), _189179), _189181)), _189183) = hAPP(hAPP(c_Power_Opower__class_Opower(_189177), _189179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _189181), _189183)))], (2810 ^ _106296) ^ [_189457, _189459] : [class_Rings_Ocomm__semiring__1(_189457), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_189457), c_Groups_Ozero__class_Ozero(_189457)), _189459) = c_Groups_Ozero__class_Ozero(_189457))], (2816 ^ _106296) ^ [_189689, _189691] : [class_Rings_Ocomm__semiring__1(_189689), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_189689), _189691), c_Groups_Ozero__class_Ozero(_189689)) = c_Groups_Ozero__class_Ozero(_189689))], (2822 ^ _106296) ^ [_189921, _189923] : [class_Groups_Omonoid__add(_189921), -(c_Groups_Oplus__class_Oplus(_189921, c_Groups_Ozero__class_Ozero(_189921), _189923) = _189923)], (2828 ^ _106296) ^ [_190141, _190143] : [class_Rings_Ocomm__semiring__1(_190141), -(c_Groups_Oplus__class_Oplus(_190141, c_Groups_Ozero__class_Ozero(_190141), _190143) = _190143)], (2834 ^ _106296) ^ [_190361, _190363] : [class_Groups_Ocomm__monoid__add(_190361), -(c_Groups_Oplus__class_Oplus(_190361, c_Groups_Ozero__class_Ozero(_190361), _190363) = _190363)], (2840 ^ _106296) ^ [_190581, _190583] : [class_Groups_Olinordered__ab__group__add(_190581), 2843 ^ _106296 : [(2844 ^ _106296) ^ [] : [c_Groups_Ozero__class_Ozero(_190581) = c_Groups_Oplus__class_Oplus(_190581, _190583, _190583), -(_190583 = c_Groups_Ozero__class_Ozero(_190581))], (2850 ^ _106296) ^ [] : [_190583 = c_Groups_Ozero__class_Ozero(_190581), -(c_Groups_Ozero__class_Ozero(_190581) = c_Groups_Oplus__class_Oplus(_190581, _190583, _190583))]]], (2856 ^ _106296) ^ [_191063, _191065] : [class_Groups_Omonoid__add(_191063), -(c_Groups_Oplus__class_Oplus(_191063, _191065, c_Groups_Ozero__class_Ozero(_191063)) = _191065)], (2862 ^ _106296) ^ [_191283, _191285] : [class_Rings_Ocomm__semiring__1(_191283), -(c_Groups_Oplus__class_Oplus(_191283, _191285, c_Groups_Ozero__class_Ozero(_191283)) = _191285)], (2868 ^ _106296) ^ [_191503, _191505] : [class_Groups_Ocomm__monoid__add(_191503), -(c_Groups_Oplus__class_Oplus(_191503, _191505, c_Groups_Ozero__class_Ozero(_191503)) = _191505)], (2874 ^ _106296) ^ [_191737, _191739, _191741] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_191737), 2877 ^ _106296 : [(2878 ^ _106296) ^ [] : [_191739 = c_Groups_Oplus__class_Oplus(_191737, _191739, _191741), -(_191741 = c_Groups_Ozero__class_Ozero(_191737))], (2884 ^ _106296) ^ [] : [_191741 = c_Groups_Ozero__class_Ozero(_191737), -(_191739 = c_Groups_Oplus__class_Oplus(_191737, _191739, _191741))]]], (2890 ^ _106296) ^ [_192257, _192259, _192261, _192263] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_192257), 2893 ^ _106296 : [(2894 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_192257, c_Groups_Oplus__class_Oplus(_192257, _192259, _192261), c_Groups_Oplus__class_Oplus(_192257, _192263, _192261)), -(c_Orderings_Oord__class_Oless(_192257, _192259, _192263))], (2900 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_192257, _192259, _192263), -(c_Orderings_Oord__class_Oless(_192257, c_Groups_Oplus__class_Oplus(_192257, _192259, _192261), c_Groups_Oplus__class_Oplus(_192257, _192263, _192261)))]]], (2906 ^ _106296) ^ [_192805, _192807, _192809, _192811] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_192805), 2909 ^ _106296 : [(2910 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_192805, c_Groups_Oplus__class_Oplus(_192805, _192807, _192809), c_Groups_Oplus__class_Oplus(_192805, _192807, _192811)), -(c_Orderings_Oord__class_Oless(_192805, _192809, _192811))], (2916 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_192805, _192809, _192811), -(c_Orderings_Oord__class_Oless(_192805, c_Groups_Oplus__class_Oplus(_192805, _192807, _192809), c_Groups_Oplus__class_Oplus(_192805, _192807, _192811)))]]], (2922 ^ _106296) ^ [_193353, _193355, _193357, _193359] : [class_Groups_Oordered__cancel__ab__semigroup__add(_193353), c_Orderings_Oord__class_Oless(_193353, _193355, _193357), -(c_Orderings_Oord__class_Oless(_193353, c_Groups_Oplus__class_Oplus(_193353, _193355, _193359), c_Groups_Oplus__class_Oplus(_193353, _193357, _193359)))], (2932 ^ _106296) ^ [_193718, _193720, _193722, _193724] : [class_Groups_Oordered__cancel__ab__semigroup__add(_193718), c_Orderings_Oord__class_Oless(_193718, _193720, _193722), -(c_Orderings_Oord__class_Oless(_193718, c_Groups_Oplus__class_Oplus(_193718, _193724, _193720), c_Groups_Oplus__class_Oplus(_193718, _193724, _193722)))], (2942 ^ _106296) ^ [_194097, _194099, _194101, _194103, _194105] : [class_Groups_Oordered__cancel__ab__semigroup__add(_194097), c_Orderings_Oord__class_Oless(_194097, _194099, _194101), c_Orderings_Oord__class_Oless(_194097, _194103, _194105), -(c_Orderings_Oord__class_Oless(_194097, c_Groups_Oplus__class_Oplus(_194097, _194099, _194103), c_Groups_Oplus__class_Oplus(_194097, _194101, _194105)))], (2956 ^ _106296) ^ [_194575, _194577, _194579, _194581] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_194575), c_Orderings_Oord__class_Oless(_194575, c_Groups_Oplus__class_Oplus(_194575, _194577, _194579), c_Groups_Oplus__class_Oplus(_194575, _194581, _194579)), -(c_Orderings_Oord__class_Oless(_194575, _194577, _194581))], (2966 ^ _106296) ^ [_194940, _194942, _194944, _194946] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_194940), c_Orderings_Oord__class_Oless(_194940, c_Groups_Oplus__class_Oplus(_194940, _194942, _194944), c_Groups_Oplus__class_Oplus(_194940, _194942, _194946)), -(c_Orderings_Oord__class_Oless(_194940, _194944, _194946))], (2976 ^ _106296) ^ [_195305, _195307, _195309, _195311] : [class_Rings_Ocomm__semiring__1(_195305), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195305), _195307), c_Groups_Oplus__class_Oplus(_195305, _195309, _195311)) = c_Groups_Oplus__class_Oplus(_195305, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195305), _195307), _195309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195305), _195307), _195311)))], (2982 ^ _106296) ^ [_195631, _195633, _195635, _195637, _195639] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_195631), 2985 ^ _106296 : [(2996 ^ _106296) ^ [] : [-(c_Groups_Oplus__class_Oplus(_195631, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195631), _195633), _195637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195631), _195635), _195639)) = c_Groups_Oplus__class_Oplus(_195631, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195631), _195633), _195639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195631), _195635), _195637))), 2999 ^ _106296 : [(3000 ^ _106296) ^ [] : [_195633 = _195635], (3002 ^ _106296) ^ [] : [_195637 = _195639]]], (2986 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_195631, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195631), _195633), _195637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195631), _195635), _195639)) = c_Groups_Oplus__class_Oplus(_195631, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195631), _195633), _195639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_195631), _195635), _195637)), -(_195633 = _195635), -(_195637 = _195639)]]], (3004 ^ _106296) ^ [_196467, _196469, _196471, _196473] : [class_Rings_Ocomm__semiring__1(_196467), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_196467), c_Groups_Oplus__class_Oplus(_196467, _196469, _196471)), _196473) = c_Groups_Oplus__class_Oplus(_196467, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_196467), _196469), _196473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_196467), _196471), _196473)))], (3010 ^ _106296) ^ [_196779, _196781, _196783, _196785] : [class_Rings_Ocomm__semiring__1(_196779), -(c_Groups_Oplus__class_Oplus(_196779, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_196779), _196781), _196783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_196779), _196785), _196783)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_196779), c_Groups_Oplus__class_Oplus(_196779, _196781, _196785)), _196783))], (3016 ^ _106296) ^ [_197105, _197107, _197109, _197111, _197113] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_197105), 3019 ^ _106296 : [(3030 ^ _106296) ^ [] : [3031 ^ _106296 : [(3032 ^ _106296) ^ [] : [_197107 = _197111], (3034 ^ _106296) ^ [] : [_197109 = _197113]], -(c_Groups_Oplus__class_Oplus(_197105, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197105), _197107), _197109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197105), _197111), _197113)) = c_Groups_Oplus__class_Oplus(_197105, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197105), _197107), _197113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197105), _197111), _197109)))], (3020 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_197105, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197105), _197107), _197109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197105), _197111), _197113)) = c_Groups_Oplus__class_Oplus(_197105, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197105), _197107), _197113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197105), _197111), _197109)), -(_197107 = _197111), -(_197109 = _197113)]]], (3038 ^ _106296) ^ [_197907, _197909] : [class_Groups_Omonoid__mult(_197907), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_197907), c_Groups_Oone__class_Oone(_197907)), _197909) = _197909)], (3044 ^ _106296) ^ [_198135, _198137] : [class_Rings_Ocomm__semiring__1(_198135), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_198135), c_Groups_Oone__class_Oone(_198135)), _198137) = _198137)], (3050 ^ _106296) ^ [_198363, _198365] : [class_Groups_Ocomm__monoid__mult(_198363), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_198363), c_Groups_Oone__class_Oone(_198363)), _198365) = _198365)], (3056 ^ _106296) ^ [_198591, _198593] : [class_Groups_Omonoid__mult(_198591), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_198591), _198593), c_Groups_Oone__class_Oone(_198591)) = _198593)], (3062 ^ _106296) ^ [_198819, _198821] : [class_Rings_Ocomm__semiring__1(_198819), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_198819), _198821), c_Groups_Oone__class_Oone(_198819)) = _198821)], (3068 ^ _106296) ^ [_199047, _199049] : [class_Groups_Ocomm__monoid__mult(_199047), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_199047), _199049), c_Groups_Oone__class_Oone(_199047)) = _199049)], (3074 ^ _106296) ^ [_199303, _199305, _199307, _199309] : [class_Rings_Ocomm__semiring__1(_199303), -(hAPP(hAPP(c_Power_Opower__class_Opower(_199303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_199303), _199305), _199307)), _199309) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_199303), hAPP(hAPP(c_Power_Opower__class_Opower(_199303), _199305), _199309)), hAPP(hAPP(c_Power_Opower__class_Opower(_199303), _199307), _199309)))], (3080 ^ _106296) ^ [_199603, _199605] : [class_Rings_Ocomm__semiring__1(_199603), -(hAPP(hAPP(c_Power_Opower__class_Opower(_199603), _199605), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _199605)], (3086 ^ _106296) ^ [_199827, _199829] : [class_Groups_Olinordered__ab__group__add(_199827), 3089 ^ _106296 : [(3090 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_199827, c_Groups_Ozero__class_Ozero(_199827), c_Groups_Oplus__class_Oplus(_199827, _199829, _199829)), -(c_Orderings_Oord__class_Oless(_199827, c_Groups_Ozero__class_Ozero(_199827), _199829))], (3096 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_199827, c_Groups_Ozero__class_Ozero(_199827), _199829), -(c_Orderings_Oord__class_Oless(_199827, c_Groups_Ozero__class_Ozero(_199827), c_Groups_Oplus__class_Oplus(_199827, _199829, _199829)))]]], (3102 ^ _106296) ^ [_200315, _200317] : [class_Groups_Olinordered__ab__group__add(_200315), 3105 ^ _106296 : [(3106 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_200315, c_Groups_Oplus__class_Oplus(_200315, _200317, _200317), c_Groups_Ozero__class_Ozero(_200315)), -(c_Orderings_Oord__class_Oless(_200315, _200317, c_Groups_Ozero__class_Ozero(_200315)))], (3112 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_200315, _200317, c_Groups_Ozero__class_Ozero(_200315)), -(c_Orderings_Oord__class_Oless(_200315, c_Groups_Oplus__class_Oplus(_200315, _200317, _200317), c_Groups_Ozero__class_Ozero(_200315)))]]], (3119 ^ _106296) ^ [] : [-(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), 3117 ^ []), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (3121 ^ _106296) ^ [_200881] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _200881, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3123 ^ _106296) ^ [] : [-(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)))], (3125 ^ _106296) ^ [] : [-(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)))], (3137 ^ _106296) ^ [_201392, _201394] : [3138 ^ _106296 : [(3139 ^ _106296) ^ [] : [_201394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3141 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _201392)]], -(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), _201392), _201394)))], (3127 ^ _106296) ^ [_201124, _201126] : [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), _201124), _201126)), -(_201126 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _201124))], (3145 ^ _106296) ^ [_201694, _201696] : [_201694 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _201694), _201696), -(_201696 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_201694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3155 ^ _106296) ^ [_202020, _202022, _202024] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _202020, _202022), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _202024), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _202024), _202020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _202024), _202022)))], (3165 ^ _106296) ^ [_202373, _202375, _202377] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _202373, _202375), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _202377), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _202373), _202377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _202375), _202377)))], (3175 ^ _106296) ^ [_202726, _202728, _202730] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _202726), 3178 ^ _106296 : [(3179 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _202726), _202728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _202726), _202730)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _202728, _202730))], (3185 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _202728, _202730), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _202726), _202728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _202726), _202730)))]]], (3191 ^ _106296) ^ [_203246, _203248] : [class_Groups_Ogroup__add(_203246), -(c_Groups_Ominus__class_Ominus(_203246, c_Groups_Ozero__class_Ozero(_203246), _203248) = c_Groups_Ouminus__class_Ouminus(_203246, _203248))], (3197 ^ _106296) ^ [_203514, _203516, _203518, _203520, _203522] : [class_Groups_Oab__group__add(_203514), c_Groups_Ominus__class_Ominus(_203514, _203516, _203518) = c_Groups_Ominus__class_Ominus(_203514, _203520, _203522), 3204 ^ _106296 : [(3205 ^ _106296) ^ [] : [_203516 = _203518, -(_203520 = _203522)], (3211 ^ _106296) ^ [] : [_203520 = _203522, -(_203516 = _203518)]]], (3217 ^ _106296) ^ [_204151, _204153, _204155] : [class_Groups_Ogroup__add(_204151), 3220 ^ _106296 : [(3221 ^ _106296) ^ [] : [c_Groups_Ouminus__class_Ouminus(_204151, _204153) = c_Groups_Ouminus__class_Ouminus(_204151, _204155), -(_204153 = _204155)], (3227 ^ _106296) ^ [] : [_204153 = _204155, -(c_Groups_Ouminus__class_Ouminus(_204151, _204153) = c_Groups_Ouminus__class_Ouminus(_204151, _204155))]]], (3233 ^ _106296) ^ [_204657, _204659, _204661] : [class_Groups_Ogroup__add(_204657), 3236 ^ _106296 : [(3237 ^ _106296) ^ [] : [c_Groups_Ouminus__class_Ouminus(_204657, _204659) = _204661, -(c_Groups_Ouminus__class_Ouminus(_204657, _204661) = _204659)], (3243 ^ _106296) ^ [] : [c_Groups_Ouminus__class_Ouminus(_204657, _204661) = _204659, -(c_Groups_Ouminus__class_Ouminus(_204657, _204659) = _204661)]]], (3249 ^ _106296) ^ [_205163, _205165, _205167] : [class_Groups_Ogroup__add(_205163), 3252 ^ _106296 : [(3253 ^ _106296) ^ [] : [_205165 = c_Groups_Ouminus__class_Ouminus(_205163, _205167), -(_205167 = c_Groups_Ouminus__class_Ouminus(_205163, _205165))], (3259 ^ _106296) ^ [] : [_205167 = c_Groups_Ouminus__class_Ouminus(_205163, _205165), -(_205165 = c_Groups_Ouminus__class_Ouminus(_205163, _205167))]]], (3265 ^ _106296) ^ [_205669, _205671, _205673] : [class_Groups_Ogroup__add(_205669), -(c_Groups_Ominus__class_Ominus(_205669, _205671, c_Groups_Ouminus__class_Ouminus(_205669, _205673)) = c_Groups_Oplus__class_Oplus(_205669, _205671, _205673))], (3271 ^ _106296) ^ [_205919, _205921, _205923] : [class_Rings_Ocomm__ring__1(_205919), -(c_Groups_Ominus__class_Ominus(_205919, _205921, _205923) = c_Groups_Oplus__class_Oplus(_205919, _205921, c_Groups_Ouminus__class_Ouminus(_205919, _205923)))], (3277 ^ _106296) ^ [_206169, _206171, _206173] : [class_Groups_Oab__group__add(_206169), -(c_Groups_Ominus__class_Ominus(_206169, _206171, _206173) = c_Groups_Oplus__class_Oplus(_206169, _206171, c_Groups_Ouminus__class_Ouminus(_206169, _206173)))], (3283 ^ _106296) ^ [_206419, _206421, _206423] : [class_Groups_Ogroup__add(_206419), -(c_Groups_Ominus__class_Ominus(_206419, _206421, _206423) = c_Groups_Oplus__class_Oplus(_206419, _206421, c_Groups_Ouminus__class_Ouminus(_206419, _206423)))], (3289 ^ _106296) ^ [_206669, _206671, _206673] : [class_Groups_Oab__group__add(_206669), -(c_Groups_Ouminus__class_Ouminus(_206669, c_Groups_Ominus__class_Ominus(_206669, _206671, _206673)) = c_Groups_Ominus__class_Ominus(_206669, _206673, _206671))], (3295 ^ _106296) ^ [_206905, _206907] : [class_Groups_Ogroup__add(_206905), -(c_Groups_Ouminus__class_Ouminus(_206905, c_Groups_Ouminus__class_Ouminus(_206905, _206907)) = _206907)], (3301 ^ _106296) ^ [_207139, _207141, _207143] : [class_Groups_Ogroup__add(_207139), 3304 ^ _106296 : [(3305 ^ _106296) ^ [] : [c_Groups_Ominus__class_Ominus(_207139, _207141, _207143) = c_Groups_Ozero__class_Ozero(_207139), -(_207141 = _207143)], (3311 ^ _106296) ^ [] : [_207141 = _207143, -(c_Groups_Ominus__class_Ominus(_207139, _207141, _207143) = c_Groups_Ozero__class_Ozero(_207139))]]], (3317 ^ _106296) ^ [_207645, _207647, _207649] : [class_Groups_Oab__group__add(_207645), 3320 ^ _106296 : [(3321 ^ _106296) ^ [] : [_207647 = _207649, -(c_Groups_Ominus__class_Ominus(_207645, _207647, _207649) = c_Groups_Ozero__class_Ozero(_207645))], (3327 ^ _106296) ^ [] : [c_Groups_Ominus__class_Ominus(_207645, _207647, _207649) = c_Groups_Ozero__class_Ozero(_207645), -(_207647 = _207649)]]], (3333 ^ _106296) ^ [_208137, _208139] : [class_Groups_Ogroup__add(_208137), -(c_Groups_Ominus__class_Ominus(_208137, _208139, _208139) = c_Groups_Ozero__class_Ozero(_208137))], (3339 ^ _106296) ^ [_208357, _208359] : [class_Groups_Ogroup__add(_208357), -(c_Groups_Ominus__class_Ominus(_208357, _208359, c_Groups_Ozero__class_Ozero(_208357)) = _208359)], (3345 ^ _106296) ^ [_208577, _208579] : [class_Groups_Olinordered__ab__group__add(_208577), 3348 ^ _106296 : [(3349 ^ _106296) ^ [] : [c_Groups_Ouminus__class_Ouminus(_208577, _208579) = _208579, -(_208579 = c_Groups_Ozero__class_Ozero(_208577))], (3355 ^ _106296) ^ [] : [_208579 = c_Groups_Ozero__class_Ozero(_208577), -(c_Groups_Ouminus__class_Ouminus(_208577, _208579) = _208579)]]], (3361 ^ _106296) ^ [_209050, _209052] : [class_Groups_Ogroup__add(_209050), 3364 ^ _106296 : [(3365 ^ _106296) ^ [] : [c_Groups_Ouminus__class_Ouminus(_209050, _209052) = c_Groups_Ozero__class_Ozero(_209050), -(_209052 = c_Groups_Ozero__class_Ozero(_209050))], (3371 ^ _106296) ^ [] : [_209052 = c_Groups_Ozero__class_Ozero(_209050), -(c_Groups_Ouminus__class_Ouminus(_209050, _209052) = c_Groups_Ozero__class_Ozero(_209050))]]], (3377 ^ _106296) ^ [_209529, _209531] : [class_Groups_Olinordered__ab__group__add(_209529), 3380 ^ _106296 : [(3381 ^ _106296) ^ [] : [_209531 = c_Groups_Ouminus__class_Ouminus(_209529, _209531), -(_209531 = c_Groups_Ozero__class_Ozero(_209529))], (3387 ^ _106296) ^ [] : [_209531 = c_Groups_Ozero__class_Ozero(_209529), -(_209531 = c_Groups_Ouminus__class_Ouminus(_209529, _209531))]]], (3393 ^ _106296) ^ [_210002, _210004] : [class_Groups_Ogroup__add(_210002), 3396 ^ _106296 : [(3397 ^ _106296) ^ [] : [c_Groups_Ozero__class_Ozero(_210002) = c_Groups_Ouminus__class_Ouminus(_210002, _210004), -(c_Groups_Ozero__class_Ozero(_210002) = _210004)], (3403 ^ _106296) ^ [] : [c_Groups_Ozero__class_Ozero(_210002) = _210004, -(c_Groups_Ozero__class_Ozero(_210002) = c_Groups_Ouminus__class_Ouminus(_210002, _210004))]]], (3409 ^ _106296) ^ [_210467] : [class_Groups_Ogroup__add(_210467), -(c_Groups_Ouminus__class_Ouminus(_210467, c_Groups_Ozero__class_Ozero(_210467)) = c_Groups_Ozero__class_Ozero(_210467))], (3415 ^ _106296) ^ [_210725, _210727, _210729, _210731, _210733] : [class_Groups_Oordered__ab__group__add(_210725), c_Groups_Ominus__class_Ominus(_210725, _210727, _210729) = c_Groups_Ominus__class_Ominus(_210725, _210731, _210733), 3422 ^ _106296 : [(3423 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_210725, _210727, _210729), -(c_Orderings_Oord__class_Oless(_210725, _210731, _210733))], (3429 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_210725, _210731, _210733), -(c_Orderings_Oord__class_Oless(_210725, _210727, _210729))]]], (3435 ^ _106296) ^ [_211368, _211370, _211372] : [class_Groups_Oordered__ab__group__add(_211368), 3438 ^ _106296 : [(3439 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_211368, c_Groups_Ouminus__class_Ouminus(_211368, _211370), c_Groups_Ouminus__class_Ouminus(_211368, _211372)), -(c_Orderings_Oord__class_Oless(_211368, _211372, _211370))], (3445 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_211368, _211372, _211370), -(c_Orderings_Oord__class_Oless(_211368, c_Groups_Ouminus__class_Ouminus(_211368, _211370), c_Groups_Ouminus__class_Ouminus(_211368, _211372)))]]], (3451 ^ _106296) ^ [_211880, _211882, _211884] : [class_Groups_Oordered__ab__group__add(_211880), 3454 ^ _106296 : [(3455 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_211880, c_Groups_Ouminus__class_Ouminus(_211880, _211882), _211884), -(c_Orderings_Oord__class_Oless(_211880, c_Groups_Ouminus__class_Ouminus(_211880, _211884), _211882))], (3461 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_211880, c_Groups_Ouminus__class_Ouminus(_211880, _211884), _211882), -(c_Orderings_Oord__class_Oless(_211880, c_Groups_Ouminus__class_Ouminus(_211880, _211882), _211884))]]], (3467 ^ _106296) ^ [_212392, _212394, _212396] : [class_Groups_Oordered__ab__group__add(_212392), 3470 ^ _106296 : [(3471 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_212392, _212394, c_Groups_Ouminus__class_Ouminus(_212392, _212396)), -(c_Orderings_Oord__class_Oless(_212392, _212396, c_Groups_Ouminus__class_Ouminus(_212392, _212394)))], (3477 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_212392, _212396, c_Groups_Ouminus__class_Ouminus(_212392, _212394)), -(c_Orderings_Oord__class_Oless(_212392, _212394, c_Groups_Ouminus__class_Ouminus(_212392, _212396)))]]], (3483 ^ _106296) ^ [_212918, _212920, _212922, _212924] : [class_RealVector_Oreal__normed__algebra(_212918), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212918), c_Groups_Ominus__class_Ominus(_212918, _212920, _212922)), _212924) = c_Groups_Ominus__class_Ominus(_212918, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212918), _212920), _212924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212918), _212922), _212924)))], (3489 ^ _106296) ^ [_213230, _213232, _213234, _213236] : [class_RealVector_Oreal__normed__algebra(_213230), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213230), c_Groups_Ominus__class_Ominus(_213230, _213232, _213234)), _213236) = c_Groups_Ominus__class_Ominus(_213230, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213230), _213232), _213236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213230), _213234), _213236)))], (3495 ^ _106296) ^ [_213542, _213544, _213546, _213548] : [class_RealVector_Oreal__normed__algebra(_213542), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213542), _213544), c_Groups_Ominus__class_Ominus(_213542, _213546, _213548)) = c_Groups_Ominus__class_Ominus(_213542, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213542), _213544), _213546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213542), _213544), _213548)))], (3501 ^ _106296) ^ [_213854, _213856, _213858, _213860] : [class_RealVector_Oreal__normed__algebra(_213854), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213854), _213856), c_Groups_Ominus__class_Ominus(_213854, _213858, _213860)) = c_Groups_Ominus__class_Ominus(_213854, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213854), _213856), _213858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_213854), _213856), _213860)))], (3507 ^ _106296) ^ [_214152, _214154, _214156] : [class_Groups_Ogroup__add(_214152), -(c_Groups_Ominus__class_Ominus(_214152, c_Groups_Oplus__class_Oplus(_214152, _214154, _214156), _214156) = _214154)], (3513 ^ _106296) ^ [_214396, _214398, _214400] : [class_Groups_Ogroup__add(_214396), -(c_Groups_Oplus__class_Oplus(_214396, c_Groups_Ominus__class_Ominus(_214396, _214398, _214400), _214400) = _214398)], (3519 ^ _106296) ^ [_214640, _214642, _214644] : [class_Rings_Oidom(_214640), 3522 ^ _106296 : [(3533 ^ _106296) ^ [] : [3534 ^ _106296 : [(3535 ^ _106296) ^ [] : [_214642 = _214644], (3537 ^ _106296) ^ [] : [_214642 = c_Groups_Ouminus__class_Ouminus(_214640, _214644)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_214640), _214642), _214642) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_214640), _214644), _214644))], (3523 ^ _106296) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_214640), _214642), _214642) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_214640), _214644), _214644), -(_214642 = _214644), -(_214642 = c_Groups_Ouminus__class_Ouminus(_214640, _214644))]]], (3541 ^ _106296) ^ [_215349, _215351, _215353] : [class_Rings_Oring(_215349), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_215349), c_Groups_Ouminus__class_Ouminus(_215349, _215351)), c_Groups_Ouminus__class_Ouminus(_215349, _215353)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_215349), _215351), _215353))], (3547 ^ _106296) ^ [_215621, _215623, _215625] : [class_Rings_Oring(_215621), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_215621), c_Groups_Ouminus__class_Ouminus(_215621, _215623)), _215625) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_215621), _215623), c_Groups_Ouminus__class_Ouminus(_215621, _215625)))], (3553 ^ _106296) ^ [_215893, _215895, _215897] : [class_RealVector_Oreal__normed__algebra(_215893), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_215893), c_Groups_Ouminus__class_Ouminus(_215893, _215895)), _215897) = c_Groups_Ouminus__class_Ouminus(_215893, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_215893), _215895), _215897)))], (3559 ^ _106296) ^ [_216165, _216167, _216169] : [class_RealVector_Oreal__normed__algebra(_216165), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216165), c_Groups_Ouminus__class_Ouminus(_216165, _216167)), _216169) = c_Groups_Ouminus__class_Ouminus(_216165, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216165), _216167), _216169)))], (3565 ^ _106296) ^ [_216437, _216439, _216441] : [class_RealVector_Oreal__normed__algebra(_216437), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216437), _216439), c_Groups_Ouminus__class_Ouminus(_216437, _216441)) = c_Groups_Ouminus__class_Ouminus(_216437, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216437), _216439), _216441)))], (3571 ^ _106296) ^ [_216709, _216711, _216713] : [class_RealVector_Oreal__normed__algebra(_216709), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216709), _216711), c_Groups_Ouminus__class_Ouminus(_216709, _216713)) = c_Groups_Ouminus__class_Ouminus(_216709, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216709), _216711), _216713)))], (3577 ^ _106296) ^ [_216981, _216983, _216985] : [class_Rings_Oring(_216981), -(c_Groups_Ouminus__class_Ouminus(_216981, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216981), _216983), _216985)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_216981), c_Groups_Ouminus__class_Ouminus(_216981, _216983)), _216985))], (3583 ^ _106296) ^ [_217253, _217255, _217257] : [class_Rings_Oring(_217253), -(c_Groups_Ouminus__class_Ouminus(_217253, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_217253), _217255), _217257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_217253), _217255), c_Groups_Ouminus__class_Ouminus(_217253, _217257)))], (3589 ^ _106296) ^ [_217525, _217527, _217529] : [class_Groups_Ogroup__add(_217525), -(c_Groups_Oplus__class_Oplus(_217525, c_Groups_Ouminus__class_Ouminus(_217525, _217527), c_Groups_Oplus__class_Oplus(_217525, _217527, _217529)) = _217529)], (3595 ^ _106296) ^ [_217775, _217777, _217779] : [class_Groups_Ogroup__add(_217775), -(c_Groups_Oplus__class_Oplus(_217775, _217777, c_Groups_Oplus__class_Oplus(_217775, c_Groups_Ouminus__class_Ouminus(_217775, _217777), _217779)) = _217779)], (3601 ^ _106296) ^ [_218025, _218027, _218029] : [class_Groups_Ogroup__add(_218025), -(c_Groups_Ouminus__class_Ouminus(_218025, c_Groups_Oplus__class_Oplus(_218025, _218027, _218029)) = c_Groups_Oplus__class_Oplus(_218025, c_Groups_Ouminus__class_Ouminus(_218025, _218029), c_Groups_Ouminus__class_Ouminus(_218025, _218027)))], (3607 ^ _106296) ^ [_218287, _218289, _218291] : [class_Groups_Oab__group__add(_218287), -(c_Groups_Ouminus__class_Ouminus(_218287, c_Groups_Oplus__class_Oplus(_218287, _218289, _218291)) = c_Groups_Oplus__class_Oplus(_218287, c_Groups_Ouminus__class_Ouminus(_218287, _218289), c_Groups_Ouminus__class_Ouminus(_218287, _218291)))], (3613 ^ _106296) ^ [_218549, _218551, _218553] : [class_RealVector_Oreal__normed__vector(_218549), -(c_RealVector_Onorm__class_Onorm(_218549, c_Groups_Ominus__class_Ominus(_218549, _218551, _218553)) = c_RealVector_Onorm__class_Onorm(_218549, c_Groups_Ominus__class_Ominus(_218549, _218553, _218551)))], (3619 ^ _106296) ^ [_218791, _218793] : [class_RealVector_Oreal__normed__vector(_218791), -(c_RealVector_Onorm__class_Onorm(_218791, c_Groups_Ouminus__class_Ouminus(_218791, _218793)) = c_RealVector_Onorm__class_Onorm(_218791, _218793))], (3625 ^ _106296) ^ [_219017, _219019] : [class_Rings_Odivision__ring__inverse__zero(_219017), -(c_Rings_Oinverse__class_Oinverse(_219017, c_Groups_Ouminus__class_Ouminus(_219017, _219019)) = c_Groups_Ouminus__class_Ouminus(_219017, c_Rings_Oinverse__class_Oinverse(_219017, _219019)))], (3631 ^ _106296) ^ [_219263, _219265, _219267] : [class_Groups_Oordered__ab__group__add(_219263), 3634 ^ _106296 : [(3635 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_219263, _219265, _219267), -(c_Orderings_Oord__class_Oless(_219263, c_Groups_Ominus__class_Ominus(_219263, _219265, _219267), c_Groups_Ozero__class_Ozero(_219263)))], (3641 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_219263, c_Groups_Ominus__class_Ominus(_219263, _219265, _219267), c_Groups_Ozero__class_Ozero(_219263)), -(c_Orderings_Oord__class_Oless(_219263, _219265, _219267))]]], (3647 ^ _106296) ^ [_219761, _219763] : [class_Rings_Olinordered__idom(_219761), 3650 ^ _106296 : [(3651 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_219761, _219763, c_Groups_Ouminus__class_Ouminus(_219761, _219763)), -(c_Orderings_Oord__class_Oless(_219761, _219763, c_Groups_Ozero__class_Ozero(_219761)))], (3657 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_219761, _219763, c_Groups_Ozero__class_Ozero(_219761)), -(c_Orderings_Oord__class_Oless(_219761, _219763, c_Groups_Ouminus__class_Ouminus(_219761, _219763)))]]], (3663 ^ _106296) ^ [_220240, _220242] : [class_Groups_Olinordered__ab__group__add(_220240), 3666 ^ _106296 : [(3667 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_220240, c_Groups_Ouminus__class_Ouminus(_220240, _220242), _220242), -(c_Orderings_Oord__class_Oless(_220240, c_Groups_Ozero__class_Ozero(_220240), _220242))], (3673 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_220240, c_Groups_Ozero__class_Ozero(_220240), _220242), -(c_Orderings_Oord__class_Oless(_220240, c_Groups_Ouminus__class_Ouminus(_220240, _220242), _220242))]]], (3679 ^ _106296) ^ [_220719, _220721] : [class_Groups_Oordered__ab__group__add(_220719), 3682 ^ _106296 : [(3683 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_220719, c_Groups_Ouminus__class_Ouminus(_220719, _220721), c_Groups_Ozero__class_Ozero(_220719)), -(c_Orderings_Oord__class_Oless(_220719, c_Groups_Ozero__class_Ozero(_220719), _220721))], (3689 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_220719, c_Groups_Ozero__class_Ozero(_220719), _220721), -(c_Orderings_Oord__class_Oless(_220719, c_Groups_Ouminus__class_Ouminus(_220719, _220721), c_Groups_Ozero__class_Ozero(_220719)))]]], (3695 ^ _106296) ^ [_221204, _221206] : [class_Groups_Oordered__ab__group__add(_221204), 3698 ^ _106296 : [(3699 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_221204, c_Groups_Ozero__class_Ozero(_221204), c_Groups_Ouminus__class_Ouminus(_221204, _221206)), -(c_Orderings_Oord__class_Oless(_221204, _221206, c_Groups_Ozero__class_Ozero(_221204)))], (3705 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_221204, _221206, c_Groups_Ozero__class_Ozero(_221204)), -(c_Orderings_Oord__class_Oless(_221204, c_Groups_Ozero__class_Ozero(_221204), c_Groups_Ouminus__class_Ouminus(_221204, _221206)))]]], (3711 ^ _106296) ^ [_221703, _221705, _221707] : [class_Groups_Ogroup__add(_221703), 3714 ^ _106296 : [(3715 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_221703, _221705, _221707) = c_Groups_Ozero__class_Ozero(_221703), -(_221707 = c_Groups_Ouminus__class_Ouminus(_221703, _221705))], (3721 ^ _106296) ^ [] : [_221707 = c_Groups_Ouminus__class_Ouminus(_221703, _221705), -(c_Groups_Oplus__class_Oplus(_221703, _221705, _221707) = c_Groups_Ozero__class_Ozero(_221703))]]], (3727 ^ _106296) ^ [_222218, _222220, _222222] : [class_Groups_Ogroup__add(_222218), c_Groups_Oplus__class_Oplus(_222218, _222220, _222222) = c_Groups_Ozero__class_Ozero(_222218), -(c_Groups_Ouminus__class_Ouminus(_222218, _222220) = _222222)], (3737 ^ _106296) ^ [_222543, _222545] : [class_Groups_Oab__group__add(_222543), -(c_Groups_Oplus__class_Oplus(_222543, c_Groups_Ouminus__class_Ouminus(_222543, _222545), _222545) = c_Groups_Ozero__class_Ozero(_222543))], (3743 ^ _106296) ^ [_222769, _222771] : [class_Groups_Ogroup__add(_222769), -(c_Groups_Oplus__class_Oplus(_222769, c_Groups_Ouminus__class_Ouminus(_222769, _222771), _222771) = c_Groups_Ozero__class_Ozero(_222769))], (3749 ^ _106296) ^ [_223009, _223011, _223013] : [class_Groups_Ogroup__add(_223009), 3752 ^ _106296 : [(3753 ^ _106296) ^ [] : [_223011 = c_Groups_Ouminus__class_Ouminus(_223009, _223013), -(c_Groups_Oplus__class_Oplus(_223009, _223011, _223013) = c_Groups_Ozero__class_Ozero(_223009))], (3759 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_223009, _223011, _223013) = c_Groups_Ozero__class_Ozero(_223009), -(_223011 = c_Groups_Ouminus__class_Ouminus(_223009, _223013))]]], (3765 ^ _106296) ^ [_223510, _223512] : [class_Groups_Ogroup__add(_223510), -(c_Groups_Oplus__class_Oplus(_223510, _223512, c_Groups_Ouminus__class_Ouminus(_223510, _223512)) = c_Groups_Ozero__class_Ozero(_223510))], (3771 ^ _106296) ^ [_223792, _223794, _223796, _223798, _223800, _223802] : [class_Rings_Oring(_223792), 3774 ^ _106296 : [(3775 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_223792, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223792), _223794), _223796), _223798) = c_Groups_Oplus__class_Oplus(_223792, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223792), _223800), _223796), _223802), -(c_Groups_Oplus__class_Oplus(_223792, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223792), c_Groups_Ominus__class_Ominus(_223792, _223794, _223800)), _223796), _223798) = _223802)], (3781 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_223792, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223792), c_Groups_Ominus__class_Ominus(_223792, _223794, _223800)), _223796), _223798) = _223802, -(c_Groups_Oplus__class_Oplus(_223792, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223792), _223794), _223796), _223798) = c_Groups_Oplus__class_Oplus(_223792, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_223792), _223800), _223796), _223802))]]], (3787 ^ _106296) ^ [_224490, _224492, _224494, _224496, _224498, _224500] : [class_Rings_Oring(_224490), 3790 ^ _106296 : [(3791 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_224490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224490), _224492), _224494), _224496) = c_Groups_Oplus__class_Oplus(_224490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224490), _224498), _224494), _224500), -(_224496 = c_Groups_Oplus__class_Oplus(_224490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224490), c_Groups_Ominus__class_Ominus(_224490, _224498, _224492)), _224494), _224500))], (3797 ^ _106296) ^ [] : [_224496 = c_Groups_Oplus__class_Oplus(_224490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224490), c_Groups_Ominus__class_Ominus(_224490, _224498, _224492)), _224494), _224500), -(c_Groups_Oplus__class_Oplus(_224490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224490), _224492), _224494), _224496) = c_Groups_Oplus__class_Oplus(_224490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224490), _224498), _224494), _224500))]]], (3803 ^ _106296) ^ [_225174, _225176, _225178, _225180, _225182] : [class_RealVector_Oreal__normed__algebra(_225174), -(c_Groups_Ominus__class_Ominus(_225174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225174), _225176), _225178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225174), _225180), _225182)) = c_Groups_Oplus__class_Oplus(_225174, c_Groups_Oplus__class_Oplus(_225174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225174), c_Groups_Ominus__class_Ominus(_225174, _225176, _225180)), c_Groups_Ominus__class_Ominus(_225174, _225178, _225182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225174), c_Groups_Ominus__class_Ominus(_225174, _225176, _225180)), _225182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225174), _225180), c_Groups_Ominus__class_Ominus(_225174, _225178, _225182))))], (3809 ^ _106296) ^ [_225578, _225580, _225582, _225584, _225586] : [class_Rings_Oring(_225578), -(c_Groups_Ominus__class_Ominus(_225578, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225578), _225580), _225582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225578), _225584), _225586)) = c_Groups_Oplus__class_Oplus(_225578, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225578), _225580), c_Groups_Ominus__class_Ominus(_225578, _225582, _225586)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225578), c_Groups_Ominus__class_Ominus(_225578, _225580, _225584)), _225586)))], (3815 ^ _106296) ^ [_225900, _225902] : [class_Rings_Oring__1__no__zero__divisors(_225900), 3818 ^ _106296 : [(3829 ^ _106296) ^ [] : [3830 ^ _106296 : [(3831 ^ _106296) ^ [] : [_225902 = c_Groups_Oone__class_Oone(_225900)], (3833 ^ _106296) ^ [] : [_225902 = c_Groups_Ouminus__class_Ouminus(_225900, c_Groups_Oone__class_Oone(_225900))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225900), _225902), _225902) = c_Groups_Oone__class_Oone(_225900))], (3819 ^ _106296) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225900), _225902), _225902) = c_Groups_Oone__class_Oone(_225900), -(_225902 = c_Groups_Oone__class_Oone(_225900)), -(_225902 = c_Groups_Ouminus__class_Ouminus(_225900, c_Groups_Oone__class_Oone(_225900)))]]], (3837 ^ _106296) ^ [_226567, _226569] : [class_Rings_Ocomm__ring__1(_226567), -(c_Groups_Ouminus__class_Ouminus(_226567, _226569) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226567), c_Groups_Ouminus__class_Ouminus(_226567, c_Groups_Oone__class_Oone(_226567))), _226569))], (3843 ^ _106296) ^ [_226807, _226809] : [class_Rings_Odivision__ring(_226807), -(_226809 = c_Groups_Ozero__class_Ozero(_226807)), -(c_Rings_Oinverse__class_Oinverse(_226807, c_Groups_Ouminus__class_Ouminus(_226807, _226809)) = c_Groups_Ouminus__class_Ouminus(_226807, c_Rings_Oinverse__class_Oinverse(_226807, _226809)))], (3853 ^ _106296) ^ [_227191, _227193, _227195, _227197, _227199, _227201] : [class_Rings_Oordered__ring(_227191), 3856 ^ _106296 : [(3857 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_227191, c_Groups_Oplus__class_Oplus(_227191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227191), _227193), _227195), _227197), c_Groups_Oplus__class_Oplus(_227191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227191), _227199), _227195), _227201)), -(c_Orderings_Oord__class_Oless(_227191, c_Groups_Oplus__class_Oplus(_227191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227191), c_Groups_Ominus__class_Ominus(_227191, _227193, _227199)), _227195), _227197), _227201))], (3863 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_227191, c_Groups_Oplus__class_Oplus(_227191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227191), c_Groups_Ominus__class_Ominus(_227191, _227193, _227199)), _227195), _227197), _227201), -(c_Orderings_Oord__class_Oless(_227191, c_Groups_Oplus__class_Oplus(_227191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227191), _227193), _227195), _227197), c_Groups_Oplus__class_Oplus(_227191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227191), _227199), _227195), _227201)))]]], (3869 ^ _106296) ^ [_227895, _227897, _227899, _227901, _227903, _227905] : [class_Rings_Oordered__ring(_227895), 3872 ^ _106296 : [(3873 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_227895, c_Groups_Oplus__class_Oplus(_227895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227895), _227897), _227899), _227901), c_Groups_Oplus__class_Oplus(_227895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227895), _227903), _227899), _227905)), -(c_Orderings_Oord__class_Oless(_227895, _227901, c_Groups_Oplus__class_Oplus(_227895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227895), c_Groups_Ominus__class_Ominus(_227895, _227903, _227897)), _227899), _227905)))], (3879 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_227895, _227901, c_Groups_Oplus__class_Oplus(_227895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227895), c_Groups_Ominus__class_Ominus(_227895, _227903, _227897)), _227899), _227905)), -(c_Orderings_Oord__class_Oless(_227895, c_Groups_Oplus__class_Oplus(_227895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227895), _227897), _227899), _227901), c_Groups_Oplus__class_Oplus(_227895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227895), _227903), _227899), _227905)))]]], (3885 ^ _106296) ^ [_228543, _228545] : [class_Rings_Oring__1(_228543), -(c_Groups_Ominus__class_Ominus(_228543, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228543), _228545), _228545), c_Groups_Oone__class_Oone(_228543)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228543), c_Groups_Oplus__class_Oplus(_228543, _228545, c_Groups_Oone__class_Oone(_228543))), c_Groups_Ominus__class_Ominus(_228543, _228545, c_Groups_Oone__class_Oone(_228543))))], (3891 ^ _106296) ^ [_228833, _228835, _228837] : [class_Rings_Odivision__ring(_228833), -(_228835 = c_Groups_Ozero__class_Ozero(_228833)), -(_228837 = c_Groups_Ozero__class_Ozero(_228833)), -(c_Groups_Ominus__class_Ominus(_228833, c_Rings_Oinverse__class_Oinverse(_228833, _228835), c_Rings_Oinverse__class_Oinverse(_228833, _228837)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228833), c_Rings_Oinverse__class_Oinverse(_228833, _228835)), c_Groups_Ominus__class_Ominus(_228833, _228837, _228835))), c_Rings_Oinverse__class_Oinverse(_228833, _228837)))], (3905 ^ _106296) ^ [_229333, _229335, _229337] : [class_Rings_Oring__1(_229333), -(hAPP(hAPP(c_Power_Opower__class_Opower(_229333), c_Groups_Ouminus__class_Ouminus(_229333, _229335)), _229337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229333), hAPP(hAPP(c_Power_Opower__class_Opower(_229333), c_Groups_Ouminus__class_Ouminus(_229333, c_Groups_Oone__class_Oone(_229333))), _229337)), hAPP(hAPP(c_Power_Opower__class_Opower(_229333), _229335), _229337)))], (3911 ^ _106296) ^ [_229641, _229643, _229645] : [3912 ^ _106296 : [(3913 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _229641, _229643))], (3915 ^ _106296) ^ [] : [hBOOL(hAPP(hAPP(_229645, _229643), _229641))]], 3918 ^ _106296 : [(3919 ^ _106296) ^ [] : [-(_229641 = _229643)], (3921 ^ _106296) ^ [] : [hBOOL(hAPP(hAPP(_229645, _229643), _229641))]], 3924 ^ _106296 : [(3925 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _229643, _229641))], (3927 ^ _106296) ^ [] : [hBOOL(hAPP(hAPP(_229645, _229643), _229641))]], -(hBOOL(hAPP(hAPP(_229645, _229643), _229641)))], (3931 ^ _106296) ^ [_230318, _230320] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _230318, _230320), _230318 = _230320], (3937 ^ _106296) ^ [_230531, _230533] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _230531, _230533), _230533 = _230531], (3943 ^ _106296) ^ [_230714] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _230714, _230714)], (3945 ^ _106296) ^ [_230822, _230824] : [-(_230822 = _230824), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _230822, _230824)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _230824, _230822))], (3965 ^ _106296) ^ [_231419, _231421] : [3966 ^ _106296 : [(3967 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _231419, _231421)], (3969 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _231421, _231419)]], _231419 = _231421], (3955 ^ _106296) ^ [_231160, _231162] : [-(_231160 = _231162), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _231160, _231162)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _231162, _231160))], (3973 ^ _106296) ^ [_231680] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _231680, _231680)], (3975 ^ _106296) ^ [_231831, _231833, _231835] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _231831, _231833) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _231835, _231833), -(_231831 = _231835)], (3981 ^ _106296) ^ [_232015, _232017, _232019] : [_232015 = _232019, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232015, _232017) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232019, _232017))], (3987 ^ _106296) ^ [_232292, _232294, _232296] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232292, _232294) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232292, _232296), -(_232294 = _232296)], (3993 ^ _106296) ^ [_232476, _232478, _232480] : [_232478 = _232480, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232476, _232478) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232476, _232480))], (3999 ^ _106296) ^ [_232709, _232711, _232713] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232709, _232711), _232713) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232709, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232711, _232713)))], (4001 ^ _106296) ^ [_232835, _232837, _232839] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232835, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232837, _232839)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232837, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232835, _232839)))], (4003 ^ _106296) ^ [_232947, _232949] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232947, _232949) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _232949, _232947))], (4005 ^ _106296) ^ [_233063, _233065, _233067] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _233063), _233065)), _233067) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _233063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _233065), _233067)))], (4007 ^ _106296) ^ [_233183, _233185] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _233183), _233185) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _233185), _233183))], (4009 ^ _106296) ^ [_233274] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _233274, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4011 ^ _106296) ^ [_233397] : [-(_233397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _233397))], (4017 ^ _106296) ^ [_233558] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _233558), _233558 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4023 ^ _106296) ^ [_233737] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _233737, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4025 ^ _106296) ^ [_233845, _233847] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _233845, _233847), _233847 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4031 ^ _106296) ^ [_234044] : [-(_234044 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _234044))], (4037 ^ _106296) ^ [_234253, _234255] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _234253, _234255) = _234253, -(_234255 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4043 ^ _106296) ^ [_234500, _234502] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _234500, _234502) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 4046 ^ _106296 : [(4047 ^ _106296) ^ [] : [-(_234500 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4049 ^ _106296) ^ [] : [-(_234502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4051 ^ _106296) ^ [_234745, _234747] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _234745, _234747) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _234745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _234747 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4061 ^ _106296) ^ [_235025] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _235025, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _235025)], (4063 ^ _106296) ^ [_235107] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _235107) = _235107)], (4065 ^ _106296) ^ [_235189] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _235189) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4067 ^ _106296) ^ [_235270] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _235270), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4079 ^ _106296) ^ [_235676, _235678] : [4080 ^ _106296 : [(4081 ^ _106296) ^ [] : [_235676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4083 ^ _106296) ^ [] : [_235678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _235676), _235678) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4069 ^ _106296) ^ [_235412, _235414] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _235412), _235414) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_235412 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_235414 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4097 ^ _106296) ^ [_236303, _236305, _236307] : [4098 ^ _106296 : [(4099 ^ _106296) ^ [] : [_236303 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4101 ^ _106296) ^ [] : [_236305 = _236307]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _236303), _236305) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _236303), _236307))], (4087 ^ _106296) ^ [_236017, _236019, _236021] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _236017), _236019) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _236017), _236021), -(_236017 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_236019 = _236021)], (4115 ^ _106296) ^ [_236950, _236952, _236954] : [4116 ^ _106296 : [(4117 ^ _106296) ^ [] : [_236952 = _236954], (4119 ^ _106296) ^ [] : [_236950 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _236950), _236952) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _236950), _236954))], (4105 ^ _106296) ^ [_236664, _236666, _236668] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _236664), _236666) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _236664), _236668), -(_236666 = _236668), -(_236664 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4133 ^ _106296) ^ [_237597, _237599, _237601] : [4134 ^ _106296 : [(4135 ^ _106296) ^ [] : [_237597 = _237601], (4137 ^ _106296) ^ [] : [_237599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _237597), _237599) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _237601), _237599))], (4123 ^ _106296) ^ [_237311, _237313, _237315] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _237311), _237313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _237315), _237313), -(_237311 = _237315), -(_237313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4141 ^ _106296) ^ [_237929, _237931, _237933] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _237929, _237931), _237933), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _237929, _237933))], (4147 ^ _106296) ^ [_238185, _238187, _238189, _238191] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _238185, _238187), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238189, _238187) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238185, _238191), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _238189, _238191))], (4157 ^ _106296) ^ [_238552, _238554, _238556, _238558] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _238552, _238554), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _238556, _238558), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238552, _238556), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238554, _238558)))], (4167 ^ _106296) ^ [_238907, _238909, _238911] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _238907, _238909), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238907, _238911), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238909, _238911)))], (4173 ^ _106296) ^ [_239157, _239159, _239161] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _239157, _239159), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _239157, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239161, _239159)))], (4179 ^ _106296) ^ [_239399, _239401, _239403] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _239399, _239401), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _239399, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239401, _239403)))], (4185 ^ _106296) ^ [_239670, _239672, _239674] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239670, _239672), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239670, _239674)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _239672, _239674))], (4191 ^ _106296) ^ [_239858, _239860, _239862] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _239860, _239862), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239858, _239860), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239858, _239862)))], (4197 ^ _106296) ^ [_240080, _240082] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240080, _240082), _240082)], (4199 ^ _106296) ^ [_240178, _240180] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240178, _240180), _240178)], (4201 ^ _106296) ^ [_240305, _240307, _240309, _240311] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _240305), _240307), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _240309), _240307), _240311)) = 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, _240305, _240309)), _240307), _240311))], (4203 ^ _106296) ^ [_240451, _240453, _240455] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240451, _240453)), _240455) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _240451), _240455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _240453), _240455)))], (4205 ^ _106296) ^ [_240587, _240589, _240591] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _240587), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240589, _240591)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _240587), _240589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _240587), _240591)))], (4207 ^ _106296) ^ [_240753, _240755] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _240753), _240755) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 4210 ^ _106296 : [(4211 ^ _106296) ^ [] : [-(_240753 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4213 ^ _106296) ^ [] : [-(_240755 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (4215 ^ _106296) ^ [_241002, _241004] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _241002), _241004) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _241002 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _241004 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (4225 ^ _106296) ^ [_241286] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _241286), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _241286)], (4227 ^ _106296) ^ [_241428, _241430] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _241428), _241430), 4230 ^ _106296 : [(4231 ^ _106296) ^ [] : [-(_241428 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4233 ^ _106296) ^ [] : [-(_241430 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (4235 ^ _106296) ^ [_241677, _241679] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _241677), _241679)), _241677 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _241679 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (4245 ^ _106296) ^ [_241961] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _241961) = _241961)], (4257 ^ _106296) ^ [_242366, _242368] : [4258 ^ _106296 : [(4259 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _242366)], (4261 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _242368)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _242366, _242368)))], (4247 ^ _106296) ^ [_242100, _242102] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _242100, _242102)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _242100)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _242102))], (4265 ^ _106296) ^ [_242695, _242697] : [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), _242695), _242697)), 4268 ^ _106296 : [(4269 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _242695))], (4271 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _242697))]]], (4273 ^ _106296) ^ [_242950, _242952] : [-(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), _242950), _242952))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _242950), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _242952)], (4283 ^ _106296) ^ [_243312, _243314, _243316] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _243312), _243314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _243312), _243316)), 4286 ^ _106296 : [(4287 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _243312))], (4289 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _243314, _243316))]]], (4291 ^ _106296) ^ [_243587, _243589, _243591] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _243587), _243589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _243587), _243591))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _243587), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _243589, _243591)], (4301 ^ _106296) ^ [_243971, _243973, _243975] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _243971), _243973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _243975), _243973)), 4304 ^ _106296 : [(4305 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _243973))], (4307 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _243971, _243975))]]], (4309 ^ _106296) ^ [_244246, _244248, _244250] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244246), _244248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244250), _244248))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _244248), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _244246, _244250)], (4319 ^ _106296) ^ [_244601, _244603, _244605] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _244601), 4322 ^ _106296 : [(4323 ^ _106296) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244601), _244603) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244601), _244605), -(_244603 = _244605)], (4329 ^ _106296) ^ [] : [_244603 = _244605, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244601), _244603) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _244601), _244605))]]], (4335 ^ _106296) ^ [_245129, _245131, _245133] : [class_Rings_Odivision__ring(_245129), -(_245131 = c_Groups_Ozero__class_Ozero(_245129)), -(_245133 = c_Groups_Ozero__class_Ozero(_245129)), -(c_Groups_Ominus__class_Ominus(_245129, c_Rings_Oinverse__class_Oinverse(_245129, _245131), c_Rings_Oinverse__class_Oinverse(_245129, _245133)) = c_Groups_Ouminus__class_Ouminus(_245129, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_245129), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_245129), c_Rings_Oinverse__class_Oinverse(_245129, _245131)), c_Groups_Ominus__class_Ominus(_245129, _245131, _245133))), c_Rings_Oinverse__class_Oinverse(_245129, _245133))))], (4349 ^ _106296) ^ [_245606, _245608] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _245606, _245608) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _245606, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _245608)))], (4351 ^ _106296) ^ [_245726, _245728] : [-(_245726 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_245728 = 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), _245726), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 4358 ^ [_245726, _245728]), _245728)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (4362 ^ _106296) ^ [_246148, _246150] : [class_Rings_Olinordered__idom(_246148), 4365 ^ _106296 : [(4366 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_246148, c_Groups_Oplus__class_Oplus(_246148, _246150, _246150), c_Groups_Ozero__class_Ozero(_246148)), -(c_Orderings_Oord__class_Oless(_246148, _246150, c_Groups_Ozero__class_Ozero(_246148)))], (4372 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_246148, _246150, c_Groups_Ozero__class_Ozero(_246148)), -(c_Orderings_Oord__class_Oless(_246148, c_Groups_Oplus__class_Oplus(_246148, _246150, _246150), c_Groups_Ozero__class_Ozero(_246148)))]]], (4378 ^ _106296) ^ [_246622] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _246622) = 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, _246622, 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, _246622, 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, _246622, 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, _246622, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (4396 ^ _106296) ^ [_247140] : [class_Power_Opower(_247140), -(c_Power_Opower__class_Opower(_247140) = c_Power_Opower_Opower(_247140, c_Groups_Oone__class_Oone(_247140), c_Groups_Otimes__class_Otimes(_247140)))], (4402 ^ _106296) ^ [_247376, _247378, _247380] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _247376, _247378), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _247376, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _247380, _247378)))], (4408 ^ _106296) ^ [_247589, _247591] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _247589, _247591) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _247589, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _247591)))], (4410 ^ _106296) ^ [_247694, _247696] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _247694, _247696) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _247694, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _247696)))], (4412 ^ _106296) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (4414 ^ _106296) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (4416 ^ _106296) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Complex_Oii))], (4418 ^ _106296) ^ [_247942] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _247942) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4420 ^ _106296) ^ [_248024] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _248024, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _248024)], (4422 ^ _106296) ^ [_248106] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _248106, _248106) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4424 ^ _106296) ^ [_248217, _248219] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _248217, _248219) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _248219, _248217) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_248217 = _248219)], (4434 ^ _106296) ^ [_248546, _248548, _248550] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _248546, _248548), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _248546, _248550), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _248550, _248548), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _248550, _248546)))], (4444 ^ _106296) ^ [_248891, _248893, _248895] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _248891, _248893), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _248891, _248895), _248893))], (4450 ^ _106296) ^ [_249118, _249120, _249122] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _249118, _249120), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _249122, _249120)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _249118, _249122))], (4452 ^ _106296) ^ [_249244, _249246, _249248] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _249244, _249246), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _249244, _249248)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _249246, _249248))], (4454 ^ _106296) ^ [_249370, _249372, _249374] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _249370, _249372), _249374) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _249370, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _249372, _249374)))], (4456 ^ _106296) ^ [_249482, _249484] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _249482, _249484), _249482) = _249484)], (4458 ^ _106296) ^ [_249584, _249586] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _249584, _249586), _249586) = _249584)], (4460 ^ _106296) ^ [_249700, _249702, _249704] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _249700, _249702)), _249704) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _249700), _249704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _249702), _249704)))], (4462 ^ _106296) ^ [_249836, _249838, _249840] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _249836), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _249838, _249840)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _249836), _249838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _249836), _249840)))], (4464 ^ _106296) ^ [_249973, _249975] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _249973), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _249975), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _249975, _249973), _249975))], (4474 ^ _106296) ^ [_250315, _250317] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _250315, _250317)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _250317, _250315))], (4480 ^ _106296) ^ [_250489, _250491] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _250491, _250489), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _250489, _250491)))], (4486 ^ _106296) ^ [_250698, _250700] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _250698, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250698, _250700)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4488 ^ _106296) ^ [_250786] : [-(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), _250786)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _250786))], (4490 ^ _106296) ^ [_250902, _250904] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _250902, _250904)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250904, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _250902, _250904)) = _250902)], (4496 ^ _106296) ^ [_251176, _251178, _251180] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _251176, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _251178, _251180)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251176, _251180), _251178))], (4502 ^ _106296) ^ [_251364, _251366, _251368] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251364, _251368), _251366), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _251364, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _251366, _251368)))], (4508 ^ _106296) ^ [_251631, _251633] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _251631, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _251633)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_251631 = _251633)], (4514 ^ _106296) ^ [_251807, _251809] : [_251807 = _251809, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _251807, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _251809)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4520 ^ _106296) ^ [_252062, _252064] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _252062, _252064) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_252064 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _252062))], (4526 ^ _106296) ^ [_252238, _252240] : [_252240 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _252238), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _252238, _252240) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4548 ^ _106296) ^ [_253038, _253040, _253042] : [-(hBOOL(hAPP(_253038, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _253040, _253042)))), 4551 ^ _106296 : [(4552 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _253040, _253042))], (4554 ^ _106296) ^ [] : [hBOOL(hAPP(_253038, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 4556 ^ _106296 : [(4557 ^ _106296) ^ [] : [-(_253040 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _253042, 4555 ^ [_253038, _253040, _253042]))], (4559 ^ _106296) ^ [] : [hBOOL(hAPP(_253038, 4555 ^ [_253038, _253040, _253042]))]]], (4532 ^ _106296) ^ [_252507, _252509, _252511] : [hBOOL(hAPP(_252507, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _252509, _252511))), 4535 ^ _106296 : [(4536 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _252509, _252511), -(hBOOL(hAPP(_252507, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4542 ^ _106296) ^ [_252839] : [_252509 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252511, _252839), -(hBOOL(hAPP(_252507, _252839)))]]], (4579 ^ _106296) ^ [_254199, _254201, _254203] : [-(hBOOL(hAPP(_254199, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _254201, _254203)))), 4582 ^ _106296 : [(4583 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _254201, _254203))], (4585 ^ _106296) ^ [] : [hBOOL(hAPP(_254199, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 4587 ^ _106296 : [(4588 ^ _106296) ^ [] : [-(_254201 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _254203, 4586 ^ [_254199, _254201, _254203]))], (4590 ^ _106296) ^ [] : [hBOOL(hAPP(_254199, 4586 ^ [_254199, _254201, _254203]))]]], (4563 ^ _106296) ^ [_253660, _253662, _253664] : [hBOOL(hAPP(_253660, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _253662, _253664))), 4566 ^ _106296 : [(4567 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _253662, _253664), -(hBOOL(hAPP(_253660, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4573 ^ _106296) ^ [_253998] : [_253662 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _253664, _253998), -(hBOOL(hAPP(_253660, _253998)))]]], (4594 ^ _106296) ^ [_254815, _254817] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _254815, _254817)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _254815), _254817))], (4600 ^ _106296) ^ [_254995, _254997] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _254995), _254997), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _254995, _254997)))], (4606 ^ _106296) ^ [_255254, _255256] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _255254, _255256), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _255256, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _255254)))], (4612 ^ _106296) ^ [_255434, _255436] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _255436, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _255434)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _255434, _255436), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (4618 ^ _106296) ^ [_255677, _255679, _255681, _255683] : [-(hAPP(hAPP(c_Power_Opower_Opower(_255677, _255679, _255681), _255683), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _255679)], (4620 ^ _106296) ^ [] : [-(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)))], (4622 ^ _106296) ^ [_255852, _255854, _255856] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _255852), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255854, _255856)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _255852), _255854)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _255852), _255856)))], (4624 ^ _106296) ^ [_255990, _255992, _255994] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _255990), _255992)), _255994) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _255990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _255992), _255994)))], (4626 ^ _106296) ^ [_256145, _256147] : [_256145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256145), _256147) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4632 ^ _106296) ^ [_256319, _256321] : [-(_256319 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256319), _256321) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _256321, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _256319, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _256321)))], (4638 ^ _106296) ^ [_256594, _256596] : [_256594 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _256596), _256594) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4644 ^ _106296) ^ [_256768, _256770] : [-(_256768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _256770), _256768) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256770), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _256770), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _256768, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (4650 ^ _106296) ^ [_257041, _257043, _257045] : [class_Power_Opower(_257041), 4653 ^ _106296 : [(4654 ^ _106296) ^ [] : [_257043 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_257041), _257045), _257043) = c_Groups_Oone__class_Oone(_257041))], (4660 ^ _106296) ^ [] : [-(_257043 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_257041), _257045), _257043) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257041), _257045), hAPP(hAPP(c_Power_Opower__class_Opower(_257041), _257045), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _257043, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (4666 ^ _106296) ^ [_257611, _257613, _257615] : [class_Groups_Omonoid__mult(_257611), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _257613), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257611), hAPP(hAPP(c_Power_Opower__class_Opower(_257611), _257615), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _257613, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _257615) = hAPP(hAPP(c_Power_Opower__class_Opower(_257611), _257615), _257613))], (4676 ^ _106296) ^ [_257976, _257978] : [class_Groups_Olinordered__ab__group__add(_257976), 4679 ^ _106296 : [(4680 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_257976, _257978, _257978) = c_Groups_Ozero__class_Ozero(_257976), -(_257978 = c_Groups_Ozero__class_Ozero(_257976))], (4686 ^ _106296) ^ [] : [_257978 = c_Groups_Ozero__class_Ozero(_257976), -(c_Groups_Oplus__class_Oplus(_257976, _257978, _257978) = c_Groups_Ozero__class_Ozero(_257976))]]], (4692 ^ _106296) ^ [_258500, _258502, _258504, _258506, _258508] : [class_Groups_Oab__group__add(_258500), -(c_Groups_Ominus__class_Ominus(_258500, c_Groups_Oplus__class_Oplus(_258500, _258502, _258504), c_Groups_Oplus__class_Oplus(_258500, _258506, _258508)) = c_Groups_Oplus__class_Oplus(_258500, c_Groups_Ominus__class_Ominus(_258500, _258502, _258506), c_Groups_Ominus__class_Ominus(_258500, _258504, _258508)))], (4698 ^ _106296) ^ [_258788, _258790, _258792] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _258788, _258790), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _258788, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _258790, _258792)))], (4704 ^ _106296) ^ [_259030, _259032, _259034] : [class_Groups_Oab__group__add(_259030), -(c_Groups_Ominus__class_Ominus(_259030, c_Groups_Ouminus__class_Ouminus(_259030, _259032), c_Groups_Ouminus__class_Ouminus(_259030, _259034)) = c_Groups_Ouminus__class_Ouminus(_259030, c_Groups_Ominus__class_Ominus(_259030, _259032, _259034)))], (4710 ^ _106296) ^ [_259278, _259280] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _259278), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _259280), 4718 ^ _106296 : [(4719 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4717 ^ [_259278, _259280]))], (4721 ^ _106296) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 4717 ^ [_259278, _259280]), _259278) = _259280)]]], (4723 ^ _106296) ^ [_259747, _259749] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _259747), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _259749), 4731 ^ _106296 : [(4732 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4730 ^ [_259747, _259749]))], (4734 ^ _106296) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 4730 ^ [_259747, _259749]), _259747) = _259749)], (4736 ^ _106296) ^ [_260251] : [-(_260251 = 4730 ^ [_259747, _259749]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _260251), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _260251), _259747) = _259749]]], (4746 ^ _106296) ^ [] : [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))], (4748 ^ _106296) ^ [_260642, _260644] : [-(c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _260642, _260644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oexpi(_260642)), c_Complex_Oexpi(_260644)))], (4750 ^ _106296) ^ [] : [-(c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (4752 ^ _106296) ^ [] : [-(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____)))], (4754 ^ _106296) ^ [_260844] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _260844) = _260844)], (4756 ^ _106296) ^ [_260925] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _260925), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _260925)], (4758 ^ _106296) ^ [_261023, _261025] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261023), _261025) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261025), _261023))], (4760 ^ _106296) ^ [_261143, _261145, _261147] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261143), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _261145, _261147)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261143), _261145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261143), _261147)))], (4762 ^ _106296) ^ [_261279, _261281, _261283] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261279), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _261281, _261283)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261279), _261281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261279), _261283)))], (4764 ^ _106296) ^ [_261401, _261403] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _261401)), _261403) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261401), _261403)))], (4766 ^ _106296) ^ [_261527, _261529, _261531] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261527), _261529)), _261531) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261529), _261531)))], (4768 ^ _106296) ^ [_261661, _261663, _261665] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _261661, _261663)), _261665) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261661), _261665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261663), _261665)))], (4770 ^ _106296) ^ [_261797, _261799, _261801] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _261797, _261799)), _261801) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261797), _261801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261799), _261801)))], (4772 ^ _106296) ^ [_261934, _261936] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _261934), 4775 ^ _106296 : [(4776 ^ _106296) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261934), _261936) = c_Groups_Oone__class_Oone(tc_Int_Oint), 4779 ^ _106296 : [(4780 ^ _106296) ^ [] : [-(_261934 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (4782 ^ _106296) ^ [] : [-(_261936 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (4784 ^ _106296) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _261934), _261936) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _261934 = c_Groups_Oone__class_Oone(tc_Int_Oint), _261936 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (4794 ^ _106296) ^ [_262586, _262588, _262590] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _262586, _262588), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _262590), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _262590), _262586), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _262590), _262588)))], (4804 ^ _106296) ^ [_262924, _262926, _262928] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _262924, _262926), _262928) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _262924, _262928), _262926))], (4806 ^ _106296) ^ [_263051, _263053] : [class_Groups_Ozero(_263051), 4809 ^ _106296 : [(4810 ^ _106296) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_263051, _263053) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_263053 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_263051)))], (4816 ^ _106296) ^ [] : [_263053 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_263051)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_263051, _263053) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4822 ^ _106296) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (4824 ^ _106296) ^ [] : [-(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))))))], (4826 ^ _106296) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (4828 ^ _106296) ^ [_263716, _263718, _263720, _263722] : [class_Rings_Olinordered__semidom(_263716), c_Orderings_Oord__class_Oless(_263716, _263718, _263720), c_Orderings_Oord__class_Oless__eq(_263716, c_Groups_Ozero__class_Ozero(_263716), _263718), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _263722), -(c_Orderings_Oord__class_Oless(_263716, hAPP(hAPP(c_Power_Opower__class_Opower(_263716), _263718), _263722), hAPP(hAPP(c_Power_Opower__class_Opower(_263716), _263720), _263722)))], (4846 ^ _106296) ^ [_264285, _264287, _264289] : [class_Rings_Ocomm__ring__1(_264285), -(c_Groups_Ominus__class_Ominus(_264285, hAPP(hAPP(c_Power_Opower__class_Opower(_264285), _264287), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_264285), _264289), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_264285), c_Groups_Ominus__class_Ominus(_264285, _264287, _264289)), c_Groups_Oplus__class_Oplus(_264285, _264287, _264289)))], (4852 ^ _106296) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p))], (4854 ^ _106296) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____))], (4856 ^ _106296) ^ [_264646] : [-(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____), _264646))))], (4858 ^ _106296) ^ [] : [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)], (4860 ^ _106296) ^ [_264783] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _264783) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _264783)))], (4862 ^ _106296) ^ [_264871] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _264871))], (4864 ^ _106296) ^ [_264950] : [-(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____), _264950))))], (4866 ^ _106296) ^ [_265050] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _265050), 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____), _265050)), v_m____))], (4872 ^ _106296) ^ [] : [-(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)))], (4874 ^ _106296) ^ [_265300] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _265300, c_Nat_OSuc(_265300)))], (4876 ^ _106296) ^ [_265410, _265412] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _265410, _265412), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_265410), c_Nat_OSuc(_265412)))], (4882 ^ _106296) ^ [_265603] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_265603)))], (4884 ^ _106296) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____))], (4886 ^ _106296) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____))], (4888 ^ _106296) ^ [] : [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))))))], (4890 ^ _106296) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4892 ^ _106296) ^ [_265951, _265953] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _265951, _265953), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _265951, _265953), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (4898 ^ _106296) ^ [_266125, _266127] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _266125, _266127), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _266125, _266127))], (4904 ^ _106296) ^ [_266378, _266380] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _266378, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _266380, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _266378, _266380))], (4910 ^ _106296) ^ [_266552, _266554] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _266552, _266554), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _266552, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _266554, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (4916 ^ _106296) ^ [_266747] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _266747), _266747) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4918 ^ _106296) ^ [_266875, _266877, _266879] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _266875, _266877), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _266877, _266875)), _266879) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_266877), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266875, _266879)))], (4924 ^ _106296) ^ [_267147, _267149, _267151] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _267147, _267149), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _267151, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _267149, _267147))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _267151, _267147), c_Nat_OSuc(_267149)))], (4930 ^ _106296) ^ [_267390, _267392] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _267390, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _267392)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _267390, _267392))], (4932 ^ _106296) ^ [_267495, _267497] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _267495, _267497) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _267495, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _267497)))], (4934 ^ _106296) ^ [_267600, _267602] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _267600, _267602)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _267600), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _267602)))], (4936 ^ _106296) ^ [_267697] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _267697)) = _267697)], (4938 ^ _106296) ^ [_267810, _267812] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _267810, _267812), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_267812), _267810) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _267812, _267810)))], (4944 ^ _106296) ^ [_268074, _268076, _268078, _268080] : [class_Rings_Olinordered__semidom(_268074), c_Orderings_Oord__class_Oless__eq(_268074, hAPP(hAPP(c_Power_Opower__class_Opower(_268074), _268076), c_Nat_OSuc(_268078)), hAPP(hAPP(c_Power_Opower__class_Opower(_268074), _268080), c_Nat_OSuc(_268078))), c_Orderings_Oord__class_Oless__eq(_268074, c_Groups_Ozero__class_Ozero(_268074), _268080), -(c_Orderings_Oord__class_Oless__eq(_268074, _268076, _268080))], (4958 ^ _106296) ^ [_268566, _268568, _268570, _268572] : [class_Rings_Olinordered__semidom(_268566), hAPP(hAPP(c_Power_Opower__class_Opower(_268566), _268568), c_Nat_OSuc(_268570)) = hAPP(hAPP(c_Power_Opower__class_Opower(_268566), _268572), c_Nat_OSuc(_268570)), c_Orderings_Oord__class_Oless__eq(_268566, c_Groups_Ozero__class_Ozero(_268566), _268568), c_Orderings_Oord__class_Oless__eq(_268566, c_Groups_Ozero__class_Ozero(_268566), _268572), -(_268568 = _268572)], (4976 ^ _106296) ^ [_269157, _269159, _269161, _269163] : [class_Rings_Olinordered__semidom(_269157), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _269159, _269161), c_Orderings_Oord__class_Oless__eq(_269157, c_Groups_Oone__class_Oone(_269157), _269163), -(c_Orderings_Oord__class_Oless__eq(_269157, hAPP(hAPP(c_Power_Opower__class_Opower(_269157), _269163), _269159), hAPP(hAPP(c_Power_Opower__class_Opower(_269157), _269163), _269161)))], (4990 ^ _106296) ^ [_269642, _269644] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _269642), _269644)), 4993 ^ _106296 : [(4994 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _269642))], (4996 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _269644))]]], (4998 ^ _106296) ^ [_269897, _269899] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _269897), _269899))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _269897), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _269899)], (5008 ^ _106296) ^ [_270259, _270261, _270263] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_270259)), _270261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_270259)), _270263)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _270261, _270263))], (5014 ^ _106296) ^ [_270463, _270465, _270467] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _270465, _270467), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_270463)), _270465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_270463)), _270467)))], (5020 ^ _106296) ^ [_270717, _270719] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _270717), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _270717), _270719)))], (5026 ^ _106296) ^ [_270971, _270973, _270975, _270977] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_270971), c_Orderings_Oord__class_Oless__eq(_270971, c_Groups_Oplus__class_Oplus(_270971, _270973, _270975), c_Groups_Oplus__class_Oplus(_270971, _270973, _270977)), -(c_Orderings_Oord__class_Oless__eq(_270971, _270975, _270977))], (5036 ^ _106296) ^ [_271336, _271338, _271340, _271342] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_271336), c_Orderings_Oord__class_Oless__eq(_271336, c_Groups_Oplus__class_Oplus(_271336, _271338, _271340), c_Groups_Oplus__class_Oplus(_271336, _271342, _271340)), -(c_Orderings_Oord__class_Oless__eq(_271336, _271338, _271342))], (5046 ^ _106296) ^ [_271715, _271717, _271719, _271721, _271723] : [class_Groups_Oordered__ab__semigroup__add(_271715), c_Orderings_Oord__class_Oless__eq(_271715, _271717, _271719), c_Orderings_Oord__class_Oless__eq(_271715, _271721, _271723), -(c_Orderings_Oord__class_Oless__eq(_271715, c_Groups_Oplus__class_Oplus(_271715, _271717, _271721), c_Groups_Oplus__class_Oplus(_271715, _271719, _271723)))], (5060 ^ _106296) ^ [_272193, _272195, _272197, _272199] : [class_Groups_Oordered__ab__semigroup__add(_272193), c_Orderings_Oord__class_Oless__eq(_272193, _272195, _272197), -(c_Orderings_Oord__class_Oless__eq(_272193, c_Groups_Oplus__class_Oplus(_272193, _272199, _272195), c_Groups_Oplus__class_Oplus(_272193, _272199, _272197)))], (5070 ^ _106296) ^ [_272558, _272560, _272562, _272564] : [class_Groups_Oordered__ab__semigroup__add(_272558), c_Orderings_Oord__class_Oless__eq(_272558, _272560, _272562), -(c_Orderings_Oord__class_Oless__eq(_272558, c_Groups_Oplus__class_Oplus(_272558, _272560, _272564), c_Groups_Oplus__class_Oplus(_272558, _272562, _272564)))], (5080 ^ _106296) ^ [_272923, _272925, _272927, _272929] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_272923), 5083 ^ _106296 : [(5084 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_272923, c_Groups_Oplus__class_Oplus(_272923, _272925, _272927), c_Groups_Oplus__class_Oplus(_272923, _272925, _272929)), -(c_Orderings_Oord__class_Oless__eq(_272923, _272927, _272929))], (5090 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_272923, _272927, _272929), -(c_Orderings_Oord__class_Oless__eq(_272923, c_Groups_Oplus__class_Oplus(_272923, _272925, _272927), c_Groups_Oplus__class_Oplus(_272923, _272925, _272929)))]]], (5096 ^ _106296) ^ [_273471, _273473, _273475, _273477] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_273471), 5099 ^ _106296 : [(5100 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_273471, c_Groups_Oplus__class_Oplus(_273471, _273473, _273475), c_Groups_Oplus__class_Oplus(_273471, _273477, _273475)), -(c_Orderings_Oord__class_Oless__eq(_273471, _273473, _273477))], (5106 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_273471, _273473, _273477), -(c_Orderings_Oord__class_Oless__eq(_273471, c_Groups_Oplus__class_Oplus(_273471, _273473, _273475), c_Groups_Oplus__class_Oplus(_273471, _273477, _273475)))]]], (5112 ^ _106296) ^ [_273961] : [c_Nat_OSuc(_273961) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5114 ^ _106296) ^ [_274040] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_274040)], (5116 ^ _106296) ^ [_274119] : [c_Nat_OSuc(_274119) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5118 ^ _106296) ^ [_274198] : [c_Nat_OSuc(_274198) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5120 ^ _106296) ^ [_274277] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_274277)], (5122 ^ _106296) ^ [_274356] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_274356)], (5124 ^ _106296) ^ [_274507, _274509, _274511, _274513, _274515] : [class_Groups_Oordered__ab__group__add(_274507), c_Groups_Ominus__class_Ominus(_274507, _274509, _274511) = c_Groups_Ominus__class_Ominus(_274507, _274513, _274515), 5131 ^ _106296 : [(5132 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_274507, _274509, _274511), -(c_Orderings_Oord__class_Oless__eq(_274507, _274513, _274515))], (5138 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_274507, _274513, _274515), -(c_Orderings_Oord__class_Oless__eq(_274507, _274509, _274511))]]], (5144 ^ _106296) ^ [_275165, _275167] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _275165, _275167), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_275165), _275167))], (5150 ^ _106296) ^ [_275335, _275337] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_275335), _275337), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _275335, _275337))], (5156 ^ _106296) ^ [_275584, _275586] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _275584, c_Nat_OSuc(_275586)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _275584, _275586))], (5162 ^ _106296) ^ [_275754, _275756] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _275754, _275756), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _275754, c_Nat_OSuc(_275756)))], (5168 ^ _106296) ^ [_276003, _276005] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_276003), _276005), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276003, _276005))], (5174 ^ _106296) ^ [_276173, _276175] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276173, _276175), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_276173), _276175))], (5180 ^ _106296) ^ [_276393, _276395] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _276393, _276395), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276393, c_Nat_OSuc(_276395)))], (5186 ^ _106296) ^ [_276611, _276613] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276611, _276613), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_276611), _276613))], (5192 ^ _106296) ^ [_276829, _276831] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _276829, _276831), 5195 ^ _106296 : [(5196 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276831, c_Nat_OSuc(_276829)), -(_276831 = _276829)], (5202 ^ _106296) ^ [] : [_276831 = _276829, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276831, c_Nat_OSuc(_276829)))]]], (5208 ^ _106296) ^ [_277300, _277302] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_277300), _277302), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _277300, _277302))], (5214 ^ _106296) ^ [_277488] : [_277488 = c_Nat_OSuc(_277488)], (5216 ^ _106296) ^ [_277567] : [c_Nat_OSuc(_277567) = _277567], (5218 ^ _106296) ^ [_277646] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_277646), _277646)], (5220 ^ _106296) ^ [_277785, _277787] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _277785, _277787)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_277787), _277785))], (5226 ^ _106296) ^ [_277958, _277960] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_277960), _277958), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _277958, _277960)], (5242 ^ _106296) ^ [_278472, _278474] : [5243 ^ _106296 : [(5244 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278472, _278474)], (5246 ^ _106296) ^ [] : [_278472 = c_Nat_OSuc(_278474)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278472, c_Nat_OSuc(_278474)))], (5232 ^ _106296) ^ [_278208, _278210] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278208, c_Nat_OSuc(_278210)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _278208, _278210)), -(_278208 = c_Nat_OSuc(_278210))], (5250 ^ _106296) ^ [_278799, _278801] : [c_Nat_OSuc(_278799) = c_Nat_OSuc(_278801), -(_278799 = _278801)], (5256 ^ _106296) ^ [_278969, _278971] : [_278969 = _278971, -(c_Nat_OSuc(_278969) = c_Nat_OSuc(_278971))], (5262 ^ _106296) ^ [_279218, _279220] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_279218), c_Nat_OSuc(_279220)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279218, _279220))], (5268 ^ _106296) ^ [_279392, _279394] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279392, _279394), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_279392), c_Nat_OSuc(_279394)))], (5274 ^ _106296) ^ [_279616, _279618] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279616, _279618), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279616, c_Nat_OSuc(_279618)))], (5280 ^ _106296) ^ [_279834, _279836] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279834, c_Nat_OSuc(_279836)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _279834, _279836)), -(_279834 = c_Nat_OSuc(_279836))], (5290 ^ _106296) ^ [_280148, _280150] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_280148), _280150), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _280148, _280150))], (5296 ^ _106296) ^ [_280366, _280368] : [c_Nat_OSuc(_280366) = c_Nat_OSuc(_280368), -(_280366 = _280368)], (5302 ^ _106296) ^ [_280613, _280615] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _280613, _280615), 5305 ^ _106296 : [(5306 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _280613, _280615))], (5308 ^ _106296) ^ [] : [_280613 = _280615]]], (5310 ^ _106296) ^ [_280855, _280857] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _280855, _280857)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _280855, _280857), -(_280855 = _280857)], (5320 ^ _106296) ^ [_281163, _281165] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _281163, _281165)), -(_281163 = _281165), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _281165, _281163))], (5330 ^ _106296) ^ [_281453, _281455] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281453, _281455) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281455, _281453))], (5332 ^ _106296) ^ [_281569, _281571, _281573] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281569, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281571, _281573)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281571, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281569, _281573)))], (5334 ^ _106296) ^ [_281695, _281697, _281699] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281695, _281697), _281699) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281695, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281697, _281699)))], (5336 ^ _106296) ^ [_281836, _281838, _281840] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _281836, _281838), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281840, _281836), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _281840, _281838)))], (5342 ^ _106296) ^ [_282100, _282102, _282104, _282106] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _282100, _282102), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _282104, _282106), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _282100, _282104), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _282102, _282106)))], (5352 ^ _106296) ^ [_282455, _282457, _282459] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _282455, _282457), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _282455, _282459), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _282457, _282459)))], (5358 ^ _106296) ^ [_282691, _282693] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _282691, _282693), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _282691, c_Groups_Oone__class_Oone(tc_Int_Oint)), _282693))], (5364 ^ _106296) ^ [_282899] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _282899), -(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), _282899)))], (5370 ^ _106296) ^ [_283130] : [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), _283130), _283130), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _283130, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5376 ^ _106296) ^ [_283306] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _283306, 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), _283306), _283306), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5382 ^ _106296) ^ [_283561, _283563] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _283561, c_Groups_Oone__class_Oone(tc_Int_Oint)), _283563), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _283561, _283563))], (5388 ^ _106296) ^ [_283735, _283737] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _283735, _283737), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _283735, c_Groups_Oone__class_Oone(tc_Int_Oint)), _283737))], (5404 ^ _106296) ^ [_284252, _284254] : [5405 ^ _106296 : [(5406 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _284252, _284254)], (5408 ^ _106296) ^ [] : [_284252 = _284254]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _284252, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _284254, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (5394 ^ _106296) ^ [_283988, _283990] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _283988, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _283990, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _283988, _283990)), -(_283988 = _283990)], (5412 ^ _106296) ^ [_284579, _284581] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _284579, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _284581, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _284579, _284581))], (5418 ^ _106296) ^ [_284753, _284755] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _284753, _284755), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _284753, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _284755, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (5424 ^ _106296) ^ [_284948] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _284948, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _284948)], (5426 ^ _106296) ^ [_285074] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _285074), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _285074))], (5432 ^ _106296) ^ [_285234] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _285234), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _285234))], (5438 ^ _106296) ^ [_285415] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _285415) = _285415)], (5440 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5442 ^ _106296) ^ [_285549] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _285549), _285549) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (5444 ^ _106296) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (5446 ^ _106296) ^ [_285716, _285718] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_285716), c_Nat_OSuc(_285718)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _285716, _285718))], (5452 ^ _106296) ^ [_285938, _285940] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_285938), _285940), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _285938, _285940))], (5458 ^ _106296) ^ [_286156, _286158] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _286156, c_Nat_OSuc(_286158)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _286156, _286158)), -(_286156 = _286158)], (5468 ^ _106296) ^ [_286480, _286482, _286484] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _286480, _286482), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _286482, _286484), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_286480), _286484))], (5478 ^ _106296) ^ [_286799, _286801] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _286799, _286801), -(c_Nat_OSuc(_286799) = _286801), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_286799), _286801))], (5488 ^ _106296) ^ [_287113, _287115] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _287113, _287115), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _287113, c_Nat_OSuc(_287115)))], (5494 ^ _106296) ^ [_287331, _287333] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _287331, _287333)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _287331, c_Nat_OSuc(_287333)), -(_287333 = _287331)], (5504 ^ _106296) ^ [_287641, _287643] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _287641, _287643)), 5507 ^ _106296 : [(5508 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _287641, c_Nat_OSuc(_287643)), -(_287641 = _287643)], (5514 ^ _106296) ^ [] : [_287641 = _287643, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _287641, c_Nat_OSuc(_287643)))]]], (5520 ^ _106296) ^ [_288144, _288146] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_288144), c_Nat_OSuc(_288146)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _288144, _288146))], (5526 ^ _106296) ^ [_288318, _288320] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _288318, _288320), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_288318), c_Nat_OSuc(_288320)))], (5542 ^ _106296) ^ [_288831, _288833] : [5543 ^ _106296 : [(5544 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _288831, _288833)], (5546 ^ _106296) ^ [] : [_288831 = _288833]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _288831, c_Nat_OSuc(_288833)))], (5532 ^ _106296) ^ [_288571, _288573] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _288571, c_Nat_OSuc(_288573)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _288571, _288573)), -(_288571 = _288573)], (5550 ^ _106296) ^ [_289154, _289156] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _289154, _289156)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _289156, c_Nat_OSuc(_289154)))], (5556 ^ _106296) ^ [_289327, _289329] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _289329, c_Nat_OSuc(_289327)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _289327, _289329)], (5562 ^ _106296) ^ [_289562, _289564, _289566] : [class_Groups_Oordered__ab__group__add(_289562), 5565 ^ _106296 : [(5566 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289562, _289564, c_Groups_Ouminus__class_Ouminus(_289562, _289566)), -(c_Orderings_Oord__class_Oless__eq(_289562, _289566, c_Groups_Ouminus__class_Ouminus(_289562, _289564)))], (5572 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289562, _289566, c_Groups_Ouminus__class_Ouminus(_289562, _289564)), -(c_Orderings_Oord__class_Oless__eq(_289562, _289564, c_Groups_Ouminus__class_Ouminus(_289562, _289566)))]]], (5578 ^ _106296) ^ [_290074, _290076, _290078] : [class_Groups_Oordered__ab__group__add(_290074), 5581 ^ _106296 : [(5582 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290074, c_Groups_Ouminus__class_Ouminus(_290074, _290076), _290078), -(c_Orderings_Oord__class_Oless__eq(_290074, c_Groups_Ouminus__class_Ouminus(_290074, _290078), _290076))], (5588 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290074, c_Groups_Ouminus__class_Ouminus(_290074, _290078), _290076), -(c_Orderings_Oord__class_Oless__eq(_290074, c_Groups_Ouminus__class_Ouminus(_290074, _290076), _290078))]]], (5594 ^ _106296) ^ [_290586, _290588, _290590] : [class_Groups_Oordered__ab__group__add(_290586), 5597 ^ _106296 : [(5598 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290586, c_Groups_Ouminus__class_Ouminus(_290586, _290588), c_Groups_Ouminus__class_Ouminus(_290586, _290590)), -(c_Orderings_Oord__class_Oless__eq(_290586, _290590, _290588))], (5604 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290586, _290590, _290588), -(c_Orderings_Oord__class_Oless__eq(_290586, c_Groups_Ouminus__class_Ouminus(_290586, _290588), c_Groups_Ouminus__class_Ouminus(_290586, _290590)))]]], (5610 ^ _106296) ^ [_291098, _291100, _291102] : [class_Groups_Oordered__ab__group__add(_291098), c_Orderings_Oord__class_Oless__eq(_291098, _291100, _291102), -(c_Orderings_Oord__class_Oless__eq(_291098, c_Groups_Ouminus__class_Ouminus(_291098, _291102), c_Groups_Ouminus__class_Ouminus(_291098, _291100)))], (5620 ^ _106296) ^ [_291406, _291408] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_291406), _291408) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _291406, c_Nat_OSuc(_291408)))], (5622 ^ _106296) ^ [_291512, _291514] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_291512), _291514) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _291512, _291514)))], (5624 ^ _106296) ^ [_291618, _291620] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _291618, c_Nat_OSuc(_291620)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _291618, _291620)))], (5626 ^ _106296) ^ [_291710] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _291710))], (5628 ^ _106296) ^ [_291833] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _291833, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_291833 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5634 ^ _106296) ^ [_291991] : [_291991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _291991, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5640 ^ _106296) ^ [_292242, _292244, _292246] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_292242)), _292244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_292242)), _292246), -(_292244 = _292246)], (5646 ^ _106296) ^ [_292442, _292444, _292446] : [_292444 = _292446, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_292442)), _292444) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_292442)), _292446))], (5652 ^ _106296) ^ [_292691, _292693, _292695] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_292691), _292693), c_Nat_OSuc(_292695)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _292691, _292693), _292695))], (5654 ^ _106296) ^ [_292807, _292809] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_292807), c_Nat_OSuc(_292809)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _292807, _292809))], (5656 ^ _106296) ^ [_292928, _292930] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292928, _292930), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _292928, _292930))], (5662 ^ _106296) ^ [_293142, _293144] : [5663 ^ _106296 : [(5664 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293142, _293144)], (5666 ^ _106296) ^ [] : [_293142 = _293144]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _293142, _293144))], (5670 ^ _106296) ^ [_293430, _293432] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _293430, _293432), -(_293430 = _293432), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293430, _293432))], (5680 ^ _106296) ^ [_293736, _293738] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293736, _293738), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _293736, _293738))], (5696 ^ _106296) ^ [_294235, _294237] : [5697 ^ _106296 : [(5698 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _294235, _294237)], (5700 ^ _106296) ^ [] : [_294235 = _294237]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _294235, _294237))], (5686 ^ _106296) ^ [_293979, _293981] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _293979, _293981), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293979, _293981)), -(_293979 = _293981)], (5704 ^ _106296) ^ [_294554, _294556] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _294554, _294556), 5707 ^ _106296 : [(5708 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _294554, _294556))], (5710 ^ _106296) ^ [] : [_294554 = _294556]]], (5712 ^ _106296) ^ [_294796, _294798] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _294796, _294798)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _294796, _294798), -(_294796 = _294798)], (5722 ^ _106296) ^ [_295133, _295135] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _295133, _295135), 5725 ^ _106296 : [(5726 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _295133, _295135))], (5728 ^ _106296) ^ [] : [_295133 = _295135]]], (5730 ^ _106296) ^ [_295375, _295377] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _295375, _295377)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _295375, _295377), -(_295375 = _295377)], (5750 ^ _106296) ^ [_295968, _295970] : [5751 ^ _106296 : [(5752 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _295968, _295970)], (5754 ^ _106296) ^ [] : [_295968 = _295970]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _295968, _295970))], (5740 ^ _106296) ^ [_295712, _295714] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _295712, _295714), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _295712, _295714)), -(_295712 = _295714)], (5758 ^ _106296) ^ [_296272, _296274, _296276] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296272, _296274), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296272, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _296274, _296276)))], (5764 ^ _106296) ^ [_296514, _296516, _296518] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296514, _296516), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296514, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _296518, _296516)))], (5770 ^ _106296) ^ [_296756, _296758, _296760] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _296756, _296758), _296760), 5773 ^ _106296 : [(5774 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296756, _296760))], (5776 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296758, _296760))]]], (5778 ^ _106296) ^ [_297081, _297083, _297085] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _297081, _297083), _297085), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297081, _297085))], (5784 ^ _106296) ^ [_297323, _297325, _297327] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _297323, _297325), _297327), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297325, _297327))], (5790 ^ _106296) ^ [_297579, _297581, _297583, _297585] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297579, _297581), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297583, _297585), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _297579, _297583), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _297581, _297585)))], (5800 ^ _106296) ^ [_297934, _297936, _297938] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297934, _297936), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _297934, _297938), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _297936, _297938)))], (5806 ^ _106296) ^ [_298184, _298186, _298188] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _298184, _298186), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _298184, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _298188, _298186)))], (5812 ^ _106296) ^ [_298426, _298428, _298430] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _298426, _298428), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _298426, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _298428, _298430)))], (5818 ^ _106296) ^ [_298697, _298699, _298701] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _298697, _298699), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _298697, _298701)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _298699, _298701))], (5824 ^ _106296) ^ [_298885, _298887, _298889] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _298887, _298889), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _298885, _298887), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _298885, _298889)))], (5830 ^ _106296) ^ [_299152, _299154] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _299152, _299154), -(_299154 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _299152, 5833 ^ [_299152, _299154]))], (5837 ^ _106296) ^ [_299385, _299387] : [5838 ^ _106296 : [(5839 ^ _106296) ^ [_299460] : [_299387 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _299385, _299460)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _299385, _299387))], (5843 ^ _106296) ^ [_299614, _299616] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _299614, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _299614, _299616)))], (5845 ^ _106296) ^ [_299713, _299715] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _299713, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _299715, _299713)))], (5847 ^ _106296) ^ [_299798] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _299798, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _299798), _299798)))], (5849 ^ _106296) ^ [_299883] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _299883, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _299883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _299883), _299883))))], (5851 ^ _106296) ^ [_300017, _300019, _300021] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _300017, _300019), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _300017), _300021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _300019), _300021)))], (5857 ^ _106296) ^ [_300275, _300277, _300279] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _300275, _300277), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _300279), _300275), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _300279), _300277)))], (5863 ^ _106296) ^ [_300547, _300549, _300551, _300553] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _300547, _300549), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _300551, _300553), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _300547), _300551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _300549), _300553)))], (5873 ^ _106296) ^ [_300910, _300912, _300914] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _300910, _300912), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _300910, _300914), 5880 ^ _106296 : [(5881 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _300912, _300910), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _300914, _300910)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _300912, _300914))], (5887 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _300912, _300914), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _300912, _300910), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _300914, _300910)))]]], (5893 ^ _106296) ^ [_301527, _301529, _301531] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _301527, _301529), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _301527, _301531), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _301529, _301527), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _301531, _301527)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _301529, _301531))], (5903 ^ _106296) ^ [_301886, _301888, _301890] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _301886, _301888), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _301886, _301890), 5910 ^ _106296 : [(5911 ^ _106296) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _301888, _301886) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _301890, _301886), -(_301888 = _301890)], (5917 ^ _106296) ^ [] : [_301888 = _301890, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _301888, _301886) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _301890, _301886))]]], (5923 ^ _106296) ^ [_302483, _302485] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _302483, _302485), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _302485, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _302485, _302483)) = _302483)], (5929 ^ _106296) ^ [_302725, _302727, _302729] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _302725, _302727), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _302725, _302729), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _302727, _302729)))], (5935 ^ _106296) ^ [_302975, _302977, _302979] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _302975, _302977), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _302979, _302977), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _302979, _302975)))], (5941 ^ _106296) ^ [_303196, _303198] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _303196, _303198), _303196))], (5943 ^ _106296) ^ [_303324, _303326, _303328] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _303324, _303326), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _303328, _303324), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _303328, _303326)))], (5949 ^ _106296) ^ [_303574, _303576, _303578] : [class_Rings_Olinordered__semidom(_303574), c_Orderings_Oord__class_Oless__eq(_303574, c_Groups_Ozero__class_Ozero(_303574), _303576), c_Orderings_Oord__class_Oless__eq(_303574, _303576, c_Groups_Oone__class_Oone(_303574)), -(c_Orderings_Oord__class_Oless__eq(_303574, hAPP(hAPP(c_Power_Opower__class_Opower(_303574), _303576), c_Nat_OSuc(_303578)), _303576))], (5963 ^ _106296) ^ [_304036, _304038, _304040, _304042] : [class_Rings_Olinordered__semidom(_304036), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _304038, _304040), c_Orderings_Oord__class_Oless__eq(_304036, c_Groups_Ozero__class_Ozero(_304036), _304042), c_Orderings_Oord__class_Oless__eq(_304036, _304042, c_Groups_Oone__class_Oone(_304036)), -(c_Orderings_Oord__class_Oless__eq(_304036, hAPP(hAPP(c_Power_Opower__class_Opower(_304036), _304042), _304040), hAPP(hAPP(c_Power_Opower__class_Opower(_304036), _304042), _304038)))], (5981 ^ _106296) ^ [_304623, _304625, _304627, _304629] : [class_Rings_Olinordered__semidom(_304623), c_Orderings_Oord__class_Oless(_304623, c_Groups_Oone__class_Oone(_304623), _304625), 5988 ^ _106296 : [(5989 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_304623, hAPP(hAPP(c_Power_Opower__class_Opower(_304623), _304625), _304627), hAPP(hAPP(c_Power_Opower__class_Opower(_304623), _304625), _304629)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _304627, _304629))], (5995 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _304627, _304629), -(c_Orderings_Oord__class_Oless__eq(_304623, hAPP(hAPP(c_Power_Opower__class_Opower(_304623), _304625), _304627), hAPP(hAPP(c_Power_Opower__class_Opower(_304623), _304625), _304629)))]]], (6001 ^ _106296) ^ [_305298, _305300, _305302, _305304] : [class_Rings_Olinordered__semidom(_305298), c_Orderings_Oord__class_Oless(_305298, c_Groups_Oone__class_Oone(_305298), _305300), c_Orderings_Oord__class_Oless__eq(_305298, hAPP(hAPP(c_Power_Opower__class_Opower(_305298), _305300), _305302), hAPP(hAPP(c_Power_Opower__class_Opower(_305298), _305300), _305304)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _305302, _305304))], (6015 ^ _106296) ^ [_305782, _305784, _305786, _305788] : [class_Groups_Omonoid__mult(_305782), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _305784, _305786), -(hAPP(hAPP(c_Power_Opower__class_Opower(_305782), _305788), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_305786), _305784)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305782), hAPP(hAPP(c_Power_Opower__class_Opower(_305782), _305788), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _305786, _305784))), _305788))], (6025 ^ _106296) ^ [_306197, _306199, _306201, _306203] : [class_Rings_Ocomm__ring__1(_306197), -(hAPP(c_Polynomial_Opoly(_306197, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_306197)), c_Polynomial_Omonom(_306197, c_Groups_Oone__class_Oone(_306197), _306199)), _306201)), _306203) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_306197), hAPP(hAPP(c_Power_Opower__class_Opower(_306197), _306203), _306199)), hAPP(c_Polynomial_Opoly(_306197, _306201), _306203)))], (6031 ^ _106296) ^ [_306532, _306534, _306536, _306538, _306540] : [-(hAPP(hAPP(c_Power_Opower_Opower(_306532, _306534, _306536), _306538), c_Nat_OSuc(_306540)) = hAPP(hAPP(_306536, _306538), hAPP(hAPP(c_Power_Opower_Opower(_306532, _306534, _306536), _306538), _306540)))], (6033 ^ _106296) ^ [_306675, _306677] : [class_Rings_Olinordered__ring(_306675), -(c_Orderings_Oord__class_Oless__eq(_306675, c_Groups_Ozero__class_Ozero(_306675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_306675), _306677), _306677)))], (6039 ^ _106296) ^ [_306919, _306921, _306923] : [class_Rings_Olinordered__ring__strict(_306919), 6042 ^ _106296 : [(6043 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_306919, c_Groups_Ozero__class_Ozero(_306919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_306919), _306921), _306923)), 6048 ^ _106296 : [(6049 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_306919, c_Groups_Ozero__class_Ozero(_306919), _306921))], (6051 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_306919, c_Groups_Ozero__class_Ozero(_306919), _306923))]], 6052 ^ _106296 : [(6053 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_306919, _306921, c_Groups_Ozero__class_Ozero(_306919)))], (6055 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_306919, _306923, c_Groups_Ozero__class_Ozero(_306919)))]]], (6057 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_306919, c_Groups_Ozero__class_Ozero(_306919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_306919), _306921), _306923))), 6058 ^ _106296 : [(6059 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_306919, c_Groups_Ozero__class_Ozero(_306919), _306921), c_Orderings_Oord__class_Oless__eq(_306919, c_Groups_Ozero__class_Ozero(_306919), _306923)], (6065 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_306919, _306921, c_Groups_Ozero__class_Ozero(_306919)), c_Orderings_Oord__class_Oless__eq(_306919, _306923, c_Groups_Ozero__class_Ozero(_306919))]]]]], (6073 ^ _106296) ^ [_307968, _307970, _307972] : [class_Rings_Olinordered__ring__strict(_307968), 6076 ^ _106296 : [(6077 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_307968, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307968), _307970), _307972), c_Groups_Ozero__class_Ozero(_307968)), 6082 ^ _106296 : [(6083 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_307968, c_Groups_Ozero__class_Ozero(_307968), _307970))], (6085 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_307968, _307972, c_Groups_Ozero__class_Ozero(_307968)))]], 6086 ^ _106296 : [(6087 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_307968, _307970, c_Groups_Ozero__class_Ozero(_307968)))], (6089 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_307968, c_Groups_Ozero__class_Ozero(_307968), _307972))]]], (6091 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_307968, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307968), _307970), _307972), c_Groups_Ozero__class_Ozero(_307968))), 6092 ^ _106296 : [(6093 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_307968, c_Groups_Ozero__class_Ozero(_307968), _307970), c_Orderings_Oord__class_Oless__eq(_307968, _307972, c_Groups_Ozero__class_Ozero(_307968))], (6099 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_307968, _307970, c_Groups_Ozero__class_Ozero(_307968)), c_Orderings_Oord__class_Oless__eq(_307968, c_Groups_Ozero__class_Ozero(_307968), _307972)]]]]], (6107 ^ _106296) ^ [_309017, _309019, _309021] : [class_Rings_Oordered__cancel__semiring(_309017), c_Orderings_Oord__class_Oless__eq(_309017, c_Groups_Ozero__class_Ozero(_309017), _309019), c_Orderings_Oord__class_Oless__eq(_309017, c_Groups_Ozero__class_Ozero(_309017), _309021), -(c_Orderings_Oord__class_Oless__eq(_309017, c_Groups_Ozero__class_Ozero(_309017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309017), _309019), _309021)))], (6121 ^ _106296) ^ [_309465, _309467, _309469] : [class_Rings_Oordered__cancel__semiring(_309465), c_Orderings_Oord__class_Oless__eq(_309465, c_Groups_Ozero__class_Ozero(_309465), _309467), c_Orderings_Oord__class_Oless__eq(_309465, _309469, c_Groups_Ozero__class_Ozero(_309465)), -(c_Orderings_Oord__class_Oless__eq(_309465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309465), _309467), _309469), c_Groups_Ozero__class_Ozero(_309465)))], (6135 ^ _106296) ^ [_309913, _309915, _309917] : [class_Rings_Oordered__cancel__semiring(_309913), c_Orderings_Oord__class_Oless__eq(_309913, c_Groups_Ozero__class_Ozero(_309913), _309915), c_Orderings_Oord__class_Oless__eq(_309913, _309917, c_Groups_Ozero__class_Ozero(_309913)), -(c_Orderings_Oord__class_Oless__eq(_309913, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309913), _309917), _309915), c_Groups_Ozero__class_Ozero(_309913)))], (6149 ^ _106296) ^ [_310361, _310363, _310365] : [class_Rings_Oordered__cancel__semiring(_310361), c_Orderings_Oord__class_Oless__eq(_310361, _310363, c_Groups_Ozero__class_Ozero(_310361)), c_Orderings_Oord__class_Oless__eq(_310361, c_Groups_Ozero__class_Ozero(_310361), _310365), -(c_Orderings_Oord__class_Oless__eq(_310361, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310361), _310363), _310365), c_Groups_Ozero__class_Ozero(_310361)))], (6163 ^ _106296) ^ [_310809, _310811, _310813] : [class_Rings_Oordered__ring(_310809), c_Orderings_Oord__class_Oless__eq(_310809, _310811, c_Groups_Ozero__class_Ozero(_310809)), c_Orderings_Oord__class_Oless__eq(_310809, _310813, c_Groups_Ozero__class_Ozero(_310809)), -(c_Orderings_Oord__class_Oless__eq(_310809, c_Groups_Ozero__class_Ozero(_310809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310809), _310811), _310813)))], (6177 ^ _106296) ^ [_311271, _311273, _311275, _311277] : [class_Rings_Oordered__semiring(_311271), c_Orderings_Oord__class_Oless__eq(_311271, _311273, _311275), c_Orderings_Oord__class_Oless__eq(_311271, c_Groups_Ozero__class_Ozero(_311271), _311277), -(c_Orderings_Oord__class_Oless__eq(_311271, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311271), _311273), _311277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311271), _311275), _311277)))], (6191 ^ _106296) ^ [_311755, _311757, _311759, _311761] : [class_Rings_Oordered__semiring(_311755), c_Orderings_Oord__class_Oless__eq(_311755, _311757, _311759), c_Orderings_Oord__class_Oless__eq(_311755, c_Groups_Ozero__class_Ozero(_311755), _311761), -(c_Orderings_Oord__class_Oless__eq(_311755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311755), _311761), _311757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311755), _311761), _311759)))], (6205 ^ _106296) ^ [_312239, _312241, _312243, _312245] : [class_Rings_Oordered__comm__semiring(_312239), c_Orderings_Oord__class_Oless__eq(_312239, _312241, _312243), c_Orderings_Oord__class_Oless__eq(_312239, c_Groups_Ozero__class_Ozero(_312239), _312245), -(c_Orderings_Oord__class_Oless__eq(_312239, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312239), _312245), _312241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312239), _312245), _312243)))], (6219 ^ _106296) ^ [_312723, _312725, _312727, _312729] : [class_Rings_Oordered__ring(_312723), c_Orderings_Oord__class_Oless__eq(_312723, _312725, _312727), c_Orderings_Oord__class_Oless__eq(_312723, _312729, c_Groups_Ozero__class_Ozero(_312723)), -(c_Orderings_Oord__class_Oless__eq(_312723, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312723), _312727), _312729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312723), _312725), _312729)))], (6233 ^ _106296) ^ [_313207, _313209, _313211, _313213] : [class_Rings_Oordered__ring(_313207), c_Orderings_Oord__class_Oless__eq(_313207, _313209, _313211), c_Orderings_Oord__class_Oless__eq(_313207, _313213, c_Groups_Ozero__class_Ozero(_313207)), -(c_Orderings_Oord__class_Oless__eq(_313207, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313207), _313213), _313211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313207), _313213), _313209)))], (6247 ^ _106296) ^ [_313705, _313707, _313709, _313711, _313713] : [class_Rings_Oordered__semiring(_313705), c_Orderings_Oord__class_Oless__eq(_313705, _313707, _313709), c_Orderings_Oord__class_Oless__eq(_313705, _313711, _313713), c_Orderings_Oord__class_Oless__eq(_313705, c_Groups_Ozero__class_Ozero(_313705), _313707), c_Orderings_Oord__class_Oless__eq(_313705, c_Groups_Ozero__class_Ozero(_313705), _313711), -(c_Orderings_Oord__class_Oless__eq(_313705, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313705), _313707), _313711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313705), _313709), _313713)))], (6269 ^ _106296) ^ [_314427, _314429, _314431, _314433, _314435] : [class_Rings_Oordered__semiring(_314427), c_Orderings_Oord__class_Oless__eq(_314427, _314429, _314431), c_Orderings_Oord__class_Oless__eq(_314427, _314433, _314435), c_Orderings_Oord__class_Oless__eq(_314427, c_Groups_Ozero__class_Ozero(_314427), _314431), c_Orderings_Oord__class_Oless__eq(_314427, c_Groups_Ozero__class_Ozero(_314427), _314433), -(c_Orderings_Oord__class_Oless__eq(_314427, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314427), _314429), _314433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314427), _314431), _314435)))], (6291 ^ _106296) ^ [_315121, _315123, _315125] : [class_Rings_Oordered__ring(_315121), -(c_Orderings_Oord__class_Oless__eq(_315121, c_Groups_Ozero__class_Ozero(_315121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315121), _315123), _315125))), 6296 ^ _106296 : [(6297 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_315121, c_Groups_Ozero__class_Ozero(_315121), _315123), c_Orderings_Oord__class_Oless__eq(_315121, c_Groups_Ozero__class_Ozero(_315121), _315125)], (6303 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_315121, _315123, c_Groups_Ozero__class_Ozero(_315121)), c_Orderings_Oord__class_Oless__eq(_315121, _315125, c_Groups_Ozero__class_Ozero(_315121))]]], (6311 ^ _106296) ^ [_315750, _315752, _315754] : [class_Rings_Oordered__cancel__semiring(_315750), -(c_Orderings_Oord__class_Oless__eq(_315750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315750), _315752), _315754), c_Groups_Ozero__class_Ozero(_315750))), 6316 ^ _106296 : [(6317 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_315750, c_Groups_Ozero__class_Ozero(_315750), _315752), c_Orderings_Oord__class_Oless__eq(_315750, _315754, c_Groups_Ozero__class_Ozero(_315750))], (6323 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_315750, _315752, c_Groups_Ozero__class_Ozero(_315750)), c_Orderings_Oord__class_Oless__eq(_315750, c_Groups_Ozero__class_Ozero(_315750), _315754)]]], (6331 ^ _106296) ^ [_316365, _316367] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_316365), c_Groups_Ozero__class_Ozero(_316365)), c_Nat_OSuc(_316367)) = c_Groups_Ozero__class_Ozero(_316365)), class_Power_Opower(_316365), class_Rings_Osemiring__0(_316365)], (6341 ^ _106296) ^ [_316688, _316690] : [class_Groups_Olinordered__ab__group__add(_316688), 6344 ^ _106296 : [(6345 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_316688, c_Groups_Ozero__class_Ozero(_316688), c_Groups_Oplus__class_Oplus(_316688, _316690, _316690)), -(c_Orderings_Oord__class_Oless__eq(_316688, c_Groups_Ozero__class_Ozero(_316688), _316690))], (6351 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_316688, c_Groups_Ozero__class_Ozero(_316688), _316690), -(c_Orderings_Oord__class_Oless__eq(_316688, c_Groups_Ozero__class_Ozero(_316688), c_Groups_Oplus__class_Oplus(_316688, _316690, _316690)))]]], (6357 ^ _106296) ^ [_317176, _317178] : [class_Groups_Olinordered__ab__group__add(_317176), 6360 ^ _106296 : [(6361 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_317176, c_Groups_Oplus__class_Oplus(_317176, _317178, _317178), c_Groups_Ozero__class_Ozero(_317176)), -(c_Orderings_Oord__class_Oless__eq(_317176, _317178, c_Groups_Ozero__class_Ozero(_317176)))], (6367 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_317176, _317178, c_Groups_Ozero__class_Ozero(_317176)), -(c_Orderings_Oord__class_Oless__eq(_317176, c_Groups_Oplus__class_Oplus(_317176, _317178, _317178), c_Groups_Ozero__class_Ozero(_317176)))]]], (6373 ^ _106296) ^ [_317678, _317680, _317682] : [class_Groups_Oordered__comm__monoid__add(_317678), c_Orderings_Oord__class_Oless__eq(_317678, c_Groups_Ozero__class_Ozero(_317678), _317680), c_Orderings_Oord__class_Oless__eq(_317678, c_Groups_Ozero__class_Ozero(_317678), _317682), -(c_Orderings_Oord__class_Oless__eq(_317678, c_Groups_Ozero__class_Ozero(_317678), c_Groups_Oplus__class_Oplus(_317678, _317680, _317682)))], (6387 ^ _106296) ^ [_318118, _318120, _318122] : [class_Groups_Oordered__comm__monoid__add(_318118), c_Orderings_Oord__class_Oless__eq(_318118, c_Groups_Ozero__class_Ozero(_318118), _318120), c_Orderings_Oord__class_Oless__eq(_318118, c_Groups_Ozero__class_Ozero(_318118), _318122), 6398 ^ _106296 : [(6399 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(_318118, _318120, _318122) = c_Groups_Ozero__class_Ozero(_318118), 6402 ^ _106296 : [(6403 ^ _106296) ^ [] : [-(_318120 = c_Groups_Ozero__class_Ozero(_318118))], (6405 ^ _106296) ^ [] : [-(_318122 = c_Groups_Ozero__class_Ozero(_318118))]]], (6407 ^ _106296) ^ [] : [-(c_Groups_Oplus__class_Oplus(_318118, _318120, _318122) = c_Groups_Ozero__class_Ozero(_318118)), _318120 = c_Groups_Ozero__class_Ozero(_318118), _318122 = c_Groups_Ozero__class_Ozero(_318118)]]], (6417 ^ _106296) ^ [_319012, _319014, _319016, _319018] : [class_Groups_Oordered__comm__monoid__add(_319012), c_Orderings_Oord__class_Oless__eq(_319012, c_Groups_Ozero__class_Ozero(_319012), _319014), c_Orderings_Oord__class_Oless__eq(_319012, _319016, _319018), -(c_Orderings_Oord__class_Oless__eq(_319012, _319016, c_Groups_Oplus__class_Oplus(_319012, _319014, _319018)))], (6431 ^ _106296) ^ [_319472, _319474, _319476, _319478] : [class_Groups_Oordered__comm__monoid__add(_319472), c_Orderings_Oord__class_Oless__eq(_319472, c_Groups_Ozero__class_Ozero(_319472), _319474), c_Orderings_Oord__class_Oless__eq(_319472, _319476, _319478), -(c_Orderings_Oord__class_Oless__eq(_319472, _319476, c_Groups_Oplus__class_Oplus(_319472, _319478, _319474)))], (6445 ^ _106296) ^ [_319918, _319920, _319922] : [class_Groups_Oordered__comm__monoid__add(_319918), c_Orderings_Oord__class_Oless__eq(_319918, _319920, c_Groups_Ozero__class_Ozero(_319918)), c_Orderings_Oord__class_Oless__eq(_319918, _319922, c_Groups_Ozero__class_Ozero(_319918)), -(c_Orderings_Oord__class_Oless__eq(_319918, c_Groups_Oplus__class_Oplus(_319918, _319920, _319922), c_Groups_Ozero__class_Ozero(_319918)))], (6459 ^ _106296) ^ [_320330] : [class_Rings_Olinordered__semidom(_320330), c_Orderings_Oord__class_Oless__eq(_320330, c_Groups_Oone__class_Oone(_320330), c_Groups_Ozero__class_Ozero(_320330))], (6465 ^ _106296) ^ [_320529] : [class_Rings_Olinordered__semidom(_320529), -(c_Orderings_Oord__class_Oless__eq(_320529, c_Groups_Ozero__class_Ozero(_320529), c_Groups_Oone__class_Oone(_320529)))], (6471 ^ _106296) ^ [_320783, _320785, _320787, _320789, _320791] : [class_Groups_Oordered__cancel__ab__semigroup__add(_320783), c_Orderings_Oord__class_Oless(_320783, _320785, _320787), c_Orderings_Oord__class_Oless__eq(_320783, _320789, _320791), -(c_Orderings_Oord__class_Oless(_320783, c_Groups_Oplus__class_Oplus(_320783, _320785, _320789), c_Groups_Oplus__class_Oplus(_320783, _320787, _320791)))], (6485 ^ _106296) ^ [_321275, _321277, _321279, _321281, _321283] : [class_Groups_Oordered__cancel__ab__semigroup__add(_321275), c_Orderings_Oord__class_Oless__eq(_321275, _321277, _321279), c_Orderings_Oord__class_Oless(_321275, _321281, _321283), -(c_Orderings_Oord__class_Oless(_321275, c_Groups_Oplus__class_Oplus(_321275, _321277, _321281), c_Groups_Oplus__class_Oplus(_321275, _321279, _321283)))], (6499 ^ _106296) ^ [_321739, _321741, _321743] : [class_Groups_Oordered__ab__group__add(_321739), 6502 ^ _106296 : [(6503 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321739, _321741, _321743), -(c_Orderings_Oord__class_Oless__eq(_321739, c_Groups_Ominus__class_Ominus(_321739, _321741, _321743), c_Groups_Ozero__class_Ozero(_321739)))], (6509 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321739, c_Groups_Ominus__class_Ominus(_321739, _321741, _321743), c_Groups_Ozero__class_Ozero(_321739)), -(c_Orderings_Oord__class_Oless__eq(_321739, _321741, _321743))]]], (6515 ^ _106296) ^ [_322251, _322253, _322255] : [class_Rings_Ocomm__semiring__1(_322251), -(hAPP(hAPP(c_Power_Opower__class_Opower(_322251), _322253), c_Nat_OSuc(_322255)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322251), _322253), hAPP(hAPP(c_Power_Opower__class_Opower(_322251), _322253), _322255)))], (6521 ^ _106296) ^ [_322531, _322533, _322535] : [class_Rings_Ocomm__semiring__1(_322531), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322531), _322533), hAPP(hAPP(c_Power_Opower__class_Opower(_322531), _322533), _322535)) = hAPP(hAPP(c_Power_Opower__class_Opower(_322531), _322533), c_Nat_OSuc(_322535)))], (6527 ^ _106296) ^ [_322811, _322813, _322815] : [class_Rings_Ocomm__semiring__1(_322811), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322811), hAPP(hAPP(c_Power_Opower__class_Opower(_322811), _322813), _322815)), _322813) = hAPP(hAPP(c_Power_Opower__class_Opower(_322811), _322813), c_Nat_OSuc(_322815)))], (6533 ^ _106296) ^ [_323091, _323093, _323095] : [class_Power_Opower(_323091), -(hAPP(hAPP(c_Power_Opower__class_Opower(_323091), _323093), c_Nat_OSuc(_323095)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323091), _323093), hAPP(hAPP(c_Power_Opower__class_Opower(_323091), _323093), _323095)))], (6539 ^ _106296) ^ [_323371, _323373, _323375] : [class_Groups_Omonoid__mult(_323371), -(hAPP(hAPP(c_Power_Opower__class_Opower(_323371), _323373), c_Nat_OSuc(_323375)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323371), hAPP(hAPP(c_Power_Opower__class_Opower(_323371), _323373), _323375)), _323373))], (6545 ^ _106296) ^ [_323637, _323639] : [class_Groups_Olinordered__ab__group__add(_323637), 6548 ^ _106296 : [(6549 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_323637, c_Groups_Ouminus__class_Ouminus(_323637, _323639), _323639), -(c_Orderings_Oord__class_Oless__eq(_323637, c_Groups_Ozero__class_Ozero(_323637), _323639))], (6555 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_323637, c_Groups_Ozero__class_Ozero(_323637), _323639), -(c_Orderings_Oord__class_Oless__eq(_323637, c_Groups_Ouminus__class_Ouminus(_323637, _323639), _323639))]]], (6561 ^ _106296) ^ [_324116, _324118] : [class_Groups_Oordered__ab__group__add(_324116), 6564 ^ _106296 : [(6565 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_324116, c_Groups_Ouminus__class_Ouminus(_324116, _324118), c_Groups_Ozero__class_Ozero(_324116)), -(c_Orderings_Oord__class_Oless__eq(_324116, c_Groups_Ozero__class_Ozero(_324116), _324118))], (6571 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_324116, c_Groups_Ozero__class_Ozero(_324116), _324118), -(c_Orderings_Oord__class_Oless__eq(_324116, c_Groups_Ouminus__class_Ouminus(_324116, _324118), c_Groups_Ozero__class_Ozero(_324116)))]]], (6577 ^ _106296) ^ [_324601, _324603] : [class_Groups_Olinordered__ab__group__add(_324601), 6580 ^ _106296 : [(6581 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_324601, _324603, c_Groups_Ouminus__class_Ouminus(_324601, _324603)), -(c_Orderings_Oord__class_Oless__eq(_324601, _324603, c_Groups_Ozero__class_Ozero(_324601)))], (6587 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_324601, _324603, c_Groups_Ozero__class_Ozero(_324601)), -(c_Orderings_Oord__class_Oless__eq(_324601, _324603, c_Groups_Ouminus__class_Ouminus(_324601, _324603)))]]], (6593 ^ _106296) ^ [_325080, _325082] : [class_Groups_Oordered__ab__group__add(_325080), 6596 ^ _106296 : [(6597 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_325080, c_Groups_Ozero__class_Ozero(_325080), c_Groups_Ouminus__class_Ouminus(_325080, _325082)), -(c_Orderings_Oord__class_Oless__eq(_325080, _325082, c_Groups_Ozero__class_Ozero(_325080)))], (6603 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_325080, _325082, c_Groups_Ozero__class_Ozero(_325080)), -(c_Orderings_Oord__class_Oless__eq(_325080, c_Groups_Ozero__class_Ozero(_325080), c_Groups_Ouminus__class_Ouminus(_325080, _325082)))]]], (6609 ^ _106296) ^ [_325579, _325581, _325583] : [class_Rings_Olinordered__semidom(_325579), c_Orderings_Oord__class_Oless__eq(_325579, c_Groups_Ozero__class_Ozero(_325579), _325581), -(c_Orderings_Oord__class_Oless__eq(_325579, c_Groups_Ozero__class_Ozero(_325579), hAPP(hAPP(c_Power_Opower__class_Opower(_325579), _325581), _325583)))], (6619 ^ _106296) ^ [_325942, _325944, _325946, _325948] : [class_Rings_Olinordered__semidom(_325942), c_Orderings_Oord__class_Oless__eq(_325942, _325944, _325946), c_Orderings_Oord__class_Oless__eq(_325942, c_Groups_Ozero__class_Ozero(_325942), _325944), -(c_Orderings_Oord__class_Oless__eq(_325942, hAPP(hAPP(c_Power_Opower__class_Opower(_325942), _325944), _325948), hAPP(hAPP(c_Power_Opower__class_Opower(_325942), _325946), _325948)))], (6633 ^ _106296) ^ [_326384] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326384, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_326384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_326384 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6643 ^ _106296) ^ [_326705, _326707] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326705, c_Nat_OSuc(_326707)), -(_326705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6651 ^ _106296 : [(6652 ^ _106296) ^ [] : [-(_326705 = c_Nat_OSuc(6650 ^ [_326705, _326707]))], (6654 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 6650 ^ [_326705, _326707], _326707))]]], (6656 ^ _106296) ^ [_327117, _327119] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327117, c_Nat_OSuc(_327119))), 6657 ^ _106296 : [(6658 ^ _106296) ^ [] : [_327117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6660 ^ _106296) ^ [_327286] : [_327117 = c_Nat_OSuc(_327286), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327286, _327119)]]], (6668 ^ _106296) ^ [_327584] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327584, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_327584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6674 ^ _106296) ^ [_327742] : [_327742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327742, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6680 ^ _106296) ^ [_327965] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _327965), -(_327965 = c_Nat_OSuc(6683 ^ [_327965]))], (6687 ^ _106296) ^ [_328180] : [6688 ^ _106296 : [(6689 ^ _106296) ^ [_328251] : [_328180 = c_Nat_OSuc(_328251)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _328180))], (6693 ^ _106296) ^ [_328443, _328445] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _328443, _328445) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6698 ^ _106296 : [(6699 ^ _106296) ^ [] : [-(_328443 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6701 ^ _106296) ^ [] : [-(_328445 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 6702 ^ _106296 : [(6703 ^ _106296) ^ [] : [-(_328443 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6705 ^ _106296) ^ [] : [-(_328445 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (6707 ^ _106296) ^ [_328853, _328855] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _328853, _328855) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 6708 ^ _106296 : [(6709 ^ _106296) ^ [] : [_328853 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _328855 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6715 ^ _106296) ^ [] : [_328853 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _328855 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6723 ^ _106296) ^ [_329354, _329356] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _329354, _329356), 6728 ^ _106296 : [(6729 ^ _106296) ^ [] : [-(_329354 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6731 ^ _106296) ^ [] : [-(_329356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 6732 ^ _106296 : [(6733 ^ _106296) ^ [] : [-(_329354 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6735 ^ _106296) ^ [] : [-(_329356 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (6737 ^ _106296) ^ [_329764, _329766] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _329764, _329766)), 6738 ^ _106296 : [(6739 ^ _106296) ^ [] : [_329764 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _329766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6745 ^ _106296) ^ [] : [_329764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _329766 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6753 ^ _106296) ^ [_330250, _330252, _330254] : [class_Rings_Olinordered__semidom(_330250), c_Orderings_Oord__class_Oless__eq(_330250, c_Groups_Oone__class_Oone(_330250), _330252), -(c_Orderings_Oord__class_Oless__eq(_330250, c_Groups_Oone__class_Oone(_330250), hAPP(hAPP(c_Power_Opower__class_Opower(_330250), _330252), _330254)))], (6763 ^ _106296) ^ [_330614, _330616] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _330614), _330616) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6766 ^ _106296 : [(6767 ^ _106296) ^ [] : [-(_330614 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6769 ^ _106296) ^ [] : [-(_330616 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (6771 ^ _106296) ^ [_330863, _330865] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _330863), _330865) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _330863 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _330865 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6781 ^ _106296) ^ [_331176, _331178] : [class_Fields_Olinordered__field__inverse__zero(_331176), 6784 ^ _106296 : [(6785 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_331176, c_Groups_Ozero__class_Ozero(_331176), c_Rings_Oinverse__class_Oinverse(_331176, _331178)), -(c_Orderings_Oord__class_Oless__eq(_331176, c_Groups_Ozero__class_Ozero(_331176), _331178))], (6791 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_331176, c_Groups_Ozero__class_Ozero(_331176), _331178), -(c_Orderings_Oord__class_Oless__eq(_331176, c_Groups_Ozero__class_Ozero(_331176), c_Rings_Oinverse__class_Oinverse(_331176, _331178)))]]], (6797 ^ _106296) ^ [_331661, _331663] : [class_Fields_Olinordered__field__inverse__zero(_331661), 6800 ^ _106296 : [(6801 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_331661, c_Rings_Oinverse__class_Oinverse(_331661, _331663), c_Groups_Ozero__class_Ozero(_331661)), -(c_Orderings_Oord__class_Oless__eq(_331661, _331663, c_Groups_Ozero__class_Ozero(_331661)))], (6807 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_331661, _331663, c_Groups_Ozero__class_Ozero(_331661)), -(c_Orderings_Oord__class_Oless__eq(_331661, c_Rings_Oinverse__class_Oinverse(_331661, _331663), c_Groups_Ozero__class_Ozero(_331661)))]]], (6813 ^ _106296) ^ [_332175, _332177] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _332175, _332177), -(_332177 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _332175, 6816 ^ [_332175, _332177])))], (6820 ^ _106296) ^ [_332414, _332416] : [6821 ^ _106296 : [(6822 ^ _106296) ^ [_332491] : [_332416 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _332414, _332491))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _332414, _332416))], (6826 ^ _106296) ^ [_332647, _332649] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _332647, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _332649, _332647))))], (6828 ^ _106296) ^ [_332748, _332750] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _332748, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _332748, _332750))))], (6830 ^ _106296) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6832 ^ _106296) ^ [_332960, _332962, _332964] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_332960)), _332962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_332960)), _332964)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _332962, _332964))], (6838 ^ _106296) ^ [_333164, _333166, _333168] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _333166, _333168), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_333164)), _333166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_333164)), _333168)))], (6844 ^ _106296) ^ [_333403, _333405] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _333403, _333405), c_Nat_OSuc(_333403)))], (6846 ^ _106296) ^ [_333504, _333506] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_333504)), _333506) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _333506, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _333504), _333506)))], (6848 ^ _106296) ^ [_333616, _333618] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _333616), c_Nat_OSuc(_333618)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _333616, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _333616), _333618)))], (6850 ^ _106296) ^ [_333714] : [-(c_Nat_OSuc(_333714) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _333714))], (6852 ^ _106296) ^ [_333798] : [-(c_Nat_OSuc(_333798) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _333798, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6854 ^ _106296) ^ [_333896, _333898] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _333896, c_Nat_OSuc(_333898)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _333896, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _333898))], (6856 ^ _106296) ^ [_333990] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_333990), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _333990)], (6858 ^ _106296) ^ [_334132, _334134] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _334132, _334134) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334132, _334134))], (6864 ^ _106296) ^ [_334304, _334306] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334304, _334306), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _334304, _334306) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6870 ^ _106296) ^ [_334526, _334528] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334526, _334528), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _334526, _334528) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6876 ^ _106296) ^ [_334746, _334748] : [class_RealVector_Oreal__normed__vector(_334746), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_334746, _334748)))], (6882 ^ _106296) ^ [_334976, _334978, _334980] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _334976, _334978), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334980, _334976), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _334976, _334980), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _334978, _334980)))], (6892 ^ _106296) ^ [_335321, _335323, _335325] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _335321, _335323), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _335321, _335325), 6899 ^ _106296 : [(6900 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _335323, _335321), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _335325, _335321)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _335323, _335325))], (6906 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _335323, _335325), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _335323, _335321), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _335325, _335321)))]]], (6912 ^ _106296) ^ [_335938, _335940, _335942] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _335938, _335940), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _335940, _335942), _335938) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _335940, _335938), _335942))], (6918 ^ _106296) ^ [_336202, _336204, _336206] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _336202, _336204), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _336204, _336202), _336206) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _336204, _336206), _336202))], (6924 ^ _106296) ^ [_336466, _336468, _336470] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _336466, _336468), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _336470, _336468), _336466) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _336470, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _336468, _336466)))], (6930 ^ _106296) ^ [_336730, _336732, _336734] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _336730, _336732), 6933 ^ _106296 : [(6934 ^ _106296) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _336732, _336730) = _336734, -(_336732 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _336734, _336730))], (6940 ^ _106296) ^ [] : [_336732 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _336734, _336730), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _336732, _336730) = _336734)]]], (6946 ^ _106296) ^ [_337232, _337234] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _337232, _337234), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _337234, _337232), _337232) = _337234)], (6952 ^ _106296) ^ [_337474, _337476, _337478] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _337474, _337476), 6955 ^ _106296 : [(6956 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _337478, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _337476, _337474)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _337478, _337474), _337476))], (6962 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _337478, _337474), _337476), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _337478, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _337476, _337474)))]]], (6968 ^ _106296) ^ [_337996, _337998, _338000] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _337996, _337998), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _338000, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _337998, _337996)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _338000, _337998), _337996))], (6974 ^ _106296) ^ [_338246, _338248] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _338246, _338248), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _338246, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _338248, _338246)) = _338248)], (6980 ^ _106296) ^ [_338488, _338490, _338492] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _338488, _338490), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _338492, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _338490, _338492), _338488)))], (6986 ^ _106296) ^ [_338767, _338769, _338771] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _338767, _338769), _338771), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _338767, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _338771, _338769)))], (6992 ^ _106296) ^ [_338955, _338957, _338959] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _338955, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _338959, _338957)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _338955, _338957), _338959))], (6998 ^ _106296) ^ [_339207, _339209, _339211] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _339207, _339209), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _339211, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _339209, _339207)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _339211, _339207), _339209))], (7004 ^ _106296) ^ [_339486, _339488] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _339486, _339488), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _339486, _339488), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7010 ^ _106296) ^ [_339660, _339662] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _339660, _339662), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _339660, _339662))], (7026 ^ _106296) ^ [_340177, _340179] : [7027 ^ _106296 : [(7028 ^ _106296) ^ [] : [_340179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7030 ^ _106296) ^ [] : [_340177 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _340177), _340179) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7016 ^ _106296) ^ [_339913, _339915] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _339913), _339915) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_339915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_339913 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7034 ^ _106296) ^ [_340446] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _340446) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7036 ^ _106296) ^ [_340541, _340543] : [-(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), _340541), _340541)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _340543), _340543)))], (7038 ^ _106296) ^ [_340637] : [-(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, _340637)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _340637)))], (7040 ^ _106296) ^ [_340782, _340784, _340786, _340788] : [class_Rings_Olinordered__ring__strict(_340782), c_Orderings_Oord__class_Oless(_340782, c_Groups_Ozero__class_Ozero(_340782), _340784), 7047 ^ _106296 : [(7048 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_340782, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340782), _340784), _340786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340782), _340784), _340788)), -(c_Orderings_Oord__class_Oless__eq(_340782, _340786, _340788))], (7054 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_340782, _340786, _340788), -(c_Orderings_Oord__class_Oless__eq(_340782, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340782), _340784), _340786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340782), _340784), _340788)))]]], (7060 ^ _106296) ^ [_341457, _341459, _341461, _341463] : [class_Rings_Olinordered__ring__strict(_341457), c_Orderings_Oord__class_Oless(_341457, _341459, c_Groups_Ozero__class_Ozero(_341457)), 7067 ^ _106296 : [(7068 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_341457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341457), _341459), _341461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341457), _341459), _341463)), -(c_Orderings_Oord__class_Oless__eq(_341457, _341463, _341461))], (7074 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_341457, _341463, _341461), -(c_Orderings_Oord__class_Oless__eq(_341457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341457), _341459), _341461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341457), _341459), _341463)))]]], (7080 ^ _106296) ^ [_342146, _342148, _342150, _342152, _342154] : [class_Rings_Olinordered__semiring__strict(_342146), c_Orderings_Oord__class_Oless(_342146, _342148, _342150), c_Orderings_Oord__class_Oless(_342146, _342152, _342154), c_Orderings_Oord__class_Oless(_342146, c_Groups_Ozero__class_Ozero(_342146), _342150), c_Orderings_Oord__class_Oless__eq(_342146, c_Groups_Ozero__class_Ozero(_342146), _342152), -(c_Orderings_Oord__class_Oless(_342146, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342146), _342148), _342152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342146), _342150), _342154)))], (7102 ^ _106296) ^ [_342868, _342870, _342872, _342874, _342876] : [class_Rings_Olinordered__semiring__strict(_342868), c_Orderings_Oord__class_Oless(_342868, _342870, _342872), c_Orderings_Oord__class_Oless(_342868, _342874, _342876), c_Orderings_Oord__class_Oless__eq(_342868, c_Groups_Ozero__class_Ozero(_342868), _342870), c_Orderings_Oord__class_Oless__eq(_342868, c_Groups_Ozero__class_Ozero(_342868), _342874), -(c_Orderings_Oord__class_Oless(_342868, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342868), _342870), _342874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342868), _342872), _342876)))], (7124 ^ _106296) ^ [_343590, _343592, _343594, _343596, _343598] : [class_Rings_Olinordered__semiring__strict(_343590), c_Orderings_Oord__class_Oless(_343590, _343592, _343594), c_Orderings_Oord__class_Oless__eq(_343590, _343596, _343598), c_Orderings_Oord__class_Oless__eq(_343590, c_Groups_Ozero__class_Ozero(_343590), _343592), c_Orderings_Oord__class_Oless(_343590, c_Groups_Ozero__class_Ozero(_343590), _343596), -(c_Orderings_Oord__class_Oless(_343590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343590), _343592), _343596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343590), _343594), _343598)))], (7146 ^ _106296) ^ [_344312, _344314, _344316, _344318, _344320] : [class_Rings_Olinordered__semiring__strict(_344312), c_Orderings_Oord__class_Oless__eq(_344312, _344314, _344316), c_Orderings_Oord__class_Oless(_344312, _344318, _344320), c_Orderings_Oord__class_Oless(_344312, c_Groups_Ozero__class_Ozero(_344312), _344314), c_Orderings_Oord__class_Oless__eq(_344312, c_Groups_Ozero__class_Ozero(_344312), _344318), -(c_Orderings_Oord__class_Oless(_344312, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344312), _344314), _344318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344312), _344316), _344320)))], (7168 ^ _106296) ^ [_345020, _345022, _345024, _345026] : [class_Rings_Olinordered__semiring(_345020), c_Orderings_Oord__class_Oless(_345020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345020), _345022), _345024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345020), _345026), _345024)), c_Orderings_Oord__class_Oless__eq(_345020, c_Groups_Ozero__class_Ozero(_345020), _345024), -(c_Orderings_Oord__class_Oless(_345020, _345022, _345026))], (7182 ^ _106296) ^ [_345504, _345506, _345508, _345510] : [class_Rings_Olinordered__semiring__strict(_345504), c_Orderings_Oord__class_Oless(_345504, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345504), _345506), _345508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345504), _345510), _345508)), c_Orderings_Oord__class_Oless__eq(_345504, c_Groups_Ozero__class_Ozero(_345504), _345508), -(c_Orderings_Oord__class_Oless(_345504, _345506, _345510))], (7196 ^ _106296) ^ [_345988, _345990, _345992, _345994] : [class_Rings_Olinordered__semiring(_345988), c_Orderings_Oord__class_Oless(_345988, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345988), _345990), _345992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345988), _345990), _345994)), c_Orderings_Oord__class_Oless__eq(_345988, c_Groups_Ozero__class_Ozero(_345988), _345990), -(c_Orderings_Oord__class_Oless(_345988, _345992, _345994))], (7210 ^ _106296) ^ [_346472, _346474, _346476, _346478] : [class_Rings_Olinordered__semiring__strict(_346472), c_Orderings_Oord__class_Oless(_346472, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346472), _346474), _346476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346472), _346474), _346478)), c_Orderings_Oord__class_Oless__eq(_346472, c_Groups_Ozero__class_Ozero(_346472), _346474), -(c_Orderings_Oord__class_Oless(_346472, _346476, _346478))], (7224 ^ _106296) ^ [_346956, _346958, _346960, _346962] : [class_Rings_Olinordered__semiring__strict(_346956), c_Orderings_Oord__class_Oless__eq(_346956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346956), _346958), _346960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346956), _346962), _346960)), c_Orderings_Oord__class_Oless(_346956, c_Groups_Ozero__class_Ozero(_346956), _346960), -(c_Orderings_Oord__class_Oless__eq(_346956, _346958, _346962))], (7238 ^ _106296) ^ [_347440, _347442, _347444, _347446] : [class_Rings_Olinordered__semiring__strict(_347440), c_Orderings_Oord__class_Oless__eq(_347440, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347440), _347442), _347444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347440), _347442), _347446)), c_Orderings_Oord__class_Oless(_347440, c_Groups_Ozero__class_Ozero(_347440), _347442), -(c_Orderings_Oord__class_Oless__eq(_347440, _347444, _347446))], (7252 ^ _106296) ^ [_347910, _347912, _347914] : [class_Groups_Oordered__comm__monoid__add(_347910), c_Orderings_Oord__class_Oless(_347910, c_Groups_Ozero__class_Ozero(_347910), _347912), c_Orderings_Oord__class_Oless__eq(_347910, c_Groups_Ozero__class_Ozero(_347910), _347914), -(c_Orderings_Oord__class_Oless(_347910, c_Groups_Ozero__class_Ozero(_347910), c_Groups_Oplus__class_Oplus(_347910, _347912, _347914)))], (7266 ^ _106296) ^ [_348350, _348352, _348354] : [class_Groups_Oordered__comm__monoid__add(_348350), c_Orderings_Oord__class_Oless__eq(_348350, c_Groups_Ozero__class_Ozero(_348350), _348352), c_Orderings_Oord__class_Oless(_348350, c_Groups_Ozero__class_Ozero(_348350), _348354), -(c_Orderings_Oord__class_Oless(_348350, c_Groups_Ozero__class_Ozero(_348350), c_Groups_Oplus__class_Oplus(_348350, _348352, _348354)))], (7280 ^ _106296) ^ [_348804, _348806, _348808, _348810] : [class_Groups_Oordered__comm__monoid__add(_348804), c_Orderings_Oord__class_Oless(_348804, c_Groups_Ozero__class_Ozero(_348804), _348806), c_Orderings_Oord__class_Oless__eq(_348804, _348808, _348810), -(c_Orderings_Oord__class_Oless(_348804, _348808, c_Groups_Oplus__class_Oplus(_348804, _348806, _348810)))], (7294 ^ _106296) ^ [_349264, _349266, _349268, _349270] : [class_Groups_Oordered__comm__monoid__add(_349264), c_Orderings_Oord__class_Oless__eq(_349264, c_Groups_Ozero__class_Ozero(_349264), _349266), c_Orderings_Oord__class_Oless(_349264, _349268, _349270), -(c_Orderings_Oord__class_Oless(_349264, _349268, c_Groups_Oplus__class_Oplus(_349264, _349266, _349270)))], (7308 ^ _106296) ^ [_349710, _349712, _349714] : [class_Groups_Oordered__comm__monoid__add(_349710), c_Orderings_Oord__class_Oless(_349710, _349712, c_Groups_Ozero__class_Ozero(_349710)), c_Orderings_Oord__class_Oless__eq(_349710, _349714, c_Groups_Ozero__class_Ozero(_349710)), -(c_Orderings_Oord__class_Oless(_349710, c_Groups_Oplus__class_Oplus(_349710, _349712, _349714), c_Groups_Ozero__class_Ozero(_349710)))], (7322 ^ _106296) ^ [_350150, _350152, _350154] : [class_Groups_Oordered__comm__monoid__add(_350150), c_Orderings_Oord__class_Oless__eq(_350150, _350152, c_Groups_Ozero__class_Ozero(_350150)), c_Orderings_Oord__class_Oless(_350150, _350154, c_Groups_Ozero__class_Ozero(_350150)), -(c_Orderings_Oord__class_Oless(_350150, c_Groups_Oplus__class_Oplus(_350150, _350152, _350154), c_Groups_Ozero__class_Ozero(_350150)))], (7336 ^ _106296) ^ [_350590, _350592, _350594] : [class_Rings_Olinordered__ring(_350590), -(c_Orderings_Oord__class_Oless__eq(_350590, c_Groups_Ozero__class_Ozero(_350590), c_Groups_Oplus__class_Oplus(_350590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350590), _350592), _350592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350590), _350594), _350594))))], (7342 ^ _106296) ^ [_350864, _350866, _350868] : [class_Rings_Olinordered__ring__strict(_350864), 7345 ^ _106296 : [(7346 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_350864, c_Groups_Oplus__class_Oplus(_350864, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350864), _350866), _350866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350864), _350868), _350868)), c_Groups_Ozero__class_Ozero(_350864)), 7349 ^ _106296 : [(7350 ^ _106296) ^ [] : [-(_350866 = c_Groups_Ozero__class_Ozero(_350864))], (7352 ^ _106296) ^ [] : [-(_350868 = c_Groups_Ozero__class_Ozero(_350864))]]], (7354 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_350864, c_Groups_Oplus__class_Oplus(_350864, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350864), _350866), _350866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350864), _350868), _350868)), c_Groups_Ozero__class_Ozero(_350864))), _350866 = c_Groups_Ozero__class_Ozero(_350864), _350868 = c_Groups_Ozero__class_Ozero(_350864)]]], (7364 ^ _106296) ^ [_351597, _351599, _351601] : [class_Rings_Olinordered__idom(_351597), c_Orderings_Oord__class_Oless__eq(_351597, c_Groups_Ozero__class_Ozero(_351597), _351599), c_Orderings_Oord__class_Oless__eq(_351597, c_Groups_Ozero__class_Ozero(_351597), _351601), c_Orderings_Oord__class_Oless__eq(_351597, _351601, c_Groups_Oone__class_Oone(_351597)), -(c_Orderings_Oord__class_Oless__eq(_351597, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351597), _351599), _351601), _351599))], (7382 ^ _106296) ^ [_352140, _352142, _352144] : [class_Rings_Olinordered__idom(_352140), c_Orderings_Oord__class_Oless__eq(_352140, c_Groups_Ozero__class_Ozero(_352140), _352142), c_Orderings_Oord__class_Oless__eq(_352140, c_Groups_Ozero__class_Ozero(_352140), _352144), c_Orderings_Oord__class_Oless__eq(_352140, _352144, c_Groups_Oone__class_Oone(_352140)), -(c_Orderings_Oord__class_Oless__eq(_352140, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352140), _352144), _352142), _352142))], (7400 ^ _106296) ^ [_352683, _352685, _352687] : [class_Rings_Olinordered__semidom(_352683), c_Orderings_Oord__class_Oless(_352683, c_Groups_Oone__class_Oone(_352683), _352685), -(c_Orderings_Oord__class_Oless(_352683, c_Groups_Oone__class_Oone(_352683), hAPP(hAPP(c_Power_Opower__class_Opower(_352683), _352685), c_Nat_OSuc(_352687))))], (7410 ^ _106296) ^ [_353050, _353052, _353054, _353056] : [class_Rings_Olinordered__semidom(_353050), c_Orderings_Oord__class_Oless(_353050, hAPP(hAPP(c_Power_Opower__class_Opower(_353050), _353052), _353054), hAPP(hAPP(c_Power_Opower__class_Opower(_353050), _353056), _353054)), c_Orderings_Oord__class_Oless__eq(_353050, c_Groups_Ozero__class_Ozero(_353050), _353056), -(c_Orderings_Oord__class_Oless(_353050, _353052, _353056))], (7424 ^ _106296) ^ [_353562, _353564, _353566, _353568, _353570, _353572] : [class_Rings_Oordered__ring(_353562), 7427 ^ _106296 : [(7428 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_353562, c_Groups_Oplus__class_Oplus(_353562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353562), _353564), _353566), _353568), c_Groups_Oplus__class_Oplus(_353562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353562), _353570), _353566), _353572)), -(c_Orderings_Oord__class_Oless__eq(_353562, _353568, c_Groups_Oplus__class_Oplus(_353562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353562), c_Groups_Ominus__class_Ominus(_353562, _353570, _353564)), _353566), _353572)))], (7434 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_353562, _353568, c_Groups_Oplus__class_Oplus(_353562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353562), c_Groups_Ominus__class_Ominus(_353562, _353570, _353564)), _353566), _353572)), -(c_Orderings_Oord__class_Oless__eq(_353562, c_Groups_Oplus__class_Oplus(_353562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353562), _353564), _353566), _353568), c_Groups_Oplus__class_Oplus(_353562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353562), _353570), _353566), _353572)))]]], (7440 ^ _106296) ^ [_354266, _354268, _354270, _354272, _354274, _354276] : [class_Rings_Oordered__ring(_354266), 7443 ^ _106296 : [(7444 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_354266, c_Groups_Oplus__class_Oplus(_354266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354266), _354268), _354270), _354272), c_Groups_Oplus__class_Oplus(_354266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354266), _354274), _354270), _354276)), -(c_Orderings_Oord__class_Oless__eq(_354266, c_Groups_Oplus__class_Oplus(_354266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354266), c_Groups_Ominus__class_Ominus(_354266, _354268, _354274)), _354270), _354272), _354276))], (7450 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_354266, c_Groups_Oplus__class_Oplus(_354266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354266), c_Groups_Ominus__class_Ominus(_354266, _354268, _354274)), _354270), _354272), _354276), -(c_Orderings_Oord__class_Oless__eq(_354266, c_Groups_Oplus__class_Oplus(_354266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354266), _354268), _354270), _354272), c_Groups_Oplus__class_Oplus(_354266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354266), _354274), _354270), _354276)))]]], (7456 ^ _106296) ^ [_354928, _354930, _354932] : [class_Rings_Oidom(_354928), 7459 ^ _106296 : [(7470 ^ _106296) ^ [] : [7471 ^ _106296 : [(7472 ^ _106296) ^ [] : [_354930 = _354932], (7474 ^ _106296) ^ [] : [_354930 = c_Groups_Ouminus__class_Ouminus(_354928, _354932)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_354928), _354930), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_354928), _354932), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (7460 ^ _106296) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_354928), _354930), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_354928), _354932), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_354930 = _354932), -(_354930 = c_Groups_Ouminus__class_Ouminus(_354928, _354932))]]], (7478 ^ _106296) ^ [_355637, _355639, _355641] : [class_Fields_Olinordered__field(_355637), c_Orderings_Oord__class_Oless__eq(_355637, _355639, _355641), c_Orderings_Oord__class_Oless(_355637, c_Groups_Ozero__class_Ozero(_355637), _355639), -(c_Orderings_Oord__class_Oless__eq(_355637, c_Rings_Oinverse__class_Oinverse(_355637, _355641), c_Rings_Oinverse__class_Oinverse(_355637, _355639)))], (7492 ^ _106296) ^ [_356073, _356075, _356077] : [class_Fields_Olinordered__field(_356073), c_Orderings_Oord__class_Oless__eq(_356073, _356075, _356077), c_Orderings_Oord__class_Oless(_356073, _356077, c_Groups_Ozero__class_Ozero(_356073)), -(c_Orderings_Oord__class_Oless__eq(_356073, c_Rings_Oinverse__class_Oinverse(_356073, _356077), c_Rings_Oinverse__class_Oinverse(_356073, _356075)))], (7506 ^ _106296) ^ [_356509, _356511, _356513] : [class_Fields_Olinordered__field(_356509), c_Orderings_Oord__class_Oless__eq(_356509, c_Rings_Oinverse__class_Oinverse(_356509, _356511), c_Rings_Oinverse__class_Oinverse(_356509, _356513)), c_Orderings_Oord__class_Oless(_356509, c_Groups_Ozero__class_Ozero(_356509), _356511), -(c_Orderings_Oord__class_Oless__eq(_356509, _356513, _356511))], (7520 ^ _106296) ^ [_356945, _356947, _356949] : [class_Fields_Olinordered__field(_356945), c_Orderings_Oord__class_Oless__eq(_356945, c_Rings_Oinverse__class_Oinverse(_356945, _356947), c_Rings_Oinverse__class_Oinverse(_356945, _356949)), c_Orderings_Oord__class_Oless(_356945, _356949, c_Groups_Ozero__class_Ozero(_356945)), -(c_Orderings_Oord__class_Oless__eq(_356945, _356949, _356947))], (7534 ^ _106296) ^ [_357367, _357369] : [class_Fields_Olinordered__field__inverse__zero(_357367), 7537 ^ _106296 : [(7548 ^ _106296) ^ [] : [7549 ^ _106296 : [(7550 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_357367, _357369, c_Groups_Ozero__class_Ozero(_357367))], (7552 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_357367, c_Groups_Oone__class_Oone(_357367), _357369)]], -(c_Orderings_Oord__class_Oless__eq(_357367, c_Rings_Oinverse__class_Oinverse(_357367, _357369), c_Groups_Oone__class_Oone(_357367)))], (7538 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_357367, c_Rings_Oinverse__class_Oinverse(_357367, _357369), c_Groups_Oone__class_Oone(_357367)), -(c_Orderings_Oord__class_Oless__eq(_357367, _357369, c_Groups_Ozero__class_Ozero(_357367))), -(c_Orderings_Oord__class_Oless__eq(_357367, c_Groups_Oone__class_Oone(_357367), _357369))]]], (7556 ^ _106296) ^ [_358019, _358021] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _358019), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _358021), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _358021), _358019)))], (7566 ^ _106296) ^ [_358336, _358338] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _358336), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _358338), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _358336, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _358336), _358338)))], (7576 ^ _106296) ^ [_358653, _358655] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _358653), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _358655), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _358653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _358655), _358653)))], (7586 ^ _106296) ^ [_358956] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _358956), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _358956, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _358956)], (7592 ^ _106296) ^ [_359174, _359176] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _359174), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _359174, c_Nat_OSuc(_359176)), _359174))], (7598 ^ _106296) ^ [_359400, _359402] : [class_RealVector_Oreal__normed__vector(_359400), 7601 ^ _106296 : [(7602 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_359400, _359402), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_359402 = c_Groups_Ozero__class_Ozero(_359400))], (7608 ^ _106296) ^ [] : [_359402 = c_Groups_Ozero__class_Ozero(_359400), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_359400, _359402), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (7614 ^ _106296) ^ [_359890, _359892, _359894] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _359890), 7617 ^ _106296 : [(7618 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359890), _359892), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359890), _359894)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _359892, _359894))], (7624 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _359892, _359894), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359890), _359892), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359890), _359894)))]]], (7640 ^ _106296) ^ [_360744, _360746, _360748] : [7641 ^ _106296 : [(7642 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _360746))], (7644 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360744, _360748)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _360744), _360746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _360748), _360746)))], (7630 ^ _106296) ^ [_360453, _360455, _360457] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _360453), _360455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _360457), _360455)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _360455), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360453, _360457))], (7658 ^ _106296) ^ [_361403, _361405, _361407] : [7659 ^ _106296 : [(7660 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _361403))], (7662 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361405, _361407)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _361403), _361405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _361403), _361407)))], (7648 ^ _106296) ^ [_361112, _361114, _361116] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _361112), _361114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _361112), _361116)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _361112), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361114, _361116))], (7666 ^ _106296) ^ [_361742, _361744, _361746] : [class_RealVector_Oreal__normed__algebra(_361742), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_361742, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361742), _361744), _361746)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_361742, _361744)), c_RealVector_Onorm__class_Onorm(_361742, _361746))))], (7672 ^ _106296) ^ [_362018, _362020, _362022] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _362018), 7675 ^ _106296 : [(7676 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362020), _362018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362022), _362018)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _362020, _362022))], (7682 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _362020, _362022), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362020), _362018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362022), _362018)))]]], (7688 ^ _106296) ^ [_362552, _362554, _362556] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _362552), 7691 ^ _106296 : [(7692 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362552), _362554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362552), _362556)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _362554, _362556))], (7698 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _362554, _362556), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362552), _362554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362552), _362556)))]]], (7704 ^ _106296) ^ [_363086, _363088, _363090] : [class_RealVector_Oreal__normed__vector(_363086), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_363086, c_Groups_Oplus__class_Oplus(_363086, _363088, _363090)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_363086, _363088), c_RealVector_Onorm__class_Onorm(_363086, _363090))))], (7710 ^ _106296) ^ [_363350, _363352, _363354] : [class_RealVector_Oreal__normed__vector(_363350), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_363350, c_Groups_Ominus__class_Ominus(_363350, _363352, _363354)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_363350, _363352), c_RealVector_Onorm__class_Onorm(_363350, _363354))))], (7716 ^ _106296) ^ [_363642, _363644, _363646, _363648, _363650] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363642, _363644), 7719 ^ _106296 : [(7720 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _363642), _363646), _363648) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _363644), _363646), _363650), -(_363648 = 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, _363644, _363642)), _363646), _363650))], (7726 ^ _106296) ^ [] : [_363648 = 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, _363644, _363642)), _363646), _363650), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _363642), _363646), _363648) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _363644), _363646), _363650))]]], (7732 ^ _106296) ^ [_364296, _364298, _364300, _364302, _364304] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _364296, _364298), -(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), _364296), _364300), _364302), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _364298), _364300), _364304)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _364302, 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, _364298, _364296)), _364300), _364304)))], (7738 ^ _106296) ^ [_364652, _364654, _364656, _364658, _364660] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _364652, _364654), 7741 ^ _106296 : [(7742 ^ _106296) ^ [] : [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), _364652), _364656), _364658), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _364654), _364656), _364660)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _364658, 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, _364654, _364652)), _364656), _364660)))], (7748 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _364658, 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, _364654, _364652)), _364656), _364660)), -(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), _364652), _364656), _364658), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _364654), _364656), _364660)))]]], (7754 ^ _106296) ^ [_365312, _365314, _365316, _365318, _365320] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _365312, _365314), 7757 ^ _106296 : [(7758 ^ _106296) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365314), _365316), _365318) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365312), _365316), _365320), -(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, _365314, _365312)), _365316), _365318) = _365320)], (7764 ^ _106296) ^ [] : [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, _365314, _365312)), _365316), _365318) = _365320, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365314), _365316), _365318) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365312), _365316), _365320))]]], (7770 ^ _106296) ^ [_365966, _365968, _365970, _365972, _365974] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _365966, _365968), -(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), _365968), _365970), _365972), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365966), _365970), _365974)) = 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, _365968, _365966)), _365970), _365972), _365974))], (7776 ^ _106296) ^ [_366322, _366324, _366326, _366328, _366330] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _366322, _366324), 7779 ^ _106296 : [(7780 ^ _106296) ^ [] : [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), _366324), _366326), _366328), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _366322), _366326), _366330)), -(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, _366324, _366322)), _366326), _366328), _366330))], (7786 ^ _106296) ^ [] : [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, _366324, _366322)), _366326), _366328), _366330), -(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), _366324), _366326), _366328), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _366322), _366326), _366330)))]]], (7792 ^ _106296) ^ [_366954, _366956, _366958] : [class_RealVector_Oreal__normed__algebra__1(_366954), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_366954, hAPP(hAPP(c_Power_Opower__class_Opower(_366954), _366956), _366958)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_366954, _366956)), _366958)))], (7798 ^ _106296) ^ [_367224, _367226, _367228] : [class_RealVector_Oreal__normed__vector(_367224), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_367224, _367226), c_RealVector_Onorm__class_Onorm(_367224, _367228)), c_RealVector_Onorm__class_Onorm(_367224, c_Groups_Oplus__class_Oplus(_367224, _367226, _367228))))], (7804 ^ _106296) ^ [_367488, _367490, _367492] : [class_RealVector_Oreal__normed__vector(_367488), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_367488, _367490), c_RealVector_Onorm__class_Onorm(_367488, _367492)), c_RealVector_Onorm__class_Onorm(_367488, c_Groups_Ominus__class_Ominus(_367488, _367490, _367492))))], (7810 ^ _106296) ^ [_367767, _367769] : [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, _367767, _367769)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _367767), _367769))], (7816 ^ _106296) ^ [_367947, _367949] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _367947), _367949), -(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, _367947, _367949)))], (7822 ^ _106296) ^ [_368206, _368208] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _368206, _368208), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _368208, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _368206)))], (7828 ^ _106296) ^ [_368386, _368388] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _368388, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _368386)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _368386, _368388), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7834 ^ _106296) ^ [_368601, _368603] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _368601), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _368601, _368603)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _368603))))], (7836 ^ _106296) ^ [_368713, _368715] : [-(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, _368713, _368715)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _368713)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _368715)))], (7838 ^ _106296) ^ [_368854, _368856, _368858] : [class_Rings_Olinordered__semidom(_368854), c_Orderings_Oord__class_Oless(_368854, c_Groups_Ozero__class_Ozero(_368854), _368856), c_Orderings_Oord__class_Oless(_368854, _368856, c_Groups_Oone__class_Oone(_368854)), -(c_Orderings_Oord__class_Oless(_368854, hAPP(hAPP(c_Power_Opower__class_Opower(_368854), _368856), c_Nat_OSuc(_368858)), c_Groups_Oone__class_Oone(_368854)))], (7852 ^ _106296) ^ [_369348, _369350, _369352, _369354, _369356, _369358] : [class_Rings_Olinordered__semiring__1(_369348), c_Orderings_Oord__class_Oless__eq(_369348, _369350, _369352), c_Orderings_Oord__class_Oless__eq(_369348, _369354, _369352), c_Orderings_Oord__class_Oless__eq(_369348, c_Groups_Ozero__class_Ozero(_369348), _369356), c_Orderings_Oord__class_Oless__eq(_369348, c_Groups_Ozero__class_Ozero(_369348), _369358), c_Groups_Oplus__class_Oplus(_369348, _369356, _369358) = c_Groups_Oone__class_Oone(_369348), -(c_Orderings_Oord__class_Oless__eq(_369348, c_Groups_Oplus__class_Oplus(_369348, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369348), _369356), _369350), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369348), _369358), _369354)), _369352))], (7878 ^ _106296) ^ [_370175, _370177] : [class_Fields_Olinordered__field__inverse__zero(_370175), 7881 ^ _106296 : [(7882 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_370175, c_Groups_Oone__class_Oone(_370175), c_Rings_Oinverse__class_Oinverse(_370175, _370177)), 7885 ^ _106296 : [(7886 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_370175, c_Groups_Ozero__class_Ozero(_370175), _370177))], (7888 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_370175, _370177, c_Groups_Oone__class_Oone(_370175)))]]], (7890 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_370175, c_Groups_Oone__class_Oone(_370175), c_Rings_Oinverse__class_Oinverse(_370175, _370177))), c_Orderings_Oord__class_Oless(_370175, c_Groups_Ozero__class_Ozero(_370175), _370177), c_Orderings_Oord__class_Oless__eq(_370175, _370177, c_Groups_Oone__class_Oone(_370175))]]], (7900 ^ _106296) ^ [_370827, _370829] : [class_Fields_Olinordered__field__inverse__zero(_370827), 7903 ^ _106296 : [(7914 ^ _106296) ^ [] : [7915 ^ _106296 : [(7916 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_370827, _370829, c_Groups_Ozero__class_Ozero(_370827))], (7918 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_370827, c_Groups_Oone__class_Oone(_370827), _370829)]], -(c_Orderings_Oord__class_Oless(_370827, c_Rings_Oinverse__class_Oinverse(_370827, _370829), c_Groups_Oone__class_Oone(_370827)))], (7904 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_370827, c_Rings_Oinverse__class_Oinverse(_370827, _370829), c_Groups_Oone__class_Oone(_370827)), -(c_Orderings_Oord__class_Oless__eq(_370827, _370829, c_Groups_Ozero__class_Ozero(_370827))), -(c_Orderings_Oord__class_Oless(_370827, c_Groups_Oone__class_Oone(_370827), _370829))]]], (7922 ^ _106296) ^ [_371479, _371481] : [class_Fields_Olinordered__field(_371479), c_Orderings_Oord__class_Oless(_371479, c_Groups_Ozero__class_Ozero(_371479), _371481), c_Orderings_Oord__class_Oless__eq(_371479, _371481, c_Groups_Oone__class_Oone(_371479)), -(c_Orderings_Oord__class_Oless__eq(_371479, c_Groups_Oone__class_Oone(_371479), c_Rings_Oinverse__class_Oinverse(_371479, _371481)))], (7936 ^ _106296) ^ [_371917, _371919, _371921, _371923] : [class_Rings_Olinordered__semidom(_371917), hAPP(hAPP(c_Power_Opower__class_Opower(_371917), _371919), _371921) = hAPP(hAPP(c_Power_Opower__class_Opower(_371917), _371923), _371921), c_Orderings_Oord__class_Oless__eq(_371917, c_Groups_Ozero__class_Ozero(_371917), _371919), c_Orderings_Oord__class_Oless__eq(_371917, c_Groups_Ozero__class_Ozero(_371917), _371923), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _371921), -(_371919 = _371923)], (7958 ^ _106296) ^ [_372557] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _372557), -(_372557 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _372557, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (7964 ^ _106296) ^ [_372761] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _372761), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _372761, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _372761)], (7970 ^ _106296) ^ [_372999, _373001] : [_372999 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _372999, _373001) = _373001)], (7976 ^ _106296) ^ [_373169, _373171] : [-(_373169 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _373169, _373171) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _373169, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _373171)))], (7982 ^ _106296) ^ [_373454, _373456, _373458, _373460, _373462] : [class_RealVector_Oreal__normed__vector(_373454), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_373454, c_Groups_Ominus__class_Ominus(_373454, c_Groups_Oplus__class_Oplus(_373454, _373456, _373458), c_Groups_Oplus__class_Oplus(_373454, _373460, _373462))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_373454, c_Groups_Ominus__class_Ominus(_373454, _373456, _373460)), c_RealVector_Onorm__class_Onorm(_373454, c_Groups_Ominus__class_Ominus(_373454, _373458, _373462)))))], (7988 ^ _106296) ^ [_373790, _373792, _373794, _373796, _373798] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _373790, _373792), 7991 ^ _106296 : [(7992 ^ _106296) ^ [] : [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), _373790), _373794), _373796), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _373792), _373794), _373798)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373796, 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, _373792, _373790)), _373794), _373798)))], (7998 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373796, 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, _373792, _373790)), _373794), _373798)), -(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), _373790), _373794), _373796), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _373792), _373794), _373798)))]]], (8004 ^ _106296) ^ [_374450, _374452, _374454, _374456, _374458] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _374450, _374452), 8007 ^ _106296 : [(8008 ^ _106296) ^ [] : [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), _374452), _374454), _374456), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _374450), _374454), _374458)), -(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, _374452, _374450)), _374454), _374456), _374458))], (8014 ^ _106296) ^ [] : [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, _374452, _374450)), _374454), _374456), _374458), -(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), _374452), _374454), _374456), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _374450), _374454), _374458)))]]], (8020 ^ _106296) ^ [_375124, _375126, _375128, _375130, _375132, _375134] : [class_Rings_Olinordered__semiring__1__strict(_375124), c_Orderings_Oord__class_Oless(_375124, _375126, _375128), c_Orderings_Oord__class_Oless(_375124, _375130, _375128), c_Orderings_Oord__class_Oless__eq(_375124, c_Groups_Ozero__class_Ozero(_375124), _375132), c_Orderings_Oord__class_Oless__eq(_375124, c_Groups_Ozero__class_Ozero(_375124), _375134), c_Groups_Oplus__class_Oplus(_375124, _375132, _375134) = c_Groups_Oone__class_Oone(_375124), -(c_Orderings_Oord__class_Oless(_375124, c_Groups_Oplus__class_Oplus(_375124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375124), _375132), _375126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375124), _375134), _375130)), _375128))], (8047 ^ _106296) ^ [] : [-(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))))), 8045 ^ []) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8050 ^ _106296) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 8048 ^ []) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (8052 ^ _106296) ^ [_376132] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 8048 ^ []), _376132) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _376132)))], (8054 ^ _106296) ^ [] : [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____), 8057 ^ []) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8061 ^ _106296) ^ [_376381] : [-(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____)), _376381) = 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), _376381), v_k____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a____, v_s____)), _376381))))], (8063 ^ _106296) ^ [] : [-(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____)))], (8065 ^ _106296) ^ [] : [-(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))))], (8067 ^ _106296) ^ [_376587] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _376587) = 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____)), _376587)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))], (8069 ^ _106296) ^ [] : [-(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))], (8071 ^ _106296) ^ [] : [-(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____)))], (8073 ^ _106296) ^ [] : [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____)))], (8075 ^ _106296) ^ [_376879] : [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____)), _376879)), 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____), _376879)), 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)))))], (8081 ^ _106296) ^ [_377063] : [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____), _377063)), 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____)), _377063)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8087 ^ _106296) ^ [_377268] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377268, _377268))], (8089 ^ _106296) ^ [_377376, _377378] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377376, _377378)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377378, _377376))], (8095 ^ _106296) ^ [_377591, _377593] : [_377591 = _377593, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377591, _377593))], (8101 ^ _106296) ^ [_377817, _377819, _377821] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377817, _377819), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377819, _377821), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377817, _377821))], (8111 ^ _106296) ^ [_378132, _378134] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378132, _378134), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _378134, _378132), -(_378132 = _378134)], (8121 ^ _106296) ^ [_378406] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _378406, _378406))], (8123 ^ _106296) ^ [_378514, _378516] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _378514, _378516)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _378516, _378514))], (8129 ^ _106296) ^ [_378743, _378745, _378747] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _378743, _378745), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _378745, _378747), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _378743, _378747))], (8139 ^ _106296) ^ [_379058, _379060] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _379058, _379060), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _379060, _379058), -(_379058 = _379060)], (8149 ^ _106296) ^ [_379332] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _379332, _379332))], (8151 ^ _106296) ^ [_379440, _379442] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _379440, _379442)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _379442, _379440))], (8157 ^ _106296) ^ [_379669, _379671, _379673] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _379669, _379671), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _379671, _379673), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _379669, _379673))], (8167 ^ _106296) ^ [_379984, _379986] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _379984, _379986), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _379986, _379984), -(_379984 = _379986)], (8177 ^ _106296) ^ [_380330, _380332, _380334] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_380330, _380332, _380334), 8180 ^ _106296 : [(8181 ^ _106296) ^ [_380477, _380479] : [-(hAPP(_380334, _380479) = hAPP(_380334, _380477))]]], (8183 ^ _106296) ^ [_380555, _380557, _380559] : [hAPP(_380559, 8184 ^ [_380555, _380557, _380559]) = hAPP(_380559, 8185 ^ [_380555, _380557, _380559]), -(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_380555, _380557, _380559))], (8191 ^ _106296) ^ [_380967, _380969, _380971, _380973] : [class_Rings_Ocomm__semiring__0(_380967), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_380967), c_Polynomial_Osmult(_380967, _380969, _380971), c_Polynomial_OpCons(_380967, _380973, _380971)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_380967)), -(_380971 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_380967)))], (8201 ^ _106296) ^ [] : [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____)), 8204 ^ [])), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8209 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8207 ^ []))], (8211 ^ _106296) ^ [_381596] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _381596), 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____), _381596)), 8207 ^ []))], (8217 ^ _106296) ^ [_381810] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, _381810), 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, _381810))), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _381810), 8224 ^ [_381810]) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8230 ^ _106296) ^ [] : [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____)), 8227 ^ []) = 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____)), 8228 ^ [])], (8232 ^ _106296) ^ [_382341, _382343, _382345] : [class_RealVector_Oreal__normed__div__algebra(_382341), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _382343, c_RealVector_Onorm__class_Onorm(_382341, _382345)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _382343), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_382341, c_Rings_Oinverse__class_Oinverse(_382341, _382345)), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _382343)))], (8246 ^ _106296) ^ [_382785, _382787, _382789] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _382785), _382785 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _382787, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _382785), _382789)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _382787), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _382789, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8260 ^ _106296) ^ [_383227, _383229, _383231] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _383227), _383227 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _383229, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _383227), _383231)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _383229, _383227), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _383231))], (8274 ^ _106296) ^ [_383711, _383713, _383715, _383717, _383719, _383721] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _383711), _383713), _383715) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _383717), _383719), _383721), 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), _383717), _383719), _383721), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _383715, _383711), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _383721), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _383717), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _383717, _383711), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _383719, _383713))], (8300 ^ _106296) ^ [_384584, _384586, _384588, _384590, _384592] : [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), _384584), _384586), _384588), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _384584), _384590), _384592)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _384592, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _384584, _384592), c_Orderings_Oord__class_Oless(tc_Int_Oint, _384584, _384588), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _384590, _384586))], (8318 ^ _106296) ^ [_385221, _385223, _385225, _385227, _385229, _385231] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _385221), _385223), _385225) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _385227), _385229), _385231), 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), _385227), _385229), _385231)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _385231, _385227), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _385225), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _385227), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _385227, _385221), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _385223, _385229))], (8344 ^ _106296) ^ [_386094, _386096, _386098, _386100, _386102] : [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), _386094), _386096), _386098), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _386094), _386100), _386102)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _386098), c_Orderings_Oord__class_Oless(tc_Int_Oint, _386098, _386094), c_Orderings_Oord__class_Oless(tc_Int_Oint, _386102, _386094), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _386096, _386100))], (8362 ^ _106296) ^ [_386689, _386691, _386693] : [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), _386689), _386691), _386693), 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), _386693), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _386689), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _386691, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8376 ^ _106296) ^ [_387133, _387135, _387137] : [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), _387133), _387135), _387137)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _387137, _387133), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _387133), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _387135))], (8390 ^ _106296) ^ [_387591, _387593, _387595, _387597] : [class_Rings_Ocomm__semiring__0(_387591), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_387591)), c_Polynomial_OpCons(_387591, _387593, _387595)), _387597) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_387591), c_Polynomial_Osmult(_387591, _387593, _387597), c_Polynomial_OpCons(_387591, c_Groups_Ozero__class_Ozero(_387591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_387591)), _387595), _387597))))], (8396 ^ _106296) ^ [_387919, _387921, _387923, _387925] : [class_Rings_Ocomm__semiring__0(_387919), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_387919)), _387921), c_Polynomial_OpCons(_387919, _387923, _387925)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_387919), c_Polynomial_Osmult(_387919, _387923, _387921), c_Polynomial_OpCons(_387919, c_Groups_Ozero__class_Ozero(_387919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_387919)), _387921), _387925))))], (8402 ^ _106296) ^ [_388219, _388221] : [class_Groups_Oab__group__add(_388219), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_388219), _388221, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388219))) = _388221)], (8408 ^ _106296) ^ [_388447, _388449] : [class_Groups_Oab__group__add(_388447), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_388447), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388447)), _388449) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_388447), _388449))], (8414 ^ _106296) ^ [_388671] : [class_Groups_Oab__group__add(_388671), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_388671), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388671))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388671)))], (8420 ^ _106296) ^ [_388913, _388915, _388917] : [class_Int_Oring__char__0(_388913), class_Rings_Oidom(_388913), 8427 ^ _106296 : [(8428 ^ _106296) ^ [] : [c_Polynomial_Opoly(_388913, _388915) = c_Polynomial_Opoly(_388913, _388917), -(_388915 = _388917)], (8434 ^ _106296) ^ [] : [_388915 = _388917, -(c_Polynomial_Opoly(_388913, _388915) = c_Polynomial_Opoly(_388913, _388917))]]], (8440 ^ _106296) ^ [_389540, _389542, _389544, _389546, _389548] : [class_Groups_Ozero(_389540), 8443 ^ _106296 : [(8444 ^ _106296) ^ [] : [c_Polynomial_OpCons(_389540, _389542, _389544) = c_Polynomial_OpCons(_389540, _389546, _389548), 8447 ^ _106296 : [(8448 ^ _106296) ^ [] : [-(_389542 = _389546)], (8450 ^ _106296) ^ [] : [-(_389544 = _389548)]]], (8452 ^ _106296) ^ [] : [-(c_Polynomial_OpCons(_389540, _389542, _389544) = c_Polynomial_OpCons(_389540, _389546, _389548)), _389542 = _389546, _389544 = _389548]]], (8462 ^ _106296) ^ [_390260, _390262, _390264] : [class_Rings_Ocomm__ring(_390260), -(c_Polynomial_Osmult(_390260, _390262, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_390260), _390264)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_390260), c_Polynomial_Osmult(_390260, _390262, _390264)))], (8468 ^ _106296) ^ [_390538, _390540, _390542, _390544] : [class_Rings_Ocomm__ring(_390538), -(c_Polynomial_Osmult(_390538, _390540, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_390538), _390542, _390544)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_390538), c_Polynomial_Osmult(_390538, _390540, _390542), c_Polynomial_Osmult(_390538, _390540, _390544)))], (8474 ^ _106296) ^ [_390834, _390836, _390838, _390840] : [class_Groups_Ozero(_390834), 8477 ^ _106296 : [(8478 ^ _106296) ^ [] : [c_Polynomial_Omonom(_390834, _390836, _390838) = c_Polynomial_Omonom(_390834, _390840, _390838), -(_390836 = _390840)], (8484 ^ _106296) ^ [] : [_390836 = _390840, -(c_Polynomial_Omonom(_390834, _390836, _390838) = c_Polynomial_Omonom(_390834, _390840, _390838))]]], (8490 ^ _106296) ^ [_391348, _391350] : [class_Rings_Ocomm__semiring__1(_391348), -(hAPP(c_Polynomial_Opoly(_391348, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_391348))), _391350) = c_Groups_Oone__class_Oone(_391348))], (8496 ^ _106296) ^ [_391608, _391610, _391612, _391614] : [class_Rings_Ocomm__ring(_391608), -(hAPP(c_Polynomial_Opoly(_391608, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_391608), _391610, _391612)), _391614) = c_Groups_Ominus__class_Ominus(_391608, hAPP(c_Polynomial_Opoly(_391608, _391610), _391614), hAPP(c_Polynomial_Opoly(_391608, _391612), _391614)))], (8502 ^ _106296) ^ [_391926, _391928, _391930, _391932, _391934] : [class_Groups_Oab__group__add(_391926), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_391926), c_Polynomial_OpCons(_391926, _391928, _391930), c_Polynomial_OpCons(_391926, _391932, _391934)) = c_Polynomial_OpCons(_391926, c_Groups_Ominus__class_Ominus(_391926, _391928, _391932), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_391926), _391930, _391934)))], (8508 ^ _106296) ^ [_392236, _392238, _392240, _392242] : [class_Rings_Ocomm__semiring__0(_392236), -(c_Polynomial_Osmult(_392236, _392238, c_Polynomial_Osmult(_392236, _392240, _392242)) = c_Polynomial_Osmult(_392236, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392236), _392238), _392240), _392242))], (8514 ^ _106296) ^ [_392510, _392512, _392514] : [class_Rings_Ocomm__ring(_392510), -(hAPP(c_Polynomial_Opoly(_392510, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_392510), _392512)), _392514) = c_Groups_Ouminus__class_Ouminus(_392510, hAPP(c_Polynomial_Opoly(_392510, _392512), _392514)))], (8520 ^ _106296) ^ [_392792, _392794, _392796, _392798] : [class_Rings_Ocomm__semiring__1(_392792), -(hAPP(c_Polynomial_Opoly(_392792, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_392792)), _392794), _392796)), _392798) = hAPP(hAPP(c_Power_Opower__class_Opower(_392792), hAPP(c_Polynomial_Opoly(_392792, _392794), _392798)), _392796))], (8526 ^ _106296) ^ [_393086, _393088, _393090] : [class_Groups_Oab__group__add(_393086), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_393086), c_Polynomial_OpCons(_393086, _393088, _393090)) = c_Polynomial_OpCons(_393086, c_Groups_Ouminus__class_Ouminus(_393086, _393088), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_393086), _393090)))], (8532 ^ _106296) ^ [_393356, _393358, _393360] : [class_Groups_Oab__group__add(_393356), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_393356), c_Polynomial_OpCons(_393356, _393358, _393360)) = c_Polynomial_OpCons(_393356, c_Groups_Ouminus__class_Ouminus(_393356, _393358), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_393356), _393360)))], (8538 ^ _106296) ^ [_393612, _393614] : [class_Rings_Ocomm__semiring__1(_393612), -(c_Polynomial_Osmult(_393612, c_Groups_Oone__class_Oone(_393612), _393614) = _393614)], (8544 ^ _106296) ^ [_393860, _393862, _393864, _393866] : [class_Rings_Ocomm__ring(_393860), -(c_Polynomial_Osmult(_393860, c_Groups_Ominus__class_Ominus(_393860, _393862, _393864), _393866) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_393860), c_Polynomial_Osmult(_393860, _393862, _393866), c_Polynomial_Osmult(_393860, _393864, _393866)))], (8550 ^ _106296) ^ [_394138, _394140, _394142] : [class_Rings_Ocomm__ring(_394138), -(c_Polynomial_Osmult(_394138, c_Groups_Ouminus__class_Ouminus(_394138, _394140), _394142) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_394138), c_Polynomial_Osmult(_394138, _394140, _394142)))], (8556 ^ _106296) ^ [_394384, _394386] : [class_Int_Oring__char__0(_394384), class_Rings_Oidom(_394384), 8563 ^ _106296 : [(8564 ^ _106296) ^ [] : [c_Polynomial_Opoly(_394384, _394386) = c_Polynomial_Opoly(_394384, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394384))), -(_394386 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394384)))], (8570 ^ _106296) ^ [] : [_394386 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394384)), -(c_Polynomial_Opoly(_394384, _394386) = c_Polynomial_Opoly(_394384, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394384))))]]], (8576 ^ _106296) ^ [_394973, _394975] : [class_Rings_Ocomm__semiring__0(_394973), -(c_Polynomial_Osmult(_394973, _394975, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394973))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_394973)))], (8582 ^ _106296) ^ [_395233, _395235, _395237, _395239] : [class_Groups_Oab__group__add(_395233), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_395233), c_Polynomial_Omonom(_395233, _395235, _395237), c_Polynomial_Omonom(_395233, _395239, _395237)) = c_Polynomial_Omonom(_395233, c_Groups_Ominus__class_Ominus(_395233, _395235, _395239), _395237))], (8588 ^ _106296) ^ [_395511, _395513, _395515] : [class_Groups_Oab__group__add(_395511), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_395511), c_Polynomial_Omonom(_395511, _395513, _395515)) = c_Polynomial_Omonom(_395511, c_Groups_Ouminus__class_Ouminus(_395511, _395513), _395515))], (8594 ^ _106296) ^ [_395757, _395759] : [class_Groups_Ocomm__monoid__add(_395757), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_395757), _395759, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_395757))) = _395759)], (8600 ^ _106296) ^ [_395985, _395987] : [class_Groups_Ocomm__monoid__add(_395985), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_395985), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_395985)), _395987) = _395987)], (8606 ^ _106296) ^ [_396213, _396215] : [class_Rings_Ocomm__semiring__0(_396213), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_396213)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_396213))), _396215) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_396213)))], (8612 ^ _106296) ^ [_396457, _396459] : [class_Rings_Ocomm__semiring__0(_396457), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_396457)), _396459), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_396457))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_396457)))], (8618 ^ _106296) ^ [_396729, _396731, _396733, _396735] : [class_Rings_Ocomm__semiring__0(_396729), -(c_Polynomial_Osmult(_396729, _396731, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_396729), _396733, _396735)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_396729), c_Polynomial_Osmult(_396729, _396731, _396733), c_Polynomial_Osmult(_396729, _396731, _396735)))], (8624 ^ _106296) ^ [_397025, _397027, _397029, _397031] : [class_Rings_Ocomm__semiring__0(_397025), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_397025)), _397027), c_Polynomial_Osmult(_397025, _397029, _397031)) = c_Polynomial_Osmult(_397025, _397029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_397025)), _397027), _397031)))], (8630 ^ _106296) ^ [_397329, _397331, _397333, _397335] : [class_Rings_Ocomm__semiring__0(_397329), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_397329)), c_Polynomial_Osmult(_397329, _397331, _397333)), _397335) = c_Polynomial_Osmult(_397329, _397331, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_397329)), _397333), _397335)))], (8636 ^ _106296) ^ [_397633, _397635, _397637, _397639] : [class_Rings_Ocomm__semiring__0(_397633), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_397633)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_397633), _397635, _397637)), _397639) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_397633), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_397633)), _397635), _397639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_397633)), _397637), _397639)))], (8642 ^ _106296) ^ [_397937, _397939] : [class_Rings_Ocomm__semiring__0(_397937), -(hAPP(c_Polynomial_Opoly(_397937, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_397937))), _397939) = c_Groups_Ozero__class_Ozero(_397937))], (8648 ^ _106296) ^ [_398155] : [class_Groups_Ozero(_398155), -(c_Polynomial_OpCons(_398155, c_Groups_Ozero__class_Ozero(_398155), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398155))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398155)))], (8654 ^ _106296) ^ [_398399, _398401, _398403] : [class_Groups_Ozero(_398399), 8657 ^ _106296 : [(8658 ^ _106296) ^ [] : [c_Polynomial_OpCons(_398399, _398401, _398403) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398399)), 8661 ^ _106296 : [(8662 ^ _106296) ^ [] : [-(_398401 = c_Groups_Ozero__class_Ozero(_398399))], (8664 ^ _106296) ^ [] : [-(_398403 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398399)))]]], (8666 ^ _106296) ^ [] : [-(c_Polynomial_OpCons(_398399, _398401, _398403) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398399))), _398401 = c_Groups_Ozero__class_Ozero(_398399), _398403 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398399))]]], (8676 ^ _106296) ^ [_399079, _399081] : [class_Rings_Ocomm__semiring__0(_399079), -(c_Polynomial_Osmult(_399079, c_Groups_Ozero__class_Ozero(_399079), _399081) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_399079)))], (8682 ^ _106296) ^ [_399321, _399323, _399325] : [class_Rings_Oidom(_399321), 8685 ^ _106296 : [(8696 ^ _106296) ^ [] : [8697 ^ _106296 : [(8698 ^ _106296) ^ [] : [_399323 = c_Groups_Ozero__class_Ozero(_399321)], (8700 ^ _106296) ^ [] : [_399325 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_399321))]], -(c_Polynomial_Osmult(_399321, _399323, _399325) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_399321)))], (8686 ^ _106296) ^ [] : [c_Polynomial_Osmult(_399321, _399323, _399325) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_399321)), -(_399323 = c_Groups_Ozero__class_Ozero(_399321)), -(_399325 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_399321)))]]], (8704 ^ _106296) ^ [_399987] : [class_Rings_Ocomm__semiring__1(_399987), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_399987)) = c_Polynomial_OpCons(_399987, c_Groups_Oone__class_Oone(_399987), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_399987))))], (8710 ^ _106296) ^ [_400245, _400247, _400249, _400251] : [class_Rings_Ocomm__semiring__0(_400245), -(hAPP(c_Polynomial_Opoly(_400245, c_Polynomial_Osmult(_400245, _400247, _400249)), _400251) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_400245), _400247), hAPP(c_Polynomial_Opoly(_400245, _400249), _400251)))], (8716 ^ _106296) ^ [_400541, _400543, _400545, _400547] : [class_Rings_Ocomm__semiring__0(_400541), -(c_Polynomial_Osmult(_400541, _400543, c_Polynomial_OpCons(_400541, _400545, _400547)) = c_Polynomial_OpCons(_400541, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_400541), _400543), _400545), c_Polynomial_Osmult(_400541, _400543, _400547)))], (8722 ^ _106296) ^ [_400809, _400811] : [class_Groups_Ozero(_400809), -(c_Polynomial_Omonom(_400809, c_Groups_Ozero__class_Ozero(_400809), _400811) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_400809)))], (8728 ^ _106296) ^ [_401051, _401053, _401055] : [class_Groups_Ozero(_401051), 8731 ^ _106296 : [(8732 ^ _106296) ^ [] : [c_Polynomial_Omonom(_401051, _401053, _401055) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_401051)), -(_401053 = c_Groups_Ozero__class_Ozero(_401051))], (8738 ^ _106296) ^ [] : [_401053 = c_Groups_Ozero__class_Ozero(_401051), -(c_Polynomial_Omonom(_401051, _401053, _401055) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_401051)))]]], (8744 ^ _106296) ^ [_401583, _401585, _401587, _401589] : [class_Rings_Ocomm__semiring__0(_401583), -(hAPP(c_Polynomial_Opoly(_401583, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_401583), _401585, _401587)), _401589) = c_Groups_Oplus__class_Oplus(_401583, hAPP(c_Polynomial_Opoly(_401583, _401585), _401589), hAPP(c_Polynomial_Opoly(_401583, _401587), _401589)))], (8750 ^ _106296) ^ [_401887, _401889, _401891, _401893] : [class_Rings_Ocomm__semiring__0(_401887), -(hAPP(c_Polynomial_Opoly(_401887, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_401887)), _401889), _401891)), _401893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_401887), hAPP(c_Polynomial_Opoly(_401887, _401889), _401893)), hAPP(c_Polynomial_Opoly(_401887, _401891), _401893)))], (8756 ^ _106296) ^ [_402221, _402223, _402225, _402227, _402229] : [class_Groups_Ocomm__monoid__add(_402221), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_402221), c_Polynomial_OpCons(_402221, _402223, _402225), c_Polynomial_OpCons(_402221, _402227, _402229)) = c_Polynomial_OpCons(_402221, c_Groups_Oplus__class_Oplus(_402221, _402223, _402227), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_402221), _402225, _402229)))], (8762 ^ _106296) ^ [_402531, _402533, _402535, _402537] : [class_Rings_Ocomm__semiring__0(_402531), c_Polynomial_Osmult(_402531, _402533, _402535) = c_Polynomial_OpCons(_402531, _402537, _402535), -(_402535 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402531)))], (8772 ^ _106296) ^ [_402900, _402902, _402904, _402906] : [class_Rings_Ocomm__semiring__0(_402900), -(c_Polynomial_Osmult(_402900, c_Groups_Oplus__class_Oplus(_402900, _402902, _402904), _402906) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_402900), c_Polynomial_Osmult(_402900, _402902, _402906), c_Polynomial_Osmult(_402900, _402904, _402906)))], (8778 ^ _106296) ^ [_403192, _403194, _403196, _403198] : [class_Rings_Ocomm__semiring__0(_403192), -(c_Polynomial_Osmult(_403192, _403194, c_Polynomial_Omonom(_403192, _403196, _403198)) = c_Polynomial_Omonom(_403192, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_403192), _403194), _403196), _403198))], (8784 ^ _106296) ^ [_403480, _403482, _403484, _403486] : [class_Groups_Ocomm__monoid__add(_403480), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_403480), c_Polynomial_Omonom(_403480, _403482, _403484), c_Polynomial_Omonom(_403480, _403486, _403484)) = c_Polynomial_Omonom(_403480, c_Groups_Oplus__class_Oplus(_403480, _403482, _403486), _403484))], (8790 ^ _106296) ^ [_403772, _403774, _403776, _403778] : [class_Rings_Ocomm__semiring__0(_403772), -(hAPP(c_Polynomial_Opoly(_403772, c_Polynomial_OpCons(_403772, _403774, _403776)), _403778) = c_Groups_Oplus__class_Oplus(_403772, _403774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_403772), _403778), hAPP(c_Polynomial_Opoly(_403772, _403776), _403778))))], (8796 ^ _106296) ^ [_404062, _404064, _404066] : [class_Groups_Ozero(_404062), -(c_Polynomial_Omonom(_404062, _404064, c_Nat_OSuc(_404066)) = c_Polynomial_OpCons(_404062, c_Groups_Ozero__class_Ozero(_404062), c_Polynomial_Omonom(_404062, _404064, _404066)))], (8802 ^ _106296) ^ [_404336, _404338, _404340, _404342] : [class_Rings_Ocomm__semiring__1(_404336), -(hAPP(c_Polynomial_Opoly(_404336, c_Polynomial_Omonom(_404336, _404338, _404340)), _404342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404336), _404338), hAPP(hAPP(c_Power_Opower__class_Opower(_404336), _404342), _404340)))], (8808 ^ _106296) ^ [_404608, _404610] : [class_Groups_Ozero(_404608), -(c_Polynomial_Omonom(_404608, _404610, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_404608, _404610, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_404608))))], (8814 ^ _106296) ^ [_404882, _404884, _404886, _404888, _404890] : [class_Rings_Ocomm__semiring__0(_404882), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_404882)), c_Polynomial_Omonom(_404882, _404884, _404886)), c_Polynomial_Omonom(_404882, _404888, _404890)) = c_Polynomial_Omonom(_404882, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404882), _404884), _404888), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404886, _404890)))], (8820 ^ _106296) ^ [_405204, _405206, _405208, _405210] : [class_RealVector_Oreal__normed__vector(_405204), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _405206, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_405204, _405208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _405206), c_RealVector_Onorm__class_Onorm(_405204, _405210))), -(_405208 = c_Groups_Ozero__class_Ozero(_405204))], (8834 ^ _106296) ^ [_405664, _405666, _405668] : [class_Rings_Ocomm__ring__1(_405664), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_405664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_405664)), c_Polynomial_OpCons(_405664, c_Groups_Ouminus__class_Ouminus(_405664, _405666), c_Polynomial_OpCons(_405664, c_Groups_Oone__class_Oone(_405664), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_405664))))), c_Polynomial_Osynthetic__div(_405664, _405668, _405666)), c_Polynomial_OpCons(_405664, hAPP(c_Polynomial_Opoly(_405664, _405668), _405666), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_405664)))) = _405668)], (8840 ^ _106296) ^ [_405980, _405982] : [class_Rings_Ocomm__semiring__0(_405980), -(c_Polynomial_Osynthetic__div(_405980, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_405980)), _405982) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_405980)))], (8846 ^ _106296) ^ [_406240, _406242, _406244, _406246] : [class_Rings_Ocomm__semiring__0(_406240), -(c_Polynomial_Osynthetic__div(_406240, c_Polynomial_OpCons(_406240, _406242, _406244), _406246) = c_Polynomial_OpCons(_406240, hAPP(c_Polynomial_Opoly(_406240, _406244), _406246), c_Polynomial_Osynthetic__div(_406240, _406244, _406246)))], (8852 ^ _106296) ^ [_406533, _406535] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406533, _406535), -(_406535 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406533, 8855 ^ [_406533, _406535]))], (8859 ^ _106296) ^ [_406766, _406768] : [8860 ^ _106296 : [(8861 ^ _106296) ^ [_406841] : [_406768 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406766, _406841)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406766, _406768))], (8865 ^ _106296) ^ [_407024, _407026, _407028] : [class_Rings_Ocomm__semiring__0(_407024), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_407024), _407026, c_Polynomial_Osmult(_407024, _407028, c_Polynomial_Osynthetic__div(_407024, _407026, _407028))) = c_Polynomial_OpCons(_407024, hAPP(c_Polynomial_Opoly(_407024, _407026), _407028), c_Polynomial_Osynthetic__div(_407024, _407026, _407028)))], (8871 ^ _106296) ^ [_407336, _407338, _407340, _407342, _407344] : [class_Rings_Ocomm__semiring__0(_407336), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_407336), _407338, c_Polynomial_Osmult(_407336, _407340, _407342)) = c_Polynomial_OpCons(_407336, _407344, _407342), 8878 ^ _106296 : [(8879 ^ _106296) ^ [] : [-(_407344 = hAPP(c_Polynomial_Opoly(_407336, _407338), _407340))], (8881 ^ _106296) ^ [] : [-(_407342 = c_Polynomial_Osynthetic__div(_407336, _407338, _407340))]]], (8883 ^ _106296) ^ [_407792, _407794] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _407792), -(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), _407792), _407794)))], (8889 ^ _106296) ^ [_408018, _408020] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _408018), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _408020), -(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), _408018), _408020)))], (8899 ^ _106296) ^ [] : [-(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)))], (8901 ^ _106296) ^ [] : [-(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)))], (8903 ^ _106296) ^ [_408441, _408443] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _408441), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _408443), -(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, _408441, _408443)))], (8913 ^ _106296) ^ [_408782, _408784, _408786, _408788] : [class_Rings_Ocomm__semiring__0(_408782), -(c_Polynomial_Opcompose(_408782, c_Polynomial_OpCons(_408782, _408784, _408786), _408788) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_408782), c_Polynomial_OpCons(_408782, _408784, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_408782))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_408782)), _408788), c_Polynomial_Opcompose(_408782, _408786, _408788))))], (8920 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8918 ^ []))], (8922 ^ _106296) ^ [_409181] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _409181), 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____), _409181)), 8918 ^ []))], (8928 ^ _106296) ^ [_409409, _409411] : [class_Rings_Ocomm__semiring__0(_409409), -(c_Polynomial_Opcompose(_409409, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_409409)), _409411) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_409409)))], (8934 ^ _106296) ^ [_409669, _409671, _409673, _409675] : [class_Rings_Ocomm__semiring__0(_409669), -(hAPP(c_Polynomial_Opoly(_409669, c_Polynomial_Opcompose(_409669, _409671, _409673)), _409675) = hAPP(c_Polynomial_Opoly(_409669, _409671), hAPP(c_Polynomial_Opoly(_409669, _409673), _409675)))], (8940 ^ _106296) ^ [_409947, _409949, _409951] : [class_Rings_Oidom(_409947), 8943 ^ _106296 : [(8954 ^ _106296) ^ [] : [8955 ^ _106296 : [(8956 ^ _106296) ^ [] : [_409949 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_409947))], (8958 ^ _106296) ^ [] : [-(c_Polynomial_Oorder(_409947, _409951, _409949) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_409947, _409949), _409951) = c_Groups_Ozero__class_Ozero(_409947))], (8944 ^ _106296) ^ [] : [hAPP(c_Polynomial_Opoly(_409947, _409949), _409951) = c_Groups_Ozero__class_Ozero(_409947), -(_409949 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_409947))), c_Polynomial_Oorder(_409947, _409951, _409949) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (8964 ^ _106296) ^ [] : [8962 ^ [] = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (8966 ^ _106296) ^ [] : [8961 ^ [] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8969 ^ _106296) ^ [] : [-(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, 8967 ^ []), 8961 ^ []), 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____)))], (8971 ^ _106296) ^ [_411069] : [-(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____)), _411069) = 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), _411069), 8961 ^ [])), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, 8962 ^ [], 8967 ^ [])), _411069))))], (8973 ^ _106296) ^ [_411204, _411206] : [class_Orderings_Opreorder(_411204), -(c_Orderings_Oord__class_Oless__eq(_411204, _411206, _411206))], (8979 ^ _106296) ^ [_411428, _411430, _411432] : [class_Rings_Oidom(_411428), -(_411430 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_411428))), 8986 ^ _106296 : [(8987 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_411428), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_411428)), c_Polynomial_OpCons(_411428, c_Groups_Ouminus__class_Ouminus(_411428, _411432), c_Polynomial_OpCons(_411428, c_Groups_Oone__class_Oone(_411428), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_411428))))), c_Polynomial_Oorder(_411428, _411432, _411430)), _411430))], (8989 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_411428), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_411428)), c_Polynomial_OpCons(_411428, c_Groups_Ouminus__class_Ouminus(_411428, _411432), c_Polynomial_OpCons(_411428, c_Groups_Oone__class_Oone(_411428), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_411428))))), c_Nat_OSuc(c_Polynomial_Oorder(_411428, _411432, _411430))), _411430)]]], (8991 ^ _106296) ^ [_411964, _411966] : [class_Rings_Ocomm__semiring__1(_411964), -(c_Rings_Odvd__class_Odvd(_411964, _411966, c_Groups_Ozero__class_Ozero(_411964)))], (8997 ^ _106296) ^ [_412206, _412208, _412210, _412212] : [class_Fields_Ofield(_412206), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_412206), _412208, c_Polynomial_Osmult(_412206, _412210, _412212)), -(_412210 = c_Groups_Ozero__class_Ozero(_412206)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_412206), _412208, _412212))], (9011 ^ _106296) ^ [_412675, _412677, _412679, _412681] : [class_Fields_Ofield(_412675), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_412675), _412677, _412679), -(_412681 = c_Groups_Ozero__class_Ozero(_412675)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_412675), c_Polynomial_Osmult(_412675, _412681, _412677), _412679))], (9025 ^ _106296) ^ [_413144, _413146, _413148, _413150] : [class_Fields_Ofield(_413144), -(_413146 = c_Groups_Ozero__class_Ozero(_413144)), 9032 ^ _106296 : [(9033 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_413144), _413148, c_Polynomial_Osmult(_413144, _413146, _413150)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_413144), _413148, _413150))], (9039 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_413144), _413148, _413150), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_413144), _413148, c_Polynomial_Osmult(_413144, _413146, _413150)))]]], (9045 ^ _106296) ^ [_413796, _413798, _413800, _413802] : [class_Rings_Ocomm__semiring__1(_413796), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_413796), _413798, _413800), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_413796), _413798, c_Polynomial_Osmult(_413796, _413802, _413800)))], (9055 ^ _106296) ^ [_414161, _414163, _414165, _414167] : [class_Rings_Ocomm__semiring__1(_414161), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_414161), c_Polynomial_Osmult(_414161, _414163, _414165), _414167), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_414161), _414165, _414167))], (9065 ^ _106296) ^ [_414526, _414528, _414530, _414532] : [class_Rings_Ocomm__semiring__1(_414526), c_Rings_Odvd__class_Odvd(_414526, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414526), _414528), _414530), _414532), -(c_Rings_Odvd__class_Odvd(_414526, _414530, _414532))], (9075 ^ _106296) ^ [_414891, _414893, _414895, _414897] : [class_Rings_Ocomm__semiring__1(_414891), c_Rings_Odvd__class_Odvd(_414891, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414891), _414893), _414895), _414897), -(c_Rings_Odvd__class_Odvd(_414891, _414893, _414897))], (9085 ^ _106296) ^ [_415256, _415258, _415260, _415262] : [class_Rings_Odvd(_415256), _415258 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415256), _415260), _415262), -(c_Rings_Odvd__class_Odvd(_415256, _415260, _415258))], (9095 ^ _106296) ^ [_415633, _415635, _415637, _415639, _415641] : [class_Rings_Ocomm__semiring__1(_415633), c_Rings_Odvd__class_Odvd(_415633, _415635, _415637), c_Rings_Odvd__class_Odvd(_415633, _415639, _415641), -(c_Rings_Odvd__class_Odvd(_415633, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415633), _415635), _415639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415633), _415637), _415641)))], (9109 ^ _106296) ^ [_416127, _416129, _416131, _416133] : [class_Rings_Ocomm__semiring__1(_416127), c_Rings_Odvd__class_Odvd(_416127, _416129, _416131), -(c_Rings_Odvd__class_Odvd(_416127, _416129, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416127), _416133), _416131)))], (9119 ^ _106296) ^ [_416492, _416494, _416496, _416498] : [class_Rings_Ocomm__semiring__1(_416492), c_Rings_Odvd__class_Odvd(_416492, _416494, _416496), -(c_Rings_Odvd__class_Odvd(_416492, _416494, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416492), _416496), _416498)))], (9129 ^ _106296) ^ [_416843, _416845, _416847] : [class_Rings_Ocomm__semiring__1(_416843), -(c_Rings_Odvd__class_Odvd(_416843, _416845, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416843), _416847), _416845)))], (9135 ^ _106296) ^ [_417089, _417091, _417093] : [class_Rings_Ocomm__semiring__1(_417089), -(c_Rings_Odvd__class_Odvd(_417089, _417091, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417089), _417091), _417093)))], (9141 ^ _106296) ^ [_417349, _417351, _417353, _417355] : [class_Rings_Oidom(_417349), 9144 ^ _106296 : [(9155 ^ _106296) ^ [] : [9156 ^ _106296 : [(9157 ^ _106296) ^ [] : [_417351 = c_Groups_Ozero__class_Ozero(_417349)], (9159 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(_417349, _417353, _417355)]], -(c_Rings_Odvd__class_Odvd(_417349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417349), _417351), _417353), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417349), _417351), _417355)))], (9145 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(_417349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417349), _417351), _417353), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417349), _417351), _417355)), -(_417351 = c_Groups_Ozero__class_Ozero(_417349)), -(c_Rings_Odvd__class_Odvd(_417349, _417353, _417355))]]], (9163 ^ _106296) ^ [_418097, _418099, _418101, _418103] : [class_Rings_Oidom(_418097), 9166 ^ _106296 : [(9177 ^ _106296) ^ [] : [9178 ^ _106296 : [(9179 ^ _106296) ^ [] : [_418101 = c_Groups_Ozero__class_Ozero(_418097)], (9181 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(_418097, _418099, _418103)]], -(c_Rings_Odvd__class_Odvd(_418097, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418097), _418099), _418101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418097), _418103), _418101)))], (9167 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(_418097, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418097), _418099), _418101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418097), _418103), _418101)), -(_418101 = c_Groups_Ozero__class_Ozero(_418097)), -(c_Rings_Odvd__class_Odvd(_418097, _418099, _418103))]]], (9185 ^ _106296) ^ [_418817, _418819] : [class_Rings_Ocomm__semiring__1(_418817), -(c_Rings_Odvd__class_Odvd(_418817, _418819, _418819))], (9191 ^ _106296) ^ [_419055, _419057, _419059, _419061] : [class_Rings_Ocomm__semiring__1(_419055), c_Rings_Odvd__class_Odvd(_419055, _419057, _419059), c_Rings_Odvd__class_Odvd(_419055, _419059, _419061), -(c_Rings_Odvd__class_Odvd(_419055, _419057, _419061))], (9205 ^ _106296) ^ [_419475, _419477] : [class_Rings_Ocomm__semiring__1(_419475), c_Rings_Odvd__class_Odvd(_419475, c_Groups_Ozero__class_Ozero(_419475), _419477), -(_419477 = c_Groups_Ozero__class_Ozero(_419475))], (9215 ^ _106296) ^ [_419810, _419812, _419814, _419816] : [class_Rings_Ocomm__semiring__1(_419810), c_Rings_Odvd__class_Odvd(_419810, _419812, _419814), c_Rings_Odvd__class_Odvd(_419810, _419812, _419816), -(c_Rings_Odvd__class_Odvd(_419810, _419812, c_Groups_Oplus__class_Oplus(_419810, _419814, _419816)))], (9229 ^ _106296) ^ [_420266, _420268, _420270, _420272] : [class_Rings_Ocomm__ring__1(_420266), c_Rings_Odvd__class_Odvd(_420266, _420268, _420270), c_Rings_Odvd__class_Odvd(_420266, _420268, _420272), -(c_Rings_Odvd__class_Odvd(_420266, _420268, c_Groups_Ominus__class_Ominus(_420266, _420270, _420272)))], (9243 ^ _106296) ^ [_420708, _420710, _420712] : [class_Rings_Ocomm__ring__1(_420708), 9246 ^ _106296 : [(9247 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(_420708, _420710, c_Groups_Ouminus__class_Ouminus(_420708, _420712)), -(c_Rings_Odvd__class_Odvd(_420708, _420710, _420712))], (9253 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(_420708, _420710, _420712), -(c_Rings_Odvd__class_Odvd(_420708, _420710, c_Groups_Ouminus__class_Ouminus(_420708, _420712)))]]], (9259 ^ _106296) ^ [_421211, _421213, _421215] : [class_Rings_Ocomm__ring__1(_421211), 9262 ^ _106296 : [(9263 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(_421211, c_Groups_Ouminus__class_Ouminus(_421211, _421213), _421215), -(c_Rings_Odvd__class_Odvd(_421211, _421213, _421215))], (9269 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(_421211, _421213, _421215), -(c_Rings_Odvd__class_Odvd(_421211, c_Groups_Ouminus__class_Ouminus(_421211, _421213), _421215))]]], (9275 ^ _106296) ^ [_421700, _421702] : [class_Rings_Ocomm__semiring__1(_421700), -(c_Rings_Odvd__class_Odvd(_421700, c_Groups_Oone__class_Oone(_421700), _421702))], (9281 ^ _106296) ^ [_421942, _421944, _421946, _421948] : [class_Rings_Ocomm__semiring__1(_421942), c_Rings_Odvd__class_Odvd(_421942, _421944, _421946), -(c_Rings_Odvd__class_Odvd(_421942, hAPP(hAPP(c_Power_Opower__class_Opower(_421942), _421944), _421948), hAPP(hAPP(c_Power_Opower__class_Opower(_421942), _421946), _421948)))], (9291 ^ _106296) ^ [_422337, _422339, _422341, _422343, _422345] : [class_Rings_Ocomm__semiring__1(_422337), c_Rings_Odvd__class_Odvd(_422337, hAPP(hAPP(c_Power_Opower__class_Opower(_422337), _422339), _422341), _422343), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _422345, _422341), -(c_Rings_Odvd__class_Odvd(_422337, hAPP(hAPP(c_Power_Opower__class_Opower(_422337), _422339), _422345), _422343))], (9305 ^ _106296) ^ [_422845, _422847, _422849, _422851, _422853] : [class_Rings_Ocomm__semiring__1(_422845), c_Rings_Odvd__class_Odvd(_422845, _422847, _422849), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _422851, _422853), -(c_Rings_Odvd__class_Odvd(_422845, hAPP(hAPP(c_Power_Opower__class_Opower(_422845), _422847), _422851), hAPP(hAPP(c_Power_Opower__class_Opower(_422845), _422849), _422853)))], (9319 ^ _106296) ^ [_423339, _423341, _423343, _423345] : [class_Rings_Ocomm__semiring__1(_423339), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _423341, _423343), -(c_Rings_Odvd__class_Odvd(_423339, hAPP(hAPP(c_Power_Opower__class_Opower(_423339), _423345), _423341), hAPP(hAPP(c_Power_Opower__class_Opower(_423339), _423345), _423343)))], (9329 ^ _106296) ^ [_423720, _423722, _423724, _423726] : [class_Fields_Ofield(_423720), 9332 ^ _106296 : [(9349 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_423720), c_Polynomial_Osmult(_423720, _423722, _423724), _423726)), 9352 ^ _106296 : [(9353 ^ _106296) ^ [] : [-(_423722 = c_Groups_Ozero__class_Ozero(_423720))], (9355 ^ _106296) ^ [] : [_423726 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_423720))]], 9356 ^ _106296 : [(9357 ^ _106296) ^ [] : [_423722 = c_Groups_Ozero__class_Ozero(_423720)], (9359 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_423720), _423724, _423726)]]], (9333 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_423720), c_Polynomial_Osmult(_423720, _423722, _423724), _423726), 9336 ^ _106296 : [(9337 ^ _106296) ^ [] : [_423722 = c_Groups_Ozero__class_Ozero(_423720), -(_423726 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_423720)))], (9343 ^ _106296) ^ [] : [-(_423722 = c_Groups_Ozero__class_Ozero(_423720)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_423720), _423724, _423726))]]]]], (9363 ^ _106296) ^ [_424790, _424792, _424794] : [class_Orderings_Olinorder(_424790), -(c_Orderings_Oord__class_Oless__eq(_424790, _424792, _424794)), -(c_Orderings_Oord__class_Oless__eq(_424790, _424794, _424792))], (9373 ^ _106296) ^ [_425146, _425148, _425150, _425152, _425154] : [class_Orderings_Oord(_425146), c_Orderings_Oord__class_Oless__eq(tc_fun(_425148, _425146), _425150, _425152), -(c_Orderings_Oord__class_Oless__eq(_425146, hAPP(_425150, _425154), hAPP(_425152, _425154)))], (9383 ^ _106296) ^ [_425523, _425525, _425527, _425529] : [class_Orderings_Oorder(_425523), c_Orderings_Oord__class_Oless__eq(_425523, _425525, _425527), c_Orderings_Oord__class_Oless__eq(_425523, _425529, _425525), -(c_Orderings_Oord__class_Oless__eq(_425523, _425529, _425527))], (9397 ^ _106296) ^ [_425957, _425959, _425961] : [class_Orderings_Oorder(_425957), c_Orderings_Oord__class_Oless__eq(_425957, _425959, _425961), c_Orderings_Oord__class_Oless__eq(_425957, _425961, _425959), -(_425961 = _425959)], (9411 ^ _106296) ^ [_426389, _426391, _426393, _426395] : [class_Orderings_Opreorder(_426389), c_Orderings_Oord__class_Oless__eq(_426389, _426391, _426393), c_Orderings_Oord__class_Oless__eq(_426389, _426393, _426395), -(c_Orderings_Oord__class_Oless__eq(_426389, _426391, _426395))], (9425 ^ _106296) ^ [_426823, _426825, _426827] : [class_Orderings_Oorder(_426823), c_Orderings_Oord__class_Oless__eq(_426823, _426825, _426827), c_Orderings_Oord__class_Oless__eq(_426823, _426827, _426825), -(_426825 = _426827)], (9439 ^ _106296) ^ [_427255, _427257, _427259, _427261] : [class_Orderings_Oorder(_427255), c_Orderings_Oord__class_Oless__eq(_427255, _427257, _427259), _427257 = _427261, -(c_Orderings_Oord__class_Oless__eq(_427255, _427261, _427259))], (9453 ^ _106296) ^ [_427701, _427703, _427705, _427707] : [class_Orderings_Oord(_427701), c_Orderings_Oord__class_Oless__eq(_427701, _427703, _427705), _427705 = _427707, -(c_Orderings_Oord__class_Oless__eq(_427701, _427703, _427707))], (9467 ^ _106296) ^ [_428147, _428149, _428151, _428153] : [class_Orderings_Oorder(_428147), _428149 = _428151, c_Orderings_Oord__class_Oless__eq(_428147, _428153, _428151), -(c_Orderings_Oord__class_Oless__eq(_428147, _428153, _428149))], (9481 ^ _106296) ^ [_428593, _428595, _428597, _428599] : [class_Orderings_Oord(_428593), _428595 = _428597, c_Orderings_Oord__class_Oless__eq(_428593, _428597, _428599), -(c_Orderings_Oord__class_Oless__eq(_428593, _428595, _428599))], (9495 ^ _106296) ^ [_429025, _429027, _429029] : [class_Orderings_Oorder(_429025), c_Orderings_Oord__class_Oless__eq(_429025, _429027, _429029), 9502 ^ _106296 : [(9503 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_429025, _429029, _429027), -(_429029 = _429027)], (9509 ^ _106296) ^ [] : [_429029 = _429027, -(c_Orderings_Oord__class_Oless__eq(_429025, _429029, _429027))]]], (9515 ^ _106296) ^ [_429639, _429641, _429643, _429645, _429647] : [class_Orderings_Oord(_429639), c_Orderings_Oord__class_Oless__eq(tc_fun(_429641, _429639), _429643, _429645), -(c_Orderings_Oord__class_Oless__eq(_429639, hAPP(_429643, _429647), hAPP(_429645, _429647)))], (9525 ^ _106296) ^ [_430002, _430004, _430006] : [class_Orderings_Opreorder(_430002), _430004 = _430006, -(c_Orderings_Oord__class_Oless__eq(_430002, _430004, _430006))], (9535 ^ _106296) ^ [_430325, _430327, _430329] : [class_Orderings_Oorder(_430325), 9538 ^ _106296 : [(9539 ^ _106296) ^ [] : [_430327 = _430329, 9542 ^ _106296 : [(9543 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_430325, _430327, _430329))], (9545 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_430325, _430329, _430327))]]], (9547 ^ _106296) ^ [] : [-(_430327 = _430329), c_Orderings_Oord__class_Oless__eq(_430325, _430327, _430329), c_Orderings_Oord__class_Oless__eq(_430325, _430329, _430327)]]], (9557 ^ _106296) ^ [_430983, _430985, _430987] : [class_Orderings_Olinorder(_430983), -(c_Orderings_Oord__class_Oless__eq(_430983, _430985, _430987)), -(c_Orderings_Oord__class_Oless__eq(_430983, _430987, _430985))], (9567 ^ _106296) ^ [_431323, _431325, _431327, _431329] : [class_Orderings_Oord(_431323), 9570 ^ _106296 : [(9571 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_431325, _431323), _431327, _431329), 9574 ^ _106296 : [(9575 ^ _106296) ^ [_431582] : [-(c_Orderings_Oord__class_Oless__eq(_431323, hAPP(_431327, _431582), hAPP(_431329, _431582)))]]], (9577 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_431323, hAPP(_431327, 9578 ^ [_431323, _431325, _431327, _431329]), hAPP(_431329, 9578 ^ [_431323, _431325, _431327, _431329])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_431325, _431323), _431327, _431329))]]], (9584 ^ _106296) ^ [_431950, _431952] : [class_Orderings_Opreorder(_431950), c_Orderings_Oord__class_Oless(_431950, _431952, _431952)], (9590 ^ _106296) ^ [_432175, _432177, _432179] : [class_Orderings_Olinorder(_432175), 9593 ^ _106296 : [(9604 ^ _106296) ^ [] : [9605 ^ _106296 : [(9606 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_432175, _432177, _432179)], (9608 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_432175, _432179, _432177)]], _432177 = _432179], (9594 ^ _106296) ^ [] : [-(_432177 = _432179), -(c_Orderings_Oord__class_Oless(_432175, _432177, _432179)), -(c_Orderings_Oord__class_Oless(_432175, _432179, _432177))]]], (9612 ^ _106296) ^ [_432835, _432837, _432839] : [class_Orderings_Olinorder(_432835), 9615 ^ _106296 : [(9626 ^ _106296) ^ [] : [9627 ^ _106296 : [(9628 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_432835, _432839, _432837)], (9630 ^ _106296) ^ [] : [_432837 = _432839]], c_Orderings_Oord__class_Oless(_432835, _432837, _432839)], (9616 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_432835, _432837, _432839)), -(c_Orderings_Oord__class_Oless(_432835, _432839, _432837)), -(_432837 = _432839)]]], (9634 ^ _106296) ^ [_433495, _433497, _433499] : [class_Orderings_Olinorder(_433495), -(c_Orderings_Oord__class_Oless(_433495, _433497, _433499)), -(_433497 = _433499), -(c_Orderings_Oord__class_Oless(_433495, _433499, _433497))], (9648 ^ _106296) ^ [_433915, _433917, _433919] : [class_Orderings_Olinorder(_433915), -(c_Orderings_Oord__class_Oless(_433915, _433917, _433919)), 9655 ^ _106296 : [(9656 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_433915, _433919, _433917)), -(_433919 = _433917)], (9662 ^ _106296) ^ [] : [_433919 = _433917, c_Orderings_Oord__class_Oless(_433915, _433919, _433917)]]], (9668 ^ _106296) ^ [_434506, _434508, _434510] : [class_Orderings_Olinorder(_434506), -(_434508 = _434510), -(c_Orderings_Oord__class_Oless(_434506, _434508, _434510)), -(c_Orderings_Oord__class_Oless(_434506, _434510, _434508))], (9682 ^ _106296) ^ [_434930, _434932, _434934] : [class_Orderings_Oorder(_434930), c_Orderings_Oord__class_Oless(_434930, _434932, _434934), _434932 = _434934], (9692 ^ _106296) ^ [_435254, _435256, _435258] : [class_Orderings_Opreorder(_435254), c_Orderings_Oord__class_Oless(_435254, _435256, _435258), c_Orderings_Oord__class_Oless(_435254, _435258, _435256)], (9702 ^ _106296) ^ [_435580, _435582, _435584] : [class_Orderings_Opreorder(_435580), c_Orderings_Oord__class_Oless(_435580, _435582, _435584), c_Orderings_Oord__class_Oless(_435580, _435584, _435582)], (9712 ^ _106296) ^ [_435906, _435908, _435910] : [class_Orderings_Oorder(_435906), c_Orderings_Oord__class_Oless(_435906, _435908, _435910), _435908 = _435910], (9722 ^ _106296) ^ [_436230, _436232, _436234] : [class_Orderings_Oorder(_436230), c_Orderings_Oord__class_Oless(_436230, _436232, _436234), _436234 = _436232], (9732 ^ _106296) ^ [_436554, _436556, _436558] : [class_Orderings_Opreorder(_436554), c_Orderings_Oord__class_Oless(_436554, _436556, _436558), c_Orderings_Oord__class_Oless(_436554, _436558, _436556)], (9742 ^ _106296) ^ [_436880, _436882, _436884] : [class_Orderings_Oorder(_436880), c_Orderings_Oord__class_Oless(_436880, _436882, _436884), c_Orderings_Oord__class_Oless(_436880, _436884, _436882)], (9752 ^ _106296) ^ [_437220, _437222, _437224, _437226] : [class_Orderings_Oord(_437220), _437222 = _437224, c_Orderings_Oord__class_Oless(_437220, _437224, _437226), -(c_Orderings_Oord__class_Oless(_437220, _437222, _437226))], (9766 ^ _106296) ^ [_437666, _437668, _437670, _437672] : [class_Orderings_Oorder(_437666), _437668 = _437670, c_Orderings_Oord__class_Oless(_437666, _437672, _437670), -(c_Orderings_Oord__class_Oless(_437666, _437672, _437668))], (9780 ^ _106296) ^ [_438112, _438114, _438116, _438118] : [class_Orderings_Oord(_438112), c_Orderings_Oord__class_Oless(_438112, _438114, _438116), _438116 = _438118, -(c_Orderings_Oord__class_Oless(_438112, _438114, _438118))], (9794 ^ _106296) ^ [_438558, _438560, _438562, _438564] : [class_Orderings_Oorder(_438558), c_Orderings_Oord__class_Oless(_438558, _438560, _438562), _438560 = _438564, -(c_Orderings_Oord__class_Oless(_438558, _438564, _438562))], (9808 ^ _106296) ^ [_439004, _439006, _439008, _439010] : [class_Orderings_Opreorder(_439004), c_Orderings_Oord__class_Oless(_439004, _439006, _439008), c_Orderings_Oord__class_Oless(_439004, _439008, _439010), -(c_Orderings_Oord__class_Oless(_439004, _439006, _439010))], (9822 ^ _106296) ^ [_439452, _439454, _439456, _439458] : [class_Orderings_Oorder(_439452), c_Orderings_Oord__class_Oless(_439452, _439454, _439456), c_Orderings_Oord__class_Oless(_439452, _439458, _439454), -(c_Orderings_Oord__class_Oless(_439452, _439458, _439456))], (9836 ^ _106296) ^ [_439886, _439888, _439890] : [class_Orderings_Opreorder(_439886), c_Orderings_Oord__class_Oless(_439886, _439888, _439890), c_Orderings_Oord__class_Oless(_439886, _439890, _439888)], (9846 ^ _106296) ^ [_440212, _440214, _440216] : [class_Orderings_Olinorder(_440212), -(c_Orderings_Oord__class_Oless(_440212, _440214, _440216)), -(_440214 = _440216), -(c_Orderings_Oord__class_Oless(_440212, _440216, _440214))], (9860 ^ _106296) ^ [_440636, _440638, _440640] : [class_Rings_Ocomm__semiring__1(_440636), 9865 ^ _106296 : [(9866 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _440638)], (9868 ^ _106296) ^ [] : [_440640 = c_Groups_Oone__class_Oone(_440636)]], -(c_Rings_Odvd__class_Odvd(_440636, _440640, hAPP(hAPP(c_Power_Opower__class_Opower(_440636), _440640), _440638)))], (9872 ^ _106296) ^ [_441057, _441059, _441061] : [class_Rings_Oidom(_441057), 9875 ^ _106296 : [(9876 ^ _106296) ^ [] : [hAPP(c_Polynomial_Opoly(_441057, _441059), _441061) = c_Groups_Ozero__class_Ozero(_441057), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_441057), c_Polynomial_OpCons(_441057, c_Groups_Ouminus__class_Ouminus(_441057, _441061), c_Polynomial_OpCons(_441057, c_Groups_Oone__class_Oone(_441057), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_441057)))), _441059))], (9882 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_441057), c_Polynomial_OpCons(_441057, c_Groups_Ouminus__class_Ouminus(_441057, _441061), c_Polynomial_OpCons(_441057, c_Groups_Oone__class_Oone(_441057), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_441057)))), _441059), -(hAPP(c_Polynomial_Opoly(_441057, _441059), _441061) = c_Groups_Ozero__class_Ozero(_441057))]]], (9888 ^ _106296) ^ [_441629, _441631, _441633] : [class_Rings_Oidom(_441629), 9891 ^ _106296 : [(9892 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_441629), c_Polynomial_OpCons(_441629, _441631, c_Polynomial_OpCons(_441629, c_Groups_Oone__class_Oone(_441629), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_441629)))), _441633), -(hAPP(c_Polynomial_Opoly(_441629, _441633), c_Groups_Ouminus__class_Ouminus(_441629, _441631)) = c_Groups_Ozero__class_Ozero(_441629))], (9898 ^ _106296) ^ [] : [hAPP(c_Polynomial_Opoly(_441629, _441633), c_Groups_Ouminus__class_Ouminus(_441629, _441631)) = c_Groups_Ozero__class_Ozero(_441629), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_441629), c_Polynomial_OpCons(_441629, _441631, c_Polynomial_OpCons(_441629, c_Groups_Oone__class_Oone(_441629), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_441629)))), _441633))]]], (9904 ^ _106296) ^ [_442201, _442203, _442205] : [class_Rings_Oidom(_442201), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_442201), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_442201)), c_Polynomial_OpCons(_442201, c_Groups_Ouminus__class_Ouminus(_442201, _442203), c_Polynomial_OpCons(_442201, c_Groups_Oone__class_Oone(_442201), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_442201))))), c_Polynomial_Oorder(_442201, _442203, _442205)), _442205))], (9910 ^ _106296) ^ [_442511, _442513, _442515, _442517] : [class_Orderings_Oorder(_442511), c_Orderings_Oord__class_Oless__eq(_442511, _442513, _442515), c_Orderings_Oord__class_Oless(_442511, _442517, _442513), -(c_Orderings_Oord__class_Oless(_442511, _442517, _442515))], (9924 ^ _106296) ^ [_442959, _442961, _442963, _442965] : [class_Orderings_Opreorder(_442959), c_Orderings_Oord__class_Oless__eq(_442959, _442961, _442963), c_Orderings_Oord__class_Oless(_442959, _442963, _442965), -(c_Orderings_Oord__class_Oless(_442959, _442961, _442965))], (9938 ^ _106296) ^ [_443407, _443409, _443411, _443413] : [class_Orderings_Oorder(_443407), c_Orderings_Oord__class_Oless(_443407, _443409, _443411), c_Orderings_Oord__class_Oless__eq(_443407, _443413, _443409), -(c_Orderings_Oord__class_Oless(_443407, _443413, _443411))], (9952 ^ _106296) ^ [_443855, _443857, _443859, _443861] : [class_Orderings_Opreorder(_443855), c_Orderings_Oord__class_Oless(_443855, _443857, _443859), c_Orderings_Oord__class_Oless__eq(_443855, _443859, _443861), -(c_Orderings_Oord__class_Oless(_443855, _443857, _443861))], (9966 ^ _106296) ^ [_444289, _444291, _444293] : [class_Orderings_Oorder(_444289), c_Orderings_Oord__class_Oless__eq(_444289, _444291, _444293), -(_444293 = _444291), -(c_Orderings_Oord__class_Oless(_444289, _444291, _444293))], (9980 ^ _106296) ^ [_444710, _444712, _444714] : [class_Orderings_Oorder(_444710), c_Orderings_Oord__class_Oless__eq(_444710, _444712, _444714), -(_444712 = _444714), -(c_Orderings_Oord__class_Oless(_444710, _444712, _444714))], (9994 ^ _106296) ^ [_445131, _445133, _445135] : [class_Orderings_Oorder(_445131), c_Orderings_Oord__class_Oless__eq(_445131, _445133, _445135), -(c_Orderings_Oord__class_Oless(_445131, _445133, _445135)), -(_445133 = _445135)], (10008 ^ _106296) ^ [_445550, _445552, _445554] : [class_Orderings_Olinorder(_445550), c_Orderings_Oord__class_Oless__eq(_445550, _445552, _445554), 10015 ^ _106296 : [(10016 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_445550, _445552, _445554)), -(_445552 = _445554)], (10022 ^ _106296) ^ [] : [_445552 = _445554, c_Orderings_Oord__class_Oless(_445550, _445552, _445554)]]], (10028 ^ _106296) ^ [_446138, _446140, _446142] : [class_Orderings_Opreorder(_446138), c_Orderings_Oord__class_Oless(_446138, _446140, _446142), -(c_Orderings_Oord__class_Oless__eq(_446138, _446140, _446142))], (10038 ^ _106296) ^ [_446463, _446465, _446467] : [class_Orderings_Olinorder(_446463), c_Orderings_Oord__class_Oless__eq(_446463, _446465, _446467), c_Orderings_Oord__class_Oless(_446463, _446467, _446465)], (10048 ^ _106296) ^ [_446789, _446791, _446793] : [class_Orderings_Oorder(_446789), -(_446791 = _446793), c_Orderings_Oord__class_Oless__eq(_446789, _446793, _446791), -(c_Orderings_Oord__class_Oless(_446789, _446793, _446791))], (10062 ^ _106296) ^ [_447210, _447212, _447214] : [class_Orderings_Oorder(_447210), -(_447212 = _447214), c_Orderings_Oord__class_Oless__eq(_447210, _447212, _447214), -(c_Orderings_Oord__class_Oless(_447210, _447212, _447214))], (10076 ^ _106296) ^ [_447631, _447633, _447635] : [class_Orderings_Olinorder(_447631), -(c_Orderings_Oord__class_Oless(_447631, _447633, _447635)), 10083 ^ _106296 : [(10084 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_447631, _447633, _447635), -(_447633 = _447635)], (10090 ^ _106296) ^ [] : [_447633 = _447635, -(c_Orderings_Oord__class_Oless__eq(_447631, _447633, _447635))]]], (10096 ^ _106296) ^ [_448220, _448222, _448224] : [class_Orderings_Olinorder(_448220), -(c_Orderings_Oord__class_Oless__eq(_448220, _448222, _448224)), -(c_Orderings_Oord__class_Oless(_448220, _448224, _448222))], (10106 ^ _106296) ^ [_448548, _448550, _448552] : [class_Orderings_Olinorder(_448548), -(c_Orderings_Oord__class_Oless(_448548, _448550, _448552)), -(c_Orderings_Oord__class_Oless__eq(_448548, _448552, _448550))], (10116 ^ _106296) ^ [_448876, _448878, _448880] : [class_Orderings_Oorder(_448876), 10119 ^ _106296 : [(10130 ^ _106296) ^ [] : [10131 ^ _106296 : [(10132 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_448876, _448878, _448880)], (10134 ^ _106296) ^ [] : [_448878 = _448880]], -(c_Orderings_Oord__class_Oless__eq(_448876, _448878, _448880))], (10120 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_448876, _448878, _448880), -(c_Orderings_Oord__class_Oless(_448876, _448878, _448880)), -(_448878 = _448880)]]], (10138 ^ _106296) ^ [_449534, _449536, _449538] : [class_Orderings_Opreorder(_449534), 10141 ^ _106296 : [(10142 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_449534, _449536, _449538), 10145 ^ _106296 : [(10146 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_449534, _449536, _449538))], (10148 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_449534, _449538, _449536)]]], (10150 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_449534, _449536, _449538)), c_Orderings_Oord__class_Oless__eq(_449534, _449536, _449538), -(c_Orderings_Oord__class_Oless__eq(_449534, _449538, _449536))]]], (10160 ^ _106296) ^ [_450197, _450199, _450201] : [class_Orderings_Oorder(_450197), 10163 ^ _106296 : [(10164 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_450197, _450199, _450201), 10167 ^ _106296 : [(10168 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_450197, _450199, _450201))], (10170 ^ _106296) ^ [] : [_450199 = _450201]]], (10172 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_450197, _450199, _450201)), c_Orderings_Oord__class_Oless__eq(_450197, _450199, _450201), -(_450199 = _450201)]]], (10182 ^ _106296) ^ [_450857, _450859, _450861] : [class_Orderings_Olinorder(_450857), -(c_Orderings_Oord__class_Oless__eq(_450857, _450859, _450861)), -(c_Orderings_Oord__class_Oless(_450857, _450861, _450859))], (10192 ^ _106296) ^ [_451183, _451185, _451187] : [class_Orderings_Olinorder(_451183), 10195 ^ _106296 : [(10196 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_451183, _451185, _451187)), -(c_Orderings_Oord__class_Oless(_451183, _451187, _451185))], (10202 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(_451183, _451187, _451185), c_Orderings_Oord__class_Oless__eq(_451183, _451185, _451187)]]], (10208 ^ _106296) ^ [_451679, _451681, _451683] : [class_Orderings_Olinorder(_451679), 10211 ^ _106296 : [(10212 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_451679, _451681, _451683)), -(c_Orderings_Oord__class_Oless__eq(_451679, _451683, _451681))], (10218 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(_451679, _451683, _451681), c_Orderings_Oord__class_Oless(_451679, _451681, _451683)]]], (10224 ^ _106296) ^ [_452175, _452177, _452179] : [class_Rings_Oidom(_452175), -(_452177 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_452175))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_452175), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_452175)), c_Polynomial_OpCons(_452175, c_Groups_Ouminus__class_Ouminus(_452175, _452179), c_Polynomial_OpCons(_452175, c_Groups_Oone__class_Oone(_452175), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_452175))))), c_Nat_OSuc(c_Polynomial_Oorder(_452175, _452179, _452177))), _452177)], (10234 ^ _106296) ^ [_452594, _452596, _452598, _452600] : [class_Rings_Ocomm__ring(_452594), class_Rings_Odvd(_452594), c_Rings_Odvd__class_Odvd(_452594, _452596, _452598), 10245 ^ _106296 : [(10246 ^ _106296) ^ [_452997, _452999] : [c_Rings_Odvd__class_Odvd(_452594, _452596, c_Groups_Oplus__class_Oplus(_452594, _452999, _452600)), -(c_Rings_Odvd__class_Odvd(_452594, _452596, c_Groups_Oplus__class_Oplus(_452594, c_Groups_Ominus__class_Ominus(_452594, _452999, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452594), _452997), _452598)), _452600)))], (10252 ^ _106296) ^ [_453235, _453237] : [c_Rings_Odvd__class_Odvd(_452594, _452596, c_Groups_Oplus__class_Oplus(_452594, c_Groups_Ominus__class_Ominus(_452594, _453237, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452594), _453235), _452598)), _452600)), -(c_Rings_Odvd__class_Odvd(_452594, _452596, c_Groups_Oplus__class_Oplus(_452594, _453237, _452600)))]]], (10258 ^ _106296) ^ [_453562, _453564, _453566, _453568] : [class_Rings_Ocomm__ring(_453562), class_Rings_Odvd(_453562), c_Rings_Odvd__class_Odvd(_453562, _453564, _453566), 10269 ^ _106296 : [(10270 ^ _106296) ^ [_453965, _453967] : [c_Rings_Odvd__class_Odvd(_453562, _453564, c_Groups_Oplus__class_Oplus(_453562, _453967, _453568)), -(c_Rings_Odvd__class_Odvd(_453562, _453564, c_Groups_Oplus__class_Oplus(_453562, c_Groups_Ominus__class_Ominus(_453562, _453967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453562), _453965), _453566)), _453568)))], (10276 ^ _106296) ^ [_454203, _454205] : [c_Rings_Odvd__class_Odvd(_453562, _453564, c_Groups_Oplus__class_Oplus(_453562, c_Groups_Ominus__class_Ominus(_453562, _454205, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453562), _454203), _453566)), _453568)), -(c_Rings_Odvd__class_Odvd(_453562, _453564, c_Groups_Oplus__class_Oplus(_453562, _454205, _453568)))]]], (10282 ^ _106296) ^ [_454473] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _454473))], (10284 ^ _106296) ^ [_454609, _454611, _454613, _454615] : [class_Orderings_Oord(_454609), 10287 ^ _106296 : [(10288 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_454611, _454609), _454613, _454615), 10291 ^ _106296 : [(10292 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_454611, _454609), _454613, _454615))], (10294 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_454611, _454609), _454615, _454613)]]], (10296 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_454611, _454609), _454613, _454615)), c_Orderings_Oord__class_Oless__eq(tc_fun(_454611, _454609), _454613, _454615), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_454611, _454609), _454615, _454613))]]], (10306 ^ _106296) ^ [_455307, _455309] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _455307), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _455309), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _455307, _455309), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _455309, _455307), -(_455307 = _455309)], (10324 ^ _106296) ^ [_455806, _455808, _455810] : [-(_455806 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10327 ^ _106296 : [(10328 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _455808, _455810), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _455806), _455808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _455806), _455810)))], (10334 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _455806), _455808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _455806), _455810)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _455808, _455810))]]], (10340 ^ _106296) ^ [_456327, _456329] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _456327), c_Orderings_Oord__class_Oless(tc_Int_Oint, _456327, _456329), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _456329, _456327)], (10350 ^ _106296) ^ [_456647, _456649, _456651] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _456647), _456649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _456647), _456651)), -(_456647 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _456649, _456651))], (10360 ^ _106296) ^ [_457002] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _457002, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_457002 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10366 ^ _106296) ^ [_457160] : [_457160 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _457160, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10372 ^ _106296) ^ [_457368, _457370] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _457368), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _457368, _457370), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _457370, _457368)], (10392 ^ _106296) ^ [_458007, _458009, _458011] : [10393 ^ _106296 : [(10394 ^ _106296) ^ [] : [_458007 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10396 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _458009, _458011)]], -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458007), _458009), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458007), _458011)))], (10382 ^ _106296) ^ [_457717, _457719, _457721] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _457717), _457719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _457717), _457721)), -(_457717 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _457719, _457721))], (10400 ^ _106296) ^ [_458358, _458360] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _458358, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _458360, _458358)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _458358, _458360))], (10406 ^ _106296) ^ [_458532, _458534] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _458532, _458534), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _458532, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _458534, _458532)))], (10412 ^ _106296) ^ [_458799, _458801, _458803] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _458799, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _458801, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _458799), _458803))), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _458799, _458801))], (10418 ^ _106296) ^ [_458991, _458993, _458995] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _458991, _458993), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _458991, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _458993, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _458991), _458995))))], (10424 ^ _106296) ^ [_459275, _459277, _459279, _459281, _459283] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _459275, _459277), 10427 ^ _106296 : [(10428 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _459275, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _459279, _459281)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _459275, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _459279, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _459283), _459277)), _459281)))], (10434 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _459275, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _459279, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _459283), _459277)), _459281)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _459275, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _459279, _459281)))]]], (10440 ^ _106296) ^ [_459859, _459861, _459863] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _459859, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _459861, _459863)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _459859, _459863), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _459859, _459861))], (10450 ^ _106296) ^ [_460211, _460213] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _460211, _460213), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _460211, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _460213)))], (10456 ^ _106296) ^ [_460383, _460385] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _460383, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _460385)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _460383, _460385))], (10462 ^ _106296) ^ [_460634, _460636] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _460634, _460636), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _460634), _460636))], (10468 ^ _106296) ^ [_460806, _460808] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _460806), _460808), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _460806, _460808))], (10474 ^ _106296) ^ [_461042, _461044, _461046] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461042, _461044), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461042, _461046), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461042, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _461044, _461046)))], (10484 ^ _106296) ^ [_461380] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461380, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_461380 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10490 ^ _106296) ^ [_461538] : [_461538 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461538, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10496 ^ _106296) ^ [_461760, _461762, _461764] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461760, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _461762, _461764)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461760, _461764), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _461764, _461762), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461760, _461762))], (10510 ^ _106296) ^ [_462192, _462194, _462196] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _462192, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _462194, _462196)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _462192, _462194), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _462196, _462194), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _462192, _462196))], (10524 ^ _106296) ^ [_462610, _462612] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _462610, _462612), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _462612), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _462610, _462612))], (10534 ^ _106296) ^ [_462915, _462917] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _462915, _462917), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _462917), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _462915, _462917))], (10544 ^ _106296) ^ [_463234, _463236, _463238] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _463234), 10547 ^ _106296 : [(10548 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _463234), _463236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _463234), _463238)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _463236, _463238))], (10554 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _463236, _463238), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _463234), _463236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _463234), _463238)))]]], (10560 ^ _106296) ^ [_463768, _463770, _463772] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _463768), _463770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _463768), _463772)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _463768), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _463770, _463772))], (10570 ^ _106296) ^ [_464107, _464109] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _464107), 10573 ^ _106296 : [(10574 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464107), _464109), _464107), -(_464109 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10580 ^ _106296) ^ [] : [_464109 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464107), _464109), _464107))]]], (10586 ^ _106296) ^ [_464590, _464592] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _464590), 10589 ^ _106296 : [(10590 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464592), _464590), _464590), -(_464592 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10596 ^ _106296) ^ [] : [_464592 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464592), _464590), _464590))]]], (10602 ^ _106296) ^ [_465087, _465089, _465091] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _465087), _465089), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _465087), _465091)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _465087), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465089, _465091))], (10612 ^ _106296) ^ [_465440, _465442, _465444] : [class_Rings_Odvd(_465440), class_Rings_Osemiring__0(_465440), 10619 ^ _106296 : [(10620 ^ _106296) ^ [] : [10621 ^ _106296 : [(10622 ^ _106296) ^ [_465749] : [hBOOL(hAPP(_465442, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465440), _465444), _465749)))]], 10624 ^ _106296 : [(10625 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(_465440, _465444, c_Groups_Oplus__class_Oplus(_465440, 10623 ^ [_465440, _465442, _465444], c_Groups_Ozero__class_Ozero(_465440))))], (10627 ^ _106296) ^ [] : [-(hBOOL(hAPP(_465442, 10623 ^ [_465440, _465442, _465444])))]]], (10629 ^ _106296) ^ [] : [-(hBOOL(hAPP(_465442, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465440), _465444), 10636 ^ [_465440, _465442, _465444])))), 10630 ^ _106296 : [(10631 ^ _106296) ^ [_466089] : [c_Rings_Odvd__class_Odvd(_465440, _465444, c_Groups_Oplus__class_Oplus(_465440, _466089, c_Groups_Ozero__class_Ozero(_465440))), hBOOL(hAPP(_465442, _466089))]]]]], (10640 ^ _106296) ^ [_466488, _466490, _466492] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _466488), _466490), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _466492), _466490)), -(_466490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _466488, _466492))], (10650 ^ _106296) ^ [_466842, _466844, _466846] : [-(_466842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10653 ^ _106296 : [(10654 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _466844), _466842), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _466846), _466842)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _466844, _466846))], (10660 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _466844, _466846), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _466844), _466842), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _466846), _466842)))]]], (10666 ^ _106296) ^ [_467334] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _467334, _467334))], (10668 ^ _106296) ^ [_467471, _467473] : [_467471 = _467473, 10671 ^ _106296 : [(10672 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _467471, _467473))], (10674 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _467473, _467471))]]], (10676 ^ _106296) ^ [_467712, _467714] : [-(_467712 = _467714), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _467712, _467714), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _467714, _467712)], (10686 ^ _106296) ^ [_468046, _468048] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468046, _468048), 10691 ^ _106296 : [(10692 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468046, _468048))], (10694 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468048, _468046)]], -(_468046 = _468048)], (10698 ^ _106296) ^ [_468380, _468382] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468380, _468382)), 10699 ^ _106296 : [(10706 ^ _106296) ^ [] : [_468380 = _468382], (10700 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468380, _468382), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468382, _468380))]]], (10710 ^ _106296) ^ [_468793, _468795] : [10717 ^ _106296 : [(10718 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468793, _468795))], (10720 ^ _106296) ^ [] : [_468793 = _468795]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468793, _468795), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _468795, _468793))], (10722 ^ _106296) ^ [_469129, _469131] : [10729 ^ _106296 : [(10730 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _469129, _469131))], (10732 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _469131, _469129)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _469129, _469131), -(_469129 = _469131)], (10734 ^ _106296) ^ [_469515, _469517] : [-(_469515 = _469517), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _469515, _469517), 10741 ^ _106296 : [(10742 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _469515, _469517))], (10744 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _469517, _469515)]]], (10746 ^ _106296) ^ [_469899, _469901] : [_469899 = _469901, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _469899, _469901))], (10752 ^ _106296) ^ [_470111, _470113] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470111, _470113), 10755 ^ _106296 : [(10756 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470113, _470111), -(_470113 = _470111)], (10762 ^ _106296) ^ [] : [_470113 = _470111, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470113, _470111))]]], (10768 ^ _106296) ^ [_470576, _470578] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470576, _470578), 10773 ^ _106296 : [(10774 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470576, _470578))], (10776 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470578, _470576)]], -(_470576 = _470578)], (10780 ^ _106296) ^ [_470958, _470960] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470958, _470960), -(_470958 = _470960), 10787 ^ _106296 : [(10788 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470958, _470960))], (10790 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _470960, _470958)]]], (10792 ^ _106296) ^ [_471356, _471358, _471360] : [_471356 = _471358, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471358, _471360), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471356, _471360))], (10802 ^ _106296) ^ [_471683, _471685, _471687] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471683, _471685), _471685 = _471687, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471683, _471687))], (10812 ^ _106296) ^ [_471996, _471998] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471996, _471998), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _471998, _471996), -(_471996 = _471998)], (10822 ^ _106296) ^ [_472299, _472301] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472299, _472301), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472301, _472299), -(_472299 = _472301)], (10832 ^ _106296) ^ [_472616, _472618, _472620] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472616, _472618), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472618, _472620), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472616, _472620))], (10842 ^ _106296) ^ [_472945, _472947, _472949] : [_472945 = _472947, 10853 ^ _106296 : [(10854 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472945, _472949))], (10856 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472949, _472945)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472947, _472949), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _472949, _472947))], (10858 ^ _106296) ^ [_473450, _473452, _473454] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _473450, _473452), 10869 ^ _106296 : [(10870 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _473450, _473454))], (10872 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _473454, _473450)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _473452, _473454), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _473454, _473452))], (10874 ^ _106296) ^ [_473943, _473945] : [_473943 = _473945, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _473943, _473945), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _473945, _473943))], (10884 ^ _106296) ^ [_474250, _474252] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474250, _474252), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474252, _474250)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474252, _474250), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474250, _474252))], (10898 ^ _106296) ^ [_474655, _474657] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474655, _474657)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474655, _474657), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474657, _474655))], (10908 ^ _106296) ^ [_474963, _474965] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474963, _474965), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474965, _474963)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474965, _474963), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _474963, _474965))], (10922 ^ _106296) ^ [_475368, _475370] : [_475368 = _475370, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475368, _475370), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475370, _475368))], (10932 ^ _106296) ^ [_475675, _475677] : [_475677 = _475675, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475675, _475677), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475677, _475675))], (10942 ^ _106296) ^ [_475996, _475998, _476000] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475996, _475998), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475998, _475996)), _475998 = _476000, 10953 ^ _106296 : [(10954 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _475996, _476000))], (10956 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476000, _475996)]]], (10958 ^ _106296) ^ [_476503, _476505, _476507] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476503, _476505), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476505, _476503)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476505, _476507), 10969 ^ _106296 : [(10970 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476503, _476507))], (10972 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476507, _476503)]]], (10974 ^ _106296) ^ [_476998, _477000] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476998, _477000), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477000, _476998)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477000, _476998), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476998, _477000))], (10988 ^ _106296) ^ [_477417, _477419, _477421] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477417, _477419), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477419, _477417)), 11003 ^ _106296 : [(11004 ^ _106296) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477417, _477421))], (11006 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477421, _477417)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477419, _477421), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _477421, _477419))], (11008 ^ _106296) ^ [_478010, _478012] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _478010, _478012), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _478012, _478010)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _478012, _478010), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _478010, _478012))], (11022 ^ _106296) ^ [_478386] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _478386, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11024 ^ _106296) ^ [_478465] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _478465))], (11026 ^ _106296) ^ [_478573, _478575] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478573), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _478575, _478573), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478575))], (11036 ^ _106296) ^ [_478892, _478894, _478896] : [-(_478892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11039 ^ _106296 : [(11040 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _478894), _478892), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _478896), _478892)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _478894, _478896))], (11046 ^ _106296) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _478894, _478896), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _478894), _478892), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _478896), _478892)))]]], (11052 ^ _106296) ^ [_479427, _479429, _479431] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _479427), _479429), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _479431), _479429)), -(_479429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _479427, _479431))], (11062 ^ _106296) ^ [_479795, _479797, _479799, _479801] : [class_RealVector_Oreal__normed__vector(_479795), class_Orderings_Oord(_479797), 11072 ^ _106296 : [(11073 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_479797, _479799, 11071 ^ [_479795, _479797, _479799, _479801]))], (11075 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_479795, c_Groups_Ominus__class_Ominus(_479795, hAPP(_479801, _479799), hAPP(_479801, 11071 ^ [_479795, _479797, _479799, _479801]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]], 11076 ^ _106296 : [(11077 ^ _106296) ^ [_480353] : [c_Orderings_Oord__class_Oless__eq(_479797, _479799, _480353), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_479795, hAPP(_479801, _480353)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_479795, hAPP(_479801, _479799)))))]]], (11084 ^ _106296) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 11082 ^ []) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (11086 ^ _106296) ^ [_480727] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 11082 ^ []), _480727) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _480727)))], (11088 ^ _106296) ^ [_480846, _480848] : [class_RealVector_Oreal__normed__algebra(_480846), 11092 ^ _106296 : [(11093 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11091 ^ [_480846, _480848]))], (11095 ^ _106296) ^ [_481145] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_480846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480846), _481145), _480848)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_480846, _481145)), 11091 ^ [_480846, _480848])))]]], (11097 ^ _106296) ^ [_481291, _481293] : [class_RealVector_Oreal__normed__algebra(_481291), 11101 ^ _106296 : [(11102 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11100 ^ [_481291, _481293]))], (11104 ^ _106296) ^ [_481590] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_481291, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481291), _481293), _481590)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_481291, _481590)), 11100 ^ [_481291, _481293])))]]], (11106 ^ _106296) ^ [_481722] : [class_RealVector_Oreal__normed__algebra(_481722), 11110 ^ _106296 : [(11111 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11109 ^ [_481722]))], (11113 ^ _106296) ^ [_482051, _482053] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_481722, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481722), _482053), _482051)), 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(_481722, _482053)), c_RealVector_Onorm__class_Onorm(_481722, _482051))), 11109 ^ [_481722])))]]], (11115 ^ _106296) ^ [_482224, _482226] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _482224, _482226), -(c_Nat__Transfer_Otsub(_482226, _482224) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _482226, _482224))], (11121 ^ _106296) ^ [_482402, _482404] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _482402, _482404)), -(c_Nat__Transfer_Otsub(_482404, _482402) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11127 ^ _106296) ^ [_482625, _482627] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _482625), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _482627), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_482625, _482627)))], (11137 ^ _106296) ^ [_482936, _482938] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _482936, _482938), -(c_Nat__Transfer_Otsub(_482938, _482936) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _482938, _482936))], (11143 ^ _106296) ^ [_483176, _483178, _483180] : [class_Rings_Olinordered__idom(_483176), 11146 ^ _106296 : [(11147 ^ _106296) ^ [] : [c_Polynomial_Opos__poly(_483176, c_Polynomial_OpCons(_483176, _483178, _483180)), -(c_Polynomial_Opos__poly(_483176, _483180)), 11154 ^ _106296 : [(11155 ^ _106296) ^ [] : [-(_483180 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483176)))], (11157 ^ _106296) ^ [] : [-(c_Orderings_Oord__class_Oless(_483176, c_Groups_Ozero__class_Ozero(_483176), _483178))]]], (11159 ^ _106296) ^ [] : [-(c_Polynomial_Opos__poly(_483176, c_Polynomial_OpCons(_483176, _483178, _483180))), 11160 ^ _106296 : [(11161 ^ _106296) ^ [] : [c_Polynomial_Opos__poly(_483176, _483180)], (11163 ^ _106296) ^ [] : [_483180 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483176)), c_Orderings_Oord__class_Oless(_483176, c_Groups_Ozero__class_Ozero(_483176), _483178)]]]]], (11171 ^ _106296) ^ [_484011, _484013] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _484011), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _484013), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _484013), _484011), _484013) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _484013), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _484011, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (11181 ^ _106296) ^ [_484368, _484370, _484372] : [class_Rings_Olinordered__idom(_484368), 11184 ^ _106296 : [(11195 ^ _106296) ^ [] : [11196 ^ _106296 : [(11197 ^ _106296) ^ [] : [_484370 = _484372], (11199 ^ _106296) ^ [] : [c_Polynomial_Opos__poly(_484368, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_484368), _484372, _484370))]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_484368), _484370, _484372))], (11185 ^ _106296) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_484368), _484370, _484372), -(_484370 = _484372), -(c_Polynomial_Opos__poly(_484368, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_484368), _484372, _484370)))]]], (11203 ^ _106296) ^ [_485033, _485035] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _485033), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _485035), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _485033, _485035)))], (11213 ^ _106296) ^ [_485360, _485362, _485364] : [class_Rings_Olinordered__idom(_485360), c_Polynomial_Opos__poly(_485360, _485362), c_Polynomial_Opos__poly(_485360, _485364), -(c_Polynomial_Opos__poly(_485360, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_485360), _485362, _485364)))], (11227 ^ _106296) ^ [_485758] : [class_Rings_Olinordered__idom(_485758), c_Polynomial_Opos__poly(_485758, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_485758)))], (11233 ^ _106296) ^ [_485983, _485985, _485987] : [class_Rings_Olinordered__idom(_485983), c_Polynomial_Opos__poly(_485983, _485985), c_Polynomial_Opos__poly(_485983, _485987), -(c_Polynomial_Opos__poly(_485983, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_485983)), _485985), _485987)))], (11247 ^ _106296) ^ [_486403, _486405] : [class_Divides_Osemiring__div(_486403), -(c_Divides_Odiv__class_Odiv(_486403, _486405, c_Groups_Ozero__class_Ozero(_486403)) = c_Groups_Ozero__class_Ozero(_486403))], (11253 ^ _106296) ^ [_486627, _486629] : [class_Divides_Osemiring__div(_486627), -(c_Divides_Odiv__class_Odiv(_486627, c_Groups_Ozero__class_Ozero(_486627), _486629) = c_Groups_Ozero__class_Ozero(_486627))], (11259 ^ _106296) ^ [_486822] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _486822) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11261 ^ _106296) ^ [_486961, _486963, _486965, _486967] : [class_Divides_Osemiring__div(_486961), 11264 ^ _106296 : [(11265 ^ _106296) ^ [] : [_486963 = c_Groups_Ozero__class_Ozero(_486961), -(c_Divides_Odiv__class_Odiv(_486961, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486961), _486963), _486965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486961), _486963), _486967)) = c_Groups_Ozero__class_Ozero(_486961))], (11271 ^ _106296) ^ [] : [-(_486963 = c_Groups_Ozero__class_Ozero(_486961)), -(c_Divides_Odiv__class_Odiv(_486961, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486961), _486963), _486965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486961), _486963), _486967)) = c_Divides_Odiv__class_Odiv(_486961, _486965, _486967))]]], (11277 ^ _106296) ^ [_487571, _487573, _487575] : [class_Divides_Osemiring__div(_487571), -(_487573 = c_Groups_Ozero__class_Ozero(_487571)), -(c_Divides_Odiv__class_Odiv(_487571, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487571), _487575), _487573), _487573) = _487575)], (11287 ^ _106296) ^ [_487923, _487925, _487927] : [class_Divides_Osemiring__div(_487923), -(_487925 = c_Groups_Ozero__class_Ozero(_487923)), -(c_Divides_Odiv__class_Odiv(_487923, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487923), _487925), _487927), _487925) = _487927)], (11297 ^ _106296) ^ [_488289, _488291, _488293, _488295] : [class_Divides_Osemiring__div(_488289), -(_488291 = c_Groups_Ozero__class_Ozero(_488289)), -(c_Divides_Odiv__class_Odiv(_488289, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488289), _488293), _488291), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488289), _488295), _488291)) = c_Divides_Odiv__class_Odiv(_488289, _488293, _488295))], (11307 ^ _106296) ^ [_488647] : [class_Groups_Ocancel__comm__monoid__add(_488647), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_488647)))], (11313 ^ _106296) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11315 ^ _106296) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11317 ^ _106296) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11319 ^ _106296) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11321 ^ _106296) ^ [_489063, _489065] : [class_Orderings_Opreorder(_489063), -(class_Orderings_Opreorder(tc_fun(_489065, _489063)))], (11327 ^ _106296) ^ [_489275, _489277] : [class_Orderings_Oorder(_489275), -(class_Orderings_Oorder(tc_fun(_489277, _489275)))], (11333 ^ _106296) ^ [_489487, _489489] : [class_Orderings_Oord(_489487), -(class_Orderings_Oord(tc_fun(_489489, _489487)))], (11339 ^ _106296) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11341 ^ _106296) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11343 ^ _106296) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11345 ^ _106296) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11347 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11349 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11351 ^ _106296) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11353 ^ _106296) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11355 ^ _106296) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11357 ^ _106296) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11359 ^ _106296) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11361 ^ _106296) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11363 ^ _106296) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11365 ^ _106296) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11367 ^ _106296) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11369 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11371 ^ _106296) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11373 ^ _106296) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11375 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11377 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11379 ^ _106296) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11381 ^ _106296) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11383 ^ _106296) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11385 ^ _106296) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (11387 ^ _106296) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11389 ^ _106296) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11391 ^ _106296) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11393 ^ _106296) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11395 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11397 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (11399 ^ _106296) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (11401 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11403 ^ _106296) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11405 ^ _106296) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11407 ^ _106296) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (11409 ^ _106296) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (11411 ^ _106296) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (11413 ^ _106296) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11415 ^ _106296) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11417 ^ _106296) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (11419 ^ _106296) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11421 ^ _106296) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11423 ^ _106296) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11425 ^ _106296) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11427 ^ _106296) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (11429 ^ _106296) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (11431 ^ _106296) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (11433 ^ _106296) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (11435 ^ _106296) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11437 ^ _106296) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11439 ^ _106296) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11441 ^ _106296) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11443 ^ _106296) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11445 ^ _106296) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11447 ^ _106296) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (11449 ^ _106296) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11451 ^ _106296) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11453 ^ _106296) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11455 ^ _106296) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11457 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11459 ^ _106296) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11461 ^ _106296) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11463 ^ _106296) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11465 ^ _106296) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11467 ^ _106296) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (11469 ^ _106296) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11471 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11473 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11475 ^ _106296) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11477 ^ _106296) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11479 ^ _106296) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11481 ^ _106296) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (11483 ^ _106296) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11485 ^ _106296) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11487 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11489 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (11491 ^ _106296) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (11493 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (11495 ^ _106296) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (11497 ^ _106296) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (11499 ^ _106296) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11501 ^ _106296) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (11503 ^ _106296) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11505 ^ _106296) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (11507 ^ _106296) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (11509 ^ _106296) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11511 ^ _106296) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (11513 ^ _106296) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (11515 ^ _106296) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (11517 ^ _106296) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11519 ^ _106296) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (11521 ^ _106296) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (11523 ^ _106296) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (11525 ^ _106296) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11527 ^ _106296) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (11529 ^ _106296) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (11531 ^ _106296) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (11533 ^ _106296) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (11535 ^ _106296) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (11537 ^ _106296) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (11539 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (11541 ^ _106296) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (11543 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (11545 ^ _106296) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (11547 ^ _106296) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (11549 ^ _106296) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (11551 ^ _106296) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (11553 ^ _106296) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (11555 ^ _106296) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (11557 ^ _106296) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (11559 ^ _106296) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (11561 ^ _106296) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11563 ^ _106296) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11565 ^ _106296) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (11567 ^ _106296) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (11569 ^ _106296) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11571 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (11573 ^ _106296) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11575 ^ _106296) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11577 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (11579 ^ _106296) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (11581 ^ _106296) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (11583 ^ _106296) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (11585 ^ _106296) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11587 ^ _106296) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11589 ^ _106296) ^ [] : [-(class_Fields_Olinordered__field(tc_RealDef_Oreal))], (11591 ^ _106296) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (11593 ^ _106296) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (11595 ^ _106296) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11597 ^ _106296) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11599 ^ _106296) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (11601 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (11603 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (11605 ^ _106296) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (11607 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11609 ^ _106296) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11611 ^ _106296) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11613 ^ _106296) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (11615 ^ _106296) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11617 ^ _106296) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11619 ^ _106296) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11621 ^ _106296) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (11623 ^ _106296) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11625 ^ _106296) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11627 ^ _106296) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11629 ^ _106296) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (11631 ^ _106296) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (11633 ^ _106296) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (11635 ^ _106296) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (11637 ^ _106296) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11639 ^ _106296) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11641 ^ _106296) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11643 ^ _106296) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11645 ^ _106296) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11647 ^ _106296) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11649 ^ _106296) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11651 ^ _106296) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11653 ^ _106296) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11655 ^ _106296) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (11657 ^ _106296) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11659 ^ _106296) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11661 ^ _106296) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (11663 ^ _106296) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11665 ^ _106296) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11667 ^ _106296) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11669 ^ _106296) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11671 ^ _106296) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11673 ^ _106296) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11675 ^ _106296) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11677 ^ _106296) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (11679 ^ _106296) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11681 ^ _106296) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11683 ^ _106296) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11685 ^ _106296) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11687 ^ _106296) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11689 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11691 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (11693 ^ _106296) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (11695 ^ _106296) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11697 ^ _106296) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11699 ^ _106296) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11701 ^ _106296) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11703 ^ _106296) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11705 ^ _106296) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (11707 ^ _106296) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11709 ^ _106296) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11711 ^ _106296) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11713 ^ _106296) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (11715 ^ _106296) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (11717 ^ _106296) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (11719 ^ _106296) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11721 ^ _106296) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (11723 ^ _106296) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (11725 ^ _106296) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11727 ^ _106296) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11729 ^ _106296) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (11731 ^ _106296) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (11733 ^ _106296) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (11735 ^ _106296) ^ [_500179] : [class_Rings_Oidom(_500179), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_500179)))], (11741 ^ _106296) ^ [_500369] : [class_Rings_Olinordered__idom(_500369), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_500369)))], (11747 ^ _106296) ^ [_500559] : [class_Rings_Olinordered__idom(_500559), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_500559)))], (11753 ^ _106296) ^ [_500749] : [class_Rings_Olinordered__idom(_500749), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_500749)))], (11759 ^ _106296) ^ [_500939] : [class_Rings_Olinordered__idom(_500939), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_500939)))], (11765 ^ _106296) ^ [_501129] : [class_Rings_Olinordered__idom(_501129), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_501129)))], (11771 ^ _106296) ^ [_501319] : [class_Rings_Olinordered__idom(_501319), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_501319)))], (11777 ^ _106296) ^ [_501509] : [class_Rings_Olinordered__idom(_501509), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_501509)))], (11783 ^ _106296) ^ [_501699] : [class_Rings_Olinordered__idom(_501699), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_501699)))], (11789 ^ _106296) ^ [_501889] : [class_Groups_Ocancel__comm__monoid__add(_501889), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_501889)))], (11795 ^ _106296) ^ [_502079] : [class_Rings_Oidom(_502079), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_502079)))], (11801 ^ _106296) ^ [_502269] : [class_Rings_Olinordered__idom(_502269), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_502269)))], (11807 ^ _106296) ^ [_502459] : [class_Rings_Olinordered__idom(_502459), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_502459)))], (11813 ^ _106296) ^ [_502649] : [class_Rings_Oidom(_502649), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_502649)))], (11819 ^ _106296) ^ [_502839] : [class_Rings_Olinordered__idom(_502839), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_502839)))], (11825 ^ _106296) ^ [_503029] : [class_Rings_Olinordered__idom(_503029), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_503029)))], (11831 ^ _106296) ^ [_503219] : [class_Rings_Olinordered__idom(_503219), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_503219)))], (11837 ^ _106296) ^ [_503409] : [class_Groups_Ocancel__comm__monoid__add(_503409), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_503409)))], (11843 ^ _106296) ^ [_503599] : [class_Rings_Olinordered__idom(_503599), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_503599)))], (11849 ^ _106296) ^ [_503789] : [class_Rings_Olinordered__idom(_503789), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_503789)))], (11855 ^ _106296) ^ [_503979] : [class_Rings_Ocomm__semiring__0(_503979), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_503979)))], (11861 ^ _106296) ^ [_504169] : [class_Rings_Ocomm__semiring__1(_504169), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_504169)))], (11867 ^ _106296) ^ [_504359] : [class_Groups_Ocomm__monoid__add(_504359), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_504359)))], (11873 ^ _106296) ^ [_504549] : [class_Rings_Olinordered__idom(_504549), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_504549)))], (11879 ^ _106296) ^ [_504739] : [class_Rings_Oidom(_504739), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_504739)))], (11885 ^ _106296) ^ [_504929] : [class_Groups_Ocomm__monoid__add(_504929), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_504929)))], (11891 ^ _106296) ^ [_505119] : [class_Rings_Olinordered__idom(_505119), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_505119)))], (11897 ^ _106296) ^ [_505309] : [class_Rings_Olinordered__idom(_505309), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_505309)))], (11903 ^ _106296) ^ [_505499] : [class_Rings_Ocomm__semiring__1(_505499), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_505499)))], (11909 ^ _106296) ^ [_505689] : [class_Rings_Ocomm__semiring__0(_505689), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_505689)))], (11915 ^ _106296) ^ [_505879] : [class_Fields_Ofield(_505879), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_505879)))], (11921 ^ _106296) ^ [_506069] : [class_Rings_Ocomm__semiring__0(_506069), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_506069)))], (11927 ^ _106296) ^ [_506259] : [class_Groups_Oab__group__add(_506259), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_506259)))], (11933 ^ _106296) ^ [_506449] : [class_Rings_Ocomm__semiring__1(_506449), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_506449)))], (11939 ^ _106296) ^ [_506639] : [class_Rings_Olinordered__idom(_506639), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_506639)))], (11945 ^ _106296) ^ [_506829] : [class_Rings_Olinordered__idom(_506829), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_506829)))], (11951 ^ _106296) ^ [_507019] : [class_Rings_Olinordered__idom(_507019), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_507019)))], (11957 ^ _106296) ^ [_507209] : [class_Rings_Ocomm__semiring__1(_507209), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_507209)))], (11963 ^ _106296) ^ [_507399] : [class_Rings_Ocomm__ring__1(_507399), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_507399)))], (11969 ^ _106296) ^ [_507589] : [class_Groups_Ocomm__monoid__add(_507589), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_507589)))], (11975 ^ _106296) ^ [_507779] : [class_Rings_Ocomm__semiring__0(_507779), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_507779)))], (11981 ^ _106296) ^ [_507969] : [class_Groups_Oab__group__add(_507969), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_507969)))], (11987 ^ _106296) ^ [_508159] : [class_Rings_Ocomm__semiring__0(_508159), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_508159)))], (11993 ^ _106296) ^ [_508349] : [class_Rings_Ocomm__ring(_508349), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_508349)))], (11999 ^ _106296) ^ [_508539] : [class_Rings_Olinordered__idom(_508539), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_508539)))], (12005 ^ _106296) ^ [_508729] : [class_Rings_Olinordered__idom(_508729), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_508729)))], (12011 ^ _106296) ^ [_508919] : [class_Rings_Ocomm__semiring__0(_508919), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_508919)))], (12017 ^ _106296) ^ [_509109] : [class_Rings_Olinordered__idom(_509109), -(class_Orderings_Oord(tc_Polynomial_Opoly(_509109)))], (12023 ^ _106296) ^ [_509299] : [class_Rings_Ocomm__ring__1(_509299), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_509299)))], (12029 ^ _106296) ^ [_509489] : [class_Rings_Ocomm__semiring__1(_509489), -(class_Power_Opower(tc_Polynomial_Opoly(_509489)))], (12035 ^ _106296) ^ [_509679] : [class_Groups_Ozero(_509679), -(class_Groups_Ozero(tc_Polynomial_Opoly(_509679)))], (12041 ^ _106296) ^ [_509869] : [class_Rings_Ocomm__ring(_509869), -(class_Rings_Oring(tc_Polynomial_Opoly(_509869)))], (12047 ^ _106296) ^ [_510059] : [class_Rings_Oidom(_510059), -(class_Rings_Oidom(tc_Polynomial_Opoly(_510059)))], (12053 ^ _106296) ^ [_510249] : [class_Rings_Ocomm__semiring__1(_510249), -(class_Groups_Oone(tc_Polynomial_Opoly(_510249)))], (12059 ^ _106296) ^ [_510439] : [class_Rings_Ocomm__semiring__1(_510439), -(class_Rings_Odvd(tc_Polynomial_Opoly(_510439)))], (12065 ^ _106296) ^ [_510609] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _510609), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _510609, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _510609, 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____))), -(v_thesis____)]], input).
% 101.89/98.79 ncf('1',plain,[v_thesis____],start(12079 ^ 0)).
% 101.89/98.79 ncf('1.1',plain,[-(v_thesis____), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1048 ^ [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____))]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1048 ^ [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____))], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1048 ^ [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____))], 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____)))],extension(12065 ^ 1,bind([[_510609], [1048 ^ [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____))]]]))).
% 101.89/98.79 ncf('1.1.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1048 ^ [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____))])), 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____)))],extension(1045 ^ 2,bind([[_127338], [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____))]]))).
% 101.89/98.79 ncf('1.1.1.1',plain,[-(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____))))],extension(1058 ^ 3)).
% 101.89/98.79 ncf('1.1.2',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1048 ^ [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____))], c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), 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____)))],extension(1045 ^ 2,bind([[_127338], [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____))]]))).
% 101.89/98.79 ncf('1.1.2.1',plain,[-(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____))))],extension(1058 ^ 3)).
% 101.89/98.79 ncf('1.1.3',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1048 ^ [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____))], 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____)))), 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____)))],extension(1045 ^ 2,bind([[_127338], [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____))]]))).
% 101.89/98.79 ncf('1.1.3.1',plain,[-(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____))))],extension(1058 ^ 3)).
% 101.89/98.79 %-----------------------------------------------------
% 101.89/98.79 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------