%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW217+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n013.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 12:25:46 EDT 2023

% Result   : Theorem 0.56s 1.38s
% Output   : Proof 0.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW217+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n013.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 22:31:35 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.56/1.38  
% 0.56/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.56/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/1.38  %-----------------------------------------------------
% 0.56/1.38  ncf(matrix, plain, [(12358 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)))), v_e)], (786 ^ _191474) ^ [_215715, _215717, _215719, _215721, _215723, _215725] : [-(c_Polynomial_Oorder(_215725, _215721, _215717) = c_Polynomial_Oorder(_215723, _215719, _215715)), _215725 = _215723, _215721 = _215719, _215717 = _215715], (800 ^ _191474) ^ [_216231, _216233, _216235, _216237, _216239, _216241] : [-(c_Polynomial_Opcompose(_216241, _216237, _216233) = c_Polynomial_Opcompose(_216239, _216235, _216231)), _216241 = _216239, _216237 = _216235, _216233 = _216231], (814 ^ _191474) ^ [_216747, _216749, _216751, _216753, _216755, _216757] : [-(c_Polynomial_Osynthetic__div(_216757, _216753, _216749) = c_Polynomial_Osynthetic__div(_216755, _216751, _216747)), _216757 = _216755, _216753 = _216751, _216749 = _216747], (828 ^ _191474) ^ [_217207, _217209] : [_217209 = _217207, -(c_Complex_Oexpi(_217209) = c_Complex_Oexpi(_217207))], (834 ^ _191474) ^ [_217425, _217427] : [_217427 = _217425, -(c_RComplete_Onatceiling(_217427) = c_RComplete_Onatceiling(_217425))], (840 ^ _191474) ^ [_217643, _217645] : [_217645 = _217643, -(c_RComplete_Onatfloor(_217645) = c_RComplete_Onatfloor(_217643))], (846 ^ _191474) ^ [_217889, _217891, _217893, _217895] : [-(c_Complex_Orcis(_217895, _217891) = c_Complex_Orcis(_217893, _217889)), _217895 = _217893, _217891 = _217889], (856 ^ _191474) ^ [_218276, _218278, _218280, _218282, _218284, _218286] : [-(c_Power_Opower_Opower(_218286, _218282, _218278) = c_Power_Opower_Opower(_218284, _218280, _218276)), _218286 = _218284, _218282 = _218280, _218278 = _218276], (870 ^ _191474) ^ [_218764, _218766, _218768, _218770] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_218770, _218766) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_218768, _218764)), _218770 = _218768, _218766 = _218764], (880 ^ _191474) ^ [_219123, _219125, _219127, _219129] : [-(c_Polynomial_Odegree(_219129, _219125) = c_Polynomial_Odegree(_219127, _219123)), _219129 = _219127, _219125 = _219123], (890 ^ _191474) ^ [_219482, _219484, _219486, _219488] : [-(c_Nat__Transfer_Otsub(_219488, _219484) = c_Nat__Transfer_Otsub(_219486, _219482)), _219488 = _219486, _219484 = _219482], (900 ^ _191474) ^ [_219813, _219815] : [_219815 = _219813, -(c_Power_Opower__class_Opower(_219815) = c_Power_Opower__class_Opower(_219813))], (906 ^ _191474) ^ [_220031, _220033] : [_220033 = _220031, -(c_Transcendental_Oln(_220033) = c_Transcendental_Oln(_220031))], (912 ^ _191474) ^ [_220305, _220307, _220309, _220311, _220313, _220315] : [-(c_Rings_Oinverse__class_Odivide(_220315, _220311, _220307) = c_Rings_Oinverse__class_Odivide(_220313, _220309, _220305)), _220315 = _220313, _220311 = _220309, _220307 = _220305], (926 ^ _191474) ^ [_220793, _220795, _220797, _220799] : [-(c_RealDef_Oreal(_220799, _220795) = c_RealDef_Oreal(_220797, _220793)), _220799 = _220797, _220795 = _220793], (936 ^ _191474) ^ [_221124, _221126] : [_221126 = _221124, -(c_Nat_OSuc(_221126) = c_Nat_OSuc(_221124))], (942 ^ _191474) ^ [_221398, _221400, _221402, _221404, _221406, _221408] : [-(c_Divides_Odiv__class_Odiv(_221408, _221404, _221400) = c_Divides_Odiv__class_Odiv(_221406, _221402, _221398)), _221408 = _221406, _221404 = _221402, _221400 = _221398], (956 ^ _191474) ^ [_221914, _221916, _221918, _221920, _221922, _221924] : [-(c_Groups_Oplus__class_Oplus(_221924, _221920, _221916) = c_Groups_Oplus__class_Oplus(_221922, _221918, _221914)), _221924 = _221922, _221920 = _221918, _221916 = _221914], (970 ^ _191474) ^ [_222374, _222376] : [_222376 = _222374, -(c_Groups_Oone__class_Oone(_222376) = c_Groups_Oone__class_Oone(_222374))], (976 ^ _191474) ^ [_222592, _222594] : [_222594 = _222592, -(c_Groups_Ozero__class_Ozero(_222594) = c_Groups_Ozero__class_Ozero(_222592))], (982 ^ _191474) ^ [_222866, _222868, _222870, _222872, _222874, _222876] : [-(c_Divides_Odiv__class_Omod(_222876, _222872, _222868) = c_Divides_Odiv__class_Omod(_222874, _222870, _222866)), _222876 = _222874, _222872 = _222870, _222868 = _222866], (996 ^ _191474) ^ [_223354, _223356, _223358, _223360] : [-(tc_fun(_223360, _223356) = tc_fun(_223358, _223354)), _223360 = _223358, _223356 = _223354], (1006 ^ _191474) ^ [_223685, _223687] : [_223687 = _223685, -(tc_Polynomial_Opoly(_223687) = tc_Polynomial_Opoly(_223685))], (1012 ^ _191474) ^ [_223903, _223905] : [_223905 = _223903, -(c_Groups_Otimes__class_Otimes(_223905) = c_Groups_Otimes__class_Otimes(_223903))], (1018 ^ _191474) ^ [_224149, _224151, _224153, _224155] : [-(c_RealVector_Onorm__class_Onorm(_224155, _224151) = c_RealVector_Onorm__class_Onorm(_224153, _224149)), _224155 = _224153, _224151 = _224149], (1028 ^ _191474) ^ [_224508, _224510, _224512, _224514] : [-(hAPP(_224514, _224510) = hAPP(_224512, _224508)), _224514 = _224512, _224510 = _224508], (1038 ^ _191474) ^ [_224867, _224869, _224871, _224873] : [-(c_Polynomial_Opoly(_224873, _224869) = c_Polynomial_Opoly(_224871, _224867)), _224873 = _224871, _224869 = _224867], (1048 ^ _191474) ^ [_225234, _225236, _225238, _225240, _225242, _225244] : [-(c_Groups_Ominus__class_Ominus(_225244, _225240, _225236) = c_Groups_Ominus__class_Ominus(_225242, _225238, _225234)), _225244 = _225242, _225240 = _225238, _225236 = _225234], (2 ^ _191474) ^ [_191618] : [-(_191618 = _191618)], (4 ^ _191474) ^ [_191725, _191727] : [_191727 = _191725, -(_191725 = _191727)], (10 ^ _191474) ^ [_191929, _191931, _191933] : [-(_191933 = _191929), _191933 = _191931, _191931 = _191929], (20 ^ _191474) ^ [_192270, _192272, _192274, _192276] : [-(c_SEQ_Odecseq(_192274, _192270)), c_SEQ_Odecseq(_192276, _192272), _192276 = _192274, _192272 = _192270], (34 ^ _191474) ^ [_192798, _192800, _192802, _192804, _192806, _192808, _192810, _192812, _192814, _192816] : [-(c_Polynomial_Opdivmod__rel(_192814, _192810, _192806, _192802, _192798)), c_Polynomial_Opdivmod__rel(_192816, _192812, _192808, _192804, _192800), _192816 = _192814, _192812 = _192810, _192808 = _192806, _192804 = _192802, _192800 = _192798], (60 ^ _191474) ^ [_193673, _193675] : [-(hBOOL(_193673)), _193675 = _193673, hBOOL(_193675)], (70 ^ _191474) ^ [_194024, _194026, _194028, _194030, _194032, _194034] : [-(c_Orderings_Oord__class_Oless__eq(_194032, _194028, _194024)), c_Orderings_Oord__class_Oless__eq(_194034, _194030, _194026), _194034 = _194032, _194030 = _194028, _194026 = _194024], (88 ^ _191474) ^ [_194577, _194579] : [-(class_Fields_Olinordered__field__inverse__zero(_194577)), _194579 = _194577, class_Fields_Olinordered__field__inverse__zero(_194579)], (98 ^ _191474) ^ [_194872, _194874] : [-(class_Fields_Olinordered__field(_194872)), _194874 = _194872, class_Fields_Olinordered__field(_194874)], (108 ^ _191474) ^ [_195167, _195169] : [-(class_RealVector_Oreal__normed__div__algebra(_195167)), _195169 = _195167, class_RealVector_Oreal__normed__div__algebra(_195169)], (118 ^ _191474) ^ [_195462, _195464] : [-(class_Rings_Odivision__ring__inverse__zero(_195462)), _195464 = _195462, class_Rings_Odivision__ring__inverse__zero(_195464)], (128 ^ _191474) ^ [_195757, _195759] : [-(class_RealVector_Oreal__normed__algebra__1(_195757)), _195759 = _195757, class_RealVector_Oreal__normed__algebra__1(_195759)], (138 ^ _191474) ^ [_196052, _196054] : [-(class_RealVector_Oreal__normed__algebra(_196052)), _196054 = _196052, class_RealVector_Oreal__normed__algebra(_196054)], (148 ^ _191474) ^ [_196347, _196349] : [-(class_RealVector_Oreal__normed__vector(_196347)), _196349 = _196347, class_RealVector_Oreal__normed__vector(_196349)], (158 ^ _191474) ^ [_196642, _196644] : [-(class_RealVector_Oreal__normed__field(_196642)), _196644 = _196642, class_RealVector_Oreal__normed__field(_196644)], (168 ^ _191474) ^ [_196937, _196939] : [-(class_Fields_Ofield__inverse__zero(_196937)), _196939 = _196937, class_Fields_Ofield__inverse__zero(_196939)], (178 ^ _191474) ^ [_197232, _197234] : [-(class_RealVector_Oreal__field(_197232)), _197234 = _197232, class_RealVector_Oreal__field(_197234)], (188 ^ _191474) ^ [_197527, _197529] : [-(class_Rings_Odivision__ring(_197527)), _197529 = _197527, class_Rings_Odivision__ring(_197529)], (198 ^ _191474) ^ [_197822, _197824] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_197822)), _197824 = _197822, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_197824)], (208 ^ _191474) ^ [_198117, _198119] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_198117)), _198119 = _198117, class_Groups_Oordered__cancel__ab__semigroup__add(_198119)], (218 ^ _191474) ^ [_198412, _198414] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_198412)), _198414 = _198412, class_Groups_Oordered__ab__semigroup__add__imp__le(_198414)], (228 ^ _191474) ^ [_198707, _198709] : [-(class_Rings_Olinordered__comm__semiring__strict(_198707)), _198709 = _198707, class_Rings_Olinordered__comm__semiring__strict(_198709)], (238 ^ _191474) ^ [_199002, _199004] : [-(class_Rings_Olinordered__semiring__1__strict(_199002)), _199004 = _199002, class_Rings_Olinordered__semiring__1__strict(_199004)], (248 ^ _191474) ^ [_199297, _199299] : [-(class_Rings_Olinordered__semiring__strict(_199297)), _199299 = _199297, class_Rings_Olinordered__semiring__strict(_199299)], (258 ^ _191474) ^ [_199592, _199594] : [-(class_Groups_Oordered__ab__semigroup__add(_199592)), _199594 = _199592, class_Groups_Oordered__ab__semigroup__add(_199594)], (268 ^ _191474) ^ [_199887, _199889] : [-(class_Groups_Oordered__comm__monoid__add(_199887)), _199889 = _199887, class_Groups_Oordered__comm__monoid__add(_199889)], (278 ^ _191474) ^ [_200182, _200184] : [-(class_Groups_Olinordered__ab__group__add(_200182)), _200184 = _200182, class_Groups_Olinordered__ab__group__add(_200184)], (288 ^ _191474) ^ [_200477, _200479] : [-(class_Groups_Ocancel__ab__semigroup__add(_200477)), _200479 = _200477, class_Groups_Ocancel__ab__semigroup__add(_200479)], (298 ^ _191474) ^ [_200772, _200774] : [-(class_Rings_Oring__1__no__zero__divisors(_200772)), _200774 = _200772, class_Rings_Oring__1__no__zero__divisors(_200774)], (308 ^ _191474) ^ [_201067, _201069] : [-(class_Rings_Oordered__cancel__semiring(_201067)), _201069 = _201067, class_Rings_Oordered__cancel__semiring(_201069)], (318 ^ _191474) ^ [_201362, _201364] : [-(class_Rings_Olinordered__ring__strict(_201362)), _201364 = _201362, class_Rings_Olinordered__ring__strict(_201364)], (328 ^ _191474) ^ [_201657, _201659] : [-(class_Rings_Oring__no__zero__divisors(_201657)), _201659 = _201657, class_Rings_Oring__no__zero__divisors(_201659)], (338 ^ _191474) ^ [_201952, _201954] : [-(class_Rings_Oordered__comm__semiring(_201952)), _201954 = _201952, class_Rings_Oordered__comm__semiring(_201954)], (348 ^ _191474) ^ [_202247, _202249] : [-(class_Rings_Olinordered__semiring__1(_202247)), _202249 = _202247, class_Rings_Olinordered__semiring__1(_202249)], (358 ^ _191474) ^ [_202542, _202544] : [-(class_Groups_Oordered__ab__group__add(_202542)), _202544 = _202542, class_Groups_Oordered__ab__group__add(_202544)], (368 ^ _191474) ^ [_202837, _202839] : [-(class_Groups_Ocancel__comm__monoid__add(_202837)), _202839 = _202837, class_Groups_Ocancel__comm__monoid__add(_202839)], (378 ^ _191474) ^ [_203132, _203134] : [-(class_Groups_Ocancel__semigroup__add(_203132)), _203134 = _203132, class_Groups_Ocancel__semigroup__add(_203134)], (388 ^ _191474) ^ [_203427, _203429] : [-(class_Rings_Olinordered__semiring(_203427)), _203429 = _203427, class_Rings_Olinordered__semiring(_203429)], (398 ^ _191474) ^ [_203722, _203724] : [-(class_Rings_Olinordered__semidom(_203722)), _203724 = _203722, class_Rings_Olinordered__semidom(_203724)], (408 ^ _191474) ^ [_204017, _204019] : [-(class_Groups_Oab__semigroup__mult(_204017)), _204019 = _204017, class_Groups_Oab__semigroup__mult(_204019)], (418 ^ _191474) ^ [_204312, _204314] : [-(class_Groups_Ocomm__monoid__mult(_204312)), _204314 = _204312, class_Groups_Ocomm__monoid__mult(_204314)], (428 ^ _191474) ^ [_204607, _204609] : [-(class_Groups_Oab__semigroup__add(_204607)), _204609 = _204607, class_Groups_Oab__semigroup__add(_204609)], (438 ^ _191474) ^ [_204902, _204904] : [-(class_Rings_Oordered__semiring(_204902)), _204904 = _204902, class_Rings_Oordered__semiring(_204904)], (448 ^ _191474) ^ [_205197, _205199] : [-(class_Rings_Ono__zero__divisors(_205197)), _205199 = _205197, class_Rings_Ono__zero__divisors(_205199)], (458 ^ _191474) ^ [_205492, _205494] : [-(class_Rings_Olinordered__ring(_205492)), _205494 = _205492, class_Rings_Olinordered__ring(_205494)], (468 ^ _191474) ^ [_205787, _205789] : [-(class_Divides_Osemiring__div(_205787)), _205789 = _205787, class_Divides_Osemiring__div(_205789)], (478 ^ _191474) ^ [_206082, _206084] : [-(class_Rings_Ocomm__semiring(_206082)), _206084 = _206082, class_Rings_Ocomm__semiring(_206084)], (488 ^ _191474) ^ [_206377, _206379] : [-(class_Rings_Ozero__neq__one(_206377)), _206379 = _206377, class_Rings_Ozero__neq__one(_206379)], (498 ^ _191474) ^ [_206672, _206674] : [-(class_Rings_Oordered__ring(_206672)), _206674 = _206672, class_Rings_Oordered__ring(_206674)], (508 ^ _191474) ^ [_206967, _206969] : [-(class_Orderings_Opreorder(_206967)), _206969 = _206967, class_Orderings_Opreorder(_206969)], (518 ^ _191474) ^ [_207262, _207264] : [-(class_Orderings_Olinorder(_207262)), _207264 = _207262, class_Orderings_Olinorder(_207264)], (528 ^ _191474) ^ [_207557, _207559] : [-(class_Groups_Omonoid__mult(_207557)), _207559 = _207557, class_Groups_Omonoid__mult(_207559)], (538 ^ _191474) ^ [_207852, _207854] : [-(class_Groups_Ocomm__monoid__add(_207852)), _207854 = _207852, class_Groups_Ocomm__monoid__add(_207854)], (548 ^ _191474) ^ [_208147, _208149] : [-(class_Groups_Omonoid__add(_208147)), _208149 = _208147, class_Groups_Omonoid__add(_208149)], (558 ^ _191474) ^ [_208442, _208444] : [-(class_Rings_Osemiring__0(_208442)), _208444 = _208442, class_Rings_Osemiring__0(_208444)], (568 ^ _191474) ^ [_208737, _208739] : [-(class_Groups_Oab__group__add(_208737)), _208739 = _208737, class_Groups_Oab__group__add(_208739)], (578 ^ _191474) ^ [_209032, _209034] : [-(class_Groups_Ogroup__add(_209032)), _209034 = _209032, class_Groups_Ogroup__add(_209034)], (588 ^ _191474) ^ [_209327, _209329] : [-(class_Fields_Ofield(_209327)), _209329 = _209327, class_Fields_Ofield(_209329)], (598 ^ _191474) ^ [_209622, _209624] : [-(class_Divides_Oring__div(_209622)), _209624 = _209622, class_Divides_Oring__div(_209624)], (608 ^ _191474) ^ [_209917, _209919] : [-(class_Rings_Omult__zero(_209917)), _209919 = _209917, class_Rings_Omult__zero(_209919)], (618 ^ _191474) ^ [_210212, _210214] : [-(class_Orderings_Oorder(_210212)), _210214 = _210212, class_Orderings_Oorder(_210214)], (628 ^ _191474) ^ [_210507, _210509] : [-(class_Int_Oring__char__0(_210507)), _210509 = _210507, class_Int_Oring__char__0(_210509)], (638 ^ _191474) ^ [_210802, _210804] : [-(class_Rings_Ocomm__semiring__0(_210802)), _210804 = _210802, class_Rings_Ocomm__semiring__0(_210804)], (648 ^ _191474) ^ [_211097, _211099] : [-(class_Rings_Osemiring(_211097)), _211099 = _211097, class_Rings_Osemiring(_211099)], (658 ^ _191474) ^ [_211392, _211394] : [-(class_Rings_Olinordered__idom(_211392)), _211394 = _211392, class_Rings_Olinordered__idom(_211394)], (668 ^ _191474) ^ [_211687, _211689] : [-(class_Orderings_Oord(_211687)), _211689 = _211687, class_Orderings_Oord(_211689)], (678 ^ _191474) ^ [_211982, _211984] : [-(class_Rings_Ocomm__ring__1(_211982)), _211984 = _211982, class_Rings_Ocomm__ring__1(_211984)], (688 ^ _191474) ^ [_212277, _212279] : [-(class_Rings_Oring__1(_212277)), _212279 = _212277, class_Rings_Oring__1(_212279)], (698 ^ _191474) ^ [_212572, _212574] : [-(class_Power_Opower(_212572)), _212574 = _212572, class_Power_Opower(_212574)], (708 ^ _191474) ^ [_212867, _212869] : [-(class_Groups_Ozero(_212867)), _212869 = _212867, class_Groups_Ozero(_212869)], (718 ^ _191474) ^ [_213162, _213164] : [-(class_Rings_Ocomm__ring(_213162)), _213164 = _213162, class_Rings_Ocomm__ring(_213164)], (728 ^ _191474) ^ [_213457, _213459] : [-(class_Rings_Oring(_213457)), _213459 = _213457, class_Rings_Oring(_213459)], (738 ^ _191474) ^ [_213752, _213754] : [-(class_Rings_Oidom(_213752)), _213754 = _213752, class_Rings_Oidom(_213754)], (748 ^ _191474) ^ [_214047, _214049] : [-(class_Rings_Ocomm__semiring__1(_214047)), _214049 = _214047, class_Rings_Ocomm__semiring__1(_214049)], (758 ^ _191474) ^ [_214342, _214344] : [-(class_Groups_Oone(_214342)), _214344 = _214342, class_Groups_Oone(_214344)], (768 ^ _191474) ^ [_214673, _214675, _214677, _214679, _214681, _214683] : [-(c_Orderings_Oord__class_Oless(_214681, _214677, _214673)), c_Orderings_Oord__class_Oless(_214683, _214679, _214675), _214683 = _214681, _214679 = _214677, _214675 = _214673], (1062 ^ _191474) ^ [_225868, _225870] : [hAPP(_225868, 1063 ^ [_225868, _225870]) = hAPP(_225870, 1063 ^ [_225868, _225870]), -(_225868 = _225870)], (1069 ^ _191474) ^ [] : [v_w____ = v_z], (1071 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_e))], (1073 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), v_da____))], (1075 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_da____), v_m____), v_e))], (1078 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1076 ^ []))], (1080 ^ _191474) ^ [_226502] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _226502, v_z)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_z, v_z)))), v_e)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _226502, v_z))), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _226502, v_z)), 1076 ^ [])], (1090 ^ _191474) ^ [_226897, _226899, _226901, _226903, _226905] : [class_RealVector_Oreal__normed__algebra(_226897), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_226897, _226899), _226901), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_226897, _226903), _226905), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_226897, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226897), _226899), _226903)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _226901), _226905)))], (1104 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_da____), v_m____)))], (1106 ^ _191474) ^ [_227444, _227446, _227448] : [class_RealVector_Oreal__normed__div__algebra(_227444), -(c_RealVector_Onorm__class_Onorm(_227444, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_227444), _227446), _227448)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_227444, _227446)), c_RealVector_Onorm__class_Onorm(_227444, _227448)))], (1112 ^ _191474) ^ [_227675] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _227675, v_z)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), _227675))], (1114 ^ _191474) ^ [_227820, _227822, _227824, _227826] : [class_Rings_Ocomm__ring(_227820), -(hAPP(c_Polynomial_Opoly(_227820, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_227820), _227822, _227824)), _227826) = c_Groups_Ominus__class_Ominus(_227820, hAPP(c_Polynomial_Opoly(_227820, _227822), _227826), hAPP(c_Polynomial_Opoly(_227820, _227824), _227826)))], (1120 ^ _191474) ^ [_228124, _228126, _228128, _228130] : [class_Rings_Ocomm__semiring__0(_228124), -(hAPP(c_Polynomial_Opoly(_228124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_228124)), _228126), _228128)), _228130) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228124), hAPP(c_Polynomial_Opoly(_228124, _228126), _228130)), hAPP(c_Polynomial_Opoly(_228124, _228128), _228130)))], (1126 ^ _191474) ^ [_228430, _228432, _228434] : [class_RealVector_Oreal__normed__vector(_228430), -(c_RealVector_Onorm__class_Onorm(_228430, c_Groups_Ominus__class_Ominus(_228430, _228432, _228434)) = c_RealVector_Onorm__class_Onorm(_228430, c_Groups_Ominus__class_Ominus(_228430, _228434, _228432)))], (1132 ^ _191474) ^ [_228700, _228702, _228704, _228706] : [class_RealVector_Oreal__normed__algebra(_228700), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228700), _228702), c_Groups_Ominus__class_Ominus(_228700, _228704, _228706)) = c_Groups_Ominus__class_Ominus(_228700, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228700), _228702), _228704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_228700), _228702), _228706)))], (1138 ^ _191474) ^ [_229012, _229014, _229016, _229018] : [class_RealVector_Oreal__normed__algebra(_229012), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229012), _229014), c_Groups_Ominus__class_Ominus(_229012, _229016, _229018)) = c_Groups_Ominus__class_Ominus(_229012, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229012), _229014), _229016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229012), _229014), _229018)))], (1144 ^ _191474) ^ [_229324, _229326, _229328, _229330] : [class_RealVector_Oreal__normed__algebra(_229324), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229324), c_Groups_Ominus__class_Ominus(_229324, _229326, _229328)), _229330) = c_Groups_Ominus__class_Ominus(_229324, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229324), _229326), _229330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229324), _229328), _229330)))], (1150 ^ _191474) ^ [_229636, _229638, _229640, _229642] : [class_RealVector_Oreal__normed__algebra(_229636), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229636), c_Groups_Ominus__class_Ominus(_229636, _229638, _229640)), _229642) = c_Groups_Ominus__class_Ominus(_229636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229636), _229638), _229642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_229636), _229640), _229642)))], (1156 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_m____))], (1158 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_da____))], (1160 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_d____))], (1162 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_da____))], (1164 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), v_da____))], (1166 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1168 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____)))], (1170 ^ _191474) ^ [] : [-(c_Polynomial_Odegree(tc_Complex_Ocomplex, v_q____) = c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))], (1172 ^ _191474) ^ [_230344, _230346] : [class_RealVector_Oreal__normed__vector(_230344), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_230344, _230346)))], (1178 ^ _191474) ^ [_230546] : [class_RealVector_Oreal__normed__vector(_230546), -(c_RealVector_Onorm__class_Onorm(_230546, c_Groups_Ozero__class_Ozero(_230546)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1184 ^ _191474) ^ [_230758, _230760] : [class_Rings_Ocomm__semiring__0(_230758), -(hAPP(c_Polynomial_Opoly(_230758, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_230758))), _230760) = c_Groups_Ozero__class_Ozero(_230758))], (1190 ^ _191474) ^ [_230990, _230992] : [class_RealVector_Oreal__normed__vector(_230990), 1193 ^ _191474 : [(1194 ^ _191474) ^ [] : [c_RealVector_Onorm__class_Onorm(_230990, _230992) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_230992 = c_Groups_Ozero__class_Ozero(_230990))], (1200 ^ _191474) ^ [] : [_230992 = c_Groups_Ozero__class_Ozero(_230990), -(c_RealVector_Onorm__class_Onorm(_230990, _230992) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1206 ^ _191474) ^ [_231463, _231465] : [class_RealVector_Oreal__normed__vector(_231463), 1209 ^ _191474 : [(1210 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_231463, _231465), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_231465 = c_Groups_Ozero__class_Ozero(_231463))], (1216 ^ _191474) ^ [] : [_231465 = c_Groups_Ozero__class_Ozero(_231463), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_231463, _231465), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (1222 ^ _191474) ^ [_231939, _231941] : [class_RealVector_Oreal__normed__algebra(_231939), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_231939), _231941), c_Groups_Ozero__class_Ozero(_231939)) = c_Groups_Ozero__class_Ozero(_231939))], (1228 ^ _191474) ^ [_232171, _232173] : [class_RealVector_Oreal__normed__algebra(_232171), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232171), _232173), c_Groups_Ozero__class_Ozero(_232171)) = c_Groups_Ozero__class_Ozero(_232171))], (1234 ^ _191474) ^ [_232403, _232405] : [class_RealVector_Oreal__normed__algebra(_232403), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232403), c_Groups_Ozero__class_Ozero(_232403)), _232405) = c_Groups_Ozero__class_Ozero(_232403))], (1240 ^ _191474) ^ [_232635, _232637] : [class_RealVector_Oreal__normed__algebra(_232635), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_232635), c_Groups_Ozero__class_Ozero(_232635)), _232637) = c_Groups_Ozero__class_Ozero(_232635))], (1246 ^ _191474) ^ [_232867, _232869] : [class_RealVector_Oreal__normed__vector(_232867), 1249 ^ _191474 : [(1250 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_232867, _232869)), _232869 = c_Groups_Ozero__class_Ozero(_232867)], (1256 ^ _191474) ^ [] : [-(_232869 = c_Groups_Ozero__class_Ozero(_232867)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_232867, _232869)))]]], (1262 ^ _191474) ^ [_233359, _233361, _233363] : [class_RealVector_Oreal__normed__vector(_233359), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_233359, _233361), c_RealVector_Onorm__class_Onorm(_233359, _233363)), c_RealVector_Onorm__class_Onorm(_233359, c_Groups_Ominus__class_Ominus(_233359, _233361, _233363))))], (1268 ^ _191474) ^ [_233609, _233611] : [class_RealVector_Oreal__normed__vector(_233609), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_233609, _233611), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1274 ^ _191474) ^ [_233840, _233842, _233844] : [class_RealVector_Oreal__normed__algebra(_233840), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_233840, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233840), _233842), _233844)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_233840, _233842)), c_RealVector_Onorm__class_Onorm(_233840, _233844))))], (1280 ^ _191474) ^ [_234116, _234118, _234120] : [class_Int_Oring__char__0(_234116), class_Rings_Oidom(_234116), 1287 ^ _191474 : [(1288 ^ _191474) ^ [] : [c_Polynomial_Opoly(_234116, _234118) = c_Polynomial_Opoly(_234116, _234120), -(_234118 = _234120)], (1294 ^ _191474) ^ [] : [_234118 = _234120, -(c_Polynomial_Opoly(_234116, _234118) = c_Polynomial_Opoly(_234116, _234120))]]], (1300 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_d____), v_m____), v_e))], (1302 ^ _191474) ^ [] : [-(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), v_d____), v_m____)))], (1304 ^ _191474) ^ [_234793] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _234793), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(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_cs____), _234793)), v_m____))], (1310 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1312 ^ _191474) ^ [_235043] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _235043) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_z, _235043)))], (1314 ^ _191474) ^ [_235188, _235190, _235192, _235194] : [class_RealVector_Oreal__normed__vector(_235188), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _235190, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_235188, _235192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _235190), c_RealVector_Onorm__class_Onorm(_235188, _235194))), -(_235192 = c_Groups_Ozero__class_Ozero(_235188))], (1328 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____)))], (1330 ^ _191474) ^ [_235701, _235703, _235705] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _235701), 1333 ^ _191474 : [(1334 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _235701), _235703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _235701), _235705)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _235703, _235705))], (1340 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _235703, _235705), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _235701), _235703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _235701), _235705)))]]], (1346 ^ _191474) ^ [_236235, _236237, _236239] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _236235), 1349 ^ _191474 : [(1350 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _236237), _236235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _236239), _236235)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _236237, _236239))], (1356 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _236237, _236239), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _236237), _236235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _236239), _236235)))]]], (1362 ^ _191474) ^ [_236783, _236785, _236787, _236789] : [class_Rings_Olinordered__semiring__strict(_236783), c_Orderings_Oord__class_Oless__eq(_236783, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236783), _236785), _236787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236783), _236785), _236789)), c_Orderings_Oord__class_Oless(_236783, c_Groups_Ozero__class_Ozero(_236783), _236785), -(c_Orderings_Oord__class_Oless__eq(_236783, _236787, _236789))], (1376 ^ _191474) ^ [_237267, _237269, _237271, _237273] : [class_Rings_Olinordered__semiring__strict(_237267), c_Orderings_Oord__class_Oless__eq(_237267, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_237267), _237269), _237271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_237267), _237273), _237271)), c_Orderings_Oord__class_Oless(_237267, c_Groups_Ozero__class_Ozero(_237267), _237271), -(c_Orderings_Oord__class_Oless__eq(_237267, _237269, _237273))], (1390 ^ _191474) ^ [_237751, _237753, _237755, _237757] : [class_Rings_Olinordered__semiring__strict(_237751), c_Orderings_Oord__class_Oless(_237751, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_237751), _237753), _237755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_237751), _237753), _237757)), c_Orderings_Oord__class_Oless__eq(_237751, c_Groups_Ozero__class_Ozero(_237751), _237753), -(c_Orderings_Oord__class_Oless(_237751, _237755, _237757))], (1404 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_d____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1406 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1408 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_d____, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____)))], (1410 ^ _191474) ^ [_238352] : [class_Groups_Ozero(_238352), -(c_Polynomial_Odegree(_238352, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_238352))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1416 ^ _191474) ^ [_238568, _238570] : [class_Rings_Odivision__ring__inverse__zero(_238568), 1419 ^ _191474 : [(1420 ^ _191474) ^ [] : [_238570 = c_Groups_Ozero__class_Ozero(_238568), -(c_Rings_Oinverse__class_Odivide(_238568, _238570, _238570) = c_Groups_Ozero__class_Ozero(_238568))], (1426 ^ _191474) ^ [] : [-(_238570 = c_Groups_Ozero__class_Ozero(_238568)), -(c_Rings_Oinverse__class_Odivide(_238568, _238570, _238570) = c_Groups_Oone__class_Oone(_238568))]]], (1432 ^ _191474) ^ [_239092, _239094, _239096, _239098] : [class_RealVector_Oreal__normed__field(_239092), -(c_Rings_Oinverse__class_Odivide(_239092, c_Groups_Oplus__class_Oplus(_239092, _239094, _239096), _239098) = c_Groups_Oplus__class_Oplus(_239092, c_Rings_Oinverse__class_Odivide(_239092, _239094, _239098), c_Rings_Oinverse__class_Odivide(_239092, _239096, _239098)))], (1438 ^ _191474) ^ [_239352, _239354] : [class_Rings_Odivision__ring(_239352), -(_239354 = c_Groups_Ozero__class_Ozero(_239352)), -(c_Rings_Oinverse__class_Odivide(_239352, _239354, _239354) = c_Groups_Oone__class_Oone(_239352))], (1448 ^ _191474) ^ [_239682, _239684, _239686] : [class_Rings_Odivision__ring(_239682), -(_239684 = c_Groups_Ozero__class_Ozero(_239682)), 1455 ^ _191474 : [(1456 ^ _191474) ^ [] : [c_Rings_Oinverse__class_Odivide(_239682, _239686, _239684) = c_Groups_Oone__class_Oone(_239682), -(_239686 = _239684)], (1462 ^ _191474) ^ [] : [_239686 = _239684, -(c_Rings_Oinverse__class_Odivide(_239682, _239686, _239684) = c_Groups_Oone__class_Oone(_239682))]]], (1468 ^ _191474) ^ [_240302, _240304, _240306, _240308] : [class_Rings_Odivision__ring(_240302), -(c_Rings_Oinverse__class_Odivide(_240302, c_Groups_Oplus__class_Oplus(_240302, _240304, _240306), _240308) = c_Groups_Oplus__class_Oplus(_240302, c_Rings_Oinverse__class_Odivide(_240302, _240304, _240308), c_Rings_Oinverse__class_Odivide(_240302, _240306, _240308)))], (1474 ^ _191474) ^ [_240562, _240564] : [class_Rings_Odivision__ring(_240562), -(c_Rings_Oinverse__class_Odivide(_240562, _240564, c_Groups_Oone__class_Oone(_240562)) = _240564)], (1480 ^ _191474) ^ [_240782, _240784] : [class_Rings_Olinordered__semidom(_240782), -(c_Orderings_Oord__class_Oless(_240782, _240784, c_Groups_Oplus__class_Oplus(_240782, _240784, c_Groups_Oone__class_Oone(_240782))))], (1486 ^ _191474) ^ [_241018, _241020, _241022] : [-(c_RealVector_Onorm__class_Onorm(_241018, c_Rings_Oinverse__class_Odivide(_241018, _241020, _241022)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_241018, _241020), c_RealVector_Onorm__class_Onorm(_241018, _241022))), class_Fields_Ofield__inverse__zero(_241018), class_RealVector_Oreal__normed__field(_241018)], (1496 ^ _191474) ^ [_241357, _241359] : [class_Rings_Odivision__ring__inverse__zero(_241357), -(c_Rings_Oinverse__class_Odivide(_241357, _241359, c_Groups_Ozero__class_Ozero(_241357)) = c_Groups_Ozero__class_Ozero(_241357))], (1502 ^ _191474) ^ [_241581, _241583] : [class_Rings_Odivision__ring(_241581), -(c_Rings_Oinverse__class_Odivide(_241581, c_Groups_Ozero__class_Ozero(_241581), _241583) = c_Groups_Ozero__class_Ozero(_241581))], (1508 ^ _191474) ^ [_241791] : [class_RealVector_Oreal__normed__algebra__1(_241791), -(c_RealVector_Onorm__class_Onorm(_241791, c_Groups_Oone__class_Oone(_241791)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (1514 ^ _191474) ^ [_242031, _242033, _242035, _242037] : [class_Rings_Odivision__ring(_242031), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242031), _242033), c_Rings_Oinverse__class_Odivide(_242031, _242035, _242037)) = c_Rings_Oinverse__class_Odivide(_242031, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242031), _242033), _242035), _242037))], (1520 ^ _191474) ^ [_242327, _242329, _242331, _242333] : [class_Rings_Odivision__ring(_242327), -(c_Rings_Oinverse__class_Odivide(_242327, c_Groups_Ominus__class_Ominus(_242327, _242329, _242331), _242333) = c_Groups_Ominus__class_Ominus(_242327, c_Rings_Oinverse__class_Odivide(_242327, _242329, _242333), c_Rings_Oinverse__class_Odivide(_242327, _242331, _242333)))], (1526 ^ _191474) ^ [_242615, _242617, _242619, _242621] : [class_Rings_Ocomm__semiring(_242615), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242615), c_Groups_Oplus__class_Oplus(_242615, _242617, _242619)), _242621) = c_Groups_Oplus__class_Oplus(_242615, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242615), _242617), _242621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242615), _242619), _242621)))], (1532 ^ _191474) ^ [_242941, _242943, _242945, _242947, _242949] : [class_Rings_Osemiring(_242941), -(c_Groups_Oplus__class_Oplus(_242941, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242941), _242943), _242945), c_Groups_Oplus__class_Oplus(_242941, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242941), _242947), _242945), _242949)) = c_Groups_Oplus__class_Oplus(_242941, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242941), c_Groups_Oplus__class_Oplus(_242941, _242943, _242947)), _242945), _242949))], (1538 ^ _191474) ^ [_243275, _243277, _243279, _243281] : [class_Rings_Ocomm__semiring__0(_243275), -(hAPP(c_Polynomial_Opoly(_243275, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_243275), _243277, _243279)), _243281) = c_Groups_Oplus__class_Oplus(_243275, hAPP(c_Polynomial_Opoly(_243275, _243277), _243281), hAPP(c_Polynomial_Opoly(_243275, _243279), _243281)))], (1544 ^ _191474) ^ [_243537] : [class_Rings_Ozero__neq__one(_243537), c_Groups_Ozero__class_Ozero(_243537) = c_Groups_Oone__class_Oone(_243537)], (1550 ^ _191474) ^ [_243734] : [class_Rings_Ozero__neq__one(_243734), c_Groups_Oone__class_Oone(_243734) = c_Groups_Ozero__class_Ozero(_243734)], (1556 ^ _191474) ^ [_243945, _243947] : [class_Rings_Ocomm__semiring__1(_243945), -(hAPP(c_Polynomial_Opoly(_243945, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_243945))), _243947) = c_Groups_Oone__class_Oone(_243945))], (1562 ^ _191474) ^ [_244205, _244207, _244209, _244211] : [class_Groups_Oab__group__add(_244205), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_244205, _244207), _244209), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_244205, _244211), _244209), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_244205, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_244205), _244207, _244211)), _244209))], (1576 ^ _191474) ^ [_244683, _244685, _244687, _244689] : [class_Groups_Oab__group__add(_244683), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_244683, _244685), _244687), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_244683, _244689), _244687), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_244683, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_244683), _244685, _244689)), _244687))], (1590 ^ _191474) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (1592 ^ _191474) ^ [_245156] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _245156) = _245156)], (1594 ^ _191474) ^ [_245252] : [class_Rings_Olinordered__semidom(_245252), -(c_Orderings_Oord__class_Oless(_245252, c_Groups_Ozero__class_Ozero(_245252), c_Groups_Oplus__class_Oplus(_245252, c_Groups_Oone__class_Oone(_245252), c_Groups_Oone__class_Oone(_245252))))], (1600 ^ _191474) ^ [_245476, _245478] : [class_Rings_Oring__1(_245476), -(c_Groups_Ominus__class_Ominus(_245476, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_245476), _245478), _245478), c_Groups_Oone__class_Oone(_245476)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_245476), c_Groups_Oplus__class_Oplus(_245476, _245478, c_Groups_Oone__class_Oone(_245476))), c_Groups_Ominus__class_Ominus(_245476, _245478, c_Groups_Oone__class_Oone(_245476))))], (1606 ^ _191474) ^ [_245766, _245768, _245770] : [class_RealVector_Oreal__normed__field(_245766), -(_245768 = c_Groups_Ozero__class_Ozero(_245766)), -(c_RealVector_Onorm__class_Onorm(_245766, c_Rings_Oinverse__class_Odivide(_245766, _245770, _245768)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_245766, _245770), c_RealVector_Onorm__class_Onorm(_245766, _245768)))], (1616 ^ _191474) ^ [_246128, _246130, _246132] : [class_RealVector_Oreal__normed__vector(_246128), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_246128, c_Groups_Oplus__class_Oplus(_246128, _246130, _246132)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_246128, _246130), c_RealVector_Onorm__class_Onorm(_246128, _246132))))], (1622 ^ _191474) ^ [_246420, _246422, _246424, _246426, _246428] : [class_RealVector_Oreal__normed__vector(_246420), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_246420, _246422), _246424), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_246420, _246426), _246428), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_246420, c_Groups_Oplus__class_Oplus(_246420, _246422, _246426)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _246424, _246428)))], (1636 ^ _191474) ^ [_246944, _246946, _246948, _246950, _246952, _246954] : [class_Rings_Olinordered__semiring__1(_246944), c_Orderings_Oord__class_Oless__eq(_246944, _246946, _246948), c_Orderings_Oord__class_Oless__eq(_246944, _246950, _246948), c_Orderings_Oord__class_Oless__eq(_246944, c_Groups_Ozero__class_Ozero(_246944), _246952), c_Orderings_Oord__class_Oless__eq(_246944, c_Groups_Ozero__class_Ozero(_246944), _246954), c_Groups_Oplus__class_Oplus(_246944, _246952, _246954) = c_Groups_Oone__class_Oone(_246944), -(c_Orderings_Oord__class_Oless__eq(_246944, c_Groups_Oplus__class_Oplus(_246944, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_246944), _246952), _246946), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_246944), _246954), _246950)), _246948))], (1662 ^ _191474) ^ [_247771, _247773] : [class_RealVector_Oreal__normed__field(_247771), -(c_Rings_Oinverse__class_Odivide(_247771, c_Groups_Ozero__class_Ozero(_247771), _247773) = c_Groups_Ozero__class_Ozero(_247771))], (1668 ^ _191474) ^ [_248023, _248025, _248027, _248029] : [class_RealVector_Oreal__normed__field(_248023), -(c_Rings_Oinverse__class_Odivide(_248023, c_Groups_Ominus__class_Ominus(_248023, _248025, _248027), _248029) = c_Groups_Ominus__class_Ominus(_248023, c_Rings_Oinverse__class_Odivide(_248023, _248025, _248029), c_Rings_Oinverse__class_Odivide(_248023, _248027, _248029)))], (1674 ^ _191474) ^ [_248311, _248313, _248315, _248317] : [class_RealVector_Oreal__normed__algebra(_248311), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248311), _248313), c_Groups_Oplus__class_Oplus(_248311, _248315, _248317)) = c_Groups_Oplus__class_Oplus(_248311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248311), _248313), _248315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248311), _248313), _248317)))], (1680 ^ _191474) ^ [_248623, _248625, _248627, _248629] : [class_RealVector_Oreal__normed__algebra(_248623), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248623), _248625), c_Groups_Oplus__class_Oplus(_248623, _248627, _248629)) = c_Groups_Oplus__class_Oplus(_248623, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248623), _248625), _248627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248623), _248625), _248629)))], (1686 ^ _191474) ^ [_248935, _248937, _248939, _248941] : [class_RealVector_Oreal__normed__algebra(_248935), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248935), c_Groups_Oplus__class_Oplus(_248935, _248937, _248939)), _248941) = c_Groups_Oplus__class_Oplus(_248935, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248935), _248937), _248941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248935), _248939), _248941)))], (1692 ^ _191474) ^ [_249247, _249249, _249251, _249253] : [class_RealVector_Oreal__normed__algebra(_249247), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249247), c_Groups_Oplus__class_Oplus(_249247, _249249, _249251)), _249253) = c_Groups_Oplus__class_Oplus(_249247, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249247), _249249), _249253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249247), _249251), _249253)))], (1698 ^ _191474) ^ [_249559, _249561, _249563, _249565] : [class_Rings_Odivision__ring(_249559), -(_249561 = c_Groups_Ozero__class_Ozero(_249559)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249559), _249563), _249561) = _249565, -(_249563 = c_Rings_Oinverse__class_Odivide(_249559, _249565, _249561))], (1712 ^ _191474) ^ [_250032, _250034, _250036, _250038] : [class_Rings_Odivision__ring(_250032), -(_250034 = c_Groups_Ozero__class_Ozero(_250032)), _250036 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250032), _250038), _250034), -(c_Rings_Oinverse__class_Odivide(_250032, _250036, _250034) = _250038)], (1726 ^ _191474) ^ [_250505, _250507, _250509, _250511] : [class_Rings_Odivision__ring(_250505), -(_250507 = c_Groups_Ozero__class_Ozero(_250505)), 1733 ^ _191474 : [(1734 ^ _191474) ^ [] : [c_Rings_Oinverse__class_Odivide(_250505, _250509, _250507) = _250511, -(_250509 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250505), _250511), _250507))], (1740 ^ _191474) ^ [] : [_250509 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250505), _250511), _250507), -(c_Rings_Oinverse__class_Odivide(_250505, _250509, _250507) = _250511)]]], (1746 ^ _191474) ^ [_251163, _251165, _251167, _251169] : [class_Rings_Odivision__ring(_251163), -(_251165 = c_Groups_Ozero__class_Ozero(_251163)), 1753 ^ _191474 : [(1754 ^ _191474) ^ [] : [_251167 = c_Rings_Oinverse__class_Odivide(_251163, _251169, _251165), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251163), _251167), _251165) = _251169)], (1760 ^ _191474) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_251163), _251167), _251165) = _251169, -(_251167 = c_Rings_Oinverse__class_Odivide(_251163, _251169, _251165))]]], (1766 ^ _191474) ^ [_251821, _251823, _251825, _251827] : [class_Rings_Olinordered__semidom(_251821), c_Orderings_Oord__class_Oless(_251821, c_Groups_Ozero__class_Ozero(_251821), _251823), c_Orderings_Oord__class_Oless(_251821, _251825, _251827), -(c_Orderings_Oord__class_Oless(_251821, _251825, c_Groups_Oplus__class_Oplus(_251821, _251823, _251827)))], (1780 ^ _191474) ^ [_252239] : [class_Rings_Olinordered__semidom(_252239), -(c_Orderings_Oord__class_Oless__eq(_252239, c_Groups_Ozero__class_Ozero(_252239), c_Groups_Oone__class_Oone(_252239)))], (1786 ^ _191474) ^ [_252437] : [class_Rings_Olinordered__semidom(_252437), c_Orderings_Oord__class_Oless__eq(_252437, c_Groups_Oone__class_Oone(_252437), c_Groups_Ozero__class_Ozero(_252437))], (1792 ^ _191474) ^ [_252692, _252694, _252696, _252698, _252700] : [class_Rings_Oring(_252692), -(c_Groups_Ominus__class_Ominus(_252692, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252692), _252694), _252696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252692), _252698), _252700)) = c_Groups_Oplus__class_Oplus(_252692, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252692), _252694), c_Groups_Ominus__class_Ominus(_252692, _252696, _252700)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252692), c_Groups_Ominus__class_Ominus(_252692, _252694, _252698)), _252700)))], (1798 ^ _191474) ^ [_253070, _253072, _253074, _253076, _253078, _253080] : [class_Rings_Oring(_253070), 1801 ^ _191474 : [(1802 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_253070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253070), _253072), _253074), _253076) = c_Groups_Oplus__class_Oplus(_253070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253070), _253078), _253074), _253080), -(_253076 = c_Groups_Oplus__class_Oplus(_253070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253070), c_Groups_Ominus__class_Ominus(_253070, _253078, _253072)), _253074), _253080))], (1808 ^ _191474) ^ [] : [_253076 = c_Groups_Oplus__class_Oplus(_253070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253070), c_Groups_Ominus__class_Ominus(_253070, _253078, _253072)), _253074), _253080), -(c_Groups_Oplus__class_Oplus(_253070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253070), _253072), _253074), _253076) = c_Groups_Oplus__class_Oplus(_253070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253070), _253078), _253074), _253080))]]], (1814 ^ _191474) ^ [_253768, _253770, _253772, _253774, _253776, _253778] : [class_Rings_Oring(_253768), 1817 ^ _191474 : [(1818 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_253768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253768), _253770), _253772), _253774) = c_Groups_Oplus__class_Oplus(_253768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253768), _253776), _253772), _253778), -(c_Groups_Oplus__class_Oplus(_253768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253768), c_Groups_Ominus__class_Ominus(_253768, _253770, _253776)), _253772), _253774) = _253778)], (1824 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_253768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253768), c_Groups_Ominus__class_Ominus(_253768, _253770, _253776)), _253772), _253774) = _253778, -(c_Groups_Oplus__class_Oplus(_253768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253768), _253770), _253772), _253774) = c_Groups_Oplus__class_Oplus(_253768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253768), _253776), _253772), _253778))]]], (1830 ^ _191474) ^ [_254396] : [class_Rings_Olinordered__semidom(_254396), -(c_Orderings_Oord__class_Oless(_254396, c_Groups_Ozero__class_Ozero(_254396), c_Groups_Oone__class_Oone(_254396)))], (1836 ^ _191474) ^ [_254594] : [class_Rings_Olinordered__semidom(_254594), c_Orderings_Oord__class_Oless(_254594, c_Groups_Oone__class_Oone(_254594), c_Groups_Ozero__class_Ozero(_254594))], (1842 ^ _191474) ^ [_254821, _254823, _254825] : [class_Rings_Olinordered__semidom(_254821), c_Orderings_Oord__class_Oless(_254821, c_Groups_Oone__class_Oone(_254821), _254823), c_Orderings_Oord__class_Oless(_254821, c_Groups_Oone__class_Oone(_254821), _254825), -(c_Orderings_Oord__class_Oless(_254821, c_Groups_Oone__class_Oone(_254821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254821), _254823), _254825)))], (1872 ^ _191474) ^ [_255719, _255721] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _255719, _255721))), 1875 ^ _191474 : [(1876 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _255719, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1878 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _255721)]], 1879 ^ _191474 : [(1880 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _255719)], (1882 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _255721, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1856 ^ _191474) ^ [_255284, _255286] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _255284, _255286)), 1859 ^ _191474 : [(1860 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _255284, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _255286))], (1866 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _255284)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _255286, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (1886 ^ _191474) ^ [_256186, _256188] : [class_Int_Oring__char__0(_256186), class_Rings_Oidom(_256186), 1893 ^ _191474 : [(1894 ^ _191474) ^ [] : [c_Polynomial_Opoly(_256186, _256188) = c_Polynomial_Opoly(_256186, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_256186))), -(_256188 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_256186)))], (1900 ^ _191474) ^ [] : [_256188 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_256186)), -(c_Polynomial_Opoly(_256186, _256188) = c_Polynomial_Opoly(_256186, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_256186))))]]], (1906 ^ _191474) ^ [_256817, _256819, _256821, _256823, _256825] : [class_RealVector_Oreal__normed__vector(_256817), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_256817, c_Groups_Ominus__class_Ominus(_256817, c_Groups_Oplus__class_Oplus(_256817, _256819, _256821), c_Groups_Oplus__class_Oplus(_256817, _256823, _256825))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_256817, c_Groups_Ominus__class_Ominus(_256817, _256819, _256823)), c_RealVector_Onorm__class_Onorm(_256817, c_Groups_Ominus__class_Ominus(_256817, _256821, _256825)))))], (1912 ^ _191474) ^ [_257167, _257169, _257171, _257173, _257175, _257177] : [class_Rings_Olinordered__semiring__1__strict(_257167), c_Orderings_Oord__class_Oless(_257167, _257169, _257171), c_Orderings_Oord__class_Oless(_257167, _257173, _257171), c_Orderings_Oord__class_Oless__eq(_257167, c_Groups_Ozero__class_Ozero(_257167), _257175), c_Orderings_Oord__class_Oless__eq(_257167, c_Groups_Ozero__class_Ozero(_257167), _257177), c_Groups_Oplus__class_Oplus(_257167, _257175, _257177) = c_Groups_Oone__class_Oone(_257167), -(c_Orderings_Oord__class_Oless(_257167, c_Groups_Oplus__class_Oplus(_257167, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257167), _257175), _257169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257167), _257177), _257173)), _257171))], (1938 ^ _191474) ^ [_257994, _257996] : [class_Rings_Ocomm__semiring__0(_257994), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_257994)), _257996), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_257994))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_257994)))], (1944 ^ _191474) ^ [_258238, _258240] : [class_Rings_Ocomm__semiring__0(_258238), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_258238)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_258238))), _258240) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_258238)))], (1950 ^ _191474) ^ [_258482, _258484] : [class_Groups_Oab__group__add(_258482), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_258482), _258484, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_258482))) = _258484)], (1956 ^ _191474) ^ [_258766, _258768, _258770, _258772, _258774, _258776] : [class_Rings_Oordered__ring(_258766), 1959 ^ _191474 : [(1960 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_258766, c_Groups_Oplus__class_Oplus(_258766, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258766), _258768), _258770), _258772), c_Groups_Oplus__class_Oplus(_258766, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258766), _258774), _258770), _258776)), -(c_Orderings_Oord__class_Oless__eq(_258766, _258772, c_Groups_Oplus__class_Oplus(_258766, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258766), c_Groups_Ominus__class_Ominus(_258766, _258774, _258768)), _258770), _258776)))], (1966 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_258766, _258772, c_Groups_Oplus__class_Oplus(_258766, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258766), c_Groups_Ominus__class_Ominus(_258766, _258774, _258768)), _258770), _258776)), -(c_Orderings_Oord__class_Oless__eq(_258766, c_Groups_Oplus__class_Oplus(_258766, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258766), _258768), _258770), _258772), c_Groups_Oplus__class_Oplus(_258766, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258766), _258774), _258770), _258776)))]]], (1972 ^ _191474) ^ [_259470, _259472, _259474, _259476, _259478, _259480] : [class_Rings_Oordered__ring(_259470), 1975 ^ _191474 : [(1976 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_259470, c_Groups_Oplus__class_Oplus(_259470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259470), _259472), _259474), _259476), c_Groups_Oplus__class_Oplus(_259470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259470), _259478), _259474), _259480)), -(c_Orderings_Oord__class_Oless__eq(_259470, c_Groups_Oplus__class_Oplus(_259470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259470), c_Groups_Ominus__class_Ominus(_259470, _259472, _259478)), _259474), _259476), _259480))], (1982 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_259470, c_Groups_Oplus__class_Oplus(_259470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259470), c_Groups_Ominus__class_Ominus(_259470, _259472, _259478)), _259474), _259476), _259480), -(c_Orderings_Oord__class_Oless__eq(_259470, c_Groups_Oplus__class_Oplus(_259470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259470), _259472), _259474), _259476), c_Groups_Oplus__class_Oplus(_259470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259470), _259478), _259474), _259480)))]]], (1988 ^ _191474) ^ [_260174, _260176, _260178, _260180, _260182, _260184] : [class_Rings_Oordered__ring(_260174), 1991 ^ _191474 : [(1992 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_260174, c_Groups_Oplus__class_Oplus(_260174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260174), _260176), _260178), _260180), c_Groups_Oplus__class_Oplus(_260174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260174), _260182), _260178), _260184)), -(c_Orderings_Oord__class_Oless(_260174, _260180, c_Groups_Oplus__class_Oplus(_260174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260174), c_Groups_Ominus__class_Ominus(_260174, _260182, _260176)), _260178), _260184)))], (1998 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_260174, _260180, c_Groups_Oplus__class_Oplus(_260174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260174), c_Groups_Ominus__class_Ominus(_260174, _260182, _260176)), _260178), _260184)), -(c_Orderings_Oord__class_Oless(_260174, c_Groups_Oplus__class_Oplus(_260174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260174), _260176), _260178), _260180), c_Groups_Oplus__class_Oplus(_260174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260174), _260182), _260178), _260184)))]]], (2004 ^ _191474) ^ [_260878, _260880, _260882, _260884, _260886, _260888] : [class_Rings_Oordered__ring(_260878), 2007 ^ _191474 : [(2008 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_260878, c_Groups_Oplus__class_Oplus(_260878, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260878), _260880), _260882), _260884), c_Groups_Oplus__class_Oplus(_260878, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260878), _260886), _260882), _260888)), -(c_Orderings_Oord__class_Oless(_260878, c_Groups_Oplus__class_Oplus(_260878, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260878), c_Groups_Ominus__class_Ominus(_260878, _260880, _260886)), _260882), _260884), _260888))], (2014 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_260878, c_Groups_Oplus__class_Oplus(_260878, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260878), c_Groups_Ominus__class_Ominus(_260878, _260880, _260886)), _260882), _260884), _260888), -(c_Orderings_Oord__class_Oless(_260878, c_Groups_Oplus__class_Oplus(_260878, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260878), _260880), _260882), _260884), c_Groups_Oplus__class_Oplus(_260878, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260878), _260886), _260882), _260888)))]]], (2020 ^ _191474) ^ [_261540, _261542, _261544] : [class_Rings_Olinordered__idom(_261540), c_Orderings_Oord__class_Oless__eq(_261540, c_Groups_Ozero__class_Ozero(_261540), _261542), c_Orderings_Oord__class_Oless__eq(_261540, c_Groups_Ozero__class_Ozero(_261540), _261544), c_Orderings_Oord__class_Oless__eq(_261540, _261544, c_Groups_Oone__class_Oone(_261540)), -(c_Orderings_Oord__class_Oless__eq(_261540, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_261540), _261544), _261542), _261542))], (2038 ^ _191474) ^ [_262083, _262085, _262087] : [class_Rings_Olinordered__idom(_262083), c_Orderings_Oord__class_Oless__eq(_262083, c_Groups_Ozero__class_Ozero(_262083), _262085), c_Orderings_Oord__class_Oless__eq(_262083, c_Groups_Ozero__class_Ozero(_262083), _262087), c_Orderings_Oord__class_Oless__eq(_262083, _262087, c_Groups_Oone__class_Oone(_262083)), -(c_Orderings_Oord__class_Oless__eq(_262083, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262083), _262085), _262087), _262085))], (2056 ^ _191474) ^ [_262654, _262656, _262658, _262660, _262662] : [class_RealVector_Oreal__normed__algebra(_262654), -(c_Groups_Ominus__class_Ominus(_262654, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262654), _262656), _262658), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262654), _262660), _262662)) = c_Groups_Oplus__class_Oplus(_262654, c_Groups_Oplus__class_Oplus(_262654, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262654), c_Groups_Ominus__class_Ominus(_262654, _262656, _262660)), c_Groups_Ominus__class_Ominus(_262654, _262658, _262662)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262654), c_Groups_Ominus__class_Ominus(_262654, _262656, _262660)), _262662)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262654), _262660), c_Groups_Ominus__class_Ominus(_262654, _262658, _262662))))], (2062 ^ _191474) ^ [_263030, _263032, _263034] : [class_RealVector_Oreal__normed__vector(_263030), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_263030, _263032), c_RealVector_Onorm__class_Onorm(_263030, _263034)), c_RealVector_Onorm__class_Onorm(_263030, c_Groups_Oplus__class_Oplus(_263030, _263032, _263034))))], (2068 ^ _191474) ^ [_263294, _263296, _263298] : [class_Rings_Olinordered__idom(_263294), -(_263296 = _263298), -(c_Orderings_Oord__class_Oless(_263294, _263296, _263298)), -(c_Orderings_Oord__class_Oless(_263294, _263298, _263296))], (2082 ^ _191474) ^ [_263704, _263706] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _263704, _263706), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _263706, _263704), -(_263704 = _263706)], (2092 ^ _191474) ^ [_264021, _264023, _264025] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _264021, _264023), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _264023, _264025), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _264021, _264025))], (2102 ^ _191474) ^ [_264336, _264338] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _264336, _264338)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _264338, _264336))], (2108 ^ _191474) ^ [_264522] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _264522, _264522))], (2110 ^ _191474) ^ [_264615, _264617] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _264615), _264617) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _264617), _264615))], (2112 ^ _191474) ^ [_264735, _264737, _264739] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _264735), _264737)), _264739) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _264735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _264737), _264739)))], (2114 ^ _191474) ^ [_264870, _264872] : [class_Rings_Omult__zero(_264870), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_264870), c_Groups_Ozero__class_Ozero(_264870)), _264872) = c_Groups_Ozero__class_Ozero(_264870))], (2120 ^ _191474) ^ [_265102, _265104] : [class_Rings_Omult__zero(_265102), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265102), _265104), c_Groups_Ozero__class_Ozero(_265102)) = c_Groups_Ozero__class_Ozero(_265102))], (2126 ^ _191474) ^ [_265348, _265350, _265352] : [class_Rings_Oring__no__zero__divisors(_265348), 2129 ^ _191474 : [(2140 ^ _191474) ^ [] : [2141 ^ _191474 : [(2142 ^ _191474) ^ [] : [_265350 = c_Groups_Ozero__class_Ozero(_265348)], (2144 ^ _191474) ^ [] : [_265352 = c_Groups_Ozero__class_Ozero(_265348)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265348), _265350), _265352) = c_Groups_Ozero__class_Ozero(_265348))], (2130 ^ _191474) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_265348), _265350), _265352) = c_Groups_Ozero__class_Ozero(_265348), -(_265350 = c_Groups_Ozero__class_Ozero(_265348)), -(_265352 = c_Groups_Ozero__class_Ozero(_265348))]]], (2148 ^ _191474) ^ [_266042, _266044, _266046] : [class_Rings_Ono__zero__divisors(_266042), -(_266044 = c_Groups_Ozero__class_Ozero(_266042)), -(_266046 = c_Groups_Ozero__class_Ozero(_266042)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266042), _266044), _266046) = c_Groups_Ozero__class_Ozero(_266042)], (2162 ^ _191474) ^ [_266491, _266493, _266495] : [class_Rings_Ono__zero__divisors(_266491), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266491), _266493), _266495) = c_Groups_Ozero__class_Ozero(_266491), -(_266493 = c_Groups_Ozero__class_Ozero(_266491)), -(_266495 = c_Groups_Ozero__class_Ozero(_266491))], (2176 ^ _191474) ^ [_266949, _266951] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _266949, _266951), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _266949, _266951), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (2182 ^ _191474) ^ [_267123, _267125] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _267123, _267125), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _267123, _267125))], (2188 ^ _191474) ^ [_267376, _267378] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _267376, _267378), 2191 ^ _191474 : [(2192 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _267376, _267378))], (2194 ^ _191474) ^ [] : [_267376 = _267378]]], (2196 ^ _191474) ^ [_267618, _267620] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _267618, _267620)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _267618, _267620), -(_267618 = _267620)], (2216 ^ _191474) ^ [_268211, _268213] : [2217 ^ _191474 : [(2218 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _268211, _268213)], (2220 ^ _191474) ^ [] : [_268211 = _268213]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _268211, _268213))], (2206 ^ _191474) ^ [_267955, _267957] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _267955, _267957), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _267955, _267957)), -(_267955 = _267957)], (2224 ^ _191474) ^ [_268515, _268517, _268519] : [-(_268515 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 2227 ^ _191474 : [(2228 ^ _191474) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _268517), _268515) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _268519), _268515), -(_268517 = _268519)], (2234 ^ _191474) ^ [] : [_268517 = _268519, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _268517), _268515) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _268519), _268515))]]], (2240 ^ _191474) ^ [_269044, _269046, _269048] : [-(_269044 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 2243 ^ _191474 : [(2244 ^ _191474) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _269044), _269046) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _269044), _269048), -(_269046 = _269048)], (2250 ^ _191474) ^ [] : [_269046 = _269048, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _269044), _269046) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _269044), _269048))]]], (2256 ^ _191474) ^ [_269573, _269575, _269577] : [class_Rings_Oordered__cancel__semiring(_269573), -(c_Orderings_Oord__class_Oless__eq(_269573, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269573), _269575), _269577), c_Groups_Ozero__class_Ozero(_269573))), 2261 ^ _191474 : [(2262 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_269573, c_Groups_Ozero__class_Ozero(_269573), _269575), c_Orderings_Oord__class_Oless__eq(_269573, _269577, c_Groups_Ozero__class_Ozero(_269573))], (2268 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_269573, _269575, c_Groups_Ozero__class_Ozero(_269573)), c_Orderings_Oord__class_Oless__eq(_269573, c_Groups_Ozero__class_Ozero(_269573), _269577)]]], (2276 ^ _191474) ^ [_270202, _270204, _270206] : [class_Rings_Oordered__ring(_270202), -(c_Orderings_Oord__class_Oless__eq(_270202, c_Groups_Ozero__class_Ozero(_270202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270202), _270204), _270206))), 2281 ^ _191474 : [(2282 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_270202, c_Groups_Ozero__class_Ozero(_270202), _270204), c_Orderings_Oord__class_Oless__eq(_270202, c_Groups_Ozero__class_Ozero(_270202), _270206)], (2288 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_270202, _270204, c_Groups_Ozero__class_Ozero(_270202)), c_Orderings_Oord__class_Oless__eq(_270202, _270206, c_Groups_Ozero__class_Ozero(_270202))]]], (2296 ^ _191474) ^ [_270859, _270861, _270863, _270865, _270867] : [class_Rings_Oordered__semiring(_270859), c_Orderings_Oord__class_Oless__eq(_270859, _270861, _270863), c_Orderings_Oord__class_Oless__eq(_270859, _270865, _270867), c_Orderings_Oord__class_Oless__eq(_270859, c_Groups_Ozero__class_Ozero(_270859), _270863), c_Orderings_Oord__class_Oless__eq(_270859, c_Groups_Ozero__class_Ozero(_270859), _270865), -(c_Orderings_Oord__class_Oless__eq(_270859, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270859), _270861), _270865), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270859), _270863), _270867)))], (2318 ^ _191474) ^ [_271581, _271583, _271585, _271587, _271589] : [class_Rings_Oordered__semiring(_271581), c_Orderings_Oord__class_Oless__eq(_271581, _271583, _271585), c_Orderings_Oord__class_Oless__eq(_271581, _271587, _271589), c_Orderings_Oord__class_Oless__eq(_271581, c_Groups_Ozero__class_Ozero(_271581), _271583), c_Orderings_Oord__class_Oless__eq(_271581, c_Groups_Ozero__class_Ozero(_271581), _271587), -(c_Orderings_Oord__class_Oless__eq(_271581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271581), _271583), _271587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271581), _271585), _271589)))], (2340 ^ _191474) ^ [_272289, _272291, _272293, _272295] : [class_Rings_Oordered__ring(_272289), c_Orderings_Oord__class_Oless__eq(_272289, _272291, _272293), c_Orderings_Oord__class_Oless__eq(_272289, _272295, c_Groups_Ozero__class_Ozero(_272289)), -(c_Orderings_Oord__class_Oless__eq(_272289, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272289), _272295), _272293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272289), _272295), _272291)))], (2354 ^ _191474) ^ [_272773, _272775, _272777, _272779] : [class_Rings_Oordered__ring(_272773), c_Orderings_Oord__class_Oless__eq(_272773, _272775, _272777), c_Orderings_Oord__class_Oless__eq(_272773, _272779, c_Groups_Ozero__class_Ozero(_272773)), -(c_Orderings_Oord__class_Oless__eq(_272773, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272773), _272777), _272779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272773), _272775), _272779)))], (2368 ^ _191474) ^ [_273257, _273259, _273261, _273263] : [class_Rings_Oordered__comm__semiring(_273257), c_Orderings_Oord__class_Oless__eq(_273257, _273259, _273261), c_Orderings_Oord__class_Oless__eq(_273257, c_Groups_Ozero__class_Ozero(_273257), _273263), -(c_Orderings_Oord__class_Oless__eq(_273257, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273257), _273263), _273259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273257), _273263), _273261)))], (2382 ^ _191474) ^ [_273741, _273743, _273745, _273747] : [class_Rings_Oordered__semiring(_273741), c_Orderings_Oord__class_Oless__eq(_273741, _273743, _273745), c_Orderings_Oord__class_Oless__eq(_273741, c_Groups_Ozero__class_Ozero(_273741), _273747), -(c_Orderings_Oord__class_Oless__eq(_273741, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273741), _273747), _273743), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273741), _273747), _273745)))], (2396 ^ _191474) ^ [_274225, _274227, _274229, _274231] : [class_Rings_Oordered__semiring(_274225), c_Orderings_Oord__class_Oless__eq(_274225, _274227, _274229), c_Orderings_Oord__class_Oless__eq(_274225, c_Groups_Ozero__class_Ozero(_274225), _274231), -(c_Orderings_Oord__class_Oless__eq(_274225, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274225), _274227), _274231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274225), _274229), _274231)))], (2410 ^ _191474) ^ [_274695, _274697, _274699] : [class_Rings_Oordered__ring(_274695), c_Orderings_Oord__class_Oless__eq(_274695, _274697, c_Groups_Ozero__class_Ozero(_274695)), c_Orderings_Oord__class_Oless__eq(_274695, _274699, c_Groups_Ozero__class_Ozero(_274695)), -(c_Orderings_Oord__class_Oless__eq(_274695, c_Groups_Ozero__class_Ozero(_274695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274695), _274697), _274699)))], (2424 ^ _191474) ^ [_275143, _275145, _275147] : [class_Rings_Oordered__cancel__semiring(_275143), c_Orderings_Oord__class_Oless__eq(_275143, _275145, c_Groups_Ozero__class_Ozero(_275143)), c_Orderings_Oord__class_Oless__eq(_275143, c_Groups_Ozero__class_Ozero(_275143), _275147), -(c_Orderings_Oord__class_Oless__eq(_275143, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275143), _275145), _275147), c_Groups_Ozero__class_Ozero(_275143)))], (2438 ^ _191474) ^ [_275591, _275593, _275595] : [class_Rings_Oordered__cancel__semiring(_275591), c_Orderings_Oord__class_Oless__eq(_275591, c_Groups_Ozero__class_Ozero(_275591), _275593), c_Orderings_Oord__class_Oless__eq(_275591, _275595, c_Groups_Ozero__class_Ozero(_275591)), -(c_Orderings_Oord__class_Oless__eq(_275591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275591), _275595), _275593), c_Groups_Ozero__class_Ozero(_275591)))], (2452 ^ _191474) ^ [_276039, _276041, _276043] : [class_Rings_Oordered__cancel__semiring(_276039), c_Orderings_Oord__class_Oless__eq(_276039, c_Groups_Ozero__class_Ozero(_276039), _276041), c_Orderings_Oord__class_Oless__eq(_276039, _276043, c_Groups_Ozero__class_Ozero(_276039)), -(c_Orderings_Oord__class_Oless__eq(_276039, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276039), _276041), _276043), c_Groups_Ozero__class_Ozero(_276039)))], (2466 ^ _191474) ^ [_276487, _276489, _276491] : [class_Rings_Oordered__cancel__semiring(_276487), c_Orderings_Oord__class_Oless__eq(_276487, c_Groups_Ozero__class_Ozero(_276487), _276489), c_Orderings_Oord__class_Oless__eq(_276487, c_Groups_Ozero__class_Ozero(_276487), _276491), -(c_Orderings_Oord__class_Oless__eq(_276487, c_Groups_Ozero__class_Ozero(_276487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276487), _276489), _276491)))], (2480 ^ _191474) ^ [_276935, _276937, _276939] : [class_Rings_Olinordered__ring__strict(_276935), 2483 ^ _191474 : [(2484 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_276935, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276935), _276937), _276939), c_Groups_Ozero__class_Ozero(_276935)), 2489 ^ _191474 : [(2490 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_276935, c_Groups_Ozero__class_Ozero(_276935), _276937))], (2492 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_276935, _276939, c_Groups_Ozero__class_Ozero(_276935)))]], 2493 ^ _191474 : [(2494 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_276935, _276937, c_Groups_Ozero__class_Ozero(_276935)))], (2496 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_276935, c_Groups_Ozero__class_Ozero(_276935), _276939))]]], (2498 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_276935, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276935), _276937), _276939), c_Groups_Ozero__class_Ozero(_276935))), 2499 ^ _191474 : [(2500 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_276935, c_Groups_Ozero__class_Ozero(_276935), _276937), c_Orderings_Oord__class_Oless__eq(_276935, _276939, c_Groups_Ozero__class_Ozero(_276935))], (2506 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_276935, _276937, c_Groups_Ozero__class_Ozero(_276935)), c_Orderings_Oord__class_Oless__eq(_276935, c_Groups_Ozero__class_Ozero(_276935), _276939)]]]]], (2514 ^ _191474) ^ [_277984, _277986, _277988] : [class_Rings_Olinordered__ring__strict(_277984), 2517 ^ _191474 : [(2518 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_277984, c_Groups_Ozero__class_Ozero(_277984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277984), _277986), _277988)), 2523 ^ _191474 : [(2524 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_277984, c_Groups_Ozero__class_Ozero(_277984), _277986))], (2526 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_277984, c_Groups_Ozero__class_Ozero(_277984), _277988))]], 2527 ^ _191474 : [(2528 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_277984, _277986, c_Groups_Ozero__class_Ozero(_277984)))], (2530 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_277984, _277988, c_Groups_Ozero__class_Ozero(_277984)))]]], (2532 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_277984, c_Groups_Ozero__class_Ozero(_277984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277984), _277986), _277988))), 2533 ^ _191474 : [(2534 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_277984, c_Groups_Ozero__class_Ozero(_277984), _277986), c_Orderings_Oord__class_Oless__eq(_277984, c_Groups_Ozero__class_Ozero(_277984), _277988)], (2540 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_277984, _277986, c_Groups_Ozero__class_Ozero(_277984)), c_Orderings_Oord__class_Oless__eq(_277984, _277988, c_Groups_Ozero__class_Ozero(_277984))]]]]], (2548 ^ _191474) ^ [_279019, _279021] : [class_Rings_Olinordered__ring(_279019), -(c_Orderings_Oord__class_Oless__eq(_279019, c_Groups_Ozero__class_Ozero(_279019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279019), _279021), _279021)))], (2554 ^ _191474) ^ [_279249, _279251] : [class_Rings_Olinordered__ring(_279249), c_Orderings_Oord__class_Oless(_279249, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279249), _279251), _279251), c_Groups_Ozero__class_Ozero(_279249))], (2560 ^ _191474) ^ [_279508, _279510, _279512, _279514] : [class_Rings_Olinordered__ring__strict(_279508), 2563 ^ _191474 : [(2564 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_279508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279508), _279510), _279512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279508), _279514), _279512)), 2569 ^ _191474 : [(2570 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_279508, c_Groups_Ozero__class_Ozero(_279508), _279512))], (2572 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_279508, _279510, _279514))]], 2573 ^ _191474 : [(2574 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_279508, _279512, c_Groups_Ozero__class_Ozero(_279508)))], (2576 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_279508, _279514, _279510))]]], (2578 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_279508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279508), _279510), _279512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279508), _279514), _279512))), 2579 ^ _191474 : [(2580 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_279508, c_Groups_Ozero__class_Ozero(_279508), _279512), c_Orderings_Oord__class_Oless(_279508, _279510, _279514)], (2586 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_279508, _279512, c_Groups_Ozero__class_Ozero(_279508)), c_Orderings_Oord__class_Oless(_279508, _279514, _279510)]]]]], (2594 ^ _191474) ^ [_280611, _280613, _280615, _280617] : [class_Rings_Olinordered__ring__strict(_280611), 2597 ^ _191474 : [(2598 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_280611, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280611), _280613), _280615), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280611), _280613), _280617)), 2603 ^ _191474 : [(2604 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_280611, c_Groups_Ozero__class_Ozero(_280611), _280613))], (2606 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_280611, _280615, _280617))]], 2607 ^ _191474 : [(2608 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_280611, _280613, c_Groups_Ozero__class_Ozero(_280611)))], (2610 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_280611, _280617, _280615))]]], (2612 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_280611, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280611), _280613), _280615), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280611), _280613), _280617))), 2613 ^ _191474 : [(2614 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_280611, c_Groups_Ozero__class_Ozero(_280611), _280613), c_Orderings_Oord__class_Oless(_280611, _280615, _280617)], (2620 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_280611, _280613, c_Groups_Ozero__class_Ozero(_280611)), c_Orderings_Oord__class_Oless(_280611, _280617, _280615)]]]]], (2628 ^ _191474) ^ [_281714, _281716, _281718, _281720] : [class_Rings_Olinordered__ring__strict(_281714), c_Orderings_Oord__class_Oless(_281714, c_Groups_Ozero__class_Ozero(_281714), _281716), 2635 ^ _191474 : [(2636 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_281714, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_281714), _281716), _281718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_281714), _281716), _281720)), -(c_Orderings_Oord__class_Oless(_281714, _281718, _281720))], (2642 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_281714, _281718, _281720), -(c_Orderings_Oord__class_Oless(_281714, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_281714), _281716), _281718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_281714), _281716), _281720)))]]], (2648 ^ _191474) ^ [_282375, _282377, _282379] : [class_Rings_Olinordered__semiring__strict(_282375), c_Orderings_Oord__class_Oless(_282375, c_Groups_Ozero__class_Ozero(_282375), _282377), c_Orderings_Oord__class_Oless(_282375, c_Groups_Ozero__class_Ozero(_282375), _282379), -(c_Orderings_Oord__class_Oless(_282375, c_Groups_Ozero__class_Ozero(_282375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_282375), _282377), _282379)))], (2662 ^ _191474) ^ [_282823, _282825, _282827] : [class_Rings_Olinordered__semiring__strict(_282823), c_Orderings_Oord__class_Oless(_282823, c_Groups_Ozero__class_Ozero(_282823), _282825), c_Orderings_Oord__class_Oless(_282823, _282827, c_Groups_Ozero__class_Ozero(_282823)), -(c_Orderings_Oord__class_Oless(_282823, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_282823), _282825), _282827), c_Groups_Ozero__class_Ozero(_282823)))], (2676 ^ _191474) ^ [_283271, _283273, _283275] : [class_Rings_Olinordered__semiring__strict(_283271), c_Orderings_Oord__class_Oless(_283271, c_Groups_Ozero__class_Ozero(_283271), _283273), c_Orderings_Oord__class_Oless(_283271, _283275, c_Groups_Ozero__class_Ozero(_283271)), -(c_Orderings_Oord__class_Oless(_283271, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283271), _283275), _283273), c_Groups_Ozero__class_Ozero(_283271)))], (2690 ^ _191474) ^ [_283719, _283721, _283723] : [class_Rings_Olinordered__semiring__strict(_283719), c_Orderings_Oord__class_Oless(_283719, c_Groups_Ozero__class_Ozero(_283719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283719), _283721), _283723)), c_Orderings_Oord__class_Oless(_283719, c_Groups_Ozero__class_Ozero(_283719), _283721), -(c_Orderings_Oord__class_Oless(_283719, c_Groups_Ozero__class_Ozero(_283719), _283723))], (2704 ^ _191474) ^ [_284167, _284169, _284171] : [class_Rings_Olinordered__semiring__strict(_284167), c_Orderings_Oord__class_Oless(_284167, c_Groups_Ozero__class_Ozero(_284167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284167), _284169), _284171)), c_Orderings_Oord__class_Oless(_284167, c_Groups_Ozero__class_Ozero(_284167), _284171), -(c_Orderings_Oord__class_Oless(_284167, c_Groups_Ozero__class_Ozero(_284167), _284169))], (2718 ^ _191474) ^ [_284629, _284631, _284633, _284635] : [class_Rings_Olinordered__ring__strict(_284629), c_Orderings_Oord__class_Oless(_284629, _284631, c_Groups_Ozero__class_Ozero(_284629)), 2725 ^ _191474 : [(2726 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_284629, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284629), _284631), _284633), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284629), _284631), _284635)), -(c_Orderings_Oord__class_Oless(_284629, _284635, _284633))], (2732 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_284629, _284635, _284633), -(c_Orderings_Oord__class_Oless(_284629, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284629), _284631), _284633), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284629), _284631), _284635)))]]], (2738 ^ _191474) ^ [_285290, _285292, _285294] : [class_Rings_Olinordered__semiring__strict(_285290), c_Orderings_Oord__class_Oless(_285290, _285292, c_Groups_Ozero__class_Ozero(_285290)), c_Orderings_Oord__class_Oless(_285290, c_Groups_Ozero__class_Ozero(_285290), _285294), -(c_Orderings_Oord__class_Oless(_285290, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285290), _285292), _285294), c_Groups_Ozero__class_Ozero(_285290)))], (2752 ^ _191474) ^ [_285738, _285740, _285742] : [class_Rings_Olinordered__ring__strict(_285738), c_Orderings_Oord__class_Oless(_285738, _285740, c_Groups_Ozero__class_Ozero(_285738)), c_Orderings_Oord__class_Oless(_285738, _285742, c_Groups_Ozero__class_Ozero(_285738)), -(c_Orderings_Oord__class_Oless(_285738, c_Groups_Ozero__class_Ozero(_285738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285738), _285740), _285742)))], (2766 ^ _191474) ^ [_286200, _286202, _286204, _286206] : [class_Rings_Olinordered__semiring__strict(_286200), c_Orderings_Oord__class_Oless(_286200, _286202, _286204), c_Orderings_Oord__class_Oless(_286200, c_Groups_Ozero__class_Ozero(_286200), _286206), -(c_Orderings_Oord__class_Oless(_286200, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286200), _286202), _286206), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286200), _286204), _286206)))], (2780 ^ _191474) ^ [_286684, _286686, _286688, _286690] : [class_Rings_Olinordered__semiring__strict(_286684), c_Orderings_Oord__class_Oless(_286684, _286686, _286688), c_Orderings_Oord__class_Oless(_286684, c_Groups_Ozero__class_Ozero(_286684), _286690), -(c_Orderings_Oord__class_Oless(_286684, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286684), _286690), _286686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286684), _286690), _286688)))], (2794 ^ _191474) ^ [_287168, _287170, _287172, _287174] : [class_Rings_Olinordered__comm__semiring__strict(_287168), c_Orderings_Oord__class_Oless(_287168, _287170, _287172), c_Orderings_Oord__class_Oless(_287168, c_Groups_Ozero__class_Ozero(_287168), _287174), -(c_Orderings_Oord__class_Oless(_287168, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287168), _287174), _287170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287168), _287174), _287172)))], (2808 ^ _191474) ^ [_287652, _287654, _287656, _287658] : [class_Rings_Olinordered__ring__strict(_287652), c_Orderings_Oord__class_Oless(_287652, _287654, _287656), c_Orderings_Oord__class_Oless(_287652, _287658, c_Groups_Ozero__class_Ozero(_287652)), -(c_Orderings_Oord__class_Oless(_287652, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287652), _287656), _287658), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287652), _287654), _287658)))], (2822 ^ _191474) ^ [_288136, _288138, _288140, _288142] : [class_Rings_Olinordered__ring__strict(_288136), c_Orderings_Oord__class_Oless(_288136, _288138, _288140), c_Orderings_Oord__class_Oless(_288136, _288142, c_Groups_Ozero__class_Ozero(_288136)), -(c_Orderings_Oord__class_Oless(_288136, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_288136), _288142), _288140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_288136), _288142), _288138)))], (2836 ^ _191474) ^ [_288606, _288608, _288610] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _288606), 2839 ^ _191474 : [(2840 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _288608), _288606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _288610), _288606)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _288608, _288610))], (2846 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _288608, _288610), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _288608), _288606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _288610), _288606)))]]], (2852 ^ _191474) ^ [_289126, _289128] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _289126), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _289128), -(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), _289126), _289128)))], (2862 ^ _191474) ^ [_289457, _289459, _289461] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _289457), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _289459, _289461), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _289457), _289459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _289457), _289461)))], (2872 ^ _191474) ^ [_289824, _289826, _289828, _289830] : [class_Rings_Olinordered__ring__strict(_289824), c_Orderings_Oord__class_Oless(_289824, c_Groups_Ozero__class_Ozero(_289824), _289826), 2879 ^ _191474 : [(2880 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289824, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289824), _289826), _289828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289824), _289826), _289830)), -(c_Orderings_Oord__class_Oless__eq(_289824, _289828, _289830))], (2886 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289824, _289828, _289830), -(c_Orderings_Oord__class_Oless__eq(_289824, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289824), _289826), _289828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289824), _289826), _289830)))]]], (2892 ^ _191474) ^ [_290499, _290501, _290503, _290505] : [class_Rings_Olinordered__ring__strict(_290499), c_Orderings_Oord__class_Oless(_290499, _290501, c_Groups_Ozero__class_Ozero(_290499)), 2899 ^ _191474 : [(2900 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290499, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_290499), _290501), _290503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_290499), _290501), _290505)), -(c_Orderings_Oord__class_Oless__eq(_290499, _290505, _290503))], (2906 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_290499, _290505, _290503), -(c_Orderings_Oord__class_Oless__eq(_290499, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_290499), _290501), _290503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_290499), _290501), _290505)))]]], (2912 ^ _191474) ^ [_291188, _291190, _291192, _291194, _291196] : [class_Rings_Olinordered__semiring__strict(_291188), c_Orderings_Oord__class_Oless(_291188, _291190, _291192), c_Orderings_Oord__class_Oless(_291188, _291194, _291196), c_Orderings_Oord__class_Oless(_291188, c_Groups_Ozero__class_Ozero(_291188), _291192), c_Orderings_Oord__class_Oless__eq(_291188, c_Groups_Ozero__class_Ozero(_291188), _291194), -(c_Orderings_Oord__class_Oless(_291188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291188), _291190), _291194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291188), _291192), _291196)))], (2934 ^ _191474) ^ [_291910, _291912, _291914, _291916, _291918] : [class_Rings_Olinordered__semiring__strict(_291910), c_Orderings_Oord__class_Oless(_291910, _291912, _291914), c_Orderings_Oord__class_Oless(_291910, _291916, _291918), c_Orderings_Oord__class_Oless__eq(_291910, c_Groups_Ozero__class_Ozero(_291910), _291912), c_Orderings_Oord__class_Oless__eq(_291910, c_Groups_Ozero__class_Ozero(_291910), _291916), -(c_Orderings_Oord__class_Oless(_291910, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291910), _291912), _291916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291910), _291914), _291918)))], (2956 ^ _191474) ^ [_292632, _292634, _292636, _292638, _292640] : [class_Rings_Olinordered__semiring__strict(_292632), c_Orderings_Oord__class_Oless(_292632, _292634, _292636), c_Orderings_Oord__class_Oless__eq(_292632, _292638, _292640), c_Orderings_Oord__class_Oless__eq(_292632, c_Groups_Ozero__class_Ozero(_292632), _292634), c_Orderings_Oord__class_Oless(_292632, c_Groups_Ozero__class_Ozero(_292632), _292638), -(c_Orderings_Oord__class_Oless(_292632, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292632), _292634), _292638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292632), _292636), _292640)))], (2978 ^ _191474) ^ [_293354, _293356, _293358, _293360, _293362] : [class_Rings_Olinordered__semiring__strict(_293354), c_Orderings_Oord__class_Oless__eq(_293354, _293356, _293358), c_Orderings_Oord__class_Oless(_293354, _293360, _293362), c_Orderings_Oord__class_Oless(_293354, c_Groups_Ozero__class_Ozero(_293354), _293356), c_Orderings_Oord__class_Oless__eq(_293354, c_Groups_Ozero__class_Ozero(_293354), _293360), -(c_Orderings_Oord__class_Oless(_293354, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293354), _293356), _293360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293354), _293358), _293362)))], (3000 ^ _191474) ^ [_294062, _294064, _294066, _294068] : [class_Rings_Olinordered__semiring(_294062), c_Orderings_Oord__class_Oless(_294062, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_294062), _294064), _294066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_294062), _294068), _294066)), c_Orderings_Oord__class_Oless__eq(_294062, c_Groups_Ozero__class_Ozero(_294062), _294066), -(c_Orderings_Oord__class_Oless(_294062, _294064, _294068))], (3014 ^ _191474) ^ [_294546, _294548, _294550, _294552] : [class_Rings_Olinordered__semiring__strict(_294546), c_Orderings_Oord__class_Oless(_294546, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_294546), _294548), _294550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_294546), _294552), _294550)), c_Orderings_Oord__class_Oless__eq(_294546, c_Groups_Ozero__class_Ozero(_294546), _294550), -(c_Orderings_Oord__class_Oless(_294546, _294548, _294552))], (3028 ^ _191474) ^ [_295030, _295032, _295034, _295036] : [class_Rings_Olinordered__semiring(_295030), c_Orderings_Oord__class_Oless(_295030, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295030), _295032), _295034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295030), _295032), _295036)), c_Orderings_Oord__class_Oless__eq(_295030, c_Groups_Ozero__class_Ozero(_295030), _295032), -(c_Orderings_Oord__class_Oless(_295030, _295034, _295036))], (3043 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3041 ^ []))], (3045 ^ _191474) ^ [_295591] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _295591), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(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_cs____), _295591)), 3041 ^ []))], (3052 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3050 ^ []))], (3054 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 3050 ^ [], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (3056 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 3050 ^ [], c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____)))], (3059 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3057 ^ []))], (3061 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 3057 ^ [], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (3063 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 3057 ^ [], c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____)))], (3065 ^ _191474) ^ [_296279, _296281, _296283, _296285] : [class_Fields_Olinordered__field__inverse__zero(_296279), 3068 ^ _191474 : [(3095 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_296279, _296281, c_Rings_Oinverse__class_Odivide(_296279, _296283, _296285))), 3098 ^ _191474 : [(3099 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_296279, c_Groups_Ozero__class_Ozero(_296279), _296285))], (3101 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_296279, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296279), _296281), _296285), _296283)]], 3102 ^ _191474 : [(3103 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_296279, c_Groups_Ozero__class_Ozero(_296279), _296285)], (3105 ^ _191474) ^ [] : [3106 ^ _191474 : [(3107 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_296279, _296285, c_Groups_Ozero__class_Ozero(_296279)))], (3109 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_296279, _296283, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296279), _296281), _296285))]], 3110 ^ _191474 : [(3111 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_296279, _296285, c_Groups_Ozero__class_Ozero(_296279))], (3113 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_296279, _296281, c_Groups_Ozero__class_Ozero(_296279))]]]]], (3069 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_296279, _296281, c_Rings_Oinverse__class_Odivide(_296279, _296283, _296285)), 3072 ^ _191474 : [(3073 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_296279, c_Groups_Ozero__class_Ozero(_296279), _296285), -(c_Orderings_Oord__class_Oless__eq(_296279, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296279), _296281), _296285), _296283))], (3079 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_296279, c_Groups_Ozero__class_Ozero(_296279), _296285)), 3082 ^ _191474 : [(3083 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_296279, _296285, c_Groups_Ozero__class_Ozero(_296279)), -(c_Orderings_Oord__class_Oless__eq(_296279, _296283, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296279), _296281), _296285)))], (3089 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_296279, _296285, c_Groups_Ozero__class_Ozero(_296279))), -(c_Orderings_Oord__class_Oless__eq(_296279, _296281, c_Groups_Ozero__class_Ozero(_296279)))]]]]]]], (3117 ^ _191474) ^ [_297935, _297937, _297939, _297941] : [class_Fields_Olinordered__field__inverse__zero(_297935), 3120 ^ _191474 : [(3147 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_297935, c_Rings_Oinverse__class_Odivide(_297935, _297937, _297939), _297941)), 3150 ^ _191474 : [(3151 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_297935, c_Groups_Ozero__class_Ozero(_297935), _297939))], (3153 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_297935, _297937, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297935), _297941), _297939))]], 3154 ^ _191474 : [(3155 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_297935, c_Groups_Ozero__class_Ozero(_297935), _297939)], (3157 ^ _191474) ^ [] : [3158 ^ _191474 : [(3159 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_297935, _297939, c_Groups_Ozero__class_Ozero(_297935)))], (3161 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_297935, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297935), _297941), _297939), _297937)]], 3162 ^ _191474 : [(3163 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_297935, _297939, c_Groups_Ozero__class_Ozero(_297935))], (3165 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_297935, c_Groups_Ozero__class_Ozero(_297935), _297941)]]]]], (3121 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_297935, c_Rings_Oinverse__class_Odivide(_297935, _297937, _297939), _297941), 3124 ^ _191474 : [(3125 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_297935, c_Groups_Ozero__class_Ozero(_297935), _297939), -(c_Orderings_Oord__class_Oless__eq(_297935, _297937, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297935), _297941), _297939)))], (3131 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_297935, c_Groups_Ozero__class_Ozero(_297935), _297939)), 3134 ^ _191474 : [(3135 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_297935, _297939, c_Groups_Ozero__class_Ozero(_297935)), -(c_Orderings_Oord__class_Oless__eq(_297935, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297935), _297941), _297939), _297937))], (3141 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_297935, _297939, c_Groups_Ozero__class_Ozero(_297935))), -(c_Orderings_Oord__class_Oless__eq(_297935, c_Groups_Ozero__class_Ozero(_297935), _297941))]]]]]]], (3169 ^ _191474) ^ [_299591, _299593, _299595, _299597] : [class_Fields_Olinordered__field(_299591), c_Orderings_Oord__class_Oless(_299591, c_Groups_Ozero__class_Ozero(_299591), _299593), 3176 ^ _191474 : [(3177 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_299591, _299595, c_Rings_Oinverse__class_Odivide(_299591, _299597, _299593)), -(c_Orderings_Oord__class_Oless__eq(_299591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299591), _299595), _299593), _299597))], (3183 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_299591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299591), _299595), _299593), _299597), -(c_Orderings_Oord__class_Oless__eq(_299591, _299595, c_Rings_Oinverse__class_Odivide(_299591, _299597, _299593)))]]], (3189 ^ _191474) ^ [_300254, _300256, _300258, _300260] : [class_Fields_Olinordered__field(_300254), c_Orderings_Oord__class_Oless(_300254, c_Groups_Ozero__class_Ozero(_300254), _300256), 3196 ^ _191474 : [(3197 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_300254, c_Rings_Oinverse__class_Odivide(_300254, _300258, _300256), _300260), -(c_Orderings_Oord__class_Oless__eq(_300254, _300258, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300254), _300260), _300256)))], (3203 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_300254, _300258, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300254), _300260), _300256)), -(c_Orderings_Oord__class_Oless__eq(_300254, c_Rings_Oinverse__class_Odivide(_300254, _300258, _300256), _300260))]]], (3209 ^ _191474) ^ [_300917, _300919, _300921, _300923] : [class_Fields_Olinordered__field(_300917), c_Orderings_Oord__class_Oless(_300917, c_Groups_Ozero__class_Ozero(_300917), _300919), c_Orderings_Oord__class_Oless__eq(_300917, _300921, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300917), _300923), _300919)), -(c_Orderings_Oord__class_Oless__eq(_300917, c_Rings_Oinverse__class_Odivide(_300917, _300921, _300919), _300923))], (3223 ^ _191474) ^ [_301393, _301395, _301397, _301399] : [class_Fields_Olinordered__field(_301393), c_Orderings_Oord__class_Oless(_301393, c_Groups_Ozero__class_Ozero(_301393), _301395), c_Orderings_Oord__class_Oless__eq(_301393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301393), _301397), _301395), _301399), -(c_Orderings_Oord__class_Oless__eq(_301393, _301397, c_Rings_Oinverse__class_Odivide(_301393, _301399, _301395)))], (3237 ^ _191474) ^ [_301869, _301871, _301873, _301875] : [class_Fields_Olinordered__field(_301869), c_Orderings_Oord__class_Oless(_301869, _301871, c_Groups_Ozero__class_Ozero(_301869)), 3244 ^ _191474 : [(3245 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_301869, _301873, c_Rings_Oinverse__class_Odivide(_301869, _301875, _301871)), -(c_Orderings_Oord__class_Oless__eq(_301869, _301875, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301869), _301873), _301871)))], (3251 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_301869, _301875, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301869), _301873), _301871)), -(c_Orderings_Oord__class_Oless__eq(_301869, _301873, c_Rings_Oinverse__class_Odivide(_301869, _301875, _301871)))]]], (3257 ^ _191474) ^ [_302532, _302534, _302536, _302538] : [class_Fields_Olinordered__field(_302532), c_Orderings_Oord__class_Oless(_302532, _302534, c_Groups_Ozero__class_Ozero(_302532)), 3264 ^ _191474 : [(3265 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_302532, c_Rings_Oinverse__class_Odivide(_302532, _302536, _302534), _302538), -(c_Orderings_Oord__class_Oless__eq(_302532, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302532), _302538), _302534), _302536))], (3271 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_302532, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302532), _302538), _302534), _302536), -(c_Orderings_Oord__class_Oless__eq(_302532, c_Rings_Oinverse__class_Odivide(_302532, _302536, _302534), _302538))]]], (3277 ^ _191474) ^ [_303196, _303198] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _303196, _303198), -(_303198 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303196, 3280 ^ [_303196, _303198]))], (3284 ^ _191474) ^ [_303429, _303431] : [3285 ^ _191474 : [(3286 ^ _191474) ^ [_303504] : [_303431 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _303429, _303504)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _303429, _303431))], (3290 ^ _191474) ^ [_303687, _303689, _303691] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _303687, _303689), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _303691, _303687), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _303691, _303689)))], (3296 ^ _191474) ^ [_303922, _303924, _303926] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _303922, _303924)), _303926) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _303922), _303926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _303924), _303926)))], (3298 ^ _191474) ^ [_304059, _304061] : [class_Groups_Ocomm__monoid__add(_304059), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_304059), _304061, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304059))) = _304061)], (3304 ^ _191474) ^ [_304287, _304289] : [class_Groups_Ocomm__monoid__add(_304287), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_304287), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304287)), _304289) = _304289)], (3310 ^ _191474) ^ [_304529, _304531, _304533] : [class_Groups_Ocomm__monoid__add(_304529), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_304529, _304531), c_Polynomial_Odegree(_304529, _304533)), -(c_Polynomial_Odegree(_304529, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_304529), _304533, _304531)) = c_Polynomial_Odegree(_304529, _304533))], (3320 ^ _191474) ^ [_304888, _304890, _304892] : [class_Groups_Ocomm__monoid__add(_304888), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_304888, _304890), c_Polynomial_Odegree(_304888, _304892)), -(c_Polynomial_Odegree(_304888, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_304888), _304890, _304892)) = c_Polynomial_Odegree(_304888, _304892))], (3330 ^ _191474) ^ [_305261, _305263, _305265, _305267] : [class_Groups_Ocomm__monoid__add(_305261), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_305261, _305263), _305265), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_305261, _305267), _305265), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_305261, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_305261), _305263, _305267)), _305265))], (3344 ^ _191474) ^ [_305739, _305741, _305743, _305745] : [class_Groups_Ocomm__monoid__add(_305739), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_305739, _305741), _305743), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_305739, _305745), _305743), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_305739, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_305739), _305741, _305745)), _305743))], (3358 ^ _191474) ^ [_306175] : [class_Rings_Ocomm__semiring__1(_306175), -(c_Polynomial_Odegree(_306175, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_306175))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3364 ^ _191474) ^ [_306419, _306421, _306423, _306425] : [class_Rings_Ocomm__semiring__0(_306419), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_306419)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_306419), _306421, _306423)), _306425) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_306419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_306419)), _306421), _306425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_306419)), _306423), _306425)))], (3370 ^ _191474) ^ [_306752, _306754] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306752), _306752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306754), _306754)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3373 ^ _191474 : [(3374 ^ _191474) ^ [] : [-(_306752 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3376 ^ _191474) ^ [] : [-(_306754 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (3378 ^ _191474) ^ [_307021, _307023] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _307021), _307021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _307023), _307023)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _307021 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _307023 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (3388 ^ _191474) ^ [_307368, _307370, _307372] : [class_Rings_Ocomm__semiring__0(_307368), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_307368, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_307368)), _307370), _307372)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_307368, _307370), c_Polynomial_Odegree(_307368, _307372))))], (3394 ^ _191474) ^ [_307644, _307646, _307648] : [class_RealVector_Oreal__normed__vector(_307644), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_307644, c_Groups_Ominus__class_Ominus(_307644, _307646, _307648)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_307644, _307646), c_RealVector_Onorm__class_Onorm(_307644, _307648))))], (3400 ^ _191474) ^ [_307879, _307881] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _307879), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _307879, _307881)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _307881))))], (3402 ^ _191474) ^ [_308020, _308022, _308024] : [class_Rings_Oidom(_308020), -(_308022 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_308020))), -(_308024 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_308020))), -(c_Polynomial_Odegree(_308020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_308020)), _308022), _308024)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_308020, _308022), c_Polynomial_Odegree(_308020, _308024)))], (3416 ^ _191474) ^ [_308530, _308532, _308534, _308536, _308538] : [class_Fields_Ofield__inverse__zero(_308530), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308530), c_Rings_Oinverse__class_Odivide(_308530, _308532, _308534)), c_Rings_Oinverse__class_Odivide(_308530, _308536, _308538)) = c_Rings_Oinverse__class_Odivide(_308530, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308530), _308532), _308536), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308530), _308534), _308538)))], (3422 ^ _191474) ^ [_308842, _308844, _308846] : [class_Fields_Olinordered__field__inverse__zero(_308842), 3425 ^ _191474 : [(3426 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_308842, c_Groups_Ozero__class_Ozero(_308842), c_Rings_Oinverse__class_Odivide(_308842, _308844, _308846)), 3431 ^ _191474 : [(3432 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_308842, c_Groups_Ozero__class_Ozero(_308842), _308844))], (3434 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_308842, c_Groups_Ozero__class_Ozero(_308842), _308846))]], 3435 ^ _191474 : [(3436 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_308842, _308844, c_Groups_Ozero__class_Ozero(_308842)))], (3438 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_308842, _308846, c_Groups_Ozero__class_Ozero(_308842)))]]], (3440 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_308842, c_Groups_Ozero__class_Ozero(_308842), c_Rings_Oinverse__class_Odivide(_308842, _308844, _308846))), 3441 ^ _191474 : [(3442 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_308842, c_Groups_Ozero__class_Ozero(_308842), _308844), c_Orderings_Oord__class_Oless__eq(_308842, c_Groups_Ozero__class_Ozero(_308842), _308846)], (3448 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_308842, _308844, c_Groups_Ozero__class_Ozero(_308842)), c_Orderings_Oord__class_Oless__eq(_308842, _308846, c_Groups_Ozero__class_Ozero(_308842))]]]]], (3456 ^ _191474) ^ [_309879, _309881, _309883] : [class_Fields_Olinordered__field__inverse__zero(_309879), 3459 ^ _191474 : [(3460 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_309879, c_Rings_Oinverse__class_Odivide(_309879, _309881, _309883), c_Groups_Ozero__class_Ozero(_309879)), 3465 ^ _191474 : [(3466 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_309879, c_Groups_Ozero__class_Ozero(_309879), _309881))], (3468 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_309879, _309883, c_Groups_Ozero__class_Ozero(_309879)))]], 3469 ^ _191474 : [(3470 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_309879, _309881, c_Groups_Ozero__class_Ozero(_309879)))], (3472 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_309879, c_Groups_Ozero__class_Ozero(_309879), _309883))]]], (3474 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_309879, c_Rings_Oinverse__class_Odivide(_309879, _309881, _309883), c_Groups_Ozero__class_Ozero(_309879))), 3475 ^ _191474 : [(3476 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_309879, c_Groups_Ozero__class_Ozero(_309879), _309881), c_Orderings_Oord__class_Oless__eq(_309879, _309883, c_Groups_Ozero__class_Ozero(_309879))], (3482 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_309879, _309881, c_Groups_Ozero__class_Ozero(_309879)), c_Orderings_Oord__class_Oless__eq(_309879, c_Groups_Ozero__class_Ozero(_309879), _309883)]]]]], (3490 ^ _191474) ^ [_310930, _310932, _310934, _310936] : [class_Fields_Olinordered__field__inverse__zero(_310930), c_Orderings_Oord__class_Oless__eq(_310930, _310932, _310934), c_Orderings_Oord__class_Oless__eq(_310930, c_Groups_Ozero__class_Ozero(_310930), _310936), -(c_Orderings_Oord__class_Oless__eq(_310930, c_Rings_Oinverse__class_Odivide(_310930, _310932, _310936), c_Rings_Oinverse__class_Odivide(_310930, _310934, _310936)))], (3504 ^ _191474) ^ [_311398, _311400, _311402, _311404] : [class_Fields_Olinordered__field__inverse__zero(_311398), c_Orderings_Oord__class_Oless__eq(_311398, _311400, _311402), c_Orderings_Oord__class_Oless__eq(_311398, _311404, c_Groups_Ozero__class_Ozero(_311398)), -(c_Orderings_Oord__class_Oless__eq(_311398, c_Rings_Oinverse__class_Odivide(_311398, _311402, _311404), c_Rings_Oinverse__class_Odivide(_311398, _311400, _311404)))], (3518 ^ _191474) ^ [_311852, _311854, _311856] : [class_Fields_Olinordered__field__inverse__zero(_311852), 3521 ^ _191474 : [(3522 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_311852, c_Groups_Ozero__class_Ozero(_311852), c_Rings_Oinverse__class_Odivide(_311852, _311854, _311856)), 3527 ^ _191474 : [(3528 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_311852, c_Groups_Ozero__class_Ozero(_311852), _311854))], (3530 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_311852, c_Groups_Ozero__class_Ozero(_311852), _311856))]], 3531 ^ _191474 : [(3532 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_311852, _311854, c_Groups_Ozero__class_Ozero(_311852)))], (3534 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_311852, _311856, c_Groups_Ozero__class_Ozero(_311852)))]]], (3536 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_311852, c_Groups_Ozero__class_Ozero(_311852), c_Rings_Oinverse__class_Odivide(_311852, _311854, _311856))), 3537 ^ _191474 : [(3538 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_311852, c_Groups_Ozero__class_Ozero(_311852), _311854), c_Orderings_Oord__class_Oless(_311852, c_Groups_Ozero__class_Ozero(_311852), _311856)], (3544 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_311852, _311854, c_Groups_Ozero__class_Ozero(_311852)), c_Orderings_Oord__class_Oless(_311852, _311856, c_Groups_Ozero__class_Ozero(_311852))]]]]], (3552 ^ _191474) ^ [_312889, _312891, _312893] : [class_Fields_Olinordered__field__inverse__zero(_312889), 3555 ^ _191474 : [(3556 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_312889, c_Rings_Oinverse__class_Odivide(_312889, _312891, _312893), c_Groups_Ozero__class_Ozero(_312889)), 3561 ^ _191474 : [(3562 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_312889, c_Groups_Ozero__class_Ozero(_312889), _312891))], (3564 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_312889, _312893, c_Groups_Ozero__class_Ozero(_312889)))]], 3565 ^ _191474 : [(3566 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_312889, _312891, c_Groups_Ozero__class_Ozero(_312889)))], (3568 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_312889, c_Groups_Ozero__class_Ozero(_312889), _312893))]]], (3570 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_312889, c_Rings_Oinverse__class_Odivide(_312889, _312891, _312893), c_Groups_Ozero__class_Ozero(_312889))), 3571 ^ _191474 : [(3572 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_312889, c_Groups_Ozero__class_Ozero(_312889), _312891), c_Orderings_Oord__class_Oless(_312889, _312893, c_Groups_Ozero__class_Ozero(_312889))], (3578 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_312889, _312891, c_Groups_Ozero__class_Ozero(_312889)), c_Orderings_Oord__class_Oless(_312889, c_Groups_Ozero__class_Ozero(_312889), _312893)]]]]], (3586 ^ _191474) ^ [_313926, _313928, _313930] : [class_Fields_Olinordered__field(_313926), c_Orderings_Oord__class_Oless(_313926, c_Groups_Ozero__class_Ozero(_313926), _313928), c_Orderings_Oord__class_Oless(_313926, c_Groups_Ozero__class_Ozero(_313926), _313930), -(c_Orderings_Oord__class_Oless(_313926, c_Groups_Ozero__class_Ozero(_313926), c_Rings_Oinverse__class_Odivide(_313926, _313928, _313930)))], (3600 ^ _191474) ^ [_314366, _314368, _314370] : [class_Fields_Olinordered__field(_314366), c_Orderings_Oord__class_Oless(_314366, c_Groups_Ozero__class_Ozero(_314366), _314368), c_Orderings_Oord__class_Oless(_314366, _314370, c_Groups_Ozero__class_Ozero(_314366)), -(c_Orderings_Oord__class_Oless(_314366, c_Rings_Oinverse__class_Odivide(_314366, _314368, _314370), c_Groups_Ozero__class_Ozero(_314366)))], (3614 ^ _191474) ^ [_314806, _314808, _314810] : [class_Fields_Olinordered__field(_314806), c_Orderings_Oord__class_Oless(_314806, _314808, c_Groups_Ozero__class_Ozero(_314806)), c_Orderings_Oord__class_Oless(_314806, c_Groups_Ozero__class_Ozero(_314806), _314810), -(c_Orderings_Oord__class_Oless(_314806, c_Rings_Oinverse__class_Odivide(_314806, _314808, _314810), c_Groups_Ozero__class_Ozero(_314806)))], (3628 ^ _191474) ^ [_315246, _315248, _315250] : [class_Fields_Olinordered__field(_315246), c_Orderings_Oord__class_Oless(_315246, _315248, c_Groups_Ozero__class_Ozero(_315246)), c_Orderings_Oord__class_Oless(_315246, _315250, c_Groups_Ozero__class_Ozero(_315246)), -(c_Orderings_Oord__class_Oless(_315246, c_Groups_Ozero__class_Ozero(_315246), c_Rings_Oinverse__class_Odivide(_315246, _315248, _315250)))], (3642 ^ _191474) ^ [_315700, _315702, _315704, _315706] : [class_Fields_Olinordered__field(_315700), c_Orderings_Oord__class_Oless(_315700, _315702, _315704), c_Orderings_Oord__class_Oless(_315700, c_Groups_Ozero__class_Ozero(_315700), _315706), -(c_Orderings_Oord__class_Oless(_315700, c_Rings_Oinverse__class_Odivide(_315700, _315702, _315706), c_Rings_Oinverse__class_Odivide(_315700, _315704, _315706)))], (3656 ^ _191474) ^ [_316168, _316170, _316172, _316174] : [class_Fields_Olinordered__field(_316168), c_Orderings_Oord__class_Oless(_316168, _316170, _316172), c_Orderings_Oord__class_Oless(_316168, _316174, c_Groups_Ozero__class_Ozero(_316168)), -(c_Orderings_Oord__class_Oless(_316168, c_Rings_Oinverse__class_Odivide(_316168, _316172, _316174), c_Rings_Oinverse__class_Odivide(_316168, _316170, _316174)))], (3670 ^ _191474) ^ [_316636, _316638, _316640, _316642] : [class_Fields_Ofield__inverse__zero(_316636), 3673 ^ _191474 : [(3690 ^ _191474) ^ [] : [-(_316638 = c_Rings_Oinverse__class_Odivide(_316636, _316640, _316642)), 3693 ^ _191474 : [(3694 ^ _191474) ^ [] : [_316642 = c_Groups_Ozero__class_Ozero(_316636)], (3696 ^ _191474) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316636), _316638), _316642) = _316640]], 3697 ^ _191474 : [(3698 ^ _191474) ^ [] : [-(_316642 = c_Groups_Ozero__class_Ozero(_316636))], (3700 ^ _191474) ^ [] : [_316638 = c_Groups_Ozero__class_Ozero(_316636)]]], (3674 ^ _191474) ^ [] : [_316638 = c_Rings_Oinverse__class_Odivide(_316636, _316640, _316642), 3677 ^ _191474 : [(3678 ^ _191474) ^ [] : [-(_316642 = c_Groups_Ozero__class_Ozero(_316636)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316636), _316638), _316642) = _316640)], (3684 ^ _191474) ^ [] : [_316642 = c_Groups_Ozero__class_Ozero(_316636), -(_316638 = c_Groups_Ozero__class_Ozero(_316636))]]]]], (3704 ^ _191474) ^ [_317720, _317722, _317724, _317726] : [class_Fields_Ofield__inverse__zero(_317720), 3707 ^ _191474 : [(3724 ^ _191474) ^ [] : [-(c_Rings_Oinverse__class_Odivide(_317720, _317722, _317724) = _317726), 3727 ^ _191474 : [(3728 ^ _191474) ^ [] : [_317724 = c_Groups_Ozero__class_Ozero(_317720)], (3730 ^ _191474) ^ [] : [_317722 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317720), _317726), _317724)]], 3731 ^ _191474 : [(3732 ^ _191474) ^ [] : [-(_317724 = c_Groups_Ozero__class_Ozero(_317720))], (3734 ^ _191474) ^ [] : [_317726 = c_Groups_Ozero__class_Ozero(_317720)]]], (3708 ^ _191474) ^ [] : [c_Rings_Oinverse__class_Odivide(_317720, _317722, _317724) = _317726, 3711 ^ _191474 : [(3712 ^ _191474) ^ [] : [-(_317724 = c_Groups_Ozero__class_Ozero(_317720)), -(_317722 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317720), _317726), _317724))], (3718 ^ _191474) ^ [] : [_317724 = c_Groups_Ozero__class_Ozero(_317720), -(_317726 = c_Groups_Ozero__class_Ozero(_317720))]]]]], (3738 ^ _191474) ^ [_318804, _318806, _318808, _318810] : [class_Fields_Ofield__inverse__zero(_318804), -(_318806 = c_Groups_Ozero__class_Ozero(_318804)), -(c_Rings_Oinverse__class_Odivide(_318804, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318804), _318808), _318806), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318804), _318810), _318806)) = c_Rings_Oinverse__class_Odivide(_318804, _318808, _318810))], (3748 ^ _191474) ^ [_319204, _319206, _319208, _319210] : [class_Fields_Ofield__inverse__zero(_319204), -(_319206 = c_Groups_Ozero__class_Ozero(_319204)), -(c_Rings_Oinverse__class_Odivide(_319204, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_319204), _319206), _319208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_319204), _319206), _319210)) = c_Rings_Oinverse__class_Odivide(_319204, _319208, _319210))], (3758 ^ _191474) ^ [_319618, _319620, _319622, _319624, _319626] : [class_Fields_Ofield(_319618), -(_319620 = c_Groups_Ozero__class_Ozero(_319618)), -(_319622 = c_Groups_Ozero__class_Ozero(_319618)), 3769 ^ _191474 : [(3770 ^ _191474) ^ [] : [c_Rings_Oinverse__class_Odivide(_319618, _319624, _319620) = c_Rings_Oinverse__class_Odivide(_319618, _319626, _319622), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_319618), _319624), _319622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_319618), _319626), _319620))], (3776 ^ _191474) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_319618), _319624), _319622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_319618), _319626), _319620), -(c_Rings_Oinverse__class_Odivide(_319618, _319624, _319620) = c_Rings_Oinverse__class_Odivide(_319618, _319626, _319622))]]], (3782 ^ _191474) ^ [_320426, _320428, _320430] : [class_Fields_Olinordered__field(_320426), c_Orderings_Oord__class_Oless__eq(_320426, c_Groups_Ozero__class_Ozero(_320426), _320428), c_Orderings_Oord__class_Oless(_320426, c_Groups_Ozero__class_Ozero(_320426), _320430), -(c_Orderings_Oord__class_Oless__eq(_320426, c_Groups_Ozero__class_Ozero(_320426), c_Rings_Oinverse__class_Odivide(_320426, _320428, _320430)))], (3796 ^ _191474) ^ [_320866, _320868, _320870] : [class_Fields_Olinordered__field(_320866), c_Orderings_Oord__class_Oless__eq(_320866, c_Groups_Ozero__class_Ozero(_320866), _320868), c_Orderings_Oord__class_Oless(_320866, _320870, c_Groups_Ozero__class_Ozero(_320866)), -(c_Orderings_Oord__class_Oless__eq(_320866, c_Rings_Oinverse__class_Odivide(_320866, _320868, _320870), c_Groups_Ozero__class_Ozero(_320866)))], (3810 ^ _191474) ^ [_321334, _321336, _321338, _321340, _321342] : [class_Fields_Olinordered__field(_321334), c_Orderings_Oord__class_Oless(_321334, c_Groups_Ozero__class_Ozero(_321334), _321336), c_Orderings_Oord__class_Oless__eq(_321334, _321336, _321338), c_Orderings_Oord__class_Oless(_321334, c_Groups_Ozero__class_Ozero(_321334), _321340), c_Orderings_Oord__class_Oless(_321334, _321340, _321342), -(c_Orderings_Oord__class_Oless(_321334, c_Rings_Oinverse__class_Odivide(_321334, _321336, _321342), c_Rings_Oinverse__class_Odivide(_321334, _321338, _321340)))], (3832 ^ _191474) ^ [_322040, _322042, _322044, _322046, _322048] : [class_Fields_Olinordered__field(_322040), c_Orderings_Oord__class_Oless__eq(_322040, c_Groups_Ozero__class_Ozero(_322040), _322042), c_Orderings_Oord__class_Oless(_322040, _322042, _322044), c_Orderings_Oord__class_Oless(_322040, c_Groups_Ozero__class_Ozero(_322040), _322046), c_Orderings_Oord__class_Oless__eq(_322040, _322046, _322048), -(c_Orderings_Oord__class_Oless(_322040, c_Rings_Oinverse__class_Odivide(_322040, _322042, _322048), c_Rings_Oinverse__class_Odivide(_322040, _322044, _322046)))], (3854 ^ _191474) ^ [_322746, _322748, _322750, _322752, _322754] : [class_Fields_Olinordered__field(_322746), c_Orderings_Oord__class_Oless__eq(_322746, c_Groups_Ozero__class_Ozero(_322746), _322748), c_Orderings_Oord__class_Oless__eq(_322746, _322748, _322750), c_Orderings_Oord__class_Oless(_322746, c_Groups_Ozero__class_Ozero(_322746), _322752), c_Orderings_Oord__class_Oless__eq(_322746, _322752, _322754), -(c_Orderings_Oord__class_Oless__eq(_322746, c_Rings_Oinverse__class_Odivide(_322746, _322748, _322754), c_Rings_Oinverse__class_Odivide(_322746, _322750, _322752)))], (3876 ^ _191474) ^ [_323424, _323426, _323428] : [class_Fields_Olinordered__field(_323424), c_Orderings_Oord__class_Oless__eq(_323424, _323426, c_Groups_Ozero__class_Ozero(_323424)), c_Orderings_Oord__class_Oless(_323424, c_Groups_Ozero__class_Ozero(_323424), _323428), -(c_Orderings_Oord__class_Oless__eq(_323424, c_Rings_Oinverse__class_Odivide(_323424, _323426, _323428), c_Groups_Ozero__class_Ozero(_323424)))], (3890 ^ _191474) ^ [_323864, _323866, _323868] : [class_Fields_Olinordered__field(_323864), c_Orderings_Oord__class_Oless__eq(_323864, _323866, c_Groups_Ozero__class_Ozero(_323864)), c_Orderings_Oord__class_Oless(_323864, _323868, c_Groups_Ozero__class_Ozero(_323864)), -(c_Orderings_Oord__class_Oless__eq(_323864, c_Groups_Ozero__class_Ozero(_323864), c_Rings_Oinverse__class_Odivide(_323864, _323866, _323868)))], (3904 ^ _191474) ^ [_324318, _324320, _324322, _324324] : [class_Fields_Olinordered__field(_324318), c_Orderings_Oord__class_Oless(_324318, _324320, _324322), c_Orderings_Oord__class_Oless(_324318, _324324, c_Groups_Ozero__class_Ozero(_324318)), c_Orderings_Oord__class_Oless(_324318, c_Groups_Ozero__class_Ozero(_324318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324318), _324320), _324322)), -(c_Orderings_Oord__class_Oless(_324318, c_Rings_Oinverse__class_Odivide(_324318, _324324, _324320), c_Rings_Oinverse__class_Odivide(_324318, _324324, _324322)))], (3922 ^ _191474) ^ [_324905, _324907, _324909, _324911] : [class_Fields_Olinordered__field(_324905), c_Orderings_Oord__class_Oless(_324905, _324907, _324909), c_Orderings_Oord__class_Oless(_324905, c_Groups_Ozero__class_Ozero(_324905), _324911), c_Orderings_Oord__class_Oless(_324905, c_Groups_Ozero__class_Ozero(_324905), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324905), _324909), _324907)), -(c_Orderings_Oord__class_Oless(_324905, c_Rings_Oinverse__class_Odivide(_324905, _324911, _324909), c_Rings_Oinverse__class_Odivide(_324905, _324911, _324907)))], (3940 ^ _191474) ^ [_325492, _325494, _325496, _325498] : [class_Fields_Olinordered__field(_325492), c_Orderings_Oord__class_Oless(_325492, _325494, c_Groups_Ozero__class_Ozero(_325492)), 3947 ^ _191474 : [(3948 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_325492, c_Rings_Oinverse__class_Odivide(_325492, _325496, _325494), _325498), -(c_Orderings_Oord__class_Oless(_325492, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325492), _325498), _325494), _325496))], (3954 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_325492, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325492), _325498), _325494), _325496), -(c_Orderings_Oord__class_Oless(_325492, c_Rings_Oinverse__class_Odivide(_325492, _325496, _325494), _325498))]]], (3960 ^ _191474) ^ [_326155, _326157, _326159, _326161] : [class_Fields_Olinordered__field(_326155), c_Orderings_Oord__class_Oless(_326155, _326157, c_Groups_Ozero__class_Ozero(_326155)), 3967 ^ _191474 : [(3968 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_326155, _326159, c_Rings_Oinverse__class_Odivide(_326155, _326161, _326157)), -(c_Orderings_Oord__class_Oless(_326155, _326161, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326155), _326159), _326157)))], (3974 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_326155, _326161, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326155), _326159), _326157)), -(c_Orderings_Oord__class_Oless(_326155, _326159, c_Rings_Oinverse__class_Odivide(_326155, _326161, _326157)))]]], (3980 ^ _191474) ^ [_326818, _326820, _326822, _326824] : [class_Fields_Olinordered__field(_326818), c_Orderings_Oord__class_Oless(_326818, c_Groups_Ozero__class_Ozero(_326818), _326820), c_Orderings_Oord__class_Oless(_326818, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326818), _326822), _326820), _326824), -(c_Orderings_Oord__class_Oless(_326818, _326822, c_Rings_Oinverse__class_Odivide(_326818, _326824, _326820)))], (3994 ^ _191474) ^ [_327294, _327296, _327298, _327300] : [class_Fields_Olinordered__field(_327294), c_Orderings_Oord__class_Oless(_327294, c_Groups_Ozero__class_Ozero(_327294), _327296), c_Orderings_Oord__class_Oless(_327294, _327298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327294), _327300), _327296)), -(c_Orderings_Oord__class_Oless(_327294, c_Rings_Oinverse__class_Odivide(_327294, _327298, _327296), _327300))], (4008 ^ _191474) ^ [_327770, _327772, _327774, _327776] : [class_Fields_Olinordered__field(_327770), c_Orderings_Oord__class_Oless(_327770, c_Groups_Ozero__class_Ozero(_327770), _327772), 4015 ^ _191474 : [(4016 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_327770, c_Rings_Oinverse__class_Odivide(_327770, _327774, _327772), _327776), -(c_Orderings_Oord__class_Oless(_327770, _327774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327770), _327776), _327772)))], (4022 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_327770, _327774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327770), _327776), _327772)), -(c_Orderings_Oord__class_Oless(_327770, c_Rings_Oinverse__class_Odivide(_327770, _327774, _327772), _327776))]]], (4028 ^ _191474) ^ [_328433, _328435, _328437, _328439] : [class_Fields_Olinordered__field(_328433), c_Orderings_Oord__class_Oless(_328433, c_Groups_Ozero__class_Ozero(_328433), _328435), 4035 ^ _191474 : [(4036 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_328433, _328437, c_Rings_Oinverse__class_Odivide(_328433, _328439, _328435)), -(c_Orderings_Oord__class_Oless(_328433, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328433), _328437), _328435), _328439))], (4042 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_328433, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328433), _328437), _328435), _328439), -(c_Orderings_Oord__class_Oless(_328433, _328437, c_Rings_Oinverse__class_Odivide(_328433, _328439, _328435)))]]], (4048 ^ _191474) ^ [_329096, _329098, _329100, _329102] : [class_Fields_Olinordered__field__inverse__zero(_329096), 4051 ^ _191474 : [(4078 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_329096, c_Rings_Oinverse__class_Odivide(_329096, _329098, _329100), _329102)), 4081 ^ _191474 : [(4082 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_329096, c_Groups_Ozero__class_Ozero(_329096), _329100))], (4084 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_329096, _329098, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329096), _329102), _329100))]], 4085 ^ _191474 : [(4086 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_329096, c_Groups_Ozero__class_Ozero(_329096), _329100)], (4088 ^ _191474) ^ [] : [4089 ^ _191474 : [(4090 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_329096, _329100, c_Groups_Ozero__class_Ozero(_329096)))], (4092 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_329096, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329096), _329102), _329100), _329098)]], 4093 ^ _191474 : [(4094 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_329096, _329100, c_Groups_Ozero__class_Ozero(_329096))], (4096 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_329096, c_Groups_Ozero__class_Ozero(_329096), _329102)]]]]], (4052 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_329096, c_Rings_Oinverse__class_Odivide(_329096, _329098, _329100), _329102), 4055 ^ _191474 : [(4056 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_329096, c_Groups_Ozero__class_Ozero(_329096), _329100), -(c_Orderings_Oord__class_Oless(_329096, _329098, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329096), _329102), _329100)))], (4062 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_329096, c_Groups_Ozero__class_Ozero(_329096), _329100)), 4065 ^ _191474 : [(4066 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_329096, _329100, c_Groups_Ozero__class_Ozero(_329096)), -(c_Orderings_Oord__class_Oless(_329096, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329096), _329102), _329100), _329098))], (4072 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_329096, _329100, c_Groups_Ozero__class_Ozero(_329096))), -(c_Orderings_Oord__class_Oless(_329096, c_Groups_Ozero__class_Ozero(_329096), _329102))]]]]]]], (4100 ^ _191474) ^ [_330752, _330754, _330756, _330758] : [class_Fields_Olinordered__field__inverse__zero(_330752), 4103 ^ _191474 : [(4130 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_330752, _330754, c_Rings_Oinverse__class_Odivide(_330752, _330756, _330758))), 4133 ^ _191474 : [(4134 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_330752, c_Groups_Ozero__class_Ozero(_330752), _330758))], (4136 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_330752, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330752), _330754), _330758), _330756)]], 4137 ^ _191474 : [(4138 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_330752, c_Groups_Ozero__class_Ozero(_330752), _330758)], (4140 ^ _191474) ^ [] : [4141 ^ _191474 : [(4142 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_330752, _330758, c_Groups_Ozero__class_Ozero(_330752)))], (4144 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_330752, _330756, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330752), _330754), _330758))]], 4145 ^ _191474 : [(4146 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_330752, _330758, c_Groups_Ozero__class_Ozero(_330752))], (4148 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_330752, _330754, c_Groups_Ozero__class_Ozero(_330752))]]]]], (4104 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_330752, _330754, c_Rings_Oinverse__class_Odivide(_330752, _330756, _330758)), 4107 ^ _191474 : [(4108 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_330752, c_Groups_Ozero__class_Ozero(_330752), _330758), -(c_Orderings_Oord__class_Oless(_330752, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330752), _330754), _330758), _330756))], (4114 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_330752, c_Groups_Ozero__class_Ozero(_330752), _330758)), 4117 ^ _191474 : [(4118 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_330752, _330758, c_Groups_Ozero__class_Ozero(_330752)), -(c_Orderings_Oord__class_Oless(_330752, _330756, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330752), _330754), _330758)))], (4124 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_330752, _330758, c_Groups_Ozero__class_Ozero(_330752))), -(c_Orderings_Oord__class_Oless(_330752, _330754, c_Groups_Ozero__class_Ozero(_330752)))]]]]]]], (4152 ^ _191474) ^ [_332408, _332410, _332412, _332414] : [class_Fields_Ofield__inverse__zero(_332408), -(_332410 = c_Groups_Ozero__class_Ozero(_332408)), -(c_Groups_Oplus__class_Oplus(_332408, _332412, c_Rings_Oinverse__class_Odivide(_332408, _332414, _332410)) = c_Rings_Oinverse__class_Odivide(_332408, c_Groups_Oplus__class_Oplus(_332408, _332414, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332408), _332412), _332410)), _332410))], (4162 ^ _191474) ^ [_332808, _332810, _332812, _332814] : [class_Fields_Ofield(_332808), -(_332810 = c_Groups_Ozero__class_Ozero(_332808)), -(c_Groups_Oplus__class_Oplus(_332808, _332812, c_Rings_Oinverse__class_Odivide(_332808, _332814, _332810)) = c_Rings_Oinverse__class_Odivide(_332808, c_Groups_Oplus__class_Oplus(_332808, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332808), _332810), _332812), _332814), _332810))], (4172 ^ _191474) ^ [_333208, _333210, _333212, _333214] : [class_Fields_Ofield__inverse__zero(_333208), -(_333210 = c_Groups_Ozero__class_Ozero(_333208)), -(c_Groups_Oplus__class_Oplus(_333208, c_Rings_Oinverse__class_Odivide(_333208, _333212, _333210), _333214) = c_Rings_Oinverse__class_Odivide(_333208, c_Groups_Oplus__class_Oplus(_333208, _333212, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333208), _333214), _333210)), _333210))], (4182 ^ _191474) ^ [_333608, _333610, _333612, _333614] : [class_Fields_Ofield(_333608), -(_333610 = c_Groups_Ozero__class_Ozero(_333608)), -(c_Groups_Oplus__class_Oplus(_333608, c_Rings_Oinverse__class_Odivide(_333608, _333612, _333610), _333614) = c_Rings_Oinverse__class_Odivide(_333608, c_Groups_Oplus__class_Oplus(_333608, _333612, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333608), _333610), _333614)), _333610))], (4192 ^ _191474) ^ [_334022, _334024, _334026, _334028, _334030] : [class_Fields_Ofield(_334022), -(_334024 = c_Groups_Ozero__class_Ozero(_334022)), -(_334026 = c_Groups_Ozero__class_Ozero(_334022)), -(c_Groups_Oplus__class_Oplus(_334022, c_Rings_Oinverse__class_Odivide(_334022, _334028, _334024), c_Rings_Oinverse__class_Odivide(_334022, _334030, _334026)) = c_Rings_Oinverse__class_Odivide(_334022, c_Groups_Oplus__class_Oplus(_334022, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334022), _334028), _334026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334022), _334030), _334024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334022), _334024), _334026)))], (4206 ^ _191474) ^ [_334594, _334596, _334598, _334600, _334602] : [class_Fields_Ofield(_334594), -(_334596 = c_Groups_Ozero__class_Ozero(_334594)), -(_334598 = c_Groups_Ozero__class_Ozero(_334594)), -(c_Groups_Ominus__class_Ominus(_334594, c_Rings_Oinverse__class_Odivide(_334594, _334600, _334596), c_Rings_Oinverse__class_Odivide(_334594, _334602, _334598)) = c_Rings_Oinverse__class_Odivide(_334594, c_Groups_Ominus__class_Ominus(_334594, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334594), _334600), _334598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334594), _334602), _334596)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334594), _334596), _334598)))], (4220 ^ _191474) ^ [_335152, _335154, _335156, _335158] : [class_Fields_Ofield(_335152), -(_335154 = c_Groups_Ozero__class_Ozero(_335152)), -(c_Groups_Ominus__class_Ominus(_335152, c_Rings_Oinverse__class_Odivide(_335152, _335156, _335154), _335158) = c_Rings_Oinverse__class_Odivide(_335152, c_Groups_Ominus__class_Ominus(_335152, _335156, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335152), _335154), _335158)), _335154))], (4230 ^ _191474) ^ [_335552, _335554, _335556, _335558] : [class_Fields_Ofield(_335552), -(_335554 = c_Groups_Ozero__class_Ozero(_335552)), -(c_Groups_Ominus__class_Ominus(_335552, _335556, c_Rings_Oinverse__class_Odivide(_335552, _335558, _335554)) = c_Rings_Oinverse__class_Odivide(_335552, c_Groups_Ominus__class_Ominus(_335552, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335552), _335554), _335556), _335558), _335554))], (4240 ^ _191474) ^ [_335938, _335940, _335942] : [class_Fields_Olinordered__field(_335938), c_Orderings_Oord__class_Oless(_335938, _335940, _335942), -(c_Orderings_Oord__class_Oless(_335938, _335940, c_Rings_Oinverse__class_Odivide(_335938, c_Groups_Oplus__class_Oplus(_335938, _335940, _335942), c_Groups_Oplus__class_Oplus(_335938, c_Groups_Oone__class_Oone(_335938), c_Groups_Oone__class_Oone(_335938)))))], (4250 ^ _191474) ^ [_336295, _336297, _336299] : [class_Fields_Olinordered__field(_336295), c_Orderings_Oord__class_Oless(_336295, _336297, _336299), -(c_Orderings_Oord__class_Oless(_336295, c_Rings_Oinverse__class_Odivide(_336295, c_Groups_Oplus__class_Oplus(_336295, _336297, _336299), c_Groups_Oplus__class_Oplus(_336295, c_Groups_Oone__class_Oone(_336295), c_Groups_Oone__class_Oone(_336295))), _336299))], (4260 ^ _191474) ^ [_336666, _336668, _336670, _336672] : [class_Fields_Olinordered__field__inverse__zero(_336666), c_Orderings_Oord__class_Oless__eq(_336666, _336668, _336670), c_Orderings_Oord__class_Oless__eq(_336666, _336672, c_Groups_Ozero__class_Ozero(_336666)), c_Orderings_Oord__class_Oless(_336666, c_Groups_Ozero__class_Ozero(_336666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336666), _336668), _336670)), -(c_Orderings_Oord__class_Oless__eq(_336666, c_Rings_Oinverse__class_Odivide(_336666, _336672, _336668), c_Rings_Oinverse__class_Odivide(_336666, _336672, _336670)))], (4278 ^ _191474) ^ [_337253, _337255, _337257, _337259] : [class_Fields_Olinordered__field(_337253), c_Orderings_Oord__class_Oless__eq(_337253, _337255, _337257), c_Orderings_Oord__class_Oless__eq(_337253, c_Groups_Ozero__class_Ozero(_337253), _337259), c_Orderings_Oord__class_Oless(_337253, c_Groups_Ozero__class_Ozero(_337253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337253), _337257), _337255)), -(c_Orderings_Oord__class_Oless__eq(_337253, c_Rings_Oinverse__class_Odivide(_337253, _337259, _337257), c_Rings_Oinverse__class_Odivide(_337253, _337259, _337255)))], (4296 ^ _191474) ^ [_337783] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _337783))], (4298 ^ _191474) ^ [_337861] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _337861, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4300 ^ _191474) ^ [_337954, _337956] : [-(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, _337954, _337956)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _337954)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _337956)))], (4302 ^ _191474) ^ [_338137, _338139, _338141, _338143, _338145, _338147] : [class_RealVector_Oreal__field(_338137), -(c_Rings_Oinverse__class_Odivide(_338137, c_Groups_Ominus__class_Ominus(_338137, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338137), _338139), _338141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338137), _338143), _338145)), _338147) = c_Groups_Oplus__class_Oplus(_338137, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338137), _338139), c_Rings_Oinverse__class_Odivide(_338137, c_Groups_Ominus__class_Ominus(_338137, _338141, _338145), _338147)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338137), c_Rings_Oinverse__class_Odivide(_338137, c_Groups_Ominus__class_Ominus(_338137, _338139, _338143), _338147)), _338145)))], (4308 ^ _191474) ^ [_338503, _338505, _338507] : [class_Rings_Olinordered__ring__strict(_338503), 4311 ^ _191474 : [(4322 ^ _191474) ^ [] : [4323 ^ _191474 : [(4324 ^ _191474) ^ [] : [-(_338505 = c_Groups_Ozero__class_Ozero(_338503))], (4326 ^ _191474) ^ [] : [-(_338507 = c_Groups_Ozero__class_Ozero(_338503))]], -(c_Orderings_Oord__class_Oless(_338503, c_Groups_Ozero__class_Ozero(_338503), c_Groups_Oplus__class_Oplus(_338503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338503), _338505), _338505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338503), _338507), _338507))))], (4312 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_338503, c_Groups_Ozero__class_Ozero(_338503), c_Groups_Oplus__class_Oplus(_338503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338503), _338505), _338505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338503), _338507), _338507))), _338505 = c_Groups_Ozero__class_Ozero(_338503), _338507 = c_Groups_Ozero__class_Ozero(_338503)]]], (4330 ^ _191474) ^ [_339240, _339242, _339244] : [class_Rings_Olinordered__ring(_339240), c_Orderings_Oord__class_Oless(_339240, c_Groups_Oplus__class_Oplus(_339240, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339240), _339242), _339242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339240), _339244), _339244)), c_Groups_Ozero__class_Ozero(_339240))], (4336 ^ _191474) ^ [_339515, _339517, _339519] : [class_Rings_Olinordered__ring(_339515), -(c_Orderings_Oord__class_Oless__eq(_339515, c_Groups_Ozero__class_Ozero(_339515), c_Groups_Oplus__class_Oplus(_339515, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339515), _339517), _339517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339515), _339519), _339519))))], (4342 ^ _191474) ^ [_339789, _339791, _339793] : [class_Rings_Olinordered__ring__strict(_339789), 4345 ^ _191474 : [(4346 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_339789, c_Groups_Oplus__class_Oplus(_339789, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339789), _339791), _339791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339789), _339793), _339793)), c_Groups_Ozero__class_Ozero(_339789)), 4349 ^ _191474 : [(4350 ^ _191474) ^ [] : [-(_339791 = c_Groups_Ozero__class_Ozero(_339789))], (4352 ^ _191474) ^ [] : [-(_339793 = c_Groups_Ozero__class_Ozero(_339789))]]], (4354 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_339789, c_Groups_Oplus__class_Oplus(_339789, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339789), _339791), _339791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339789), _339793), _339793)), c_Groups_Ozero__class_Ozero(_339789))), _339791 = c_Groups_Ozero__class_Ozero(_339789), _339793 = c_Groups_Ozero__class_Ozero(_339789)]]], (4364 ^ _191474) ^ [_340507, _340509, _340511] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _340507), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _340509, _340511)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _340507), _340509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _340507), _340511)))], (4366 ^ _191474) ^ [_340629, _340631] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _340629, _340631), _340631) = _340629)], (4368 ^ _191474) ^ [_340731, _340733] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _340731, _340733), _340731) = _340733)], (4370 ^ _191474) ^ [_340847, _340849, _340851] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _340847, _340849), _340851) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _340847, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _340849, _340851)))], (4372 ^ _191474) ^ [_340973, _340975, _340977] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _340973, _340975)), _340977) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _340973), _340977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _340975), _340977)))], (4374 ^ _191474) ^ [_341109, _341111, _341113] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341109, _341111), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341109, _341113)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _341111, _341113))], (4376 ^ _191474) ^ [_341235, _341237, _341239] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341235, _341237), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341239, _341237)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _341235, _341239))], (4378 ^ _191474) ^ [_341405, _341407, _341409] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341405, _341407) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341409, _341407), -(_341405 = _341409)], (4384 ^ _191474) ^ [_341589, _341591, _341593] : [_341589 = _341593, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341589, _341591) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341593, _341591))], (4390 ^ _191474) ^ [_341866, _341868, _341870] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341866, _341868) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _341866, _341870), -(_341868 = _341870)], (4396 ^ _191474) ^ [_342050, _342052, _342054] : [_342052 = _342054, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342050, _342052) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342050, _342054))], (4402 ^ _191474) ^ [_342283, _342285, _342287] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342283, _342285), _342287) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342283, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342285, _342287)))], (4404 ^ _191474) ^ [_342409, _342411, _342413] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342409, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342411, _342413)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342411, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342409, _342413)))], (4406 ^ _191474) ^ [_342521, _342523] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342521, _342523) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342523, _342521))], (4408 ^ _191474) ^ [_342638, _342640] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _342638, _342640) = _342638, -(_342640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4414 ^ _191474) ^ [_342856, _342858] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _342856, _342858) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _342858, _342856) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_342856 = _342858)], (4424 ^ _191474) ^ [_343171, _343173] : [_343171 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343171), _343173), -(_343173 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_343171 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4444 ^ _191474) ^ [_343812, _343814, _343816] : [4445 ^ _191474 : [(4446 ^ _191474) ^ [] : [_343812 = _343816], (4448 ^ _191474) ^ [] : [_343814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343812), _343814) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343816), _343814))], (4434 ^ _191474) ^ [_343526, _343528, _343530] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343526), _343528) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _343530), _343528), -(_343526 = _343530), -(_343528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4462 ^ _191474) ^ [_344459, _344461, _344463] : [4463 ^ _191474 : [(4464 ^ _191474) ^ [] : [_344461 = _344463], (4466 ^ _191474) ^ [] : [_344459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344459), _344461) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344459), _344463))], (4452 ^ _191474) ^ [_344173, _344175, _344177] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344173), _344175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344173), _344177), -(_344175 = _344177), -(_344173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4480 ^ _191474) ^ [_345070, _345072] : [4481 ^ _191474 : [(4482 ^ _191474) ^ [] : [_345070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4484 ^ _191474) ^ [] : [_345072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _345070), _345072) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4470 ^ _191474) ^ [_344806, _344808] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _344806), _344808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_344806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_344808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4488 ^ _191474) ^ [_345397, _345399] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _345397, _345399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 4491 ^ _191474 : [(4492 ^ _191474) ^ [] : [-(_345397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4494 ^ _191474) ^ [] : [-(_345399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4496 ^ _191474) ^ [_345642, _345644] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _345642, _345644) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _345642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _345644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4506 ^ _191474) ^ [_345936, _345938] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _345936, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _345936, _345938)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4508 ^ _191474) ^ [_346073, _346075] : [_346073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _346073), _346075) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4514 ^ _191474) ^ [_346247, _346249] : [-(_346247 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _346247), _346249) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _346249, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _346247, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _346249)))], (4520 ^ _191474) ^ [_346473] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _346473, _346473) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4522 ^ _191474) ^ [_346555] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _346555, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _346555)], (4524 ^ _191474) ^ [_346637] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _346637, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _346637)], (4526 ^ _191474) ^ [_346719] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _346719), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4528 ^ _191474) ^ [_346803] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _346803) = _346803)], (4530 ^ _191474) ^ [_346885] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _346885) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4532 ^ _191474) ^ [_346966] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _346966) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4534 ^ _191474) ^ [_347047] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _347047, _347047)], (4536 ^ _191474) ^ [_347139, _347141] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _347139, _347141), _347139)], (4538 ^ _191474) ^ [_347237, _347239] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _347237, _347239), _347239)], (4550 ^ _191474) ^ [_347639, _347641] : [4551 ^ _191474 : [(4552 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _347639, _347641)], (4554 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _347641, _347639)]], _347639 = _347641], (4540 ^ _191474) ^ [_347380, _347382] : [-(_347380 = _347382), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _347380, _347382)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _347382, _347380))], (4558 ^ _191474) ^ [_347973, _347975, _347977] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _347973, _347975), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _347973, _347977)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _347975, _347977))], (4564 ^ _191474) ^ [_348161, _348163, _348165] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _348163, _348165), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _348161, _348163), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _348161, _348165)))], (4570 ^ _191474) ^ [_348399, _348401] : [-(_348399 = _348401), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _348399, _348401)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _348401, _348399))], (4580 ^ _191474) ^ [_348678] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _348678, _348678)], (4582 ^ _191474) ^ [_348786, _348788] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _348786, _348788), _348788 = _348786], (4588 ^ _191474) ^ [_348999, _349001] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _348999, _349001), _348999 = _349001], (4594 ^ _191474) ^ [_349226, _349228, _349230] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349226, _349228), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349226, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _349228, _349230)))], (4600 ^ _191474) ^ [_349468, _349470, _349472] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349468, _349470), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349468, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _349472, _349470)))], (4606 ^ _191474) ^ [_349710, _349712, _349714] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349710, _349712), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _349710, _349714), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _349712, _349714)))], (4612 ^ _191474) ^ [_349974, _349976, _349978, _349980] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349974, _349976), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349978, _349980), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _349974, _349978), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _349976, _349980)))], (4622 ^ _191474) ^ [_350343, _350345, _350347, _350349] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _350343, _350345), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _350347, _350345) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _350343, _350349), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _350347, _350349))], (4632 ^ _191474) ^ [_350696, _350698, _350700] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _350696, _350698), _350700), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _350696, _350700))], (4638 ^ _191474) ^ [_350938, _350940, _350942] : [4639 ^ _191474 : [(4640 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _350938, _350940))], (4642 ^ _191474) ^ [] : [hBOOL(hAPP(hAPP(_350942, _350940), _350938))]], 4645 ^ _191474 : [(4646 ^ _191474) ^ [] : [-(_350938 = _350940)], (4648 ^ _191474) ^ [] : [hBOOL(hAPP(hAPP(_350942, _350940), _350938))]], 4651 ^ _191474 : [(4652 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _350940, _350938))], (4654 ^ _191474) ^ [] : [hBOOL(hAPP(hAPP(_350942, _350940), _350938))]], -(hBOOL(hAPP(hAPP(_350942, _350940), _350938)))], (4658 ^ _191474) ^ [_351629, _351631, _351633] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _351629, _351631), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _351629, _351633), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _351633, _351631), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _351633, _351629)))], (4668 ^ _191474) ^ [_351974, _351976, _351978] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _351974, _351976), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _351974, _351978), _351976))], (4674 ^ _191474) ^ [_352202, _352204] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _352202, _352204)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _352204, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _352202, _352204)) = _352202)], (4680 ^ _191474) ^ [_352476, _352478, _352480] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _352476, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _352478, _352480)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _352476, _352480), _352478))], (4686 ^ _191474) ^ [_352664, _352666, _352668] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _352664, _352668), _352666), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _352664, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _352666, _352668)))], (4692 ^ _191474) ^ [_352916, _352918, _352920] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _352916, _352918), _352920), 4695 ^ _191474 : [(4696 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _352916, _352920))], (4698 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _352918, _352920))]]], (4700 ^ _191474) ^ [_353241, _353243, _353245] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _353241, _353243), _353245), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _353241, _353245))], (4706 ^ _191474) ^ [_353483, _353485, _353487] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _353483, _353485), _353487), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _353485, _353487))], (4712 ^ _191474) ^ [_353725, _353727, _353729] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _353725, _353727), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _353725, _353729), 4719 ^ _191474 : [(4720 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _353727, _353725), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _353729, _353725)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _353727, _353729))], (4726 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _353727, _353729), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _353727, _353725), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _353729, _353725)))]]], (4732 ^ _191474) ^ [_354342, _354344, _354346] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _354342, _354344), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _354342, _354346), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _354344, _354342), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _354346, _354342)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _354344, _354346))], (4742 ^ _191474) ^ [_354701, _354703, _354705] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _354701, _354703), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _354701, _354705), 4749 ^ _191474 : [(4750 ^ _191474) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _354703, _354701) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _354705, _354701), -(_354703 = _354705)], (4756 ^ _191474) ^ [] : [_354703 = _354705, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _354703, _354701) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _354705, _354701))]]], (4762 ^ _191474) ^ [_355326, _355328, _355330, _355332] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _355326, _355328), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _355330, _355332), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _355326), _355330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _355328), _355332)))], (4772 ^ _191474) ^ [_355703, _355705, _355707, _355709] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _355703, _355705), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _355707, _355709), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _355703, _355707), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _355705, _355709)))], (4782 ^ _191474) ^ [_356044, _356046] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356044, _356046), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356046, _356044), -(_356044 = _356046)], (4792 ^ _191474) ^ [_356361, _356363, _356365] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356361, _356363), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356363, _356365), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356361, _356365))], (4802 ^ _191474) ^ [_356690, _356692, _356694] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356690, _356692), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _356692, _356694), _356690) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _356692, _356690), _356694))], (4808 ^ _191474) ^ [_356954, _356956, _356958] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356954, _356956), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _356956, _356954), _356958) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _356956, _356958), _356954))], (4814 ^ _191474) ^ [_357218, _357220, _357222] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _357218, _357220), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _357222, _357220), _357218) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _357222, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _357220, _357218)))], (4820 ^ _191474) ^ [_357482, _357484, _357486] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _357482, _357484), 4823 ^ _191474 : [(4824 ^ _191474) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _357484, _357482) = _357486, -(_357484 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _357486, _357482))], (4830 ^ _191474) ^ [] : [_357484 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _357486, _357482), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _357484, _357482) = _357486)]]], (4836 ^ _191474) ^ [_357984, _357986] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _357984, _357986), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _357986, _357984), _357984) = _357986)], (4842 ^ _191474) ^ [_358226, _358228, _358230] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _358226, _358228), 4845 ^ _191474 : [(4846 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _358230, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _358228, _358226)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _358230, _358226), _358228))], (4852 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _358230, _358226), _358228), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _358230, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _358228, _358226)))]]], (4858 ^ _191474) ^ [_358748, _358750, _358752] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _358748, _358750), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _358752, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _358750, _358748)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _358752, _358750), _358748))], (4864 ^ _191474) ^ [_358998, _359000] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _358998, _359000), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _358998, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _359000, _358998)) = _359000)], (4870 ^ _191474) ^ [_359226, _359228] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _359226, _359228), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _359228, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _359228, _359226)) = _359226)], (4876 ^ _191474) ^ [_359468, _359470, _359472] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _359468, _359470), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _359468, _359472), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _359470, _359472)))], (4882 ^ _191474) ^ [_359718, _359720, _359722] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _359718, _359720), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _359722, _359720), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _359722, _359718)))], (4888 ^ _191474) ^ [_359968, _359970, _359972] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _359968, _359970), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359972), _359968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359972), _359970)))], (4894 ^ _191474) ^ [_360226, _360228, _360230] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360226, _360228), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _360226), _360230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _360228), _360230)))], (4900 ^ _191474) ^ [_360484, _360486, _360488] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360484, _360486), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _360484, _360488), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _360486, _360488)))], (4906 ^ _191474) ^ [_360734, _360736, _360738] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360734, _360736), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360738, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _360736, _360738), _360734)))], (4912 ^ _191474) ^ [_360984, _360986, _360988] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360984, _360986), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360984, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _360988, _360986)))], (4918 ^ _191474) ^ [_361226, _361228, _361230] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361226, _361228), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361226, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _361228, _361230)))], (4924 ^ _191474) ^ [_361454, _361456] : [_361454 = _361456, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361454, _361456))], (4930 ^ _191474) ^ [_361709, _361711, _361713] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _361709, _361711), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _361709, _361713)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361711, _361713))], (4936 ^ _191474) ^ [_361897, _361899, _361901] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361899, _361901), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _361897, _361899), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _361897, _361901)))], (4942 ^ _191474) ^ [_362178, _362180, _362182] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _362178, _362180), _362182), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362178, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _362182, _362180)))], (4948 ^ _191474) ^ [_362366, _362368, _362370] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362366, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _362370, _362368)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _362366, _362368), _362370))], (4954 ^ _191474) ^ [_362618, _362620, _362622] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362618, _362620), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _362622, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _362620, _362618)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _362622, _362618), _362620))], (4960 ^ _191474) ^ [_362868, _362870] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362868, _362870)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362870, _362868))], (4966 ^ _191474) ^ [_363112, _363114] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363112, _363114), -(_363114 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _363112, 4969 ^ [_363112, _363114]))], (4973 ^ _191474) ^ [_363345, _363347] : [4974 ^ _191474 : [(4975 ^ _191474) ^ [_363420] : [_363347 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _363345, _363420)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363345, _363347))], (4979 ^ _191474) ^ [_363574, _363576] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _363574, _363576), _363574))], (4981 ^ _191474) ^ [_363659] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363659, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _363659), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _363659), _363659))))], (4983 ^ _191474) ^ [_363764, _363766] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363764, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _363764, _363766)))], (4985 ^ _191474) ^ [_363863, _363865] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363863, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _363865, _363863)))], (4987 ^ _191474) ^ [_363948] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _363948, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _363948), _363948)))], (4989 ^ _191474) ^ [_364033] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _364033, _364033))], (4991 ^ _191474) ^ [_364183, _364185, _364187, _364189, _364191] : [class_Groups_Oab__group__add(_364183), -(c_Groups_Ominus__class_Ominus(_364183, c_Groups_Oplus__class_Oplus(_364183, _364185, _364187), c_Groups_Oplus__class_Oplus(_364183, _364189, _364191)) = c_Groups_Oplus__class_Oplus(_364183, c_Groups_Ominus__class_Ominus(_364183, _364185, _364189), c_Groups_Ominus__class_Ominus(_364183, _364187, _364191)))], (4997 ^ _191474) ^ [_364443] : [-(_364443 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _364443))], (5003 ^ _191474) ^ [_364666, _364668, _364670] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _364666, _364668), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _364670), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _364670), _364666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _364670), _364668)))], (5013 ^ _191474) ^ [_365019, _365021, _365023] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _365019, _365021), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _365023), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365019), _365023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365021), _365023)))], (5023 ^ _191474) ^ [_365358, _365360] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _365358, _365360), _365360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5029 ^ _191474) ^ [_365571, _365573] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _365571), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _365573), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _365573, _365571), _365573))], (5039 ^ _191474) ^ [_365927, _365929, _365931] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365927), _365929), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _365931), _365929)), 5042 ^ _191474 : [(5043 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _365929))], (5045 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _365927, _365931))]]], (5047 ^ _191474) ^ [_366202, _366204, _366206] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _366202), _366204), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _366206), _366204))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _366204), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _366202, _366206)], (5057 ^ _191474) ^ [_366586, _366588, _366590] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _366586), _366588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _366586), _366590)), 5060 ^ _191474 : [(5061 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _366586))], (5063 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _366588, _366590))]]], (5065 ^ _191474) ^ [_366861, _366863, _366865] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _366861), _366863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _366861), _366865))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _366861), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _366863, _366865)], (5075 ^ _191474) ^ [_367172] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _367172, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5077 ^ _191474) ^ [_367309, _367311] : [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), _367309), _367311)), 5080 ^ _191474 : [(5081 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _367309))], (5083 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _367311))]]], (5085 ^ _191474) ^ [_367564, _367566] : [-(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), _367564), _367566))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _367564), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _367566)], (5105 ^ _191474) ^ [_368178, _368180] : [5106 ^ _191474 : [(5107 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _368178)], (5109 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _368180)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _368178, _368180)))], (5095 ^ _191474) ^ [_367912, _367914] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _367912, _367914)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _367912)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _367914))], (5113 ^ _191474) ^ [_368507, _368509] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _368507, _368509)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _368509, _368507))], (5119 ^ _191474) ^ [_368681, _368683] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _368683, _368681), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _368681, _368683)))], (5141 ^ _191474) ^ [_369479, _369481, _369483] : [-(hBOOL(hAPP(_369479, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _369481, _369483)))), 5144 ^ _191474 : [(5145 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _369481, _369483))], (5147 ^ _191474) ^ [] : [hBOOL(hAPP(_369479, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 5149 ^ _191474 : [(5150 ^ _191474) ^ [] : [-(_369481 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _369483, 5148 ^ [_369479, _369481, _369483]))], (5152 ^ _191474) ^ [] : [hBOOL(hAPP(_369479, 5148 ^ [_369479, _369481, _369483]))]]], (5125 ^ _191474) ^ [_368948, _368950, _368952] : [hBOOL(hAPP(_368948, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _368950, _368952))), 5128 ^ _191474 : [(5129 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _368950, _368952), -(hBOOL(hAPP(_368948, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5135 ^ _191474) ^ [_369280] : [_368950 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _368952, _369280), -(hBOOL(hAPP(_368948, _369280)))]]], (5172 ^ _191474) ^ [_370640, _370642, _370644] : [-(hBOOL(hAPP(_370640, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _370642, _370644)))), 5175 ^ _191474 : [(5176 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _370642, _370644))], (5178 ^ _191474) ^ [] : [hBOOL(hAPP(_370640, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 5180 ^ _191474 : [(5181 ^ _191474) ^ [] : [-(_370642 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _370644, 5179 ^ [_370640, _370642, _370644]))], (5183 ^ _191474) ^ [] : [hBOOL(hAPP(_370640, 5179 ^ [_370640, _370642, _370644]))]]], (5156 ^ _191474) ^ [_370101, _370103, _370105] : [hBOOL(hAPP(_370101, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _370103, _370105))), 5159 ^ _191474 : [(5160 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _370103, _370105), -(hBOOL(hAPP(_370101, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5166 ^ _191474) ^ [_370439] : [_370103 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _370105, _370439), -(hBOOL(hAPP(_370101, _370439)))]]], (5187 ^ _191474) ^ [_371242] : [-(_371242 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _371242))], (5193 ^ _191474) ^ [_371403] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _371403), _371403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5199 ^ _191474) ^ [_371582] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _371582, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5201 ^ _191474) ^ [_371690, _371692] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _371690, _371692), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _371690, _371692) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5207 ^ _191474) ^ [_371939, _371941] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _371939, _371941) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _371939, _371941))], (5213 ^ _191474) ^ [_372111, _372113] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _372111, _372113), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _372111, _372113) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5219 ^ _191474) ^ [_372348] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _372348, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_372348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5225 ^ _191474) ^ [_372506] : [_372506 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _372506, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5231 ^ _191474) ^ [_372685] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _372685))], (5233 ^ _191474) ^ [_372793, _372795] : [5234 ^ _191474 : [(5235 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _372793, _372795)], (5237 ^ _191474) ^ [] : [_372793 = _372795]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _372793, _372795))], (5241 ^ _191474) ^ [_373095, _373097, _373099] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _373095, _373097), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _373095, _373099), 5248 ^ _191474 : [(5249 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _373097, _373095), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _373099, _373095)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373097, _373099))], (5255 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373097, _373099), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _373097, _373095), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _373099, _373095)))]]], (5261 ^ _191474) ^ [_373712, _373714, _373716] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _373712, _373714), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _373716, _373712), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _373712, _373716), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _373714, _373716)))], (5271 ^ _191474) ^ [_374043, _374045] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _374043, _374045), -(_374043 = _374045), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374043, _374045))], (5281 ^ _191474) ^ [_374349, _374351] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374349, _374351), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _374349, _374351))], (5297 ^ _191474) ^ [_374848, _374850] : [5298 ^ _191474 : [(5299 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374848, _374850)], (5301 ^ _191474) ^ [] : [_374848 = _374850]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _374848, _374850))], (5287 ^ _191474) ^ [_374592, _374594] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _374592, _374594), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _374592, _374594)), -(_374592 = _374594)], (5305 ^ _191474) ^ [_375167, _375169] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375167, _375169), 5308 ^ _191474 : [(5309 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _375167, _375169))], (5311 ^ _191474) ^ [] : [_375167 = _375169]]], (5313 ^ _191474) ^ [_375409, _375411] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _375409, _375411)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _375409, _375411), -(_375409 = _375411)], (5323 ^ _191474) ^ [_375731, _375733, _375735] : [class_Rings_Olinordered__ring__strict(_375731), 5326 ^ _191474 : [(5327 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_375731, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375731), _375733), _375733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375731), _375735), _375735)) = c_Groups_Ozero__class_Ozero(_375731), 5330 ^ _191474 : [(5331 ^ _191474) ^ [] : [-(_375733 = c_Groups_Ozero__class_Ozero(_375731))], (5333 ^ _191474) ^ [] : [-(_375735 = c_Groups_Ozero__class_Ozero(_375731))]]], (5335 ^ _191474) ^ [] : [-(c_Groups_Oplus__class_Oplus(_375731, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375731), _375733), _375733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375731), _375735), _375735)) = c_Groups_Ozero__class_Ozero(_375731)), _375733 = c_Groups_Ozero__class_Ozero(_375731), _375735 = c_Groups_Ozero__class_Ozero(_375731)]]], (5355 ^ _191474) ^ [_376781, _376783, _376785] : [5356 ^ _191474 : [(5357 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _376783))], (5359 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _376781, _376785)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _376781), _376783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _376785), _376783)))], (5345 ^ _191474) ^ [_376490, _376492, _376494] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _376490), _376492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _376494), _376492)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _376492), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _376490, _376494))], (5373 ^ _191474) ^ [_377440, _377442, _377444] : [5374 ^ _191474 : [(5375 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _377440))], (5377 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377442, _377444)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _377440), _377442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _377440), _377444)))], (5363 ^ _191474) ^ [_377149, _377151, _377153] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _377149), _377151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _377149), _377153)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _377149), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _377151, _377153))], (5381 ^ _191474) ^ [_377764, _377766, _377768] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_377764, _377766), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_377764, _377768), hAPP(_377764, _377766)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _377768, _377766))), _377766)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_377764, _377768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_377764, _377768), hAPP(_377764, _377766)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _377768, _377766))), _377768)))], (5383 ^ _191474) ^ [_377951, _377953, _377955] : [class_Groups_Oordered__comm__monoid__add(_377951), c_Orderings_Oord__class_Oless__eq(_377951, _377953, c_Groups_Ozero__class_Ozero(_377951)), c_Orderings_Oord__class_Oless(_377951, _377955, c_Groups_Ozero__class_Ozero(_377951)), -(c_Orderings_Oord__class_Oless(_377951, c_Groups_Oplus__class_Oplus(_377951, _377953, _377955), c_Groups_Ozero__class_Ozero(_377951)))], (5397 ^ _191474) ^ [_378391, _378393, _378395] : [class_Groups_Oordered__comm__monoid__add(_378391), c_Orderings_Oord__class_Oless(_378391, _378393, c_Groups_Ozero__class_Ozero(_378391)), c_Orderings_Oord__class_Oless__eq(_378391, _378395, c_Groups_Ozero__class_Ozero(_378391)), -(c_Orderings_Oord__class_Oless(_378391, c_Groups_Oplus__class_Oplus(_378391, _378393, _378395), c_Groups_Ozero__class_Ozero(_378391)))], (5411 ^ _191474) ^ [_378845, _378847, _378849, _378851] : [class_Groups_Oordered__comm__monoid__add(_378845), c_Orderings_Oord__class_Oless__eq(_378845, c_Groups_Ozero__class_Ozero(_378845), _378847), c_Orderings_Oord__class_Oless(_378845, _378849, _378851), -(c_Orderings_Oord__class_Oless(_378845, _378849, c_Groups_Oplus__class_Oplus(_378845, _378847, _378851)))], (5425 ^ _191474) ^ [_379305, _379307, _379309, _379311] : [class_Groups_Oordered__comm__monoid__add(_379305), c_Orderings_Oord__class_Oless(_379305, c_Groups_Ozero__class_Ozero(_379305), _379307), c_Orderings_Oord__class_Oless__eq(_379305, _379309, _379311), -(c_Orderings_Oord__class_Oless(_379305, _379309, c_Groups_Oplus__class_Oplus(_379305, _379307, _379311)))], (5439 ^ _191474) ^ [_379751, _379753, _379755] : [class_Groups_Oordered__comm__monoid__add(_379751), c_Orderings_Oord__class_Oless__eq(_379751, c_Groups_Ozero__class_Ozero(_379751), _379753), c_Orderings_Oord__class_Oless(_379751, c_Groups_Ozero__class_Ozero(_379751), _379755), -(c_Orderings_Oord__class_Oless(_379751, c_Groups_Ozero__class_Ozero(_379751), c_Groups_Oplus__class_Oplus(_379751, _379753, _379755)))], (5453 ^ _191474) ^ [_380191, _380193, _380195] : [class_Groups_Oordered__comm__monoid__add(_380191), c_Orderings_Oord__class_Oless(_380191, c_Groups_Ozero__class_Ozero(_380191), _380193), c_Orderings_Oord__class_Oless__eq(_380191, c_Groups_Ozero__class_Ozero(_380191), _380195), -(c_Orderings_Oord__class_Oless(_380191, c_Groups_Ozero__class_Ozero(_380191), c_Groups_Oplus__class_Oplus(_380191, _380193, _380195)))], (5467 ^ _191474) ^ [_380659, _380661, _380663, _380665, _380667] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _380659, _380661), 5470 ^ _191474 : [(5471 ^ _191474) ^ [] : [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), _380661), _380663), _380665), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _380659), _380663), _380667)), -(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, _380661, _380659)), _380663), _380665), _380667))], (5477 ^ _191474) ^ [] : [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, _380661, _380659)), _380663), _380665), _380667), -(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), _380661), _380663), _380665), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _380659), _380663), _380667)))]]], (5483 ^ _191474) ^ [_381248] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _381248) = _381248)], (5485 ^ _191474) ^ [_381387, _381389] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _381387), _381389), 5488 ^ _191474 : [(5489 ^ _191474) ^ [] : [-(_381387 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5491 ^ _191474) ^ [] : [-(_381389 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5493 ^ _191474) ^ [_381636, _381638] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _381636), _381638)), _381636 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _381638 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5503 ^ _191474) ^ [_381920] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _381920), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _381920)], (5505 ^ _191474) ^ [_382062, _382064] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382062), _382064) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 5508 ^ _191474 : [(5509 ^ _191474) ^ [] : [-(_382062 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5511 ^ _191474) ^ [] : [-(_382064 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5513 ^ _191474) ^ [_382311, _382313] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382311), _382313) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _382311 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _382313 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5523 ^ _191474) ^ [_382609, _382611] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382609), _382611) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382611), _382609))], (5525 ^ _191474) ^ [_382729, _382731, _382733] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382729), _382731)), _382733) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382731), _382733)))], (5527 ^ _191474) ^ [_382863, _382865, _382867] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _382863, _382865)), _382867) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382863), _382867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382865), _382867)))], (5529 ^ _191474) ^ [_382999, _383001, _383003] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _382999, _383001), _383003) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _382999, _383003), _383001))], (5531 ^ _191474) ^ [_383125, _383127, _383129] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _383125), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _383127, _383129)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _383125), _383127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _383125), _383129)))], (5533 ^ _191474) ^ [_383262, _383264] : [class_Groups_Ozero(_383262), 5536 ^ _191474 : [(5537 ^ _191474) ^ [] : [c_Groups_Ozero__class_Ozero(_383262) = _383264, -(_383264 = c_Groups_Ozero__class_Ozero(_383262))], (5543 ^ _191474) ^ [] : [_383264 = c_Groups_Ozero__class_Ozero(_383262), -(c_Groups_Ozero__class_Ozero(_383262) = _383264)]]], (5549 ^ _191474) ^ [_383760, _383762, _383764, _383766] : [class_Groups_Oab__semigroup__mult(_383760), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383760), _383762), _383764)), _383766) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383760), _383762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383760), _383764), _383766)))], (5555 ^ _191474) ^ [_384072, _384074, _384076, _384078] : [class_Groups_Oab__semigroup__add(_384072), -(c_Groups_Oplus__class_Oplus(_384072, c_Groups_Oplus__class_Oplus(_384072, _384074, _384076), _384078) = c_Groups_Oplus__class_Oplus(_384072, _384074, c_Groups_Oplus__class_Oplus(_384072, _384076, _384078)))], (5561 ^ _191474) ^ [_384352, _384354, _384356, _384358] : [class_Groups_Ocancel__semigroup__add(_384352), 5564 ^ _191474 : [(5565 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_384352, _384354, _384356) = c_Groups_Oplus__class_Oplus(_384352, _384354, _384358), -(_384356 = _384358)], (5571 ^ _191474) ^ [] : [_384356 = _384358, -(c_Groups_Oplus__class_Oplus(_384352, _384354, _384356) = c_Groups_Oplus__class_Oplus(_384352, _384354, _384358))]]], (5577 ^ _191474) ^ [_384894, _384896, _384898, _384900] : [class_Groups_Ocancel__semigroup__add(_384894), 5580 ^ _191474 : [(5581 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_384894, _384896, _384898) = c_Groups_Oplus__class_Oplus(_384894, _384900, _384898), -(_384896 = _384900)], (5587 ^ _191474) ^ [] : [_384896 = _384900, -(c_Groups_Oplus__class_Oplus(_384894, _384896, _384898) = c_Groups_Oplus__class_Oplus(_384894, _384900, _384898))]]], (5593 ^ _191474) ^ [_385436, _385438, _385440, _385442] : [class_Groups_Ocancel__semigroup__add(_385436), c_Groups_Oplus__class_Oplus(_385436, _385438, _385440) = c_Groups_Oplus__class_Oplus(_385436, _385438, _385442), -(_385440 = _385442)], (5603 ^ _191474) ^ [_385797, _385799, _385801, _385803] : [class_Groups_Ocancel__ab__semigroup__add(_385797), c_Groups_Oplus__class_Oplus(_385797, _385799, _385801) = c_Groups_Oplus__class_Oplus(_385797, _385799, _385803), -(_385801 = _385803)], (5613 ^ _191474) ^ [_386158, _386160, _386162, _386164] : [class_Groups_Ocancel__semigroup__add(_386158), c_Groups_Oplus__class_Oplus(_386158, _386160, _386162) = c_Groups_Oplus__class_Oplus(_386158, _386164, _386162), -(_386160 = _386164)], (5623 ^ _191474) ^ [_386533, _386535, _386537, _386539, _386541] : [class_Groups_Oab__group__add(_386533), c_Groups_Ominus__class_Ominus(_386533, _386535, _386537) = c_Groups_Ominus__class_Ominus(_386533, _386539, _386541), 5630 ^ _191474 : [(5631 ^ _191474) ^ [] : [_386535 = _386537, -(_386539 = _386541)], (5637 ^ _191474) ^ [] : [_386539 = _386541, -(_386535 = _386537)]]], (5643 ^ _191474) ^ [_387156, _387158] : [class_Groups_Oone(_387156), 5646 ^ _191474 : [(5647 ^ _191474) ^ [] : [c_Groups_Oone__class_Oone(_387156) = _387158, -(_387158 = c_Groups_Oone__class_Oone(_387156))], (5653 ^ _191474) ^ [] : [_387158 = c_Groups_Oone__class_Oone(_387156), -(c_Groups_Oone__class_Oone(_387156) = _387158)]]], (5669 ^ _191474) ^ [_387955, _387957, _387959] : [5670 ^ _191474 : [(5671 ^ _191474) ^ [] : [_387955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5673 ^ _191474) ^ [] : [_387957 = _387959]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _387955), _387957) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _387955), _387959))], (5659 ^ _191474) ^ [_387669, _387671, _387673] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _387669), _387671) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _387669), _387673), -(_387669 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_387671 = _387673)], (5677 ^ _191474) ^ [_388286, _388288, _388290, _388292] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388286), _388288), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388290), _388288), _388292)) = 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, _388286, _388290)), _388288), _388292))], (5679 ^ _191474) ^ [_388433, _388435] : [class_Groups_Omonoid__add(_388433), -(c_Groups_Oplus__class_Oplus(_388433, c_Groups_Ozero__class_Ozero(_388433), _388435) = _388435)], (5685 ^ _191474) ^ [_388653, _388655] : [class_Groups_Ocomm__monoid__add(_388653), -(c_Groups_Oplus__class_Oplus(_388653, c_Groups_Ozero__class_Ozero(_388653), _388655) = _388655)], (5691 ^ _191474) ^ [_388873, _388875] : [class_Groups_Olinordered__ab__group__add(_388873), 5694 ^ _191474 : [(5695 ^ _191474) ^ [] : [c_Groups_Ozero__class_Ozero(_388873) = c_Groups_Oplus__class_Oplus(_388873, _388875, _388875), -(_388875 = c_Groups_Ozero__class_Ozero(_388873))], (5701 ^ _191474) ^ [] : [_388875 = c_Groups_Ozero__class_Ozero(_388873), -(c_Groups_Ozero__class_Ozero(_388873) = c_Groups_Oplus__class_Oplus(_388873, _388875, _388875))]]], (5707 ^ _191474) ^ [_389355, _389357] : [class_Groups_Omonoid__add(_389355), -(c_Groups_Oplus__class_Oplus(_389355, _389357, c_Groups_Ozero__class_Ozero(_389355)) = _389357)], (5713 ^ _191474) ^ [_389575, _389577] : [class_Groups_Ocomm__monoid__add(_389575), -(c_Groups_Oplus__class_Oplus(_389575, _389577, c_Groups_Ozero__class_Ozero(_389575)) = _389577)], (5719 ^ _191474) ^ [_389823, _389825, _389827, _389829] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_389823), 5722 ^ _191474 : [(5723 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_389823, c_Groups_Oplus__class_Oplus(_389823, _389825, _389827), c_Groups_Oplus__class_Oplus(_389823, _389829, _389827)), -(c_Orderings_Oord__class_Oless__eq(_389823, _389825, _389829))], (5729 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_389823, _389825, _389829), -(c_Orderings_Oord__class_Oless__eq(_389823, c_Groups_Oplus__class_Oplus(_389823, _389825, _389827), c_Groups_Oplus__class_Oplus(_389823, _389829, _389827)))]]], (5735 ^ _191474) ^ [_390371, _390373, _390375, _390377] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_390371), 5738 ^ _191474 : [(5739 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_390371, c_Groups_Oplus__class_Oplus(_390371, _390373, _390375), c_Groups_Oplus__class_Oplus(_390371, _390373, _390377)), -(c_Orderings_Oord__class_Oless__eq(_390371, _390375, _390377))], (5745 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_390371, _390375, _390377), -(c_Orderings_Oord__class_Oless__eq(_390371, c_Groups_Oplus__class_Oplus(_390371, _390373, _390375), c_Groups_Oplus__class_Oplus(_390371, _390373, _390377)))]]], (5751 ^ _191474) ^ [_390919, _390921, _390923, _390925] : [class_Groups_Oordered__ab__semigroup__add(_390919), c_Orderings_Oord__class_Oless__eq(_390919, _390921, _390923), -(c_Orderings_Oord__class_Oless__eq(_390919, c_Groups_Oplus__class_Oplus(_390919, _390921, _390925), c_Groups_Oplus__class_Oplus(_390919, _390923, _390925)))], (5761 ^ _191474) ^ [_391284, _391286, _391288, _391290] : [class_Groups_Oordered__ab__semigroup__add(_391284), c_Orderings_Oord__class_Oless__eq(_391284, _391286, _391288), -(c_Orderings_Oord__class_Oless__eq(_391284, c_Groups_Oplus__class_Oplus(_391284, _391290, _391286), c_Groups_Oplus__class_Oplus(_391284, _391290, _391288)))], (5771 ^ _191474) ^ [_391663, _391665, _391667, _391669, _391671] : [class_Groups_Oordered__ab__semigroup__add(_391663), c_Orderings_Oord__class_Oless__eq(_391663, _391665, _391667), c_Orderings_Oord__class_Oless__eq(_391663, _391669, _391671), -(c_Orderings_Oord__class_Oless__eq(_391663, c_Groups_Oplus__class_Oplus(_391663, _391665, _391669), c_Groups_Oplus__class_Oplus(_391663, _391667, _391671)))], (5785 ^ _191474) ^ [_392141, _392143, _392145, _392147] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_392141), c_Orderings_Oord__class_Oless__eq(_392141, c_Groups_Oplus__class_Oplus(_392141, _392143, _392145), c_Groups_Oplus__class_Oplus(_392141, _392147, _392145)), -(c_Orderings_Oord__class_Oless__eq(_392141, _392143, _392147))], (5795 ^ _191474) ^ [_392506, _392508, _392510, _392512] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_392506), c_Orderings_Oord__class_Oless__eq(_392506, c_Groups_Oplus__class_Oplus(_392506, _392508, _392510), c_Groups_Oplus__class_Oplus(_392506, _392508, _392512)), -(c_Orderings_Oord__class_Oless__eq(_392506, _392510, _392512))], (5805 ^ _191474) ^ [_392871, _392873, _392875, _392877] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_392871), c_Orderings_Oord__class_Oless(_392871, c_Groups_Oplus__class_Oplus(_392871, _392873, _392875), c_Groups_Oplus__class_Oplus(_392871, _392873, _392877)), -(c_Orderings_Oord__class_Oless(_392871, _392875, _392877))], (5815 ^ _191474) ^ [_393236, _393238, _393240, _393242] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_393236), c_Orderings_Oord__class_Oless(_393236, c_Groups_Oplus__class_Oplus(_393236, _393238, _393240), c_Groups_Oplus__class_Oplus(_393236, _393242, _393240)), -(c_Orderings_Oord__class_Oless(_393236, _393238, _393242))], (5825 ^ _191474) ^ [_393615, _393617, _393619, _393621, _393623] : [class_Groups_Oordered__cancel__ab__semigroup__add(_393615), c_Orderings_Oord__class_Oless(_393615, _393617, _393619), c_Orderings_Oord__class_Oless(_393615, _393621, _393623), -(c_Orderings_Oord__class_Oless(_393615, c_Groups_Oplus__class_Oplus(_393615, _393617, _393621), c_Groups_Oplus__class_Oplus(_393615, _393619, _393623)))], (5839 ^ _191474) ^ [_394093, _394095, _394097, _394099] : [class_Groups_Oordered__cancel__ab__semigroup__add(_394093), c_Orderings_Oord__class_Oless(_394093, _394095, _394097), -(c_Orderings_Oord__class_Oless(_394093, c_Groups_Oplus__class_Oplus(_394093, _394099, _394095), c_Groups_Oplus__class_Oplus(_394093, _394099, _394097)))], (5849 ^ _191474) ^ [_394458, _394460, _394462, _394464] : [class_Groups_Oordered__cancel__ab__semigroup__add(_394458), c_Orderings_Oord__class_Oless(_394458, _394460, _394462), -(c_Orderings_Oord__class_Oless(_394458, c_Groups_Oplus__class_Oplus(_394458, _394460, _394464), c_Groups_Oplus__class_Oplus(_394458, _394462, _394464)))], (5859 ^ _191474) ^ [_394823, _394825, _394827, _394829] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_394823), 5862 ^ _191474 : [(5863 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_394823, c_Groups_Oplus__class_Oplus(_394823, _394825, _394827), c_Groups_Oplus__class_Oplus(_394823, _394825, _394829)), -(c_Orderings_Oord__class_Oless(_394823, _394827, _394829))], (5869 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_394823, _394827, _394829), -(c_Orderings_Oord__class_Oless(_394823, c_Groups_Oplus__class_Oplus(_394823, _394825, _394827), c_Groups_Oplus__class_Oplus(_394823, _394825, _394829)))]]], (5875 ^ _191474) ^ [_395371, _395373, _395375, _395377] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_395371), 5878 ^ _191474 : [(5879 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_395371, c_Groups_Oplus__class_Oplus(_395371, _395373, _395375), c_Groups_Oplus__class_Oplus(_395371, _395377, _395375)), -(c_Orderings_Oord__class_Oless(_395371, _395373, _395377))], (5885 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_395371, _395373, _395377), -(c_Orderings_Oord__class_Oless(_395371, c_Groups_Oplus__class_Oplus(_395371, _395373, _395375), c_Groups_Oplus__class_Oplus(_395371, _395377, _395375)))]]], (5891 ^ _191474) ^ [_395905, _395907, _395909] : [class_Groups_Ogroup__add(_395905), 5894 ^ _191474 : [(5895 ^ _191474) ^ [] : [c_Groups_Ominus__class_Ominus(_395905, _395907, _395909) = c_Groups_Ozero__class_Ozero(_395905), -(_395907 = _395909)], (5901 ^ _191474) ^ [] : [_395907 = _395909, -(c_Groups_Ominus__class_Ominus(_395905, _395907, _395909) = c_Groups_Ozero__class_Ozero(_395905))]]], (5907 ^ _191474) ^ [_396411, _396413, _396415] : [class_Groups_Oab__group__add(_396411), 5910 ^ _191474 : [(5911 ^ _191474) ^ [] : [_396413 = _396415, -(c_Groups_Ominus__class_Ominus(_396411, _396413, _396415) = c_Groups_Ozero__class_Ozero(_396411))], (5917 ^ _191474) ^ [] : [c_Groups_Ominus__class_Ominus(_396411, _396413, _396415) = c_Groups_Ozero__class_Ozero(_396411), -(_396413 = _396415)]]], (5923 ^ _191474) ^ [_396903, _396905] : [class_Groups_Ogroup__add(_396903), -(c_Groups_Ominus__class_Ominus(_396903, _396905, _396905) = c_Groups_Ozero__class_Ozero(_396903))], (5929 ^ _191474) ^ [_397123, _397125] : [class_Groups_Ogroup__add(_397123), -(c_Groups_Ominus__class_Ominus(_397123, _397125, c_Groups_Ozero__class_Ozero(_397123)) = _397125)], (5935 ^ _191474) ^ [_397385, _397387, _397389, _397391, _397393] : [class_Groups_Oordered__ab__group__add(_397385), c_Groups_Ominus__class_Ominus(_397385, _397387, _397389) = c_Groups_Ominus__class_Ominus(_397385, _397391, _397393), 5942 ^ _191474 : [(5943 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_397385, _397387, _397389), -(c_Orderings_Oord__class_Oless__eq(_397385, _397391, _397393))], (5949 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_397385, _397391, _397393), -(c_Orderings_Oord__class_Oless__eq(_397385, _397387, _397389))]]], (5955 ^ _191474) ^ [_398056, _398058, _398060, _398062, _398064] : [class_Groups_Oordered__ab__group__add(_398056), c_Groups_Ominus__class_Ominus(_398056, _398058, _398060) = c_Groups_Ominus__class_Ominus(_398056, _398062, _398064), 5962 ^ _191474 : [(5963 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_398056, _398058, _398060), -(c_Orderings_Oord__class_Oless(_398056, _398062, _398064))], (5969 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_398056, _398062, _398064), -(c_Orderings_Oord__class_Oless(_398056, _398058, _398060))]]], (5975 ^ _191474) ^ [_398685, _398687] : [class_Groups_Ocomm__monoid__mult(_398685), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_398685), _398687), c_Groups_Oone__class_Oone(_398685)) = _398687)], (5981 ^ _191474) ^ [_398913, _398915] : [class_Groups_Omonoid__mult(_398913), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_398913), _398915), c_Groups_Oone__class_Oone(_398913)) = _398915)], (5987 ^ _191474) ^ [_399141, _399143] : [class_Groups_Ocomm__monoid__mult(_399141), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_399141), c_Groups_Oone__class_Oone(_399141)), _399143) = _399143)], (5993 ^ _191474) ^ [_399369, _399371] : [class_Groups_Omonoid__mult(_399369), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_399369), c_Groups_Oone__class_Oone(_399369)), _399371) = _399371)], (5999 ^ _191474) ^ [_399611, _399613, _399615] : [class_Groups_Ogroup__add(_399611), -(c_Groups_Ominus__class_Ominus(_399611, c_Groups_Oplus__class_Oplus(_399611, _399613, _399615), _399615) = _399613)], (6005 ^ _191474) ^ [_399855, _399857, _399859] : [class_Groups_Ogroup__add(_399855), -(c_Groups_Oplus__class_Oplus(_399855, c_Groups_Ominus__class_Ominus(_399855, _399857, _399859), _399859) = _399857)], (6011 ^ _191474) ^ [_400099, _400101, _400103] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400099), 6014 ^ _191474 : [(6015 ^ _191474) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400099), _400101) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400099), _400103), -(_400101 = _400103)], (6021 ^ _191474) ^ [] : [_400101 = _400103, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400099), _400101) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400099), _400103))]]], (6027 ^ _191474) ^ [_400627, _400629, _400631] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400627), 6030 ^ _191474 : [(6031 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400627), _400629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400627), _400631)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _400629, _400631))], (6037 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _400629, _400631), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400627), _400629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400627), _400631)))]]], (6043 ^ _191474) ^ [_401189, _401191, _401193, _401195, _401197] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401189, _401191), 6046 ^ _191474 : [(6047 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401189), _401193), _401195) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401191), _401193), _401197), -(_401195 = 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, _401191, _401189)), _401193), _401197))], (6053 ^ _191474) ^ [] : [_401195 = 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, _401191, _401189)), _401193), _401197), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401189), _401193), _401195) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401191), _401193), _401197))]]], (6059 ^ _191474) ^ [_401843, _401845, _401847, _401849, _401851] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401843, _401845), -(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), _401843), _401847), _401849), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401845), _401847), _401851)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401849, 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, _401845, _401843)), _401847), _401851)))], (6065 ^ _191474) ^ [_402199, _402201, _402203, _402205, _402207] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402199, _402201), 6068 ^ _191474 : [(6069 ^ _191474) ^ [] : [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), _402199), _402203), _402205), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402201), _402203), _402207)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402205, 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, _402201, _402199)), _402203), _402207)))], (6075 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402205, 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, _402201, _402199)), _402203), _402207)), -(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), _402199), _402203), _402205), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402201), _402203), _402207)))]]], (6081 ^ _191474) ^ [_402859, _402861, _402863, _402865, _402867] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402859, _402861), 6084 ^ _191474 : [(6085 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402861), _402863), _402865) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402859), _402863), _402867), -(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, _402861, _402859)), _402863), _402865) = _402867)], (6091 ^ _191474) ^ [] : [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, _402861, _402859)), _402863), _402865) = _402867, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402861), _402863), _402865) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402859), _402863), _402867))]]], (6097 ^ _191474) ^ [_403513, _403515, _403517, _403519, _403521] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403513, _403515), -(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), _403515), _403517), _403519), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403513), _403517), _403521)) = 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, _403515, _403513)), _403517), _403519), _403521))], (6103 ^ _191474) ^ [_403869, _403871, _403873, _403875, _403877] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403869, _403871), 6106 ^ _191474 : [(6107 ^ _191474) ^ [] : [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), _403871), _403873), _403875), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403869), _403873), _403877)), -(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, _403871, _403869)), _403873), _403875), _403877))], (6113 ^ _191474) ^ [] : [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, _403871, _403869)), _403873), _403875), _403877), -(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), _403871), _403873), _403875), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403869), _403873), _403877)))]]], (6119 ^ _191474) ^ [_404487, _404489] : [class_Groups_Olinordered__ab__group__add(_404487), 6122 ^ _191474 : [(6123 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_404487, c_Groups_Ozero__class_Ozero(_404487), c_Groups_Oplus__class_Oplus(_404487, _404489, _404489)), -(c_Orderings_Oord__class_Oless__eq(_404487, c_Groups_Ozero__class_Ozero(_404487), _404489))], (6129 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_404487, c_Groups_Ozero__class_Ozero(_404487), _404489), -(c_Orderings_Oord__class_Oless__eq(_404487, c_Groups_Ozero__class_Ozero(_404487), c_Groups_Oplus__class_Oplus(_404487, _404489, _404489)))]]], (6135 ^ _191474) ^ [_404975, _404977] : [class_Groups_Olinordered__ab__group__add(_404975), 6138 ^ _191474 : [(6139 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_404975, c_Groups_Oplus__class_Oplus(_404975, _404977, _404977), c_Groups_Ozero__class_Ozero(_404975)), -(c_Orderings_Oord__class_Oless__eq(_404975, _404977, c_Groups_Ozero__class_Ozero(_404975)))], (6145 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_404975, _404977, c_Groups_Ozero__class_Ozero(_404975)), -(c_Orderings_Oord__class_Oless__eq(_404975, c_Groups_Oplus__class_Oplus(_404975, _404977, _404977), c_Groups_Ozero__class_Ozero(_404975)))]]], (6151 ^ _191474) ^ [_405477, _405479, _405481] : [class_Groups_Oordered__comm__monoid__add(_405477), c_Orderings_Oord__class_Oless__eq(_405477, c_Groups_Ozero__class_Ozero(_405477), _405479), c_Orderings_Oord__class_Oless__eq(_405477, c_Groups_Ozero__class_Ozero(_405477), _405481), -(c_Orderings_Oord__class_Oless__eq(_405477, c_Groups_Ozero__class_Ozero(_405477), c_Groups_Oplus__class_Oplus(_405477, _405479, _405481)))], (6165 ^ _191474) ^ [_405917, _405919, _405921] : [class_Groups_Oordered__comm__monoid__add(_405917), c_Orderings_Oord__class_Oless__eq(_405917, c_Groups_Ozero__class_Ozero(_405917), _405919), c_Orderings_Oord__class_Oless__eq(_405917, c_Groups_Ozero__class_Ozero(_405917), _405921), 6176 ^ _191474 : [(6177 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_405917, _405919, _405921) = c_Groups_Ozero__class_Ozero(_405917), 6180 ^ _191474 : [(6181 ^ _191474) ^ [] : [-(_405919 = c_Groups_Ozero__class_Ozero(_405917))], (6183 ^ _191474) ^ [] : [-(_405921 = c_Groups_Ozero__class_Ozero(_405917))]]], (6185 ^ _191474) ^ [] : [-(c_Groups_Oplus__class_Oplus(_405917, _405919, _405921) = c_Groups_Ozero__class_Ozero(_405917)), _405919 = c_Groups_Ozero__class_Ozero(_405917), _405921 = c_Groups_Ozero__class_Ozero(_405917)]]], (6195 ^ _191474) ^ [_406811, _406813, _406815, _406817] : [class_Groups_Oordered__comm__monoid__add(_406811), c_Orderings_Oord__class_Oless__eq(_406811, c_Groups_Ozero__class_Ozero(_406811), _406813), c_Orderings_Oord__class_Oless__eq(_406811, _406815, _406817), -(c_Orderings_Oord__class_Oless__eq(_406811, _406815, c_Groups_Oplus__class_Oplus(_406811, _406813, _406817)))], (6209 ^ _191474) ^ [_407271, _407273, _407275, _407277] : [class_Groups_Oordered__comm__monoid__add(_407271), c_Orderings_Oord__class_Oless__eq(_407271, c_Groups_Ozero__class_Ozero(_407271), _407273), c_Orderings_Oord__class_Oless__eq(_407271, _407275, _407277), -(c_Orderings_Oord__class_Oless__eq(_407271, _407275, c_Groups_Oplus__class_Oplus(_407271, _407277, _407273)))], (6223 ^ _191474) ^ [_407717, _407719, _407721] : [class_Groups_Oordered__comm__monoid__add(_407717), c_Orderings_Oord__class_Oless__eq(_407717, _407719, c_Groups_Ozero__class_Ozero(_407717)), c_Orderings_Oord__class_Oless__eq(_407717, _407721, c_Groups_Ozero__class_Ozero(_407717)), -(c_Orderings_Oord__class_Oless__eq(_407717, c_Groups_Oplus__class_Oplus(_407717, _407719, _407721), c_Groups_Ozero__class_Ozero(_407717)))], (6237 ^ _191474) ^ [_408143, _408145] : [class_Groups_Olinordered__ab__group__add(_408143), 6240 ^ _191474 : [(6241 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_408143, c_Groups_Ozero__class_Ozero(_408143), c_Groups_Oplus__class_Oplus(_408143, _408145, _408145)), -(c_Orderings_Oord__class_Oless(_408143, c_Groups_Ozero__class_Ozero(_408143), _408145))], (6247 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_408143, c_Groups_Ozero__class_Ozero(_408143), _408145), -(c_Orderings_Oord__class_Oless(_408143, c_Groups_Ozero__class_Ozero(_408143), c_Groups_Oplus__class_Oplus(_408143, _408145, _408145)))]]], (6253 ^ _191474) ^ [_408631, _408633] : [class_Groups_Olinordered__ab__group__add(_408631), 6256 ^ _191474 : [(6257 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_408631, c_Groups_Oplus__class_Oplus(_408631, _408633, _408633), c_Groups_Ozero__class_Ozero(_408631)), -(c_Orderings_Oord__class_Oless(_408631, _408633, c_Groups_Ozero__class_Ozero(_408631)))], (6263 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_408631, _408633, c_Groups_Ozero__class_Ozero(_408631)), -(c_Orderings_Oord__class_Oless(_408631, c_Groups_Oplus__class_Oplus(_408631, _408633, _408633), c_Groups_Ozero__class_Ozero(_408631)))]]], (6269 ^ _191474) ^ [_409133, _409135, _409137] : [class_Groups_Oordered__comm__monoid__add(_409133), c_Orderings_Oord__class_Oless(_409133, c_Groups_Ozero__class_Ozero(_409133), _409135), c_Orderings_Oord__class_Oless(_409133, c_Groups_Ozero__class_Ozero(_409133), _409137), -(c_Orderings_Oord__class_Oless(_409133, c_Groups_Ozero__class_Ozero(_409133), c_Groups_Oplus__class_Oplus(_409133, _409135, _409137)))], (6283 ^ _191474) ^ [_409573, _409575, _409577] : [class_Groups_Oordered__comm__monoid__add(_409573), c_Orderings_Oord__class_Oless(_409573, _409575, c_Groups_Ozero__class_Ozero(_409573)), c_Orderings_Oord__class_Oless(_409573, _409577, c_Groups_Ozero__class_Ozero(_409573)), -(c_Orderings_Oord__class_Oless(_409573, c_Groups_Oplus__class_Oplus(_409573, _409575, _409577), c_Groups_Ozero__class_Ozero(_409573)))], (6297 ^ _191474) ^ [_410041, _410043, _410045, _410047, _410049] : [class_Groups_Oordered__cancel__ab__semigroup__add(_410041), c_Orderings_Oord__class_Oless(_410041, _410043, _410045), c_Orderings_Oord__class_Oless__eq(_410041, _410047, _410049), -(c_Orderings_Oord__class_Oless(_410041, c_Groups_Oplus__class_Oplus(_410041, _410043, _410047), c_Groups_Oplus__class_Oplus(_410041, _410045, _410049)))], (6311 ^ _191474) ^ [_410533, _410535, _410537, _410539, _410541] : [class_Groups_Oordered__cancel__ab__semigroup__add(_410533), c_Orderings_Oord__class_Oless__eq(_410533, _410535, _410537), c_Orderings_Oord__class_Oless(_410533, _410539, _410541), -(c_Orderings_Oord__class_Oless(_410533, c_Groups_Oplus__class_Oplus(_410533, _410535, _410539), c_Groups_Oplus__class_Oplus(_410533, _410537, _410541)))], (6325 ^ _191474) ^ [_410997, _410999, _411001] : [class_Groups_Oordered__ab__group__add(_410997), 6328 ^ _191474 : [(6329 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_410997, _410999, _411001), -(c_Orderings_Oord__class_Oless__eq(_410997, c_Groups_Ominus__class_Ominus(_410997, _410999, _411001), c_Groups_Ozero__class_Ozero(_410997)))], (6335 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_410997, c_Groups_Ominus__class_Ominus(_410997, _410999, _411001), c_Groups_Ozero__class_Ozero(_410997)), -(c_Orderings_Oord__class_Oless__eq(_410997, _410999, _411001))]]], (6341 ^ _191474) ^ [_411509, _411511, _411513] : [class_Groups_Oordered__ab__group__add(_411509), 6344 ^ _191474 : [(6345 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_411509, _411511, _411513), -(c_Orderings_Oord__class_Oless(_411509, c_Groups_Ominus__class_Ominus(_411509, _411511, _411513), c_Groups_Ozero__class_Ozero(_411509)))], (6351 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_411509, c_Groups_Ominus__class_Ominus(_411509, _411511, _411513), c_Groups_Ozero__class_Ozero(_411509)), -(c_Orderings_Oord__class_Oless(_411509, _411511, _411513))]]], (6357 ^ _191474) ^ [_412021, _412023, _412025] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _412021), 6360 ^ _191474 : [(6361 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412021), _412023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412021), _412025)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412023, _412025))], (6367 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412023, _412025), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412021), _412023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412021), _412025)))]]], (6373 ^ _191474) ^ [_412583, _412585, _412587, _412589, _412591] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412583, _412585), 6376 ^ _191474 : [(6377 ^ _191474) ^ [] : [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), _412583), _412587), _412589), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412585), _412587), _412591)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _412589, 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, _412585, _412583)), _412587), _412591)))], (6383 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _412589, 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, _412585, _412583)), _412587), _412591)), -(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), _412583), _412587), _412589), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412585), _412587), _412591)))]]], (6389 ^ _191474) ^ [_413216] : [-(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), _413216), _413216))), -(_413216 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6395 ^ _191474) ^ [_413389] : [_413389 = 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), _413389), _413389))], (6401 ^ _191474) ^ [_413624, _413626, _413628] : [class_Rings_Ocomm__semiring__1(_413624), -(c_Groups_Oplus__class_Oplus(_413624, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413624), _413626), _413628), _413628) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413624), c_Groups_Oplus__class_Oplus(_413624, _413626, c_Groups_Oone__class_Oone(_413624))), _413628))], (6407 ^ _191474) ^ [_413904, _413906, _413908] : [class_Rings_Ocomm__semiring__1(_413904), -(c_Groups_Oplus__class_Oplus(_413904, _413906, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413904), _413908), _413906)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413904), c_Groups_Oplus__class_Oplus(_413904, _413908, c_Groups_Oone__class_Oone(_413904))), _413906))], (6413 ^ _191474) ^ [_414170, _414172] : [class_Rings_Ocomm__semiring__1(_414170), -(c_Groups_Oplus__class_Oplus(_414170, _414172, _414172) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414170), c_Groups_Oplus__class_Oplus(_414170, c_Groups_Oone__class_Oone(_414170), c_Groups_Oone__class_Oone(_414170))), _414172))], (6419 ^ _191474) ^ [_414474, _414476, _414478, _414480, _414482, _414484] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_414474), -(_414476 = c_Groups_Ozero__class_Ozero(_414474)), c_Groups_Oplus__class_Oplus(_414474, _414478, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414474), _414476), _414482)) = c_Groups_Oplus__class_Oplus(_414474, _414480, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414474), _414476), _414484)), _414478 = _414480, -(_414482 = _414484)], (6437 ^ _191474) ^ [_415094, _415096, _415098] : [class_Rings_Ocomm__semiring__1(_415094), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415094), _415096), _415098) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415094), _415098), _415096))], (6443 ^ _191474) ^ [_415368, _415370, _415372, _415374] : [class_Rings_Ocomm__semiring__1(_415368), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415368), _415370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415368), _415372), _415374)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415368), _415372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415368), _415370), _415374)))], (6449 ^ _191474) ^ [_415680, _415682, _415684, _415686] : [class_Rings_Ocomm__semiring__1(_415680), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415680), _415682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415680), _415684), _415686)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415680), _415682), _415684)), _415686))], (6455 ^ _191474) ^ [_415992, _415994, _415996, _415998] : [class_Rings_Ocomm__semiring__1(_415992), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415992), _415994), _415996)), _415998) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415992), _415994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_415992), _415996), _415998)))], (6461 ^ _191474) ^ [_416304, _416306, _416308, _416310] : [class_Rings_Ocomm__semiring__1(_416304), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416304), _416306), _416308)), _416310) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416304), _416306), _416310)), _416308))], (6467 ^ _191474) ^ [_416630, _416632, _416634, _416636, _416638] : [class_Rings_Ocomm__semiring__1(_416630), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416630), _416632), _416634)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416630), _416636), _416638)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416630), _416632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416630), _416634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416630), _416636), _416638))))], (6473 ^ _191474) ^ [_416994, _416996, _416998, _417000, _417002] : [class_Rings_Ocomm__semiring__1(_416994), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416994), _416996), _416998)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416994), _417000), _417002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416994), _417000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416994), _416996), _416998)), _417002)))], (6479 ^ _191474) ^ [_417358, _417360, _417362, _417364, _417366] : [class_Rings_Ocomm__semiring__1(_417358), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417358), _417360), _417362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417358), _417364), _417366)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417358), _417360), _417364)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_417358), _417362), _417366)))], (6485 ^ _191474) ^ [_417722, _417724, _417726, _417728, _417730] : [class_Rings_Ocomm__semiring__1(_417722), -(c_Groups_Oplus__class_Oplus(_417722, c_Groups_Oplus__class_Oplus(_417722, _417724, _417726), c_Groups_Oplus__class_Oplus(_417722, _417728, _417730)) = c_Groups_Oplus__class_Oplus(_417722, c_Groups_Oplus__class_Oplus(_417722, _417724, _417728), c_Groups_Oplus__class_Oplus(_417722, _417726, _417730)))], (6491 ^ _191474) ^ [_418024, _418026, _418028, _418030] : [class_Rings_Ocomm__semiring__1(_418024), -(c_Groups_Oplus__class_Oplus(_418024, c_Groups_Oplus__class_Oplus(_418024, _418026, _418028), _418030) = c_Groups_Oplus__class_Oplus(_418024, c_Groups_Oplus__class_Oplus(_418024, _418026, _418030), _418028))], (6497 ^ _191474) ^ [_418304, _418306, _418308, _418310] : [class_Rings_Ocomm__semiring__1(_418304), -(c_Groups_Oplus__class_Oplus(_418304, c_Groups_Oplus__class_Oplus(_418304, _418306, _418308), _418310) = c_Groups_Oplus__class_Oplus(_418304, _418306, c_Groups_Oplus__class_Oplus(_418304, _418308, _418310)))], (6503 ^ _191474) ^ [_418584, _418586, _418588, _418590] : [class_Rings_Ocomm__semiring__1(_418584), -(c_Groups_Oplus__class_Oplus(_418584, _418586, c_Groups_Oplus__class_Oplus(_418584, _418588, _418590)) = c_Groups_Oplus__class_Oplus(_418584, c_Groups_Oplus__class_Oplus(_418584, _418586, _418588), _418590))], (6509 ^ _191474) ^ [_418864, _418866, _418868, _418870] : [class_Rings_Ocomm__semiring__1(_418864), -(c_Groups_Oplus__class_Oplus(_418864, _418866, c_Groups_Oplus__class_Oplus(_418864, _418868, _418870)) = c_Groups_Oplus__class_Oplus(_418864, _418868, c_Groups_Oplus__class_Oplus(_418864, _418866, _418870)))], (6515 ^ _191474) ^ [_419130, _419132, _419134] : [class_Rings_Ocomm__semiring__1(_419130), -(c_Groups_Oplus__class_Oplus(_419130, _419132, _419134) = c_Groups_Oplus__class_Oplus(_419130, _419134, _419132))], (6521 ^ _191474) ^ [_419360, _419362] : [class_Rings_Ocomm__semiring__1(_419360), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_419360), c_Groups_Ozero__class_Ozero(_419360)), _419362) = c_Groups_Ozero__class_Ozero(_419360))], (6527 ^ _191474) ^ [_419592, _419594] : [class_Rings_Ocomm__semiring__1(_419592), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_419592), _419594), c_Groups_Ozero__class_Ozero(_419592)) = c_Groups_Ozero__class_Ozero(_419592))], (6533 ^ _191474) ^ [_419838, _419840, _419842] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_419838), 6536 ^ _191474 : [(6537 ^ _191474) ^ [] : [_419840 = c_Groups_Oplus__class_Oplus(_419838, _419840, _419842), -(_419842 = c_Groups_Ozero__class_Ozero(_419838))], (6543 ^ _191474) ^ [] : [_419842 = c_Groups_Ozero__class_Ozero(_419838), -(_419840 = c_Groups_Oplus__class_Oplus(_419838, _419840, _419842))]]], (6549 ^ _191474) ^ [_420330, _420332] : [class_Rings_Ocomm__semiring__1(_420330), -(c_Groups_Oplus__class_Oplus(_420330, _420332, c_Groups_Ozero__class_Ozero(_420330)) = _420332)], (6555 ^ _191474) ^ [_420550, _420552] : [class_Rings_Ocomm__semiring__1(_420550), -(c_Groups_Oplus__class_Oplus(_420550, c_Groups_Ozero__class_Ozero(_420550), _420552) = _420552)], (6561 ^ _191474) ^ [_420798, _420800, _420802, _420804] : [class_Rings_Ocomm__semiring__1(_420798), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420798), _420800), c_Groups_Oplus__class_Oplus(_420798, _420802, _420804)) = c_Groups_Oplus__class_Oplus(_420798, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420798), _420800), _420802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420798), _420800), _420804)))], (6567 ^ _191474) ^ [_421124, _421126, _421128, _421130, _421132] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_421124), 6570 ^ _191474 : [(6581 ^ _191474) ^ [] : [-(c_Groups_Oplus__class_Oplus(_421124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421124), _421126), _421130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421124), _421128), _421132)) = c_Groups_Oplus__class_Oplus(_421124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421124), _421126), _421132), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421124), _421128), _421130))), 6584 ^ _191474 : [(6585 ^ _191474) ^ [] : [_421126 = _421128], (6587 ^ _191474) ^ [] : [_421130 = _421132]]], (6571 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_421124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421124), _421126), _421130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421124), _421128), _421132)) = c_Groups_Oplus__class_Oplus(_421124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421124), _421126), _421132), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421124), _421128), _421130)), -(_421126 = _421128), -(_421130 = _421132)]]], (6589 ^ _191474) ^ [_421960, _421962, _421964, _421966] : [class_Rings_Ocomm__semiring__1(_421960), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421960), c_Groups_Oplus__class_Oplus(_421960, _421962, _421964)), _421966) = c_Groups_Oplus__class_Oplus(_421960, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421960), _421962), _421966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421960), _421964), _421966)))], (6595 ^ _191474) ^ [_422272, _422274, _422276, _422278] : [class_Rings_Ocomm__semiring__1(_422272), -(c_Groups_Oplus__class_Oplus(_422272, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422272), _422274), _422276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422272), _422278), _422276)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422272), c_Groups_Oplus__class_Oplus(_422272, _422274, _422278)), _422276))], (6601 ^ _191474) ^ [_422598, _422600, _422602, _422604, _422606] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_422598), 6604 ^ _191474 : [(6615 ^ _191474) ^ [] : [6616 ^ _191474 : [(6617 ^ _191474) ^ [] : [_422600 = _422604], (6619 ^ _191474) ^ [] : [_422602 = _422606]], -(c_Groups_Oplus__class_Oplus(_422598, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422598), _422600), _422602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422598), _422604), _422606)) = c_Groups_Oplus__class_Oplus(_422598, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422598), _422600), _422606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422598), _422604), _422602)))], (6605 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_422598, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422598), _422600), _422602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422598), _422604), _422606)) = c_Groups_Oplus__class_Oplus(_422598, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422598), _422600), _422606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422598), _422604), _422602)), -(_422600 = _422604), -(_422602 = _422606)]]], (6623 ^ _191474) ^ [_423400, _423402] : [class_Rings_Ocomm__semiring__1(_423400), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423400), c_Groups_Oone__class_Oone(_423400)), _423402) = _423402)], (6629 ^ _191474) ^ [_423628, _423630] : [class_Rings_Ocomm__semiring__1(_423628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423628), _423630), c_Groups_Oone__class_Oone(_423628)) = _423630)], (6635 ^ _191474) ^ [_423841, _423843] : [-(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _423841), _423843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _423841), _423841)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _423843, _423841))], (6637 ^ _191474) ^ [_423970, _423972] : [class_Rings_Olinordered__idom(_423970), 6640 ^ _191474 : [(6641 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_423970, c_Groups_Oplus__class_Oplus(_423970, _423972, _423972), c_Groups_Ozero__class_Ozero(_423970)), -(c_Orderings_Oord__class_Oless(_423970, _423972, c_Groups_Ozero__class_Ozero(_423970)))], (6647 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_423970, _423972, c_Groups_Ozero__class_Ozero(_423970)), -(c_Orderings_Oord__class_Oless(_423970, c_Groups_Oplus__class_Oplus(_423970, _423972, _423972), c_Groups_Ozero__class_Ozero(_423970)))]]], (6653 ^ _191474) ^ [_424458, _424460] : [class_Groups_Ozero(_424458), 6656 ^ _191474 : [(6657 ^ _191474) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_424458, _424460) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_424460 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424458)))], (6663 ^ _191474) ^ [] : [_424460 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424458)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_424458, _424460) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6669 ^ _191474) ^ [_424951, _424953, _424955] : [class_Rings_Oidom(_424951), 6672 ^ _191474 : [(6683 ^ _191474) ^ [] : [6684 ^ _191474 : [(6685 ^ _191474) ^ [] : [_424953 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424951))], (6687 ^ _191474) ^ [] : [-(c_Polynomial_Oorder(_424951, _424955, _424953) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_424951, _424953), _424955) = c_Groups_Ozero__class_Ozero(_424951))], (6673 ^ _191474) ^ [] : [hAPP(c_Polynomial_Opoly(_424951, _424953), _424955) = c_Groups_Ozero__class_Ozero(_424951), -(_424953 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424951))), c_Polynomial_Oorder(_424951, _424955, _424953) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (6692 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6690 ^ []))], (6694 ^ _191474) ^ [_425746] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _425746), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(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_cs____), _425746)), 6690 ^ []))], (6700 ^ _191474) ^ [_425974, _425976] : [class_Groups_Olinordered__ab__group__add(_425974), 6703 ^ _191474 : [(6704 ^ _191474) ^ [] : [c_Groups_Oplus__class_Oplus(_425974, _425976, _425976) = c_Groups_Ozero__class_Ozero(_425974), -(_425976 = c_Groups_Ozero__class_Ozero(_425974))], (6710 ^ _191474) ^ [] : [_425976 = c_Groups_Ozero__class_Ozero(_425974), -(c_Groups_Oplus__class_Oplus(_425974, _425976, _425976) = c_Groups_Ozero__class_Ozero(_425974))]]], (6716 ^ _191474) ^ [_426470, _426472, _426474] : [class_Rings_Oidom(_426470), -(_426472 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_426470))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(_426470, _426474, _426472), c_Polynomial_Odegree(_426470, _426472)))], (6727 ^ _191474) ^ [] : [-(c_Polynomial_Odegree(tc_Complex_Ocomplex, 6725 ^ []) = c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))], (6729 ^ _191474) ^ [_426894] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 6725 ^ []), _426894) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_z, _426894)))], (6731 ^ _191474) ^ [_427013, _427015] : [class_Orderings_Opreorder(_427013), -(c_Orderings_Oord__class_Oless__eq(_427013, _427015, _427015))], (6737 ^ _191474) ^ [_427223, _427225] : [class_RealVector_Oreal__normed__field(_427223), 6741 ^ _191474 : [(6742 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6740 ^ [_427223, _427225]))], (6744 ^ _191474) ^ [_427514] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_427223, c_Rings_Oinverse__class_Odivide(_427223, _427514, _427225)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_427223, _427514)), 6740 ^ [_427223, _427225])))]]], (6746 ^ _191474) ^ [_427656, _427658] : [class_RealVector_Oreal__normed__algebra(_427656), 6750 ^ _191474 : [(6751 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6749 ^ [_427656, _427658]))], (6753 ^ _191474) ^ [_427955] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_427656, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427656), _427955), _427658)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_427656, _427955)), 6749 ^ [_427656, _427658])))]]], (6755 ^ _191474) ^ [_428115, _428117, _428119] : [class_Orderings_Olinorder(_428115), -(c_Orderings_Oord__class_Oless__eq(_428115, _428117, _428119)), -(c_Orderings_Oord__class_Oless__eq(_428115, _428119, _428117))], (6765 ^ _191474) ^ [_428471, _428473, _428475, _428477, _428479] : [class_Orderings_Oord(_428471), c_Orderings_Oord__class_Oless__eq(tc_fun(_428473, _428471), _428475, _428477), -(c_Orderings_Oord__class_Oless__eq(_428471, hAPP(_428475, _428479), hAPP(_428477, _428479)))], (6775 ^ _191474) ^ [_428848, _428850, _428852, _428854] : [class_Orderings_Oorder(_428848), c_Orderings_Oord__class_Oless__eq(_428848, _428850, _428852), c_Orderings_Oord__class_Oless__eq(_428848, _428854, _428850), -(c_Orderings_Oord__class_Oless__eq(_428848, _428854, _428852))], (6789 ^ _191474) ^ [_429282, _429284, _429286] : [class_Orderings_Oorder(_429282), c_Orderings_Oord__class_Oless__eq(_429282, _429284, _429286), c_Orderings_Oord__class_Oless__eq(_429282, _429286, _429284), -(_429286 = _429284)], (6803 ^ _191474) ^ [_429714, _429716, _429718, _429720] : [class_Orderings_Opreorder(_429714), c_Orderings_Oord__class_Oless__eq(_429714, _429716, _429718), c_Orderings_Oord__class_Oless__eq(_429714, _429718, _429720), -(c_Orderings_Oord__class_Oless__eq(_429714, _429716, _429720))], (6817 ^ _191474) ^ [_430148, _430150, _430152] : [class_Orderings_Oorder(_430148), c_Orderings_Oord__class_Oless__eq(_430148, _430150, _430152), c_Orderings_Oord__class_Oless__eq(_430148, _430152, _430150), -(_430150 = _430152)], (6831 ^ _191474) ^ [_430580, _430582, _430584, _430586] : [class_Orderings_Oorder(_430580), c_Orderings_Oord__class_Oless__eq(_430580, _430582, _430584), _430582 = _430586, -(c_Orderings_Oord__class_Oless__eq(_430580, _430586, _430584))], (6845 ^ _191474) ^ [_431026, _431028, _431030, _431032] : [class_Orderings_Oord(_431026), c_Orderings_Oord__class_Oless__eq(_431026, _431028, _431030), _431030 = _431032, -(c_Orderings_Oord__class_Oless__eq(_431026, _431028, _431032))], (6859 ^ _191474) ^ [_431472, _431474, _431476, _431478] : [class_Orderings_Oorder(_431472), _431474 = _431476, c_Orderings_Oord__class_Oless__eq(_431472, _431478, _431476), -(c_Orderings_Oord__class_Oless__eq(_431472, _431478, _431474))], (6873 ^ _191474) ^ [_431918, _431920, _431922, _431924] : [class_Orderings_Oord(_431918), _431920 = _431922, c_Orderings_Oord__class_Oless__eq(_431918, _431922, _431924), -(c_Orderings_Oord__class_Oless__eq(_431918, _431920, _431924))], (6887 ^ _191474) ^ [_432350, _432352, _432354] : [class_Orderings_Oorder(_432350), c_Orderings_Oord__class_Oless__eq(_432350, _432352, _432354), 6894 ^ _191474 : [(6895 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_432350, _432354, _432352), -(_432354 = _432352)], (6901 ^ _191474) ^ [] : [_432354 = _432352, -(c_Orderings_Oord__class_Oless__eq(_432350, _432354, _432352))]]], (6907 ^ _191474) ^ [_432964, _432966, _432968, _432970, _432972] : [class_Orderings_Oord(_432964), c_Orderings_Oord__class_Oless__eq(tc_fun(_432966, _432964), _432968, _432970), -(c_Orderings_Oord__class_Oless__eq(_432964, hAPP(_432968, _432972), hAPP(_432970, _432972)))], (6917 ^ _191474) ^ [_433327, _433329, _433331] : [class_Orderings_Opreorder(_433327), _433329 = _433331, -(c_Orderings_Oord__class_Oless__eq(_433327, _433329, _433331))], (6927 ^ _191474) ^ [_433650, _433652, _433654] : [class_Orderings_Oorder(_433650), 6930 ^ _191474 : [(6931 ^ _191474) ^ [] : [_433652 = _433654, 6934 ^ _191474 : [(6935 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_433650, _433652, _433654))], (6937 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_433650, _433654, _433652))]]], (6939 ^ _191474) ^ [] : [-(_433652 = _433654), c_Orderings_Oord__class_Oless__eq(_433650, _433652, _433654), c_Orderings_Oord__class_Oless__eq(_433650, _433654, _433652)]]], (6949 ^ _191474) ^ [_434308, _434310, _434312] : [class_Orderings_Olinorder(_434308), -(c_Orderings_Oord__class_Oless__eq(_434308, _434310, _434312)), -(c_Orderings_Oord__class_Oless__eq(_434308, _434312, _434310))], (6959 ^ _191474) ^ [_434648, _434650, _434652, _434654] : [class_Orderings_Oord(_434648), 6962 ^ _191474 : [(6963 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_434650, _434648), _434652, _434654), 6966 ^ _191474 : [(6967 ^ _191474) ^ [_434907] : [-(c_Orderings_Oord__class_Oless__eq(_434648, hAPP(_434652, _434907), hAPP(_434654, _434907)))]]], (6969 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_434648, hAPP(_434652, 6970 ^ [_434648, _434650, _434652, _434654]), hAPP(_434654, 6970 ^ [_434648, _434650, _434652, _434654])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_434650, _434648), _434652, _434654))]]], (6976 ^ _191474) ^ [_435275, _435277] : [class_Orderings_Opreorder(_435275), c_Orderings_Oord__class_Oless(_435275, _435277, _435277)], (6982 ^ _191474) ^ [_435500, _435502, _435504] : [class_Orderings_Olinorder(_435500), 6985 ^ _191474 : [(6996 ^ _191474) ^ [] : [6997 ^ _191474 : [(6998 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_435500, _435502, _435504)], (7000 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_435500, _435504, _435502)]], _435502 = _435504], (6986 ^ _191474) ^ [] : [-(_435502 = _435504), -(c_Orderings_Oord__class_Oless(_435500, _435502, _435504)), -(c_Orderings_Oord__class_Oless(_435500, _435504, _435502))]]], (7004 ^ _191474) ^ [_436160, _436162, _436164] : [class_Orderings_Olinorder(_436160), 7007 ^ _191474 : [(7018 ^ _191474) ^ [] : [7019 ^ _191474 : [(7020 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_436160, _436164, _436162)], (7022 ^ _191474) ^ [] : [_436162 = _436164]], c_Orderings_Oord__class_Oless(_436160, _436162, _436164)], (7008 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_436160, _436162, _436164)), -(c_Orderings_Oord__class_Oless(_436160, _436164, _436162)), -(_436162 = _436164)]]], (7026 ^ _191474) ^ [_436820, _436822, _436824] : [class_Orderings_Olinorder(_436820), -(c_Orderings_Oord__class_Oless(_436820, _436822, _436824)), -(_436822 = _436824), -(c_Orderings_Oord__class_Oless(_436820, _436824, _436822))], (7040 ^ _191474) ^ [_437240, _437242, _437244] : [class_Orderings_Olinorder(_437240), -(c_Orderings_Oord__class_Oless(_437240, _437242, _437244)), 7047 ^ _191474 : [(7048 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_437240, _437244, _437242)), -(_437244 = _437242)], (7054 ^ _191474) ^ [] : [_437244 = _437242, c_Orderings_Oord__class_Oless(_437240, _437244, _437242)]]], (7060 ^ _191474) ^ [_437831, _437833, _437835] : [class_Orderings_Olinorder(_437831), -(_437833 = _437835), -(c_Orderings_Oord__class_Oless(_437831, _437833, _437835)), -(c_Orderings_Oord__class_Oless(_437831, _437835, _437833))], (7074 ^ _191474) ^ [_438255, _438257, _438259] : [class_Orderings_Oorder(_438255), c_Orderings_Oord__class_Oless(_438255, _438257, _438259), _438257 = _438259], (7084 ^ _191474) ^ [_438579, _438581, _438583] : [class_Orderings_Opreorder(_438579), c_Orderings_Oord__class_Oless(_438579, _438581, _438583), c_Orderings_Oord__class_Oless(_438579, _438583, _438581)], (7094 ^ _191474) ^ [_438905, _438907, _438909] : [class_Orderings_Opreorder(_438905), c_Orderings_Oord__class_Oless(_438905, _438907, _438909), c_Orderings_Oord__class_Oless(_438905, _438909, _438907)], (7104 ^ _191474) ^ [_439231, _439233, _439235] : [class_Orderings_Oorder(_439231), c_Orderings_Oord__class_Oless(_439231, _439233, _439235), _439233 = _439235], (7114 ^ _191474) ^ [_439555, _439557, _439559] : [class_Orderings_Oorder(_439555), c_Orderings_Oord__class_Oless(_439555, _439557, _439559), _439559 = _439557], (7124 ^ _191474) ^ [_439879, _439881, _439883] : [class_Orderings_Opreorder(_439879), c_Orderings_Oord__class_Oless(_439879, _439881, _439883), c_Orderings_Oord__class_Oless(_439879, _439883, _439881)], (7134 ^ _191474) ^ [_440205, _440207, _440209] : [class_Orderings_Oorder(_440205), c_Orderings_Oord__class_Oless(_440205, _440207, _440209), c_Orderings_Oord__class_Oless(_440205, _440209, _440207)], (7144 ^ _191474) ^ [_440545, _440547, _440549, _440551] : [class_Orderings_Oord(_440545), _440547 = _440549, c_Orderings_Oord__class_Oless(_440545, _440549, _440551), -(c_Orderings_Oord__class_Oless(_440545, _440547, _440551))], (7158 ^ _191474) ^ [_440991, _440993, _440995, _440997] : [class_Orderings_Oorder(_440991), _440993 = _440995, c_Orderings_Oord__class_Oless(_440991, _440997, _440995), -(c_Orderings_Oord__class_Oless(_440991, _440997, _440993))], (7172 ^ _191474) ^ [_441437, _441439, _441441, _441443] : [class_Orderings_Oord(_441437), c_Orderings_Oord__class_Oless(_441437, _441439, _441441), _441441 = _441443, -(c_Orderings_Oord__class_Oless(_441437, _441439, _441443))], (7186 ^ _191474) ^ [_441883, _441885, _441887, _441889] : [class_Orderings_Oorder(_441883), c_Orderings_Oord__class_Oless(_441883, _441885, _441887), _441885 = _441889, -(c_Orderings_Oord__class_Oless(_441883, _441889, _441887))], (7200 ^ _191474) ^ [_442329, _442331, _442333, _442335] : [class_Orderings_Opreorder(_442329), c_Orderings_Oord__class_Oless(_442329, _442331, _442333), c_Orderings_Oord__class_Oless(_442329, _442333, _442335), -(c_Orderings_Oord__class_Oless(_442329, _442331, _442335))], (7214 ^ _191474) ^ [_442777, _442779, _442781, _442783] : [class_Orderings_Oorder(_442777), c_Orderings_Oord__class_Oless(_442777, _442779, _442781), c_Orderings_Oord__class_Oless(_442777, _442783, _442779), -(c_Orderings_Oord__class_Oless(_442777, _442783, _442781))], (7228 ^ _191474) ^ [_443211, _443213, _443215] : [class_Orderings_Opreorder(_443211), c_Orderings_Oord__class_Oless(_443211, _443213, _443215), c_Orderings_Oord__class_Oless(_443211, _443215, _443213)], (7238 ^ _191474) ^ [_443537, _443539, _443541] : [class_Orderings_Olinorder(_443537), -(c_Orderings_Oord__class_Oless(_443537, _443539, _443541)), -(_443539 = _443541), -(c_Orderings_Oord__class_Oless(_443537, _443541, _443539))], (7252 ^ _191474) ^ [_443961, _443963, _443965] : [class_Orderings_Olinorder(_443961), 7255 ^ _191474 : [(7256 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_443961, _443963, _443965)), -(c_Orderings_Oord__class_Oless__eq(_443961, _443965, _443963))], (7262 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_443961, _443965, _443963), c_Orderings_Oord__class_Oless(_443961, _443963, _443965)]]], (7268 ^ _191474) ^ [_444457, _444459, _444461] : [class_Orderings_Olinorder(_444457), 7271 ^ _191474 : [(7272 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_444457, _444459, _444461)), -(c_Orderings_Oord__class_Oless(_444457, _444461, _444459))], (7278 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_444457, _444461, _444459), c_Orderings_Oord__class_Oless__eq(_444457, _444459, _444461)]]], (7284 ^ _191474) ^ [_444953, _444955, _444957] : [class_Orderings_Olinorder(_444953), -(c_Orderings_Oord__class_Oless__eq(_444953, _444955, _444957)), -(c_Orderings_Oord__class_Oless(_444953, _444957, _444955))], (7294 ^ _191474) ^ [_445279, _445281, _445283] : [class_Orderings_Oorder(_445279), 7297 ^ _191474 : [(7298 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_445279, _445281, _445283), 7301 ^ _191474 : [(7302 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_445279, _445281, _445283))], (7304 ^ _191474) ^ [] : [_445281 = _445283]]], (7306 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_445279, _445281, _445283)), c_Orderings_Oord__class_Oless__eq(_445279, _445281, _445283), -(_445281 = _445283)]]], (7316 ^ _191474) ^ [_445939, _445941, _445943] : [class_Orderings_Opreorder(_445939), 7319 ^ _191474 : [(7320 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_445939, _445941, _445943), 7323 ^ _191474 : [(7324 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_445939, _445941, _445943))], (7326 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_445939, _445943, _445941)]]], (7328 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_445939, _445941, _445943)), c_Orderings_Oord__class_Oless__eq(_445939, _445941, _445943), -(c_Orderings_Oord__class_Oless__eq(_445939, _445943, _445941))]]], (7338 ^ _191474) ^ [_446602, _446604, _446606] : [class_Orderings_Oorder(_446602), 7341 ^ _191474 : [(7352 ^ _191474) ^ [] : [7353 ^ _191474 : [(7354 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_446602, _446604, _446606)], (7356 ^ _191474) ^ [] : [_446604 = _446606]], -(c_Orderings_Oord__class_Oless__eq(_446602, _446604, _446606))], (7342 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_446602, _446604, _446606), -(c_Orderings_Oord__class_Oless(_446602, _446604, _446606)), -(_446604 = _446606)]]], (7360 ^ _191474) ^ [_447260, _447262, _447264] : [class_Orderings_Olinorder(_447260), -(c_Orderings_Oord__class_Oless(_447260, _447262, _447264)), -(c_Orderings_Oord__class_Oless__eq(_447260, _447264, _447262))], (7370 ^ _191474) ^ [_447588, _447590, _447592] : [class_Orderings_Olinorder(_447588), -(c_Orderings_Oord__class_Oless__eq(_447588, _447590, _447592)), -(c_Orderings_Oord__class_Oless(_447588, _447592, _447590))], (7380 ^ _191474) ^ [_447916, _447918, _447920] : [class_Orderings_Olinorder(_447916), -(c_Orderings_Oord__class_Oless(_447916, _447918, _447920)), 7387 ^ _191474 : [(7388 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_447916, _447918, _447920), -(_447918 = _447920)], (7394 ^ _191474) ^ [] : [_447918 = _447920, -(c_Orderings_Oord__class_Oless__eq(_447916, _447918, _447920))]]], (7400 ^ _191474) ^ [_448505, _448507, _448509] : [class_Orderings_Oorder(_448505), -(_448507 = _448509), c_Orderings_Oord__class_Oless__eq(_448505, _448507, _448509), -(c_Orderings_Oord__class_Oless(_448505, _448507, _448509))], (7414 ^ _191474) ^ [_448926, _448928, _448930] : [class_Orderings_Oorder(_448926), -(_448928 = _448930), c_Orderings_Oord__class_Oless__eq(_448926, _448930, _448928), -(c_Orderings_Oord__class_Oless(_448926, _448930, _448928))], (7428 ^ _191474) ^ [_449347, _449349, _449351] : [class_Orderings_Olinorder(_449347), c_Orderings_Oord__class_Oless__eq(_449347, _449349, _449351), c_Orderings_Oord__class_Oless(_449347, _449351, _449349)], (7438 ^ _191474) ^ [_449673, _449675, _449677] : [class_Orderings_Opreorder(_449673), c_Orderings_Oord__class_Oless(_449673, _449675, _449677), -(c_Orderings_Oord__class_Oless__eq(_449673, _449675, _449677))], (7448 ^ _191474) ^ [_449998, _450000, _450002] : [class_Orderings_Olinorder(_449998), c_Orderings_Oord__class_Oless__eq(_449998, _450000, _450002), 7455 ^ _191474 : [(7456 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_449998, _450000, _450002)), -(_450000 = _450002)], (7462 ^ _191474) ^ [] : [_450000 = _450002, c_Orderings_Oord__class_Oless(_449998, _450000, _450002)]]], (7468 ^ _191474) ^ [_450586, _450588, _450590] : [class_Orderings_Oorder(_450586), c_Orderings_Oord__class_Oless__eq(_450586, _450588, _450590), -(c_Orderings_Oord__class_Oless(_450586, _450588, _450590)), -(_450588 = _450590)], (7482 ^ _191474) ^ [_451005, _451007, _451009] : [class_Orderings_Oorder(_451005), c_Orderings_Oord__class_Oless__eq(_451005, _451007, _451009), -(_451007 = _451009), -(c_Orderings_Oord__class_Oless(_451005, _451007, _451009))], (7496 ^ _191474) ^ [_451426, _451428, _451430] : [class_Orderings_Oorder(_451426), c_Orderings_Oord__class_Oless__eq(_451426, _451428, _451430), -(_451430 = _451428), -(c_Orderings_Oord__class_Oless(_451426, _451428, _451430))], (7510 ^ _191474) ^ [_451861, _451863, _451865, _451867] : [class_Orderings_Opreorder(_451861), c_Orderings_Oord__class_Oless(_451861, _451863, _451865), c_Orderings_Oord__class_Oless__eq(_451861, _451865, _451867), -(c_Orderings_Oord__class_Oless(_451861, _451863, _451867))], (7524 ^ _191474) ^ [_452309, _452311, _452313, _452315] : [class_Orderings_Oorder(_452309), c_Orderings_Oord__class_Oless(_452309, _452311, _452313), c_Orderings_Oord__class_Oless__eq(_452309, _452315, _452311), -(c_Orderings_Oord__class_Oless(_452309, _452315, _452313))], (7538 ^ _191474) ^ [_452757, _452759, _452761, _452763] : [class_Orderings_Opreorder(_452757), c_Orderings_Oord__class_Oless__eq(_452757, _452759, _452761), c_Orderings_Oord__class_Oless(_452757, _452761, _452763), -(c_Orderings_Oord__class_Oless(_452757, _452759, _452763))], (7552 ^ _191474) ^ [_453205, _453207, _453209, _453211] : [class_Orderings_Oorder(_453205), c_Orderings_Oord__class_Oless__eq(_453205, _453207, _453209), c_Orderings_Oord__class_Oless(_453205, _453211, _453207), -(c_Orderings_Oord__class_Oless(_453205, _453211, _453209))], (7566 ^ _191474) ^ [_453611] : [class_RealVector_Oreal__normed__algebra(_453611), 7570 ^ _191474 : [(7571 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7569 ^ [_453611]))], (7573 ^ _191474) ^ [_453940, _453942] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_453611, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453611), _453942), _453940)), 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(_453611, _453942)), c_RealVector_Onorm__class_Onorm(_453611, _453940))), 7569 ^ [_453611])))]]], (7575 ^ _191474) ^ [_454093, _454095] : [class_RealVector_Oreal__normed__algebra(_454093), 7579 ^ _191474 : [(7580 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7578 ^ [_454093, _454095]))], (7582 ^ _191474) ^ [_454392] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_454093, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454093), _454095), _454392)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_454093, _454392)), 7578 ^ [_454093, _454095])))]]], (7584 ^ _191474) ^ [_454524] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _454524) = 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, _454524, 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, _454524, 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, _454524, 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, _454524, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7602 ^ _191474) ^ [_455070, _455072, _455074] : [class_Rings_Ocomm__semiring__0(_455070), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_455070, c_Polynomial_Opcompose(_455070, _455072, _455074)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_455070, _455072)), c_Polynomial_Odegree(_455070, _455074))))], (7608 ^ _191474) ^ [_455352, _455354, _455356, _455358] : [class_Orderings_Oord(_455352), 7611 ^ _191474 : [(7612 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_455354, _455352), _455356, _455358), 7615 ^ _191474 : [(7616 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_455354, _455352), _455356, _455358))], (7618 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_455354, _455352), _455358, _455356)]]], (7620 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_455354, _455352), _455356, _455358)), c_Orderings_Oord__class_Oless__eq(tc_fun(_455354, _455352), _455356, _455358), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_455354, _455352), _455358, _455356))]]], (7630 ^ _191474) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (7632 ^ _191474) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (7634 ^ _191474) ^ [_456154, _456156] : [class_Rings_Ocomm__semiring__0(_456154), -(c_Polynomial_Opcompose(_456154, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456154)), _456156) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456154)))], (7640 ^ _191474) ^ [_456414, _456416, _456418, _456420] : [class_Rings_Ocomm__semiring__0(_456414), -(hAPP(c_Polynomial_Opoly(_456414, c_Polynomial_Opcompose(_456414, _456416, _456418)), _456420) = hAPP(c_Polynomial_Opoly(_456414, _456416), hAPP(c_Polynomial_Opoly(_456414, _456418), _456420)))], (7646 ^ _191474) ^ [_456720, _456722, _456724, _456726, _456728] : [class_Fields_Ofield(_456720), 7649 ^ _191474 : [(7672 ^ _191474) ^ [] : [-(c_Polynomial_Opdivmod__rel(_456720, _456722, _456724, _456726, _456728)), _456722 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_456720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_456720)), _456726), _456724), _456728), 7679 ^ _191474 : [(7680 ^ _191474) ^ [] : [-(_456724 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456720)))], (7682 ^ _191474) ^ [] : [_456726 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456720))]], 7683 ^ _191474 : [(7684 ^ _191474) ^ [] : [_456724 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456720))], (7686 ^ _191474) ^ [] : [_456728 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456720))], (7688 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_456720, _456728), c_Polynomial_Odegree(_456720, _456724))]]], (7650 ^ _191474) ^ [] : [c_Polynomial_Opdivmod__rel(_456720, _456722, _456724, _456726, _456728), 7653 ^ _191474 : [(7654 ^ _191474) ^ [] : [-(_456722 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_456720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_456720)), _456726), _456724), _456728))], (7656 ^ _191474) ^ [] : [_456724 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456720)), -(_456726 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456720)))], (7662 ^ _191474) ^ [] : [-(_456724 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456720))), -(_456728 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456720))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_456720, _456728), c_Polynomial_Odegree(_456720, _456724)))]]]]], (7692 ^ _191474) ^ [_458246, _458248, _458250] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458246, _458248), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458246, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _458248, _458250)))], (7698 ^ _191474) ^ [_458488, _458490, _458492] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458488, _458490), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458488, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _458492, _458490)))], (7704 ^ _191474) ^ [_458716, _458718] : [class_Fields_Ofield(_458716), -(c_Polynomial_Opdivmod__rel(_458716, _458718, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_458716)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_458716)), _458718))], (7710 ^ _191474) ^ [_458946, _458948] : [class_Fields_Ofield(_458946), -(c_Polynomial_Opdivmod__rel(_458946, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_458946)), _458948, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_458946)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_458946))))], (7716 ^ _191474) ^ [_459212, _459214, _459216, _459218] : [class_Fields_Ofield(_459212), 7719 ^ _191474 : [(7720 ^ _191474) ^ [] : [c_Polynomial_Opdivmod__rel(_459212, _459214, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459212)), _459216, _459218), 7723 ^ _191474 : [(7724 ^ _191474) ^ [] : [-(_459216 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459212)))], (7726 ^ _191474) ^ [] : [-(_459218 = _459214)]]], (7728 ^ _191474) ^ [] : [-(c_Polynomial_Opdivmod__rel(_459212, _459214, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459212)), _459216, _459218)), _459216 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459212)), _459218 = _459214]]], (7738 ^ _191474) ^ [_459933, _459935, _459937, _459939] : [class_Fields_Ofield(_459933), 7741 ^ _191474 : [(7742 ^ _191474) ^ [] : [c_Polynomial_Opdivmod__rel(_459933, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459933)), _459935, _459937, _459939), 7745 ^ _191474 : [(7746 ^ _191474) ^ [] : [-(_459937 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459933)))], (7748 ^ _191474) ^ [] : [-(_459939 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459933)))]]], (7750 ^ _191474) ^ [] : [-(c_Polynomial_Opdivmod__rel(_459933, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459933)), _459935, _459937, _459939)), _459937 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459933)), _459939 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_459933))]]], (7760 ^ _191474) ^ [_460708, _460710, _460712, _460714, _460716, _460718, _460720] : [class_Fields_Ofield(_460708), c_Polynomial_Opdivmod__rel(_460708, _460710, _460712, _460714, _460716), c_Polynomial_Opdivmod__rel(_460708, _460710, _460712, _460718, _460720), -(_460714 = _460718)], (7774 ^ _191474) ^ [_461246, _461248, _461250, _461252, _461254, _461256, _461258] : [class_Fields_Ofield(_461246), c_Polynomial_Opdivmod__rel(_461246, _461248, _461250, _461252, _461254), c_Polynomial_Opdivmod__rel(_461246, _461248, _461250, _461256, _461258), -(_461254 = _461258)], (7788 ^ _191474) ^ [_461784, _461786, _461788, _461790, _461792, _461794, _461796] : [class_Fields_Ofield(_461784), c_Polynomial_Opdivmod__rel(_461784, _461786, _461788, _461790, _461792), c_Polynomial_Opdivmod__rel(_461784, _461786, _461788, _461794, _461796), 7799 ^ _191474 : [(7800 ^ _191474) ^ [] : [-(_461790 = _461794)], (7802 ^ _191474) ^ [] : [-(_461792 = _461796)]]], (7804 ^ _191474) ^ [_462421, _462423, _462425, _462427, _462429, _462431, _462433, _462435] : [class_Fields_Ofield(_462421), c_Polynomial_Opdivmod__rel(_462421, _462423, _462425, _462427, _462429), c_Polynomial_Opdivmod__rel(_462421, _462427, _462431, _462433, _462435), -(c_Polynomial_Opdivmod__rel(_462421, _462423, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_462421)), _462425), _462431), _462433, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_462421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_462421)), _462425), _462435), _462429)))], (7818 ^ _191474) ^ [_462975, _462977, _462979] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462975, _462977), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462975, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _462977, _462979)))], (7824 ^ _191474) ^ [_463217, _463219, _463221] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _463217, _463219), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _463217, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _463221, _463219)))], (7830 ^ _191474) ^ [_463445, _463447] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _463445, _463447), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _463445, _463447))], (7837 ^ _191474) ^ [_463737, _463739] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7835 ^ [_463737, _463739]))], (7839 ^ _191474) ^ [_463820, _463822, _463824] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _463820), _463822), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _463824), _463820)), 7835 ^ [_463822, _463824]))], (7845 ^ _191474) ^ [_464080, _464082] : [-(hBOOL(hAPP(_464080, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_464080, _464082)), 7853 ^ _191474 : [(7854 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 7852 ^ [_464080, _464082], _464082))], (7862 ^ _191474) ^ [] : [-(hBOOL(hAPP(_464080, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 7852 ^ [_464080, _464082], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (7856 ^ _191474) ^ [_464516] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _464516, 7852 ^ [_464080, _464082]), hBOOL(hAPP(_464080, _464516))]]], (7864 ^ _191474) ^ [_464829, _464831] : [class_RealVector_Oreal__normed__field(_464829), 7868 ^ _191474 : [(7869 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7867 ^ [_464829, _464831]))], (7871 ^ _191474) ^ [_465120] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_464829, c_Rings_Oinverse__class_Odivide(_464829, _465120, _464831)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_464829, _465120)), 7867 ^ [_464829, _464831])))]]], (7873 ^ _191474) ^ [_465262, _465264] : [class_RealVector_Oreal__normed__algebra(_465262), 7877 ^ _191474 : [(7878 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7876 ^ [_465262, _465264]))], (7880 ^ _191474) ^ [_465561] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_465262, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465262), _465561), _465264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_465262, _465561)), 7876 ^ [_465262, _465264])))]]], (7882 ^ _191474) ^ [_465707, _465709] : [class_RealVector_Oreal__normed__algebra(_465707), 7886 ^ _191474 : [(7887 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7885 ^ [_465707, _465709]))], (7889 ^ _191474) ^ [_466006] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_465707, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465707), _465709), _466006)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_465707, _466006)), 7885 ^ [_465707, _465709])))]]], (7891 ^ _191474) ^ [_466138] : [class_RealVector_Oreal__normed__algebra(_466138), 7895 ^ _191474 : [(7896 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7894 ^ [_466138]))], (7898 ^ _191474) ^ [_466467, _466469] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_466138, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466138), _466469), _466467)), 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(_466138, _466469)), c_RealVector_Onorm__class_Onorm(_466138, _466467))), 7894 ^ [_466138])))]]], (7900 ^ _191474) ^ [_466634, _466636, _466638] : [class_Fields_Olinordered__field__inverse__zero(_466634), 7906 ^ _191474 : [(7907 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_466634, c_Groups_Ozero__class_Ozero(_466634), 7905 ^ [_466634, _466636, _466638]))], (7909 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(_466634, 7905 ^ [_466634, _466636, _466638], c_Groups_Oone__class_Oone(_466634)))], (7911 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_466634, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466634), 7905 ^ [_466634, _466636, _466638]), _466636), _466638)]], -(c_Orderings_Oord__class_Oless__eq(_466634, _466636, _466638))], (7915 ^ _191474) ^ [_467248, _467250, _467252] : [class_Rings_Ocomm__semiring__0(_467248), -(c_Polynomial_Odegree(_467248, c_Polynomial_Osynthetic__div(_467248, _467250, _467252)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Polynomial_Odegree(_467248, _467250), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7921 ^ _191474) ^ [_467504, _467506, _467508] : [class_Rings_Ocomm__semiring__0(_467504), 7924 ^ _191474 : [(7925 ^ _191474) ^ [] : [c_Polynomial_Osynthetic__div(_467504, _467506, _467508) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_467504)), -(c_Polynomial_Odegree(_467504, _467506) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7931 ^ _191474) ^ [] : [c_Polynomial_Odegree(_467504, _467506) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Osynthetic__div(_467504, _467506, _467508) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_467504)))]]], (7937 ^ _191474) ^ [_468011, _468013] : [class_Rings_Ocomm__semiring__0(_468011), -(c_Polynomial_Osynthetic__div(_468011, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_468011)), _468013) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_468011)))], (7943 ^ _191474) ^ [] : [-(c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (7945 ^ _191474) ^ [_468282] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _468282), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _468282, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_468282), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7951 ^ _191474) ^ [_468540, _468542, _468544, _468546] : [class_RealVector_Oreal__normed__vector(_468540), class_Orderings_Oord(_468542), 7961 ^ _191474 : [(7962 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_468542, _468544, 7960 ^ [_468540, _468542, _468544, _468546]))], (7964 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_468540, c_Groups_Ominus__class_Ominus(_468540, hAPP(_468546, _468544), hAPP(_468546, 7960 ^ [_468540, _468542, _468544, _468546]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]], 7965 ^ _191474 : [(7966 ^ _191474) ^ [_469098] : [c_Orderings_Oord__class_Oless__eq(_468542, _468544, _469098), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_468540, hAPP(_468546, _469098)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_468540, hAPP(_468546, _468544)))))]]], (7972 ^ _191474) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7974 ^ _191474) ^ [_469435, _469437] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _469435, _469437), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_469435), c_RComplete_Onatceiling(_469437)))], (7980 ^ _191474) ^ [_469628] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_469628)))], (7982 ^ _191474) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7984 ^ _191474) ^ [_469777] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _469777, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_469777) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7990 ^ _191474) ^ [_469972, _469974] : [-(c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _469972, _469974)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oexpi(_469972)), c_Complex_Oexpi(_469974)))], (7992 ^ _191474) ^ [_470112] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_470112), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _470112, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7998 ^ _191474) ^ [_470276] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _470276, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_470276), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8004 ^ _191474) ^ [_470476] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _470476), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _470476, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_470476), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8010 ^ _191474) ^ [_470706, _470708] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _470706), _470708), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _470708, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _470706), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_470708) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _470706, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8020 ^ _191474) ^ [_471041, _471043] : [class_Orderings_Oorder(_471041), 8023 ^ _191474 : [(8034 ^ _191474) ^ [] : [8037 ^ _191474 : [(8038 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 8035 ^ [_471041, _471043], 8036 ^ [_471041, _471043]))], (8040 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_471041, hAPP(_471043, 8036 ^ [_471041, _471043]), hAPP(_471043, 8035 ^ [_471041, _471043]))]], -(c_SEQ_Odecseq(_471041, _471043))], (8024 ^ _191474) ^ [] : [c_SEQ_Odecseq(_471041, _471043), 8027 ^ _191474 : [(8028 ^ _191474) ^ [_471317, _471319] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _471319, _471317), -(c_Orderings_Oord__class_Oless__eq(_471041, hAPP(_471043, _471317), hAPP(_471043, _471319)))]]]]], (8044 ^ _191474) ^ [_471913] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _471913)))], (8046 ^ _191474) ^ [_472024, _472026] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472024), _472026), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _472026, c_RealDef_Oreal(tc_Nat_Onat, _472024))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_472026), _472024))], (8052 ^ _191474) ^ [_472272, _472274] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472272), _472274), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472272, c_RComplete_Onatfloor(_472274)))], (8058 ^ _191474) ^ [_472467] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _472467)) = _472467)], (8060 ^ _191474) ^ [_472550] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _472550)) = _472550)], (8062 ^ _191474) ^ [_472662, _472664] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _472662), 8065 ^ _191474 : [(8066 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472664, c_RComplete_Onatfloor(_472662)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472664), _472662))], (8072 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472664), _472662), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472664, c_RComplete_Onatfloor(_472662)))]]], (8078 ^ _191474) ^ [_473131] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _473131), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_473131)), _473131))], (8084 ^ _191474) ^ [_473320] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _473320, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_473320))))], (8086 ^ _191474) ^ [_473408] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _473408, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_473408)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8088 ^ _191474) ^ [_473554, _473556] : [c_RealDef_Oreal(tc_Nat_Onat, _473554) = c_RealDef_Oreal(tc_Nat_Onat, _473556), -(_473554 = _473556)], (8094 ^ _191474) ^ [_473728, _473730] : [_473728 = _473730, -(c_RealDef_Oreal(tc_Nat_Onat, _473728) = c_RealDef_Oreal(tc_Nat_Onat, _473730))], (8100 ^ _191474) ^ [_473967] : [c_RealDef_Oreal(tc_Nat_Onat, _473967) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_473967 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8106 ^ _191474) ^ [_474129] : [_474129 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _474129) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8112 ^ _191474) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8114 ^ _191474) ^ [_474364] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _474364), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8116 ^ _191474) ^ [_474504, _474506] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _474504), c_RealDef_Oreal(tc_Nat_Onat, _474506)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _474504, _474506))], (8122 ^ _191474) ^ [_474682, _474684] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _474682, _474684), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _474682), c_RealDef_Oreal(tc_Nat_Onat, _474684)))], (8128 ^ _191474) ^ [_474939, _474941] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _474939), c_RealDef_Oreal(tc_Nat_Onat, _474941)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _474939, _474941))], (8134 ^ _191474) ^ [_475117, _475119] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _475117, _475119), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _475117), c_RealDef_Oreal(tc_Nat_Onat, _475119)))], (8140 ^ _191474) ^ [_475345, _475347] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _475345), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _475345, c_RealDef_Oreal(tc_Nat_Onat, _475347)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_475345), _475347))], (8150 ^ _191474) ^ [_475645, _475647] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475645), _475647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _475645)), c_RealDef_Oreal(tc_Nat_Onat, _475647)))], (8152 ^ _191474) ^ [_475760, _475762] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _475760, _475762)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _475760), c_RealDef_Oreal(tc_Nat_Onat, _475762)))], (8154 ^ _191474) ^ [_475886, _475888] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _475886), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _475886, c_RealDef_Oreal(tc_Nat_Onat, _475888))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_475886), _475888))], (8160 ^ _191474) ^ [_476128, _476130] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_476128), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _476130), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _476128, c_RealDef_Oreal(tc_Nat_Onat, _476130)))], (8166 ^ _191474) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8168 ^ _191474) ^ [_476413, _476415] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _476413), _476415), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _476415, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _476413), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_476415) = _476413)], (8178 ^ _191474) ^ [_476711] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _476711, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_476711))))], (8180 ^ _191474) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8182 ^ _191474) ^ [_476848] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_476848)))], (8184 ^ _191474) ^ [_476958, _476960] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _476958, _476960), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_476958), c_RComplete_Onatfloor(_476960)))], (8190 ^ _191474) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8192 ^ _191474) ^ [_477248] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477248), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_477248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8198 ^ _191474) ^ [_477412] : [_477412 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477412), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (8204 ^ _191474) ^ [_477626, _477628] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _477626, _477628), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _477628, _477626)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477628), c_RealDef_Oreal(tc_Nat_Onat, _477626)))], (8210 ^ _191474) ^ [_477872, _477874] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _477872, c_RealDef_Oreal(tc_Nat_Onat, _477874)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_477872), _477874))], (8216 ^ _191474) ^ [_478082] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _478082, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_478082) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8222 ^ _191474) ^ [_478307] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _478307)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478307))], (8228 ^ _191474) ^ [_478473] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478473), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _478473)))], (8234 ^ _191474) ^ [_478718, _478720] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _478718, _478720), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _478718), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _478720)))], (8240 ^ _191474) ^ [_478904, _478906] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _478904), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _478906)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _478904, _478906))], (8246 ^ _191474) ^ [_479169, _479171] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _479169, _479171), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _479169), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _479171), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8252 ^ _191474) ^ [_479355, _479357] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _479355), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _479357), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _479355, _479357))], (8258 ^ _191474) ^ [_479591, _479593] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _479591), 8261 ^ _191474 : [(8262 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_479591), _479593), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _479591, c_RealDef_Oreal(tc_Nat_Onat, _479593)))], (8268 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _479591, c_RealDef_Oreal(tc_Nat_Onat, _479593)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_479591), _479593))]]], (8274 ^ _191474) ^ [_480074, _480076] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _480074), _480076), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _480076, c_RealDef_Oreal(tc_Nat_Onat, _480074))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_480076), _480074))], (8280 ^ _191474) ^ [_480337] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_480337)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _480337))], (8286 ^ _191474) ^ [_480501] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _480501), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_480501)))], (8292 ^ _191474) ^ [_480715, _480717] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _480715), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _480715, c_RealDef_Oreal(tc_Nat_Onat, _480717))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_480715), _480717))], (8298 ^ _191474) ^ [_480957, _480959] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _480957), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _480959), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_480957)), c_RComplete_Onatfloor(_480959)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _480957), _480959))))], (8308 ^ _191474) ^ [_481284] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _481284), 8312 ^ _191474 : [(8313 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 8311 ^ [_481284], c_Groups_Oone__class_Oone(tc_Nat_Onat))), _481284))], (8315 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _481284, c_RealDef_Oreal(tc_Nat_Onat, 8311 ^ [_481284])))]]], (8317 ^ _191474) ^ [_481661, _481663] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _481661), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _481663), -(c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _481661, c_RealDef_Oreal(tc_Nat_Onat, _481663))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_RComplete_Onatfloor(_481661), _481663))], (8327 ^ _191474) ^ [_481994, _481996] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _481994), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _481996)), _481994), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _481994, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _481996)))], (8333 ^ _191474) ^ [_482282, _482284, _482286, _482288] : [class_Rings_Ocomm__semiring__1(_482282), -(hAPP(hAPP(c_Power_Opower__class_Opower(_482282), hAPP(hAPP(c_Power_Opower__class_Opower(_482282), _482284), _482286)), _482288) = hAPP(hAPP(c_Power_Opower__class_Opower(_482282), _482284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482286), _482288)))], (8339 ^ _191474) ^ [_482590, _482592, _482594, _482596] : [class_Rings_Ocomm__semiring__1(_482590), -(hAPP(hAPP(c_Power_Opower__class_Opower(_482590), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_482590), _482592), _482594)), _482596) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_482590), hAPP(hAPP(c_Power_Opower__class_Opower(_482590), _482592), _482596)), hAPP(hAPP(c_Power_Opower__class_Opower(_482590), _482594), _482596)))], (8345 ^ _191474) ^ [_482890, _482892] : [class_Rings_Ocomm__semiring__1(_482890), -(hAPP(hAPP(c_Power_Opower__class_Opower(_482890), _482892), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _482892)], (8351 ^ _191474) ^ [_483128, _483130, _483132] : [class_RealVector_Oreal__normed__algebra__1(_483128), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_483128, hAPP(hAPP(c_Power_Opower__class_Opower(_483128), _483130), _483132)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_483128, _483130)), _483132)))], (8357 ^ _191474) ^ [_483398, _483400, _483402] : [class_RealVector_Oreal__normed__div__algebra(_483398), -(c_RealVector_Onorm__class_Onorm(_483398, hAPP(hAPP(c_Power_Opower__class_Opower(_483398), _483400), _483402)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_483398, _483400)), _483402))], (8363 ^ _191474) ^ [_483680, _483682, _483684, _483686] : [class_Rings_Ocomm__semiring__1(_483680), -(hAPP(c_Polynomial_Opoly(_483680, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_483680)), _483682), _483684)), _483686) = hAPP(hAPP(c_Power_Opower__class_Opower(_483680), hAPP(c_Polynomial_Opoly(_483680, _483682), _483686)), _483684))], (8369 ^ _191474) ^ [_483994, _483996, _483998] : [_483994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483994), _483996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483994), _483998)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8375 ^ _191474) ^ [_484194, _484196, _484198] : [-(_484194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _484194), _484196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _484194), _484198)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _484196, _484198))], (8381 ^ _191474) ^ [_484455, _484457] : [class_Rings_Ocomm__semiring__1(_484455), -(hAPP(hAPP(c_Power_Opower__class_Opower(_484455), _484457), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_484455))], (8387 ^ _191474) ^ [_484711, _484713, _484715, _484717] : [class_Rings_Ocomm__semiring__1(_484711), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484711), hAPP(hAPP(c_Power_Opower__class_Opower(_484711), _484713), _484715)), hAPP(hAPP(c_Power_Opower__class_Opower(_484711), _484713), _484717)) = hAPP(hAPP(c_Power_Opower__class_Opower(_484711), _484713), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _484715, _484717)))], (8393 ^ _191474) ^ [_485017, _485019, _485021] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _485017), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _485017), _485019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _485017), _485021)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _485019, _485021))], (8399 ^ _191474) ^ [_485260, _485262] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _485260, _485262)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _485260), c_RealDef_Oreal(tc_Nat_Onat, _485262))))], (8401 ^ _191474) ^ [_485372, _485374] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _485372), c_RealDef_Oreal(tc_Nat_Onat, _485374)), c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _485372, _485374)))))], (8403 ^ _191474) ^ [_485488, _485490] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _485488), c_RealDef_Oreal(tc_Nat_Onat, _485490)), c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _485488, _485490))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8405 ^ _191474) ^ [_485633, _485635, _485637] : [class_Groups_Omonoid__mult(_485633), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _485635), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485633), hAPP(hAPP(c_Power_Opower__class_Opower(_485633), _485637), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _485635, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _485637) = hAPP(hAPP(c_Power_Opower__class_Opower(_485633), _485637), _485635))], (8415 ^ _191474) ^ [_486012, _486014, _486016] : [class_Power_Opower(_486012), 8418 ^ _191474 : [(8419 ^ _191474) ^ [] : [_486014 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_486012), _486016), _486014) = c_Groups_Oone__class_Oone(_486012))], (8425 ^ _191474) ^ [] : [-(_486014 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_486012), _486016), _486014) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486012), _486016), hAPP(hAPP(c_Power_Opower__class_Opower(_486012), _486016), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _486014, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (8431 ^ _191474) ^ [_486596, _486598, _486600, _486602] : [class_Rings_Olinordered__semidom(_486596), c_Orderings_Oord__class_Oless(_486596, _486598, _486600), c_Orderings_Oord__class_Oless__eq(_486596, c_Groups_Ozero__class_Ozero(_486596), _486598), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _486602), -(c_Orderings_Oord__class_Oless(_486596, hAPP(hAPP(c_Power_Opower__class_Opower(_486596), _486598), _486602), hAPP(hAPP(c_Power_Opower__class_Opower(_486596), _486600), _486602)))], (8473 ^ _191474) ^ [_487973, _487975, _487977] : [-(hBOOL(hAPP(_487973, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _487975, _487977)))), 8476 ^ _191474 : [(8477 ^ _191474) ^ [] : [-(_487977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8479 ^ _191474) ^ [] : [hBOOL(hAPP(_487973, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 8480 ^ _191474 : [(8481 ^ _191474) ^ [] : [_487977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8485 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 8483 ^ [_487973, _487975, _487977], _487977))], (8487 ^ _191474) ^ [] : [-(_487975 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _487977), 8482 ^ [_487973, _487975, _487977]), 8483 ^ [_487973, _487975, _487977]))], (8489 ^ _191474) ^ [] : [hBOOL(hAPP(_487973, 8482 ^ [_487973, _487975, _487977]))]]], (8449 ^ _191474) ^ [_487194, _487196, _487198] : [hBOOL(hAPP(_487194, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _487196, _487198))), 8452 ^ _191474 : [(8453 ^ _191474) ^ [] : [_487198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_487194, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8459 ^ _191474) ^ [] : [-(_487198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8462 ^ _191474 : [(8463 ^ _191474) ^ [_487648, _487650] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _487648, _487198), _487196 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _487198), _487650), _487648), -(hBOOL(hAPP(_487194, _487650)))]]]]], (8493 ^ _191474) ^ [_488849, _488851, _488853] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _488849), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _488851, _488853)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _488849), _488851)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _488849), _488853)))], (8495 ^ _191474) ^ [_488987, _488989, _488991] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _488987), _488989)), _488991) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _488987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _488989), _488991)))], (8497 ^ _191474) ^ [_489136, _489138, _489140] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _489136), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _489136), _489138), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _489136), _489140)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _489138, _489140))], (8517 ^ _191474) ^ [_489772, _489774] : [8518 ^ _191474 : [(8519 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _489772)], (8521 ^ _191474) ^ [] : [_489774 = 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), _489772), _489774)))], (8507 ^ _191474) ^ [_489504, _489506] : [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), _489504), _489506)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _489504)), -(_489506 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8525 ^ _191474) ^ [_490059, _490061] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _490059), _490061)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _490059)), _490061))], (8527 ^ _191474) ^ [_490171, _490173] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _490171)), _490173) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _490171), _490173)))], (8529 ^ _191474) ^ [_490312, _490314, _490316] : [class_Rings_Ocomm__semiring__1(_490312), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_490312, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_490312)), _490314), _490316)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_490312, _490314)), _490316)))], (8535 ^ _191474) ^ [_490572, _490574] : [_490572 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_490572)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _490572), _490574)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_490572)), _490574))], (8541 ^ _191474) ^ [_490844, _490846] : [_490844 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _490846), _490844) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8547 ^ _191474) ^ [_491018, _491020] : [-(_491018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _491020), _491018) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _491020), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _491020), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _491018, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (8553 ^ _191474) ^ [_491291, _491293, _491295] : [class_Rings_Oring__1__no__zero__divisors(_491291), -(_491293 = c_Groups_Ozero__class_Ozero(_491291)), hAPP(hAPP(c_Power_Opower__class_Opower(_491291), _491293), _491295) = c_Groups_Ozero__class_Ozero(_491291)], (8563 ^ _191474) ^ [_491640, _491642, _491644] : [class_Groups_Omonoid__mult(_491640), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491640), hAPP(hAPP(c_Power_Opower__class_Opower(_491640), _491642), _491644)), _491642) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491640), _491642), hAPP(hAPP(c_Power_Opower__class_Opower(_491640), _491642), _491644)))], (8569 ^ _191474) ^ [_491946, _491948, _491950, _491952] : [class_Groups_Ocomm__monoid__mult(_491946), -(hAPP(hAPP(c_Power_Opower__class_Opower(_491946), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491946), _491948), _491950)), _491952) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491946), hAPP(hAPP(c_Power_Opower__class_Opower(_491946), _491948), _491952)), hAPP(hAPP(c_Power_Opower__class_Opower(_491946), _491950), _491952)))], (8575 ^ _191474) ^ [_492246, _492248] : [class_Groups_Omonoid__mult(_492246), -(hAPP(hAPP(c_Power_Opower__class_Opower(_492246), c_Groups_Oone__class_Oone(_492246)), _492248) = c_Groups_Oone__class_Oone(_492246))], (8581 ^ _191474) ^ [_492478, _492480] : [class_Divides_Osemiring__div(_492478), -(c_Divides_Odiv__class_Odiv(_492478, c_Groups_Ozero__class_Ozero(_492478), _492480) = c_Groups_Ozero__class_Ozero(_492478))], (8587 ^ _191474) ^ [_492702, _492704] : [class_Divides_Osemiring__div(_492702), -(c_Divides_Odiv__class_Odiv(_492702, _492704, c_Groups_Ozero__class_Ozero(_492702)) = c_Groups_Ozero__class_Ozero(_492702))], (8593 ^ _191474) ^ [_492954, _492956, _492958, _492960] : [class_Fields_Ofield__inverse__zero(_492954), -(hAPP(hAPP(c_Power_Opower__class_Opower(_492954), c_Rings_Oinverse__class_Odivide(_492954, _492956, _492958)), _492960) = c_Rings_Oinverse__class_Odivide(_492954, hAPP(hAPP(c_Power_Opower__class_Opower(_492954), _492956), _492960), hAPP(hAPP(c_Power_Opower__class_Opower(_492954), _492958), _492960)))], (8599 ^ _191474) ^ [_493238, _493240] : [class_Divides_Osemiring__div(_493238), -(c_Divides_Odiv__class_Odiv(_493238, _493240, c_Groups_Oone__class_Oone(_493238)) = _493240)], (8605 ^ _191474) ^ [_493486, _493488, _493490, _493492] : [class_Groups_Omonoid__mult(_493486), -(hAPP(hAPP(c_Power_Opower__class_Opower(_493486), _493488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _493490), _493492)) = hAPP(hAPP(c_Power_Opower__class_Opower(_493486), hAPP(hAPP(c_Power_Opower__class_Opower(_493486), _493488), _493490)), _493492))], (8611 ^ _191474) ^ [_493766, _493768] : [class_Groups_Omonoid__mult(_493766), -(hAPP(hAPP(c_Power_Opower__class_Opower(_493766), _493768), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _493768)], (8617 ^ _191474) ^ [_493975, _493977] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _493975, _493977), _493975))], (8619 ^ _191474) ^ [_494103, _494105, _494107] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _494103, _494105), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _494103, _494107), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _494105, _494107)))], (8625 ^ _191474) ^ [_494338, _494340, _494342] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _494338, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _494340), _494342)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _494338, _494340), _494342))], (8627 ^ _191474) ^ [_494495, _494497, _494499, _494501] : [class_Rings_Olinordered__semidom(_494495), c_Orderings_Oord__class_Oless__eq(_494495, _494497, _494499), c_Orderings_Oord__class_Oless__eq(_494495, c_Groups_Ozero__class_Ozero(_494495), _494497), -(c_Orderings_Oord__class_Oless__eq(_494495, hAPP(hAPP(c_Power_Opower__class_Opower(_494495), _494497), _494501), hAPP(hAPP(c_Power_Opower__class_Opower(_494495), _494499), _494501)))], (8641 ^ _191474) ^ [_494965, _494967, _494969] : [class_Rings_Olinordered__semidom(_494965), c_Orderings_Oord__class_Oless__eq(_494965, c_Groups_Ozero__class_Ozero(_494965), _494967), -(c_Orderings_Oord__class_Oless__eq(_494965, c_Groups_Ozero__class_Ozero(_494965), hAPP(hAPP(c_Power_Opower__class_Opower(_494965), _494967), _494969)))], (8651 ^ _191474) ^ [_495314, _495316, _495318] : [class_Rings_Olinordered__semidom(_495314), c_Orderings_Oord__class_Oless(_495314, c_Groups_Ozero__class_Ozero(_495314), _495316), -(c_Orderings_Oord__class_Oless(_495314, c_Groups_Ozero__class_Ozero(_495314), hAPP(hAPP(c_Power_Opower__class_Opower(_495314), _495316), _495318)))], (8661 ^ _191474) ^ [_495663, _495665, _495667] : [class_Rings_Olinordered__semidom(_495663), c_Orderings_Oord__class_Oless__eq(_495663, c_Groups_Oone__class_Oone(_495663), _495665), -(c_Orderings_Oord__class_Oless__eq(_495663, c_Groups_Oone__class_Oone(_495663), hAPP(hAPP(c_Power_Opower__class_Opower(_495663), _495665), _495667)))], (8671 ^ _191474) ^ [_496012, _496014, _496016] : [class_Power_Opower(_496012), class_Rings_Omult__zero(_496012), class_Rings_Ono__zero__divisors(_496012), class_Rings_Ozero__neq__one(_496012), 8686 ^ _191474 : [(8687 ^ _191474) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_496012), _496014), _496016) = c_Groups_Ozero__class_Ozero(_496012), 8690 ^ _191474 : [(8691 ^ _191474) ^ [] : [-(_496014 = c_Groups_Ozero__class_Ozero(_496012))], (8693 ^ _191474) ^ [] : [_496016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (8695 ^ _191474) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_496012), _496014), _496016) = c_Groups_Ozero__class_Ozero(_496012)), _496014 = c_Groups_Ozero__class_Ozero(_496012), -(_496016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8705 ^ _191474) ^ [_496995, _496997, _496999, _497001] : [class_Rings_Olinordered__semidom(_496995), c_Orderings_Oord__class_Oless(_496995, c_Groups_Oone__class_Oone(_496995), _496997), 8712 ^ _191474 : [(8713 ^ _191474) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_496995), _496997), _496999) = hAPP(hAPP(c_Power_Opower__class_Opower(_496995), _496997), _497001), -(_496999 = _497001)], (8719 ^ _191474) ^ [] : [_496999 = _497001, -(hAPP(hAPP(c_Power_Opower__class_Opower(_496995), _496997), _496999) = hAPP(hAPP(c_Power_Opower__class_Opower(_496995), _496997), _497001))]]], (8725 ^ _191474) ^ [_497664, _497666, _497668, _497670] : [class_Divides_Osemiring__div(_497664), -(_497666 = c_Groups_Ozero__class_Ozero(_497664)), -(c_Divides_Odiv__class_Odiv(_497664, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497664), _497666), _497668), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497664), _497666), _497670)) = c_Divides_Odiv__class_Odiv(_497664, _497668, _497670))], (8735 ^ _191474) ^ [_498064, _498066, _498068, _498070] : [class_Divides_Osemiring__div(_498064), -(_498066 = c_Groups_Ozero__class_Ozero(_498064)), -(c_Divides_Odiv__class_Odiv(_498064, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498064), _498068), _498066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498064), _498070), _498066)) = c_Divides_Odiv__class_Odiv(_498064, _498068, _498070))], (8745 ^ _191474) ^ [_498450, _498452, _498454] : [class_Divides_Osemiring__div(_498450), -(_498452 = c_Groups_Ozero__class_Ozero(_498450)), -(c_Divides_Odiv__class_Odiv(_498450, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498450), _498452), _498454), _498452) = _498454)], (8755 ^ _191474) ^ [_498802, _498804, _498806] : [class_Divides_Osemiring__div(_498802), -(_498804 = c_Groups_Ozero__class_Ozero(_498802)), -(c_Divides_Odiv__class_Odiv(_498802, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498802), _498806), _498804), _498804) = _498806)], (8765 ^ _191474) ^ [_499168, _499170, _499172, _499174] : [class_Divides_Osemiring__div(_499168), 8768 ^ _191474 : [(8769 ^ _191474) ^ [] : [_499170 = c_Groups_Ozero__class_Ozero(_499168), -(c_Divides_Odiv__class_Odiv(_499168, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499168), _499170), _499172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499168), _499170), _499174)) = c_Groups_Ozero__class_Ozero(_499168))], (8775 ^ _191474) ^ [] : [-(_499170 = c_Groups_Ozero__class_Ozero(_499168)), -(c_Divides_Odiv__class_Odiv(_499168, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499168), _499170), _499172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499168), _499170), _499174)) = c_Divides_Odiv__class_Odiv(_499168, _499172, _499174))]]], (8781 ^ _191474) ^ [_499792, _499794, _499796, _499798] : [class_Fields_Ofield(_499792), -(_499794 = c_Groups_Ozero__class_Ozero(_499792)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_499792), c_Rings_Oinverse__class_Odivide(_499792, _499796, _499794)), _499798) = c_Rings_Oinverse__class_Odivide(_499792, hAPP(hAPP(c_Power_Opower__class_Opower(_499792), _499796), _499798), hAPP(hAPP(c_Power_Opower__class_Opower(_499792), _499794), _499798)))], (8791 ^ _191474) ^ [_500180, _500182] : [class_Divides_Osemiring__div(_500180), -(_500182 = c_Groups_Ozero__class_Ozero(_500180)), -(c_Divides_Odiv__class_Odiv(_500180, _500182, _500182) = c_Groups_Oone__class_Oone(_500180))], (8801 ^ _191474) ^ [_500496, _500498] : [class_Power_Opower(_500496), -(hAPP(hAPP(c_Power_Opower__class_Opower(_500496), _500498), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_500496))], (8807 ^ _191474) ^ [_500752, _500754, _500756, _500758] : [class_Groups_Omonoid__mult(_500752), -(hAPP(hAPP(c_Power_Opower__class_Opower(_500752), _500754), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _500756, _500758)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500752), hAPP(hAPP(c_Power_Opower__class_Opower(_500752), _500754), _500756)), hAPP(hAPP(c_Power_Opower__class_Opower(_500752), _500754), _500758)))], (8813 ^ _191474) ^ [_501058, _501060, _501062] : [class_Fields_Ofield__inverse__zero(_501058), -(c_Rings_Oinverse__class_Odivide(_501058, c_Groups_Oone__class_Oone(_501058), hAPP(hAPP(c_Power_Opower__class_Opower(_501058), _501060), _501062)) = hAPP(hAPP(c_Power_Opower__class_Opower(_501058), c_Rings_Oinverse__class_Odivide(_501058, c_Groups_Oone__class_Oone(_501058), _501060)), _501062))], (8819 ^ _191474) ^ [_501328, _501330] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _501328, _501330), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _501328, _501330) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8825 ^ _191474) ^ [_501576, _501578, _501580, _501582] : [class_Rings_Olinordered__semidom(_501576), c_Orderings_Oord__class_Oless(_501576, hAPP(hAPP(c_Power_Opower__class_Opower(_501576), _501578), _501580), hAPP(hAPP(c_Power_Opower__class_Opower(_501576), _501582), _501580)), c_Orderings_Oord__class_Oless__eq(_501576, c_Groups_Ozero__class_Ozero(_501576), _501582), -(c_Orderings_Oord__class_Oless(_501576, _501578, _501582))], (8839 ^ _191474) ^ [_502046, _502048, _502050] : [class_Rings_Olinordered__semidom(_502046), c_Orderings_Oord__class_Oless(_502046, c_Groups_Oone__class_Oone(_502046), _502048), -(c_Orderings_Oord__class_Oless(_502046, hAPP(hAPP(c_Power_Opower__class_Opower(_502046), _502048), _502050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502046), _502048), hAPP(hAPP(c_Power_Opower__class_Opower(_502046), _502048), _502050))))], (8849 ^ _191474) ^ [_502423, _502425, _502427] : [class_Rings_Olinordered__semidom(_502423), c_Orderings_Oord__class_Oless(_502423, c_Groups_Oone__class_Oone(_502423), _502425), -(c_Orderings_Oord__class_Oless(_502423, c_Groups_Oone__class_Oone(_502423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502423), _502425), hAPP(hAPP(c_Power_Opower__class_Opower(_502423), _502425), _502427))))], (8859 ^ _191474) ^ [_502774, _502776] : [class_Power_Opower(_502774), class_Rings_Osemiring__0(_502774), 8866 ^ _191474 : [(8867 ^ _191474) ^ [] : [_502776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_502774), c_Groups_Ozero__class_Ozero(_502774)), _502776) = c_Groups_Oone__class_Oone(_502774))], (8873 ^ _191474) ^ [] : [-(_502776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_502774), c_Groups_Ozero__class_Ozero(_502774)), _502776) = c_Groups_Ozero__class_Ozero(_502774))]]], (8879 ^ _191474) ^ [_503403, _503405, _503407, _503409] : [class_Divides_Osemiring__div(_503403), -(_503405 = c_Groups_Ozero__class_Ozero(_503403)), -(c_Divides_Odiv__class_Odiv(_503403, c_Groups_Oplus__class_Oplus(_503403, _503407, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503403), _503405), _503409)), _503405) = c_Groups_Oplus__class_Oplus(_503403, _503409, c_Divides_Odiv__class_Odiv(_503403, _503407, _503405)))], (8889 ^ _191474) ^ [_503803, _503805, _503807, _503809] : [class_Divides_Osemiring__div(_503803), -(_503805 = c_Groups_Ozero__class_Ozero(_503803)), -(c_Divides_Odiv__class_Odiv(_503803, c_Groups_Oplus__class_Oplus(_503803, _503807, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503803), _503809), _503805)), _503805) = c_Groups_Oplus__class_Oplus(_503803, _503809, c_Divides_Odiv__class_Odiv(_503803, _503807, _503805)))], (8899 ^ _191474) ^ [_504189, _504191, _504193] : [class_Divides_Osemiring__div(_504189), -(_504191 = c_Groups_Ozero__class_Ozero(_504189)), -(c_Divides_Odiv__class_Odiv(_504189, c_Groups_Oplus__class_Oplus(_504189, _504191, _504193), _504191) = c_Groups_Oplus__class_Oplus(_504189, c_Divides_Odiv__class_Odiv(_504189, _504193, _504191), c_Groups_Oone__class_Oone(_504189)))], (8909 ^ _191474) ^ [_504553, _504555, _504557] : [class_Divides_Osemiring__div(_504553), -(_504555 = c_Groups_Ozero__class_Ozero(_504553)), -(c_Divides_Odiv__class_Odiv(_504553, c_Groups_Oplus__class_Oplus(_504553, _504557, _504555), _504555) = c_Groups_Oplus__class_Oplus(_504553, c_Divides_Odiv__class_Odiv(_504553, _504557, _504555), c_Groups_Oone__class_Oone(_504553)))], (8919 ^ _191474) ^ [_504931, _504933, _504935, _504937] : [class_Rings_Olinordered__semidom(_504931), c_Orderings_Oord__class_Oless(_504931, c_Groups_Oone__class_Oone(_504931), _504933), 8926 ^ _191474 : [(8927 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(_504931, hAPP(hAPP(c_Power_Opower__class_Opower(_504931), _504933), _504935), hAPP(hAPP(c_Power_Opower__class_Opower(_504931), _504933), _504937)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _504935, _504937))], (8933 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _504935, _504937), -(c_Orderings_Oord__class_Oless(_504931, hAPP(hAPP(c_Power_Opower__class_Opower(_504931), _504933), _504935), hAPP(hAPP(c_Power_Opower__class_Opower(_504931), _504933), _504937)))]]], (8939 ^ _191474) ^ [_505606, _505608, _505610, _505612] : [class_Rings_Olinordered__semidom(_505606), c_Orderings_Oord__class_Oless(_505606, c_Groups_Oone__class_Oone(_505606), _505608), c_Orderings_Oord__class_Oless(_505606, hAPP(hAPP(c_Power_Opower__class_Opower(_505606), _505608), _505610), hAPP(hAPP(c_Power_Opower__class_Opower(_505606), _505608), _505612)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _505610, _505612))], (8953 ^ _191474) ^ [_506090, _506092, _506094, _506096] : [class_Rings_Olinordered__semidom(_506090), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _506092, _506094), c_Orderings_Oord__class_Oless(_506090, c_Groups_Oone__class_Oone(_506090), _506096), -(c_Orderings_Oord__class_Oless(_506090, hAPP(hAPP(c_Power_Opower__class_Opower(_506090), _506096), _506092), hAPP(hAPP(c_Power_Opower__class_Opower(_506090), _506096), _506094)))], (8967 ^ _191474) ^ [_506574, _506576, _506578, _506580] : [class_Rings_Olinordered__semidom(_506574), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _506576, _506578), c_Orderings_Oord__class_Oless__eq(_506574, c_Groups_Oone__class_Oone(_506574), _506580), -(c_Orderings_Oord__class_Oless__eq(_506574, hAPP(hAPP(c_Power_Opower__class_Opower(_506574), _506580), _506576), hAPP(hAPP(c_Power_Opower__class_Opower(_506574), _506580), _506578)))], (8981 ^ _191474) ^ [_507044, _507046, _507048] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _507044), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _507044, _507046), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _507048, _507046), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _507048, _507044)))], (8991 ^ _191474) ^ [_507375, _507377] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _507375), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _507377), _507375), _507375) = _507377)], (8997 ^ _191474) ^ [_507607, _507609] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _507607), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _507607), _507609), _507607) = _507609)], (9003 ^ _191474) ^ [_507839, _507841] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _507839), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _507841), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _507841, _507839), _507841))], (9013 ^ _191474) ^ [_508166, _508168, _508170] : [class_Rings_Olinordered__semidom(_508166), c_Orderings_Oord__class_Oless(_508166, c_Groups_Ozero__class_Ozero(_508166), _508168), c_Orderings_Oord__class_Oless(_508166, _508168, c_Groups_Oone__class_Oone(_508166)), -(c_Orderings_Oord__class_Oless(_508166, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508166), _508168), hAPP(hAPP(c_Power_Opower__class_Opower(_508166), _508168), _508170)), hAPP(hAPP(c_Power_Opower__class_Opower(_508166), _508168), _508170)))], (9027 ^ _191474) ^ [_508656, _508658, _508660, _508662] : [class_Rings_Olinordered__semidom(_508656), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _508658, _508660), c_Orderings_Oord__class_Oless(_508656, c_Groups_Ozero__class_Ozero(_508656), _508662), c_Orderings_Oord__class_Oless(_508656, _508662, c_Groups_Oone__class_Oone(_508656)), -(c_Orderings_Oord__class_Oless(_508656, hAPP(hAPP(c_Power_Opower__class_Opower(_508656), _508662), _508660), hAPP(hAPP(c_Power_Opower__class_Opower(_508656), _508662), _508658)))], (9045 ^ _191474) ^ [_509243, _509245, _509247, _509249] : [class_Rings_Olinordered__semidom(_509243), hAPP(hAPP(c_Power_Opower__class_Opower(_509243), _509245), _509247) = hAPP(hAPP(c_Power_Opower__class_Opower(_509243), _509249), _509247), c_Orderings_Oord__class_Oless__eq(_509243, c_Groups_Ozero__class_Ozero(_509243), _509245), c_Orderings_Oord__class_Oless__eq(_509243, c_Groups_Ozero__class_Ozero(_509243), _509249), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _509247), -(_509245 = _509249)], (9067 ^ _191474) ^ [_509925, _509927, _509929, _509931] : [class_Rings_Olinordered__semidom(_509925), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _509927, _509929), c_Orderings_Oord__class_Oless__eq(_509925, c_Groups_Ozero__class_Ozero(_509925), _509931), c_Orderings_Oord__class_Oless__eq(_509925, _509931, c_Groups_Oone__class_Oone(_509925)), -(c_Orderings_Oord__class_Oless__eq(_509925, hAPP(hAPP(c_Power_Opower__class_Opower(_509925), _509931), _509929), hAPP(hAPP(c_Power_Opower__class_Opower(_509925), _509931), _509927)))], (9085 ^ _191474) ^ [_510512, _510514, _510516, _510518] : [class_Rings_Olinordered__semidom(_510512), c_Orderings_Oord__class_Oless(_510512, c_Groups_Oone__class_Oone(_510512), _510514), 9092 ^ _191474 : [(9093 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(_510512, hAPP(hAPP(c_Power_Opower__class_Opower(_510512), _510514), _510516), hAPP(hAPP(c_Power_Opower__class_Opower(_510512), _510514), _510518)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _510516, _510518))], (9099 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _510516, _510518), -(c_Orderings_Oord__class_Oless__eq(_510512, hAPP(hAPP(c_Power_Opower__class_Opower(_510512), _510514), _510516), hAPP(hAPP(c_Power_Opower__class_Opower(_510512), _510514), _510518)))]]], (9105 ^ _191474) ^ [_511187, _511189, _511191, _511193] : [class_Rings_Olinordered__semidom(_511187), c_Orderings_Oord__class_Oless(_511187, c_Groups_Oone__class_Oone(_511187), _511189), c_Orderings_Oord__class_Oless__eq(_511187, hAPP(hAPP(c_Power_Opower__class_Opower(_511187), _511189), _511191), hAPP(hAPP(c_Power_Opower__class_Opower(_511187), _511189), _511193)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _511191, _511193))], (9119 ^ _191474) ^ [_511657, _511659, _511661] : [class_Rings_Olinordered__semidom(_511657), c_Orderings_Oord__class_Oless(_511657, c_Groups_Oone__class_Oone(_511657), _511659), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _511661), -(c_Orderings_Oord__class_Oless(_511657, c_Groups_Oone__class_Oone(_511657), hAPP(hAPP(c_Power_Opower__class_Opower(_511657), _511659), _511661)))], (9133 ^ _191474) ^ [_512115, _512117, _512119, _512121] : [class_Fields_Ofield(_512115), -(_512117 = c_Groups_Ozero__class_Ozero(_512115)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _512119, _512121), -(hAPP(hAPP(c_Power_Opower__class_Opower(_512115), _512117), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _512121, _512119)) = c_Rings_Oinverse__class_Odivide(_512115, hAPP(hAPP(c_Power_Opower__class_Opower(_512115), _512117), _512121), hAPP(hAPP(c_Power_Opower__class_Opower(_512115), _512117), _512119)))], (9147 ^ _191474) ^ [_512602, _512604] : [-(_512602 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_512604 = 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), _512602), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 9154 ^ [_512602, _512604]), _512604)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9158 ^ _191474) ^ [_513010] : [class_Power_Opower(_513010), -(c_Power_Opower__class_Opower(_513010) = c_Power_Opower_Opower(_513010, c_Groups_Oone__class_Oone(_513010), c_Groups_Otimes__class_Otimes(_513010)))], (9174 ^ _191474) ^ [_513529, _513531] : [9175 ^ _191474 : [(9176 ^ _191474) ^ [] : [_513531 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9178 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _513529)]], -(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), _513529), _513531)))], (9164 ^ _191474) ^ [_513261, _513263] : [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), _513261), _513263)), -(_513263 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _513261))], (9182 ^ _191474) ^ [_513859, _513861, _513863, _513865] : [_513859 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _513861), _513863), _513865), -(_513861 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _513859, _513861) = _513863), 9189 ^ _191474 : [(9190 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _513861))], (9192 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _513865), c_Orderings_Oord__class_Oless(tc_Int_Oint, _513865, _513861)]], 9197 ^ _191474 : [(9198 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _513861)], (9200 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _513861, _513865), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _513865, c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (9258 ^ _191474) ^ [_516433, _516435, _516437] : [-(hBOOL(hAPP(_516433, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _516435, _516437)))), 9261 ^ _191474 : [(9262 ^ _191474) ^ [] : [-(_516437 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9264 ^ _191474) ^ [] : [hBOOL(hAPP(_516433, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 9267 ^ _191474 : [(9268 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _516437))], (9272 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 9270 ^ [_516433, _516435, _516437]))], (9274 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, 9270 ^ [_516433, _516435, _516437], _516437))], (9276 ^ _191474) ^ [] : [-(_516435 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _516437), 9269 ^ [_516433, _516435, _516437]), 9270 ^ [_516433, _516435, _516437]))], (9278 ^ _191474) ^ [] : [hBOOL(hAPP(_516433, 9269 ^ [_516433, _516435, _516437]))]], 9279 ^ _191474 : [(9280 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _516437, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9284 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _516437, 9282 ^ [_516433, _516435, _516437]))], (9286 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 9282 ^ [_516433, _516435, _516437], c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9288 ^ _191474) ^ [] : [-(_516435 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _516437), 9281 ^ [_516433, _516435, _516437]), 9282 ^ [_516433, _516435, _516437]))], (9290 ^ _191474) ^ [] : [hBOOL(hAPP(_516433, 9281 ^ [_516433, _516435, _516437]))]]], (9212 ^ _191474) ^ [_514813, _514815, _514817] : [hBOOL(hAPP(_514813, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _514815, _514817))), 9215 ^ _191474 : [(9216 ^ _191474) ^ [] : [_514817 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_514813, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9222 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _514817), 9225 ^ _191474 : [(9226 ^ _191474) ^ [_515334] : [-(hBOOL(hAPP(_514813, _515334))), 9227 ^ _191474 : [(9228 ^ _191474) ^ [_515456] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515456), c_Orderings_Oord__class_Oless(tc_Int_Oint, _515456, _514817), _514815 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _514817), _515334), _515456)]]]]], (9240 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _514817, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9243 ^ _191474 : [(9244 ^ _191474) ^ [_515928] : [-(hBOOL(hAPP(_514813, _515928))), 9245 ^ _191474 : [(9246 ^ _191474) ^ [_516050] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _514817, _516050), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _516050, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _514815 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _514817), _515928), _516050)]]]]]]], (9294 ^ _191474) ^ [_518068, _518070, _518072] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _518068), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _518070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _518072), _518068)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _518070, _518072), _518068))], (9300 ^ _191474) ^ [_518336, _518338, _518340] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _518336), _518336 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _518338, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _518336), _518340)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _518338), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _518340, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9314 ^ _191474) ^ [_518778, _518780, _518782] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _518778), _518778 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _518780, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _518778), _518782)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _518780, _518778), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _518782))], (9328 ^ _191474) ^ [_519220, _519222, _519224] : [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), _519220), _519222), _519224)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _519224, _519220), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _519220), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _519222))], (9342 ^ _191474) ^ [_519664, _519666, _519668] : [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), _519664), _519666), _519668), 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), _519668), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _519664), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _519666, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9356 ^ _191474) ^ [_520136, _520138, _520140, _520142, _520144] : [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), _520136), _520138), _520140), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _520136), _520142), _520144)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _520140), c_Orderings_Oord__class_Oless(tc_Int_Oint, _520140, _520136), c_Orderings_Oord__class_Oless(tc_Int_Oint, _520144, _520136), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _520138, _520142))], (9374 ^ _191474) ^ [_520773, _520775, _520777, _520779, _520781, _520783] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _520773), _520775), _520777) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _520779), _520781), _520783), 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), _520779), _520781), _520783)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _520783, _520779), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _520777), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _520779), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _520779, _520773), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _520775, _520781))], (9400 ^ _191474) ^ [_521646, _521648, _521650, _521652, _521654] : [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), _521646), _521648), _521650), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _521646), _521652), _521654)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _521654, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _521646, _521654), c_Orderings_Oord__class_Oless(tc_Int_Oint, _521646, _521650), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _521652, _521648))], (9418 ^ _191474) ^ [_522283, _522285, _522287, _522289, _522291, _522293] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _522283), _522285), _522287) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _522289), _522291), _522293), 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), _522289), _522291), _522293), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _522287, _522283), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _522293), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _522289), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _522289, _522283), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _522291, _522285))], (9444 ^ _191474) ^ [_523114, _523116] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _523114), 9447 ^ _191474 : [(9448 ^ _191474) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _523114), _523116) = c_Groups_Oone__class_Oone(tc_Int_Oint), 9451 ^ _191474 : [(9452 ^ _191474) ^ [] : [-(_523114 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9454 ^ _191474) ^ [] : [-(_523116 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (9456 ^ _191474) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _523114), _523116) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _523114 = c_Groups_Oone__class_Oone(tc_Int_Oint), _523116 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (9466 ^ _191474) ^ [_523766, _523768, _523770] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _523766, _523768), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _523770), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _523770), _523766), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _523770), _523768)))], (9476 ^ _191474) ^ [_524104, _524106, _524108] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524104), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _524106, _524108)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524104), _524106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524104), _524108)))], (9478 ^ _191474) ^ [_524240, _524242, _524244] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _524240, _524242)), _524244) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524240), _524244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524242), _524244)))], (9480 ^ _191474) ^ [_524376, _524378, _524380] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524376), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _524378, _524380)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524376), _524378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524376), _524380)))], (9482 ^ _191474) ^ [_524512, _524514, _524516] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _524512, _524514)), _524516) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524512), _524516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524514), _524516)))], (9484 ^ _191474) ^ [_524648, _524650, _524652] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524648), _524650)), _524652) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524650), _524652)))], (9486 ^ _191474) ^ [_524768, _524770] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524768), _524770) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524770), _524768))], (9488 ^ _191474) ^ [_524860] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _524860) = _524860)], (9490 ^ _191474) ^ [_524941] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524941), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _524941)], (9492 ^ _191474) ^ [_525096, _525098, _525100, _525102, _525104] : [class_Fields_Ofield(_525096), c_Polynomial_Opdivmod__rel(_525096, _525098, _525100, _525102, _525104), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_525096), _525098, _525100) = _525102)], (9502 ^ _191474) ^ [_525469, _525471, _525473, _525475] : [class_Fields_Ofield(_525469), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_525469), _525471, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_525469)), _525473), _525475)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_525469), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_525469), _525471, _525473), _525475))], (9508 ^ _191474) ^ [_525758, _525760, _525762, _525764] : [-(hAPP(hAPP(c_Power_Opower_Opower(_525758, _525760, _525762), _525764), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _525760)], (9510 ^ _191474) ^ [_525895, _525897, _525899] : [class_Fields_Ofield(_525895), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_525895, _525897), c_Polynomial_Odegree(_525895, _525899)), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_525895), _525897, _525899) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_525895)))], (9520 ^ _191474) ^ [_526235, _526237, _526239] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Orcis(_526235, _526237)), _526239) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _526235), _526239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _526239)), _526237)))], (9522 ^ _191474) ^ [_526373, _526375] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _526373), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _526375), 9530 ^ _191474 : [(9531 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9529 ^ [_526373, _526375]))], (9533 ^ _191474) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 9529 ^ [_526373, _526375]), _526373) = _526375)]]], (9535 ^ _191474) ^ [_526842, _526844] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _526842, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _526844), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _526842, _526844), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9545 ^ _191474) ^ [_527155, _527157] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _527155, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9548 ^ _191474 : [(9549 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _527157, _527155), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _527157))], (9555 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _527157), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _527157, _527155), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (9561 ^ _191474) ^ [_527635, _527637] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _527635), 9564 ^ _191474 : [(9565 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _527637, _527635), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _527637, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9571 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _527637, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _527637, _527635), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (9577 ^ _191474) ^ [_528086] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _528086) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9579 ^ _191474) ^ [_528197, _528199] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _528197), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _528199), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _528197, _528199), _528197))], (9589 ^ _191474) ^ [_528496] : [-(_528496 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _528496, _528496) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9595 ^ _191474) ^ [_528740, _528742] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _528740, _528742) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_528742 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9604 ^ _191474 : [(9605 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _528740))], (9607 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _528740, _528742))]], 9608 ^ _191474 : [(9609 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _528740, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9611 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _528742, _528740))]]], (9613 ^ _191474) ^ [_529248, _529250] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _529248, _529250) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9614 ^ _191474 : [(9615 ^ _191474) ^ [] : [_529250 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (9617 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _529248), c_Orderings_Oord__class_Oless(tc_Int_Oint, _529248, _529250)], (9623 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _529248, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _529250, _529248)]]], (9631 ^ _191474) ^ [_529801, _529803] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _529801), 9634 ^ _191474 : [(9635 ^ _191474) ^ [] : [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, _529803, _529801)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _529803))], (9641 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _529803), -(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, _529803, _529801)))]]], (9647 ^ _191474) ^ [_530281, _530283] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _530281), 9650 ^ _191474 : [(9651 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _530283, _530281)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _530281, _530283))], (9657 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _530281, _530283), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _530283, _530281)))]]], (9663 ^ _191474) ^ [_530761, _530763] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _530761), 9666 ^ _191474 : [(9667 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _530761, _530763)), 9670 ^ _191474 : [(9671 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _530763, _530761))], (9673 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _530763))]]], (9675 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _530761, _530763))), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _530763, _530761), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _530763)]]], (9685 ^ _191474) ^ [_531402, _531404] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _531402), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _531404), -(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, _531402, _531404)))], (9695 ^ _191474) ^ [_531729, _531731, _531733] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _531729), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _531731), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _531731, _531733), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _531729, _531733), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _531729, _531731)))], (9709 ^ _191474) ^ [_532155, _532157] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _532155), c_Orderings_Oord__class_Oless(tc_Int_Oint, _532157, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _532155, _532157), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9719 ^ _191474) ^ [_532468, _532470] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _532468), c_Orderings_Oord__class_Oless(tc_Int_Oint, _532468, _532470), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _532468, _532470) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9729 ^ _191474) ^ [_532779, _532781] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _532779, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9732 ^ _191474 : [(9733 ^ _191474) ^ [] : [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, _532781, _532779)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _532781, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9739 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _532781, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _532781, _532779)))]]], (9745 ^ _191474) ^ [_533259, _533261] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _533259, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _533261), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _533259, _533261), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9755 ^ _191474) ^ [_533586, _533588, _533590] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _533586, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _533588), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _533588, _533590), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _533586, _533588), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _533586, _533590)))], (9769 ^ _191474) ^ [_534012, _534014] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _534012, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _534014, _534012), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _534012, _534014) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9779 ^ _191474) ^ [_534337, _534339, _534341] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _534337, _534339), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _534341), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _534337, _534341), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _534339, _534341)))], (9789 ^ _191474) ^ [_534682, _534684, _534686] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _534682, _534684), c_Orderings_Oord__class_Oless(tc_Int_Oint, _534686, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _534684, _534686), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _534682, _534686)))], (9799 ^ _191474) ^ [_534983] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _534983), _534983) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (9801 ^ _191474) ^ [_535127, _535129] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _535127, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _535129, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _535127, _535129))], (9807 ^ _191474) ^ [_535301, _535303] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _535301, _535303), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _535301, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _535303, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9813 ^ _191474) ^ [_535554, _535556] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _535554, c_Groups_Oone__class_Oone(tc_Int_Oint)), _535556), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _535554, _535556))], (9819 ^ _191474) ^ [_535728, _535730] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _535728, _535730), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _535728, c_Groups_Oone__class_Oone(tc_Int_Oint)), _535730))], (9825 ^ _191474) ^ [_535967] : [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), _535967), _535967), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _535967, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9831 ^ _191474) ^ [_536143] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _536143, 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), _536143), _536143), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9837 ^ _191474) ^ [_536355] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _536355), -(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), _536355)))], (9843 ^ _191474) ^ [_536571, _536573] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _536571, _536573), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536571, c_Groups_Oone__class_Oone(tc_Int_Oint)), _536573))], (9859 ^ _191474) ^ [_537086, _537088] : [9860 ^ _191474 : [(9861 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _537086, _537088)], (9863 ^ _191474) ^ [] : [_537086 = _537088]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _537086, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _537088, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9849 ^ _191474) ^ [_536822, _536824] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _536822, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536824, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _536822, _536824)), -(_536822 = _536824)], (9867 ^ _191474) ^ [_537413, _537415] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _537413, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _537415, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _537413, _537415))], (9873 ^ _191474) ^ [_537587, _537589] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _537587, _537589), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _537587, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _537589, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9879 ^ _191474) ^ [_537826] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _537826), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _537826))], (9885 ^ _191474) ^ [_537986] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _537986), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _537986))], (9891 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9893 ^ _191474) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (9895 ^ _191474) ^ [_538330, _538332] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _538330, _538332), 9898 ^ _191474 : [(9899 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _538330, _538332))], (9901 ^ _191474) ^ [] : [_538330 = _538332]]], (9903 ^ _191474) ^ [_538572, _538574] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _538572, _538574)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _538572, _538574), -(_538572 = _538574)], (9913 ^ _191474) ^ [_538908, _538910, _538912, _538914] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _538908, _538910), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _538912, _538914), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _538908, _538912), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _538910, _538914)))], (9923 ^ _191474) ^ [_539220] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _539220) = _539220)], (9925 ^ _191474) ^ [_539302] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _539302, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _539302)], (9927 ^ _191474) ^ [_539427, _539429, _539431] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _539427, _539429), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _539427, _539431), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _539429, _539431)))], (9933 ^ _191474) ^ [_539663, _539665] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _539663, _539665)), -(_539663 = _539665), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _539665, _539663))], (9943 ^ _191474) ^ [_539997, _539999] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _539997, _539999), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _539997, _539999), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9949 ^ _191474) ^ [_540171, _540173] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _540171, _540173), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _540171, _540173))], (9955 ^ _191474) ^ [_540380, _540382] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540380, _540382) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540382, _540380))], (9957 ^ _191474) ^ [_540496, _540498, _540500] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540496, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540498, _540500)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540498, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540496, _540500)))], (9959 ^ _191474) ^ [_540622, _540624, _540626] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540622, _540624), _540626) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540622, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540624, _540626)))], (9961 ^ _191474) ^ [_540763, _540765, _540767] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _540763, _540765), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540767, _540763), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540767, _540765)))], (9967 ^ _191474) ^ [_540999, _541001] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _540999, _541001), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _541001, _540999), -(_540999 = _541001)], (9977 ^ _191474) ^ [_541316, _541318, _541320] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _541316, _541318), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _541318, _541320), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _541316, _541320))], (9987 ^ _191474) ^ [_541631, _541633] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _541631, _541633)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _541633, _541631))], (9993 ^ _191474) ^ [_541817] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _541817, _541817))], (9995 ^ _191474) ^ [_541938, _541940, _541942, _541944] : [-(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Complex_Orcis(_541938, _541940), c_Complex_Orcis(_541942, _541944)) = c_Complex_Orcis(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _541938, _541942), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _541940, _541944)))], (9997 ^ _191474) ^ [_542043] : [-(c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _542043) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (9999 ^ _191474) ^ [_542166, _542168, _542170, _542172] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Orcis(_542166, _542168)), c_Complex_Orcis(_542170, _542172)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _542166), _542170), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _542168, _542172)))], (10001 ^ _191474) ^ [_542304, _542306] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _542304), -(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), _542304), _542306)))], (10007 ^ _191474) ^ [_542530, _542532] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _542530), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _542532), -(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), _542530), _542532)))], (10017 ^ _191474) ^ [] : [-(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)))], (10019 ^ _191474) ^ [] : [-(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)))], (10021 ^ _191474) ^ [_542953, _542955] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _542953), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _542955), -(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, _542953, _542955)))], (10031 ^ _191474) ^ [_543266, _543268] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _543266), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _543268), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _543268), _543266), _543268) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _543268), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _543266, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (10041 ^ _191474) ^ [_543629, _543631] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _543629, _543631), -(c_Nat__Transfer_Otsub(_543631, _543629) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _543631, _543629))], (10047 ^ _191474) ^ [_543807, _543809] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _543807, _543809)), -(c_Nat__Transfer_Otsub(_543809, _543807) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10053 ^ _191474) ^ [_544030, _544032] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544030, _544032), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_544030), c_Nat_OSuc(_544032)))], (10059 ^ _191474) ^ [_544223] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544223, c_Nat_OSuc(_544223)))], (10061 ^ _191474) ^ [_544304] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_544304)))], (10063 ^ _191474) ^ [_544441, _544443, _544445, _544447, _544449] : [-(hAPP(hAPP(c_Power_Opower_Opower(_544441, _544443, _544445), _544447), c_Nat_OSuc(_544449)) = hAPP(hAPP(_544445, _544447), hAPP(hAPP(c_Power_Opower_Opower(_544441, _544443, _544445), _544447), _544449)))], (10065 ^ _191474) ^ [_544627, _544629, _544631] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_544627)), _544629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_544627)), _544631), -(_544629 = _544631)], (10071 ^ _191474) ^ [_544827, _544829, _544831] : [_544829 = _544831, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_544827)), _544829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_544827)), _544831))], (10077 ^ _191474) ^ [_545091, _545093, _545095] : [class_Rings_Ocomm__semiring__1(_545091), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545091), hAPP(hAPP(c_Power_Opower__class_Opower(_545091), _545093), _545095)), _545093) = hAPP(hAPP(c_Power_Opower__class_Opower(_545091), _545093), c_Nat_OSuc(_545095)))], (10083 ^ _191474) ^ [_545371, _545373, _545375] : [class_Rings_Ocomm__semiring__1(_545371), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545371), _545373), hAPP(hAPP(c_Power_Opower__class_Opower(_545371), _545373), _545375)) = hAPP(hAPP(c_Power_Opower__class_Opower(_545371), _545373), c_Nat_OSuc(_545375)))], (10089 ^ _191474) ^ [_545651, _545653, _545655] : [class_Rings_Ocomm__semiring__1(_545651), -(hAPP(hAPP(c_Power_Opower__class_Opower(_545651), _545653), c_Nat_OSuc(_545655)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545651), _545653), hAPP(hAPP(c_Power_Opower__class_Opower(_545651), _545653), _545655)))], (10095 ^ _191474) ^ [_545931, _545933, _545935] : [class_Groups_Omonoid__mult(_545931), -(hAPP(hAPP(c_Power_Opower__class_Opower(_545931), _545933), c_Nat_OSuc(_545935)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545931), hAPP(hAPP(c_Power_Opower__class_Opower(_545931), _545933), _545935)), _545933))], (10101 ^ _191474) ^ [_546211, _546213, _546215] : [class_Power_Opower(_546211), -(hAPP(hAPP(c_Power_Opower__class_Opower(_546211), _546213), c_Nat_OSuc(_546215)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546211), _546213), hAPP(hAPP(c_Power_Opower__class_Opower(_546211), _546213), _546215)))], (10107 ^ _191474) ^ [_546477, _546479] : [c_Nat_OSuc(_546477) = c_Nat_OSuc(_546479), -(_546477 = _546479)], (10113 ^ _191474) ^ [_546724, _546726] : [c_Nat_OSuc(_546724) = c_Nat_OSuc(_546726), -(_546724 = _546726)], (10119 ^ _191474) ^ [_546894, _546896] : [_546894 = _546896, -(c_Nat_OSuc(_546894) = c_Nat_OSuc(_546896))], (10125 ^ _191474) ^ [_547084] : [c_Nat_OSuc(_547084) = _547084], (10127 ^ _191474) ^ [_547163] : [_547163 = c_Nat_OSuc(_547163)], (10129 ^ _191474) ^ [_547242] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_547242), _547242)], (10131 ^ _191474) ^ [_547381, _547383] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _547381, _547383)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_547383), _547381))], (10137 ^ _191474) ^ [_547554, _547556] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_547556), _547554), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _547554, _547556)], (10153 ^ _191474) ^ [_548068, _548070] : [10154 ^ _191474 : [(10155 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _548068, _548070)], (10157 ^ _191474) ^ [] : [_548068 = c_Nat_OSuc(_548070)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _548068, c_Nat_OSuc(_548070)))], (10143 ^ _191474) ^ [_547804, _547806] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _547804, c_Nat_OSuc(_547806)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _547804, _547806)), -(_547804 = c_Nat_OSuc(_547806))], (10161 ^ _191474) ^ [_548395, _548397] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_548395), c_Nat_OSuc(_548397)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _548395, _548397))], (10167 ^ _191474) ^ [_548569, _548571] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _548569, _548571), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_548569), c_Nat_OSuc(_548571)))], (10173 ^ _191474) ^ [_548793, _548795] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _548793, _548795), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _548793, c_Nat_OSuc(_548795)))], (10179 ^ _191474) ^ [_549011, _549013] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _549011, c_Nat_OSuc(_549013)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _549011, _549013)), -(_549011 = c_Nat_OSuc(_549013))], (10189 ^ _191474) ^ [_549325, _549327] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_549325), _549327), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _549325, _549327))], (10195 ^ _191474) ^ [_549542, _549544, _549546] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_549542), _549544), c_Nat_OSuc(_549546)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _549542, _549544), _549546))], (10197 ^ _191474) ^ [_549658, _549660] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_549658), c_Nat_OSuc(_549660)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _549658, _549660))], (10199 ^ _191474) ^ [_549764, _549766] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _549764, c_Nat_OSuc(_549766)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _549764, _549766)))], (10201 ^ _191474) ^ [_549870, _549872] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_549870), _549872) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _549870, _549872)))], (10203 ^ _191474) ^ [_549976, _549978] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_549976), _549978) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _549976, c_Nat_OSuc(_549978)))], (10205 ^ _191474) ^ [_550097, _550099] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_550097), c_Nat_OSuc(_550099)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550097, _550099))], (10211 ^ _191474) ^ [_550319, _550321] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_550319), _550321), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550319, _550321))], (10217 ^ _191474) ^ [_550537, _550539] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550537, c_Nat_OSuc(_550539)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550537, _550539)), -(_550537 = _550539)], (10227 ^ _191474) ^ [_550861, _550863, _550865] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550861, _550863), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550863, _550865), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_550861), _550865))], (10237 ^ _191474) ^ [_551180, _551182] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551180, _551182), -(c_Nat_OSuc(_551180) = _551182), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_551180), _551182))], (10247 ^ _191474) ^ [_551494, _551496] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551494, _551496), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551494, c_Nat_OSuc(_551496)))], (10253 ^ _191474) ^ [_551712, _551714] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551712, _551714)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551712, c_Nat_OSuc(_551714)), -(_551714 = _551712)], (10263 ^ _191474) ^ [_552022, _552024] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552022, _552024)), 10266 ^ _191474 : [(10267 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552022, c_Nat_OSuc(_552024)), -(_552022 = _552024)], (10273 ^ _191474) ^ [] : [_552022 = _552024, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552022, c_Nat_OSuc(_552024)))]]], (10279 ^ _191474) ^ [_552525, _552527] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_552525), c_Nat_OSuc(_552527)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552525, _552527))], (10285 ^ _191474) ^ [_552699, _552701] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552699, _552701), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_552699), c_Nat_OSuc(_552701)))], (10301 ^ _191474) ^ [_553212, _553214] : [10302 ^ _191474 : [(10303 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553212, _553214)], (10305 ^ _191474) ^ [] : [_553212 = _553214]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553212, c_Nat_OSuc(_553214)))], (10291 ^ _191474) ^ [_552952, _552954] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552952, c_Nat_OSuc(_552954)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552952, _552954)), -(_552952 = _552954)], (10309 ^ _191474) ^ [_553535, _553537] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553535, _553537)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553537, c_Nat_OSuc(_553535)))], (10315 ^ _191474) ^ [_553708, _553710] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553710, c_Nat_OSuc(_553708)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553708, _553710)], (10321 ^ _191474) ^ [_553899] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_553899)], (10323 ^ _191474) ^ [_553978] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_553978)], (10325 ^ _191474) ^ [_554057] : [c_Nat_OSuc(_554057) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10327 ^ _191474) ^ [_554136] : [c_Nat_OSuc(_554136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10329 ^ _191474) ^ [_554215] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_554215)], (10331 ^ _191474) ^ [_554294] : [c_Nat_OSuc(_554294) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10333 ^ _191474) ^ [_554374] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _554374, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _554374)], (10335 ^ _191474) ^ [_554470, _554472] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _554470, c_Nat_OSuc(_554472)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _554470, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _554472))], (10337 ^ _191474) ^ [_554564] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_554564), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _554564)], (10339 ^ _191474) ^ [_554648] : [-(c_Nat_OSuc(_554648) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _554648))], (10341 ^ _191474) ^ [_554732] : [-(c_Nat_OSuc(_554732) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554732, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10343 ^ _191474) ^ [_554845, _554847] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _554845, _554847), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_554847), _554845) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _554847, _554845)))], (10349 ^ _191474) ^ [_555124, _555126, _555128] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_555124)), _555126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_555124)), _555128)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555126, _555128))], (10355 ^ _191474) ^ [_555328, _555330, _555332] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555330, _555332), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_555328)), _555330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_555328)), _555332)))], (10361 ^ _191474) ^ [_555567, _555569] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_555567)), _555569) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _555569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555567), _555569)))], (10363 ^ _191474) ^ [_555679, _555681] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555679), c_Nat_OSuc(_555681)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _555679, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555679), _555681)))], (10365 ^ _191474) ^ [_555791, _555793] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _555791, _555793), c_Nat_OSuc(_555791)))], (10367 ^ _191474) ^ [_555950, _555952, _555954] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_555950)), _555952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_555950)), _555954)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _555952, _555954))], (10373 ^ _191474) ^ [_556154, _556156, _556158] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _556156, _556158), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_556154)), _556156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_556154)), _556158)))], (10379 ^ _191474) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10381 ^ _191474) ^ [_556490, _556492] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _556490, _556492), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_556490), _556492))], (10387 ^ _191474) ^ [_556660, _556662] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_556660), _556662), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _556660, _556662))], (10393 ^ _191474) ^ [_556909, _556911] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _556909, c_Nat_OSuc(_556911)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556909, _556911))], (10399 ^ _191474) ^ [_557079, _557081] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557079, _557081), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557079, c_Nat_OSuc(_557081)))], (10405 ^ _191474) ^ [_557328, _557330] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_557328), _557330), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557328, _557330))], (10411 ^ _191474) ^ [_557498, _557500] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557498, _557500), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_557498), _557500))], (10417 ^ _191474) ^ [_557718, _557720] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557718, _557720), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557718, c_Nat_OSuc(_557720)))], (10423 ^ _191474) ^ [_557936, _557938] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557936, _557938), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_557936), _557938))], (10429 ^ _191474) ^ [_558154, _558156] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _558154, _558156), 10432 ^ _191474 : [(10433 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558156, c_Nat_OSuc(_558154)), -(_558156 = _558154)], (10439 ^ _191474) ^ [] : [_558156 = _558154, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558156, c_Nat_OSuc(_558154)))]]], (10445 ^ _191474) ^ [_558625, _558627] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_558625), _558627), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558625, _558627))], (10451 ^ _191474) ^ [_558828, _558830] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558828, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _558828, _558830))))], (10453 ^ _191474) ^ [_558929, _558931] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558929, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _558931, _558929))))], (10455 ^ _191474) ^ [_559074, _559076] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _559074, _559076), -(_559076 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559074, 10458 ^ [_559074, _559076])))], (10462 ^ _191474) ^ [_559313, _559315] : [10463 ^ _191474 : [(10464 ^ _191474) ^ [_559390] : [_559315 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559313, _559390))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _559313, _559315))], (10468 ^ _191474) ^ [_559590, _559592] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _559590), _559592) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10471 ^ _191474 : [(10472 ^ _191474) ^ [] : [-(_559590 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10474 ^ _191474) ^ [] : [-(_559592 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10476 ^ _191474) ^ [_559839, _559841] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _559839), _559841) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _559839 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _559841 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10486 ^ _191474) ^ [_560181, _560183] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _560181, _560183) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10491 ^ _191474 : [(10492 ^ _191474) ^ [] : [-(_560181 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10494 ^ _191474) ^ [] : [-(_560183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 10495 ^ _191474 : [(10496 ^ _191474) ^ [] : [-(_560181 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10498 ^ _191474) ^ [] : [-(_560183 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10500 ^ _191474) ^ [_560591, _560593] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _560591, _560593) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 10501 ^ _191474 : [(10502 ^ _191474) ^ [] : [_560591 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _560593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10508 ^ _191474) ^ [] : [_560591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _560593 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10516 ^ _191474) ^ [_561092, _561094] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _561092, _561094), 10521 ^ _191474 : [(10522 ^ _191474) ^ [] : [-(_561092 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10524 ^ _191474) ^ [] : [-(_561094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 10525 ^ _191474 : [(10526 ^ _191474) ^ [] : [-(_561092 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10528 ^ _191474) ^ [] : [-(_561094 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10530 ^ _191474) ^ [_561502, _561504] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _561502, _561504)), 10531 ^ _191474 : [(10532 ^ _191474) ^ [] : [_561502 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _561504 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10538 ^ _191474) ^ [] : [_561502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _561504 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10546 ^ _191474) ^ [_561989] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _561989), -(_561989 = c_Nat_OSuc(10549 ^ [_561989]))], (10553 ^ _191474) ^ [_562204] : [10554 ^ _191474 : [(10555 ^ _191474) ^ [_562275] : [_562204 = c_Nat_OSuc(_562275)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _562204))], (10559 ^ _191474) ^ [_562453] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562453, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_562453 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10565 ^ _191474) ^ [_562611] : [_562611 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562611, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10571 ^ _191474) ^ [_562848, _562850] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562848, c_Nat_OSuc(_562850)), -(_562848 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10579 ^ _191474 : [(10580 ^ _191474) ^ [] : [-(_562848 = c_Nat_OSuc(10578 ^ [_562848, _562850]))], (10582 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 10578 ^ [_562848, _562850], _562850))]]], (10584 ^ _191474) ^ [_563260, _563262] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _563260, c_Nat_OSuc(_563262))), 10585 ^ _191474 : [(10586 ^ _191474) ^ [] : [_563260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10588 ^ _191474) ^ [_563429] : [_563260 = c_Nat_OSuc(_563429), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _563429, _563262)]]], (10596 ^ _191474) ^ [_563712, _563714] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_563712), c_Groups_Ozero__class_Ozero(_563712)), c_Nat_OSuc(_563714)) = c_Groups_Ozero__class_Ozero(_563712)), class_Power_Opower(_563712), class_Rings_Osemiring__0(_563712)], (10606 ^ _191474) ^ [_564021] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564021, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_564021 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_564021 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10616 ^ _191474) ^ [_564284] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _564284) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10628 ^ _191474) ^ [_564687, _564689] : [10629 ^ _191474 : [(10630 ^ _191474) ^ [] : [_564689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10632 ^ _191474) ^ [] : [_564687 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _564687), _564689) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10618 ^ _191474) ^ [_564423, _564425] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _564423), _564425) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_564425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_564423 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10636 ^ _191474) ^ [_565013, _565015, _565017, _565019] : [class_Rings_Olinordered__semidom(_565013), hAPP(hAPP(c_Power_Opower__class_Opower(_565013), _565015), c_Nat_OSuc(_565017)) = hAPP(hAPP(c_Power_Opower__class_Opower(_565013), _565019), c_Nat_OSuc(_565017)), c_Orderings_Oord__class_Oless__eq(_565013, c_Groups_Ozero__class_Ozero(_565013), _565015), c_Orderings_Oord__class_Oless__eq(_565013, c_Groups_Ozero__class_Ozero(_565013), _565019), -(_565015 = _565019)], (10654 ^ _191474) ^ [_565604, _565606, _565608, _565610] : [class_Rings_Olinordered__semidom(_565604), c_Orderings_Oord__class_Oless__eq(_565604, hAPP(hAPP(c_Power_Opower__class_Opower(_565604), _565606), c_Nat_OSuc(_565608)), hAPP(hAPP(c_Power_Opower__class_Opower(_565604), _565610), c_Nat_OSuc(_565608))), c_Orderings_Oord__class_Oless__eq(_565604, c_Groups_Ozero__class_Ozero(_565604), _565610), -(c_Orderings_Oord__class_Oless__eq(_565604, _565606, _565610))], (10668 ^ _191474) ^ [_566082, _566084, _566086] : [class_Rings_Olinordered__semidom(_566082), c_Orderings_Oord__class_Oless(_566082, c_Groups_Oone__class_Oone(_566082), _566084), -(c_Orderings_Oord__class_Oless(_566082, c_Groups_Oone__class_Oone(_566082), hAPP(hAPP(c_Power_Opower__class_Opower(_566082), _566084), c_Nat_OSuc(_566086))))], (10678 ^ _191474) ^ [_566421, _566423] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _566421), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _566423), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _566421, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566423), _566421)))], (10688 ^ _191474) ^ [_566738, _566740] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _566738), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _566740), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _566738, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566738), _566740)))], (10698 ^ _191474) ^ [_567055, _567057] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _567055), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _567057), -(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), _567057), _567055)))], (10708 ^ _191474) ^ [_567358] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567358), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _567358, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _567358)], (10714 ^ _191474) ^ [_567576, _567578] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567576), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _567576, c_Nat_OSuc(_567578)), _567576))], (10720 ^ _191474) ^ [_567831, _567833] : [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), _567831), _567833)), 10723 ^ _191474 : [(10724 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _567831))], (10726 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _567833))]]], (10728 ^ _191474) ^ [_568086, _568088] : [-(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), _568086), _568088))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _568086), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _568088)], (10738 ^ _191474) ^ [_568376] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_568376))))], (10740 ^ _191474) ^ [_568503, _568505, _568507] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _568503, _568505), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _568505, _568503)), _568507) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_568505), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _568503, _568507)))], (10746 ^ _191474) ^ [_568775, _568777, _568779] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _568775, _568777), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _568779, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _568777, _568775))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _568779, _568775), c_Nat_OSuc(_568777)))], (10752 ^ _191474) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10754 ^ _191474) ^ [_569057] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_569057)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _569057), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10756 ^ _191474) ^ [_569176, _569178] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569176), -(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), _569176), _569178)))], (10762 ^ _191474) ^ [_569416, _569418, _569420] : [class_Rings_Olinordered__semidom(_569416), c_Orderings_Oord__class_Oless__eq(_569416, c_Groups_Ozero__class_Ozero(_569416), _569418), c_Orderings_Oord__class_Oless__eq(_569416, _569418, c_Groups_Oone__class_Oone(_569416)), -(c_Orderings_Oord__class_Oless__eq(_569416, hAPP(hAPP(c_Power_Opower__class_Opower(_569416), _569418), c_Nat_OSuc(_569420)), _569418))], (10776 ^ _191474) ^ [_569864, _569866, _569868] : [class_Rings_Olinordered__semidom(_569864), c_Orderings_Oord__class_Oless(_569864, c_Groups_Ozero__class_Ozero(_569864), _569866), c_Orderings_Oord__class_Oless(_569864, _569866, c_Groups_Oone__class_Oone(_569864)), -(c_Orderings_Oord__class_Oless(_569864, hAPP(hAPP(c_Power_Opower__class_Opower(_569864), _569866), c_Nat_OSuc(_569868)), c_Groups_Oone__class_Oone(_569864)))], (10790 ^ _191474) ^ [_570330, _570332, _570334, _570336] : [class_Groups_Omonoid__mult(_570330), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570332, _570334), -(hAPP(hAPP(c_Power_Opower__class_Opower(_570330), _570336), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_570334), _570332)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_570330), hAPP(hAPP(c_Power_Opower__class_Opower(_570330), _570336), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570334, _570332))), _570336))], (10800 ^ _191474) ^ [_570703] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _570703), -(_570703 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570703, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (10806 ^ _191474) ^ [_570907] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _570907), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570907, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _570907)], (10812 ^ _191474) ^ [_571145, _571147] : [_571145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571145, _571147) = _571147)], (10818 ^ _191474) ^ [_571315, _571317] : [-(_571315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571315, _571317) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571315, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _571317)))], (10824 ^ _191474) ^ [_571558, _571560] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _571558), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _571560, _571558)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _571560, _571558) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571560, _571558), _571558)))], (10834 ^ _191474) ^ [_571892, _571894] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _571892), 10837 ^ _191474 : [(10838 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _571894, _571892), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _571894, _571892) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10844 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _571894, _571892)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _571894, _571892) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571894, _571892), _571892)))]]], (10850 ^ _191474) ^ [_572400, _572402] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _572400), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _572402), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_572400, _572402)))], (10860 ^ _191474) ^ [_572711, _572713] : [class_Groups_Ozero(_572711), 10863 ^ _191474 : [(10864 ^ _191474) ^ [] : [_572713 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_572711)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_572711, _572713) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10870 ^ _191474) ^ [] : [-(_572713 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_572711))), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_572711, _572713) = c_Nat_OSuc(c_Polynomial_Odegree(_572711, _572713)))]]], (10876 ^ _191474) ^ [_573227, _573229, _573231] : [class_Rings_Ocomm__ring__1(_573227), -(c_Groups_Ominus__class_Ominus(_573227, hAPP(hAPP(c_Power_Opower__class_Opower(_573227), _573229), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_573227), _573231), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_573227), c_Groups_Ominus__class_Ominus(_573227, _573229, _573231)), c_Groups_Oplus__class_Oplus(_573227, _573229, _573231)))], (10882 ^ _191474) ^ [_573513, _573515] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _573513, _573515), -(c_Nat__Transfer_Otsub(_573515, _573513) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _573515, _573513))], (10888 ^ _191474) ^ [_573739, _573741] : [class_RealVector_Oreal__normed__vector(_573739), 10891 ^ _191474 : [(10904 ^ _191474) ^ [] : [10906 ^ _191474 : [(10907 ^ _191474) ^ [_574475] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_573739, hAPP(_573741, 10905 ^ [_573739, _573741, _574475])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_574475)))]], 10909 ^ _191474 : [(10910 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10908 ^ [_573739, _573741]))], (10912 ^ _191474) ^ [_574696] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_573739, hAPP(_573741, _574696)), 10908 ^ [_573739, _573741]))]]], (10892 ^ _191474) ^ [] : [10901 ^ _191474 : [(10902 ^ _191474) ^ [_574296] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_573739, hAPP(_573741, _574296)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10900 ^ [_573739, _573741]))))]], 10893 ^ _191474 : [(10894 ^ _191474) ^ [_573978] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _573978), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_573739, hAPP(_573741, 10897 ^ [_573739, _573741, _573978])), _573978)]]]]], (10914 ^ _191474) ^ [_574836, _574838] : [class_RealVector_Oreal__normed__vector(_574836), 10917 ^ _191474 : [(10930 ^ _191474) ^ [] : [10932 ^ _191474 : [(10933 ^ _191474) ^ [_575572] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_574836, hAPP(_574838, 10931 ^ [_574836, _574838, _575572])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_575572)))]], 10935 ^ _191474 : [(10936 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10934 ^ [_574836, _574838]))], (10938 ^ _191474) ^ [_575793] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_574836, hAPP(_574838, _575793)), 10934 ^ [_574836, _574838]))]]], (10918 ^ _191474) ^ [] : [10927 ^ _191474 : [(10928 ^ _191474) ^ [_575393] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_574836, hAPP(_574838, _575393)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10926 ^ [_574836, _574838]))))]], 10919 ^ _191474 : [(10920 ^ _191474) ^ [_575075] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _575075), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_574836, hAPP(_574838, 10923 ^ [_574836, _574838, _575075])), _575075)]]]]], (10940 ^ _191474) ^ [_575976, _575978, _575980] : [hBOOL(hAPP(_575976, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _575978, _575980))), 10945 ^ _191474 : [(10946 ^ _191474) ^ [] : [-(_575980 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10948 ^ _191474) ^ [] : [-(hBOOL(hAPP(_575976, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 10950 ^ _191474 : [(10951 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _575980), 10949 ^ [_575976, _575978, _575980]), _575978))], (10953 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575978, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _575980), c_Nat_OSuc(10949 ^ [_575976, _575978, _575980]))))], (10955 ^ _191474) ^ [] : [-(hBOOL(hAPP(_575976, 10949 ^ [_575976, _575978, _575980])))]]], (10957 ^ _191474) ^ [_576631, _576633, _576635] : [-(hBOOL(hAPP(_576631, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _576633, _576635)))), 10958 ^ _191474 : [(10959 ^ _191474) ^ [] : [_576635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_576631, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10965 ^ _191474) ^ [_576925] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _576635), _576925), _576633), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _576633, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _576635), c_Nat_OSuc(_576925))), hBOOL(hAPP(_576631, _576925))]]], (10977 ^ _191474) ^ [_577362, _577364, _577366] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _577362), 10980 ^ _191474 : [(10991 ^ _191474) ^ [] : [_577364 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _577366, _577362), 10994 ^ _191474 : [(10995 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _577362), _577364), _577366))], (10997 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _577366, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _577362), c_Nat_OSuc(_577364))))]]], (10981 ^ _191474) ^ [] : [-(_577364 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _577366, _577362)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _577362), _577364), _577366), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _577366, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _577362), c_Nat_OSuc(_577364)))]]], (10999 ^ _191474) ^ [_578064, _578066] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _578064), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _578064, _578066), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _578066, _578064) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _578066, _578064), _578064)))], (11009 ^ _191474) ^ [_578395, _578397] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _578395), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _578397), 11017 ^ _191474 : [(11018 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 11016 ^ [_578395, _578397])), _578395), _578397))], (11020 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _578397, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(11016 ^ [_578395, _578397]))), _578395)))]]], (11022 ^ _191474) ^ [_578895] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _578895), 11026 ^ _191474 : [(11027 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, 11025 ^ [_578895]), _578895))], (11029 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _578895, c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(11025 ^ [_578895]))))]]], (11031 ^ _191474) ^ [_579266, _579268] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _579266), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _579268), 11039 ^ _191474 : [(11040 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11038 ^ [_579266, _579268]))], (11042 ^ _191474) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 11038 ^ [_579266, _579268]), _579266) = _579268)], (11044 ^ _191474) ^ [_579770] : [-(_579770 = 11038 ^ [_579266, _579268]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _579770), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _579770), _579266) = _579268]]], (11054 ^ _191474) ^ [_580124, _580126] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _580124), -(c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _580124), _580126)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _580126)), c_Transcendental_Oln(_580124)))], (11060 ^ _191474) ^ [_580374, _580376] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _580374), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _580376), 11067 ^ _191474 : [(11068 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_580374), c_Transcendental_Oln(_580376)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _580374, _580376))], (11074 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _580374, _580376), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_580374), c_Transcendental_Oln(_580376)))]]], (11080 ^ _191474) ^ [_580945, _580947] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _580945), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _580947), 11087 ^ _191474 : [(11088 ^ _191474) ^ [] : [c_Transcendental_Oln(_580945) = c_Transcendental_Oln(_580947), -(_580945 = _580947)], (11094 ^ _191474) ^ [] : [_580945 = _580947, -(c_Transcendental_Oln(_580945) = c_Transcendental_Oln(_580947))]]], (11100 ^ _191474) ^ [_581496] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _581496), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_581496), _581496))], (11106 ^ _191474) ^ [] : [-(c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11108 ^ _191474) ^ [_581761, _581763] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _581761), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _581763), 11115 ^ _191474 : [(11116 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(_581761), c_Transcendental_Oln(_581763)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _581761, _581763))], (11122 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _581761, _581763), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(_581761), c_Transcendental_Oln(_581763)))]]], (11128 ^ _191474) ^ [_582318] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _582318), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_582318)))], (11134 ^ _191474) ^ [_582516] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _582516), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_582516)))], (11140 ^ _191474) ^ [_582714] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _582714), 11143 ^ _191474 : [(11144 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_582714)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _582714))], (11150 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _582714), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_582714)))]]], (11156 ^ _191474) ^ [_583158] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _583158), 11159 ^ _191474 : [(11160 ^ _191474) ^ [] : [c_Transcendental_Oln(_583158) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_583158 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (11166 ^ _191474) ^ [] : [_583158 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Transcendental_Oln(_583158) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (11172 ^ _191474) ^ [_583596] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _583596), 11175 ^ _191474 : [(11176 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_583596), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _583596, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11182 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _583596, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_583596), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (11188 ^ _191474) ^ [_584040] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _584040), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _584040, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_584040), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (11198 ^ _191474) ^ [_584325] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_584325)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _584325), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _584325))], (11208 ^ _191474) ^ [_584610] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _584610), 11211 ^ _191474 : [(11212 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_584610)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _584610))], (11218 ^ _191474) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _584610), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_584610)))]]], (11224 ^ _191474) ^ [_585054] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oln(_585054)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585054), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _585054))], (11234 ^ _191474) ^ [_585353, _585355] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585353), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585355), -(c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _585353), _585355)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Transcendental_Oln(_585353), c_Transcendental_Oln(_585355)))], (11244 ^ _191474) ^ [_585674] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585674), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _585674)), _585674))], (11250 ^ _191474) ^ [_585894, _585896] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585894), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585896), -(c_Transcendental_Oln(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _585894, _585896)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Transcendental_Oln(_585894), c_Transcendental_Oln(_585896)))], (11260 ^ _191474) ^ [_586225, _586227] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _586225), -(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _586227), c_RealDef_Oreal(tc_Nat_Onat, _586225)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _586227, _586225)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _586227, _586225)), c_RealDef_Oreal(tc_Nat_Onat, _586225))))], (11266 ^ _191474) ^ [_586521, _586523, _586525] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _586521, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11269 ^ _191474 : [(11288 ^ _191474) ^ [] : [11291 ^ _191474 : [(11292 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _586521, 11290 ^ [_586521, _586523, _586525]))], (11294 ^ _191474) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 11290 ^ [_586521, _586523, _586525], c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11296 ^ _191474) ^ [] : [-(_586525 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586521), 11289 ^ [_586521, _586523, _586525]), 11290 ^ [_586521, _586523, _586525]))], (11298 ^ _191474) ^ [] : [hBOOL(hAPP(hAPP(_586523, 11289 ^ [_586521, _586523, _586525]), 11290 ^ [_586521, _586523, _586525]))]], -(hBOOL(hAPP(hAPP(_586523, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _586525, _586521)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _586525, _586521))))], (11270 ^ _191474) ^ [] : [hBOOL(hAPP(hAPP(_586523, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _586525, _586521)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _586525, _586521))), 11273 ^ _191474 : [(11274 ^ _191474) ^ [_586856, _586858] : [-(hBOOL(hAPP(hAPP(_586523, _586858), _586856))), c_Orderings_Oord__class_Oless(tc_Int_Oint, _586521, _586856), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _586856, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _586525 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586521), _586858), _586856)]]]]], (11302 ^ _191474) ^ [_587948, _587950] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(_587948), _587950) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _587948, _587950)), _587950))], (11304 ^ _191474) ^ [_588044] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _588044, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11306 ^ _191474) ^ [_588175, _588177] : [c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _588175, _588177)) = _588177, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(_588175), _588177) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11312 ^ _191474) ^ [_588361, _588363] : [-(c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _588361, _588363)) = _588363), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(_588361), _588363) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _588361, _588363)))], (11318 ^ _191474) ^ [_588611, _588613, _588615] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588611, _588613), _588615) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _588611, _588615), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _588613, _588615)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _588611, _588615), c_Divides_Odiv__class_Omod(tc_Int_Oint, _588613, _588615)), _588615)))], (11320 ^ _191474) ^ [_588747, _588749] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _588747, _588749), _588749) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11322 ^ _191474) ^ [_588878, _588880, _588882] : [class_Divides_Osemiring__div(_588878), -(c_Divides_Odiv__class_Odiv(_588878, c_Divides_Odiv__class_Omod(_588878, _588880, _588882), _588882) = c_Groups_Ozero__class_Ozero(_588878))], (11328 ^ _191474) ^ [_589103] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _589103, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11330 ^ _191474) ^ [_589151] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _589151, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _589151)], (11332 ^ _191474) ^ [_589263, _589265, _589267] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _589263), _589265), _589267), _589265) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _589267, _589265))], (11334 ^ _191474) ^ [_589420, _589422, _589424, _589426] : [class_Divides_Osemiring__div(_589420), -(c_Divides_Odiv__class_Omod(_589420, c_Groups_Oplus__class_Oplus(_589420, _589422, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589420), _589424), _589426)), _589426) = c_Divides_Odiv__class_Omod(_589420, _589422, _589426))], (11340 ^ _191474) ^ [_589708, _589710, _589712, _589714] : [class_Divides_Osemiring__div(_589708), -(c_Divides_Odiv__class_Omod(_589708, c_Groups_Oplus__class_Oplus(_589708, _589710, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589708), _589712), _589714)), _589712) = c_Divides_Odiv__class_Omod(_589708, _589710, _589712))], (11346 ^ _191474) ^ [_589982, _589984, _589986] : [class_Divides_Osemiring__div(_589982), -(c_Divides_Odiv__class_Omod(_589982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589982), _589984), _589986), _589984) = c_Groups_Ozero__class_Ozero(_589982))], (11352 ^ _191474) ^ [_590238, _590240, _590242] : [class_Divides_Osemiring__div(_590238), -(c_Divides_Odiv__class_Omod(_590238, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590238), _590240), _590242), _590242) = c_Groups_Ozero__class_Ozero(_590238))], (11358 ^ _191474) ^ [_590509, _590511] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _590509, _590511) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_590509 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _590511), 11361 ^ [_590509, _590511]))], (11365 ^ _191474) ^ [_590754, _590756] : [11366 ^ _191474 : [(11367 ^ _191474) ^ [_590834] : [_590754 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _590756), _590834)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _590754, _590756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11371 ^ _191474) ^ [_591037, _591039] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _591037, _591039) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_591037 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _591039), 11374 ^ [_591037, _591039]))], (11378 ^ _191474) ^ [_591282, _591284] : [11379 ^ _191474 : [(11380 ^ _191474) ^ [_591362] : [_591282 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _591284), _591362)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _591282, _591284) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11384 ^ _191474) ^ [_591535, _591537, _591539] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _591535, _591537), _591539) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _591535, _591539), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _591537, _591539)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _591535, _591539), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _591537, _591539)), _591539)))], (11386 ^ _191474) ^ [_591686, _591688] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _591686, _591688), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _591688, _591686) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _591688, _591686), _591686))], (11392 ^ _191474) ^ [_591907, _591909] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _591907, _591909), _591907))], (11394 ^ _191474) ^ [_592020, _592022, _592024] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _592020, c_Divides_Odiv__class_Omod(tc_Int_Oint, _592022, _592024)), _592024) = c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _592020, _592022), _592024))], (11396 ^ _191474) ^ [_592150, _592152, _592154] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _592150, _592152), _592154), _592152) = c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _592150, _592154), _592152))], (11398 ^ _191474) ^ [_592309, _592311, _592313, _592315] : [class_Divides_Oring__div(_592309), -(c_Divides_Odiv__class_Omod(_592309, c_Groups_Ominus__class_Ominus(_592309, _592311, _592313), _592315) = c_Divides_Odiv__class_Omod(_592309, c_Groups_Ominus__class_Ominus(_592309, _592311, c_Divides_Odiv__class_Omod(_592309, _592313, _592315)), _592315))], (11404 ^ _191474) ^ [_592597, _592599, _592601, _592603] : [class_Divides_Oring__div(_592597), -(c_Divides_Odiv__class_Omod(_592597, c_Groups_Ominus__class_Ominus(_592597, _592599, _592601), _592603) = c_Divides_Odiv__class_Omod(_592597, c_Groups_Ominus__class_Ominus(_592597, c_Divides_Odiv__class_Omod(_592597, _592599, _592603), _592601), _592603))], (11410 ^ _191474) ^ [_592885, _592887, _592889, _592891] : [class_Divides_Oring__div(_592885), -(c_Divides_Odiv__class_Omod(_592885, c_Groups_Ominus__class_Ominus(_592885, _592887, _592889), _592891) = c_Divides_Odiv__class_Omod(_592885, c_Groups_Ominus__class_Ominus(_592885, c_Divides_Odiv__class_Omod(_592885, _592887, _592891), c_Divides_Odiv__class_Omod(_592885, _592889, _592891)), _592891))], (11416 ^ _191474) ^ [_593209, _593211, _593213, _593215, _593217, _593219] : [class_Divides_Oring__div(_593209), c_Divides_Odiv__class_Omod(_593209, _593211, _593213) = c_Divides_Odiv__class_Omod(_593209, _593215, _593213), c_Divides_Odiv__class_Omod(_593209, _593217, _593213) = c_Divides_Odiv__class_Omod(_593209, _593219, _593213), -(c_Divides_Odiv__class_Omod(_593209, c_Groups_Ominus__class_Ominus(_593209, _593211, _593217), _593213) = c_Divides_Odiv__class_Omod(_593209, c_Groups_Ominus__class_Ominus(_593209, _593215, _593219), _593213))], (11430 ^ _191474) ^ [_593771, _593773, _593775, _593777, _593779, _593781] : [class_Divides_Osemiring__div(_593771), c_Divides_Odiv__class_Omod(_593771, _593773, _593775) = c_Divides_Odiv__class_Omod(_593771, _593777, _593775), c_Divides_Odiv__class_Omod(_593771, _593779, _593775) = c_Divides_Odiv__class_Omod(_593771, _593781, _593775), -(c_Divides_Odiv__class_Omod(_593771, c_Groups_Oplus__class_Oplus(_593771, _593773, _593779), _593775) = c_Divides_Odiv__class_Omod(_593771, c_Groups_Oplus__class_Oplus(_593771, _593777, _593781), _593775))], (11444 ^ _191474) ^ [_594305, _594307, _594309, _594311] : [class_Divides_Osemiring__div(_594305), -(c_Divides_Odiv__class_Omod(_594305, c_Groups_Oplus__class_Oplus(_594305, c_Divides_Odiv__class_Omod(_594305, _594307, _594309), _594311), _594309) = c_Divides_Odiv__class_Omod(_594305, c_Groups_Oplus__class_Oplus(_594305, _594307, _594311), _594309))], (11450 ^ _191474) ^ [_594593, _594595, _594597, _594599] : [class_Divides_Osemiring__div(_594593), -(c_Divides_Odiv__class_Omod(_594593, c_Groups_Oplus__class_Oplus(_594593, _594595, c_Divides_Odiv__class_Omod(_594593, _594597, _594599)), _594599) = c_Divides_Odiv__class_Omod(_594593, c_Groups_Oplus__class_Oplus(_594593, _594595, _594597), _594599))], (11456 ^ _191474) ^ [_594881, _594883, _594885, _594887] : [class_Divides_Osemiring__div(_594881), -(c_Divides_Odiv__class_Omod(_594881, c_Groups_Oplus__class_Oplus(_594881, _594883, _594885), _594887) = c_Divides_Odiv__class_Omod(_594881, c_Groups_Oplus__class_Oplus(_594881, c_Divides_Odiv__class_Omod(_594881, _594883, _594887), c_Divides_Odiv__class_Omod(_594881, _594885, _594887)), _594887))], (11462 ^ _191474) ^ [_595177, _595179, _595181, _595183] : [class_Divides_Osemiring__div(_595177), -(c_Divides_Odiv__class_Omod(_595177, c_Groups_Oplus__class_Oplus(_595177, _595179, _595181), _595183) = c_Divides_Odiv__class_Omod(_595177, c_Groups_Oplus__class_Oplus(_595177, c_Divides_Odiv__class_Omod(_595177, _595179, _595183), _595181), _595183))], (11468 ^ _191474) ^ [_595465, _595467, _595469, _595471] : [class_Divides_Osemiring__div(_595465), -(c_Divides_Odiv__class_Omod(_595465, c_Groups_Oplus__class_Oplus(_595465, _595467, _595469), _595471) = c_Divides_Odiv__class_Omod(_595465, c_Groups_Oplus__class_Oplus(_595465, _595467, c_Divides_Odiv__class_Omod(_595465, _595469, _595471)), _595471))], (11474 ^ _191474) ^ [_595739, _595741, _595743] : [class_Divides_Osemiring__div(_595739), -(c_Divides_Odiv__class_Omod(_595739, c_Groups_Oplus__class_Oplus(_595739, _595741, _595743), _595741) = c_Divides_Odiv__class_Omod(_595739, _595743, _595741))], (11480 ^ _191474) ^ [_595991, _595993, _595995] : [class_Divides_Osemiring__div(_595991), -(c_Divides_Odiv__class_Omod(_595991, c_Groups_Oplus__class_Oplus(_595991, _595993, _595995), _595995) = c_Divides_Odiv__class_Omod(_595991, _595993, _595995))], (11486 ^ _191474) ^ [_596229, _596231] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _596229), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _596231, _596229), _596229))], (11492 ^ _191474) ^ [_596471, _596473] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596471, _596473), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _596471, _596473) = _596471)], (11498 ^ _191474) ^ [_596643, _596645] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596643, _596645)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _596643, _596645) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _596643, _596645), _596645))], (11504 ^ _191474) ^ [_596884, _596886] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596884, _596886)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _596884, _596886) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _596884, _596886), _596886))], (11510 ^ _191474) ^ [_597123, _597125] : [class_Divides_Osemiring__div(_597123), -(c_Divides_Odiv__class_Omod(_597123, _597125, _597125) = c_Groups_Ozero__class_Ozero(_597123))], (11516 ^ _191474) ^ [_597343, _597345] : [class_Divides_Osemiring__div(_597343), -(c_Divides_Odiv__class_Omod(_597343, _597345, c_Groups_Ozero__class_Ozero(_597343)) = _597345)], (11522 ^ _191474) ^ [_597563, _597565] : [class_Divides_Osemiring__div(_597563), -(c_Divides_Odiv__class_Omod(_597563, c_Groups_Ozero__class_Ozero(_597563), _597565) = c_Groups_Ozero__class_Ozero(_597563))], (11528 ^ _191474) ^ [_597787, _597789] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _597787, _597789), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _597787, _597789) = _597787)], (11534 ^ _191474) ^ [_598007, _598009] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _598007, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _598007, c_Divides_Odiv__class_Omod(tc_Int_Oint, _598009, _598007)))], (11540 ^ _191474) ^ [_598229, _598231] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598229), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _598231, _598229), _598229))], (11546 ^ _191474) ^ [_598422] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _598422, _598422) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11548 ^ _191474) ^ [_598504] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598504) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11550 ^ _191474) ^ [_598615, _598617] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598615), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _598615, _598617), _598615))], (11556 ^ _191474) ^ [_598837, _598839] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598837), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598839), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _598837, _598839)))], (11566 ^ _191474) ^ [_599150, _599152] : [class_Divides_Osemiring__div(_599150), -(c_Divides_Odiv__class_Omod(_599150, _599152, c_Groups_Oone__class_Oone(_599150)) = c_Groups_Ozero__class_Ozero(_599150))], (11572 ^ _191474) ^ [_599388, _599390, _599392] : [class_Divides_Osemiring__div(_599388), -(c_Divides_Odiv__class_Omod(_599388, c_Divides_Odiv__class_Omod(_599388, _599390, _599392), _599392) = c_Divides_Odiv__class_Omod(_599388, _599390, _599392))], (11578 ^ _191474) ^ [_599682, _599684, _599686, _599688, _599690, _599692] : [class_Divides_Osemiring__div(_599682), c_Divides_Odiv__class_Omod(_599682, _599684, _599686) = c_Divides_Odiv__class_Omod(_599682, _599688, _599686), c_Divides_Odiv__class_Omod(_599682, _599690, _599686) = c_Divides_Odiv__class_Omod(_599682, _599692, _599686), -(c_Divides_Odiv__class_Omod(_599682, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599682), _599684), _599690), _599686) = c_Divides_Odiv__class_Omod(_599682, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599682), _599688), _599692), _599686))], (11592 ^ _191474) ^ [_600232, _600234, _600236, _600238] : [class_Divides_Osemiring__div(_600232), -(c_Divides_Odiv__class_Omod(_600232, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600232), c_Divides_Odiv__class_Omod(_600232, _600234, _600236)), _600238), _600236) = c_Divides_Odiv__class_Omod(_600232, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600232), _600234), _600238), _600236))], (11598 ^ _191474) ^ [_600494] : [class_Groups_Ocancel__comm__monoid__add(_600494), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_600494)))], (11604 ^ _191474) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11606 ^ _191474) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11608 ^ _191474) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11610 ^ _191474) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11612 ^ _191474) ^ [_600910, _600912] : [class_Orderings_Opreorder(_600910), -(class_Orderings_Opreorder(tc_fun(_600912, _600910)))], (11618 ^ _191474) ^ [_601122, _601124] : [class_Orderings_Oorder(_601122), -(class_Orderings_Oorder(tc_fun(_601124, _601122)))], (11624 ^ _191474) ^ [_601334, _601336] : [class_Orderings_Oord(_601334), -(class_Orderings_Oord(tc_fun(_601336, _601334)))], (11630 ^ _191474) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11632 ^ _191474) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11634 ^ _191474) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11636 ^ _191474) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11638 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11640 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11642 ^ _191474) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11644 ^ _191474) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11646 ^ _191474) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11648 ^ _191474) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11650 ^ _191474) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11652 ^ _191474) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11654 ^ _191474) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11656 ^ _191474) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11658 ^ _191474) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11660 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11662 ^ _191474) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11664 ^ _191474) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11666 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11668 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11670 ^ _191474) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11672 ^ _191474) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11674 ^ _191474) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11676 ^ _191474) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (11678 ^ _191474) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11680 ^ _191474) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11682 ^ _191474) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11684 ^ _191474) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11686 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11688 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (11690 ^ _191474) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (11692 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11694 ^ _191474) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11696 ^ _191474) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11698 ^ _191474) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (11700 ^ _191474) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (11702 ^ _191474) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (11704 ^ _191474) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11706 ^ _191474) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11708 ^ _191474) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (11710 ^ _191474) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11712 ^ _191474) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11714 ^ _191474) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (11716 ^ _191474) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11718 ^ _191474) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11720 ^ _191474) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (11722 ^ _191474) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (11724 ^ _191474) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (11726 ^ _191474) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (11728 ^ _191474) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11730 ^ _191474) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11732 ^ _191474) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11734 ^ _191474) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11736 ^ _191474) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11738 ^ _191474) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11740 ^ _191474) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11742 ^ _191474) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11744 ^ _191474) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11746 ^ _191474) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11748 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11750 ^ _191474) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11752 ^ _191474) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11754 ^ _191474) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11756 ^ _191474) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11758 ^ _191474) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (11760 ^ _191474) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11762 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11764 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11766 ^ _191474) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11768 ^ _191474) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11770 ^ _191474) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11772 ^ _191474) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (11774 ^ _191474) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11776 ^ _191474) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11778 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11780 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (11782 ^ _191474) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (11784 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (11786 ^ _191474) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (11788 ^ _191474) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (11790 ^ _191474) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11792 ^ _191474) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (11794 ^ _191474) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11796 ^ _191474) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (11798 ^ _191474) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (11800 ^ _191474) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11802 ^ _191474) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (11804 ^ _191474) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (11806 ^ _191474) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (11808 ^ _191474) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11810 ^ _191474) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (11812 ^ _191474) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (11814 ^ _191474) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11816 ^ _191474) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (11818 ^ _191474) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (11820 ^ _191474) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (11822 ^ _191474) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (11824 ^ _191474) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (11826 ^ _191474) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (11828 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (11830 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (11832 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (11834 ^ _191474) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (11836 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (11838 ^ _191474) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (11840 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (11842 ^ _191474) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (11844 ^ _191474) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (11846 ^ _191474) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (11848 ^ _191474) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (11850 ^ _191474) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11852 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11854 ^ _191474) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (11856 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_RealDef_Oreal))], (11858 ^ _191474) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (11860 ^ _191474) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11862 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (11864 ^ _191474) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11866 ^ _191474) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11868 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (11870 ^ _191474) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (11872 ^ _191474) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (11874 ^ _191474) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (11876 ^ _191474) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11878 ^ _191474) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11880 ^ _191474) ^ [] : [-(class_Fields_Olinordered__field(tc_RealDef_Oreal))], (11882 ^ _191474) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (11884 ^ _191474) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (11886 ^ _191474) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11888 ^ _191474) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11890 ^ _191474) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (11892 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (11894 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (11896 ^ _191474) ^ [] : [-(class_RealVector_Oreal__field(tc_RealDef_Oreal))], (11898 ^ _191474) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (11900 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11902 ^ _191474) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11904 ^ _191474) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11906 ^ _191474) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (11908 ^ _191474) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11910 ^ _191474) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11912 ^ _191474) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11914 ^ _191474) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (11916 ^ _191474) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11918 ^ _191474) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11920 ^ _191474) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11922 ^ _191474) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (11924 ^ _191474) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (11926 ^ _191474) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (11928 ^ _191474) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (11930 ^ _191474) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11932 ^ _191474) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11934 ^ _191474) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11936 ^ _191474) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11938 ^ _191474) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11940 ^ _191474) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11942 ^ _191474) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11944 ^ _191474) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11946 ^ _191474) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11948 ^ _191474) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11950 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11952 ^ _191474) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (11954 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11956 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11958 ^ _191474) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11960 ^ _191474) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11962 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11964 ^ _191474) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex))], (11966 ^ _191474) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11968 ^ _191474) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11970 ^ _191474) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (11972 ^ _191474) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11974 ^ _191474) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11976 ^ _191474) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11978 ^ _191474) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11980 ^ _191474) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11982 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11984 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (11986 ^ _191474) ^ [] : [-(class_RealVector_Oreal__field(tc_Complex_Ocomplex))], (11988 ^ _191474) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (11990 ^ _191474) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11992 ^ _191474) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11994 ^ _191474) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11996 ^ _191474) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11998 ^ _191474) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (12000 ^ _191474) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (12002 ^ _191474) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (12004 ^ _191474) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (12006 ^ _191474) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (12008 ^ _191474) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (12010 ^ _191474) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (12012 ^ _191474) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (12014 ^ _191474) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (12016 ^ _191474) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (12018 ^ _191474) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (12020 ^ _191474) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (12022 ^ _191474) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (12024 ^ _191474) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (12026 ^ _191474) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (12028 ^ _191474) ^ [_612079] : [class_Rings_Oidom(_612079), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_612079)))], (12034 ^ _191474) ^ [_612269] : [class_Rings_Olinordered__idom(_612269), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_612269)))], (12040 ^ _191474) ^ [_612459] : [class_Rings_Olinordered__idom(_612459), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_612459)))], (12046 ^ _191474) ^ [_612649] : [class_Rings_Olinordered__idom(_612649), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_612649)))], (12052 ^ _191474) ^ [_612839] : [class_Rings_Olinordered__idom(_612839), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_612839)))], (12058 ^ _191474) ^ [_613029] : [class_Rings_Olinordered__idom(_613029), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_613029)))], (12064 ^ _191474) ^ [_613219] : [class_Rings_Olinordered__idom(_613219), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_613219)))], (12070 ^ _191474) ^ [_613409] : [class_Rings_Olinordered__idom(_613409), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_613409)))], (12076 ^ _191474) ^ [_613599] : [class_Rings_Olinordered__idom(_613599), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_613599)))], (12082 ^ _191474) ^ [_613789] : [class_Groups_Ocancel__comm__monoid__add(_613789), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_613789)))], (12088 ^ _191474) ^ [_613979] : [class_Rings_Oidom(_613979), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_613979)))], (12094 ^ _191474) ^ [_614169] : [class_Rings_Olinordered__idom(_614169), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_614169)))], (12100 ^ _191474) ^ [_614359] : [class_Rings_Olinordered__idom(_614359), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_614359)))], (12106 ^ _191474) ^ [_614549] : [class_Rings_Oidom(_614549), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_614549)))], (12112 ^ _191474) ^ [_614739] : [class_Rings_Olinordered__idom(_614739), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_614739)))], (12118 ^ _191474) ^ [_614929] : [class_Rings_Olinordered__idom(_614929), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_614929)))], (12124 ^ _191474) ^ [_615119] : [class_Rings_Olinordered__idom(_615119), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_615119)))], (12130 ^ _191474) ^ [_615309] : [class_Groups_Ocancel__comm__monoid__add(_615309), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_615309)))], (12136 ^ _191474) ^ [_615499] : [class_Rings_Olinordered__idom(_615499), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_615499)))], (12142 ^ _191474) ^ [_615689] : [class_Rings_Olinordered__idom(_615689), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_615689)))], (12148 ^ _191474) ^ [_615879] : [class_Rings_Ocomm__semiring__0(_615879), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_615879)))], (12154 ^ _191474) ^ [_616069] : [class_Rings_Ocomm__semiring__1(_616069), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_616069)))], (12160 ^ _191474) ^ [_616259] : [class_Groups_Ocomm__monoid__add(_616259), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_616259)))], (12166 ^ _191474) ^ [_616449] : [class_Rings_Olinordered__idom(_616449), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_616449)))], (12172 ^ _191474) ^ [_616639] : [class_Rings_Oidom(_616639), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_616639)))], (12178 ^ _191474) ^ [_616829] : [class_Groups_Ocomm__monoid__add(_616829), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_616829)))], (12184 ^ _191474) ^ [_617019] : [class_Rings_Olinordered__idom(_617019), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_617019)))], (12190 ^ _191474) ^ [_617209] : [class_Rings_Olinordered__idom(_617209), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_617209)))], (12196 ^ _191474) ^ [_617399] : [class_Rings_Ocomm__semiring__1(_617399), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_617399)))], (12202 ^ _191474) ^ [_617589] : [class_Rings_Ocomm__semiring__0(_617589), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_617589)))], (12208 ^ _191474) ^ [_617779] : [class_Fields_Ofield(_617779), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_617779)))], (12214 ^ _191474) ^ [_617969] : [class_Rings_Ocomm__semiring__0(_617969), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_617969)))], (12220 ^ _191474) ^ [_618159] : [class_Groups_Oab__group__add(_618159), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_618159)))], (12226 ^ _191474) ^ [_618349] : [class_Rings_Ocomm__semiring__1(_618349), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_618349)))], (12232 ^ _191474) ^ [_618539] : [class_Rings_Olinordered__idom(_618539), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_618539)))], (12238 ^ _191474) ^ [_618729] : [class_Rings_Olinordered__idom(_618729), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_618729)))], (12244 ^ _191474) ^ [_618919] : [class_Rings_Olinordered__idom(_618919), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_618919)))], (12250 ^ _191474) ^ [_619109] : [class_Rings_Ocomm__semiring__1(_619109), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_619109)))], (12256 ^ _191474) ^ [_619299] : [class_Rings_Ocomm__ring__1(_619299), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_619299)))], (12262 ^ _191474) ^ [_619489] : [class_Groups_Ocomm__monoid__add(_619489), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_619489)))], (12268 ^ _191474) ^ [_619679] : [class_Rings_Ocomm__semiring__0(_619679), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_619679)))], (12274 ^ _191474) ^ [_619869] : [class_Groups_Oab__group__add(_619869), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_619869)))], (12280 ^ _191474) ^ [_620059] : [class_Fields_Ofield(_620059), -(class_Divides_Oring__div(tc_Polynomial_Opoly(_620059)))], (12286 ^ _191474) ^ [_620249] : [class_Rings_Ocomm__semiring__0(_620249), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_620249)))], (12292 ^ _191474) ^ [_620439] : [class_Rings_Ocomm__ring(_620439), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_620439)))], (12298 ^ _191474) ^ [_620629] : [class_Rings_Olinordered__idom(_620629), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_620629)))], (12304 ^ _191474) ^ [_620819] : [class_Rings_Olinordered__idom(_620819), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_620819)))], (12310 ^ _191474) ^ [_621009] : [class_Rings_Ocomm__semiring__0(_621009), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_621009)))], (12316 ^ _191474) ^ [_621199] : [class_Rings_Olinordered__idom(_621199), -(class_Orderings_Oord(tc_Polynomial_Opoly(_621199)))], (12322 ^ _191474) ^ [_621389] : [class_Rings_Ocomm__ring__1(_621389), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_621389)))], (12328 ^ _191474) ^ [_621579] : [class_Rings_Ocomm__semiring__1(_621579), -(class_Power_Opower(tc_Polynomial_Opoly(_621579)))], (12334 ^ _191474) ^ [_621769] : [class_Groups_Ozero(_621769), -(class_Groups_Ozero(tc_Polynomial_Opoly(_621769)))], (12340 ^ _191474) ^ [_621959] : [class_Rings_Ocomm__ring(_621959), -(class_Rings_Oring(tc_Polynomial_Opoly(_621959)))], (12346 ^ _191474) ^ [_622149] : [class_Rings_Oidom(_622149), -(class_Rings_Oidom(tc_Polynomial_Opoly(_622149)))], (12352 ^ _191474) ^ [_622319] : [class_Rings_Ocomm__semiring__1(_622319), -(class_Groups_Oone(tc_Polynomial_Opoly(_622319)))]], input).
% 0.56/1.39  ncf('1',plain,[c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)))), v_e)],start(12358 ^ 0)).
% 0.56/1.39  ncf('1.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)))), v_e)), class_Orderings_Opreorder(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_da____), v_m____)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_da____), v_m____), v_e)],extension(7538 ^ 1,bind([[_452757, _452759, _452761, _452763], [tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_da____), v_m____), v_e]]))).
% 0.56/1.39  ncf('1.1.1',plain,[-(class_Orderings_Opreorder(tc_RealDef_Oreal))],extension(11908 ^ 2)).
% 0.56/1.39  ncf('1.1.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_da____), v_m____)))],extension(1104 ^ 2)).
% 0.56/1.39  ncf('1.1.3',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_da____), v_m____), v_e))],extension(1075 ^ 2)).
% 0.56/1.39  %-----------------------------------------------------
% 0.56/1.39  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------